qhull-2012.1/0000755000076400010400000000000011721063552014106 5ustar bbarberAdministratorsqhull-2012.1/Announce.txt0000644000076400010400000000463211720041145016413 0ustar bbarberAdministrators Qhull 2012.1 2012/02/18 http://www.qhull.org git@gitorious.org:qhull/qhull.git http://packages.debian.org/sid/libqhull5 [out-of-date] http://www6.uniovi.es/ftp/pub/mirrors/geom.umn.edu/software/ghindex.html http://www.geomview.org http://www.geom.uiuc.edu Qhull computes convex hulls, Delaunay triangulations, Voronoi diagrams, furthest-site Voronoi diagrams, and halfspace intersections about a point. It runs in 2-d, 3-d, 4-d, or higher. It implements the Quickhull algorithm for computing convex hulls. Qhull handles round-off errors from floating point arithmetic. It can approximate a convex hull. The program includes options for hull volume, facet area, partial hulls, input transformations, randomization, tracing, multiple output formats, and execution statistics. The program can be called from within your application. You can view the results in 2-d, 3-d and 4-d with Geomview. To download Qhull: http://www.qhull.org/download git@gitorious.org:qhull/qhull.git http://packages.debian.org/sid/libqhull5 [out-of-date] Download qhull-96.ps for: Barber, C. B., D.P. Dobkin, and H.T. Huhdanpaa, "The Quickhull Algorithm for Convex Hulls," ACM Trans. on Mathematical Software, 22(4):469-483, Dec. 1996. http://www.acm.org/pubs/citations/journals/toms/1996-22-4/p469-barber/ http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.117.405 Abstract: The convex hull of a set of points is the smallest convex set that contains the points. This article presents a practical convex hull algorithm that combines the two-dimensional Quickhull Algorithm with the general dimension Beneath-Beyond Algorithm. It is similar to the randomized, incremental algorithms for convex hull and Delaunay triangulation. We provide empirical evidence that the algorithm runs faster when the input contains non-extreme points, and that it uses less memory. Computational geometry algorithms have traditionally assumed that input sets are well behaved. When an algorithm is implemented with floating point arithmetic, this assumption can lead to serious errors. We briefly describe a solution to this problem when computing the convex hull in two, three, or four dimensions. The output is a set of "thick" facets that contain all possible exact convex hulls of the input. A variation is effective in five or more dimensions. qhull-2012.1/build/0000755000076400010400000000000011721063516015205 5ustar bbarberAdministratorsqhull-2012.1/build/libqhull.vcproj0000644000076400010400000003131711720322455020252 0ustar bbarberAdministrators qhull-2012.1/build/libqhull_p.vcproj0000644000076400010400000003155411720323111020562 0ustar bbarberAdministrators qhull-2012.1/build/qconvex.vcproj0000644000076400010400000002516711547745723020145 0ustar bbarberAdministrators qhull-2012.1/build/qdelaunay.vcproj0000644000076400010400000002524311566615425020434 0ustar bbarberAdministrators qhull-2012.1/build/qhalf.vcproj0000644000076400010400000002511111547745562017543 0ustar bbarberAdministrators qhull-2012.1/build/qhull.sln0000644000076400010400000003514611717073273017067 0ustar bbarberAdministratorsMicrosoft Visual Studio Solution File, Format Version 9.00 # Visual Studio 2005 Project("{8BC9CEB8-8B4A-11D0-8D11-00A0C91BC942}") = "qconvex", "qconvex.vcproj", 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{C9E3DBF2-AA34-3900-9761-5A846CAB6397}.MinSizeRel|Win32.Build.0 = MinSizeRel|Win32 {C9E3DBF2-AA34-3900-9761-5A846CAB6397}.Release|Win32.ActiveCfg = Release|Win32 {C9E3DBF2-AA34-3900-9761-5A846CAB6397}.Release|Win32.Build.0 = Release|Win32 {C9E3DBF2-AA34-3900-9761-5A846CAB6397}.RelWithDebInfo|Win32.ActiveCfg = RelWithDebInfo|Win32 {C9E3DBF2-AA34-3900-9761-5A846CAB6397}.RelWithDebInfo|Win32.Build.0 = RelWithDebInfo|Win32 EndGlobalSection GlobalSection(SolutionProperties) = preSolution HideSolutionNode = FALSE EndGlobalSection EndGlobal qhull-2012.1/build/qhull.vcproj0000644000076400010400000002511011547745723017573 0ustar bbarberAdministrators qhull-2012.1/build/qhullcpp.vcproj0000644000076400010400000002746011716461513020276 0ustar bbarberAdministrators qhull-2012.1/build/qhullstatic.vcproj0000644000076400010400000002237211707417676021013 0ustar bbarberAdministrators qhull-2012.1/build/qhullstatic_p.vcproj0000644000076400010400000002244711707420777021331 0ustar bbarberAdministrators qhull-2012.1/build/qhulltest.vcproj0000644000076400010400000014046711720344606020474 0ustar bbarberAdministrators qhull-2012.1/build/qvoronoi.vcproj0000644000076400010400000002521611547745562020332 0ustar bbarberAdministrators qhull-2012.1/build/rbox.vcproj0000644000076400010400000002506211547745723017426 0ustar bbarberAdministrators qhull-2012.1/build/testqset.vcproj0000644000076400010400000002457711707416272020332 0ustar bbarberAdministrators qhull-2012.1/build/user_eg.vcproj0000644000076400010400000002522211720322172020061 0ustar bbarberAdministrators qhull-2012.1/build/user_eg2.vcproj0000644000076400010400000002510611707417452020157 0ustar bbarberAdministrators qhull-2012.1/build/user_eg3.vcproj0000644000076400010400000002552111547745563020172 0ustar bbarberAdministrators qhull-2012.1/CMakeLists.txt0000644000076400010400000003410411721061507016646 0ustar bbarberAdministrators# CMakeLists.txt -- CMake configuration file for qhull, qhull6, and related programs # # To build with MSYS/mingw # cd build && cmake -G "MSYS Makefiles" .. && cmake .. # make # make install # # To uninstall on unix or MSYS/mingw # xargs rm /dev/null echo " done" } if test ! -f config/configure.ac ; then echo "$0: This script must be run from the Qhull top directory." exit 1 fi echo -n Copying autoconf and automake files... cp config/configure.ac . cp config/Makefile-am-main Makefile.am for d in html eg ; do cp config/Makefile-am-$d $d/Makefile.am done for d in libqhull ; do cp config/Makefile-am-$d src/$d/Makefile.am done echo -en ' done\nCopying program sources to src/libqhull...' sources="src/qconvex/qconvex.c src/qdelaunay/qdelaun.c src/qhalf/qhalf.c \ src/qhull/unix.c src/qvoronoi/qvoronoi.c src/rbox/rbox.c src/testqset/testqset.c" cp $sources src/libqhull echo " done" run aclocal \ && run libtoolize --force --copy \ && run automake --foreign --add-missing --force-missing --copy \ && run autoconf qhull-2012.1/config/changelog0000644000076400010400000001134311712660077017234 0ustar bbarberAdministratorsQhull 2012.1 2012/02/02 - Add config to distribution - Add testqset to config build - config/bootstrap.sh copies program files into src/libqhull Qhull 2011.2 (qhull6) 2011/12/02 - Removed Make-conf.sh (from the qhull 2003.1 release) - The original changelog follows - Adjusted the Makefiles for the new directory structure. - Kept qh_QHpointer=0 (static global data structure, qh_qh). It is faster. Qhull 2012 may have a new interface which passes qh_qh as a parameter. Qhull 2009.1.2 2011/11/21 - Revert to LF line endings [P. Cheeseman] - Remove out-of-date material from qhull-go.bat - Replaced QHULL-GO with a lnk file qhull 2009.1.1 2010/01/09 - Patch release of 2009.1. qh_gethash allowed a negative result, causing overwrite or segfault See git:qhull/project/patch/qhull-2003.1/poly.c-qh_gethash.patch Compared results of q_test, q_eg, q_egtest with patched poly.c, qhull-2003.1 qhull (2009.1, qhull5) This is a maintenance release done by Rafael Laboissiere . - src/rbox.c (main): Avoid problems of evaluation order when pre-incrementing arguments of strtod - src/io.c (qh_produce_output), src/stat.c (qh_initstatistics): Use %lu instead of %d in the format string for arguments of type size_t - html/qhull.man, html/rbox.man: Fix several syntax, macros, and hyphen problems in man pages - The Autotools files have been generated with modern version of autoconf (2.63), automake/aclocal (1.10.2), and libtool (2.2.6) - Some character issues in the man pages are fixed qhull (2003.1-1, qhull5) unstable; urgency=low * New upstream release. There are backward incompatibilities in the code and the soversion was bumped to libqhull5. * debian/rules: - Major rewrite of build and install rules, since we are using now the upstream tarball generated with "make dist". - Added config rule. - Use dpatch to patch src/user.h (enable qh_QHpointer). * debian/control: - Removed build-dependencies on autoconf, automake, and libtool. - Build-depends on dpatch. - Changed section of libqhull-dev package to libdevel. * debian/libqhull-dev.files: Added usr/share/doc/libqhull5/src directory. -- Rafael Laboissiere Sun, 1 Feb 2004 01:14:13 +0100 qhull (2002.1-4) unstable; urgency=low * src/Make-config.sh: Patched upstream file for proper initialization of the Autotools. * debian/install-src-html.sh: Added script for including src/*.htm source documentation files into html doc dir. * debian/control: - Bumped Standards-Version to 3.6.1 (no changes needed). - Changed build-dependencies to autoconf and automake1.7 (instead of autoconf2.13 and automake1.6). Added eperl. * debian/libqhull-dev.files: Added dir usr/share/doc/libqhull4/src. * debian/manpage.in: Added template for missing man pages. * debian/rules: - Call debian/install-src-html.sh. - Generate manpages for qconvex, qdelaunay, qhalf, and qvoronoi commands. Lintian is happy now. -- Rafael Laboissiere Thu, 18 Dec 2003 21:20:14 +0100 qhull (2002.1-3) unstable; urgency=low * New maintainer (as per http://lists.debian.org/debian-devel/1999 /debian-devel-199911/msg01061.html). * debian/rules: Use the upstream script Make-config.sh, which sets up the autoconf/automake/libtool files. Also, clean up all the generated files in the clean rule. * debian/control: Bumped Standards-Version to 3.5.7. Added Build-Dependencies to autoconf/automake/libtool. -- Rafael Laboissiere Wed, 25 Sep 2002 10:39:30 +0200 qhull (2002.1-2) unstable; urgency=low * use shared char* qh_version in library -- Barak Pearlmutter Sat, 7 Sep 2002 10:34:13 -0600 qhull (2002.1-1) unstable; urgency=low * new upstream source -- Barak Pearlmutter Thu, 5 Sep 2002 20:51:10 -0600 qhull (3.1-5) unstable; urgency=low * rephrase descriptions (closes: #141027) -- Barak Pearlmutter Thu, 11 Apr 2002 22:12:33 -0600 qhull (3.1-4) unstable; urgency=low * include executables qconvex, qhalf, qvoronoi, qdelaunay * break executables out into separate package qhull-bin -- Barak Pearlmutter Wed, 27 Mar 2002 20:26:44 -0700 qhull (3.1-3) unstable; urgency=low * rename executable qhull-rbox back to rbox -- Barak Pearlmutter Mon, 25 Mar 2002 09:13:57 -0700 qhull (3.1-2) unstable; urgency=low * src/qconvex.c did not belong in the library * qh_version was multiply defined, now defined only in qhull.c -- Barak Pearlmutter Mon, 25 Mar 2002 08:55:45 -0700 qhull (3.1-1) unstable; urgency=low * Initial Release. (closes: #108115) -- Barak Pearlmutter Sun, 24 Mar 2002 21:53:13 -0700 qhull-2012.1/config/configure.ac0000644000076400010400000000072011720333312017631 0ustar bbarberAdministratorsdnl configure.ac for the qhull package dnl Author: Rafael Laboissiere dnl Created: Mon Dec 3 21:36:21 CET 2001 dnl Draft update for 2011.2: B. Barber, dec'11 AC_INIT(qhull, 6.3.1) AC_CONFIG_SRCDIR(src/libqhull/libqhull.c) AC_CONFIG_AUX_DIR(config) AC_CONFIG_MACRO_DIR(config) AM_INIT_AUTOMAKE AC_PROG_CC AC_PROG_LIBTOOL AC_CONFIG_FILES([ Makefile src/libqhull/Makefile html/Makefile eg/Makefile config/Makefile ]) AC_OUTPUT qhull-2012.1/config/Makefile-am-eg0000644000076400010400000000106211666302275020004 0ustar bbarberAdministrators### Makefile.am for the qhull package (eg) ### Author: Rafael Laboissiere ### Created: Mon Dec 3 21:36:21 CET 2001 ### Update for 2010.1: O. Lahaye, jun'10 ### Draft update for 2011.2: B. Barber, dec'11 ### Documentation files # to: docdir = $(prefix)/share/doc/$(PACKAGE) examplesdir = $(docdir)/examples # which: examples_DATA = \ q_eg \ q_egtest \ q_test \ q_test-ok.txt \ q_test.bat \ Qhull-go.bat \ qhulltest-ok.txt ### Extra files to be included in the tarball EXTRA_DIST = $(examples_DATA) qhull-2012.1/config/Makefile-am-html0000644000076400010400000000216511666323034020356 0ustar bbarberAdministrators### Makefile.am for the qhull package (html) ### Author: Rafael Laboissiere ### Created: Mon Dec 3 21:36:21 CET 2001 ### Update for 2010.1: O. Lahaye, jun'10 ### Draft update for 2011.2: B. Barber, dec'11 ### Man pages (trick to get around .man extension) %.1: %.man cp $< $@ CLEANFILES = *.1 man_MANS = rbox.1 qhull.1 ### Documentation files # to: docdir = $(prefix)/share/doc/$(PACKAGE) htmldir = $(docdir)/html # which: html_DATA = \ index.htm \ normal_voronoi_knauss_oesterle.jpg \ qconvex.htm \ qdelau_f.htm \ qdelaun.htm \ qhalf.htm \ qhull.htm \ qvoron_f.htm \ qvoronoi.htm \ rbox.htm \ qh--4d.gif \ qh--cone.gif \ qh--dt.gif \ qh--geom.gif \ qh--half.gif \ qh--rand.gif \ qh-code.htm \ qh-eg.htm \ qh-faq.htm \ qh-get.htm \ qh-impre.htm \ qh-optc.htm \ qh-optf.htm \ qh-optg.htm \ qh-opto.htm \ qh-optp.htm \ qh-optq.htm \ qh-optt.htm \ qh-quick.htm ### Extra files to be included in the tarball EXTRA_DIST = \ $(html_DATA) \ qhull.man \ qhull.txt \ qhull-cpp.xml\ rbox.man \ rbox.txt qhull-2012.1/config/Makefile-am-libqhull0000644000076400010400000000370211720333512021215 0ustar bbarberAdministrators### Makefile.am for the qhull package (src) ### Author: Rafael Laboissiere ### Created: Mon Dec 3 21:36:21 CET 2001 ### Shared Library # to: lib_LTLIBRARIES = libqhull.la # from: libqhull_la_SOURCES = \ rboxlib.c \ user.c \ global.c \ stat.c \ io.c \ geom2.c \ poly2.c \ merge.c \ libqhull.c \ geom.c \ poly.c \ qset.c \ mem.c \ usermem.c \ userprintf.c \ userprintf_rbox.c \ random.c # how: libqhull_la_LDFLAGS = -version-info 6:3:1 -lm ### Utility programs # to: bin_PROGRAMS = qhull rbox qconvex qdelaunay qvoronoi qhalf testqset # from: qhull_SOURCES = unix.c rbox_SOURCES = rbox.c qconvex_SOURCES = qconvex.c qdelaunay_SOURCES = qdelaun.c qvoronoi_SOURCES = qvoronoi.c qhalf_SOURCES = qhalf.c testqset_SOURCES = testqset.c qset.c mem.c # how: qhull_LDADD = libqhull.la rbox_LDADD = libqhull.la qconvex_LDADD = libqhull.la qdelaunay_LDADD = libqhull.la qvoronoi_LDADD = libqhull.la qhalf_LDADD = libqhull.la ### Include files pkginclude_HEADERS = \ geom.h \ mem.h \ poly.h \ qhull_a.h \ stat.h \ io.h \ merge.h \ libqhull.h \ random.h \ qset.h \ user.h ### Example programs # to: docdir = $(prefix)/share/doc/$(PACKAGE) examplesdir = $(docdir)/examples # which: examples_DATA = \ user_eg.c \ user_eg2.c \ Makefile \ Mborland doc_DATA = \ Changes.txt \ index.htm \ qh-geom.htm \ qh-globa.htm \ qh-io.htm \ qh-mem.htm \ qh-merge.htm \ qh-poly.htm \ qh-qhull.htm \ qh-set.htm \ qh-stat.htm \ qh-user.htm ### Extra files to be included in the tarball EXTRA_DIST = \ $(doc_DATA) \ $(examples_DATA) qhull-2012.1/config/Makefile-am-main0000644000076400010400000000104011666302126020324 0ustar bbarberAdministrators### Makefile.am for the qhull package (main) ### Author: Rafael Laboissiere ### Created: Mon Dec 3 21:36:21 CET 2001 ### Documentation files # to: docdir = $(prefix)/share/doc/$(PACKAGE) # which: doc_DATA = \ index.htm \ Announce.txt \ COPYING.txt \ README.txt \ REGISTER.txt ### Extra files to be included in the tarball EXTRA_DIST = \ $(doc_DATA) \ .gitignore \ CMakeLists.txt \ File_id.diz \ QHULL-GO.lnk ### Subdirectories for Automaking SUBDIRS = src/libqhull html eg config qhull-2012.1/config/Makefile.am0000644000076400010400000000051511322222063017377 0ustar bbarberAdministrators### Makefile.am for the qhull package (config) ### Author: Rafael Laboissiere ### Created: Mon Dec 3 21:36:21 CET 2001 ### Extra files to be included in the tarball EXTRA_DIST = \ README \ bootstrap.sh \ Makefile-am-main \ Makefile-am-eg \ Makefile-am-html \ Makefile-am-src qhull-2012.1/config/patches/0000755000076400010400000000000011721063454017003 5ustar bbarberAdministratorsqhull-2012.1/config/patches/00list0000644000076400010400000000004511711014446020034 0ustar bbarberAdministratorsQHpointer.dpatch make-new-msg.dpatch qhull-2012.1/config/patches/make-new-msg.dpatch0000755000076400010400000000266011665326115022472 0ustar bbarberAdministrators#! /bin/sh -e ## QHpointer.dpatch by Rafael Laboissiere ## ## All lines beginning with `## DP:' are a description of the patch. ## DP: Access Qhull globals via a pointer to allocated memory [ -f debian/patches/00patch-opts ] && . debian/patches/00patch-opts patch_opts="${patch_opts:--f --no-backup-if-mismatch}" if [ $# -ne 1 ]; then echo >&2 "`basename $0`: script expects -patch|-unpatch as argument" exit 1 fi case "$1" in -patch) patch $patch_opts -p1 < $0;; -unpatch) patch $patch_opts -p1 -R < $0;; *) echo >&2 "`basename $0`: script expects -patch|-unpatch as argument" exit 1;; esac exit 0 --- qhull-orig/src/io.c 2004-01-31 12:00:15.000000000 +0100 +++ qhull/src/io.c 2004-02-06 09:54:18.000000000 +0100 @@ -4017,11 +4017,8 @@ qh rbox_command[strlen(qh rbox_command)-1]= '\0'; if (!strcmp (qh rbox_command, "./rbox D4")) fprintf (qh ferr, "\n\ -This is the qhull test case. If any errors or core dumps occur,\n\ -recompile qhull with 'make new'. If errors still occur, there is\n\ -an incompatibility. You should try a different compiler. You can also\n\ -change the choices in user.h. If you discover the source of the problem,\n\ -please send mail to qhull_bug@qhull.org.\n\ +This is the qhull test case. If any errors or core dumps occur,\n\ +fill a bug report against the libqhull Debian package.\n\ \n\ Type 'qhull' for a short list of options.\n"); } qhull-2012.1/config/patches/QHpointer.dpatch0000755000076400010400000000164411665326115022114 0ustar bbarberAdministrators#! /bin/sh -e ## QHpointer.dpatch by Rafael Laboissiere ## ## All lines beginning with `## DP:' are a description of the patch. ## DP: Access Qhull globals via a pointer to allocated memory [ -f debian/patches/00patch-opts ] && . debian/patches/00patch-opts patch_opts="${patch_opts:--f --no-backup-if-mismatch}" if [ $# -ne 1 ]; then echo >&2 "`basename $0`: script expects -patch|-unpatch as argument" exit 1 fi case "$1" in -patch) patch $patch_opts -p1 < $0;; -unpatch) patch $patch_opts -p1 -R < $0;; *) echo >&2 "`basename $0`: script expects -patch|-unpatch as argument" exit 1;; esac exit 0 --- qhull-orig/src/user.h 2002-04-29 11:01:46.000000000 +0200 +++ qhull/src/user.h 2004-02-02 11:04:47.000000000 +0100 @@ -509,7 +509,7 @@ see: user_eg.c for an example */ -#define qh_QHpointer 0 +#define qh_QHpointer 1 #if 0 /* sample code */ qhT *oldqhA, *oldqhB; qhull-2012.1/config/README0000644000076400010400000000156311720333426016237 0ustar bbarberAdministratorsAutotools configuration for Qhull --------------------------------- This directory contains all the files needed to bootstrap the Qhull package for using Autoconf, Automake, and Libtool. See ../README.txt for instructions on building with make, cmake, qt, and Microsoft DevStudio WARNING -- Reworked for qhull-2012.1 but not tested. Produces qhull.so Ignores the C++ interface and libqhull_p.so The patch subdirectory is out-of-date. It was not used for Qhull 2009.1 user.h sets qh_QHpointer=0 (static allocation of qh_qh) Brad Barber , 2012-01-27 Go to the top source dir and type: config/bootstrap.sh And then the usual: ./configure --prefix=/your/preferred/path/here make make install -- Rafael Laboissiere , Sun Feb 1 13:43:54 CET 2004 qhull-2012.1/COPYING.txt0000644000076400010400000000314311710144467015763 0ustar bbarberAdministrators Qhull, Copyright (c) 1993-2012 C.B. Barber Arlington, MA and The National Science and Technology Research Center for Computation and Visualization of Geometric Structures (The Geometry Center) University of Minnesota email: qhull@qhull.org This software includes Qhull from C.B. Barber and The Geometry Center. Qhull is copyrighted as noted above. Qhull is free software and may be obtained via http from www.qhull.org. It may be freely copied, modified, and redistributed under the following conditions: 1. All copyright notices must remain intact in all files. 2. A copy of this text file must be distributed along with any copies of Qhull that you redistribute; this includes copies that you have modified, or copies of programs or other software products that include Qhull. 3. If you modify Qhull, you must include a notice giving the name of the person performing the modification, the date of modification, and the reason for such modification. 4. When distributing modified versions of Qhull, or other software products that include Qhull, you must provide notice that the original source code may be obtained as noted above. 5. There is no warranty or other guarantee of fitness for Qhull, it is provided solely "as is". Bug reports or fixes may be sent to qhull_bug@qhull.org; the authors may or may not act on them as they desire. qhull-2012.1/eg/0000755000076400010400000000000011721063454014502 5ustar bbarberAdministratorsqhull-2012.1/eg/make-vcproj.sh0000755000076400010400000000615311711003634017255 0ustar bbarberAdministrators#!/bin/bash # # make-vcproj.sh -- Make sln and vcproj files from CMakeLists.txt and qhull-all.pro # # [jan'12] Additional changes made by hand for qhull 2012.1. This file updated but not tested. # # $Id: //main/2011/qhull/eg/make-vcproj.sh#5 $$Change: 1476 $ # $DateTime: 2012/01/28 09:37:56 $$Author: bbarber $ if [[ ! -f CMakeLists.txt || ! -f src/qhull-all.pro ]]; then echo "Excute eg/make-vcproj.sh from qhull directory with CMakeLists.txt and src/qhull-all.pro" exit fi echo "Set up build directories..." if [[ ! -d build-prev ]]; then echo "Backup previous build" cp -r build build-prev && rm -r build fi rm -r buildvc buildqt mkdir -p build mkdir -p buildvc mkdir -p buildqt echo "Create vcproj files with cmake and qmake..." cd buildvc && cmake -G "Visual Studio 8 2005" .. && cmake .. cd .. cd buildqt && qmake -tp vc -r ../src/qhull-all.pro cd .. if [[ ! -f CMakeLists.txt || ! -f buildvc/qhull.vcproj || ! -f buildqt/qhulltest/qhulltest.vcproj ]]; then echo "qmake and cmake did not build vcproj files in buildvc/ and buildqt" exit fi for f in buildvc/*.vcproj buildqt/qhulltest/*.vcproj; do echo $f if [[ ! ${f##*INSTALL*} || ! ${f##*ALL_BUILD*} || ! ${f##*ZERO_CHECK*} ]]; then continue fi dest=build/${f##*\/} sed -r -e 's|[cC]:\\bash\\local\\qhull|..|g' \ -e 's|[cC]:/bash/local/qhull|..|g' \ -e '\|CMake| d' \ -e 's/;CMAKE_INTDIR=..quot;[A-Za-z]*..quot;//' \ -e 's/LinkIncremental="2"/LinkIncremental="1"/' \ -e 's/RuntimeLibrary[=]/RuntimeTypeInfo="false" RuntimeLibrary=/' \ -e 's/.*RuntimeTypeInfo."TRUE".*//' \ -e 's/buildvc/build/g' \ -e 's/buildqt/build/g' \ -e 's/\.\.\\\.\./../g' \ -e 's|\.\./\.\.|..|g' \ -e 's/c:\\qt\\[0-9]\.[0-9]\.[0-9]/\$(QTDIR)/g' \ -e 's|..\\build\\[a-zA-Z]*[\\/]([_a-z0-9]*.pdb)|..\\bin\\\1|g' \ -e 's|..\\build\\[a-zA-Z]*[\\/]([_a-z0-9]*.exe)|..\\bin\\\1|g' \ -e 's|..\\build\\[a-zA-Z]*[\\/]([_a-z0-9]*.lib)|..\\lib\\\1|g' \ -e 's|..\\build\\[a-zA-Z]*[\\/]([_a-z0-9]*.dll)|..\\bin\\\1|g' \ -e 's| [a-zA-Z]*[\\/]([_a-z0-9]*.lib)| ..\\lib\\\1|g' \ -e 's/"([_a-z0-9]*.exe)/"..\\bin\\\1/g' \ $f > $dest done echo -e '\nExcept for qhulltest.vcproj,\n*.vcproj: delete empty File in Files section near end of vcproj' echo -e '\nExcept for qhulltest.vcproj,\n*.vcproj: rename debug targets to qhull_d.dll, etc.' # If need to rebuild sln sed -e '\|Project.*ALL_BUILD|,\|EndProject$| d' \ -e '\|Project.*INSTALL|,\|EndProject$| d' \ -e '\|Project.*ZERO_CHECK|,\|EndProject$| d' \ buildvc/qhull.sln >build/qhull.sln echo echo 'qhull.sln: Remove first line of each GUID list -- postProject\n.* > postProject' echo 'qhull.sln: Remove four empty project sections' echo 'qhull.sln: Remove first part of Global section.' echo 'qhull.sln: Save as PC' echo '*.vcproj: Remove libqhullcpp from AdditionalIncludeDirectories except for cpp' echo echo 'Open qhull.sln with DevStudio and add qhulltest.vcproj' echo 'Add dependencies on libqhull libqhull6_p and qhullcpp' echo 'Change Linker>OutputFile to qhulltest.exe' echo 'Remove qhulltest via Configuration Manager from Release, Debug, etc.' qhull-2012.1/eg/Qhull-go.bat0000755000076400010400000000074511663056726016704 0ustar bbarberAdministrators: Qhull-go.bat invoked as cmd.com from QHULL-GO @echo off echo. echo ========= Qhull with rbox, qconvex, qdelaunay, qvoronoi, qhalf ============ echo. echo Use arrow keys to repeat and edit commands. echo. echo Double-click window bar for full height, or echo "right-click > Properties > Layout > Window Size > Height > 50 " echo. echo Type 'qconvex' for synopsis and examples. echo. echo ========= echo. title Qhull cd bin %comspec% qhull-2012.1/eg/qhull-zip.sh0000755000076400010400000002265711720340046016774 0ustar bbarberAdministrators#!/bin/sh # # qhull-zip.sh version -- Make zip and tgz files for Qhull release # # wzzip from http://www.winzip.com/wzcline.htm # can not use path with $zip_file # odd error messages if can't locate directory # # $Id: //main/2011/qhull/eg/qhull-zip.sh#16 $$Change: 1493 $ # $DateTime: 2012/02/20 09:31:24 $$Author: bbarber $ if [[ $# -eq 0 ]]; then echo 'Missing date stamp, e.g., qhull-zip.sh 2007.1' exit fi version=$1 err_program=qhull-zip err_log=/var/tmp/qhull-zip.log [[ -e $HOME/bash/etc/road-script.sh ]] && source $HOME/bash/etc/road-script.sh \ || source /etc/road-script.sh check_err_log $LINENO "$err_log" check_err_log $LINENO "$err_step_log" log_step $LINENO "Logging to $err_log\n... and $err_step_log" log_note $LINENO "Find Qhull directory" if [[ ! -d qhull/eg && ! -d ../qhull/eg && -d ../../qhull/eg ]]; then exit_err $LINENO "qhull/eg directory not found at or above $PWD" fi if [[ ! -d qhull/eg ]]; then if [[ -d ../qhull/eg ]]; then cd .. else cd ../.. # Tested above fi fi root_dir=$(pwd) TEMP_DIR="$TMP/qhull-zip-$(ro_today2)" TEMP_FILE="$TMP/qhull-zip-$(ro_today2).txt" qhull_zip_file=qhull-$version.zip # no path or spaces qhull_tgz_file=qhull-$version-src.tgz qhullmd5_file=qhull-$version.md5sum exit_if_fail $LINENO "rm -f $qhull_zip_file $qhull_tgz_file $qhullmd5_file" ############################# log_step $LINENO "Check environment" ############################# [[ $(type -p md5sum) ]] || exit_err $LINENO "md5sum is missing" [[ $(cp --help || grep '[-]-parents') ]] || exit_err $LINENO "cp does not have --parents option" ############################# log_step $LINENO "Define functions" ############################# function check_zip_file #zip_file { local zip_file=$1 local HERE=$(ro_here) log_note $HERE "Check $zip_file" ls -l $zip_file >>$err_log exit_if_err $HERE "Did not create $zip_file" wzunzip -ybc -t $zip_file | grep -E -v -e '( OK|Zip)' >>$err_log exit_if_err $HERE "Error while checking $zip_file" } function check_tgz_file #tgz_file { local tgz_file=$1 local HERE=$(ro_here) log_note $HERE "Check $tgz_file" ls -l $tgz_file >>$err_log exit_if_err $HERE "Did not create $tgz_file" tar -tzf $tgz_file >/dev/null 2>>$err_log exit_if_err $HERE "Can not extract -- tar -tzf $tgz_file" } function convert_to_unix #dir $qhull_2ufiles -- convert files to Unix, preserving modtime from $root_dir { local temp_dir=$1 local HERE=$(ro_here) log_note $HERE "Convert files to unix format in $1" for f in $(find $temp_dir -type f | grep -E '^([^.]*|.*\.(ac|am|bashrc|c|cfg|cpp|css|d|dpatch|h|htm|html|man|pl|pri|pro|profile|sh|sql|termcap|txt|xml|xsd|xsl))$'); do exit_if_fail $HERE "d2u '$f' && touch -r '$root_dir/${f#$temp_dir/}' '$f'" done for f in $qhull_2ufiles; do exit_if_fail $HERE "d2u '$temp_dir/$f' && touch -r '$root_dir/$f' '$temp_dir/$f'" done } function create_md5sum #md5_file -- create md5sum of current directory { local md5_file=$1 local HERE=$(ro_here) log_step $HERE "Compute $md5_file" exit_if_fail $HERE "rm -f $md5_file" find . -type f | sed 's|^\./||' | sort | xargs md5sum >>$md5_file exit_if_err $HERE "md5sum failed" log_note $HERE "$(md5sum $md5_file)" } ############################# log_step $LINENO "Configure $0 for $(pwd)/qhull" ############################# md5_zip_file=qhull-$version-zip.md5sum md5_tgz_file=qhull-$version-src-tgz.md5sum # recursive qhull_dirs="qhull/config qhull/eg qhull/html qhull/src" qhull_files="qhull/build/*.sln qhull/build/*.vcproj \ qhull/Announce.txt qhull/CMakeLists.txt qhull/COPYING.txt \ qhull/File_id.diz qhull/QHULL-GO.lnk qhull/README.txt \ qhull/REGISTER.txt qhull/index.htm qhull/Makefile qhull/bin/qhull.dll \ qhull/bin/qconvex.exe qhull/bin/qdelaunay.exe qhull/bin/qhalf.exe \ qhull/bin/qhull.exe qhull/bin/qhull_p.dll qhull/bin/qvoronoi.exe \ qhull/bin/rbox.exe qhull/bin/user_eg.exe qhull/bin/user_eg2.exe \ qhull/bin/user_eg3.exe qhull/bin/testqset.exe qhull/bin/msvcr80.dll" qhull_ufiles="$qhull_dirs qhull/build/*.sln qhull/build/*.vcproj \ qhull/Announce.txt qhull/CMakeLists.txt qhull/COPYING.txt \ qhull/File_id.diz qhull/QHULL-GO.lnk qhull/README.txt \ qhull/REGISTER.txt qhull/index.htm qhull/Makefile" qhull_d2ufiles="config/changelog config/patches/00list config/Makefile-am-eg \ config/Makefile-am-html config/Makefile-am-libqhull config/Makefile-am-main config/README Makefile src/libqhull/Makefile src/libqhull/MBorland eg/q_eg eg/q_egtest eg/q_test " ############################# log_step $LINENO "Clean distribution directories" ############################# if [[ -f qhull/src/Make-config.sh || -d qhull/src/debian ]]; then exit_err $LINENO "Before continuing, remove debian build from src/" fi p4 sync -f qhull/build/... exit_if_err $LINENO "Can not 'p4 sync -f qhull.sln *.vcproj'" cd qhull && make clean exit_if_err $LINENO "Can not 'make clean'" cd .. rm -f qhull/src/qhull-all.pro.user* qhull/src/libqhull/BCC32tmp.cfg rm -f qhull/eg/eg.* qhull/*.x qhull/x.* qhull/x qhull/eg/x rm -f qhull/bin/qhulltest.exe qhull/bin/qhulltest qhull/configure.in rm -f qhull/src/libqhull/*.exe qhull/src/libqhull/*.a rm -f qhull/src/libqhull/qconvex.c qhull/src/libqhull/unix.c rm -f qhull/src/libqhull/qdelaun.c qhull/src/libqhull/qhalf.c rm -f qhull/src/libqhull/qvoronoi.c qhull/src/libqhull/rbox.c rm -f qhull/src/libqhull/user_eg.c qhull/src/libqhull/user_eg2.c rm -f qhull/src/libqhull/testqset.c qhull/Makefile.am rm -f qhull/src/libqhull/Makefile.am qhull/html/Makefile.am rm -f qhull/src/Makefile.am qhull/eg/Makefile.am rm -f qhull/configure.ac set noglob if [[ -e /bin/msysinfo && $(type -p wzzip) && $(type -p wzunzip) ]]; then ############################# log_step $LINENO "Build zip directory, $TEMP_DIR/qhull" ############################# ls -l $qhull_files $qhull_dirs >>$err_log exit_if_err $LINENO "Missing files for zip directory" log_note $LINENO "Copy \$qhull_files \$qhull_dirs to $TEMP_DIR/qhull" exit_if_fail $LINENO "rm -rf $TEMP_DIR && mkdir $TEMP_DIR" exit_if_fail $LINENO "cp -r -p --parents $qhull_files $qhull_dirs $TEMP_DIR" ############################# log_step $LINENO "Write md5sum to $md5_tgz_file" ############################# exit_if_fail $LINENO "pushd $TEMP_DIR/qhull" create_md5sum $md5_zip_file exit_if_fail $LINENO "cp -p $md5_zip_file $root_dir" ############################# log_step $LINENO "Write $qhull_zip_file" ############################# log_note $LINENO "Write \$qhull_files to $qhull_zip_file" exit_if_fail $LINENO "cd .. && mv qhull qhull-$version && md5sum qhull-$version/$md5_zip_file >>$root_dir/$qhullmd5_file" wzzip -P -r -u $qhull_zip_file qhull-$version >>$err_log exit_if_err $LINENO "wzzip does not exist or error while zipping files" check_zip_file $qhull_zip_file exit_if_fail $LINENO "popd" exit_if_fail $LINENO "mv $TEMP_DIR/$qhull_zip_file ." fi ############################# log_step $LINENO "Build tgz directory, $TEMP_DIR/qhull" ############################# log_note $LINENO "Archive these files as $qhull_tgz_file" ls -l $qhull_ufiles >>$err_log exit_if_err $LINENO "Missing files for tgz" exit_if_fail $LINENO "rm -rf $TEMP_DIR && mkdir -p $TEMP_DIR" exit_if_fail $LINENO "cp -r -p --parents $qhull_ufiles $TEMP_DIR" if [[ $IS_WINDOWS && $(type -p d2u) ]]; then log_step $LINENO "Convert to Unix line endings" convert_to_unix "$TEMP_DIR" fi ############################# log_step $LINENO "Write md5sum to $md5_tgz_file" ############################# exit_if_fail $LINENO "pushd $TEMP_DIR && cd qhull" create_md5sum $md5_tgz_file exit_if_fail $LINENO "cp -p $md5_tgz_file $root_dir" exit_if_fail $LINENO "cd .. && mv qhull qhull-$version && md5sum qhull-$version/$md5_tgz_file >>$root_dir/$qhullmd5_file" ############################# log_step $LINENO "Write $qhull_tgz_file" ############################# exit_if_fail $LINENO "tar -zcf $root_dir/$qhull_tgz_file * && popd" check_tgz_file $qhull_tgz_file log_note $LINENO "md5sum of zip and tgz files" for f in $qhull_zip_file $qhull_tgz_file; do if [[ -r $f ]]; then exit_if_fail $LINENO "md5sum $f >>$qhullmd5_file" fi done ############################# log_step $LINENO "Extract zip and tgz files to ($TEMP_DIR)" ############################# exit_if_fail $LINENO "rm -rf $TEMP_DIR" if [[ -r $root_dir/$qhull_zip_file ]]; then exit_if_fail $LINENO "mkdir -p $TEMP_DIR/zip && cd $TEMP_DIR/zip" exit_if_fail $LINENO "wzunzip -yb -d $root_dir/$qhull_zip_file" log_step $LINENO "Search for date stamps to zip/Dates.txt" find . -type f | grep -v '/bin/' | xargs grep '\-20' | grep -v -E '(page=|ISBN|sql-2005|utility-2000|written 2002-2003|tail -n -20|Spinellis|WEBSIDESTORY|D:06-5-2007|server-2005)' >Dates.txt find . -type f | grep -v '/bin/' | xargs grep -i 'qhull *20' >>Dates.txt fi if [[ -r $root_dir/$qhull_tgz_file ]]; then exit_if_fail $LINENO "mkdir -p $TEMP_DIR/tgz && cd $TEMP_DIR/tgz" exit_if_fail $LINENO "tar -zxf $root_dir/$qhull_tgz_file" fi ############################# log_step $LINENO "Compare previous zip release, Dates.txt, and md5sum. Check for virus." log_step $LINENO "Compare zip and tgz for CRLF vs LF" log_step $LINENO "Search xml files for UNDEFINED. Check page links" log_step $LINENO "Extract zip to Qhull/ and compare directories" log_step $LINENO "Finished successfully" ############################# qhull-2012.1/eg/qhulltest-ok.txt0000644000076400010400000011020411707655614017706 0ustar bbarberAdministrators********* Start testing of orgQhull::QhullVertex_test ********* Config: Using QTest library 4.7.4, Qt 4.7.4 PASS : orgQhull::QhullVertex_test::initTestCase() PASS : orgQhull::QhullVertex_test::t_constructConvert() 5 3 2 1 6 0 7 8 XFAIL : orgQhull::QhullVertex_test::t_getSet() ListIterator copy constructor not reset to BOT ..\..\src\qhulltest\QhullVertex_test.cpp(107) : failure location Point 1: p1: 0.15707 -0.521517 0.673312 Point 0: p0: -0.0992431 0.442941 0.737533 Point 2: p2: 0.554717 0.664895 0.0142947 Point 3: p3: 0.81103 -0.299563 -0.0499261 Point 6: p6: -0.15707 0.521517 -0.673312 Point 4: p4: -0.81103 0.299563 0.0499261 Point 5: p5: -0.554717 -0.664895 -0.0142947 Point 7: p7: 0.0992431 -0.442941 -0.737533 PASS : orgQhull::QhullVertex_test::t_getSet() PASS : orgQhull::QhullVertex_test::t_foreach() Vertex and vertices w/o runId: - p4 (v1): 0.5 -0.5 -0.5 neighborFacets: f1 f2 f9 p6(v6) p2(v2) p4(v1) p0(v0) Vertex and vertices w/ runId: - p4 (v1): 0.5 -0.5 -0.5 neighborFacets: f1 f2 f9 vertices: p6(v6) p2(v2) p4(v1) p0(v0) Try again with simplicial facets. No neighboring facets listed for vertices. Vertex and vertices w/o runId: - p0 (v5): -0.0222149 -0.366435 0.327062 This time with neighborFacets() defined for all vertices: - p0 (v5): -0.0222149 -0.366435 0.327062 neighborFacets: f5 f6 f7 f8 Try again with Voronoi diagram of simplicial facets. Neighboring facets automatically defined for vertices. Vertex and vertices w/o runId: - p7 (v1): 0.386746 0.0449288 0.118336 0.165595 neighborFacets: f1 f6 f9 f13 f14 f15 f16 f18 f19 f21 PASS : orgQhull::QhullVertex_test::t_io() PASS : orgQhull::QhullVertex_test::cleanupTestCase() Totals: 6 passed, 0 failed, 0 skipped ********* Finished testing of orgQhull::QhullVertex_test ********* ********* Start testing of orgQhull::Coordinates_test ********* Config: Using QTest library 4.7.4, Qt 4.7.4 PASS : orgQhull::Coordinates_test::initTestCase() PASS : orgQhull::Coordinates_test::t_construct() PASS : orgQhull::Coordinates_test::t_convert() PASS : orgQhull::Coordinates_test::t_element() PASS : orgQhull::Coordinates_test::t_readonly() PASS : orgQhull::Coordinates_test::t_operator() PASS : orgQhull::Coordinates_test::t_const_iterator() PASS : orgQhull::Coordinates_test::t_iterator() PASS : orgQhull::Coordinates_test::t_coord_iterator() PASS : orgQhull::Coordinates_test::t_mutable_coord_iterator() PASS : orgQhull::Coordinates_test::t_readwrite() PASS : orgQhull::Coordinates_test::t_search() Coordinates 1-2-3 1 2 3 PASS : orgQhull::Coordinates_test::t_io() PASS : orgQhull::Coordinates_test::cleanupTestCase() Totals: 14 passed, 0 failed, 0 skipped ********* Finished testing of orgQhull::Coordinates_test ********* ********* Start testing of orgQhull::PointCoordinates_test ********* Config: Using QTest library 4.7.4, Qt 4.7.4 PASS : orgQhull::PointCoordinates_test::initTestCase() PASS : orgQhull::PointCoordinates_test::t_construct() PASS : orgQhull::PointCoordinates_test::t_convert() INFO : Caught QH10063 Qhull error: can not change PointCoordinates dimension (from 3 to 2) PASS : orgQhull::PointCoordinates_test::t_getset() PASS : orgQhull::PointCoordinates_test::t_element() PASS : orgQhull::PointCoordinates_test::t_foreach() PASS : orgQhull::PointCoordinates_test::t_search() PASS : orgQhull::PointCoordinates_test::t_modify() PASS : orgQhull::PointCoordinates_test::t_append_points() PASS : orgQhull::PointCoordinates_test::t_coord_iterator() PointCoordinates 0-d 0 0 PointCoordinates 1-3-2 2 3 1 2 3 1 2 3 PASS : orgQhull::PointCoordinates_test::t_io() PASS : orgQhull::PointCoordinates_test::cleanupTestCase() Totals: 12 passed, 0 failed, 0 skipped ********* Finished testing of orgQhull::PointCoordinates_test ********* ********* Start testing of orgQhull::QhullFacet_test ********* Config: Using QTest library 4.7.4, Qt 4.7.4 PASS : orgQhull::QhullFacet_test::initTestCase() PASS : orgQhull::QhullFacet_test::t_constructConvert() 18 19 22 24 26 27 30 31 34 35 38 39 XFAIL : orgQhull::QhullFacet_test::t_getSet() ListIterator copy constructor not reset to BOT ..\..\src\qhulltest\QhullFacet_test.cpp(106) : failure location Hyperplane: 0.711787 0.143377 0.687607 -0.5 InnerPlane: 0.711787 0.143377 0.687607 -0.5 innerOffset+0.5 1.16573e-015 OuterPlane: 0.711787 0.143377 0.687607 -0.5 outerOffset+0.5 -2.22045e-015 Center: p10487712: 0.355893 0.0716887 0.343803 Hyperplane: 0.711787 0.143377 0.687607 -0.5 InnerPlane: 0.711787 0.143377 0.687607 -0.5 innerOffset+0.5 1.16573e-015 OuterPlane: 0.711787 0.143377 0.687607 -0.5 outerOffset+0.5 -2.22045e-015 Center: p10487712: 0.355893 0.0716887 0.343803 Hyperplane: -0.256313 0.964458 0.0642208 -0.5 InnerPlane: -0.256313 0.964458 0.0642208 -0.5 innerOffset+0.5 1.11022e-015 OuterPlane: -0.256313 0.964458 0.0642208 -0.5 outerOffset+0.5 -2.33147e-015 Center: p10488224: -0.128156 0.482229 0.0321104 Hyperplane: -0.256313 0.964458 0.0642208 -0.5 InnerPlane: -0.256313 0.964458 0.0642208 -0.5 innerOffset+0.5 1.11022e-015 OuterPlane: -0.256313 0.964458 0.0642208 -0.5 outerOffset+0.5 -2.33147e-015 Center: p10488224: -0.128156 0.482229 0.0321104 Hyperplane: -0.65396 -0.221954 0.723238 -0.5 InnerPlane: -0.65396 -0.221954 0.723238 -0.5 innerOffset+0.5 1.22125e-015 OuterPlane: -0.65396 -0.221954 0.723238 -0.5 outerOffset+0.5 -2.33147e-015 Center: p10497256: -0.32698 -0.110977 0.361619 Hyperplane: -0.65396 -0.221954 0.723238 -0.5 InnerPlane: -0.65396 -0.221954 0.723238 -0.5 innerOffset+0.5 1.22125e-015 OuterPlane: -0.65396 -0.221954 0.723238 -0.5 outerOffset+0.5 -2.33147e-015 Center: p10497256: -0.32698 -0.110977 0.361619 Hyperplane: 0.65396 0.221954 -0.723238 -0.5 InnerPlane: 0.65396 0.221954 -0.723238 -0.5 innerOffset+0.5 1.11022e-015 OuterPlane: 0.65396 0.221954 -0.723238 -0.5 outerOffset+0.5 -2.22045e-015 Center: p10488096: 0.32698 0.110977 -0.361619 Hyperplane: 0.65396 0.221954 -0.723238 -0.5 InnerPlane: 0.65396 0.221954 -0.723238 -0.5 innerOffset+0.5 1.11022e-015 OuterPlane: 0.65396 0.221954 -0.723238 -0.5 outerOffset+0.5 -2.22045e-015 Center: p10488096: 0.32698 0.110977 -0.361619 Hyperplane: 0.256313 -0.964458 -0.0642208 -0.5 InnerPlane: 0.256313 -0.964458 -0.0642208 -0.5 innerOffset+0.5 1.22125e-015 OuterPlane: 0.256313 -0.964458 -0.0642208 -0.5 outerOffset+0.5 -2.33147e-015 Center: p10497112: 0.128156 -0.482229 -0.0321104 Hyperplane: 0.256313 -0.964458 -0.0642208 -0.5 InnerPlane: 0.256313 -0.964458 -0.0642208 -0.5 innerOffset+0.5 1.22125e-015 OuterPlane: 0.256313 -0.964458 -0.0642208 -0.5 outerOffset+0.5 -2.33147e-015 Center: p10497112: 0.128156 -0.482229 -0.0321104 Hyperplane: -0.711787 -0.143377 -0.687607 -0.5 InnerPlane: -0.711787 -0.143377 -0.687607 -0.5 innerOffset+0.5 1.11022e-015 OuterPlane: -0.711787 -0.143377 -0.687607 -0.5 outerOffset+0.5 -2.22045e-015 Center: p10497280: -0.355893 -0.0716887 -0.343803 Hyperplane: -0.711787 -0.143377 -0.687607 -0.5 InnerPlane: -0.711787 -0.143377 -0.687607 -0.5 innerOffset+0.5 1.11022e-015 OuterPlane: -0.711787 -0.143377 -0.687607 -0.5 outerOffset+0.5 -2.22045e-015 Center: p10497280: -0.355893 -0.0716887 -0.343803 Voronoi vertex: 0 4.996e-016 4.996e-016 DistanceEpsilon 1e-012 PASS : orgQhull::QhullFacet_test::t_getSet() PASS : orgQhull::QhullFacet_test::t_value() PASS : orgQhull::QhullFacet_test::t_foreach() - f1 - flags: bottom tested seen coplanar - merges: 1 - normal: -0 -0 -1 - offset: -0.5 - center: 0 0 -0.5 - vertices: p6(v6) p2(v2) p4(v1) p0(v0) - neighboring facets: f2 f3 f9 f10 - ridges: - r4 tested vertices: p2(v2) p0(v0) between f1 and f3 - r3 tested vertices: p4(v1) p0(v0) between f2 and f1 - r1 tested vertices: p6(v6) p4(v1) between f9 and f1 - r2 tested vertices: p6(v6) p2(v2) between f1 and f10 - f1 - flags: bottom tested seen coplanar - merges: 1 - normal: -0 -0 -1 - offset: -0.5 - center: 0 0 -0.5 - vertices: p6(v6) p2(v2) p4(v1) p0(v0) - neighboring facets: f2 f3 f9 f10 - flags: bottom tested seen coplanar - center:0 0 -0.5 - ridges: - r4 tested vertices: p2(v2) p0(v0) between f1 and f3 - r3 tested vertices: p4(v1) p0(v0) between f2 and f1 - r1 tested vertices: p6(v6) p4(v1) between f9 and f1 - r2 tested vertices: p6(v6) p2(v2) between f1 and f10 PASS : orgQhull::QhullFacet_test::t_io() PASS : orgQhull::QhullFacet_test::cleanupTestCase() Totals: 7 passed, 0 failed, 0 skipped ********* Finished testing of orgQhull::QhullFacet_test ********* ********* Start testing of orgQhull::QhullFacetList_test ********* Config: Using QTest library 4.7.4, Qt 4.7.4 PASS : orgQhull::QhullFacetList_test::initTestCase() PASS : orgQhull::QhullFacetList_test::t_construct() PASS : orgQhull::QhullFacetList_test::t_convert() PASS : orgQhull::QhullFacetList_test::t_readonly() PASS : orgQhull::QhullFacetList_test::t_foreach() Vertices for 3 facets - p1 (v5): 0.15707 -0.521517 0.673312 neighborFacets: f6 f4 f11 - p0 (v3): -0.0992431 0.442941 0.737533 neighborFacets: f3 f4 f6 - p2 (v2): 0.554717 0.664895 0.0142947 neighborFacets: f3 f4 f8 - p3 (v1): 0.81103 -0.299563 -0.0499261 neighborFacets: f4 f8 f11 - p6 (v6): -0.15707 0.521517 -0.673312 neighborFacets: f8 f3 f13 - p4 (v0): -0.81103 0.299563 0.0499261 neighborFacets: f3 f6 f13 - p5 (v7): -0.554717 -0.664895 -0.0142947 neighborFacets: f11 f6 f13 - f4 - flags: top tested seen - merges: 1 - normal: 0.711787 0.143377 0.687607 - offset: -0.5 - center: 0.355893 0.0716887 0.343803 - vertices: p1(v5) p0(v3) p2(v2) p3(v1) - neighboring facets: f8 f3 f11 f6 - ridges: - r4 tested vertices: p0(v3) p2(v2) between f4 and f3 - r3 tested vertices: p2(v2) p3(v1) between f4 and f8 - r1 tested vertices: p1(v5) p3(v1) between f11 and f4 - r2 tested vertices: p1(v5) p0(v3) between f4 and f6 - f3 - flags: bottom tested seen - merges: 1 - normal: -0.256313 0.964458 0.0642208 - offset: -0.5 - center: -0.128156 0.482229 0.0321104 - vertices: p6(v6) p0(v3) p2(v2) p4(v0) - neighboring facets: f13 f6 f4 f8 - ridges: - r4 tested vertices: p0(v3) p2(v2) between f4 and f3 - r11 tested vertices: p0(v3) p4(v0) between f3 and f6 - r6 tested vertices: p6(v6) p4(v0) between f13 and f3 - r10 tested vertices: p6(v6) p2(v2) between f3 and f8 - f6 - flags: bottom tested seen coplanar - merges: 1 - normal: -0.65396 -0.221954 0.723238 - offset: -0.5 - center: -0.32698 -0.110977 0.361619 - vertices: p5(v7) p1(v5) p0(v3) p4(v0) - neighboring facets: f3 f4 f13 f11 - ridges: - r2 tested vertices: p1(v5) p0(v3) between f4 and f6 - r14 tested vertices: p5(v7) p1(v5) between f11 and f6 - r13 tested vertices: p5(v7) p4(v0) between f6 and f13 - r11 tested vertices: p0(v3) p4(v0) between f3 and f6 Facets only - f4 - flags: top tested seen - merges: 1 - normal: 0.711787 0.143377 0.687607 - offset: -0.5 - center: 0.355893 0.0716887 0.343803 - vertices: p1(v5) p0(v3) p2(v2) p3(v1) - neighboring facets: f8 f3 f11 f6 - ridges: - r4 tested vertices: p0(v3) p2(v2) between f4 and f3 - r3 tested vertices: p2(v2) p3(v1) between f4 and f8 - r1 tested vertices: p1(v5) p3(v1) between f11 and f4 - r2 tested vertices: p1(v5) p0(v3) between f4 and f6 - f3 - flags: bottom tested seen - merges: 1 - normal: -0.256313 0.964458 0.0642208 - offset: -0.5 - center: -0.128156 0.482229 0.0321104 - vertices: p6(v6) p0(v3) p2(v2) p4(v0) - neighboring facets: f13 f6 f4 f8 - ridges: - r4 tested vertices: p0(v3) p2(v2) between f4 and f3 - r11 tested vertices: p0(v3) p4(v0) between f3 and f6 - r6 tested vertices: p6(v6) p4(v0) between f13 and f3 - r10 tested vertices: p6(v6) p2(v2) between f3 and f8 - f6 - flags: bottom tested seen coplanar - merges: 1 - normal: -0.65396 -0.221954 0.723238 - offset: -0.5 - center: -0.32698 -0.110977 0.361619 - vertices: p5(v7) p1(v5) p0(v3) p4(v0) - neighboring facets: f3 f4 f13 f11 - ridges: - r2 tested vertices: p1(v5) p0(v3) between f4 and f6 - r14 tested vertices: p5(v7) p1(v5) between f11 and f6 - r13 tested vertices: p5(v7) p4(v0) between f6 and f13 - r11 tested vertices: p0(v3) p4(v0) between f3 and f6 PASS : orgQhull::QhullFacetList_test::t_io() PASS : orgQhull::QhullFacetList_test::cleanupTestCase() Totals: 7 passed, 0 failed, 0 skipped ********* Finished testing of orgQhull::QhullFacetList_test ********* ********* Start testing of orgQhull::QhullFacetSet_test ********* Config: Using QTest library 4.7.4, Qt 4.7.4 PASS : orgQhull::QhullFacetSet_test::initTestCase() PASS : orgQhull::QhullFacetSet_test::t_construct() PASS : orgQhull::QhullFacetSet_test::t_convert() PASS : orgQhull::QhullFacetSet_test::t_readonly() PASS : orgQhull::QhullFacetSet_test::t_foreach() - f3 - flags: bottom tested seen - merges: 1 - normal: -0.256313 0.964458 0.0642208 - offset: -0.5 - center: -0.128156 0.482229 0.0321104 - vertices: p6(v6) p0(v3) p2(v2) p4(v0) - neighboring facets: f13 f6 f4 f8 - ridges: - r4 tested vertices: p0(v3) p2(v2) between f4 and f3 - r11 tested vertices: p0(v3) p4(v0) between f3 and f6 - r6 tested vertices: p6(v6) p4(v0) between f13 and f3 - r10 tested vertices: p6(v6) p2(v2) between f3 and f8 - f6 - flags: bottom tested seen coplanar - merges: 1 - normal: -0.65396 -0.221954 0.723238 - offset: -0.5 - center: -0.32698 -0.110977 0.361619 - vertices: p5(v7) p1(v5) p0(v3) p4(v0) - neighboring facets: f3 f4 f13 f11 - ridges: - r2 tested vertices: p1(v5) p0(v3) between f4 and f6 - r14 tested vertices: p5(v7) p1(v5) between f11 and f6 - r13 tested vertices: p5(v7) p4(v0) between f6 and f13 - r11 tested vertices: p0(v3) p4(v0) between f3 and f6 Facet identifiers: f3 f6 PASS : orgQhull::QhullFacetSet_test::t_io() PASS : orgQhull::QhullFacetSet_test::cleanupTestCase() Totals: 7 passed, 0 failed, 0 skipped ********* Finished testing of orgQhull::QhullFacetSet_test ********* ********* Start testing of orgQhull::QhullHyperplane_test ********* Config: Using QTest library 4.7.4, Qt 4.7.4 PASS : orgQhull::QhullHyperplane_test::initTestCase() PASS : orgQhull::QhullHyperplane_test::t_construct() PASS : orgQhull::QhullHyperplane_test::t_convert() h18 h19 h22 h24 h26 h27 h30 h31 h34 h35 h38 h39 PASS : orgQhull::QhullHyperplane_test::t_readonly() PASS : orgQhull::QhullHyperplane_test::t_define() PASS : orgQhull::QhullHyperplane_test::t_value() PASS : orgQhull::QhullHyperplane_test::t_operator() PASS : orgQhull::QhullHyperplane_test::t_iterator() PASS : orgQhull::QhullHyperplane_test::t_const_iterator() PASS : orgQhull::QhullHyperplane_test::t_qhullHyperplane_iterator() Hyperplane: -0 -0 -1 -0.5 Hyperplane w/ runId: -0 -0 -1 -0.5 and a message -0 -0 -1 offset -0.5 PASS : orgQhull::QhullHyperplane_test::t_io() PASS : orgQhull::QhullHyperplane_test::cleanupTestCase() Totals: 12 passed, 0 failed, 0 skipped ********* Finished testing of orgQhull::QhullHyperplane_test ********* ********* Start testing of orgQhull::QhullLinkedList_test ********* Config: Using QTest library 4.7.4, Qt 4.7.4 PASS : orgQhull::QhullLinkedList_test::initTestCase() PASS : orgQhull::QhullLinkedList_test::t_construct() PASS : orgQhull::QhullLinkedList_test::t_convert() PASS : orgQhull::QhullLinkedList_test::t_element() PASS : orgQhull::QhullLinkedList_test::t_search() PASS : orgQhull::QhullLinkedList_test::t_iterator() PASS : orgQhull::QhullLinkedList_test::t_const_iterator() PASS : orgQhull::QhullLinkedList_test::t_QhullLinkedList_iterator() INFO: empty QhullVertextList INFO: - p0 (v3): -0.0992431 0.442941 0.737533 neighborFacets: f3 f4 f6 - p7 (v8): 0.0992431 -0.442941 -0.737533 neighborFacets: f8 f11 f13 - p6 (v6): -0.15707 0.521517 -0.673312 neighborFacets: f8 f3 f13 - p3 (v1): 0.81103 -0.299563 -0.0499261 neighborFacets: f4 f8 f11 - p5 (v7): -0.554717 -0.664895 -0.0142947 neighborFacets: f11 f6 f13 - p2 (v2): 0.554717 0.664895 0.0142947 neighborFacets: f3 f4 f8 - p1 (v5): 0.15707 -0.521517 0.673312 neighborFacets: f6 f4 f11 - p4 (v0): -0.81103 0.299563 0.0499261 neighborFacets: f3 f6 f13 PASS : orgQhull::QhullLinkedList_test::t_io() PASS : orgQhull::QhullLinkedList_test::cleanupTestCase() Totals: 10 passed, 0 failed, 0 skipped ********* Finished testing of orgQhull::QhullLinkedList_test ********* ********* Start testing of orgQhull::QhullPoint_test ********* Config: Using QTest library 4.7.4, Qt 4.7.4 PASS : orgQhull::QhullPoint_test::initTestCase() PASS : orgQhull::QhullPoint_test::t_construct() PASS : orgQhull::QhullPoint_test::t_convert() p1 p0 p2 p3 p6 p4 p5 p7 PASS : orgQhull::QhullPoint_test::t_readonly() PASS : orgQhull::QhullPoint_test::t_define() PASS : orgQhull::QhullPoint_test::t_operator() PASS : orgQhull::QhullPoint_test::t_iterator() PASS : orgQhull::QhullPoint_test::t_const_iterator() PASS : orgQhull::QhullPoint_test::t_qhullpoint_iterator() Point w/o runId: p4: 0.5 -0.5 -0.5 Point w/ runId: p4: 0.5 -0.5 -0.5 and a message 0.5 -0.5 -0.5 Point with id and a message p4: 0.5 -0.5 -0.5 PASS : orgQhull::QhullPoint_test::t_io() PASS : orgQhull::QhullPoint_test::cleanupTestCase() Totals: 11 passed, 0 failed, 0 skipped ********* Finished testing of orgQhull::QhullPoint_test ********* ********* Start testing of orgQhull::QhullPoints_test ********* Config: Using QTest library 4.7.4, Qt 4.7.4 PASS : orgQhull::QhullPoints_test::initTestCase() PASS : orgQhull::QhullPoints_test::t_construct() PASS : orgQhull::QhullPoints_test::t_convert() PASS : orgQhull::QhullPoints_test::t_getset() PASS : orgQhull::QhullPoints_test::t_element() PASS : orgQhull::QhullPoints_test::t_iterator() PASS : orgQhull::QhullPoints_test::t_const_iterator() PASS : orgQhull::QhullPoints_test::t_search() PASS : orgQhull::QhullPoints_test::t_points_iterator() Empty QhullPoints QhullPoints from c[] p1241312: 0 1 2 p1241336: 3 4 5 QhullPoints p0: -0.0992431 0.442941 0.737533 p1: 0.15707 -0.521517 0.673312 p2: 0.554717 0.664895 0.0142947 p3: 0.81103 -0.299563 -0.0499261 p4: -0.81103 0.299563 0.0499261 p5: -0.554717 -0.664895 -0.0142947 p6: -0.15707 0.521517 -0.673312 p7: 0.0992431 -0.442941 -0.737533 RunId p0: -0.0992431 0.442941 0.737533 p1: 0.15707 -0.521517 0.673312 p2: 0.554717 0.664895 0.0142947 p3: 0.81103 -0.299563 -0.0499261 p4: -0.81103 0.299563 0.0499261 p5: -0.554717 -0.664895 -0.0142947 p6: -0.15707 0.521517 -0.673312 p7: 0.0992431 -0.442941 -0.737533 RunId w/ message -0.0992431 0.442941 0.737533 0.15707 -0.521517 0.673312 0.554717 0.664895 0.0142947 0.81103 -0.299563 -0.0499261 -0.81103 0.299563 0.0499261 -0.554717 -0.664895 -0.0142947 -0.15707 0.521517 -0.673312 0.0992431 -0.442941 -0.737533 RunId w/ identifiers p0: -0.0992431 0.442941 0.737533 p1: 0.15707 -0.521517 0.673312 p2: 0.554717 0.664895 0.0142947 p3: 0.81103 -0.299563 -0.0499261 p4: -0.81103 0.299563 0.0499261 p5: -0.554717 -0.664895 -0.0142947 p6: -0.15707 0.521517 -0.673312 p7: 0.0992431 -0.442941 -0.737533 PASS : orgQhull::QhullPoints_test::t_io() PASS : orgQhull::QhullPoints_test::cleanupTestCase() Totals: 11 passed, 0 failed, 0 skipped ********* Finished testing of orgQhull::QhullPoints_test ********* ********* Start testing of orgQhull::QhullPointSet_test ********* Config: Using QTest library 4.7.4, Qt 4.7.4 PASS : orgQhull::QhullPointSet_test::initTestCase() PASS : orgQhull::QhullPointSet_test::t_construct() PASS : orgQhull::QhullPointSet_test::t_convert() PASS : orgQhull::QhullPointSet_test::t_element() PASS : orgQhull::QhullPointSet_test::t_iterator() PASS : orgQhull::QhullPointSet_test::t_const_iterator() PASS : orgQhull::QhullPointSet_test::t_search() PASS : orgQhull::QhullPointSet_test::t_pointset_iterator() QhullPointSet from coplanarPoints p21: 0.368247 0.129543 0.5 p51: 0.35127 -0.210684 0.5 p80: 0.313266 0.0568358 0.5 p27: 0.0344498 -0.00151988 0.5 p34: -0.000258967 -0.352467 0.5 p19: 0.44098 -0.449916 0.5 p57: -0.300445 0.416634 0.5 p97: -0.336919 0.403301 0.5 p108: -0.442525 0.486883 0.5 p48: 0.100394 0.317561 0.5 p50: 0.188981 0.202207 0.5 p75: 0.196243 0.25294 0.5 p5: -0.082514 0.186773 0.5 p12: -0.22729 -0.0635886 0.5 p23: -0.148985 0.0132737 0.5 p29: -0.340232 -0.287248 0.5 p87: -0.17844 -0.0395658 0.5 p100: -0.114231 0.126861 0.5 p7: -0.0840006 0.201191 0.5 p0: -0.499992 -0.368462 0.5 p110: 0.076173 0.238959 0.5 p28: 0.0545838 0.390737 0.5 p15: 0.404653 0.00452289 0.5 RunId p21: 0.368247 0.129543 0.5 p51: 0.35127 -0.210684 0.5 p80: 0.313266 0.0568358 0.5 p27: 0.0344498 -0.00151988 0.5 p34: -0.000258967 -0.352467 0.5 p19: 0.44098 -0.449916 0.5 p57: -0.300445 0.416634 0.5 p97: -0.336919 0.403301 0.5 p108: -0.442525 0.486883 0.5 p48: 0.100394 0.317561 0.5 p50: 0.188981 0.202207 0.5 p75: 0.196243 0.25294 0.5 p5: -0.082514 0.186773 0.5 p12: -0.22729 -0.0635886 0.5 p23: -0.148985 0.0132737 0.5 p29: -0.340232 -0.287248 0.5 p87: -0.17844 -0.0395658 0.5 p100: -0.114231 0.126861 0.5 p7: -0.0840006 0.201191 0.5 p0: -0.499992 -0.368462 0.5 p110: 0.076173 0.238959 0.5 p28: 0.0545838 0.390737 0.5 p15: 0.404653 0.00452289 0.5 RunId w/ message p21: 0.368247 0.129543 0.5 p51: 0.35127 -0.210684 0.5 p80: 0.313266 0.0568358 0.5 p27: 0.0344498 -0.00151988 0.5 p34: -0.000258967 -0.352467 0.5 p19: 0.44098 -0.449916 0.5 p57: -0.300445 0.416634 0.5 p97: -0.336919 0.403301 0.5 p108: -0.442525 0.486883 0.5 p48: 0.100394 0.317561 0.5 p50: 0.188981 0.202207 0.5 p75: 0.196243 0.25294 0.5 p5: -0.082514 0.186773 0.5 p12: -0.22729 -0.0635886 0.5 p23: -0.148985 0.0132737 0.5 p29: -0.340232 -0.287248 0.5 p87: -0.17844 -0.0395658 0.5 p100: -0.114231 0.126861 0.5 p7: -0.0840006 0.201191 0.5 p0: -0.499992 -0.368462 0.5 p110: 0.076173 0.238959 0.5 p28: 0.0545838 0.390737 0.5 p15: 0.404653 0.00452289 0.5 PASS : orgQhull::QhullPointSet_test::t_io() PASS : orgQhull::QhullPointSet_test::cleanupTestCase() Totals: 10 passed, 0 failed, 0 skipped ********* Finished testing of orgQhull::QhullPointSet_test ********* ********* Start testing of orgQhull::QhullRidge_test ********* Config: Using QTest library 4.7.4, Qt 4.7.4 PASS : orgQhull::QhullRidge_test::initTestCase() PASS : orgQhull::QhullRidge_test::t_construct() 4 3 1 2 XFAIL : orgQhull::QhullRidge_test::t_getSet() SetIterator copy constructor not reset to BOT ..\..\src\qhulltest\QhullRidge_test.cpp(105) : failure location PASS : orgQhull::QhullRidge_test::t_getSet() PASS : orgQhull::QhullRidge_test::t_foreach() Ridges Without runId - r4 tested vertices: p2(v2) p0(v0) between f1 and f3 - r3 tested vertices: p4(v1) p0(v0) between f2 and f1 - r1 tested vertices: p6(v6) p4(v1) between f9 and f1 - r2 tested vertices: p6(v6) p2(v2) between f1 and f10 Ridge - r4 tested vertices: p2(v2) p0(v0) between f1 and f3 Ridge with runId - r4 tested vertices: p2(v2) p0(v0) between f1 and f3 PASS : orgQhull::QhullRidge_test::t_io() PASS : orgQhull::QhullRidge_test::cleanupTestCase() Totals: 6 passed, 0 failed, 0 skipped ********* Finished testing of orgQhull::QhullRidge_test ********* ********* Start testing of orgQhull::QhullSet_test ********* Config: Using QTest library 4.7.4, Qt 4.7.4 PASS : orgQhull::QhullSet_test::initTestCase() PASS : orgQhull::QhullSet_test::t_qhullsetbase() PASS : orgQhull::QhullSet_test::t_convert() PASS : orgQhull::QhullSet_test::t_element() PASS : orgQhull::QhullSet_test::t_search() PASS : orgQhull::QhullSet_test::t_iterator() PASS : orgQhull::QhullSet_test::t_const_iterator() PASS : orgQhull::QhullSet_test::t_qhullset_iterator() INFO: empty set INFO: Neighboring facets - f8 - flags: bottom tested seen coplanar - merges: 1 - normal: 0.65396 0.221954 -0.723238 - offset: -0.5 - center: 0.32698 0.110977 -0.361619 - vertices: p7(v8) p6(v6) p2(v2) p3(v1) - neighboring facets: f4 f3 f11 f13 - ridges: - r3 tested vertices: p2(v2) p3(v1) between f4 and f8 - r10 tested vertices: p6(v6) p2(v2) between f3 and f8 - r17 tested vertices: p7(v8) p6(v6) between f13 and f8 - r16 tested vertices: p7(v8) p3(v1) between f8 and f11 - f3 - flags: bottom tested seen - merges: 1 - normal: -0.256313 0.964458 0.0642208 - offset: -0.5 - center: -0.128156 0.482229 0.0321104 - vertices: p6(v6) p0(v3) p2(v2) p4(v0) - neighboring facets: f13 f6 f4 f8 - ridges: - r4 tested vertices: p0(v3) p2(v2) between f4 and f3 - r11 tested vertices: p0(v3) p4(v0) between f3 and f6 - r6 tested vertices: p6(v6) p4(v0) between f13 and f3 - r10 tested vertices: p6(v6) p2(v2) between f3 and f8 - f11 - flags: top tested seen coplanar - merges: 1 - normal: 0.256313 -0.964458 -0.0642208 - offset: -0.5 - center: 0.128156 -0.482229 -0.0321104 - vertices: p7(v8) p5(v7) p1(v5) p3(v1) - neighboring facets: f4 f8 f6 f13 - ridges: - r1 tested vertices: p1(v5) p3(v1) between f11 and f4 - r16 tested vertices: p7(v8) p3(v1) between f8 and f11 - r19 tested vertices: p7(v8) p5(v7) between f11 and f13 - r14 tested vertices: p5(v7) p1(v5) between f11 and f6 - f6 - flags: bottom tested seen coplanar - merges: 1 - normal: -0.65396 -0.221954 0.723238 - offset: -0.5 - center: -0.32698 -0.110977 0.361619 - vertices: p5(v7) p1(v5) p0(v3) p4(v0) - neighboring facets: f3 f4 f13 f11 - ridges: - r2 tested vertices: p1(v5) p0(v3) between f4 and f6 - r14 tested vertices: p5(v7) p1(v5) between f11 and f6 - r13 tested vertices: p5(v7) p4(v0) between f6 and f13 - r11 tested vertices: p0(v3) p4(v0) between f3 and f6 INFO: Ridges for a facet - r4 tested vertices: p0(v3) p2(v2) between f4 and f3 - r3 tested vertices: p2(v2) p3(v1) between f4 and f8 - r1 tested vertices: p1(v5) p3(v1) between f11 and f4 - r2 tested vertices: p1(v5) p0(v3) between f4 and f6 PASS : orgQhull::QhullSet_test::t_io() PASS : orgQhull::QhullSet_test::cleanupTestCase() Totals: 10 passed, 0 failed, 0 skipped ********* Finished testing of orgQhull::QhullSet_test ********* ********* Start testing of orgQhull::QhullVertex_test ********* Config: Using QTest library 4.7.4, Qt 4.7.4 PASS : orgQhull::QhullVertex_test::initTestCase() PASS : orgQhull::QhullVertex_test::t_constructConvert() 5 3 2 1 6 0 7 8 XFAIL : orgQhull::QhullVertex_test::t_getSet() ListIterator copy constructor not reset to BOT ..\..\src\qhulltest\QhullVertex_test.cpp(107) : failure location Point 1: p1: 0.15707 -0.521517 0.673312 Point 0: p0: -0.0992431 0.442941 0.737533 Point 2: p2: 0.554717 0.664895 0.0142947 Point 3: p3: 0.81103 -0.299563 -0.0499261 Point 6: p6: -0.15707 0.521517 -0.673312 Point 4: p4: -0.81103 0.299563 0.0499261 Point 5: p5: -0.554717 -0.664895 -0.0142947 Point 7: p7: 0.0992431 -0.442941 -0.737533 PASS : orgQhull::QhullVertex_test::t_getSet() PASS : orgQhull::QhullVertex_test::t_foreach() Vertex and vertices w/o runId: - p4 (v1): 0.5 -0.5 -0.5 neighborFacets: f1 f2 f9 p6(v6) p2(v2) p4(v1) p0(v0) Vertex and vertices w/ runId: - p4 (v1): 0.5 -0.5 -0.5 neighborFacets: f1 f2 f9 vertices: p6(v6) p2(v2) p4(v1) p0(v0) Try again with simplicial facets. No neighboring facets listed for vertices. Vertex and vertices w/o runId: - p0 (v5): -0.0222149 -0.366435 0.327062 This time with neighborFacets() defined for all vertices: - p0 (v5): -0.0222149 -0.366435 0.327062 neighborFacets: f5 f6 f7 f8 Try again with Voronoi diagram of simplicial facets. Neighboring facets automatically defined for vertices. Vertex and vertices w/o runId: - p7 (v1): 0.386746 0.0449288 0.118336 0.165595 neighborFacets: f1 f6 f9 f13 f14 f15 f16 f18 f19 f21 PASS : orgQhull::QhullVertex_test::t_io() PASS : orgQhull::QhullVertex_test::cleanupTestCase() Totals: 6 passed, 0 failed, 0 skipped ********* Finished testing of orgQhull::QhullVertex_test ********* ********* Start testing of orgQhull::RboxPoints_test ********* Config: Using QTest library 4.7.4, Qt 4.7.4 PASS : orgQhull::RboxPoints_test::initTestCase() PASS : orgQhull::RboxPoints_test::t_construct() INFO : Caught QH6189 rbox error: dimension, D0, out of bounds (>=200 or <=0) INFO : Caught QH10062 Qhull error: can not set PointCoordinates dimension to -1 PASS : orgQhull::RboxPoints_test::t_error() PASS : orgQhull::RboxPoints_test::t_test() INFO : Caught QH10063 Qhull error: can not change PointCoordinates dimension (from 2 to 102) PASS : orgQhull::RboxPoints_test::t_getSet() PASS : orgQhull::RboxPoints_test::t_foreach() INFO : Caught QH10012 Qhull error: expected 4 2-d PointCoordinates but read 3 PointCoordinates plus 1 extra coordinates PASS : orgQhull::RboxPoints_test::t_change() PASS : orgQhull::RboxPoints_test::t_ostream() PASS : orgQhull::RboxPoints_test::cleanupTestCase() Totals: 9 passed, 0 failed, 0 skipped ********* Finished testing of orgQhull::RboxPoints_test ********* ********* Start testing of orgQhull::UsingLibQhull_test ********* Config: Using QTest library 4.7.4, Qt 4.7.4 PASS : orgQhull::UsingLibQhull_test::initTestCase() MachineEpsilon 2.22045e-016 angleEpsilon 8.9706e-015 distanceEpsilon 9.87561e-015 Global angleEpsilon 1 distanceEpsilon 1 INFO Caught error -- QH10057 Qhull error: missing definition for currentVertexDimension(). Need currentQhull() or setGlobalVertexDimension() PASS : orgQhull::UsingLibQhull_test::t_classMembers() pointsBegin 003E9ED0 pointsEnd 003EA010 dimension 4 INFO Caught error -- QH10059 Qhull error: missing definition for currentPoints(). Need currentQhull() or setGlobalDistanceEpsilon() PASS : orgQhull::UsingLibQhull_test::t_globalPoints() INFO : Caught QH10049 Qhull error: UsingLibQhull already in use by QhullQh.runId 330525930 PASS : orgQhull::UsingLibQhull_test::t_UsingLibQhull() INFO : Caught QH1 INFO : QH10054 Report previous NOthrow error Qhull output at end qhull: no message for error. Check cerr or error stream PASS : orgQhull::UsingLibQhull_test::t_methods() PASS : orgQhull::UsingLibQhull_test::t_cleanuptestcase() PASS : orgQhull::UsingLibQhull_test::cleanupTestCase() Totals: 7 passed, 0 failed, 0 skipped ********* Finished testing of orgQhull::UsingLibQhull_test ********* ********* Start testing of orgQhull::Qhull_test ********* Config: Using QTest library 4.7.4, Qt 4.7.4 PASS : orgQhull::Qhull_test::initTestCase() INFO : Caught QH10023 Qhull error: checkIfQhullInitialized failed. Call runQhull() first. INFO : Caught QH10069 Qhull error: can not use Qhull copy constructor if initialized() is true INFO : Caught QH10070 Qhull error: can not use Qhull copy assignment if initialized() is true INFO : Caught QH10070 Qhull error: can not use Qhull copy assignment if initialized() is true PASS : orgQhull::Qhull_test::t_construct() Expecting summary of halfspace intersect Halfspace intersection by the convex hull of 4 points in 2-d: Number of halfspaces: 4 Number of non-redundant halfspaces: 4 Number of intersection points: 4 Statistics for: normals of square | qhull H Number of points processed: 4 Number of hyperplanes created: 6 Number of distance tests for qhull: 4 CPU seconds to compute hull (after input): 0 Expecting no output from qh_fprintf() in Qhull.cpp Qhull output at end Halfspace intersection by the convex hull of 4 points in 2-d: Number of halfspaces: 4 Number of non-redundant halfspaces: 4 Number of intersection points: 4 Statistics for: normals of square | qhull H Number of points processed: 4 Number of hyperplanes created: 6 Number of distance tests for qhull: 4 CPU seconds to compute hull (after input): 0 PASS : orgQhull::Qhull_test::t_attribute() INFO : Caught QH6029 qhull error: option 'Fd' is not used with this program. It may be used with qhull. While executing: | Options selected for Qhull 2012.1 2012/01/22: run-id 330525930 INFO : Error stream without output stream qhull error: option 'Fd' is not used with this program. It may be used with qhull. While executing: | Options selected for Qhull 2012.1 2012/01/22: run-id 330525930 INFO : Caught QH6029 INFO : Error output sent to output stream without error stream qhull input error: feasible point is not clearly inside halfspace feasible point: 0 0 halfspace: -0.5 -0.5 at offset: 0.5 and distance: 0.5 The halfspace was at index 1 While executing: rbox "c" | qhull Tz H0 Options selected for Qhull 2012.1 2012/01/22: run-id 330525930 Tz-stdout Halfspace-about 0 INFO : Caught QH6023 INFO : No error stream or output stream INFO : Caught QH6029 qhull error: option 'Fd' is not used with this program. It may be used with qhull. While executing: | Options selected for Qhull 2012.1 2012/01/22: run-id 330525930 PASS : orgQhull::Qhull_test::t_message() Convex hull of 8 points in 3-d: Number of vertices: 8 Number of facets: 6 Number of non-simplicial facets: 6 Statistics for: rbox "c" | qhull s Number of points processed: 8 Number of hyperplanes created: 11 Number of distance tests for qhull: 35 Number of distance tests for merging: 84 Number of distance tests for checking: 56 Number of merged facets: 6 CPU seconds to compute hull (after input): 0 Convex hull of 8 points in 3-d: Number of vertices: 8 Number of facets: 6 Number of non-simplicial facets: 6 Statistics for: rbox "c" | qhull Number of points processed: 8 Number of hyperplanes created: 11 Number of distance tests for qhull: 35 Number of distance tests for merging: 84 Number of distance tests for checking: 56 Number of merged facets: 6 CPU seconds to compute hull (after input): 0 PASS : orgQhull::Qhull_test::t_getSet() PASS : orgQhull::Qhull_test::t_getQh() PASS : orgQhull::Qhull_test::t_getValue() PASS : orgQhull::Qhull_test::t_foreach() Expecting vertexList and facetList of a 3-d diamond. 3 6 8 12 0 0 -0.5 0 0 0.5 0 -0.5 0 0 0.5 0 -0.5 0 0 0.5 0 0 3 3 1 4 3 1 3 5 3 0 3 4 3 3 0 5 3 2 1 5 3 1 2 4 3 2 0 4 3 0 2 5 Expecting normals of a 3-d diamond. 4 8 -0.5773502691896258 0.5773502691896258 0.5773502691896258 -0.2886751345948129 0.5773502691896258 0.5773502691896258 0.5773502691896258 -0.2886751345948129 -0.5773502691896258 0.5773502691896258 -0.5773502691896258 -0.2886751345948129 0.5773502691896258 0.5773502691896258 -0.5773502691896258 -0.2886751345948129 0.5773502691896258 -0.5773502691896258 0.5773502691896258 -0.2886751345948129 -0.5773502691896258 -0.5773502691896258 0.5773502691896258 -0.2886751345948129 -0.5773502691896258 -0.5773502691896258 -0.5773502691896258 -0.2886751345948129 0.5773502691896258 -0.5773502691896258 -0.5773502691896258 -0.2886751345948129 PASS : orgQhull::Qhull_test::t_modify() PASS : orgQhull::Qhull_test::cleanupTestCase() Totals: 10 passed, 0 failed, 0 skipped ********* Finished testing of orgQhull::Qhull_test ********* Passed 121 tests. Finished test of libqhullcpp. Test libqhull with eg/q_test qhull-2012.1/eg/q_eg0000755000076400010400000000647011720316046015347 0ustar bbarberAdministrators#!/bin/sh # writes examples to eg/ # see html/qh_eg.htm if ! qconvex >/dev/null 2>&1; then if [ ! -d bin ]; then echo Run eg/q_eg from the Qhull directory exit fi if [ ! -e bin/qconvex -a ! -e bin/qconvex.exe ]; then echo 'Build qhull first. qconvex is missing from bin/ directory and $PATH' exit fi if ! qconvex >/dev/null 2>&1; then PATH=$PWD/bin:$PATH fi fi mkdir -p eg set -v rbox c D3 | qconvex s G >eg/eg.01.cube rbox c d G2.0 | qconvex s G >eg/eg.02.diamond.cube rbox s 100 D3 | qconvex s G >eg/eg.03.sphere rbox s 100 D2 | qconvex s G >eg/eg.04.circle rbox 10 l | qconvex s G >eg/eg.05.spiral rbox 1000 D2 | qconvex s C-0.03 Qc Gapcv >eg/eg.06.merge.square rbox 1000 D3 | qconvex s G >eg/eg.07.box rbox c G0.4 s 500 | qconvex s G >eg/eg.08a.cube.sphere rbox d G0.6 s 500 | qconvex s G >eg/eg.08b.diamond.sphere rbox 100 L3 G0.5 s | qconvex s G >eg/eg.09.lens rbox 100 s P0.5,0.5,0.5 | qconvex s Ga QG0 >eg/eg.10a.sphere.visible rbox 100 s P0.5,0.5,0.5 | qconvex s Ga QG-0 >eg/eg.10b.sphere.beyond rbox 100 s P0.5,0.5,0.5 | qconvex s Ga QG0 PG >eg/eg.10c.sphere.horizon rbox 100 s P0.5,0.5,0.5 | qconvex s Ga QV0 PgG >eg/eg.10d.sphere.cone rbox 100 s P0.5,0.5,0.5 | qconvex s Ga >eg/eg.10e.sphere.new rbox 100 s P0.5,0.5,0.5 | qhull s Ga QV0g Q0 >eg/eg.14.sphere.corner rbox 500 W0 | qconvex s QR0 Qc Gvp >eg/eg.15a.surface rbox 500 W0 | qconvex s QR0 Qt Qc Gvp >eg/eg.15b.triangle rbox 500 W0 | qconvex s QR0 QJ5e-2 Qc Gvp >eg/eg.15c.joggle echo 2 = rbox 6 r s D2, rbox 15 B0.3 W0.25, c G0.5 >eg/eg.data.17 echo 25 >>eg/eg.data.17 rbox 15 D2 B0.3 W0.25 c G0.5 | tail -n +3 >>eg/eg.data.17 rbox 6 r s D2 B0.2 | tail -n +3 >>eg/eg.data.17 qdelaunay s Qt eg/eg.17a.delaunay.2 qdelaunay s eg/eg.17b.delaunay.2i qdelaunay s eg/eg.17c.delaunay.2-3 qvoronoi s QJ eg/eg.17d.voronoi.2 qvoronoi s eg/eg.17e.voronoi.2i rbox c G0.1 d | qdelaunay Gt Qz >eg/eg.17f.delaunay.3 rbox 10 D2 d | qdelaunay s Qu G >eg/eg.18a.furthest.2-3 rbox 10 D2 d | qdelaunay s Qu Pd2 G >eg/eg.18b.furthest-up.2-3 rbox 10 D2 d | qvoronoi s Qu Gv >eg/eg.18c.furthest.2 rbox 10 D3 | qvoronoi s FQ QV5 p | qconvex s G >eg/eg.19.voronoi.region.3 rbox r s 20 Z1 G0.2 | qconvex s QR1 G >eg/eg.20.cone rbox 200 s | qconvex s Qc R0.014 Gpav >eg/eg.21b.roundoff.fixed rbox 1000 s| qconvex s C0.01 Qc Gcrp >eg/eg.22a.merge.sphere.01 rbox 1000 s| qconvex s C-0.01 Qc Gcrp >eg/eg.22b.merge.sphere.-01 rbox 1000 s| qconvex s C0.05 Qc Gcrpv >eg/eg.22c.merge.sphere.05 rbox 1000 s| qconvex s C-0.05 Qc Gcrpv >eg/eg.22d.merge.sphere.-05 rbox 1000 | qconvex s Gcprvah C0.1 Qc >eg/eg.23.merge.cube rbox 5000 D4 | qconvex s GD0v Pd0:0.5 C-0.02 C0.1 >eg/eg.24.merge.cube.4d-in-3d rbox 5000 D4 | qconvex s s C-0.02 C0.1 Gh >eg/eg.30.4d.merge.cube rbox 20 D3 | qdelaunay s G >eg/eg.31.4d.delaunay rbox 30 s D4 | qconvex s G Pd0d1d2D3 >eg/eg.32.4d.octant rbox 10 r s Z1 G0.3 | qconvex G >eg/eg.33a.cone rbox 10 r s Z1 G0.3 | qconvex FQ FV n | qhalf G >eg/eg.33b.cone.dual rbox 10 r s Z1 G0.3 | qconvex FQ FV n | qhalf FQ s Fp | qconvex G >eg/eg.33c.cone.halfspace echo ==the following should generate flipped and concave facets== >/dev/null rbox 200 s | qhull Q0 s R0.014 Gav Po >eg/eg.21a.roundoff.errors echo ==the preceeding should report flipped and concave facets== >/dev/null qhull-2012.1/eg/q_egtest0000755000076400010400000000407211720316046016243 0ustar bbarberAdministrators#!/bin/sh # writes examples to eg/ if ! qconvex >/dev/null 2>&1; then if [ ! -d bin ]; then echo Run eg/q_eg from the Qhull directory exit fi if [ ! -e bin/qconvex -a ! -e bin/qconvex.exe ]; then echo 'Build qhull first. qconvex is missing from bin/ directory and $PATH' exit fi if ! qconvex >/dev/null 2>&1; then PATH=$PWD/bin:$PATH fi fi mkdir -p set -v rbox d D3 | qconvex s Gnrv Tc Tv >eg/eg.t01.spheres.3 rbox d D2 | qconvex s Gnv Tc Tv >eg/eg.t02.spheres.2 rbox d D3 | qconvex s Gnrp Tc Tv >eg/eg.t03.points.3 rbox d D2 | qconvex s Gnp Tc Tv >eg/eg.t04.points.2 rbox c D4 | qconvex s C0.05 GnpcD3 Pd3:0.5 Tc Tv >eg/eg.t05.centrum.points.4-3 rbox d D3 | qconvex s Gnrc Tc Tv >eg/eg.t06.centrums.3.precise rbox d D3 | qconvex s C0.05 Gnrc Tc Tv >eg/eg.t07.centrums.3 rbox d D2 | qconvex s C0.05 Gc Tc Tv >eg/eg.t08.centrums.2 rbox d D3 | qconvex s Gnha Tc Tv >eg/eg.t09.intersect.3 rbox d D3 | qconvex s GaD0 Pd0 Tc Tv >eg/eg.t10.faces.3-2 rbox d D3 | qconvex s GnrpD0 Pd0 Tc Tv >eg/eg.t11.points.3-2 rbox d D3 | qconvex s C0.05 GnrcD0 Pd0 Tc Tv >eg/eg.t12.centrums.3-2 rbox d D3 | qconvex s GnhaD0 Pd0 Tc Tv >eg/eg.t13.intersect.3-2 rbox d D3 | qconvex s GnrvD0 Pd0 Tc Tv >eg/eg.t14.spheres.3-2 rbox c D4 | qconvex s GvD0 Pd0:0.5 Tc Tv >eg/eg.t15.spheres.4-3 rbox c D4 | qhull s Q0 C0 GpD0 Pd0:0.5 Tc Tv >eg/eg.t16.points.4-3 rbox c D4 | qconvex s GahD0 Pd0:0.5 Tc Tv >eg/eg.t17.intersect.4-3 rbox 100 s | qconvex s C-0.05 Qc Gicvprh Tc Tv >eg/eg.t18.imprecise.3 rbox 30 s D4 | qconvex s GhD0 Pd0d1d2D3 Tc >eg/eg.t19.intersect.precise.4-3 rbox 100 s P1,1,1 | qconvex s QG-0 Pgp Tc G >eg/eg.t20.notvisible rbox 100 s | qconvex s QV-10 Pgp Tc G >eg/eg.t21.notvertex rbox 100 r D2 P1,1 | qhull s Pd0:0.7 PD0:0.8 QgG0 G Tv >eg/eg.t22.split rbox 100 D2 c G1.0 | qvoronoi s A-0.95 Gna Tv >eg/eg.t23.voronoi.imprecise rbox 30 s D4 | qconvex s Gh Pd0d1d2D3 Tc >eg/eg.t24.intersect.precise.4d echo ==the following generates an error== >/dev/null rbox 1000 D4 | qhull Q0 s Po R0.005 Ga Tc Tv >eg/eg.t25.neighbors.4d echo ==the previous should generate an error== >/dev/null qhull-2012.1/eg/q_test0000755000076400010400000002763211720315764015744 0ustar bbarberAdministrators#!/bin/sh # # NOTE: all tests duplicated in q_test.bat if ! qconvex >/dev/null 2>&1; then if [ ! -d bin ]; then echo Run eg/q_test from the Qhull directory exit fi if [ ! -e bin/qconvex -a ! -e bin/qconvex.exe ]; then echo 'Build qhull first. qconvex is missing from bin/ directory and $PATH' exit fi if ! qconvex >/dev/null 2>&1; then PATH=$PWD/bin:$PATH fi fi if ! user_eg >/dev/null; then echo user_eg failed to run. It uses the shared qhull library echo 'On Linux, export LD_LIBRARY_PATH=$PWD/lib:$LD_LIBRARY_PATH' fi set -v echo === errors if 'user_eg' and 'user_eg2' not found === echo === check user_eg ${d:-`date`} ===================== user_eg "QR1 p n Qt" "v p" Fp user_eg2 "QR1 p" "v p" Fp user_eg3 rbox "10 D2" "2 D2" qhull "p" echo === check front ends ${d:-`date`} ================== qconvex - qconvex . qconvex rbox c D3 | qconvex s n Qt rbox c D2 | qconvex s i rbox c D2 | qconvex o rbox 1000 s | qconvex s Tv FA rbox c d D2 | qconvex s Qc Fx rbox y 1000 W0 | qconvex s n rbox y 1000 W0 | qconvex s QJ rbox d G1 D12 | qconvex QR0 FA rbox c D6 | qconvex FA TF500 rbox c P0 d D2 | qconvex p Fa Fc FP FI Fn FN FS Fv Fx rbox c d D2 | qconvex s i QV0 rbox c | qconvex Q0 qvoronoi - qvoronoi . qvoronoi rbox c P0 D2 | qvoronoi s o rbox c P0 D2 | qvoronoi Fi Tv rbox c P0 D2 | qvoronoi Fo rbox c P0 D2 | qvoronoi Fv rbox c P0 D2 | qvoronoi s Qu Qt Fv rbox c P0 D2 | qvoronoi Qu Fo rbox c G1 d D2 | qvoronoi s p rbox c G1 d D2 | qvoronoi QJ p rbox c P-0.1 P+0.1 P+0.1 D2 | qvoronoi s Fc FP FQ Fn FN rbox P0 c D2 | qvoronoi s Fv QV0 qdelaunay - qdelaunay . qdelaunay rbox c P0 D2 | qdelaunay s o rbox c P0 D2 | qdelaunay i rbox c P0 D2 | qdelaunay Fv rbox c P0 D2 | qdelaunay s Qu Qt Fv rbox c G1 d D2 | qdelaunay s i rbox c G1 d D2 | qhull d Qbb Ft rbox c G1 d D2 | qhull d Qbb QJ s Ft rbox M3,4 z 100 D2 | qdelaunay s rbox c P-0.1 P+0.1 P+0.1 D2 | qdelaunay s Fx Fa Fc FP FQ Fn FN rbox P0 P0 c D2 | qdelaunay s FP QV0 qhalf - qhalf . qhalf rbox d | qhull FQ n | qhalf s Qt H0,0,0 Fp rbox c | qhull FQ FV n | qhalf s i rbox c | qhull FQ FV n | qhalf o rbox d D2 | qhull FQ n | qhalf s H0 Fc FP Fn FN FQ Fv Fx echo === check quality of Qhull for ${d:-`hostname`} ${d:-`date`} rbox 1000 W0 | qhull QR2 QJ s Fs Tv rbox 1000 W0 | qhull QR2 s Fs Tv rbox 1000 s | qhull C0.02 Qc Tv rbox 500 s D4 | qhull C0.01 Qc Tv rbox 1000 s | qhull C-0.02 Qc Tv rbox 1000 s D4 | qhull C-0.01 Qc Tv rbox 200 s D5 | qhull C-0.01 Qx Qc Tv rbox 100 s D6 | qhull C-0.001 Qx Qc Tv rbox 1000 W1e-4 | qhull C-1e-6 Qc Tv rbox 1000 W5e-4 D4 | qhull C-1e-5 Qc Tv rbox 400 W1e-3 D5 | qhull C-1e-5 Qx Qc Tv echo === check input format etc. ${d:-`date`} qhull <eg/eg.01.cube Convex hull of 8 points in 3-d: Number of vertices: 8 Number of facets: 6 Number of non-simplicial facets: 6 Statistics for: rbox c D3 | qconvex s G Number of points processed: 8 Number of hyperplanes created: 11 Number of distance tests for qhull: 35 Number of distance tests for merging: 84 Number of distance tests for checking: 56 Number of merged facets: 6 CPU seconds to compute hull (after input): 0 rbox c d G2.0 | qconvex s G >eg/eg.02.diamond.cube Convex hull of 14 points in 3-d: Number of vertices: 6 Number of facets: 8 Statistics for: rbox c d G2.0 | qconvex s G Number of points processed: 6 Number of hyperplanes created: 11 Number of distance tests for qhull: 88 Number of distance tests for merging: 45 Number of distance tests for checking: 54 Number of merged facets: 1 CPU seconds to compute hull (after input): 0 rbox s 100 D3 | qconvex s G >eg/eg.03.sphere Convex hull of 100 points in 3-d: Number of vertices: 100 Number of facets: 196 Statistics for: rbox s 100 D3 | qconvex s G Number of points processed: 100 Number of hyperplanes created: 503 Number of distance tests for qhull: 1631 CPU seconds to compute hull (after input): 0 rbox s 100 D2 | qconvex s G >eg/eg.04.circle Convex hull of 100 points in 2-d: Number of vertices: 100 Number of facets: 100 Statistics for: rbox s 100 D2 | qconvex s G Number of points processed: 100 Number of hyperplanes created: 198 Number of distance tests for qhull: 891 CPU seconds to compute hull (after input): 0 rbox 10 l | qconvex s G >eg/eg.05.spiral Convex hull of 10 points in 3-d: Number of vertices: 10 Number of facets: 16 Statistics for: rbox 10 l | qconvex s G Number of points processed: 10 Number of hyperplanes created: 26 Number of distance tests for qhull: 40 CPU seconds to compute hull (after input): 0 rbox 1000 D2 | qconvex s C-0.03 Qc Gapcv >eg/eg.06.merge.square Convex hull of 1000 points in 2-d: Number of vertices: 4 Number of coplanar points: 103 Number of facets: 4 Statistics for: rbox 1000 D2 | qconvex s C-0.03 Qc Gapcv Number of points processed: 6 Number of hyperplanes created: 8 Number of distance tests for qhull: 12111 Number of distance tests for merging: 43 Number of distance tests for checking: 3736 Number of merged facets: 2 CPU seconds to compute hull (after input): 0 Maximum distance of point above facet: 0.019 (0.3x) Maximum distance of vertex below facet: -0.019 (0.3x) rbox 1000 D3 | qconvex s G >eg/eg.07.box Convex hull of 1000 points in 3-d: Number of vertices: 73 Number of facets: 142 Statistics for: rbox 1000 D3 | qconvex s G Number of points processed: 81 Number of hyperplanes created: 368 Number of distance tests for qhull: 12884 CPU seconds to compute hull (after input): 0 rbox c G0.4 s 500 | qconvex s G >eg/eg.08a.cube.sphere Convex hull of 508 points in 3-d: Number of vertices: 63 Number of facets: 122 Statistics for: rbox c G0.4 s 500 | qconvex s G Number of points processed: 99 Number of hyperplanes created: 443 Number of distance tests for qhull: 9648 CPU seconds to compute hull (after input): 0 rbox d G0.6 s 500 | qconvex s G >eg/eg.08b.diamond.sphere Convex hull of 506 points in 3-d: Number of vertices: 397 Number of facets: 790 Statistics for: rbox d G0.6 s 500 | qconvex s G Number of points processed: 409 Number of hyperplanes created: 2032 Number of distance tests for qhull: 10055 Number of distance tests for merging: 8153 Number of distance tests for checking: 10136 Number of merged facets: 1 CPU seconds to compute hull (after input): 0 rbox 100 L3 G0.5 s | qconvex s G >eg/eg.09.lens Convex hull of 100 points in 3-d: Number of vertices: 100 Number of facets: 196 Statistics for: rbox 100 L3 G0.5 s | qconvex s G Number of points processed: 100 Number of hyperplanes created: 483 Number of distance tests for qhull: 1642 CPU seconds to compute hull (after input): 0 rbox 100 s P0.5,0.5,0.5 | qconvex s Ga QG0 >eg/eg.10a.sphere.visible Convex hull of 100 points in 3-d: Number of vertices: 100 Number of facets: 196 Number of 'good' facets: 44 Statistics for: rbox 100 s P0.5,0.5,0.5 | qconvex s Ga QG0 Number of points processed: 100 Number of hyperplanes created: 513 Number of distance tests for qhull: 1704 CPU seconds to compute hull (after input): 0 rbox 100 s P0.5,0.5,0.5 | qconvex s Ga QG-0 >eg/eg.10b.sphere.beyond Convex hull of 100 points in 3-d: Number of vertices: 100 Number of facets: 196 Number of 'good' facets: 152 Statistics for: rbox 100 s P0.5,0.5,0.5 | qconvex s Ga QG-0 Number of points processed: 100 Number of hyperplanes created: 513 Number of distance tests for qhull: 1704 CPU seconds to compute hull (after input): 0 rbox 100 s P0.5,0.5,0.5 | qconvex s Ga QG0 PG >eg/eg.10c.sphere.horizon Convex hull of 100 points in 3-d: Number of vertices: 100 Number of facets: 196 Number of 'good' facets: 44 Statistics for: rbox 100 s P0.5,0.5,0.5 | qconvex s Ga QG0 PG Number of points processed: 100 Number of hyperplanes created: 513 Number of distance tests for qhull: 1704 CPU seconds to compute hull (after input): 0 rbox 100 s P0.5,0.5,0.5 | qconvex s Ga QV0 PgG >eg/eg.10d.sphere.cone Convex hull of 101 points in 3-d: Number of vertices: 85 Number of facets: 166 Number of 'good' facets: 14 Statistics for: rbox 100 s P0.5,0.5,0.5 | qconvex s Ga QV0 PgG Number of points processed: 88 Number of hyperplanes created: 429 Number of distance tests for qhull: 1594 CPU seconds to compute hull (after input): 0 rbox 100 s P0.5,0.5,0.5 | qconvex s Ga >eg/eg.10e.sphere.new Convex hull of 101 points in 3-d: Number of vertices: 85 Number of facets: 166 Statistics for: rbox 100 s P0.5,0.5,0.5 | qconvex s Ga Number of points processed: 88 Number of hyperplanes created: 429 Number of distance tests for qhull: 1594 CPU seconds to compute hull (after input): 0 rbox 100 s P0.5,0.5,0.5 | qhull s Ga QV0g Q0 >eg/eg.14.sphere.corner Convex hull of 101 points in 3-d: Number of vertices: 42 Number of facets: 80 Number of 'good' facets: 14 Statistics for: rbox 100 s P0.5,0.5,0.5 | qhull s Ga QV0g Q0 Number of points processed: 45 Number of hyperplanes created: 194 Number of distance tests for qhull: 1435 CPU seconds to compute hull (after input): 0 rbox 500 W0 | qconvex s QR0 Qc Gvp >eg/eg.15a.surface Convex hull of 500 points in 3-d: Number of vertices: 66 Number of coplanar points: 434 Number of facets: 80 Number of non-simplicial facets: 6 Statistics for: rbox 500 W0 | qconvex s QR0 Qc Gvp QR1327454200 Number of points processed: 70 Number of hyperplanes created: 211 Number of distance tests for qhull: 8277 Number of distance tests for merging: 1884 Number of distance tests for checking: 6765 Number of merged facets: 56 CPU seconds to compute hull (after input): 0 Maximum distance of point above facet: 2.3e-015 (0.3x) rbox 500 W0 | qconvex s QR0 Qt Qc Gvp >eg/eg.15b.triangle Convex hull of 500 points in 3-d: Number of vertices: 66 Number of coplanar points: 434 Number of facets: 128 Number of triangulated facets: 6 Statistics for: rbox 500 W0 | qconvex s QR0 Qt Qc Gvp QR1327454200 Number of points processed: 70 Number of hyperplanes created: 211 Number of distance tests for qhull: 8277 Number of distance tests for merging: 1950 Number of distance tests for checking: 6765 Number of merged facets: 56 CPU seconds to compute hull (after input): 0 Maximum distance of point above facet: 2.3e-015 (0.3x) rbox 500 W0 | qconvex s QR0 QJ5e-2 Qc Gvp >eg/eg.15c.joggle Convex hull of 500 points in 3-d: Number of vertices: 78 Number of coplanar points: 422 Number of facets: 152 Statistics for: rbox 500 W0 | qconvex s QR0 QJ5e-2 Qc Gvp QR1327454200 Number of points processed: 89 Number of hyperplanes created: 423 Number of distance tests for qhull: 20845 CPU seconds to compute hull (after input): 0.015 Input joggled by: 0.05 echo 2 = rbox 6 r s D2, rbox 15 B0.3 W0.25, c G0.5 >eg/eg.data.17 echo 25 >>eg/eg.data.17 rbox 15 D2 B0.3 W0.25 c G0.5 | tail -n +3 >>eg/eg.data.17 rbox 6 r s D2 B0.2 | tail -n +3 >>eg/eg.data.17 qdelaunay s Qt eg/eg.17a.delaunay.2 Delaunay triangulation by the convex hull of 25 points in 3-d: Number of input sites: 25 Number of Delaunay regions: 44 Number of triangulated facets: 1 Statistics for: = rbox 6 r s D2, rbox 15 B0.3 W0.25, c G0.5 | qdelaunay s Qt GnraD2 Number of points processed: 25 Number of hyperplanes created: 90 Number of facets in hull: 46 Number of distance tests for qhull: 289 Number of distance tests for merging: 492 Number of distance tests for checking: 307 Number of merged facets: 4 CPU seconds to compute hull (after input): 0 qdelaunay s eg/eg.17b.delaunay.2i Delaunay triangulation by the convex hull of 25 points in 3-d: Number of input sites: 25 Number of Delaunay regions: 41 Number of non-simplicial Delaunay regions: 1 Statistics for: = rbox 6 r s D2, rbox 15 B0.3 W0.25, c G0.5 | qdelaunay s GnraD2 Number of points processed: 25 Number of hyperplanes created: 90 Number of facets in hull: 42 Number of distance tests for qhull: 289 Number of distance tests for merging: 482 Number of distance tests for checking: 307 Number of merged facets: 4 CPU seconds to compute hull (after input): 0 qdelaunay s eg/eg.17c.delaunay.2-3 Delaunay triangulation by the convex hull of 25 points in 3-d: Number of input sites: 25 Number of Delaunay regions: 0 Number of non-simplicial Delaunay regions: 2 Statistics for: = rbox 6 r s D2, rbox 15 B0.3 W0.25, c G0.5 | qdelaunay s C-0 Ga Number of points processed: 25 Number of hyperplanes created: 90 Number of facets in hull: 42 Number of distance tests for qhull: 289 Number of distance tests for merging: 482 Number of distance tests for checking: 307 Number of merged facets: 4 CPU seconds to compute hull (after input): 0 qvoronoi s QJ eg/eg.17d.voronoi.2 Voronoi diagram by the convex hull of 25 points in 3-d: Number of Voronoi regions: 25 Number of Voronoi vertices: 44 Statistics for: = rbox 6 r s D2, rbox 15 B0.3 W0.25, c G0.5 | qvoronoi s QJ Gna Number of points processed: 25 Number of hyperplanes created: 99 Number of facets in hull: 46 Number of distance tests for qhull: 283 CPU seconds to compute hull (after input): 0 Input joggled by: 4.2e-011 qvoronoi s eg/eg.17e.voronoi.2i Voronoi diagram by the convex hull of 25 points in 3-d: Number of Voronoi regions: 25 Number of Voronoi vertices: 41 Number of non-simplicial Voronoi vertices: 1 Statistics for: = rbox 6 r s D2, rbox 15 B0.3 W0.25, c G0.5 | qvoronoi s Gna Number of points processed: 25 Number of hyperplanes created: 90 Number of facets in hull: 42 Number of distance tests for qhull: 289 Number of distance tests for merging: 482 Number of distance tests for checking: 307 Number of merged facets: 4 CPU seconds to compute hull (after input): 0 rbox c G0.1 d | qdelaunay Gt Qz >eg/eg.17f.delaunay.3 rbox 10 D2 d | qdelaunay s Qu G >eg/eg.18a.furthest.2-3 Furthest-site Delaunay triangulation by the convex hull of 14 points in 3-d: Number of input sites: 14 Number of Delaunay regions: 0 Statistics for: rbox 10 D2 d | qdelaunay s Qu G Number of points processed: 14 Number of hyperplanes created: 46 Number of facets in hull: 24 Number of distance tests for qhull: 85 Number of distance tests for merging: 213 Number of distance tests for checking: 304 Number of merged facets: 1 CPU seconds to compute hull (after input): 0 rbox 10 D2 d | qdelaunay s Qu Pd2 G >eg/eg.18b.furthest-up.2-3 Furthest-site Delaunay triangulation by the convex hull of 14 points in 3-d: Number of input sites: 14 Number of Delaunay regions: 7 Statistics for: rbox 10 D2 d | qdelaunay s Qu Pd2 G Number of points processed: 14 Number of hyperplanes created: 46 Number of facets in hull: 24 Number of distance tests for qhull: 85 Number of distance tests for merging: 213 Number of distance tests for checking: 304 Number of merged facets: 1 CPU seconds to compute hull (after input): 0 rbox 10 D2 d | qvoronoi s Qu Gv >eg/eg.18c.furthest.2 Furthest-site Voronoi vertices by the convex hull of 14 points in 3-d: Number of Voronoi regions: 14 Number of Voronoi vertices: 7 Statistics for: rbox 10 D2 d | qvoronoi s Qu Gv Number of points processed: 14 Number of hyperplanes created: 46 Number of facets in hull: 24 Number of distance tests for qhull: 85 Number of distance tests for merging: 213 Number of distance tests for checking: 304 Number of merged facets: 1 CPU seconds to compute hull (after input): 0 rbox 10 D3 | qvoronoi s FQ QV5 p | qconvex s G >eg/eg.19.voronoi.region.3 Voronoi diagram by the convex hull of 10 points in 4-d: Number of Voronoi regions: 10 Number of 'good' Voronoi vertices: 10 Statistics for: rbox 10 D3 | qvoronoi s FQ QV5 p Number of points processed: 10 Number of hyperplanes created: 44 Number of facets in hull: 27 Number of distance tests for qhull: 67 CPU seconds to compute hull (after input): 0 Convex hull of 10 points in 3-d: Number of vertices: 10 Number of facets: 9 Number of non-simplicial facets: 5 Statistics for: rbox 10 D3 | qvoronoi s FQ QV5 p | qconvex s G Number of points processed: 10 Number of hyperplanes created: 18 Number of distance tests for qhull: 45 Number of distance tests for merging: 130 Number of distance tests for checking: 89 Number of merged facets: 7 CPU seconds to compute hull (after input): 0 rbox r s 20 Z1 G0.2 | qconvex s QR1 G >eg/eg.20.cone Convex hull of 41 points in 3-d: Number of vertices: 41 Number of facets: 41 Number of non-simplicial facets: 21 Statistics for: rbox r s 20 Z1 G0.2 | qconvex s QR1 G QR1 Number of points processed: 41 Number of hyperplanes created: 115 Number of distance tests for qhull: 624 Number of distance tests for merging: 1584 Number of distance tests for checking: 721 Number of merged facets: 61 CPU seconds to compute hull (after input): 0 rbox 200 s | qconvex s Qc R0.014 Gpav >eg/eg.21b.roundoff.fixed Convex hull of 200 points in 3-d: Number of vertices: 65 Number of coplanar points: 135 Number of facets: 52 Number of non-simplicial facets: 43 Statistics for: rbox 200 s | qconvex s Qc R0.014 Gpav Number of points processed: 73 Number of hyperplanes created: 291 Number of distance tests for qhull: 9744 Number of distance tests for merging: 4407 Number of distance tests for checking: 4026 Number of merged facets: 176 CPU seconds to compute hull (after input): 0.015 Maximum distance of point above facet: 0.048 (0.9x) Maximum distance of vertex below facet: -0.098 (1.7x) rbox 1000 s| qconvex s C0.01 Qc Gcrp >eg/eg.22a.merge.sphere.01 Convex hull of 1000 points in 3-d: Number of vertices: 223 Number of coplanar points: 777 Number of facets: 117 Number of non-simplicial facets: 117 Statistics for: rbox 1000 s | qconvex s C0.01 Qc Gcrp Number of points processed: 1000 Number of hyperplanes created: 5545 Number of distance tests for qhull: 121035 Number of distance tests for merging: 79123 Number of distance tests for checking: 8141 Number of merged facets: 1879 CPU seconds to compute hull (after input): 0.016 Maximum distance of vertex below facet: -0.04 (1.3x) rbox 1000 s| qconvex s C-0.01 Qc Gcrp >eg/eg.22b.merge.sphere.-01 Convex hull of 1000 points in 3-d: Number of vertices: 102 Number of coplanar points: 898 Number of facets: 103 Number of non-simplicial facets: 75 Statistics for: rbox 1000 s | qconvex s C-0.01 Qc Gcrp Number of points processed: 108 Number of hyperplanes created: 467 Number of distance tests for qhull: 71156 Number of distance tests for merging: 6748 Number of distance tests for checking: 31209 Number of merged facets: 256 CPU seconds to compute hull (after input): 0.015 Maximum distance of point above facet: 0.031 (1.0x) Maximum distance of vertex below facet: -0.065 (2.2x) rbox 1000 s| qconvex s C0.05 Qc Gcrpv >eg/eg.22c.merge.sphere.05 Convex hull of 1000 points in 3-d: Number of vertices: 48 Number of coplanar points: 952 Number of facets: 26 Number of non-simplicial facets: 26 Statistics for: rbox 1000 s | qconvex s C0.05 Qc Gcrpv Number of points processed: 1000 Number of hyperplanes created: 5545 Number of distance tests for qhull: 55658 Number of distance tests for merging: 83457 Number of distance tests for checking: 7742 Number of merged facets: 1970 CPU seconds to compute hull (after input): 0.015 Maximum distance of vertex below facet: -0.21 (1.4x) rbox 1000 s| qconvex s C-0.05 Qc Gcrpv >eg/eg.22d.merge.sphere.-05 Convex hull of 1000 points in 3-d: Number of vertices: 18 Number of coplanar points: 982 Number of facets: 15 Number of non-simplicial facets: 13 Statistics for: rbox 1000 s | qconvex s C-0.05 Qc Gcrpv Number of points processed: 22 Number of hyperplanes created: 69 Number of distance tests for qhull: 44445 Number of distance tests for merging: 1034 Number of distance tests for checking: 13690 Number of merged facets: 41 CPU seconds to compute hull (after input): 0 Maximum distance of point above facet: 0.14 (0.9x) Maximum distance of vertex below facet: -0.15 (1.0x) rbox 1000 | qconvex s Gcprvah C0.1 Qc >eg/eg.23.merge.cube Convex hull of 1000 points in 3-d: Number of vertices: 8 Number of coplanar points: 741 Number of facets: 6 Number of non-simplicial facets: 6 Statistics for: rbox 1000 | qconvex s Gcprvah C0.1 Qc Number of points processed: 95 Number of hyperplanes created: 453 Number of distance tests for qhull: 60073 Number of distance tests for merging: 5413 Number of distance tests for checking: 6014 Number of merged facets: 146 CPU seconds to compute hull (after input): 0 Maximum distance of vertex below facet: -0.18 (0.6x) rbox 5000 D4 | qconvex s GD0v Pd0:0.5 C-0.02 C0.1 >eg/eg.24.merge.cube.4d-in-3d Convex hull of 5000 points in 4-d: Number of vertices: 16 Number of facets: 8 Number of 'good' facets: 1 Number of 'good' non-simplicial facets: 1 Statistics for: rbox 5000 D4 | qconvex s GD0v Pd0:0.5 C-0.02 C0.1 Number of points processed: 30 Number of hyperplanes created: 182 Number of distance tests for qhull: 658286 Number of distance tests for merging: 4770 Number of distance tests for checking: 45000 Number of merged facets: 188 CPU seconds to compute hull (after input): 0.031 Maximum distance of point above facet: 0.14 (0.4x) Maximum distance of vertex below facet: -0.31 (0.8x) rbox 5000 D4 | qconvex s s C-0.02 C0.1 Gh >eg/eg.30.4d.merge.cube Convex hull of 5000 points in 4-d: Number of vertices: 16 Number of facets: 8 Number of non-simplicial facets: 8 Statistics for: rbox 5000 D4 | qconvex s s C-0.02 C0.1 Gh Number of points processed: 30 Number of hyperplanes created: 182 Number of distance tests for qhull: 658286 Number of distance tests for merging: 4770 Number of distance tests for checking: 45000 Number of merged facets: 188 CPU seconds to compute hull (after input): 0.032 Maximum distance of point above facet: 0.14 (0.4x) Maximum distance of vertex below facet: -0.31 (0.8x) rbox 20 D3 | qdelaunay s G >eg/eg.31.4d.delaunay Delaunay triangulation by the convex hull of 20 points in 4-d: Number of input sites: 20 Number of Delaunay regions: 0 Statistics for: rbox 20 D3 | qdelaunay s G Number of points processed: 20 Number of hyperplanes created: 162 Number of facets in hull: 81 Number of distance tests for qhull: 302 CPU seconds to compute hull (after input): 0 rbox 30 s D4 | qconvex s G Pd0d1d2D3 >eg/eg.32.4d.octant Convex hull of 30 points in 4-d: Number of vertices: 30 Number of facets: 138 Number of 'good' facets: 9 Statistics for: rbox 30 s D4 | qconvex s G Pd0d1d2D3 Number of points processed: 30 Number of hyperplanes created: 340 Number of distance tests for qhull: 650 CPU seconds to compute hull (after input): 0 rbox 10 r s Z1 G0.3 | qconvex G >eg/eg.33a.cone rbox 10 r s Z1 G0.3 | qconvex FQ FV n | qhalf G >eg/eg.33b.cone.dual rbox 10 r s Z1 G0.3 | qconvex FQ FV n | qhalf FQ s Fp | qconvex G >eg/eg.33c.cone.halfspace Halfspace intersection by the convex hull of 21 points in 3-d: Number of halfspaces: 21 Number of non-redundant halfspaces: 21 Number of intersection points: 21 Number of non-simplicial intersection points: 11 Statistics for: rbox 10 r s Z1 G0.3 | qconvex FQ FV n | qhalf FQ s Fp Number of points processed: 21 Number of hyperplanes created: 48 Number of distance tests for qhull: 162 Number of distance tests for merging: 435 Number of distance tests for checking: 261 Number of merged facets: 18 CPU seconds to compute hull (after input): 0 echo ==the following should generate flipped and concave facets== >/dev/null rbox 200 s | qhull Q0 s R0.014 Gav Po >eg/eg.21a.roundoff.errors QH6136 qhull precision error: facet f506 is flipped, distance= 0.461556194655 QH6136 qhull precision error: facet f592 is flipped, distance= 0.439612545215 QH6136 qhull precision error: facet f604 is flipped, distance= 0.465768128315 QH6136 qhull precision error: facet f506 is flipped, distance= 0.468691154013 QH6136 qhull precision error: facet f592 is flipped, distance= 0.450451888758 QH6136 qhull precision error: facet f604 is flipped, distance= 0.471152553888 QH6115 qhull precision error: f127 is concave to f267, since p65(v17) is 0.02603 above QH6115 qhull precision error: f139 is concave to f285, since p13(v34) is 0.02883 above QH6115 qhull precision error: f166 is concave to f316, since p189(v18) is 0.008704 above QH6115 qhull precision error: f198 is concave to f604, since p109(v11) is 0.02657 above QH6115 qhull precision error: f242 is concave to f527, since p65(v17) is 0.02938 above QH6115 qhull precision error: f259 is concave to f462, since p59(v60) is 0.008633 above QH6115 qhull precision error: f280 is concave to f286, since p22(v65) is 0.01973 above QH6115 qhull precision error: f288 is concave to f310, since p71(v67) is 0.02406 above QH6115 qhull precision error: f297 is concave to f487, since p180(v38) is 0.008078 above QH6115 qhull precision error: f313 is concave to f496, since p63(v41) is 0.03309 above QH6115 qhull precision error: f330 is concave to f331, since p10(v64) is 0.02231 above QH6115 qhull precision error: f397 is concave to f542, since p69(v51) is 0.01923 above QH6115 qhull precision error: f399 is concave to f543, since p155(v31) is 0.01245 above QH6115 qhull precision error: f417 is concave to f552, since p184(v71) is 0.009005 above QH6115 qhull precision error: f426 is concave to f477, since p135(v95) is 0.016 above QH6115 qhull precision error: f431 is concave to f555, since p135(v95) is 0.008306 above QH6115 qhull precision error: f442 is concave to f559, since p97(v98) is 0.04007 above QH6115 qhull precision error: f444 is concave to f245, since p194(v99) is 0.0124 above QH6115 qhull precision error: f457 is concave to f505, since p70(v101) is 0.05613 above QH6115 qhull precision error: f460 is concave to f565, since p176(v61) is 0.02392 above QH6115 qhull precision error: f469 is concave to f580, since p119(v9) is 0.07256 above QH6115 qhull precision error: f472 is concave to f582, since p138(v63) is 0.04511 above QH6115 qhull precision error: f481 is concave to f624, since p79(v93) is 0.0132 above QH6115 qhull precision error: f484 is concave to f483, since p79(v93) is 0.01528 above QH6115 qhull precision error: f492 is concave to f551, since p163(v108) is 0.05382 above QH6115 qhull precision error: f501 is concave to f602, since p29(v10) is 0.01867 above QH6115 qhull precision error: f505 is concave to f457, since p128(v110) is 0.008966 above QH6113 qhull precision error: f506 is flipped(interior point is outside) QH6115 qhull precision error: f520 is concave to f541, since p100(v114) is 0.009004 above QH6115 qhull precision error: f521 is concave to f516, since p100(v114) is 0.01561 above QH6115 qhull precision error: f522 is concave to f526, since p100(v114) is 0.0118 above QH6115 qhull precision error: f534 is concave to f535, since p190(v2) is 0.01582 above QH6115 qhull precision error: f535 is concave to f534, since p154(v47) is 0.009917 above QH6115 qhull precision error: f544 is concave to f620, since p58(v91) is 0.01945 above QH6115 qhull precision error: f551 is concave to f492, since p41(v120) is 0.0114 above QH6115 qhull precision error: f559 is concave to f442, since p38(v122) is 0.01392 above QH6115 qhull precision error: f565 is concave to f460, since p73(v123) is 0.01004 above QH6115 qhull precision error: f566 is concave to f571, since p133(v16) is 0.01303 above QH6115 qhull precision error: f580 is concave to f469, since p158(v127) is 0.0104 above QH6113 qhull precision error: f592 is flipped(interior point is outside) QH6115 qhull precision error: f595 is concave to f626, since p22(v65) is 0.008193 above QH6115 qhull precision error: f603 is concave to f500, since p14(v132) is 0.00736 above QH6113 qhull precision error: f604 is flipped(interior point is outside) QH6115 qhull precision error: f619 is concave to f617, since p12(v1) is 0.007428 above Convex hull of 200 points in 3-d: Number of vertices: 138 Number of facets: 272 Statistics for: rbox 200 s | qhull Q0 s R0.014 Gav Po Number of points processed: 138 Number of hyperplanes created: 629 Number of distance tests for qhull: 4659 CPU seconds to compute hull (after input): 0 precision problems (corrected unless 'Q0' or an error) 120 coplanar half ridges in output 41 concave half ridges in output 3 flipped facets 125 coplanar horizon facets for new vertices 62 coplanar points during partitioning echo ==the preceeding should report flipped and concave facets== >/dev/null eg/q_egtest rbox d D3 | qconvex s Gnrv Tc Tv >eg/eg.t01.spheres.3 Convex hull of 6 points in 3-d: Number of vertices: 6 Number of facets: 8 Statistics for: rbox d D3 | qconvex s Gnrv Tc Tv Number of points processed: 6 Number of hyperplanes created: 11 Number of distance tests for qhull: 11 Number of distance tests for merging: 59 Number of distance tests for checking: 54 Number of merged facets: 1 CPU seconds to compute hull (after input): 0 Output completed. Verifying that all points are below outer planes of all facets. Will make 48 distance computations. rbox d D2 | qconvex s Gnv Tc Tv >eg/eg.t02.spheres.2 Convex hull of 4 points in 2-d: Number of vertices: 4 Number of facets: 4 Statistics for: rbox d D2 | qconvex s Gnv Tc Tv Number of points processed: 4 Number of hyperplanes created: 6 Number of distance tests for qhull: 4 CPU seconds to compute hull (after input): 0 Output completed. Verifying that all points are below 1.3e-015 of all facets. Will make 16 distance computations. rbox d D3 | qconvex s Gnrp Tc Tv >eg/eg.t03.points.3 Convex hull of 6 points in 3-d: Number of vertices: 6 Number of facets: 8 Statistics for: rbox d D3 | qconvex s Gnrp Tc Tv Number of points processed: 6 Number of hyperplanes created: 11 Number of distance tests for qhull: 11 Number of distance tests for merging: 59 Number of distance tests for checking: 54 Number of merged facets: 1 CPU seconds to compute hull (after input): 0 Output completed. Verifying that all points are below outer planes of all facets. Will make 48 distance computations. rbox d D2 | qconvex s Gnp Tc Tv >eg/eg.t04.points.2 Convex hull of 4 points in 2-d: Number of vertices: 4 Number of facets: 4 Statistics for: rbox d D2 | qconvex s Gnp Tc Tv Number of points processed: 4 Number of hyperplanes created: 6 Number of distance tests for qhull: 4 CPU seconds to compute hull (after input): 0 Output completed. Verifying that all points are below 1.3e-015 of all facets. Will make 16 distance computations. rbox c D4 | qconvex s C0.05 GnpcD3 Pd3:0.5 Tc Tv >eg/eg.t05.centrum.points.4-3 Convex hull of 16 points in 4-d: Number of vertices: 16 Number of facets: 8 Number of 'good' facets: 1 Number of 'good' non-simplicial facets: 1 Statistics for: rbox c D4 | qconvex s C0.05 GnpcD3 Pd3:0.5 Tc Tv Number of points processed: 16 Number of hyperplanes created: 26 Number of distance tests for qhull: 168 Number of distance tests for merging: 963 Number of distance tests for checking: 144 Number of merged facets: 36 CPU seconds to compute hull (after input): 0 Output completed. Verifying that all points are below outer planes of all facets. Will make 16 distance computations. rbox d D3 | qconvex s Gnrc Tc Tv >eg/eg.t06.centrums.3.precise Convex hull of 6 points in 3-d: Number of vertices: 6 Number of facets: 8 Statistics for: rbox d D3 | qconvex s Gnrc Tc Tv Number of points processed: 6 Number of hyperplanes created: 11 Number of distance tests for qhull: 11 Number of distance tests for merging: 59 Number of distance tests for checking: 54 Number of merged facets: 1 CPU seconds to compute hull (after input): 0 Output completed. Verifying that all points are below outer planes of all facets. Will make 48 distance computations. rbox d D3 | qconvex s C0.05 Gnrc Tc Tv >eg/eg.t07.centrums.3 Convex hull of 6 points in 3-d: Number of vertices: 6 Number of facets: 8 Statistics for: rbox d D3 | qconvex s C0.05 Gnrc Tc Tv Number of points processed: 6 Number of hyperplanes created: 11 Number of distance tests for qhull: 11 Number of distance tests for merging: 169 Number of distance tests for checking: 54 Number of merged facets: 1 CPU seconds to compute hull (after input): 0 Output completed. Verifying that all points are below outer planes of all facets. Will make 48 distance computations. rbox d D2 | qconvex s C0.05 Gc Tc Tv >eg/eg.t08.centrums.2 Convex hull of 4 points in 2-d: Number of vertices: 4 Number of facets: 4 Statistics for: rbox d D2 | qconvex s C0.05 Gc Tc Tv Number of points processed: 4 Number of hyperplanes created: 6 Number of distance tests for qhull: 4 CPU seconds to compute hull (after input): 0 Output completed. Verifying that all points are below outer planes of all facets. Will make 16 distance computations. rbox d D3 | qconvex s Gnha Tc Tv >eg/eg.t09.intersect.3 Convex hull of 6 points in 3-d: Number of vertices: 6 Number of facets: 8 Statistics for: rbox d D3 | qconvex s Gnha Tc Tv Number of points processed: 6 Number of hyperplanes created: 11 Number of distance tests for qhull: 11 Number of distance tests for merging: 59 Number of distance tests for checking: 54 Number of merged facets: 1 CPU seconds to compute hull (after input): 0 Output completed. Verifying that all points are below outer planes of all facets. Will make 48 distance computations. rbox d D3 | qconvex s GaD0 Pd0 Tc Tv >eg/eg.t10.faces.3-2 Convex hull of 6 points in 3-d: Number of vertices: 6 Number of facets: 8 Number of 'good' facets: 4 Statistics for: rbox d D3 | qconvex s GaD0 Pd0 Tc Tv Number of points processed: 6 Number of hyperplanes created: 11 Number of distance tests for qhull: 11 Number of distance tests for merging: 59 Number of distance tests for checking: 54 Number of merged facets: 1 CPU seconds to compute hull (after input): 0 Output completed. Verifying that all points are below outer planes of all facets. Will make 24 distance computations. rbox d D3 | qconvex s GnrpD0 Pd0 Tc Tv >eg/eg.t11.points.3-2 Convex hull of 6 points in 3-d: Number of vertices: 6 Number of facets: 8 Number of 'good' facets: 4 Statistics for: rbox d D3 | qconvex s GnrpD0 Pd0 Tc Tv Number of points processed: 6 Number of hyperplanes created: 11 Number of distance tests for qhull: 11 Number of distance tests for merging: 59 Number of distance tests for checking: 54 Number of merged facets: 1 CPU seconds to compute hull (after input): 0 Output completed. Verifying that all points are below outer planes of all facets. Will make 24 distance computations. rbox d D3 | qconvex s C0.05 GnrcD0 Pd0 Tc Tv >eg/eg.t12.centrums.3-2 Convex hull of 6 points in 3-d: Number of vertices: 6 Number of facets: 8 Number of 'good' facets: 4 Statistics for: rbox d D3 | qconvex s C0.05 GnrcD0 Pd0 Tc Tv Number of points processed: 6 Number of hyperplanes created: 11 Number of distance tests for qhull: 11 Number of distance tests for merging: 169 Number of distance tests for checking: 54 Number of merged facets: 1 CPU seconds to compute hull (after input): 0 Output completed. Verifying that all points are below outer planes of all facets. Will make 24 distance computations. rbox d D3 | qconvex s GnhaD0 Pd0 Tc Tv >eg/eg.t13.intersect.3-2 Convex hull of 6 points in 3-d: Number of vertices: 6 Number of facets: 8 Number of 'good' facets: 4 Statistics for: rbox d D3 | qconvex s GnhaD0 Pd0 Tc Tv Number of points processed: 6 Number of hyperplanes created: 11 Number of distance tests for qhull: 11 Number of distance tests for merging: 59 Number of distance tests for checking: 54 Number of merged facets: 1 CPU seconds to compute hull (after input): 0 Output completed. Verifying that all points are below outer planes of all facets. Will make 24 distance computations. rbox d D3 | qconvex s GnrvD0 Pd0 Tc Tv >eg/eg.t14.spheres.3-2 Convex hull of 6 points in 3-d: Number of vertices: 6 Number of facets: 8 Number of 'good' facets: 4 Statistics for: rbox d D3 | qconvex s GnrvD0 Pd0 Tc Tv Number of points processed: 6 Number of hyperplanes created: 11 Number of distance tests for qhull: 11 Number of distance tests for merging: 59 Number of distance tests for checking: 54 Number of merged facets: 1 CPU seconds to compute hull (after input): 0 Output completed. Verifying that all points are below outer planes of all facets. Will make 24 distance computations. rbox c D4 | qconvex s GvD0 Pd0:0.5 Tc Tv >eg/eg.t15.spheres.4-3 Convex hull of 16 points in 4-d: Number of vertices: 16 Number of facets: 8 Number of 'good' facets: 1 Number of 'good' non-simplicial facets: 1 Statistics for: rbox c D4 | qconvex s GvD0 Pd0:0.5 Tc Tv Number of points processed: 16 Number of hyperplanes created: 26 Number of distance tests for qhull: 168 Number of distance tests for merging: 788 Number of distance tests for checking: 144 Number of merged facets: 36 CPU seconds to compute hull (after input): 0 Output completed. Verifying that all points are below outer planes of all facets. Will make 16 distance computations. rbox c D4 | qhull s Q0 C0 GpD0 Pd0:0.5 Tc Tv >eg/eg.t16.points.4-3 Convex hull of 16 points in 4-d: Number of vertices: 16 Number of facets: 8 Number of 'good' facets: 1 Number of 'good' non-simplicial facets: 1 Statistics for: rbox c D4 | qhull s Q0 C0 GpD0 Pd0:0.5 Tc Tv Number of points processed: 16 Number of hyperplanes created: 62 Number of distance tests for qhull: 163 Number of distance tests for merging: 1304 Number of distance tests for checking: 144 Number of merged facets: 36 CPU seconds to compute hull (after input): 0 Output completed. Verifying that all points are below outer planes of all facets. Will make 16 distance computations. rbox c D4 | qconvex s GahD0 Pd0:0.5 Tc Tv >eg/eg.t17.intersect.4-3 Convex hull of 16 points in 4-d: Number of vertices: 16 Number of facets: 8 Number of 'good' facets: 1 Number of 'good' non-simplicial facets: 1 Statistics for: rbox c D4 | qconvex s GahD0 Pd0:0.5 Tc Tv Number of points processed: 16 Number of hyperplanes created: 26 Number of distance tests for qhull: 168 Number of distance tests for merging: 788 Number of distance tests for checking: 144 Number of merged facets: 36 CPU seconds to compute hull (after input): 0 Output completed. Verifying that all points are below outer planes of all facets. Will make 16 distance computations. rbox 100 s | qconvex s C-0.05 Qc Gicvprh Tc Tv >eg/eg.t18.imprecise.3 Convex hull of 100 points in 3-d: Number of vertices: 18 Number of coplanar points: 82 Number of facets: 16 Number of non-simplicial facets: 12 Statistics for: rbox 100 s | qconvex s C-0.05 Qc Gicvprh Tc Tv Number of points processed: 18 Number of hyperplanes created: 60 Number of distance tests for qhull: 3313 Number of distance tests for merging: 1030 Number of distance tests for checking: 1347 Number of merged facets: 29 CPU seconds to compute hull (after input): 0 Maximum distance of point above facet: 0.092 (0.6x) Maximum distance of vertex below facet: -0.14 (0.9x) Output completed. Verifying that all points are below outer planes of all facets. Will make 1600 distance computations. rbox 30 s D4 | qconvex s GhD0 Pd0d1d2D3 Tc >eg/eg.t19.intersect.precise.4-3 Convex hull of 30 points in 4-d: Number of vertices: 30 Number of facets: 138 Number of 'good' facets: 9 Statistics for: rbox 30 s D4 | qconvex s GhD0 Pd0d1d2D3 Tc Number of points processed: 30 Number of hyperplanes created: 340 Number of distance tests for qhull: 650 CPU seconds to compute hull (after input): 0 rbox 100 s P1,1,1 | qconvex s QG-0 Pgp Tc G >eg/eg.t20.notvisible Convex hull of 100 points in 3-d: Number of vertices: 100 Number of facets: 196 Number of 'good' facets: 125 Statistics for: rbox 100 s P1,1,1 | qconvex s QG-0 Pgp Tc G Number of points processed: 100 Number of hyperplanes created: 503 Number of distance tests for qhull: 1631 CPU seconds to compute hull (after input): 0 rbox 100 s | qconvex s QV-10 Pgp Tc G >eg/eg.t21.notvertex Convex hull of 100 points in 3-d: Number of vertices: 100 Number of facets: 196 Number of 'good' facets: 191 Statistics for: rbox 100 s | qconvex s QV-10 Pgp Tc G Number of points processed: 100 Number of hyperplanes created: 494 Number of distance tests for qhull: 1641 CPU seconds to compute hull (after input): 0 rbox 100 r D2 P1,1 | qhull s Pd0:0.7 PD0:0.8 QgG0 G Tv >eg/eg.t22.split Convex hull of 100 points in 2-d: Number of vertices: 42 Number of facets: 42 Number of 'good' facets: 3 Statistics for: rbox 100 r D2 P1,1 | qhull s Pd0:0.7 PD0:0.8 QgG0 G Tv Number of points processed: 89 Number of hyperplanes created: 176 Number of distance tests for qhull: 1099 CPU seconds to compute hull (after input): 0 Output completed. Verifying that all points are below 2.6e-015 of all good facets. Will make 303 distance computations. rbox 100 D2 c G1.0 | qvoronoi s A-0.95 Gna Tv >eg/eg.t23.voronoi.imprecise Voronoi diagram by the convex hull of 104 points in 3-d: Number of Voronoi regions: 13 Total number of nearly incident points: 91 Number of Voronoi vertices: 13 Number of non-simplicial Voronoi vertices: 5 Statistics for: rbox 100 D2 c G1.0 | qvoronoi s A-0.95 Gna Tv Number of points processed: 13 Number of hyperplanes created: 39 Number of facets in hull: 14 Number of distance tests for qhull: 2740 Number of distance tests for merging: 464 Number of distance tests for checking: 1119 Number of merged facets: 13 CPU seconds to compute hull (after input): 0 Maximum distance of point above facet: 0.098 (0.1x) Maximum distance of vertex below facet: -0.082 (0.1x) Output completed. Verifying that all points are below outer planes of all facets. Will make 1352 distance computations. rbox 30 s D4 | qconvex s Gh Pd0d1d2D3 Tc >eg/eg.t24.intersect.precise.4d Convex hull of 30 points in 4-d: Number of vertices: 30 Number of facets: 138 Number of 'good' facets: 9 Statistics for: rbox 30 s D4 | qconvex s Gh Pd0d1d2D3 Tc Number of points processed: 30 Number of hyperplanes created: 340 Number of distance tests for qhull: 650 CPU seconds to compute hull (after input): 0 echo ==the following generates an error== >/dev/null rbox 1000 D4 | qhull Q0 s Po R0.005 Ga Tc Tv >eg/eg.t25.neighbors.4d QH6136 qhull precision error: facet f491 is flipped, distance= 0.413460414284 QH6136 qhull precision error: facet f949 is flipped, distance= 0.558894018107 QH6107 qhull precision error: facets f977, f981 and f978 meet at a ridge with more than 2 neighbors. Can not continue. ERRONEOUS FACET: - f977 - flags: bottom simplicial new - normal: -0.07131 -0.04413 0.08982 -0.9924 - offset: -0.5084414 - vertices: p108(v73) p722(v63) p713(v35) p241(v7) - neighboring facets: f824 f968 f971 f978 ERRONEOUS OTHER FACET: - f981 - flags: top simplicial new - normal: -0.005308 -0.0126 0.005272 -0.9999 - offset: -0.4947257 - vertices: p108(v73) p722(v63) p713(v35) p62(v20) - neighboring facets: f825 ERRONEOUS and NEIGHBORING FACETS to output While executing: rbox 1000 D4 | qhull Q0 s Po R0.005 Ga Tc Tv Options selected for Qhull 2012.1 2012/01/22: run-id 315164332 Q0-no-premerge summary Poutput-forced Random_perturb 0.005 Gall-points Tcheck-frequently Tverify _max-width 1 Error-roundoff 0.0025 Visible-distance 0.0025 U-coplanar-distance 0.0025 Width-outside 0.005 _wide-facet 0.015 Last point added to hull was p108. Convex hull of 1000 points in 4-d: Number of vertices: 68 Number of facets: 346 Statistics for: rbox 1000 D4 | qhull Q0 s Po R0.005 Ga Tc Tv Number of points processed: 73 Number of hyperplanes created: 986 Number of distance tests for qhull: 28532 precision problems (corrected unless 'Q0' or an error) 2 flipped facets 42 coplanar horizon facets for new vertices 141 coplanar points during partitioning 9 degenerate hyperplanes recomputed with gaussian elimination 9 nearly singular or axis-parallel hyperplanes Precision problems were detected during construction of the convex hull. This occurs because convex hull algorithms assume that calculations are exact, but floating-point arithmetic has roundoff errors. To correct for precision problems, do not use 'Q0'. By default, Qhull selects 'C-0' or 'Qx' and merges non-convex facets. With option 'QJ', Qhull joggles the input to prevent precision problems. See "Imprecision in Qhull" (qh-impre.htm). If you use 'Q0', the output may include coplanar ridges, concave ridges, and flipped facets. In 4-d and higher, Qhull may produce a ridge with four neighbors or two facets with the same vertices. Qhull reports these events when they occur. It stops when a concave ridge, flipped facet, or duplicate facet occurs. If you need triangular output: - use option 'Qt' to triangulate the output - use option 'QJ' to joggle the input points and remove precision errors - use option 'Ft'. It triangulates non-simplicial facets with added points. If you must use 'Q0', try one or more of the following options. They can not guarantee an output. - use 'QbB' to scale the input to a cube. - use 'Po' to produce output and prevent partitioning for flipped facets - use 'V0' to set min. distance to visible facet as 0 instead of roundoff - use 'En' to specify a maximum roundoff error less than 0.0025. - options 'Qf', 'Qbb', and 'QR0' may also help To guarantee simplicial output: - use option 'Qt' to triangulate the output - use option 'QJ' to joggle the input points and remove precision errors - use option 'Ft' to triangulate the output by adding points - use exact arithmetic (see "Imprecision in Qhull", qh-impre.htm) echo ==the previous should generate an error== >/dev/null eg/q_test Convex hull of 8 points in 3-d: Number of vertices: 8 Number of facets: 6 Number of non-simplicial facets: 6 Statistics for: | qhull s Tcv Number of points processed: 8 Number of hyperplanes created: 11 Number of distance tests for qhull: 35 Number of distance tests for merging: 142 Number of distance tests for checking: 56 Number of merged facets: 6 CPU seconds to compute hull (after input): 0 Output completed. Verifying that all points are below outer planes of all facets. Will make 48 distance computations. Delaunay triangulation by the convex hull of 8 points in 4-d: Number of input sites: 8 Number of Delaunay regions: 11 Statistics for: | qhull s d Tcv Number of points processed: 8 Number of hyperplanes created: 28 Number of facets in hull: 16 Number of distance tests for qhull: 33 CPU seconds to compute hull (after input): 0 Output completed. Verifying that all points are below 1.4e-014 of all facets. Will make 88 distance computations. Delaunay triangulation by the convex hull of 8 points in 4-d: Number of input sites: 8 Number of Delaunay regions: 11 Statistics for: | qhull s d Tcv Number of points processed: 8 Number of hyperplanes created: 24 Number of facets in hull: 17 Number of distance tests for qhull: 31 CPU seconds to compute hull (after input): 0 Output completed. Verifying that all points are below 7.3e-015 of all facets. Will make 88 distance computations. Halfspace intersection by the convex hull of 8 points in 3-d: Number of halfspaces: 8 Number of non-redundant halfspaces: 8 Number of intersection points: 6 Number of non-simplicial intersection points: 6 Statistics for: | qhull H0 s Tcv Fp Number of points processed: 8 Number of hyperplanes created: 11 Number of distance tests for qhull: 35 Number of distance tests for merging: 142 Number of distance tests for checking: 56 Number of merged facets: 6 CPU seconds to compute hull (after input): 0 Output completed. Verifying that all points are below outer planes of all facets. Will make 48 distance computations. echo === errors if 'user_eg' and 'user_eg2' not found === === errors if user_eg and user_eg2 not found === echo === check user_eg ${d:-`date`} ===================== date === check user_eg Tue Jan 24 20:16:42 EST 2012 ===================== user_eg "QR1 p n Qt" "v p" Fp This is the output from user_eg.c It shows how qhull() may be called from an application using the qhull shared library. It is not part of qhull itself. If it appears accidently, please remove user_eg.c from your project. compute convex hull of cube after rotating input input -1 -1 -1 1 -1 -1 -1 1 -1 1 1 -1 -1 -1 1 1 -1 1 -1 1 1 1 1 1 3 8 0.9124763375291641 1.390833937612012 -0.4826674750136243 -0.5764091147442416 0.565375258822974 -1.532352227508615 -0.1847368907548403 1.250953879569599 1.183632828365285 -1.673622343028246 0.4254952007805605 0.1339480758702939 1.673622343028246 -0.4254952007805605 -0.1339480758702939 0.1847368907548403 -1.250953879569599 -1.183632828365285 0.5764091147442416 -0.565375258822974 1.532352227508615 -0.9124763375291641 -1.390833937612012 0.4826674750136243 4 12 -0.380573002749541 0.9081645691962865 -0.1743596995716652 -1 -0.380573002749541 0.9081645691962865 -0.1743596995716652 -1 0.744442726136703 0.4127293393945193 0.5248423762474955 -1 0.744442726136703 0.4127293393945193 0.5248423762474955 -1 -0.5486066141420022 -0.06994002902120672 0.8331501516894545 -1 -0.5486066141420022 -0.06994002902120672 0.8331501516894545 -1 0.5486066141420022 0.06994002902120679 -0.8331501516894545 -1 0.5486066141420022 0.06994002902120679 -0.8331501516894545 -1 0.380573002749541 -0.9081645691962865 0.1743596995716652 -1 0.380573002749541 -0.9081645691962865 0.1743596995716652 -1 -0.7444427261367029 -0.4127293393945193 -0.5248423762474955 -0.9999999999999997 -0.7444427261367029 -0.4127293393945193 -0.5248423762474955 -0.9999999999999997 8 vertices and 12 facets with normals: -0.38 0.91 -0.17 -0.38 0.91 -0.17 0.74 0.41 0.52 0.74 0.41 0.52 -0.55 -0.07 0.83 -0.55 -0.07 0.83 0.55 0.07 -0.83 0.55 0.07 -0.83 0.38 -0.91 0.17 0.38 -0.91 0.17 -0.74 -0.41 -0.52 -0.74 -0.41 -0.52 compute 3-d Delaunay triangulation seed: 1327454202 input -0.706 0.185 -0.997 0.739 0.981 0.915 -0.0492 0.993 -0.337 -0.408 -0.521 0.378 -0.174 -0.217 -0.829 -0.114 -0.874 0.268 0.414 -0.87 -0.86 0.684 -0.12 0.241 3 11 8.817140186696875 3.450584294550091 -5.020639188104951 0.5403564279616564 -0.6912825989872701 2.425011907306929 -0.1199937357891065 0.4735709729694704 0.5770495599647179 3.100407885814694 2.400973701393672 -6.350407240410952 1.236411828590869 0.4751228563895312 -1.138297941446634 -0.5020263900519639 0.2374638672802573 -0.1134692063160839 -0.08697626605473376 0.1691016807526869 -0.05020263571440065 -2.27154828024003 -2.667494449872159 -1.43761610758808 -1.575536916403145 -1.453895924539648 -0.7477231573352229 0.2382928326855393 -0.4652796623935117 -0.2533544020986503 0.06787343520023301 -0.2808240579638571 -0.1335157472366256 8 vertices and 16 facets with normals: -0.51 -0.42 0.26 0.7 0.65 -0.6 0.43 0.18 0.43 0.42 -0.68 0.42 0.82 0.32 -0.47 -0.047 -0.68 -0.27 0.39 0.55 -0.82 0.37 0.43 0.092 0.21 -0.26 0.92 -0.19 -0.13 0.52 0.64 -0.55 0.41 0.32 -0.85 -0.067 0.68 0.26 -0.63 -0.28 -0.66 0.31 -0.15 -0.66 -0.16 0.31 -0.093 -0.93 -0.59 -0.7 -0.38 -0.13 -0.68 -0.63 -0.32 -0.22 0.31 -0.61 -0.33 -0.65 0.11 -0.47 -0.23 -0.84 find 3-d Delaunay triangle closest to [0.5, 0.5, ...] -0.41 -0.52 0.38 -0.05 0.99 -0.34 0.68 -0.12 0.24 0.74 0.98 0.92 save first triangulation and compute a new triangulation seed: 1327454203 input -0.706 0.448 0.514 -0.343 0.047 -0.647 0.0449 0.351 -0.979 -0.538 0.246 -0.583 -0.512 -0.147 -0.722 0.945 0.468 0.283 -0.819 -0.736 -0.0249 0.0573 -0.942 0.102 3 11 -0.2386622335477796 -0.1566542442491845 0.1628208587902705 0.09843684708370071 0.01493208449583039 0.2089868348364177 0.5723090085175291 -0.2124517280896852 -0.3449177752423304 -0.4619263792107396 -0.09379720018847126 0.07126402711263546 0.03918182679269278 1.273584146776618 -0.1032761907666938 0.07192003860173046 0.4326707178511331 0.0563639535749717 0.1540676134834845 0.5692882636221464 -0.119465246220046 -0.2503820888867752 -0.4059765127196031 -0.1601524894225976 0.4530074947629944 -0.7123718802783976 -0.9412410897971241 -0.5748832691392634 -0.1527250737689812 -0.08932774746840733 -0.5344126046033305 0.2483559898669195 -1.217616521674434 8 vertices and 17 facets with normals: -0.14 0.22 -0.0066 0.97 0.033 -0.24 0.78 0.57 -0.4 -0.26 0.27 -0.84 0.18 0.027 0.38 -0.91 0.27 -0.32 -0.24 0.87 0.66 -0.25 -0.4 -0.58 -0.67 0.33 -0.31 0.59 -0.67 -0.14 0.1 -0.72 0.029 0.93 -0.075 -0.36 0.11 0.65 0.084 -0.75 0.2 0.73 -0.15 -0.64 0.073 -0.63 -0.7 0.34 -0.35 -0.57 -0.23 -0.7 0.33 -0.52 -0.69 -0.37 -0.69 0.26 -0.41 0.54 -0.73 -0.2 -0.11 -0.64 -0.37 0.17 -0.84 -0.35 save second triangulation and restore first one 8 vertices and 16 facets with normals: -0.51 -0.42 0.26 0.7 0.65 -0.6 0.43 0.18 0.43 0.42 -0.68 0.42 0.82 0.32 -0.47 -0.047 -0.68 -0.27 0.39 0.55 -0.82 0.37 0.43 0.092 0.21 -0.26 0.92 -0.19 -0.13 0.52 0.64 -0.55 0.41 0.32 -0.85 -0.067 0.68 0.26 -0.63 -0.28 -0.66 0.31 -0.15 -0.66 -0.16 0.31 -0.093 -0.93 -0.59 -0.7 -0.38 -0.13 -0.68 -0.63 -0.32 -0.22 0.31 -0.61 -0.33 -0.65 0.11 -0.47 -0.23 -0.84 free first triangulation and restore second one. 8 vertices and 17 facets with normals: -0.14 0.22 -0.0066 0.97 0.033 -0.24 0.78 0.57 -0.4 -0.26 0.27 -0.84 0.18 0.027 0.38 -0.91 0.27 -0.32 -0.24 0.87 0.66 -0.25 -0.4 -0.58 -0.67 0.33 -0.31 0.59 -0.67 -0.14 0.1 -0.72 0.029 0.93 -0.075 -0.36 0.11 0.65 0.084 -0.75 0.2 0.73 -0.15 -0.64 0.073 -0.63 -0.7 0.34 -0.35 -0.57 -0.23 -0.7 0.33 -0.52 -0.69 -0.37 -0.69 0.26 -0.41 0.54 -0.73 -0.2 -0.11 -0.64 -0.37 0.17 -0.84 -0.35 compute halfspace intersection about the origin for a diamond input as halfspace coefficients + offsets -1 -1 -1 -1 1 -1 -1 -1 -1 1 -1 -1 1 1 -1 -1 -1 -1 1 -1 1 -1 1 -1 -1 1 1 -1 1 1 1 -1 3 6 0 0 -1 0 -1 0 1 0 0 -1 0 0 0 1 0 0 0 1 8 vertices and 6 facets with normals: -0 -0 -1 0 -1 0 1 -0 -0 -1 -0 -0 0 1 -0 -0 -0 1 Convex hull of 8 points in 3-d: Number of vertices: 8 Number of facets: 12 Number of triangulated facets: 6 Statistics for: | qhull s Tcv QR1 p n Qt QR1 Number of points processed: 8 Number of hyperplanes created: 11 Number of distance tests for qhull: 24 Number of distance tests for merging: 186 Number of distance tests for checking: 56 Number of merged facets: 7 CPU seconds to compute hull (after input): 0 Output completed. Verifying that all points are below outer planes of all facets. Will make 96 distance computations. Voronoi diagram by the convex hull of 8 points in 4-d: Number of Voronoi regions: 8 Number of Voronoi vertices: 11 Statistics for: | qhull s d Tcv v p Number of points processed: 8 Number of hyperplanes created: 28 Number of facets in hull: 16 Number of distance tests for qhull: 33 CPU seconds to compute hull (after input): 0 Output completed. Verifying that all points are below 1.4e-014 of all facets. Will make 88 distance computations. Voronoi diagram by the convex hull of 8 points in 4-d: Number of Voronoi regions: 8 Number of Voronoi vertices: 11 Statistics for: | qhull s d Tcv v p Number of points processed: 8 Number of hyperplanes created: 24 Number of facets in hull: 17 Number of distance tests for qhull: 31 CPU seconds to compute hull (after input): 0 Output completed. Verifying that all points are below 7.3e-015 of all facets. Will make 88 distance computations. Halfspace intersection by the convex hull of 8 points in 3-d: Number of halfspaces: 8 Number of non-redundant halfspaces: 8 Number of intersection points: 6 Number of non-simplicial intersection points: 6 Statistics for: | qhull H0 s Tcv Fp Number of points processed: 8 Number of hyperplanes created: 11 Number of distance tests for qhull: 35 Number of distance tests for merging: 142 Number of distance tests for checking: 56 Number of merged facets: 6 CPU seconds to compute hull (after input): 0 Output completed. Verifying that all points are below outer planes of all facets. Will make 48 distance computations. user_eg2 "QR1 p" "v p" Fp This is the output from user_eg2.c It shows how qhull() may be called from an application in the same way as qconvex. It is not part of qhull itself. If it appears accidently, please remove user_eg2.c from your project. compute triangulated convex hull of cube after rotating input 8 vertices and 12 facets with normals: -0.38 0.91 -0.17 -0.38 0.91 -0.17 0.74 0.41 0.52 0.74 0.41 0.52 -0.55 -0.07 0.83 -0.55 -0.07 0.83 0.55 0.07 -0.83 0.55 0.07 -0.83 0.38 -0.91 0.17 0.38 -0.91 0.17 -0.74 -0.41 -0.52 -0.74 -0.41 -0.52 add points in a diamond 9 vertices and 14 facets 10 vertices and 16 facets 11 vertices and 18 facets 12 vertices and 20 facets 13 vertices and 22 facets 14 vertices and 24 facets 14 vertices and 24 facets with normals: -0.67 0.63 -0.39 0.67 -0.63 0.39 -0.1 -0.71 0.7 0.65 -0.66 0.37 0.63 -0.7 -0.34 -0.65 -0.65 -0.41 -0.62 -0.62 -0.49 -0.65 0.66 -0.37 -0.63 0.7 0.34 0.1 0.71 -0.7 0.65 0.65 0.41 0.62 0.62 0.49 -0.7 -0.13 -0.7 -0.62 -0.49 -0.62 0.11 0.7 -0.71 0.68 0.29 -0.68 0.66 -0.34 -0.67 0.67 -0.3 -0.67 -0.66 0.34 0.67 -0.67 0.3 0.67 0.7 0.13 0.7 0.62 0.49 0.62 -0.11 -0.7 0.71 -0.68 -0.29 0.68 3 14 0.9124763375291641 1.390833937612012 -0.4826674750136243 -0.5764091147442416 0.565375258822974 -1.532352227508615 -0.1847368907548403 1.250953879569599 1.183632828365285 -1.673622343028246 0.4254952007805605 0.1339480758702939 1.673622343028246 -0.4254952007805605 -0.1339480758702939 0.1847368907548403 -1.250953879569599 -1.183632828365285 0.5764091147442416 -0.565375258822974 1.532352227508615 -0.9124763375291641 -1.390833937612012 0.4826674750136243 -2 0 0 2 0 0 0 -2 0 0 2 0 0 0 -2 0 0 2 compute 2-d Delaunay triangulation seed: 1327454202 8 vertices and 12 facets with normals: -0.12 0.96 0.24 -0.46 0.77 -0.44 -0.03 -0.7 0.71 0.065 -0.78 0.62 0.21 0.57 -0.79 0.73 -0.68 -0.046 0.57 0.46 -0.68 -0.69 -0.15 -0.7 -0.61 0.095 -0.79 -0.69 -0.11 -0.71 -0.76 0.45 -0.47 -0.92 0.17 -0.36 2 9 -0.5240618706046448 0.8690922898675285 0.1358064000046035 0.3626730983099605 7.974840388221374 -7.374405564218564 0.4195468496642627 0.3335095202541082 -0.4922740987263012 -0.1088952709353415 -0.3827738348641049 0.0600803560653607 -0.4876069143265992 -0.0790832620725363 -0.8193548043760952 0.4791286600785644 -1.272050939831275 0.2416814840895872 add points to triangulation added point p8: -1 -0.7369 1.543 9 points, 0 extra points, 9 vertices, and 14 facets in total added point p9: 0.5112 -0.0827 0.2682 10 points, 0 extra points, 10 vertices, and 16 facets in total added point p10: 0.06553 -0.5621 0.3202 11 points, 0 extra points, 11 vertices, and 18 facets in total added point p11: -0.9059 0.3577 0.9486 12 points, 0 extra points, 12 vertices, and 20 facets in total added point p12: 0.3586 0.8694 0.8844 13 points, 0 extra points, 13 vertices, and 22 facets in total added point p13: -0.233 0.03883 0.0558 14 points, 0 extra points, 14 vertices, and 24 facets in total 2 20 -0.5240618706046448 0.8690922898675285 -0.7142921036252496 -0.4804985865634099 -0.3868523717342836 -1.139305762703926 -0.1156818685064501 -0.4320436976219833 0.1835775895812016 -0.2249639293216311 -0.7258967842870163 0.6025492522388728 -0.7138368277764179 0.3778481824012493 -0.947056678869817 0.1087890172824351 -3.220184924780109 0.005246869469005044 -2.144650850556788 -0.08718357304267166 0.5665005822680963 2.292036901528415 0.7037349508716335 0.4364365763155512 -0.4621934658225102 0.1363105721823742 0.1412729021729308 -0.008672999714931684 -0.5240310768018593 -0.06418916274782284 0.2007957323480979 0.3558162000371691 -0.5064628004910842 -0.1326436539669383 -0.4489169449937205 -0.1460994267569178 -0.03779347655016083 0.4959031883977701 0.01966384040606073 0.4848333325721471 find Delaunay triangle closest to [0.5, 0.5, ...] -0.23 0.04 0.36 0.87 0.51 -0.08 compute halfspace intersection about the origin for a diamond 3 6 0 0 -1 0 -1 0 1 0 0 -1 0 0 0 1 0 0 0 1 add halfspaces for cube to intersection added offset -1 and normal 1.732 0 0 8 points, 1 extra points, 9 vertices, and 9 facets in total added offset -1 and normal -1.732 0 0 8 points, 2 extra points, 10 vertices, and 12 facets in total added offset -1 and normal 0 1.732 0 8 points, 3 extra points, 11 vertices, and 15 facets in total added offset -1 and normal 0 -1.732 0 8 points, 4 extra points, 12 vertices, and 18 facets in total added offset -1 and normal 0 0 1.732 8 points, 5 extra points, 13 vertices, and 21 facets in total added offset -1 and normal 0 0 -1.732 8 points, 6 extra points, 14 vertices, and 24 facets in total 3 24 0.5773502691896257 0 -0.4226497308103742 0.5773502691896257 -0.4226497308103742 0 0.5773502691896257 0.4226497308103742 0 0.5773502691896257 0 0.4226497308103742 -0.5773502691896257 0 -0.4226497308103742 -0.5773502691896257 -0.4226497308103742 0 -0.5773502691896257 0.4226497308103742 0 -0.5773502691896257 0 0.4226497308103742 0 0.5773502691896257 -0.4226497308103742 0.4226497308103742 0.5773502691896257 0 -0.4226497308103742 0.5773502691896257 0 0 0.5773502691896257 0.4226497308103742 0 -0.5773502691896257 -0.4226497308103742 -0.4226497308103742 -0.5773502691896257 0 0.4226497308103742 -0.5773502691896257 0 0 -0.5773502691896257 0.4226497308103742 0 -0.4226497308103742 0.5773502691896257 0.4226497308103742 0 0.5773502691896257 0 0.4226497308103742 0.5773502691896257 -0.4226497308103742 0 0.5773502691896257 -0.4226497308103742 0 -0.5773502691896257 0 -0.4226497308103742 -0.5773502691896257 0.4226497308103742 0 -0.5773502691896257 0 0.4226497308103742 -0.5773502691896257 Output completed. Verifying that all points are below outer planes of all facets. Will make 96 distance computations. Convex hull of 14 points in 3-d: Number of vertices: 14 Number of facets: 24 Statistics for: user_eg cube | qhull s Tcv Q11 QR1 p QR1 Number of points processed: 14 Number of hyperplanes created: 45 Number of distance tests for qhull: 68 Number of distance tests for merging: 370 Number of distance tests for checking: 214 Number of merged facets: 7 CPU seconds to compute hull (after input): 0 Output completed. Verifying that all points are below outer planes of all facets. Will make 192 distance computations. Voronoi diagram by the convex hull of 8 points in 3-d: Number of Voronoi regions: 8 Number of Voronoi vertices: 9 Statistics for: user_eg Delaunay | qhull s d Tcv v p Number of points processed: 8 Number of hyperplanes created: 21 Number of facets in hull: 12 Number of distance tests for qhull: 35 CPU seconds to compute hull (after input): 0 Output completed. Verifying that all points are below 7.5e-015 of all facets. Will make 72 distance computations. Voronoi diagram by the convex hull of 14 points in 3-d: Number of Voronoi regions: 14 Number of Voronoi vertices: 20 Statistics for: user_eg Delaunay | qhull s d Tcv v p Number of points processed: 14 Number of hyperplanes created: 53 Number of facets in hull: 24 Number of distance tests for qhull: 81 CPU seconds to compute hull (after input): 0 Output completed. Verifying that all points are below 7.5e-015 of all facets. Will make 280 distance computations. Halfspace intersection by the convex hull of 8 points in 3-d: Number of halfspaces: 8 Number of non-redundant halfspaces: 8 Number of intersection points: 6 Number of non-simplicial intersection points: 6 Statistics for: user_eg halfspaces | qhull H0 s Tcv Fp Number of points processed: 8 Number of hyperplanes created: 11 Number of distance tests for qhull: 35 Number of distance tests for merging: 142 Number of distance tests for checking: 56 Number of merged facets: 6 CPU seconds to compute hull (after input): 0 Output completed. Verifying that all points are below outer planes of all facets. Will make 48 distance computations. Halfspace intersection by the convex hull of 14 points in 3-d: Number of halfspaces: 14 Number of non-redundant halfspaces: 14 Number of intersection points: 24 Statistics for: user_eg halfspaces | qhull H0 s Tcv Fp Number of points processed: 14 Number of hyperplanes created: 35 Number of distance tests for qhull: 59 Number of distance tests for merging: 306 Number of distance tests for checking: 214 Number of merged facets: 6 CPU seconds to compute hull (after input): 0 Output completed. Verifying that all points are below outer planes of all facets. Will make 192 distance computations. user_eg3 rbox "10 D2" "2 D2" qhull "p" rbox 10 D2 rbox 2 D2 Results of p 2 5 -0.02222276248244826 -0.4979727817680433 -0.4285431913366012 0.4745826469497594 0.3790312361708201 0.3779794437605696 0.3443122672329771 -0.1437312230875075 -0.3674659290047977 0.0001301793382784133 echo === check front ends ${d:-`date`} ================== date === check front ends Tue Jan 24 20:16:43 EST 2012 ================== qconvex - qconvex- compute the convex hull http://www.qhull.org 2012.1 2012/01/22 input (stdin): first lines: dimension and number of points (or vice-versa). other lines: point coordinates, best if one point per line comments: start with a non-numeric character options: Qt - triangulated output QJ - joggled input instead of merged facets Qc - keep coplanar points with nearest facet Qi - keep interior points with nearest facet Qhull control options: Qbk:n - scale coord k so that low bound is n QBk:n - scale coord k so that upper bound is n (QBk is 0.5) QbB - scale input to unit cube centered at the origin Qbk:0Bk:0 - remove k-th coordinate from input QJn - randomly joggle input in range [-n,n] QRn - random rotation (n=seed, n=0 time, n=-1 time/no rotate) Qs - search all points for the initial simplex QGn - good facet if visible from point n, -n for not visible QVn - good facet if it includes point n, -n if not Trace options: T4 - trace at level n, 4=all, 5=mem/gauss, -1= events Tc - check frequently during execution Ts - print statistics Tv - verify result: structure, convexity, and point inclusion Tz - send all output to stdout TFn - report summary when n or more facets created TI file - input data from file, no spaces or single quotes TO file - output results to file, may be enclosed in single quotes TPn - turn on tracing when point n added to hull TMn - turn on tracing at merge n TWn - trace merge facets when width > n TVn - stop qhull after adding point n, -n for before (see TCn) TCn - stop qhull after building cone for point n (see TVn) Precision options: Cn - radius of centrum (roundoff added). Merge facets if non-convex An - cosine of maximum angle. Merge facets if cosine > n or non-convex C-0 roundoff, A-0.99/C-0.01 pre-merge, A0.99/C0.01 post-merge Rn - randomly perturb computations by a factor of [1-n,1+n] Un - max distance below plane for a new, coplanar point Wn - min facet width for outside point (before roundoff) Output formats (may be combined; if none, produces a summary to stdout): f - facet dump G - Geomview output (see below) i - vertices incident to each facet m - Mathematica output (2-d and 3-d) n - normals with offsets o - OFF file format (dim, points and facets; Voronoi regions) p - point coordinates s - summary (stderr) More formats: Fa - area for each facet FA - compute total area and volume for option 's' Fc - count plus coplanar points for each facet use 'Qc' (default) for coplanar and 'Qi' for interior FC - centrum for each facet Fd - use cdd format for input (homogeneous with offset first) FD - use cdd format for numeric output (offset first) FF - facet dump without ridges Fi - inner plane for each facet FI - ID for each facet Fm - merge count for each facet (511 max) Fn - count plus neighboring facets for each facet FN - count plus neighboring facets for each point Fo - outer plane (or max_outside) for each facet FO - options and precision constants FP - nearest vertex for each coplanar point FQ - command used for qconvex Fs - summary: #int (8), dimension, #points, tot vertices, tot facets, for output: #vertices, #facets, #coplanar points, #non-simplicial facets #real (2), max outer plane, min vertex FS - sizes: #int (0) #real (2) tot area, tot volume Ft - triangulation with centrums for non-simplicial facets (OFF format) Fv - count plus vertices for each facet FV - average of vertices (a feasible point for 'H') Fx - extreme points (in order for 2-d) Geomview output (2-d, 3-d, and 4-d) Ga - all points as dots Gp - coplanar points and vertices as radii Gv - vertices as spheres Gi - inner planes only Gn - no planes Go - outer planes only Gc - centrums Gh - hyperplane intersections Gr - ridges GDn - drop dimension n in 3-d and 4-d output Print options: PAn - keep n largest facets by area Pdk:n - drop facet if normal[k] <= n (default 0.0) PDk:n - drop facet if normal[k] >= n Pg - print good facets (needs 'QGn' or 'QVn') PFn - keep facets whose area is at least n PG - print neighbors of good facets PMn - keep n facets with most merges Po - force output. If error, output neighborhood of facet Pp - do not report precision problems . - list of all options - - one line descriptions of all options qconvex . Qhull 2012.1 2012/01/22. Except for 'F.' and 'PG', upper-case options take an argument. incidences mathematica normals OFF_format points summary facet_dump Farea FArea_total Fcoplanars FCentrums Fd_cdd_in FD_cdd_out FFacet_xridge Finner FIDs Fmerges Fneighbors FNeigh_vertex Fouter FOptions FPoint_near FQhull Fsummary FSize Fvertices FVertex_ave Fxtremes FMaple Gvertices Gpoints Gall_points Gno_planes Ginner Gcentrums Ghyperplanes Gridges Gouter GDrop_dim PArea_keep Pdrop d0:0D0 PFacet_area_keep Pgood PGood_neighbors PMerge_keep Poutput_forced Pprecision_not QbBound 0:0.5 QbB_scale_box Qcoplanar QGood_point Qinterior QJoggle Qrandom QRotate Qsearch_1st Qtriangulate QVertex_good T4_trace Tcheck_often Tstatistics Tverify Tz_stdout TFacet_log TInput_file TPoint_trace TMerge_trace TOutput_file TWide_trace TVertex_stop TCone_stop Angle_max Centrum_size Random_dist Ucoplanar_max Wide_outside qconvex qconvex- compute the convex hull. Qhull 2012.1 2012/01/22 input (stdin): dimension, number of points, point coordinates comments start with a non-numeric character options (qconvex.htm): Qt - triangulated output QJ - joggled input instead of merged facets Tv - verify result: structure, convexity, and point inclusion . - concise list of all options - - one-line description of all options output options (subset): s - summary of results (default) i - vertices incident to each facet n - normals with offsets p - vertex coordinates (includes coplanar points if 'Qc') Fx - extreme points (convex hull vertices) FA - report total area and volume FS - compute total area and volume o - OFF format (dim, n, points, facets) G - Geomview output (2-d, 3-d, and 4-d) m - Mathematica output (2-d and 3-d) QVn - print facets that include point n, -n if not TO file- output results to file, may be enclosed in single quotes examples: rbox c D2 | qconvex s n rbox c D2 | qconvex i rbox c D2 | qconvex o rbox 1000 s | qconvex s Tv FA rbox c d D2 | qconvex s Qc Fx rbox y 1000 W0 | qconvex s n rbox y 1000 W0 | qconvex s QJ rbox d G1 D12 | qconvex QR0 FA Pp rbox c D7 | qconvex FA TF1000 rbox c D3 | qconvex s n Qt 4 12 -0 -0 -1 -0.5 -0 -0 -1 -0.5 0 -1 0 -0.5 0 -1 0 -0.5 1 -0 -0 -0.5 1 -0 -0 -0.5 -1 -0 -0 -0.5 -1 -0 -0 -0.5 0 1 -0 -0.5 0 1 -0 -0.5 -0 -0 1 -0.5 -0 -0 1 -0.5 Convex hull of 8 points in 3-d: Number of vertices: 8 Number of facets: 12 Number of triangulated facets: 6 Statistics for: rbox c D3 | qconvex s n Qt Number of points processed: 8 Number of hyperplanes created: 11 Number of distance tests for qhull: 35 Number of distance tests for merging: 108 Number of distance tests for checking: 56 Number of merged facets: 6 CPU seconds to compute hull (after input): 0 rbox c D2 | qconvex s i 4 0 2 1 0 2 3 3 1 Convex hull of 4 points in 2-d: Number of vertices: 4 Number of facets: 4 Statistics for: rbox c D2 | qconvex s i Number of points processed: 4 Number of hyperplanes created: 6 Number of distance tests for qhull: 6 CPU seconds to compute hull (after input): 0 rbox c D2 | qconvex o 2 4 4 4 -0.5 -0.5 -0.5 0.5 0.5 -0.5 0.5 0.5 2 0 2 2 1 0 2 2 3 2 3 1 rbox 1000 s | qconvex s Tv FA Convex hull of 1000 points in 3-d: Number of vertices: 1000 Number of facets: 1996 Statistics for: rbox 1000 s | qconvex s Tv FA Number of points processed: 1000 Number of hyperplanes created: 5545 Number of distance tests for qhull: 25488 CPU seconds to compute hull (after input): 0 Total facet area: 3.1201951 Total volume: 0.51650274 qhull output completed. Verifying that 1000 points are below 2.1e-015 of the nearest facet. rbox c d D2 | qconvex s Qc Fx 4 0 2 3 1 Convex hull of 8 points in 2-d: Number of vertices: 4 Number of coplanar points: 4 Number of facets: 4 Statistics for: rbox c d D2 | qconvex s Qc Fx Number of points processed: 4 Number of hyperplanes created: 6 Number of distance tests for qhull: 36 CPU seconds to compute hull (after input): 0 rbox y 1000 W0 | qconvex s n 4 4 0.2135848119563837 0.1168704340428167 0.9699086708284445 -0.09806074564261891 0.08553875579270345 -0.8316435307282575 -0.5486822022403077 -0.1234144150397865 -0.749541668500822 -0.02779445272382559 -0.6613733859014792 -0.2159556159595279 0.3120013537900506 0.9498158823230658 -0.02247097950761911 -0.02453689035981485 Convex hull of 1004 points in 3-d: Number of vertices: 4 Number of facets: 4 Statistics for: rbox y 1000 W0 | qconvex s n Number of points processed: 4 Number of hyperplanes created: 5 Number of distance tests for qhull: 11001 CPU seconds to compute hull (after input): 0 rbox y 1000 W0 | qconvex s QJ Convex hull of 1004 points in 3-d: Number of vertices: 51 Number of facets: 98 Statistics for: rbox y 1000 W0 | qconvex s QJ Number of points processed: 52 Number of hyperplanes created: 181 Number of distance tests for qhull: 6424 CPU seconds to compute hull (after input): 0 Input joggled by: 2.1e-011 rbox d G1 D12 | qconvex QR0 FA Convex hull of 24 points in 12-d: Number of vertices: 24 Number of facets: 4096 Statistics for: rbox d G1 D12 | qconvex QR0 FA QR1327454203 Number of points processed: 24 Number of hyperplanes created: 4108 Number of distance tests for qhull: 4216 Number of distance tests for merging: 121128 Number of distance tests for checking: 196656 Number of merged facets: 2036 CPU seconds to compute hull (after input): 0.109 Approximate facet area: 0.00035546337 Approximate volume: 8.5511197e-006 rbox c D6 | qconvex FA TF500 Convex hull of 64 points in 6-d: Number of vertices: 64 Number of facets: 12 Number of non-simplicial facets: 12 Statistics for: rbox c D6 | qconvex FA TF500 Number of points processed: 64 Number of hyperplanes created: 359 Number of distance tests for qhull: 2510 Number of distance tests for merging: 14115 Number of distance tests for checking: 832 Number of merged facets: 1457 CPU seconds to compute hull (after input): 0 Approximate facet area: 12 Approximate volume: 1 At 20:16:43 & 0 CPU secs, qhull has created 543 facets and merged 289. The current hull contains 91 facets and 23 vertices. There are 41 outside points. Next is point p27(v24), 0.64 above f107. At 20:16:43 & 0 CPU secs, qhull has created 1061 facets and merged 737. The current hull contains 69 facets and 33 vertices. There are 31 outside points. Next is point p22(v34), 0.52 above f610. At 20:16:43 & 0 CPU secs, qhull has created 1575 facets and merged 1230. The current hull contains 25 facets and 51 vertices. There are 13 outside points. Next is point p45(v52), 0.45 above f1476. At 20:16:43 & 0 CPU secs, qhull has created 1815 facets and merged 1457. The current hull contains 12 facets and 64 vertices. Last point was p35 Convex hull of 64 points in 6-d: Number of vertices: 64 Number of facets: 12 Number of non-simplicial facets: 12 Statistics for: rbox c D6 | qconvex FA TF500 Number of points processed: 64 Number of hyperplanes created: 359 Number of distance tests for qhull: 2510 Number of distance tests for merging: 13995 Number of distance tests for checking: 0 Number of merged facets: 1457 First post-merge with 'C3.5e-015' and 'A1.8e+308' At 20:16:43 & 0 CPU secs, qhull has created 1815 facets and merged 1457. The current hull contains 12 facets and 64 vertices. Last point was p35 Testing all coplanar points. computing area of each facet and volume of the convex hull rbox c P0 d D2 | qconvex p Fa Fc FP FI Fn FN FS Fv Fx 2 8 -0.5 -0.5 -0.5 0.5 0.5 -0.5 0.5 0.5 0 -0.5 0 0.5 -0.5 0 0.5 0 4 1 1 1 1 4 1 5 1 7 1 8 1 6 4 3 5 1 0.5 2 7 2 0.5 4 8 4 0.5 4 6 5 0.5 4 1 2 4 5 4 2 1 2 2 0 3 2 0 3 2 1 2 9 0 2 0 1 2 1 3 2 0 2 2 2 3 1 0 1 3 1 1 1 2 0 2 4 1 4 2 3 1 2 2 1 2 4 3 2 4 2 4 1 3 4 2 rbox c d D2 | qconvex s i QV0 2 0 2 1 0 Convex hull of 8 points in 2-d: Number of vertices: 4 Number of facets: 4 Number of 'good' facets: 2 Statistics for: rbox c d D2 | qconvex s i QV0 Number of points processed: 4 Number of hyperplanes created: 6 Number of distance tests for qhull: 36 CPU seconds to compute hull (after input): 0 rbox c | qconvex Q0 QH6029 qhull error: option 'Q0' is not used with this program. It may be used with qhull. While executing: | qconvex Q0 Options selected for Qhull 2012.1 2012/01/22: run-id 315181139 qvoronoi - qvoronoi- compute the Voronoi diagram http://www.qhull.org 2012.1 2012/01/22 input (stdin): first lines: dimension and number of points (or vice-versa). other lines: point coordinates, best if one point per line comments: start with a non-numeric character options: Qu - compute furthest-site Voronoi diagram Qhull control options: Qz - add point-at-infinity to Voronoi diagram Qs - search all points for the initial simplex QGn - Voronoi vertices if visible from point n, -n if not QVn - Voronoi vertices for input point n, -n if not Trace options: T4 - trace at level n, 4=all, 5=mem/gauss, -1= events Tc - check frequently during execution Ts - statistics Tv - verify result: structure, convexity, and in-circle test Tz - send all output to stdout TFn - report summary when n or more facets created TI file - input data from file, no spaces or single quotes TO file - output results to file, may be enclosed in single quotes TPn - turn on tracing when point n added to hull TMn - turn on tracing at merge n TWn - trace merge facets when width > n TVn - stop qhull after adding point n, -n for before (see TCn) TCn - stop qhull after building cone for point n (see TVn) Precision options: Cn - radius of centrum (roundoff added). Merge facets if non-convex An - cosine of maximum angle. Merge facets if cosine > n or non-convex C-0 roundoff, A-0.99/C-0.01 pre-merge, A0.99/C0.01 post-merge Rn - randomly perturb computations by a factor of [1-n,1+n] Wn - min facet width for non-coincident point (before roundoff) Output formats (may be combined; if none, produces a summary to stdout): s - summary to stderr p - Voronoi vertices o - OFF format (dim, Voronoi vertices, and Voronoi regions) i - Delaunay regions (use 'Pp' to avoid warning) f - facet dump More formats: Fc - count plus coincident points (by Voronoi vertex) Fd - use cdd format for input (homogeneous with offset first) FD - use cdd format for output (offset first) FF - facet dump without ridges Fi - separating hyperplanes for bounded Voronoi regions FI - ID for each Voronoi vertex Fm - merge count for each Voronoi vertex (511 max) Fn - count plus neighboring Voronoi vertices for each Voronoi vertex FN - count and Voronoi vertices for each Voronoi region Fo - separating hyperplanes for unbounded Voronoi regions FO - options and precision constants FP - nearest point and distance for each coincident point FQ - command used for qvoronoi Fs - summary: #int (8), dimension, #points, tot vertices, tot facets, for output: #Voronoi regions, #Voronoi vertices, #coincident points, #non-simplicial regions #real (2), max outer plane and min vertex Fv - Voronoi diagram as Voronoi vertices between adjacent input sites Fx - extreme points of Delaunay triangulation (on convex hull) Geomview options (2-d only) Ga - all points as dots Gp - coplanar points and vertices as radii Gv - vertices as spheres Gi - inner planes only Gn - no planes Go - outer planes only Gc - centrums Gh - hyperplane intersections Gr - ridges GDn - drop dimension n in 3-d and 4-d output Print options: PAn - keep n largest Voronoi vertices by 'area' Pdk:n - drop facet if normal[k] <= n (default 0.0) PDk:n - drop facet if normal[k] >= n Pg - print good Voronoi vertices (needs 'QGn' or 'QVn') PFn - keep Voronoi vertices whose 'area' is at least n PG - print neighbors of good Voronoi vertices PMn - keep n Voronoi vertices with most merges Po - force output. If error, output neighborhood of facet Pp - do not report precision problems . - list of all options - - one line descriptions of all options qvoronoi . Qhull 2012.1 2012/01/22. Except for 'F.' and 'PG', upper-case options take an argument. OFF_format p_vertices i_delaunay summary facet_dump Fcoincident Fd_cdd_in FD_cdd_out FF-dump-xridge Fi_bounded Fxtremes Fmerges Fneighbors FNeigh_region FOptions Fo_unbounded FPoint_near FQvoronoi Fsummary Fvoronoi FIDs Gvertices Gpoints Gall_points Gno_planes Ginner Gcentrums Ghyperplanes Gridges Gouter GDrop_dim PArea_keep Pdrop d0:0D0 Pgood PFacet_area_keep PGood_neighbors PMerge_keep Poutput_forced Pprecision_not QG_vertex_good Qsearch_1st Qupper_voronoi QV_point_good Qzinfinite T4_trace Tcheck_often Tstatistics Tverify Tz_stdout TFacet_log TInput_file TPoint_trace TMerge_trace TOutput_file TWide_trace TVertex_stop TCone_stop Angle_max Centrum_size Random_dist Wide_outside qvoronoi qvoronoi- compute the Voronoi diagram. Qhull 2012.1 2012/01/22 input (stdin): dimension, number of points, point coordinates comments start with a non-numeric character options (qvoronoi.htm): Qu - compute furthest-site Voronoi diagram Tv - verify result: structure, convexity, and in-circle test . - concise list of all options - - one-line description of all options output options (subset): s - summary of results (default) p - Voronoi vertices o - OFF file format (dim, Voronoi vertices, and Voronoi regions) FN - count and Voronoi vertices for each Voronoi region Fv - Voronoi diagram as Voronoi vertices between adjacent input sites Fi - separating hyperplanes for bounded regions, 'Fo' for unbounded G - Geomview output (2-d only) QVn - Voronoi vertices for input point n, -n if not TO file- output results to file, may be enclosed in single quotes examples: rbox c P0 D2 | qvoronoi s o rbox c P0 D2 | qvoronoi Fi rbox c P0 D2 | qvoronoi Fo rbox c P0 D2 | qvoronoi Fv rbox c P0 D2 | qvoronoi s Qu Fv rbox c P0 D2 | qvoronoi Qu Fo rbox c G1 d D2 | qvoronoi s p rbox c P0 D2 | qvoronoi s Fv QV0 rbox c P0 D2 | qvoronoi s o 2 5 5 1 -10.101 -10.101 0 -0.5 -0.5 0 0.5 0 0 0.5 4 4 2 1 3 3 2 0 1 3 4 0 2 3 3 0 1 3 4 0 3 Voronoi diagram by the convex hull of 5 points in 3-d: Number of Voronoi regions: 5 Number of Voronoi vertices: 4 Statistics for: rbox c P0 D2 | qvoronoi s o Number of points processed: 5 Number of hyperplanes created: 7 Number of facets in hull: 5 Number of distance tests for qhull: 8 Number of distance tests for merging: 29 Number of distance tests for checking: 30 Number of merged facets: 1 CPU seconds to compute hull (after input): 0 rbox c P0 D2 | qvoronoi Fi Tv 4 5 0 3 0.7071067811865475 -0.7071067811865475 -0.3535533905932737 5 0 1 -0.7071067811865475 -0.7071067811865475 -0.3535533905932737 5 0 2 -0.7071067811865475 0.7071067811865475 -0.3535533905932737 5 0 4 0.7071067811865475 0.7071067811865475 -0.3535533905932737 Voronoi ridge statistics 4 bounded ridges 0 max. distance of midpoint to ridge 4 bounded ridges with ok normal 2.2e-016 ave. angle to ridge 2.2e-016 max. angle to ridge Output completed. Verifying that all points are below outer planes of all facets. Will make 20 distance computations. rbox c P0 D2 | qvoronoi Fo 4 5 1 2 -1 0 -0.5 5 1 3 1 -0 -0 5 2 4 1 -0 -0 5 3 4 -1 0 0.5 rbox c P0 D2 | qvoronoi Fv 8 4 0 3 1 3 4 0 1 1 2 4 0 2 2 4 4 0 4 3 4 4 1 2 0 2 4 1 3 0 1 4 2 4 0 4 4 3 4 0 3 rbox c P0 D2 | qvoronoi s Qu Qt Fv 4 4 1 3 0 2 4 1 2 0 1 4 2 4 0 1 4 3 4 0 2 Furthest-site Voronoi vertices by the convex hull of 5 points in 3-d: Number of Voronoi regions: 5 Number of Voronoi vertices: 2 Number of triangulated facets: 1 Statistics for: rbox c P0 D2 | qvoronoi s Qu Qt Fv Number of points processed: 5 Number of hyperplanes created: 7 Number of facets in hull: 6 Number of distance tests for qhull: 8 Number of distance tests for merging: 33 Number of distance tests for checking: 30 Number of merged facets: 1 CPU seconds to compute hull (after input): 0 rbox c P0 D2 | qvoronoi Qu Fo 4 5 1 2 -0 1 0 5 1 3 1 -0 -0 5 2 4 1 -0 -0 5 3 4 -0 1 -0 rbox c G1 d D2 | qvoronoi s p 2 9 0 -1.75 -1.75 0 -0.5833333333333334 -0.5833333333333333 0 1.75 -0.5833333333333333 0.5833333333333334 1.75 0 0.5833333333333334 -0.5833333333333333 0.5833333333333334 0.5833333333333333 0 0 Voronoi diagram by the convex hull of 8 points in 3-d: Number of Voronoi regions: 8 Number of Voronoi vertices: 9 Number of non-simplicial Voronoi vertices: 1 Statistics for: rbox c G1 d D2 | qvoronoi s p Number of points processed: 8 Number of hyperplanes created: 17 Number of facets in hull: 10 Number of distance tests for qhull: 42 Number of distance tests for merging: 103 Number of distance tests for checking: 80 Number of merged facets: 3 CPU seconds to compute hull (after input): 0 rbox c G1 d D2 | qvoronoi QJ p 2 10 -2.57276422388486e-011 1.749999999802917 -2.05463598231932e-011 -1.750000000331276 0.5833333333083517 -0.5833333333052267 1.862254794815499e-011 -7.815052443180038e-011 1.750000000002628 3.498100747664324e-011 0.5833333333132078 0.5833333333796981 -0.5833333332888888 0.5833333333317835 -7.592293460589872e-011 -7.815050692933324e-011 -1.750000000049026 2.293196879294717e-011 -0.5833333333977308 -0.5833333333229861 rbox c P-0.1 P+0.1 P+0.1 D2 | qvoronoi s Fc FP FQ Fn FN 4 0 1 1 0 0 1 2 1 8 0 rbox c P-0.1 P+0.1 P+0.1 D2 | qvoronoi s Fc FP FQ Fn FN 4 3 -1 2 3 3 -1 2 3 4 -1 0 1 3 4 0 -1 2 1 7 3 3 2 0 1 1 3 3 1 2 3 0 -1 2 3 3 -1 0 3 1 -1 2 3 1 -1 3 Voronoi diagram by the convex hull of 7 points in 3-d: Number of Voronoi regions: 6 Number of nearly incident points: 1 Number of Voronoi vertices: 4 Number of non-simplicial Voronoi vertices: 2 Statistics for: rbox c P-0.1 P+0.1 P+0.1 D2 | qvoronoi s Fc FP FQ Fn FN Number of points processed: 6 Number of hyperplanes created: 8 Number of facets in hull: 5 Number of distance tests for qhull: 33 Number of distance tests for merging: 49 Number of distance tests for checking: 43 Number of merged facets: 3 CPU seconds to compute hull (after input): 0 rbox P0 c D2 | qvoronoi s Fv QV0 4 4 0 3 1 3 4 0 1 1 2 4 0 2 2 4 4 0 4 3 4 Voronoi diagram by the convex hull of 5 points in 3-d: Number of Voronoi regions: 5 Number of 'good' Voronoi vertices: 4 Statistics for: rbox P0 c D2 | qvoronoi s Fv QV0 Number of points processed: 5 Number of hyperplanes created: 7 Number of facets in hull: 5 Number of distance tests for qhull: 8 Number of distance tests for merging: 29 Number of distance tests for checking: 30 Number of merged facets: 1 CPU seconds to compute hull (after input): 0 qdelaunay - qdelaunay- compute the Delaunay triangulation http://www.qhull.org 2012.1 2012/01/22 input (stdin): first lines: dimension and number of points (or vice-versa). other lines: point coordinates, best if one point per line comments: start with a non-numeric character options: Qu - compute furthest-site Delaunay triangulation Qt - triangulated output QJ - joggled input instead of merged facets Qhull control options: QJn - randomly joggle input in range [-n,n] Qs - search all points for the initial simplex Qz - add point-at-infinity to Delaunay triangulation QGn - print Delaunay region if visible from point n, -n if not QVn - print Delaunay regions that include point n, -n if not Trace options: T4 - trace at level n, 4=all, 5=mem/gauss, -1= events Tc - check frequently during execution Ts - print statistics Tv - verify result: structure, convexity, and in-circle test Tz - send all output to stdout TFn - report summary when n or more facets created TI file - input data from file, no spaces or single quotes TO file - output results to file, may be enclosed in single quotes TPn - turn on tracing when point n added to hull TMn - turn on tracing at merge n TWn - trace merge facets when width > n TVn - stop qhull after adding point n, -n for before (see TCn) TCn - stop qhull after building cone for point n (see TVn) Precision options: Cn - radius of centrum (roundoff added). Merge facets if non-convex An - cosine of maximum angle. Merge facets if cosine > n or non-convex C-0 roundoff, A-0.99/C-0.01 pre-merge, A0.99/C0.01 post-merge Rn - randomly perturb computations by a factor of [1-n,1+n] Wn - min facet width for outside point (before roundoff) Output formats (may be combined; if none, produces a summary to stdout): f - facet dump G - Geomview output (see below) i - vertices incident to each Delaunay region m - Mathematica output (2-d only, lifted to a paraboloid) o - OFF format (dim, points, and facets as a paraboloid) p - point coordinates (lifted to a paraboloid) s - summary (stderr) More formats: Fa - area for each Delaunay region FA - compute total area for option 's' Fc - count plus coincident points for each Delaunay region Fd - use cdd format for input (homogeneous with offset first) FD - use cdd format for numeric output (offset first) FF - facet dump without ridges FI - ID of each Delaunay region Fm - merge count for each Delaunay region (511 max) FM - Maple output (2-d only, lifted to a paraboloid) Fn - count plus neighboring region for each Delaunay region FN - count plus neighboring region for each point FO - options and precision constants FP - nearest point and distance for each coincident point FQ - command used for qdelaunay Fs - summary: #int (8), dimension, #points, tot vertices, tot facets, for output: #vertices, #Delaunay regions, #coincident points, #non-simplicial regions #real (2), max outer plane, min vertex FS - sizes: #int (0) #real (2), tot area, 0 Fv - count plus vertices for each Delaunay region Fx - extreme points of Delaunay triangulation (on convex hull) Geomview options (2-d and 3-d) Ga - all points as dots Gp - coplanar points and vertices as radii Gv - vertices as spheres Gi - inner planes only Gn - no planes Go - outer planes only Gc - centrums Gh - hyperplane intersections Gr - ridges GDn - drop dimension n in 3-d and 4-d output Gt - transparent outer ridges to view 3-d Delaunay Print options: PAn - keep n largest Delaunay regions by area Pdk:n - drop facet if normal[k] <= n (default 0.0) PDk:n - drop facet if normal[k] >= n Pg - print good Delaunay regions (needs 'QGn' or 'QVn') PFn - keep Delaunay regions whose area is at least n PG - print neighbors of good regions (needs 'QGn' or 'QVn') PMn - keep n Delaunay regions with most merges Po - force output. If error, output neighborhood of facet Pp - do not report precision problems . - list of all options - - one line descriptions of all options qdelaunay . Qhull 2012.1 2012/01/22. Except for 'F.' and 'PG', upper-case options take an argument. incidences mathematica OFF_format points_lifted summary facet_dump Farea FArea_total Fcoincident Fd_cdd_in FD_cdd_out FF_dump_xridge FIDs Fmerges Fneighbors FNeigh_vertex FOptions FPoint_near FQdelaun Fsummary FSize Fvertices Fxtremes FMaple Gvertices Gpoints Gall_points Gno_planes Ginner Gcentrums Ghyperplanes Gridges Gouter GDrop_dim Gtransparent PArea_keep Pdrop d0:0D0 Pgood PFacet_area_keep PGood_neighbors PMerge_keep Poutput_forced Pprecision_not QGood_point QJoggle Qsearch_1st Qtriangulate QupperDelaunay QVertex_good Qzinfinite T4_trace Tcheck_often Tstatistics Tverify Tz_stdout TFacet_log TInput_file TPoint_trace TMerge_trace TOutput_file TWide_trace TVertex_stop TCone_stop Angle_max Centrum_size Random_dist Wide_outside qdelaunay qdelaunay- compute the Delaunay triangulation. Qhull 2012.1 2012/01/22 input (stdin): dimension, number of points, point coordinates comments start with a non-numeric character options (qdelaun.htm): Qu - furthest-site Delaunay triangulation Qt - triangulated output QJ - joggled input instead of merged facets Tv - verify result: structure, convexity, and in-circle test . - concise list of all options - - one-line description of all options output options (subset): s - summary of results (default) i - vertices incident to each Delaunay region Fx - extreme points (vertices of the convex hull) o - OFF format (shows the points lifted to a paraboloid) G - Geomview output (2-d and 3-d points lifted to a paraboloid) m - Mathematica output (2-d inputs lifted to a paraboloid) QVn - print Delaunay regions that include point n, -n if not TO file- output results to file, may be enclosed in single quotes examples: rbox c P0 D2 | qdelaunay s o rbox c P0 D2 | qdelaunay i rbox c P0 D2 | qdelaunay Fv rbox c P0 D2 | qdelaunay s Qu Fv rbox c G1 d D2 | qdelaunay s i rbox c G1 d D2 | qdelaunay Qt rbox M3,4 z 100 D2 | qdelaunay s rbox M3,4 z 100 D2 | qdelaunay s Qt rbox c P0 D2 | qdelaunay s o 3 5 4 6 0 0 0 -0.5 -0.5 1 -0.5 0.5 1 0.5 -0.5 1 0.5 0.5 1 3 3 0 1 3 0 2 1 3 4 0 3 3 0 4 2 Delaunay triangulation by the convex hull of 5 points in 3-d: Number of input sites: 5 Number of Delaunay regions: 4 Statistics for: rbox c P0 D2 | qdelaunay s o Number of points processed: 5 Number of hyperplanes created: 7 Number of facets in hull: 5 Number of distance tests for qhull: 8 Number of distance tests for merging: 29 Number of distance tests for checking: 30 Number of merged facets: 1 CPU seconds to compute hull (after input): 0 rbox c P0 D2 | qdelaunay i 4 3 0 1 0 2 1 4 0 3 0 4 2 rbox c P0 D2 | qdelaunay Fv 4 3 0 3 1 3 0 2 1 3 4 0 3 3 4 0 2 rbox c P0 D2 | qdelaunay s Qu Qt Fv 2 3 4 2 1 3 4 3 1 Furthest-site Delaunay triangulation by the convex hull of 5 points in 3-d: Number of input sites: 5 Number of Delaunay regions: 2 Number of triangulated facets: 1 Statistics for: rbox c P0 D2 | qdelaunay s Qu Qt Fv Number of points processed: 5 Number of hyperplanes created: 7 Number of facets in hull: 6 Number of distance tests for qhull: 8 Number of distance tests for merging: 33 Number of distance tests for checking: 30 Number of merged facets: 1 CPU seconds to compute hull (after input): 0 rbox c G1 d D2 | qdelaunay s i 9 2 4 0 6 1 0 4 6 0 5 3 1 6 5 1 3 7 2 7 4 2 5 7 3 4 7 5 6 Delaunay triangulation by the convex hull of 8 points in 3-d: Number of input sites: 8 Number of Delaunay regions: 9 Number of non-simplicial Delaunay regions: 1 Statistics for: rbox c G1 d D2 | qdelaunay s i Number of points processed: 8 Number of hyperplanes created: 17 Number of facets in hull: 10 Number of distance tests for qhull: 42 Number of distance tests for merging: 103 Number of distance tests for checking: 80 Number of merged facets: 3 CPU seconds to compute hull (after input): 0 rbox c G1 d D2 | qhull d Qbb Ft 2 9 12 14 -1 -1 -1 1 1 -1 1 1 0 -0.5 0 0.5 -0.5 0 0.5 0 0 0 3 2 4 0 3 6 1 0 3 4 6 0 3 5 3 1 3 6 5 1 3 3 7 2 3 7 4 2 3 5 7 3 3 8 5 6 3 8 6 4 3 8 4 7 3 8 7 5 rbox c G1 d D2 | qhull d Qbb QJ s Ft 2 8 10 15 -1.000000000061343 -0.999999999957446 -0.9999999999945448 0.9999999999532114 1.000000000029778 -0.9999999999701502 0.9999999999806051 1.000000000003233 -7.748592400792811e-011 -0.5000000000743411 2.849349704487493e-011 0.49999999991804 -0.5000000000721135 -1.37371989142159e-011 0.5000000000148132 7.166044474310069e-011 3 1 5 3 3 2 4 0 3 7 4 2 3 4 7 5 3 3 7 2 3 5 7 3 3 1 6 5 3 6 4 5 3 6 1 0 3 4 6 0 Delaunay triangulation by the convex hull of 8 points in 3-d: Number of input sites: 8 Number of Delaunay regions: 10 Statistics for: rbox c G1 d D2 | qhull d Qbb QJ s Ft Number of points processed: 8 Number of hyperplanes created: 20 Number of facets in hull: 12 Number of distance tests for qhull: 32 CPU seconds to compute hull (after input): 0 Input joggled by: 8.3e-011 rbox M3,4 z 100 D2 | qdelaunay s Delaunay triangulation by the convex hull of 100 points in 3-d: Number of input sites: 100 Number of Delaunay regions: 81 Number of non-simplicial Delaunay regions: 81 Statistics for: rbox M3,4 z 100 D2 | qdelaunay s Number of points processed: 100 Number of hyperplanes created: 262 Number of facets in hull: 86 Number of distance tests for qhull: 1652 Number of distance tests for merging: 2778 Number of distance tests for checking: 1348 Number of merged facets: 152 CPU seconds to compute hull (after input): 0 rbox c P-0.1 P+0.1 P+0.1 D2 | qdelaunay s Fx Fa Fc FP FQ Fn FN 4 4 3 6 5 4 0.2 0.2 0.3 0.3 4 0 1 1 0 0 1 2 1 8 0 rbox c P-0.1 P+0.1 P+0.1 D2 | qdelaunay s Fx Fa Fc FP FQ Fn FN 4 3 -1 2 3 3 -1 2 3 4 -1 0 1 3 4 0 -1 2 1 7 3 3 2 0 1 1 3 3 1 2 3 0 -1 2 3 3 -1 0 3 1 -1 2 3 1 -1 3 Delaunay triangulation by the convex hull of 7 points in 3-d: Number of input sites: 6 Number of nearly incident points: 1 Number of Delaunay regions: 4 Number of non-simplicial Delaunay regions: 2 Statistics for: rbox c P-0.1 P+0.1 P+0.1 D2 | qdelaunay s Fx Fa Fc FP FQ Fn FN Number of points processed: 6 Number of hyperplanes created: 8 Number of facets in hull: 5 Number of distance tests for qhull: 33 Number of distance tests for merging: 49 Number of distance tests for checking: 42 Number of merged facets: 3 CPU seconds to compute hull (after input): 0 Approximate facet area: 1 rbox P0 P0 c D2 | qdelaunay s FP QV0 1 0 1 2 0 Delaunay triangulation by the convex hull of 6 points in 3-d: Number of input sites: 5 Number of nearly incident points: 1 Number of 'good' Delaunay regions: 4 Statistics for: rbox P0 P0 c D2 | qdelaunay s FP QV0 Number of points processed: 5 Number of hyperplanes created: 7 Number of facets in hull: 5 Number of distance tests for qhull: 20 Number of distance tests for merging: 29 Number of distance tests for checking: 36 Number of merged facets: 1 CPU seconds to compute hull (after input): 0 qhalf - qhalf- compute the intersection of halfspaces about a point http://www.qhull.org 2012.1 2012/01/22 input (stdin): optional interior point: dimension, 1, coordinates first lines: dimension+1 and number of halfspaces other lines: halfspace coefficients followed by offset comments: start with a non-numeric character options: Hn,n - specify coordinates of interior point Qt - triangulated output QJ - joggled input instead of merged facets Qc - keep coplanar halfspaces Qi - keep other redundant halfspaces Qhull control options: QJn - randomly joggle input in range [-n,n] Qbk:0Bk:0 - remove k-th coordinate from input Qs - search all halfspaces for the initial simplex QGn - print intersection if visible to halfspace n, -n for not QVn - print intersections for halfspace n, -n if not Trace options: T4 - trace at level n, 4=all, 5=mem/gauss, -1= events Tc - check frequently during execution Ts - print statistics Tv - verify result: structure, convexity, and redundancy Tz - send all output to stdout TFn - report summary when n or more facets created TI file - input data from file, no spaces or single quotes TO file - output results to file, may be enclosed in single quotes TPn - turn on tracing when halfspace n added to intersection TMn - turn on tracing at merge n TWn - trace merge facets when width > n TVn - stop qhull after adding halfspace n, -n for before (see TCn) TCn - stop qhull after building cone for halfspace n (see TVn) Precision options: Cn - radius of centrum (roundoff added). Merge facets if non-convex An - cosine of maximum angle. Merge facets if cosine > n or non-convex C-0 roundoff, A-0.99/C-0.01 pre-merge, A0.99/C0.01 post-merge Rn - randomly perturb computations by a factor of [1-n,1+n] Un - max distance below plane for a new, coplanar halfspace Wn - min facet width for outside halfspace (before roundoff) Output formats (may be combined; if none, produces a summary to stdout): f - facet dump G - Geomview output (dual convex hull) i - non-redundant halfspaces incident to each intersection m - Mathematica output (dual convex hull) o - OFF format (dual convex hull: dimension, points, and facets) p - vertex coordinates of dual convex hull (coplanars if 'Qc' or 'Qi') s - summary (stderr) More formats: Fc - count plus redundant halfspaces for each intersection - Qc (default) for coplanar and Qi for other redundant Fd - use cdd format for input (homogeneous with offset first) FF - facet dump without ridges FI - ID of each intersection Fm - merge count for each intersection (511 max) FM - Maple output (dual convex hull) Fn - count plus neighboring intersections for each intersection FN - count plus intersections for each non-redundant halfspace FO - options and precision constants Fp - dim, count, and intersection coordinates FP - nearest halfspace and distance for each redundant halfspace FQ - command used for qhalf Fs - summary: #int (8), dim, #halfspaces, #non-redundant, #intersections for output: #non-redundant, #intersections, #coplanar halfspaces, #non-simplicial intersections #real (2), max outer plane, min vertex Fv - count plus non-redundant halfspaces for each intersection Fx - non-redundant halfspaces Geomview output (2-d, 3-d and 4-d; dual convex hull) Ga - all points (i.e., transformed halfspaces) as dots Gp - coplanar points and vertices as radii Gv - vertices (i.e., non-redundant halfspaces) as spheres Gi - inner planes (i.e., halfspace intersections) only Gn - no planes Go - outer planes only Gc - centrums Gh - hyperplane intersections Gr - ridges GDn - drop dimension n in 3-d and 4-d output Print options: PAn - keep n largest facets (i.e., intersections) by area Pdk:n- drop facet if normal[k] <= n (default 0.0) PDk:n- drop facet if normal[k] >= n Pg - print good facets (needs 'QGn' or 'QVn') PFn - keep facets whose area is at least n PG - print neighbors of good facets PMn - keep n facets with most merges Po - force output. If error, output neighborhood of facet Pp - do not report precision problems . - list of all options - - one line descriptions of all options qhalf . Qhull 2012.1 2012/01/22. Except for 'F.' and 'PG', upper_case options take an argument. incidences Geomview mathematica OFF_format point_dual summary facet_dump Fc_redundant Fd_cdd_in FF_dump_xridge FIDs Fmerges Fneighbors FN_intersect FOptions Fp_coordinates FP_nearest FQhalf Fsummary Fv_halfspace FMaple Fx_non_redundant Gvertices Gpoints Gall_points Gno_planes Ginner Gcentrums Ghyperplanes Gridges Gouter GDrop_dim PArea_keep Pdrop d0:0D0 Pgood PFacet_area_keep PGood_neighbors PMerge_keep Poutput_forced Pprecision_not Qbk:0Bk:0_drop Qcoplanar QG_half_good Qi_redundant QJoggle Qsearch_1st Qtriangulate QVertex_good T4_trace Tcheck_often Tstatistics Tverify Tz_stdout TFacet_log TInput_file TPoint_trace TMerge_trace TOutput_file TWide_trace TVertex_stop TCone_stop Angle_max Centrum_size Random_dist Ucoplanar_max Wide_outside qhalf qhalf- halfspace intersection about a point. Qhull 2012.1 2012/01/22 input (stdin): [dim, 1, interior point], dim+1, n, coefficients+offset comments start with a non-numeric character options (qhalf.htm): Hn,n - specify coordinates of interior point Qt - triangulated output QJ - joggled input instead of merged facets Tv - verify result: structure, convexity, and redundancy . - concise list of all options - - one-line description of all options output options (subset): s - summary of results (default) Fp - intersection coordinates Fv - non-redundant halfspaces incident to each intersection Fx - non-redundant halfspaces o - OFF file format (dual convex hull) G - Geomview output (dual convex hull) m - Mathematica output (dual convex hull) QVn - print intersections for halfspace n, -n if not TO file - output results to file, may be enclosed in single quotes examples: rbox d | qconvex FQ n | qhalf s H0,0,0 Fp rbox c | qconvex FQ FV n | qhalf s i rbox c | qconvex FQ FV n | qhalf s o rbox d | qhull FQ n | qhalf s Qt H0,0,0 Fp 3 12 0 0 0.5 0 0 0.5 0 0.5 0 0 0.5 0 -0.5 0 0 -0.5 0 0 0.5 0 0 0.5 0 0 0 -0.5 0 0 -0.5 0 0 0 -0.5 0 0 -0.5 Halfspace intersection by the convex hull of 8 points in 3-d: Number of halfspaces: 8 Number of non-redundant halfspaces: 8 Number of intersection points: 12 Number of triangulated facets: 6 Statistics for: rbox d | qhull FQ n | qhalf s Qt H0,0,0 Fp Number of points processed: 8 Number of hyperplanes created: 11 Number of distance tests for qhull: 33 Number of distance tests for merging: 119 Number of distance tests for checking: 56 Number of merged facets: 7 CPU seconds to compute hull (after input): 0 rbox c | qhull FQ FV n | qhalf s i 8 4 5 3 5 4 2 0 4 3 4 0 2 1 5 2 5 1 3 1 0 3 0 1 2 Halfspace intersection by the convex hull of 6 points in 3-d: Number of halfspaces: 6 Number of non-redundant halfspaces: 6 Number of intersection points: 8 Statistics for: rbox c | qhull FQ FV n | qhalf s i Number of points processed: 6 Number of hyperplanes created: 11 Number of distance tests for qhull: 11 Number of distance tests for merging: 45 Number of distance tests for checking: 54 Number of merged facets: 1 CPU seconds to compute hull (after input): 0 rbox c | qhull FQ FV n | qhalf o 3 6 8 12 -0 -0 -2 0 -2 0 2 -0 -0 -2 -0 -0 0 2 -0 -0 -0 2 3 4 5 3 3 5 4 2 3 0 4 3 3 4 0 2 3 1 5 2 3 5 1 3 3 1 0 3 3 0 1 2 rbox d D2 | qhull FQ n | qhalf s H0 Fc FP Fn FN FQ Fv Fx 4 0 0 0 0 0 4 2 1 2 2 0 3 2 0 3 2 1 2 4 2 0 1 2 0 2 2 1 3 2 2 3 rbox d D2 | qhull FQ n | qhalf s H0 Fc FP Fn FN FQ Fv Fx 4 2 1 0 2 2 0 2 3 1 2 3 2 4 1 0 2 3 Halfspace intersection by the convex hull of 4 points in 2-d: Number of halfspaces: 4 Number of non-redundant halfspaces: 4 Number of intersection points: 4 Statistics for: rbox d D2 | qhull FQ n | qhalf s H0 Fc FP Fn FN FQ Fv Fx Number of points processed: 4 Number of hyperplanes created: 6 Number of distance tests for qhull: 6 CPU seconds to compute hull (after input): 0 echo === check quality of Qhull for ${d:-`hostname`} ${d:-`date`} hostname date === check quality of Qhull for ispy Tue Jan 24 20:16:44 EST 2012 rbox 1000 W0 | qhull QR2 QJ s Fs Tv 10 3 1000 144 284 144 284 0 0 33 0 2 5.045982607091333e-011 -5.045982607091333e-011 Convex hull of 1000 points in 3-d: Number of vertices: 144 Number of facets: 284 Statistics for: rbox 1000 W0 | qhull QR2 QJ s Fs Tv QR2 Number of points processed: 171 Number of hyperplanes created: 1233 Number of distance tests for qhull: 33562 CPU seconds to compute hull (after input): 0 After 1 retries, input joggled by: 2.9e-011 Output completed. Verifying that all points are below 2.9e-015 of all facets. Will make 284000 distance computations. rbox 1000 W0 | qhull QR2 s Fs Tv 10 3 1000 84 98 84 98 0 6 13 0 2 1.942124858599573e-015 -1.241679291552168e-015 Convex hull of 1000 points in 3-d: Number of vertices: 84 Number of facets: 98 Number of non-simplicial facets: 6 Statistics for: rbox 1000 W0 | qhull QR2 s Fs Tv QR2 Number of points processed: 97 Number of hyperplanes created: 299 Number of distance tests for qhull: 18051 Number of distance tests for merging: 3325 Number of distance tests for checking: 15397 Number of merged facets: 92 CPU seconds to compute hull (after input): 0.015 Output completed. Verifying that all points are below outer planes of all facets. Will make 98000 distance computations. rbox 1000 s | qhull C0.02 Qc Tv Convex hull of 1000 points in 3-d: Number of vertices: 114 Number of coplanar points: 886 Number of facets: 60 Number of non-simplicial facets: 60 Statistics for: rbox 1000 s | qhull C0.02 Qc Tv Number of points processed: 1000 Number of hyperplanes created: 5545 Number of distance tests for qhull: 83858 Number of distance tests for merging: 82226 Number of distance tests for checking: 7929 Number of merged facets: 1936 CPU seconds to compute hull (after input): 0.015 Maximum distance of vertex below facet: -0.072 (1.2x) Output completed. Verifying that all points are below outer planes of all facets. Will make 60000 distance computations. rbox 500 s D4 | qhull C0.01 Qc Tv Convex hull of 500 points in 4-d: Number of vertices: 467 Number of coplanar points: 33 Number of facets: 357 Number of non-simplicial facets: 343 Statistics for: rbox 500 s D4 | qhull C0.01 Qc Tv Number of points processed: 500 Number of hyperplanes created: 11284 Number of distance tests for qhull: 41395 Number of distance tests for merging: 162691 Number of distance tests for checking: 20813 Number of merged facets: 2809 CPU seconds to compute hull (after input): 0.031 Maximum distance of vertex below facet: -0.073 (1.8x) Output completed. Verifying that all points are below outer planes of all facets. Will make 178500 distance computations. rbox 1000 s | qhull C-0.02 Qc Tv Convex hull of 1000 points in 3-d: Number of vertices: 47 Number of coplanar points: 953 Number of facets: 47 Number of non-simplicial facets: 35 Statistics for: rbox 1000 s | qhull C-0.02 Qc Tv Number of points processed: 50 Number of hyperplanes created: 199 Number of distance tests for qhull: 52519 Number of distance tests for merging: 2966 Number of distance tests for checking: 24231 Number of merged facets: 98 CPU seconds to compute hull (after input): 0.015 Maximum distance of point above facet: 0.065 (1.1x) Maximum distance of vertex below facet: -0.062 (1.0x) Output completed. Verifying that all points are below outer planes of all facets. Will make 47000 distance computations. rbox 1000 s D4 | qhull C-0.01 Qc Tv Convex hull of 1000 points in 4-d: Number of vertices: 117 Number of coplanar points: 883 Number of facets: 232 Number of non-simplicial facets: 149 Statistics for: rbox 1000 s D4 | qhull C-0.01 Qc Tv Number of points processed: 117 Number of hyperplanes created: 1232 Number of distance tests for qhull: 372627 Number of distance tests for merging: 31334 Number of distance tests for checking: 122166 Number of merged facets: 1167 CPU seconds to compute hull (after input): 0.031 Maximum distance of point above facet: 0.062 (1.5x) Maximum distance of vertex below facet: -0.064 (1.6x) Output completed. Verifying that all points are below outer planes of all facets. Will make 232000 distance computations. rbox 200 s D5 | qhull C-0.01 Qx Qc Tv Convex hull of 200 points in 5-d: Number of vertices: 160 Number of coplanar points: 40 Number of facets: 388 Number of non-simplicial facets: 342 Statistics for: rbox 200 s D5 | qhull C-0.01 Qx Qc Tv Number of points processed: 160 Number of hyperplanes created: 4522 Number of distance tests for qhull: 235312 Number of distance tests for merging: 143132 Number of distance tests for checking: 46266 Number of merged facets: 5940 CPU seconds to compute hull (after input): 0.062 Maximum distance of point above facet: 0.059 (1.2x) Maximum distance of vertex below facet: -0.11 (2.1x) QH7076 qhull input warning: exact merge ('Qx'). Verify may report that a point is outside of a facet. See qh-optq.htm#Qx Output completed. Verifying that all points are below outer planes of all facets. Will make 77600 distance computations. rbox 100 s D6 | qhull C-0.001 Qx Qc Tv Convex hull of 100 points in 6-d: Number of vertices: 100 Number of facets: 4465 Number of non-simplicial facets: 809 Statistics for: rbox 100 s D6 | qhull C-0.001 Qx Qc Tv Number of points processed: 100 Number of hyperplanes created: 20175 Number of distance tests for qhull: 33383 Number of distance tests for merging: 299744 Number of distance tests for checking: 66106 Number of merged facets: 3948 CPU seconds to compute hull (after input): 0.125 Maximum distance of point above facet: 0.0029 (0.5x) Maximum distance of vertex below facet: -0.014 (2.4x) QH7076 qhull input warning: exact merge ('Qx'). Verify may report that a point is outside of a facet. See qh-optq.htm#Qx Output completed. Verifying that all points are below outer planes of all facets. Will make 446500 distance computations. rbox 1000 W1e-4 | qhull C-1e-6 Qc Tv Convex hull of 1000 points in 3-d: Number of vertices: 144 Number of coplanar points: 75 Number of facets: 243 Number of non-simplicial facets: 26 Statistics for: rbox 1000 W1e-4 | qhull C-1e-6 Qc Tv Number of points processed: 185 Number of hyperplanes created: 939 Number of distance tests for qhull: 42000 Number of distance tests for merging: 8652 Number of distance tests for checking: 5684 Number of merged facets: 145 CPU seconds to compute hull (after input): 0 Maximum distance of point above facet: 1.3e-006 (0.4x) Maximum distance of vertex below facet: -3.2e-006 (1.1x) Output completed. Verifying that all points are below outer planes of all facets. Will make 243000 distance computations. rbox 1000 W5e-4 D4 | qhull C-1e-5 Qc Tv Convex hull of 1000 points in 4-d: Number of vertices: 290 Number of coplanar points: 433 Number of facets: 1296 Number of non-simplicial facets: 154 Statistics for: rbox 1000 W5e-4 D4 | qhull C-1e-5 Qc Tv Number of points processed: 368 Number of hyperplanes created: 6238 Number of distance tests for qhull: 182095 Number of distance tests for merging: 75580 Number of distance tests for checking: 52937 Number of merged facets: 1353 CPU seconds to compute hull (after input): 0.031 Maximum distance of point above facet: 9.1e-005 (2.3x) Maximum distance of vertex below facet: -0.00012 (2.9x) Output completed. Verifying that all points are below outer planes of all facets. Will make 1296000 distance computations. rbox 400 W1e-3 D5 | qhull C-1e-5 Qx Qc Tv Convex hull of 400 points in 5-d: Number of vertices: 305 Number of coplanar points: 35 Number of facets: 5552 Number of non-simplicial facets: 281 Statistics for: rbox 400 W1e-3 D5 | qhull C-1e-5 Qx Qc Tv Number of points processed: 336 Number of hyperplanes created: 24527 Number of distance tests for qhull: 251847 Number of distance tests for merging: 277585 Number of distance tests for checking: 61531 Number of merged facets: 1482 CPU seconds to compute hull (after input): 0.093 Maximum distance of point above facet: 5.5e-005 (1.1x) Maximum distance of vertex below facet: -0.0001 (2.1x) QH7076 qhull input warning: exact merge ('Qx'). Verify may report that a point is outside of a facet. See qh-optq.htm#Qx Output completed. Verifying that all points are below outer planes of all facets. Will make 2220800 distance computations. echo === check input format etc. ${d:-`date`} date === check input format etc. Tue Jan 24 20:16:45 EST 2012 qhull <count): 16->1 24->13 88->4 size in bytes: merge 24 ridge 16 vertex 24 facet 88 normal 24 ridge vertices 16 facet vertices or neighbors 20 Output completed. Verifying that all points are below outer planes of all facets. Will make 142000 distance computations. rbox 100 D3 | qhull T8 Tz TO q_test.log.1 tail -n -10 q_test.log.1 qh_mem 00450170 n 1022 free short: 88 bytes (tot 8984 cnt 228) qh_mem 004501C8 n 1023 free short: 88 bytes (tot 8896 cnt 227) qh_mem 00450220 n 1024 free short: 88 bytes (tot 8808 cnt 226) qh_mem 00450278 n 1025 free short: 88 bytes (tot 8720 cnt 225) qh_mem 00362CC8 n 30 free long: 96 bytes (tot 0 cnt 0) qh_mem 004502D0 n 1026 free short: 16 bytes (tot 8704 cnt 224) qh_mem 00450050 n 1027 free short: 88 bytes (tot 8616 cnt 223) qh_mem 004500A8 n 1028 free short: 88 bytes (tot 8528 cnt 222) qh_mem 00450100 n 1029 free short: 88 bytes (tot 8440 cnt 221) qh_freebuffers: finished rm q_test.log.1 rbox 100 s D3 | qhull TcvV-2 At a premature exit due to 'TVn', 'TCn', 'TRn', or precision error with 'QJn'. Convex hull of 100 points in 3-d: Number of vertices: 78 Number of facets: 152 Statistics for: rbox 100 s D3 | qhull TcvV-2 Number of points processed: 78 Number of hyperplanes created: 390 Number of distance tests for qhull: 1489 CPU seconds to compute hull (after input): 0 rbox 100 s D3 | qhull TcvC2 At a premature exit due to 'TVn', 'TCn', 'TRn', or precision error with 'QJn'. Convex hull of 100 points in 3-d: Number of vertices: 79 Number of facets: 154 Statistics for: rbox 100 s D3 | qhull TcvC2 Number of points processed: 79 Number of hyperplanes created: 395 Number of distance tests for qhull: 1496 CPU seconds to compute hull (after input): 0 rbox 100 s D3 | qhull TcvV2 At a premature exit due to 'TVn', 'TCn', 'TRn', or precision error with 'QJn'. Convex hull of 100 points in 3-d: Number of vertices: 79 Number of facets: 154 Statistics for: rbox 100 s D3 | qhull TcvV2 Number of points processed: 79 Number of hyperplanes created: 395 Number of distance tests for qhull: 1496 CPU seconds to compute hull (after input): 0 rbox 100 s D3 | qhull T1cvV2P2 At a premature exit due to 'TVn', 'TCn', 'TRn', or precision error with 'QJn'. Convex hull of 100 points in 3-d: Number of vertices: 79 Number of facets: 154 Statistics for: rbox 100 s D3 | qhull T1cvV2P2 Number of points processed: 79 Number of hyperplanes created: 395 Number of distance tests for qhull: 1496 CPU seconds to compute hull (after input): 0 qh_readpoints: read in 100 3-dimensional points qh_initqhull_globals: for rbox 100 s D3 | qhull T1cvV2P2 Trace level 1 for rbox 100 s D3 | qhull T1cvV2P2 Options selected for Qhull 2012.1 2012/01/22: run-id 315332402 Tcheck-frequently Tverify TV-stop-after-point 2 Trace-point 2 _pre-merge _zero-centrum _max-width 0.94 Error-roundoff 6.7e-016 _one-merge 4.7e-015 _near-inside 2.3e-014 Visible-distance 1.3e-015 U-coplanar-distance 1.3e-015 Width-outside 2.7e-015 _wide-facet 8.1e-015 qh_findbest: point p2 starting at f7 isnewfacets? 1, unless 0 exit if > 2.7e-015 testhorizon? 1 noupper? 0 Last point added was p41. Last merge was #0. max_outside 5.6e-017 qh_findbest: point p2 starting at f15 isnewfacets? 1, unless 0 exit if > 2.7e-015 testhorizon? 1 noupper? 0 Last point added was p52. Last merge was #0. max_outside 1.1e-016 qh_findbest: point p2 starting at f37 isnewfacets? 1, unless 0 exit if > 2.7e-015 testhorizon? 1 noupper? 0 Last point added was p73. Last merge was #0. max_outside 1.1e-016 qh_findbest: point p2 starting at f52 isnewfacets? 1, unless 0 exit if > 2.7e-015 testhorizon? 1 noupper? 0 Last point added was p87. Last merge was #0. max_outside 1.1e-016 qh_findbest: point p2 starting at f72 isnewfacets? 1, unless 0 exit if > 2.7e-015 testhorizon? 1 noupper? 0 Last point added was p76. Last merge was #0. max_outside 1.1e-016 qh_findbest: point p2 starting at f120 isnewfacets? 1, unless 0 exit if > 2.7e-015 testhorizon? 1 noupper? 0 Last point added was p84. Last merge was #0. max_outside 1.7e-016 qh_findbest: point p2 starting at f211 isnewfacets? 1, unless 0 exit if > 2.7e-015 testhorizon? 1 noupper? 0 Last point added was p10. Last merge was #0. max_outside 1.7e-016 qh_findbest: point p2 starting at f289 isnewfacets? 1, unless 0 exit if > 2.7e-015 testhorizon? 1 noupper? 0 Last point added was p6. Last merge was #0. max_outside 1.7e-016 qh_addpoint: add p2(v79) to hull of 152 facets(0.014 above f288) and 22 outside at 0 CPU secs. Previous was p56. qh_findhorizon: find horizon for point p2 facet f288 qh_findhorizon: 5 horizon facets(good 5), 3 visible(good 3), 0 coplanar qh_makenewfacets: created 5 new facets from point p2 to horizon qh_matchnewfacets: match neighbors for new facets. qh_partitionvisible: partitioned 0 points from outsidesets and 0 points from coplanarsets qh_deletevisible: delete 3 visible facets and 0 vertices qh_checkpolygon: check all facets from f390 qh_buildhull: completed the hull construction Qhull: algorithm completed qh_checkpolygon: check all facets from f62 qh_checkconvex: check all ridges are convex qh_freeqhull2: free global memory qh_freebuild: free memory from qh_inithull and qh_buildhull rbox 100 s D3 | qhull TcvF100 Convex hull of 100 points in 3-d: Number of vertices: 100 Number of facets: 196 Statistics for: rbox 100 s D3 | qhull TcvF100 Number of points processed: 100 Number of hyperplanes created: 514 Number of distance tests for qhull: 1691 CPU seconds to compute hull (after input): 0 At 20:16:52 & 0 CPU secs, qhull has created 102 facets and merged 0. The current hull contains 46 facets and 25 vertices. There are 75 outside points. Next is point p55(v26), 0.035 above f44. At 20:16:52 & 0 CPU secs, qhull has created 203 facets and merged 0. The current hull contains 86 facets and 45 vertices. There are 55 outside points. Next is point p82(v46), 0.067 above f117. At 20:16:52 & 0 CPU secs, qhull has created 306 facets and merged 0. The current hull contains 122 facets and 63 vertices. There are 37 outside points. Next is point p50(v64), 0.042 above f218. At 20:16:52 & 0 CPU secs, qhull has created 412 facets and merged 0. The current hull contains 160 facets and 82 vertices. There are 18 outside points. Next is point p60(v83), 0.031 above f307. Output completed. Verifying that all points are below 2e-015 of all facets. Will make 19600 distance computations. rbox 100 s D3 | qhull Qf Tcv Convex hull of 100 points in 3-d: Number of vertices: 100 Number of facets: 196 Statistics for: rbox 100 s D3 | qhull Qf Tcv Number of points processed: 100 Number of hyperplanes created: 504 Number of distance tests for qhull: 4423 CPU seconds to compute hull (after input): 0 Output completed. Verifying that all points are below 2e-015 of all facets. Will make 19600 distance computations. rbox 100 D3 | qhull Tcv Convex hull of 100 points in 3-d: Number of vertices: 26 Number of facets: 48 Statistics for: rbox 100 D3 | qhull Tcv Number of points processed: 28 Number of hyperplanes created: 110 Number of distance tests for qhull: 1164 CPU seconds to compute hull (after input): 0 Output completed. Verifying that all points are below outer planes of all facets. Will make 4800 distance computations. rbox 100 D3 | qhull Qs Tcv Convex hull of 100 points in 3-d: Number of vertices: 26 Number of facets: 48 Statistics for: rbox 100 D3 | qhull Qs Tcv Number of points processed: 29 Number of hyperplanes created: 105 Number of distance tests for qhull: 1176 CPU seconds to compute hull (after input): 0 Output completed. Verifying that all points are below outer planes of all facets. Will make 4800 distance computations. rbox 100 D5 | qhull Qs Tcv Convex hull of 100 points in 5-d: Number of vertices: 78 Number of facets: 1174 Statistics for: rbox 100 D5 | qhull Qs Tcv Number of points processed: 85 Number of hyperplanes created: 4015 Number of distance tests for qhull: 8584 CPU seconds to compute hull (after input): 0 QH7076 qhull input warning: exact merge ('Qx'). Verify may report that a point is outside of a facet. See qh-optq.htm#Qx Output completed. Verifying that all points are below outer planes of all facets. Will make 117400 distance computations. rbox 100 D3 | qhull Qr Tcv Convex hull of 100 points in 3-d: Number of vertices: 26 Number of facets: 48 Statistics for: rbox 100 D3 | qhull Qr Tcv Number of points processed: 56 Number of hyperplanes created: 294 Number of distance tests for qhull: 2129 Output completed. Verifying that all points are below outer planes of all facets. Will make 4800 distance computations. rbox 100 D3 | qhull Qxv Tcv Convex hull of 100 points in 3-d: Number of vertices: 26 Number of facets: 48 Statistics for: rbox 100 D3 | qhull Qxv Tcv Number of points processed: 28 Number of hyperplanes created: 110 Number of distance tests for qhull: 1164 CPU seconds to compute hull (after input): 0 QH7076 qhull input warning: exact merge ('Qx'). Verify may report that a point is outside of a facet. See qh-optq.htm#Qx Output completed. Verifying that all points are below outer planes of all facets. Will make 4800 distance computations. rbox 100 D3 | qhull Qi f Pd0 Pd1 Pd2 Tcv Vertices and facets: - p11(v14): -0.31 0.47 0.07 - p59(v8): 0.44 0.42 -0.11 - p33(v2): -0.067 0.49 -0.11 - p48(v25): 0.25 0.24 0.44 - p37(v15): 0.45 0.26 0.04 - p38(v5): 0.42 -0.25 0.42 - f42 - flags: bottom simplicial - normal: 0.1292 0.9495 0.2858 - offset: -0.4221543 - coplanar set(furthest p70): p70: 0.04762 0.3507 -0.06712 furthest distance= -0.1 - vertices: p11(v14) p59(v8) p33(v2) - neighboring facets: f52 f41 f93 - f93 - flags: top simplicial - normal: 0.142 0.9273 0.3463 - offset: -0.4120445 - coplanar set(furthest p28): p27: 0.1182 0.3419 0.068 p25: 0.1663 0.2352 0.3516 p15: 0.2743 0.2665 0.07375 p44: -0.1321 0.3861 0.167 p28: -0.1003 0.4263 0.07335 furthest distance= -0.0056 - vertices: p48(v25) p11(v14) p59(v8) - neighboring facets: f42 f94 f95 - f94 - flags: bottom simplicial - normal: 0.7783 0.4631 0.4241 - offset: -0.4905394 - vertices: p48(v25) p37(v15) p59(v8) - neighboring facets: f47 f93 f97 - f97 - flags: top simplicial - normal: 0.8488 0.2736 0.4523 - offset: -0.4744876 - vertices: p48(v25) p37(v15) p38(v5) - neighboring facets: f46 f99 f94 Output completed. Verifying that all points are below outer planes of all facets. Will make 400 distance computations. rbox c d | qhull Qc f Tcv Vertices and facets: - p6(v6): 0.5 0.5 -0.5 neighbors: f1 f9 f10 - p2(v2): -0.5 0.5 -0.5 neighbors: f1 f3 f10 - p4(v1): 0.5 -0.5 -0.5 neighbors: f1 f2 f9 - p0(v0): -0.5 -0.5 -0.5 neighbors: f1 f2 f3 - p5(v7): 0.5 -0.5 0.5 neighbors: f2 f9 f13 - p1(v3): -0.5 -0.5 0.5 neighbors: f2 f3 f13 - p7(v5): 0.5 0.5 0.5 neighbors: f9 f10 f13 - p3(v8): -0.5 0.5 0.5 neighbors: f3 f10 f13 - f1 - flags: bottom tested seen coplanar - merges: 1 - normal: -0 -0 -1 - offset: -0.5 - center: 0 0 -0.5 - coplanar set(furthest p8): p8: 0 0 -0.5 furthest distance= 0 - vertices: p6(v6) p2(v2) p4(v1) p0(v0) - neighboring facets: f2 f3 f9 f10 - ridges: - r4 tested vertices: p2(v2) p0(v0) between f1 and f3 - r3 tested vertices: p4(v1) p0(v0) between f2 and f1 - r1 tested vertices: p6(v6) p4(v1) between f9 and f1 - r2 tested vertices: p6(v6) p2(v2) between f1 and f10 - f2 - flags: top tested seen coplanar - merges: 1 - normal: 0 -1 0 - offset: -0.5 - center: 0 -0.5 0 - coplanar set(furthest p10): p10: 0 -0.5 0 furthest distance= 0 - vertices: p5(v7) p1(v3) p4(v1) p0(v0) - neighboring facets: f1 f3 f9 f13 - ridges: - r3 tested vertices: p4(v1) p0(v0) between f2 and f1 - r8 tested vertices: p1(v3) p0(v0) between f3 and f2 - r7 tested vertices: p5(v7) p1(v3) between f13 and f2 - r6 tested vertices: p5(v7) p4(v1) between f2 and f9 - f9 - flags: bottom tested seen coplanar - merges: 1 - normal: 1 -0 -0 - offset: -0.5 - center: 0.5 0 0 - coplanar set(furthest p13): p13: 0.5 0 0 furthest distance= 0 - vertices: p5(v7) p6(v6) p7(v5) p4(v1) - neighboring facets: f2 f1 f10 f13 - ridges: - r1 tested vertices: p6(v6) p4(v1) between f9 and f1 - r6 tested vertices: p5(v7) p4(v1) between f2 and f9 - r10 tested vertices: p5(v7) p7(v5) between f9 and f13 - r11 tested vertices: p6(v6) p7(v5) between f10 and f9 - f3 - flags: bottom tested seen coplanar - merges: 1 - normal: -1 -0 -0 - offset: -0.5 - center: -0.5 0 0 - coplanar set(furthest p12): p12: -0.5 0 0 furthest distance= 0 - vertices: p3(v8) p1(v3) p2(v2) p0(v0) - neighboring facets: f1 f2 f10 f13 - ridges: - r4 tested vertices: p2(v2) p0(v0) between f1 and f3 - r13 tested vertices: p3(v8) p2(v2) between f10 and f3 - r14 tested vertices: p3(v8) p1(v3) between f3 and f13 - r8 tested vertices: p1(v3) p0(v0) between f3 and f2 - f10 - flags: top tested seen coplanar - merges: 1 - normal: 0 1 -0 - offset: -0.5 - center: 0 0.5 0 - coplanar set(furthest p11): p11: 0 0.5 0 furthest distance= 0 - vertices: p3(v8) p6(v6) p7(v5) p2(v2) - neighboring facets: f3 f1 f9 f13 - ridges: - r2 tested vertices: p6(v6) p2(v2) between f1 and f10 - r11 tested vertices: p6(v6) p7(v5) between f10 and f9 - r16 tested vertices: p3(v8) p7(v5) between f13 and f10 - r13 tested vertices: p3(v8) p2(v2) between f10 and f3 - f13 - flags: bottom tested seen coplanar - merges: 1 - normal: -0 -0 1 - offset: -0.5 - center: 0 0 0.5 - coplanar set(furthest p9): p9: 0 0 0.5 furthest distance= 0 - vertices: p3(v8) p5(v7) p7(v5) p1(v3) - neighboring facets: f10 f2 f9 f3 - ridges: - r7 tested vertices: p5(v7) p1(v3) between f13 and f2 - r14 tested vertices: p3(v8) p1(v3) between f3 and f13 - r16 tested vertices: p3(v8) p7(v5) between f13 and f10 - r10 tested vertices: p5(v7) p7(v5) between f9 and f13 Output completed. Verifying that all points are below outer planes of all facets. Will make 84 distance computations. rbox c d | qhull Qc p Tcv 3 14 -0.5 -0.5 -0.5 -0.5 -0.5 0.5 -0.5 0.5 -0.5 -0.5 0.5 0.5 0.5 -0.5 -0.5 0.5 -0.5 0.5 0.5 0.5 -0.5 0.5 0.5 0.5 0 0 -0.5 0 0 0.5 0 -0.5 0 0 0.5 0 -0.5 0 0 0.5 0 0 Output completed. Verifying that all points are below outer planes of all facets. Will make 84 distance computations. rbox 100 D3 | qhull QbB FO Tcv Convex hull of 100 points in 3-d: Number of vertices: 26 Number of facets: 48 Statistics for: rbox 100 D3 | qhull QbB FO Tcv Number of points processed: 28 Number of hyperplanes created: 110 Number of distance tests for qhull: 1164 CPU seconds to compute hull (after input): 0 Options selected for Qhull 2012.1 2012/01/22: run-id 315332402 QbBound-unit-box 0.5 Tcheck-frequently Tverify _pre-merge _zero-centrum _max-width 1 Error-roundoff 6.9e-016 _one-merge 4.9e-015 _near-inside 2.4e-014 Visible-distance 1.4e-015 U-coplanar-distance 1.4e-015 Width-outside 2.8e-015 _wide-facet 8.3e-015 Output completed. Verifying that all points are below outer planes of all facets. Will make 4800 distance computations. rbox 1000 D2 B1e6 | qhull d Qbb FO Tcv Delaunay triangulation by the convex hull of 1000 points in 3-d: Number of input sites: 1000 Number of Delaunay regions: 1982 Statistics for: rbox 1000 D2 B1e6 | qhull d Qbb FO Tcv Number of points processed: 1000 Number of hyperplanes created: 5422 Number of facets in hull: 1996 Number of distance tests for qhull: 27767 CPU seconds to compute hull (after input): 0.015 Options selected for Qhull 2012.1 2012/01/22: run-id 315332402 delaunay Qbbound-last Tcheck-frequently Tverify _pre-merge _zero-centrum Pgood _max-width 2e+006 Error-roundoff 2.8e-009 _one-merge 1.9e-008 _near-inside 9.7e-008 Visible-distance 5.5e-009 U-coplanar-distance 5.5e-009 Width-outside 1.1e-008 _wide-facet 3.3e-008 qhull output completed. Verifying that 1000 points are below 8.3e-009 of the nearest facet. rbox 10 D3 | qhull QbB p Tcv 3 9 -0.08928142660407056 -0.3194671263098747 0.3605569202297553 -0.1534778158747162 0.03516440701453921 0.5 -0.01663016790622804 0.3709299907861695 0.0764863283135003 0.3932651765570926 0.4421392241401818 -0.09396622763110282 0.199424728304684 0.5 0.06620718432588452 -0.2331094527352667 0.3262436269787957 -0.1289660986727641 -0.5 0.2819439085196089 -0.5 0.4999999999999999 0.3760666748352666 0.1399187075693636 0.4888102268053206 -0.5 -0.2153953634886358 Output completed. Verifying that all points are below 2.1e-015 of all facets. Will make 140 distance computations. rbox 10 D3 | qhull Qbb p Tcv 3 9 -0.0222149361131852 -0.366434993563625 0.5972263834933854 -0.06676722137887703 -0.1566931052661437 0.6939998615477234 0.02820502736438535 0.04189077954915421 0.4000814320337247 0.3126723396709863 0.08400649026409401 0.2817873818077145 0.1781470954214661 0.1182274414396169 0.3929477075294902 -0.1220315663349177 0.01546165115708642 0.2574974761506134 -0.3072535691850387 -0.01073880122111998 0 0.3867462923626847 0.04492879989084675 0.4441034944549365 0.3789805913148268 -0.4732086509216658 0.1975155783347269 QH7040 qhull input warning: option 'Qbb' (scale-last-coordinate) is normally used with 'd' or 'v' Output completed. Verifying that all points are below 2.9e-015 of all facets. Will make 140 distance computations. rbox 10 D3 | qhull Qb0:-10B2:20 p Tcv 3 9 -5.733970380575339 -0.366434993563625 17.14322461142018 -6.400761988815289 -0.1566931052661437 20 -4.97936018866004 0.04189077954915421 11.32346018178494 -0.7218812392989191 0.08400649026409401 7.831392539952951 -2.735252796494545 0.1182274414396169 11.11287098934976 -7.227875597731384 0.01546165115708642 7.114348923589699 -10 -0.01073880122111998 -0.4870359524963758 0.3867462923626847 0.04492879989084675 12.62300161615219 0.2705209571204694 -0.4732086509216658 5.343669467959106 Output completed. Verifying that all points are below 7.5e-014 of all facets. Will make 140 distance computations. rbox 10 D3 | qhull Qb0:-10B2:20 p Tcv | qhull QbB p Tcv Output completed. Verifying that all points are below 7.5e-014 of all facets. Will make 140 distance computations. 3 9 -0.08928142660407051 -0.3194671263098747 0.3605569202297555 -0.1534778158747163 0.03516440701453921 0.5 -0.01663016790622796 0.3709299907861695 0.07648632831350066 0.3932651765570927 0.4421392241401818 -0.09396622763110274 0.1994247283046841 0.5 0.06620718432588446 -0.2331094527352668 0.3262436269787957 -0.128966098672764 -0.5 0.2819439085196089 -0.4999999999999999 0.5 0.3760666748352666 0.1399187075693635 0.4888102268053207 -0.5 -0.2153953634886357 Output completed. Verifying that all points are below 2.1e-015 of all facets. Will make 126 distance computations. rbox 10 D3 | qhull Qb1:0B1:0 d Tcv Q8 Delaunay triangulation by the convex hull of 10 points in 3-d: Number of input sites: 10 Number of Delaunay regions: 14 Statistics for: rbox 10 D3 | qhull Qb1:0B1:0 d Tcv Q8 Number of points processed: 10 Number of hyperplanes created: 32 Number of facets in hull: 16 Number of distance tests for qhull: 62 CPU seconds to compute hull (after input): 0 QH7077 qhull input warning: no outer plane check ('Q5') or no processing of near-inside points ('Q8'). Verify may report that a point is outside of a facet. Output completed. Verifying that all points are below 2e-015 of all facets. Will make 140 distance computations. rbox 10 D3 | qhull Qb1:0B1:0B2:0 d Tcv Q8 Delaunay triangulation by the convex hull of 10 points in 3-d: Number of input sites: 10 Number of Delaunay regions: 14 Statistics for: rbox 10 D3 | qhull Qb1:0B1:0B2:0 d Tcv Q8 Number of points processed: 10 Number of hyperplanes created: 32 Number of facets in hull: 16 Number of distance tests for qhull: 62 CPU seconds to compute hull (after input): 0 QH7077 qhull input warning: no outer plane check ('Q5') or no processing of near-inside points ('Q8'). Verify may report that a point is outside of a facet. Output completed. Verifying that all points are below 2e-015 of all facets. Will make 140 distance computations. rbox 10 D3 | qhull Qb1:0 d Tcv Delaunay triangulation by the convex hull of 10 points in 4-d: Number of input sites: 10 Number of Delaunay regions: 18 Statistics for: rbox 10 D3 | qhull Qb1:0 d Tcv Number of points processed: 10 Number of hyperplanes created: 44 Number of facets in hull: 27 Number of distance tests for qhull: 67 CPU seconds to compute hull (after input): 0 Output completed. Verifying that all points are below 2.9e-015 of all facets. Will make 180 distance computations. rbox 10 D3 | qhull Qb1:0B1:0 Tcv Convex hull of 10 points in 2-d: Number of vertices: 4 Number of facets: 4 Statistics for: rbox 10 D3 | qhull Qb1:0B1:0 Tcv Number of points processed: 4 Number of hyperplanes created: 6 Number of distance tests for qhull: 49 CPU seconds to compute hull (after input): 0 Output completed. Verifying that all points are below 1.3e-015 of all facets. Will make 40 distance computations. echo "== next command will error ${d:-`date`} ==" date == next command will error Tue Jan 24 20:16:53 EST 2012 == rbox 10 D2 | qhull Qb1:1B1:1 Tcv QH6154 qhull precision error: initial facet 1 is coplanar with the interior point ERRONEOUS FACET: - f1 - flags: bottom simplicial flipped - normal: 0 1 - offset: -1 - vertices: p4(v1) p1(v0) - neighboring facets: f2 f3 While executing: rbox 10 D2 | qhull Qb1:1B1:1 Tcv Options selected for Qhull 2012.1 2012/01/22: run-id 315349209 Qbound-dim-low 1 1 QBound-dim-high 1 1 Tcheck-frequently Tverify _pre-merge _zero-centrum _max-width 0.81 Error-roundoff 8.6e-016 _one-merge 4.3e-015 _near-inside 2.1e-014 Visible-distance 1.7e-015 U-coplanar-distance 1.7e-015 Width-outside 3.4e-015 _wide-facet 1e-014 precision problems (corrected unless 'Q0' or an error) 2 flipped facets The input to qhull appears to be less than 2 dimensional, or a computation has overflowed. Qhull could not construct a clearly convex simplex from points: - p0(v2): -0.022 1 - p4(v1): 0.38 1 - p1(v0): -0.43 1 The center point is coplanar with a facet, or a vertex is coplanar with a neighboring facet. The maximum round off error for computing distances is 8.6e-016. The center point, facets and distances to the center point are as follows: center point -0.02391 1 facet p4 p1 distance= 0 facet p0 p1 distance= 0 facet p0 p4 distance= 0 These points either have a maximum or minimum x-coordinate, or they maximize the determinant for k coordinates. Trial points are first selected from points that maximize a coordinate. The min and max coordinates for each dimension are: 0: -0.4285 0.379 difference= 0.8076 1: 1 1 difference= 0 If the input should be full dimensional, you have several options that may determine an initial simplex: - use 'QJ' to joggle the input and make it full dimensional - use 'QbB' to scale the points to the unit cube - use 'QR0' to randomly rotate the input for different maximum points - use 'Qs' to search all points for the initial simplex - use 'En' to specify a maximum roundoff error less than 8.6e-016. - trace execution with 'T3' to see the determinant for each point. If the input is lower dimensional: - use 'QJ' to joggle the input and make it full dimensional - use 'Qbk:0Bk:0' to delete coordinate k from the input. You should pick the coordinate with the least range. The hull will have the correct topology. - determine the flat containing the points, rotate the points into a coordinate plane, and delete the other coordinates. - add one or more points to make the input full dimensional. rbox 200 L20 D2 t | qhull FO Tcv C-0 Convex hull of 200 points in 2-d: Number of vertices: 200 Number of facets: 200 Statistics for: rbox 200 L20 D2 t1327454213 | qhull FO Tcv C-0 Number of points processed: 200 Number of hyperplanes created: 398 Number of distance tests for qhull: 2125 CPU seconds to compute hull (after input): 0 Options selected for Qhull 2012.1 2012/01/22: run-id 315349209 Tcheck-frequently Tverify Centrum-premerge- 0 _zero-centrum _max-width 1 Error-roundoff 3.4e-016 _one-merge 1.7e-015 _near-inside 8.5e-015 Visible-distance 6.8e-016 U-coplanar-distance 6.8e-016 Width-outside 1.4e-015 _wide-facet 4.1e-015 Output completed. Verifying that all points are below 1e-015 of all facets. Will make 40000 distance computations. rbox 1000 L20 t | qhull FO Tcv C-0 Convex hull of 1000 points in 3-d: Number of vertices: 50 Number of facets: 96 Statistics for: rbox 1000 L20 t1327454213 | qhull FO Tcv C-0 Number of points processed: 71 Number of hyperplanes created: 286 Number of distance tests for qhull: 13384 CPU seconds to compute hull (after input): 0 Options selected for Qhull 2012.1 2012/01/22: run-id 315349209 Tcheck-frequently Tverify Centrum-premerge- 0 _zero-centrum _max-width 1 Error-roundoff 6.9e-016 _one-merge 4.9e-015 _near-inside 2.4e-014 Visible-distance 1.4e-015 U-coplanar-distance 1.4e-015 Width-outside 2.8e-015 _wide-facet 8.3e-015 Output completed. Verifying that all points are below outer planes of all facets. Will make 96000 distance computations. rbox 200 L20 D4 t | qhull FO Tcv C-0 Convex hull of 200 points in 4-d: Number of vertices: 54 Number of facets: 243 Statistics for: rbox 200 L20 D4 t1327454213 | qhull FO Tcv C-0 Number of points processed: 66 Number of hyperplanes created: 772 Number of distance tests for qhull: 6317 CPU seconds to compute hull (after input): 0 Options selected for Qhull 2012.1 2012/01/22: run-id 315349209 Tcheck-frequently Tverify Centrum-premerge- 0 _zero-centrum _max-width 1 Error-roundoff 1e-015 _one-merge 9.1e-015 _near-inside 4.5e-014 Visible-distance 6e-015 U-coplanar-distance 6e-015 Width-outside 1.2e-014 _wide-facet 3.6e-014 Output completed. Verifying that all points are below outer planes of all facets. Will make 48600 distance computations. rbox 200 L20 D5 t | qhull FO Tcv Qx Convex hull of 200 points in 5-d: Number of vertices: 96 Number of facets: 1366 Statistics for: rbox 200 L20 D5 t1327454213 | qhull FO Tcv Qx Number of points processed: 117 Number of hyperplanes created: 5545 Number of distance tests for qhull: 21165 CPU seconds to compute hull (after input): 0.015 Options selected for Qhull 2012.1 2012/01/22: run-id 315349209 Tcheck-frequently Tverify Qxact-merge _zero-centrum _max-width 1 Error-roundoff 1.4e-015 _one-merge 1.5e-014 _near-inside 7.5e-014 Visible-distance 8.2e-015 U-coplanar-distance 8.2e-015 Width-outside 1.6e-014 _wide-facet 4.9e-014 QH7076 qhull input warning: exact merge ('Qx'). Verify may report that a point is outside of a facet. See qh-optq.htm#Qx Output completed. Verifying that all points are below outer planes of all facets. Will make 273200 distance computations. rbox 1000 W1e-3 s D2 t | qhull d FO Tcv Qu Q0 Furthest-site Delaunay triangulation by the convex hull of 1000 points in 3-d: Number of input sites: 1000 Number of Delaunay regions: 260 Statistics for: rbox 1000 W1e-3 s D2 t1327454213 | qhull d FO Tcv Qu Q0 Number of points processed: 1000 Number of hyperplanes created: 4637 Number of facets in hull: 1996 Number of distance tests for qhull: 26132 CPU seconds to compute hull (after input): 0 Options selected for Qhull 2012.1 2012/01/22: run-id 315349209 delaunay Tcheck-frequently Tverify QupperDelaunay Q0-no-premerge Pgood _max-width 1 Error-roundoff 6.9e-016 Visible-distance 6.9e-016 U-coplanar-distance 6.9e-016 Width-outside 1.4e-015 _wide-facet 4.2e-015 Output completed. Verifying that all points are below 2.1e-015 of all facets. Will make 260000 distance computations. rbox 1000 W1e-3 s D2 t | qhull d FO Tcv Qu C-0 Furthest-site Delaunay triangulation by the convex hull of 1000 points in 3-d: Number of input sites: 1000 Number of Delaunay regions: 260 Statistics for: rbox 1000 W1e-3 s D2 t1327454213 | qhull d FO Tcv Qu C-0 Number of points processed: 1000 Number of hyperplanes created: 4637 Number of facets in hull: 1996 Number of distance tests for qhull: 26132 CPU seconds to compute hull (after input): 0 Options selected for Qhull 2012.1 2012/01/22: run-id 315349209 delaunay Tcheck-frequently Tverify QupperDelaunay Centrum-premerge- 0 _zero-centrum Pgood _max-width 1 Error-roundoff 6.9e-016 _one-merge 4.9e-015 _near-inside 2.4e-014 Visible-distance 1.4e-015 U-coplanar-distance 1.4e-015 Width-outside 2.8e-015 _wide-facet 8.3e-015 Output completed. Verifying that all points are below 2.1e-015 of all facets. Will make 260000 distance computations. echo === check joggle and TRn ${d:-`date`} date === check joggle and TRn Tue Jan 24 20:16:53 EST 2012 rbox 100 W0 | qhull QJ1e-14 Qc TR100 Tv At a premature exit due to 'TVn', 'TCn', 'TRn', or precision error with 'QJn'. Convex hull of 100 points in 3-d: Number of vertices: 15 Number of coplanar points: 4 Number of facets: 25 Statistics for: rbox 100 W0 | qhull QJ1e-14 Qc TR100 Tv Number of points processed: 15 Number of hyperplanes created: 11270 Number of distance tests for qhull: 120689 CPU seconds to compute hull (after input): 0.015 Percentage of runs with precision errors: 100.0 precision problems (corrected unless 'Q0' or an error) 100 coplanar horizon facets for new vertices 400 coplanar points during partitioning rbox 100 W0 | qhull QJ1e-13 Qc TR100 Tv At a premature exit due to 'TVn', 'TCn', 'TRn', or precision error with 'QJn'. Convex hull of 100 points in 3-d: Number of vertices: 28 Number of coplanar points: 12 Number of facets: 50 Statistics for: rbox 100 W0 | qhull QJ1e-13 Qc TR100 Tv Number of points processed: 28 Number of hyperplanes created: 24800 Number of distance tests for qhull: 197857 CPU seconds to compute hull (after input): 0.031 Percentage of runs with precision errors: 63.0 precision problems (corrected unless 'Q0' or an error) 10 coplanar half ridges in output 53 coplanar horizon facets for new vertices 119 coplanar points during partitioning rbox 100 W0 | qhull QJ1e-12 Qc TR100 Tv At a premature exit due to 'TVn', 'TCn', 'TRn', or precision error with 'QJn'. Convex hull of 100 points in 3-d: Number of vertices: 40 Number of coplanar points: 16 Number of facets: 75 Statistics for: rbox 100 W0 | qhull QJ1e-12 Qc TR100 Tv Number of points processed: 40 Number of hyperplanes created: 29205 Number of distance tests for qhull: 217398 CPU seconds to compute hull (after input): 0.031 Percentage of runs with precision errors: 8.0 precision problems (corrected unless 'Q0' or an error) 2 coplanar half ridges in output 6 coplanar horizon facets for new vertices 17 coplanar points during partitioning rbox 100 W0 | qhull QJ1e-11 Qc TR100 Tv Convex hull of 100 points in 3-d: Number of vertices: 66 Number of coplanar points: 34 Number of facets: 128 Statistics for: rbox 100 W0 | qhull QJ1e-11 Qc TR100 Tv Number of points processed: 75 Number of hyperplanes created: 29630 Number of distance tests for qhull: 219104 CPU seconds to compute hull (after input): 0.031 Percentage of runs with precision errors: 0.0 precision problems (corrected unless 'Q0' or an error) 3 coplanar points during partitioning Output completed. Verifying that all points are below 2.1e-015 of all facets. Will make 12800 distance computations. rbox 100 W0 | qhull QJ1e-10 Qc TR100 Tv Convex hull of 100 points in 3-d: Number of vertices: 66 Number of coplanar points: 34 Number of facets: 128 Statistics for: rbox 100 W0 | qhull QJ1e-10 Qc TR100 Tv Number of points processed: 75 Number of hyperplanes created: 29636 Number of distance tests for qhull: 218960 CPU seconds to compute hull (after input): 0.031 Percentage of runs with precision errors: 0.0 Output completed. Verifying that all points are below 2.1e-015 of all facets. Will make 12800 distance computations. rbox 100 | qhull d QJ Qb0:1e4 QB0:1e5 Qb1:1e4 QB1:1e6 Qb2:1e5 QB2:1e7 FO Tv Delaunay triangulation by the convex hull of 100 points in 4-d: Number of input sites: 100 Number of Delaunay regions: 488 Statistics for: rbox 100 | qhull d QJ Qb0:1e4 QB0:1e5 Qb1:1e4 QB1:1e6 Qb2:1e5 QB2:1e7 FO Tv Number of points processed: 100 Number of hyperplanes created: 1578 Number of facets in hull: 560 Number of distance tests for qhull: 3924 CPU seconds to compute hull (after input): 0.015 Input joggled by: 6.7e+003 Options selected for Qhull 2012.1 2012/01/22: run-id 315349209 delaunay Qbound-dim-low 0 1e+004 QBound-dim-high 0 1e+005 Qbound-dim-low 1 1e+004 QBound-dim-high 1 1e+006 Qbound-dim-low 2 1e+005 QBound-dim-high 2 1e+007 Tverify Pgood _run 1 QJoggle 6.7e+003 _joggle-seed 16807 _max-width 1e+014 Error-roundoff 0.11 Visible-distance 0.11 U-coplanar-distance 0.11 Width-outside 0.23 _wide-facet 0.68 Output completed. Verifying that all points are below 0.34 of all facets. Will make 48800 distance computations. echo === check precision options ${d:-`date`} date === check precision options Tue Jan 24 20:16:53 EST 2012 rbox 100 D3 s | qhull E0.01 Qx Tcv FO Convex hull of 100 points in 3-d: Number of vertices: 45 Number of facets: 42 Number of non-simplicial facets: 28 Statistics for: rbox 100 D3 s | qhull E0.01 Qx Tcv FO Number of points processed: 45 Number of hyperplanes created: 160 Number of distance tests for qhull: 3992 Number of distance tests for merging: 2006 Number of distance tests for checking: 1937 Number of merged facets: 57 CPU seconds to compute hull (after input): 0 Maximum distance of point above facet: 0.048 (0.6x) Maximum distance of vertex below facet: -0.072 (0.9x) Options selected for Qhull 2012.1 2012/01/22: run-id 315349209 Distance-roundoff 0.01 Qxact-merge Tcheck-frequently Tverify _zero-centrum _max-width 0.98 _one-merge 0.07 _near-inside 0.35 Visible-distance 0.02 U-coplanar-distance 0.02 Width-outside 0.04 _wide-facet 0.12 QH7076 qhull input warning: exact merge ('Qx'). Verify may report that a point is outside of a facet. See qh-optq.htm#Qx Output completed. Verifying that all points are below outer planes of all facets. Will make 4200 distance computations. rbox 100 D3 W1e-1 | qhull W1e-3 Tcv Convex hull of 100 points in 3-d: Number of vertices: 33 Number of facets: 62 Statistics for: rbox 100 D3 W1e-1 | qhull W1e-3 Tcv Number of points processed: 37 Number of hyperplanes created: 170 Number of distance tests for qhull: 1580 CPU seconds to compute hull (after input): 0 Maximum distance of point above facet: 0.00084 Output completed. Verifying that all points are below outer planes of all facets. Will make 6200 distance computations. rbox 100 D3 W1e-1 | qhull W1e-2 Tcv Q0 Convex hull of 100 points in 3-d: Number of vertices: 28 Number of facets: 52 Statistics for: rbox 100 D3 W1e-1 | qhull W1e-2 Tcv Q0 Number of points processed: 29 Number of hyperplanes created: 128 Number of distance tests for qhull: 1442 CPU seconds to compute hull (after input): 0 precision problems (corrected unless 'Q0' or an error) 22 coplanar points during partitioning Output completed. Verifying that all points are below 0.0097 of all facets. Will make 5200 distance computations. rbox 100 D3 W1e-1 | qhull W1e-2 Tcv Convex hull of 100 points in 3-d: Number of vertices: 29 Number of facets: 54 Statistics for: rbox 100 D3 W1e-1 | qhull W1e-2 Tcv Number of points processed: 30 Number of hyperplanes created: 132 Number of distance tests for qhull: 1768 CPU seconds to compute hull (after input): 0 Maximum distance of point above facet: 0.0057 Output completed. Verifying that all points are below outer planes of all facets. Will make 5400 distance computations. rbox 100 D3 W1e-1 | qhull W1e-1 Tcv Convex hull of 100 points in 3-d: Number of vertices: 13 Number of facets: 22 Statistics for: rbox 100 D3 W1e-1 | qhull W1e-1 Tcv Number of points processed: 13 Number of hyperplanes created: 46 Number of distance tests for qhull: 2521 CPU seconds to compute hull (after input): 0 Maximum distance of point above facet: 0.098 Output completed. Verifying that all points are below outer planes of all facets. Will make 2200 distance computations. rbox 15 D2 P0 P1e-14,1e-14 | qhull d Quc Tcv Furthest-site Delaunay triangulation by the convex hull of 17 points in 3-d: Number of input sites: 17 Number of Delaunay regions: 5 Statistics for: rbox 15 D2 P0 P1e-14,1e-14 | qhull d Quc Tcv Number of points processed: 17 Number of hyperplanes created: 64 Number of facets in hull: 28 Number of distance tests for qhull: 142 Number of distance tests for merging: 527 Number of distance tests for checking: 194 Number of merged facets: 7 CPU seconds to compute hull (after input): 0 Maximum distance of point above facet: 1.6e-015 (0.3x) Output completed. Verifying that all points are below outer planes of all facets. Will make 85 distance computations. rbox 15 D3 P0 P1e-12,1e-14,1e-14 | qhull d Qcu Tcv Furthest-site Delaunay triangulation by the convex hull of 17 points in 4-d: Number of input sites: 17 Number of Delaunay regions: 14 Statistics for: rbox 15 D3 P0 P1e-12,1e-14,1e-14 | qhull d Qcu Tcv Number of points processed: 17 Number of hyperplanes created: 124 Number of facets in hull: 60 Number of distance tests for qhull: 225 CPU seconds to compute hull (after input): 0 Output completed. Verifying that all points are below 2.8e-015 of all facets. Will make 238 distance computations. rbox 1000 s D3 | qhull C-0.01 Tcv Qc Convex hull of 1000 points in 3-d: Number of vertices: 107 Number of coplanar points: 893 Number of facets: 96 Number of non-simplicial facets: 77 Statistics for: rbox 1000 s D3 | qhull C-0.01 Tcv Qc Number of points processed: 112 Number of hyperplanes created: 449 Number of distance tests for qhull: 64526 Number of distance tests for merging: 8425 Number of distance tests for checking: 23411 Number of merged facets: 256 CPU seconds to compute hull (after input): 0 Maximum distance of point above facet: 0.02 (0.7x) Maximum distance of vertex below facet: -0.035 (1.2x) Output completed. Verifying that all points are below outer planes of all facets. Will make 96000 distance computations. rbox 1000 s D3 | qhull C-0.01 V0 Qc Tcv Convex hull of 1000 points in 3-d: Number of vertices: 120 Number of coplanar points: 880 Number of facets: 82 Number of non-simplicial facets: 71 Statistics for: rbox 1000 s D3 | qhull C-0.01 V0 Qc Tcv Number of points processed: 445 Number of hyperplanes created: 2451 Number of distance tests for qhull: 172077 Number of distance tests for merging: 52430 Number of distance tests for checking: 19885 Number of merged facets: 1741 CPU seconds to compute hull (after input): 0.031 Maximum distance of point above facet: 0.032 (1.1x) Maximum distance of vertex below facet: -0.064 (2.1x) Output completed. Verifying that all points are below outer planes of all facets. Will make 82000 distance computations. rbox 1000 s D3 | qhull C-0.01 U0 Qc Tcv Convex hull of 1000 points in 3-d: Number of vertices: 107 Number of coplanar points: 893 Number of facets: 98 Number of non-simplicial facets: 77 Statistics for: rbox 1000 s D3 | qhull C-0.01 U0 Qc Tcv Number of points processed: 112 Number of hyperplanes created: 497 Number of distance tests for qhull: 64717 Number of distance tests for merging: 9106 Number of distance tests for checking: 23621 Number of merged facets: 254 CPU seconds to compute hull (after input): 0.015 Maximum distance of point above facet: 0.02 (0.7x) Maximum distance of vertex below facet: -0.035 (1.2x) Output completed. Verifying that all points are below outer planes of all facets. Will make 98000 distance computations. rbox 1000 s D3 | qhull C-0.01 V0 Qcm Tcv Convex hull of 1000 points in 3-d: Number of vertices: 106 Number of coplanar points: 894 Number of facets: 94 Number of non-simplicial facets: 71 Statistics for: rbox 1000 s D3 | qhull C-0.01 V0 Qcm Tcv Number of points processed: 114 Number of hyperplanes created: 597 Number of distance tests for qhull: 54389 Number of distance tests for merging: 10179 Number of distance tests for checking: 18597 Number of merged facets: 288 CPU seconds to compute hull (after input): 0 Maximum distance of point above facet: 0.025 (0.8x) Maximum distance of vertex below facet: -0.07 (2.3x) Output completed. Verifying that all points are below outer planes of all facets. Will make 94000 distance computations. rbox 1000 s D3 | qhull C-0.01 Qcm Tcv Convex hull of 1000 points in 3-d: Number of vertices: 103 Number of coplanar points: 897 Number of facets: 96 Number of non-simplicial facets: 69 Statistics for: rbox 1000 s D3 | qhull C-0.01 Qcm Tcv Number of points processed: 106 Number of hyperplanes created: 434 Number of distance tests for qhull: 64355 Number of distance tests for merging: 7947 Number of distance tests for checking: 23460 Number of merged facets: 234 CPU seconds to compute hull (after input): 0.015 Maximum distance of point above facet: 0.022 (0.7x) Maximum distance of vertex below facet: -0.035 (1.2x) Output completed. Verifying that all points are below outer planes of all facets. Will make 96000 distance computations. rbox 1000 s D3 | qhull C-0.01 Q1 FO Tcv Qc Convex hull of 1000 points in 3-d: Number of vertices: 105 Number of coplanar points: 895 Number of facets: 94 Number of non-simplicial facets: 70 Statistics for: rbox 1000 s D3 | qhull C-0.01 Q1 FO Tcv Qc Number of points processed: 110 Number of hyperplanes created: 457 Number of distance tests for qhull: 66717 Number of distance tests for merging: 8730 Number of distance tests for checking: 23168 Number of merged facets: 258 CPU seconds to compute hull (after input): 0 Maximum distance of point above facet: 0.02 (0.7x) Maximum distance of vertex below facet: -0.035 (1.2x) Options selected for Qhull 2012.1 2012/01/22: run-id 315366016 Centrum-premerge- 0.01 Q1-no-angle-sort Tcheck-frequently Tverify Qcoplanar-keep _max-width 1 Error-roundoff 6.9e-016 _one-merge 0.03 _near-inside 0.15 Visible-distance 0.01 U-coplanar-distance 0.01 Width-outside 0.02 _wide-facet 0.06 Output completed. Verifying that all points are below outer planes of all facets. Will make 94000 distance computations. rbox 1000 s D3 | qhull C-0.01 Q2 FO Tcv Qc Convex hull of 1000 points in 3-d: Number of vertices: 106 Number of coplanar points: 894 Number of facets: 91 Number of non-simplicial facets: 74 Statistics for: rbox 1000 s D3 | qhull C-0.01 Q2 FO Tcv Qc Number of points processed: 112 Number of hyperplanes created: 454 Number of distance tests for qhull: 64909 Number of distance tests for merging: 8602 Number of distance tests for checking: 22777 Number of merged facets: 267 CPU seconds to compute hull (after input): 0.015 Maximum distance of point above facet: 0.02 (0.7x) Maximum distance of vertex below facet: -0.049 (1.6x) Options selected for Qhull 2012.1 2012/01/22: run-id 315366016 Centrum-premerge- 0.01 Q2-no-merge-independent Tcheck-frequently Tverify Qcoplanar-keep _max-width 1 Error-roundoff 6.9e-016 _one-merge 0.03 _near-inside 0.15 Visible-distance 0.01 U-coplanar-distance 0.01 Width-outside 0.02 _wide-facet 0.06 Output completed. Verifying that all points are below outer planes of all facets. Will make 91000 distance computations. rbox 1000 s D3 | qhull C-0.01 Q3 FO Tcv Qc Convex hull of 1000 points in 3-d: Number of vertices: 112 Number of coplanar points: 888 Number of facets: 95 Number of non-simplicial facets: 78 Statistics for: rbox 1000 s D3 | qhull C-0.01 Q3 FO Tcv Qc Number of points processed: 112 Number of hyperplanes created: 453 Number of distance tests for qhull: 64248 Number of distance tests for merging: 8529 Number of distance tests for checking: 23283 Number of merged facets: 260 CPU seconds to compute hull (after input): 0.015 Maximum distance of point above facet: 0.02 (0.7x) Maximum distance of vertex below facet: -0.035 (1.2x) Options selected for Qhull 2012.1 2012/01/22: run-id 315366016 Centrum-premerge- 0.01 Q3-no-merge-vertices Tcheck-frequently Tverify Qcoplanar-keep _max-width 1 Error-roundoff 6.9e-016 _one-merge 0.03 _near-inside 0.15 Visible-distance 0.01 U-coplanar-distance 0.01 Width-outside 0.02 _wide-facet 0.06 Output completed. Verifying that all points are below outer planes of all facets. Will make 95000 distance computations. rbox 1000 s D3 | qhull C-0.01 Q4 FO Tcv Qc Convex hull of 1000 points in 3-d: Number of vertices: 107 Number of coplanar points: 893 Number of facets: 96 Number of non-simplicial facets: 77 Statistics for: rbox 1000 s D3 | qhull C-0.01 Q4 FO Tcv Qc Number of points processed: 112 Number of hyperplanes created: 449 Number of distance tests for qhull: 64526 Number of distance tests for merging: 8425 Number of distance tests for checking: 23411 Number of merged facets: 256 CPU seconds to compute hull (after input): 0.015 Maximum distance of point above facet: 0.02 (0.7x) Maximum distance of vertex below facet: -0.035 (1.2x) Options selected for Qhull 2012.1 2012/01/22: run-id 315366016 Centrum-premerge- 0.01 Q4-avoid-old-into-new Tcheck-frequently Tverify Qcoplanar-keep _max-width 1 Error-roundoff 6.9e-016 _one-merge 0.03 _near-inside 0.15 Visible-distance 0.01 U-coplanar-distance 0.01 Width-outside 0.02 _wide-facet 0.06 Output completed. Verifying that all points are below outer planes of all facets. Will make 96000 distance computations. echo === this may generate an error ${d:-`date`} date === this may generate an error Tue Jan 24 20:16:54 EST 2012 rbox 1000 s D3 | qhull C-0.01 Q5 FO Tcv Convex hull of 1000 points in 3-d: Number of vertices: 107 Number of facets: 96 Number of non-simplicial facets: 77 Statistics for: rbox 1000 s D3 | qhull C-0.01 Q5 FO Tcv Number of points processed: 112 Number of hyperplanes created: 449 Number of distance tests for qhull: 38064 Number of distance tests for merging: 8425 Number of distance tests for checking: 0 Number of merged facets: 256 CPU seconds to compute hull (after input): 0 Maximum distance of point above facet: 0.022 (0.7x) Maximum distance of vertex below facet: -0.035 (1.2x) Options selected for Qhull 2012.1 2012/01/22: run-id 315366016 Centrum-premerge- 0.01 Q5-no-check-outer Tcheck-frequently Tverify _max-width 1 Error-roundoff 6.9e-016 _one-merge 0.03 Visible-distance 0.01 U-coplanar-distance 0.01 Width-outside 0.02 _wide-facet 0.06 QH7077 qhull input warning: no outer plane check ('Q5') or no processing of near-inside points ('Q8'). Verify may report that a point is outside of a facet. Output completed. Verifying that all points are below 0.022 of all facets. Will make 96000 distance computations. echo === this should generate an error ${d:-`date`} date === this should generate an error Tue Jan 24 20:16:54 EST 2012 rbox 1000 s D3 | qhull C-0.01 Q6 FO Po Tcv Qc Convex hull of 1000 points in 3-d: Number of vertices: 114 Number of coplanar points: 886 Number of facets: 182 Number of non-simplicial facets: 40 Statistics for: rbox 1000 s D3 | qhull C-0.01 Q6 FO Po Tcv Qc Number of points processed: 114 Number of hyperplanes created: 447 Number of distance tests for qhull: 53157 Number of distance tests for merging: 3458 Number of distance tests for checking: 27470 Number of merged facets: 88 CPU seconds to compute hull (after input): 0 Maximum distance of point above facet: 0.02 (0.7x) Maximum distance of vertex below facet: -0.009 (0.3x) Options selected for Qhull 2012.1 2012/01/22: run-id 315366016 Centrum-premerge- 0.01 Q6-no-concave-merge Poutput-forced Tcheck-frequently Tverify Qcoplanar-keep _max-width 1 Error-roundoff 6.9e-016 _one-merge 0.03 _near-inside 0.15 Visible-distance 0.01 U-coplanar-distance 0.01 Width-outside 0.02 _wide-facet 0.06 QH6117 qhull precision error: f324 is concave to f325. Centrum of f324 is 0.004134 above f325 QH6117 qhull precision error: f325 is concave to f324. Centrum of f325 is 0.001027 above f324 rbox 1000 s D3 | qhull C-0.01 Q7 FO Tcv Qc Convex hull of 1000 points in 3-d: Number of vertices: 100 Number of coplanar points: 900 Number of facets: 94 Number of non-simplicial facets: 73 Statistics for: rbox 1000 s D3 | qhull C-0.01 Q7 FO Tcv Qc Number of points processed: 103 Number of hyperplanes created: 448 Number of distance tests for qhull: 70481 Number of distance tests for merging: 8005 Number of distance tests for checking: 21158 Number of merged facets: 233 CPU seconds to compute hull (after input): 0.015 Maximum distance of point above facet: 0.02 (0.7x) Maximum distance of vertex below facet: -0.042 (1.4x) Options selected for Qhull 2012.1 2012/01/22: run-id 315366016 Centrum-premerge- 0.01 Q7-no-breadth-first Tcheck-frequently Tverify Qcoplanar-keep _max-width 1 Error-roundoff 6.9e-016 _one-merge 0.03 _near-inside 0.15 Visible-distance 0.01 U-coplanar-distance 0.01 Width-outside 0.02 _wide-facet 0.06 Output completed. Verifying that all points are below outer planes of all facets. Will make 94000 distance computations. rbox 1000 s D3 | qhull C-0.01 Qx Tcv Qc Convex hull of 1000 points in 3-d: Number of vertices: 114 Number of coplanar points: 886 Number of facets: 103 Number of non-simplicial facets: 77 Statistics for: rbox 1000 s D3 | qhull C-0.01 Qx Tcv Qc Number of points processed: 114 Number of hyperplanes created: 447 Number of distance tests for qhull: 90887 Number of distance tests for merging: 5483 Number of distance tests for checking: 20583 Number of merged facets: 167 CPU seconds to compute hull (after input): 0.015 Maximum distance of point above facet: 0.02 (0.7x) Maximum distance of vertex below facet: -0.034 (1.1x) QH7076 qhull input warning: exact merge ('Qx'). Verify may report that a point is outside of a facet. See qh-optq.htm#Qx Output completed. Verifying that all points are below outer planes of all facets. Will make 103000 distance computations. echo === this may generate an error e.g., t1263080158 ${d:-`date`} date === this may generate an error e.g., t1263080158 Tue Jan 24 20:16:54 EST 2012 rbox 100 s D3 t | qhull R1e-3 Tcv Qc Convex hull of 100 points in 3-d: Number of vertices: 99 Number of coplanar points: 1 Number of facets: 170 Number of non-simplicial facets: 22 Statistics for: rbox 100 s D3 t1327454214 | qhull R1e-3 Tcv Qc Number of points processed: 100 Number of hyperplanes created: 486 Number of distance tests for qhull: 1750 Number of distance tests for merging: 3528 Number of distance tests for checking: 1354 Number of merged facets: 45 CPU seconds to compute hull (after input): 0.015 Maximum distance of point above facet: 0.0019 (0.5x) Maximum distance of vertex below facet: -0.004 (1.0x) Output completed. Verifying that all points are below outer planes of all facets. Will make 17000 distance computations. rbox 100 s D3 t | qhull R1e-2 Tcv Qc Convex hull of 100 points in 3-d: Number of vertices: 62 Number of coplanar points: 38 Number of facets: 61 Number of non-simplicial facets: 37 Statistics for: rbox 100 s D3 t1327454214 | qhull R1e-2 Tcv Qc Number of points processed: 64 Number of hyperplanes created: 273 Number of distance tests for qhull: 3715 Number of distance tests for merging: 4249 Number of distance tests for checking: 2058 Number of merged facets: 120 CPU seconds to compute hull (after input): 0 Maximum distance of point above facet: 0.028 (0.7x) Maximum distance of vertex below facet: -0.091 (2.3x) Output completed. Verifying that all points are below outer planes of all facets. Will make 6100 distance computations. rbox 500 s D3 t | qhull R0.05 A-1 Tcv Qc Convex hull of 500 points in 3-d: Number of vertices: 22 Number of coplanar points: 478 Number of facets: 17 Number of non-simplicial facets: 15 Statistics for: rbox 500 s D3 t1327454214 | qhull R0.05 A-1 Tcv Qc Number of points processed: 24 Number of hyperplanes created: 80 Number of distance tests for qhull: 22361 Number of distance tests for merging: 1531 Number of distance tests for checking: 7408 Number of merged facets: 49 CPU seconds to compute hull (after input): 0 Maximum distance of point above facet: 0.14 (0.2x) Maximum distance of vertex below facet: -0.26 (0.4x) Output completed. Verifying that all points are below outer planes of all facets. Will make 8500 distance computations. rbox 100 W0 D3 t | qhull R1e-3 Tcv Qc Convex hull of 100 points in 3-d: Number of vertices: 37 Number of coplanar points: 63 Number of facets: 46 Number of non-simplicial facets: 8 Statistics for: rbox 100 W0 D3 t1327454214 | qhull R1e-3 Tcv Qc Number of points processed: 42 Number of hyperplanes created: 142 Number of distance tests for qhull: 2042 Number of distance tests for merging: 1656 Number of distance tests for checking: 1067 Number of merged facets: 41 CPU seconds to compute hull (after input): 0.015 Maximum distance of point above facet: 0.0025 (0.6x) Maximum distance of vertex below facet: -0.0051 (1.3x) Output completed. Verifying that all points are below outer planes of all facets. Will make 4600 distance computations. rbox 100 W0 D3 t | qhull R1e-3 Qx Tcv Qc Convex hull of 100 points in 3-d: Number of vertices: 38 Number of coplanar points: 62 Number of facets: 47 Number of non-simplicial facets: 9 Statistics for: rbox 100 W0 D3 t1327454214 | qhull R1e-3 Qx Tcv Qc Number of points processed: 44 Number of hyperplanes created: 147 Number of distance tests for qhull: 2938 Number of distance tests for merging: 1582 Number of distance tests for checking: 1068 Number of merged facets: 42 CPU seconds to compute hull (after input): 0 Maximum distance of point above facet: 0.0017 (0.4x) Maximum distance of vertex below facet: -0.0048 (1.2x) QH7076 qhull input warning: exact merge ('Qx'). Verify may report that a point is outside of a facet. See qh-optq.htm#Qx Output completed. Verifying that all points are below outer planes of all facets. Will make 4700 distance computations. rbox 100 W0 D3 t | qhull R1e-2 Tcv Qc Convex hull of 100 points in 3-d: Number of vertices: 27 Number of coplanar points: 73 Number of facets: 27 Number of non-simplicial facets: 12 Statistics for: rbox 100 W0 D3 t1327454214 | qhull R1e-2 Tcv Qc Number of points processed: 33 Number of hyperplanes created: 108 Number of distance tests for qhull: 2267 Number of distance tests for merging: 1505 Number of distance tests for checking: 1069 Number of merged facets: 44 CPU seconds to compute hull (after input): 0 Maximum distance of point above facet: 0.024 (0.6x) Maximum distance of vertex below facet: -0.031 (0.8x) Output completed. Verifying that all points are below outer planes of all facets. Will make 2700 distance computations. rbox 100 W0 D3 t | qhull R1e-2 Qx Tcv Qc Convex hull of 100 points in 3-d: Number of vertices: 30 Number of coplanar points: 70 Number of facets: 30 Number of non-simplicial facets: 11 Statistics for: rbox 100 W0 D3 t1327454215 | qhull R1e-2 Qx Tcv Qc Number of points processed: 34 Number of hyperplanes created: 111 Number of distance tests for qhull: 2798 Number of distance tests for merging: 1363 Number of distance tests for checking: 1107 Number of merged facets: 38 CPU seconds to compute hull (after input): 0 Maximum distance of point above facet: 0.025 (0.6x) Maximum distance of vertex below facet: -0.05 (1.3x) QH7076 qhull input warning: exact merge ('Qx'). Verify may report that a point is outside of a facet. See qh-optq.htm#Qx Output completed. Verifying that all points are below outer planes of all facets. Will make 3000 distance computations. rbox 500 W0 D3 t | qhull R0.05 A-1 Tcv Qc Convex hull of 500 points in 3-d: Number of vertices: 8 Number of coplanar points: 492 Number of facets: 6 Number of non-simplicial facets: 6 Statistics for: rbox 500 W0 D3 t1327454215 | qhull R0.05 A-1 Tcv Qc Number of points processed: 15 Number of hyperplanes created: 46 Number of distance tests for qhull: 16005 Number of distance tests for merging: 742 Number of distance tests for checking: 3754 Number of merged facets: 26 CPU seconds to compute hull (after input): 0 Maximum distance of point above facet: 0.067 (0.1x) Maximum distance of vertex below facet: -0.17 (0.3x) Output completed. Verifying that all points are below outer planes of all facets. Will make 3000 distance computations. rbox 500 W0 D3 t | qhull R0.05 Qx Tcv Qc Convex hull of 500 points in 3-d: Number of vertices: 9 Number of coplanar points: 491 Number of facets: 7 Number of non-simplicial facets: 6 Statistics for: rbox 500 W0 D3 t1327454215 | qhull R0.05 Qx Tcv Qc Number of points processed: 18 Number of hyperplanes created: 45 Number of distance tests for qhull: 22085 Number of distance tests for merging: 596 Number of distance tests for checking: 4091 Number of merged facets: 31 CPU seconds to compute hull (after input): 0 Maximum distance of point above facet: 0.14 (0.7x) Maximum distance of vertex below facet: -0.19 (0.9x) QH7076 qhull input warning: exact merge ('Qx'). Verify may report that a point is outside of a facet. See qh-optq.htm#Qx Output completed. Verifying that all points are below outer planes of all facets. Will make 3500 distance computations. rbox 1000 W1e-20 t | qhull Tcv Qc Convex hull of 1000 points in 3-d: Number of vertices: 76 Number of coplanar points: 924 Number of facets: 90 Number of non-simplicial facets: 6 Statistics for: rbox 1000 W1e-20 t1327454215 | qhull Tcv Qc Number of points processed: 91 Number of hyperplanes created: 288 Number of distance tests for qhull: 19728 Number of distance tests for merging: 3852 Number of distance tests for checking: 28894 Number of merged facets: 88 CPU seconds to compute hull (after input): 0 Output completed. Verifying that all points are below outer planes of all facets. Will make 90000 distance computations. rbox 1000 W1e-20 D4 t | qhull Tcv Qc Convex hull of 1000 points in 4-d: Number of vertices: 270 Number of coplanar points: 730 Number of facets: 975 Number of non-simplicial facets: 8 Statistics for: rbox 1000 W1e-20 D4 t1327454215 | qhull Tcv Qc Number of points processed: 338 Number of hyperplanes created: 4074 Number of distance tests for qhull: 68477 Number of distance tests for merging: 63566 Number of distance tests for checking: 140180 Number of merged facets: 1048 CPU seconds to compute hull (after input): 0.078 Output completed. Verifying that all points are below outer planes of all facets. Will make 975000 distance computations. rbox 500 W1e-20 D5 t | qhull Tv Qc Convex hull of 500 points in 5-d: Number of vertices: 336 Number of coplanar points: 164 Number of facets: 5242 Number of non-simplicial facets: 10 Statistics for: rbox 500 W1e-20 D5 t1327454215 | qhull Tv Qc Number of points processed: 402 Number of hyperplanes created: 27379 Number of distance tests for qhull: 125805 Number of distance tests for merging: 297315 Number of distance tests for checking: 226312 Number of merged facets: 3444 CPU seconds to compute hull (after input): 0.109 QH7076 qhull input warning: exact merge ('Qx'). Verify may report that a point is outside of a facet. See qh-optq.htm#Qx Output completed. Verifying that all points are below outer planes of all facets. Will make 2621000 distance computations. rbox 100 W1e-20 D6 t | qhull Tv Qc Convex hull of 100 points in 6-d: Number of vertices: 100 Number of facets: 5769 Number of non-simplicial facets: 10 Statistics for: rbox 100 W1e-20 D6 t1327454215 | qhull Tv Qc Number of points processed: 100 Number of hyperplanes created: 21073 Number of distance tests for qhull: 33526 Number of distance tests for merging: 178809 Number of distance tests for checking: 119096 Number of merged facets: 175 CPU seconds to compute hull (after input): 0.078 QH7076 qhull input warning: exact merge ('Qx'). Verify may report that a point is outside of a facet. See qh-optq.htm#Qx Output completed. Verifying that all points are below outer planes of all facets. Will make 576900 distance computations. rbox 50 W1e-20 D6 t | qhull Qv Tv Qc Convex hull of 50 points in 6-d: Number of vertices: 50 Number of facets: 2052 Number of non-simplicial facets: 1 Statistics for: rbox 50 W1e-20 D6 t1327454215 | qhull Qv Tv Qc Number of points processed: 50 Number of hyperplanes created: 6174 Number of distance tests for qhull: 9126 Number of distance tests for merging: 3342083 Number of distance tests for checking: 42086 Number of merged facets: 2 CPU seconds to compute hull (after input): 0.125 QH7076 qhull input warning: exact merge ('Qx'). Verify may report that a point is outside of a facet. See qh-optq.htm#Qx Output completed. Verifying that all points are below outer planes of all facets. Will make 102600 distance computations. rbox 10000 D4 t | qhull QR0 Qc C-0.01 A0.3 Tv Convex hull of 10000 points in 4-d: Number of vertices: 16 Number of coplanar points: 8178 Number of facets: 8 Number of non-simplicial facets: 8 Statistics for: rbox 10000 D4 t1327454215 | qhull QR0 Qc C-0.01 A0.3 Tv QR1327454215 Number of points processed: 57 Number of hyperplanes created: 390 Number of distance tests for qhull: 1765089 Number of distance tests for merging: 14211 Number of distance tests for checking: 99978 Number of merged facets: 419 CPU seconds to compute hull (after input): 0.078 Maximum distance of point above facet: 0.062 Maximum distance of vertex below facet: -0.16 Output completed. Verifying that all points are below outer planes of all facets. Will make 80000 distance computations. rbox 1000 D2 t | qhull d QR0 Qc C-1e-8 Qu Tv Furthest-site Delaunay triangulation by the convex hull of 1000 points in 3-d: Number of input sites: 1000 Number of Delaunay regions: 16 Statistics for: rbox 1000 D2 t1327454216 | qhull d QR0 Qc C-1e-8 Qu Tv QR1327454216 Number of points processed: 1000 Number of hyperplanes created: 5607 Number of facets in hull: 1996 Number of distance tests for qhull: 29361 CPU seconds to compute hull (after input): 0 Output completed. Verifying that all points are below outer planes of all facets. Will make 16000 distance computations. rbox 300 D5 t |qhull A-0.999 Qx Qc Tcv Convex hull of 300 points in 5-d: Number of vertices: 151 Number of coplanar points: 33 Number of facets: 1587 Number of non-simplicial facets: 395 Statistics for: rbox 300 D5 t1327454216 | qhull A-0.999 Qx Qc Tcv Number of points processed: 189 Number of hyperplanes created: 11655 Number of distance tests for qhull: 177205 Number of distance tests for merging: 54298 Number of distance tests for checking: 19295 Number of merged facets: 1099 CPU seconds to compute hull (after input): 0.046 Maximum distance of vertex below facet: -0.026 (0.3x) QH7076 qhull input warning: exact merge ('Qx'). Verify may report that a point is outside of a facet. See qh-optq.htm#Qx Output completed. Verifying that all points are below outer planes of all facets. Will make 476100 distance computations. rbox 100 D6 t |qhull A-0.9999 Qx Qc Tcv Convex hull of 100 points in 6-d: Number of vertices: 84 Number of coplanar points: 1 Number of facets: 3470 Number of non-simplicial facets: 220 Statistics for: rbox 100 D6 t1327454216 | qhull A-0.9999 Qx Qc Tcv Number of points processed: 89 Number of hyperplanes created: 13314 Number of distance tests for qhull: 34056 Number of distance tests for merging: 73326 Number of distance tests for checking: 74943 Number of merged facets: 516 CPU seconds to compute hull (after input): 0.046 Maximum distance of vertex below facet: -0.0066 (0.2x) QH7076 qhull input warning: exact merge ('Qx'). Verify may report that a point is outside of a facet. See qh-optq.htm#Qx Output completed. Verifying that all points are below outer planes of all facets. Will make 347000 distance computations. rbox 50 D7 t |qhull A-0.99999 Qx Qc Tcv W0.1 Convex hull of 50 points in 7-d: Number of vertices: 46 Number of coplanar points: 2 Number of facets: 5010 Number of non-simplicial facets: 77 Statistics for: rbox 50 D7 t1327454216 | qhull A-0.99999 Qx Qc Tcv W0.1 Number of points processed: 46 Number of hyperplanes created: 14157 Number of distance tests for qhull: 32822 Number of distance tests for merging: 100043 Number of distance tests for checking: 197564 Number of merged facets: 230 CPU seconds to compute hull (after input): 0.078 Maximum distance of point above facet: 0.23 Maximum distance of vertex below facet: -0.0021 (0.2x) QH7076 qhull input warning: exact merge ('Qx'). Verify may report that a point is outside of a facet. See qh-optq.htm#Qx Output completed. Verifying that all points are below outer planes of all facets. Will make 250500 distance computations. echo === check bad cases for Qhull. May cause errors ${d:-`date`} date === check bad cases for Qhull. May cause errors Tue Jan 24 20:16:56 EST 2012 rbox 1000 L100000 s G1e-6 t | qhull Tv Convex hull of 1000 points in 3-d: Number of vertices: 996 Number of facets: 1524 Number of non-simplicial facets: 4 Statistics for: rbox 1000 L100000 s G1e-6 t1327454216 | qhull Tv Number of points processed: 996 Number of hyperplanes created: 3709 Number of distance tests for qhull: 28946 Number of distance tests for merging: 132465 Number of distance tests for checking: 118998 Number of merged facets: 465 CPU seconds to compute hull (after input): 0.015 Maximum distance of point above facet: 1.8e-015 (0.3x) qhull precision warning: The initial hull is narrow (cosine of min. angle is 1.0000000000000000). Is the input lower dimensional (e.g., on a plane in 3-d)? Qhull may produce a wide facet. Options 'QbB' (scale to unit box) or 'Qbb' (scale last coordinate) may remove this warning. Use 'Pp' to skip this warning. See 'Limitations' in qh-impre.htm. Output completed. Verifying that all points are below outer planes of all facets. Will make 1524000 distance computations. rbox 1000 L100000 s G1e-6 t | qhull Tv Q10 Convex hull of 1000 points in 3-d: Number of vertices: 996 Number of facets: 1524 Number of non-simplicial facets: 4 Statistics for: rbox 1000 L100000 s G1e-6 t1327454216 | qhull Tv Q10 Number of points processed: 996 Number of hyperplanes created: 3709 Number of distance tests for qhull: 28942 Number of distance tests for merging: 132465 Number of distance tests for checking: 118998 Number of merged facets: 465 CPU seconds to compute hull (after input): 0.031 Maximum distance of point above facet: 1.8e-015 (0.3x) Output completed. Verifying that all points are below outer planes of all facets. Will make 1524000 distance computations. rbox 1000 s Z1 G1e-13 t | qhull Tv Convex hull of 1001 points in 3-d: Number of vertices: 1001 Number of facets: 1490 Number of non-simplicial facets: 165 Statistics for: rbox 1000 s Z1 G1e-13 t1327454216 | qhull Tv Number of points processed: 1001 Number of hyperplanes created: 4496 Number of distance tests for qhull: 29800 Number of distance tests for merging: 77271 Number of distance tests for checking: 185199 Number of merged facets: 1602 CPU seconds to compute hull (after input): 0.015 Maximum distance of point above facet: 8.9e-015 (1.6x) Maximum distance of vertex below facet: -9.1e-015 (1.6x) Output completed. Verifying that all points are below outer planes of all facets. Will make 1491490 distance computations. rbox 1000 s W1e-13 P0 t | qhull d Qbb Qc Tv Delaunay triangulation by the convex hull of 1001 points in 4-d: Number of input sites: 1001 Number of Delaunay regions: 1996 Statistics for: rbox 1000 s W1e-13 P0 t1327454216 | qhull d Qbb Qc Tv Number of points processed: 1001 Number of hyperplanes created: 133732 Number of facets in hull: 2018 Number of distance tests for qhull: 210877 Number of distance tests for merging: 9912396 Number of distance tests for checking: 2007669 Number of merged facets: 127605 CPU seconds to compute hull (after input): 2.562 Maximum distance of point above facet: 2.7e-012 (136.2x) Maximum distance of vertex below facet: -8e-013 (39.9x) Output completed. Verifying that all points are below outer planes of all facets. Will make 1997996 distance computations. rbox 1000 s W1e-13 t | qhull d Tv Delaunay triangulation by the convex hull of 1000 points in 4-d: Number of input sites: 37 Total number of deleted points due to merging: 316 Total number of nearly incident points: 647 Number of Delaunay regions: 30 Number of non-simplicial Delaunay regions: 10 Statistics for: rbox 1000 s W1e-13 t1327454219 | qhull d Tv Number of points processed: 353 Number of hyperplanes created: 4824 Number of facets in hull: 53 Number of distance tests for qhull: 956652 Number of distance tests for merging: 160982 Number of distance tests for checking: 50330 Number of merged facets: 4255 CPU seconds to compute hull (after input): 0.063 Maximum distance of point above facet: 3.4e-013 (33.8x) Maximum distance of vertex below facet: -4.7e-014 (4.7x) qhull precision warning: The initial hull is narrow (cosine of min. angle is 1.0000000000000000). Is the input lower dimensional (e.g., on a plane in 3-d)? Qhull may produce a wide facet. Options 'QbB' (scale to unit box) or 'Qbb' (scale last coordinate) may remove this warning. Use 'Pp' to skip this warning. See 'Limitations' in qh-impre.htm. Output completed. Verifying that all points are below outer planes of all facets. Will make 30000 distance computations. rbox 1000 s W1e-13 t D2 | qhull d Tv Delaunay triangulation by the convex hull of 1000 points in 3-d: Number of input sites: 974 Total number of deleted points due to merging: 10 Total number of nearly incident points: 16 Number of Delaunay regions: 729 Number of non-simplicial Delaunay regions: 132 Statistics for: rbox 1000 s W1e-13 D2 t1327454219 | qhull d Tv Number of points processed: 984 Number of hyperplanes created: 3940 Number of facets in hull: 1462 Number of distance tests for qhull: 68482 Number of distance tests for merging: 47115 Number of distance tests for checking: 167978 Number of merged facets: 885 CPU seconds to compute hull (after input): 0.016 Maximum distance of point above facet: 3e-014 (5.5x) Maximum distance of vertex below facet: -7.6e-015 (1.4x) qhull precision warning: The initial hull is narrow (cosine of min. angle is 1.0000000000000000). Is the input lower dimensional (e.g., on a plane in 3-d)? Qhull may produce a wide facet. Options 'QbB' (scale to unit box) or 'Qbb' (scale last coordinate) may remove this warning. Use 'Pp' to skip this warning. See 'Limitations' in qh-impre.htm. Output completed. Verifying that all points are below outer planes of all facets. Will make 729000 distance computations. echo ======================================================= ======================================================= echo ======================================================= ======================================================= echo === The following commands may cause errors ${d:-`date`} date === The following commands may cause errors Tue Jan 24 20:16:59 EST 2012 echo ======================================================= ======================================================= echo ======================================================= ======================================================= rbox c D7 | qhull Q0 Tcv Convex hull of 128 points in 7-d: Number of vertices: 128 Number of facets: 8666 Statistics for: rbox c D7 | qhull Q0 Tcv Number of points processed: 128 Number of hyperplanes created: 12287 Number of distance tests for qhull: 32936 CPU seconds to compute hull (after input): 0.031 precision problems (corrected unless 'Q0' or an error) 41888 coplanar half ridges in output 10185 coplanar horizon facets for new vertices 8389 nearly singular or axis-parallel hyperplanes 8389 zero divisors during back substitute 11903 zero divisors during gaussian elimination qhull output completed. Verifying that 128 points are below 6.6e-015 of the nearest facet. rbox 100 s D3 | qhull Q0 E1e-3 Tc Po Convex hull of 100 points in 3-d: Number of vertices: 100 Number of facets: 196 Statistics for: rbox 100 s D3 | qhull Q0 E1e-3 Tc Po Number of points processed: 100 Number of hyperplanes created: 508 Number of distance tests for qhull: 1728 CPU seconds to compute hull (after input): 0 QH6115 qhull precision error: f100 is concave to f247, since p44(v13) is 0.002232 above QH6115 qhull precision error: f139 is concave to f274, since p90(v32) is 0.007128 above QH6115 qhull precision error: f163 is concave to f232, since p5(v6) is 0.001226 above QH6115 qhull precision error: f293 is concave to f389, since p11(v61) is 0.002161 above QH6115 qhull precision error: f307 is concave to f459, since p75(v21) is 0.01537 above precision problems (corrected unless 'Q0' or an error) 16 coplanar half ridges in output 5 concave half ridges in output 18 coplanar horizon facets for new vertices rbox 100 s D3 | qhull Q0 E1e-2 Tc Po Convex hull of 100 points in 3-d: Number of vertices: 72 Number of facets: 140 Statistics for: rbox 100 s D3 | qhull Q0 E1e-2 Tc Po Number of points processed: 72 Number of hyperplanes created: 321 Number of distance tests for qhull: 1693 CPU seconds to compute hull (after input): 0 QH6115 qhull precision error: f123 is concave to f235, since p85(v8) is 0.06092 above QH6115 qhull precision error: f177 is concave to f272, since p98(v20) is 0.03571 above QH6115 qhull precision error: f246 is concave to f252, since p7(v57) is 0.02104 above QH6115 qhull precision error: f261 is concave to f305, since p82(v60) is 0.01847 above QH6115 qhull precision error: f266 is concave to f317, since p82(v60) is 0.02592 above precision problems (corrected unless 'Q0' or an error) 52 coplanar half ridges in output 5 concave half ridges in output 54 coplanar horizon facets for new vertices 27 coplanar points during partitioning rbox 100 s D3 | qhull Q0 E1e-1 Tc Po Convex hull of 100 points in 3-d: Number of vertices: 10 Number of facets: 16 Statistics for: rbox 100 s D3 | qhull Q0 E1e-1 Tc Po Number of points processed: 10 Number of hyperplanes created: 27 Number of distance tests for qhull: 977 CPU seconds to compute hull (after input): 0 precision problems (corrected unless 'Q0' or an error) 3 coplanar half ridges in output 3 coplanar horizon facets for new vertices 59 coplanar points during partitioning rbox 100 s D3 | qhull Q0 R1e-3 Tc Po Convex hull of 100 points in 3-d: Number of vertices: 100 Number of facets: 196 Statistics for: rbox 100 s D3 | qhull Q0 R1e-3 Tc Po Number of points processed: 100 Number of hyperplanes created: 513 Number of distance tests for qhull: 1693 CPU seconds to compute hull (after input): 0 QH6115 qhull precision error: f229 is concave to f300, since p90(v34) is 0.007895 above QH6115 qhull precision error: f323 is concave to f421, since p11(v67) is 0.001894 above QH6115 qhull precision error: f343 is concave to f493, since p75(v21) is 0.011 above QH6115 qhull precision error: f493 is concave to f343, since p25(v97) is 0.000937 above precision problems (corrected unless 'Q0' or an error) 14 coplanar half ridges in output 4 concave half ridges in output 9 coplanar horizon facets for new vertices rbox 100 s D3 | qhull Q0 R1e-2 Tc Po Convex hull of 100 points in 3-d: Number of vertices: 87 Number of facets: 170 Statistics for: rbox 100 s D3 | qhull Q0 R1e-2 Tc Po Number of points processed: 87 Number of hyperplanes created: 405 Number of distance tests for qhull: 1734 CPU seconds to compute hull (after input): 0.015 QH6136 qhull precision error: facet f326 is flipped, distance= 0.51437088552 QH6136 qhull precision error: facet f326 is flipped, distance= 0.511098236347 QH6115 qhull precision error: f76 is concave to f201, since p76(v21) is 0.0101 above QH6115 qhull precision error: f96 is concave to f279, since p38(v22) is 0.008383 above QH6115 qhull precision error: f132 is concave to f140, since p57(v0) is 0.02117 above QH6115 qhull precision error: f140 is concave to f132, since p96(v34) is 0.00703 above QH6115 qhull precision error: f150 is concave to f230, since p11(v37) is 0.04121 above QH6115 qhull precision error: f161 is concave to f326, since p26(v32) is 0.01279 above QH6115 qhull precision error: f194 is concave to f281, since p73(v12) is 0.03149 above QH6115 qhull precision error: f230 is concave to f150, since p47(v52) is 0.008464 above QH6115 qhull precision error: f263 is concave to f156, since p15(v60) is 0.01055 above QH6115 qhull precision error: f277 is concave to f353, since p89(v36) is 0.005387 above QH6115 qhull precision error: f281 is concave to f194, since p66(v63) is 0.005996 above QH6115 qhull precision error: f319 is concave to f341, since p82(v70) is 0.07818 above QH6115 qhull precision error: f324 is concave to f368, since p41(v5) is 0.01436 above QH6113 qhull precision error: f326 is flipped(interior point is outside) QH6115 qhull precision error: f344 is concave to f352, since p29(v75) is 0.009226 above QH6115 qhull precision error: f348 is concave to f351, since p27(v76) is 0.008815 above QH6115 qhull precision error: f349 is concave to f350, since p15(v60) is 0.01089 above QH6115 qhull precision error: f352 is concave to f344, since p69(v77) is 0.008279 above QH6115 qhull precision error: f353 is concave to f277, since p69(v77) is 0.006627 above QH6115 qhull precision error: f385 is concave to f404, since p18(v73) is 0.007494 above QH6115 qhull precision error: f404 is concave to f385, since p13(v87) is 0.005049 above precision problems (corrected unless 'Q0' or an error) 45 coplanar half ridges in output 20 concave half ridges in output 1 flipped facets 47 coplanar horizon facets for new vertices 13 coplanar points during partitioning rbox 100 s D3 | qhull Q0 R0.05 Tc QH6136 qhull precision error: facet f160 is flipped, distance= 0.41168102504 ERRONEOUS FACET: - f160 - flags: bottom simplicial flipped - normal: -0.3615 -0.1924 0.9123 - offset: 0.4644952 - vertices: p94(v40) p19(v28) p56(v27) - neighboring facets: f107 f158 f202 QH6136 qhull precision error: facet f203 is flipped, distance= 0.448767103644 ERRONEOUS FACET: - f203 - flags: top simplicial flipped - normal: -0.2281 0.05702 -0.972 - offset: 0.4136177 - vertices: p40(v51) p83(v19) p48(v6) - neighboring facets: f123 f204 f205 A flipped facet occurs when its distance to the interior point is greater than -0.024, the maximum roundoff error. While executing: rbox 100 s D3 | qhull Q0 R0.05 Tc Options selected for Qhull 2012.1 2012/01/22: run-id 315466858 Q0-no-premerge Random_perturb 0.05 Tcheck-frequently _max-width 0.94 Error-roundoff 0.024 Visible-distance 0.024 U-coplanar-distance 0.024 Width-outside 0.048 _wide-facet 0.15 Last point added to hull was p40. Qhull has finished constructing the hull. At error exit: Convex hull of 100 points in 3-d: Number of vertices: 51 Number of facets: 98 Statistics for: rbox 100 s D3 | qhull Q0 R0.05 Tc Number of points processed: 51 Number of hyperplanes created: 206 Number of distance tests for qhull: 2041 CPU seconds to compute hull (after input): 0 precision problems (corrected unless 'Q0' or an error) 2 flipped facets 50 coplanar horizon facets for new vertices 46 coplanar points during partitioning Precision problems were detected during construction of the convex hull. This occurs because convex hull algorithms assume that calculations are exact, but floating-point arithmetic has roundoff errors. To correct for precision problems, do not use 'Q0'. By default, Qhull selects 'C-0' or 'Qx' and merges non-convex facets. With option 'QJ', Qhull joggles the input to prevent precision problems. See "Imprecision in Qhull" (qh-impre.htm). If you use 'Q0', the output may include coplanar ridges, concave ridges, and flipped facets. In 4-d and higher, Qhull may produce a ridge with four neighbors or two facets with the same vertices. Qhull reports these events when they occur. It stops when a concave ridge, flipped facet, or duplicate facet occurs. If you need triangular output: - use option 'Qt' to triangulate the output - use option 'QJ' to joggle the input points and remove precision errors - use option 'Ft'. It triangulates non-simplicial facets with added points. If you must use 'Q0', try one or more of the following options. They can not guarantee an output. - use 'QbB' to scale the input to a cube. - use 'Po' to produce output and prevent partitioning for flipped facets - use 'V0' to set min. distance to visible facet as 0 instead of roundoff - use 'En' to specify a maximum roundoff error less than 0.024. - options 'Qf', 'Qbb', and 'QR0' may also help To guarantee simplicial output: - use option 'Qt' to triangulate the output - use option 'QJ' to joggle the input points and remove precision errors - use option 'Ft' to triangulate the output by adding points - use exact arithmetic (see "Imprecision in Qhull", qh-impre.htm) rbox 100 s D3 | qhull Q0 R0.05 Tc Po Convex hull of 100 points in 3-d: Number of vertices: 51 Number of facets: 98 Statistics for: rbox 100 s D3 | qhull Q0 R0.05 Tc Po Number of points processed: 51 Number of hyperplanes created: 209 Number of distance tests for qhull: 2072 CPU seconds to compute hull (after input): 0 QH6136 qhull precision error: facet f105 is flipped, distance= 0.531034433025 QH6136 qhull precision error: facet f172 is flipped, distance= 0.351989788321 QH6136 qhull precision error: facet f105 is flipped, distance= 0.524438872687 QH6136 qhull precision error: facet f172 is flipped, distance= 0.311891927779 QH6115 qhull precision error: f30 is concave to f172, since p90(v11) is 0.05852 above QH6115 qhull precision error: f41 is concave to f70, since p28(v14) is 0.03835 above QH6115 qhull precision error: f65 is concave to f128, since p18(v19) is 0.03961 above QH6115 qhull precision error: f77 is concave to f201, since p89(v21) is 0.03681 above QH6115 qhull precision error: f99 is concave to f192, since p85(v8) is 0.1891 above QH6113 qhull precision error: f105 is flipped(interior point is outside) QH6115 qhull precision error: f143 is concave to f179, since p3(v2) is 0.0956 above QH6115 qhull precision error: f150 is concave to f185, since p70(v13) is 0.03157 above QH6115 qhull precision error: f161 is concave to f171, since p41(v5) is 0.07964 above QH6115 qhull precision error: f166 is concave to f108, since p96(v41) is 0.02537 above QH6115 qhull precision error: f169 is concave to f129, since p60(v42) is 0.02492 above QH6113 qhull precision error: f172 is flipped(interior point is outside) QH6115 qhull precision error: f183 is concave to f205, since p44(v37) is 0.1309 above QH6115 qhull precision error: f186 is concave to f207, since p5(v25) is 0.1066 above QH6115 qhull precision error: f187 is concave to f151, since p75(v47) is 0.04347 above QH6115 qhull precision error: f199 is concave to f200, since p12(v3) is 0.08495 above QH6115 qhull precision error: f201 is concave to f77, since p35(v50) is 0.02603 above precision problems (corrected unless 'Q0' or an error) 61 coplanar half ridges in output 15 concave half ridges in output 2 flipped facets 44 coplanar horizon facets for new vertices 46 coplanar points during partitioning rbox 1000 W1e-7 | qhull Q0 Tc Po Convex hull of 1000 points in 3-d: Number of vertices: 164 Number of facets: 324 Statistics for: rbox 1000 W1e-7 | qhull Q0 Tc Po Number of points processed: 221 Number of hyperplanes created: 1160 Number of distance tests for qhull: 22647 CPU seconds to compute hull (after input): 0 rbox 50 s | qhull Q0 V0.05 W0.01 Tc Po QH6136 qhull precision error: facet f105 is flipped, distance= 0.328228630954 QH6136 qhull precision error: facet f125 is flipped, distance= 0.389476173148 QH6136 qhull precision error: facet f152 is flipped, distance= 0.420187947128 QH6136 qhull precision error: facet f155 is flipped, distance= 0.396217639489 QH6136 qhull precision error: facet f161 is flipped, distance= 0.0543980568868 QH6136 qhull precision error: facet f164 is flipped, distance= 0.448464152152 QH6136 qhull precision error: facet f170 is flipped, distance= 0.430073300444 QH6136 qhull precision error: facet f105 is flipped, distance= 0.328228630954 QH6136 qhull precision error: facet f125 is flipped, distance= 0.389476173148 QH6136 qhull precision error: facet f152 is flipped, distance= 0.420187947128 QH6136 qhull precision error: facet f155 is flipped, distance= 0.396217639489 QH6136 qhull precision error: facet f161 is flipped, distance= 0.0543980568868 QH6136 qhull precision error: facet f164 is flipped, distance= 0.448464152152 QH6136 qhull precision error: facet f170 is flipped, distance= 0.430073300444 QH6115 qhull precision error: f25 is concave to f60, since p41(v8) is 0.1672 above QH6115 qhull precision error: f25 is concave to f155, since p19(v2) is 0.01771 above QH6115 qhull precision error: f38 is concave to f70, since p0(v13) is 0.06094 above QH6115 qhull precision error: f39 is concave to f145, since p8(v11) is 0.2589 above QH6115 qhull precision error: f45 is concave to f72, since p5(v15) is 0.02091 above QH6115 qhull precision error: f47 is concave to f98, since p5(v15) is 0.05573 above QH6115 qhull precision error: f47 is concave to f96, since p42(v7) is 0.05284 above QH6115 qhull precision error: f50 is concave to f59, since p49(v16) is 0.01059 above QH6115 qhull precision error: f54 is concave to f84, since p28(v17) is 0.03013 above QH6115 qhull precision error: f54 is concave to f152, since p29(v1) is 0.2143 above QH6115 qhull precision error: f59 is concave to f50, since p1(v19) is 0.01736 above QH6115 qhull precision error: f60 is concave to f25, since p1(v19) is 0.02263 above QH6115 qhull precision error: f62 is concave to f119, since p14(v5) is 0.02783 above QH6115 qhull precision error: f65 is concave to f120, since p16(v10) is 0.003387 above QH6115 qhull precision error: f70 is concave to f38, since p9(v22) is 0.04722 above QH6115 qhull precision error: f71 is concave to f73, since p9(v22) is 0.04568 above QH6115 qhull precision error: f72 is concave to f45, since p31(v23) is 0.02334 above QH6115 qhull precision error: f73 is concave to f71, since p31(v23) is 0.04141 above QH6115 qhull precision error: f78 is concave to f125, since p38(v24) is 0.01386 above QH6115 qhull precision error: f84 is concave to f54, since p25(v26) is 0.01696 above QH6115 qhull precision error: f87 is concave to f93, since p14(v5) is 0.01836 above QH6115 qhull precision error: f88 is concave to f112, since p4(v27) is 0.04742 above QH6115 qhull precision error: f91 is concave to f161, since p26(v28) is 0.3121 above QH6115 qhull precision error: f93 is concave to f87, since p26(v28) is 0.01572 above QH6115 qhull precision error: f96 is concave to f47, since p21(v29) is 0.02763 above QH6115 qhull precision error: f98 is concave to f47, since p20(v30) is 0.03086 above QH6113 qhull precision error: f105 is flipped(interior point is outside) QH6115 qhull precision error: f106 is concave to f149, since p29(v1) is 0.0618 above QH6115 qhull precision error: f112 is concave to f88, since p6(v34) is 0.02917 above QH6115 qhull precision error: f119 is concave to f62, since p39(v36) is 0.006072 above QH6115 qhull precision error: f120 is concave to f65, since p39(v36) is 0.001213 above QH6113 qhull precision error: f125 is flipped(interior point is outside) QH6115 qhull precision error: f134 is concave to f139, since p46(v40) is 0.07699 above QH6115 qhull precision error: f139 is concave to f134, since p47(v41) is 0.01871 above QH6115 qhull precision error: f141 is concave to f144, since p47(v41) is 0.1017 above QH6115 qhull precision error: f144 is concave to f14 Convex hull of 50 points in 3-d: Number of vertices: 50 Number of facets: 96 Statistics for: rbox 50 s | qhull Q0 V0.05 W0.01 Tc Po Number of points processed: 50 Number of hyperplanes created: 171 Number of distance tests for qhull: 552 CPU seconds to compute hull (after input): 0 1, since p35(v42) is 0.03263 above QH6115 qhull precision error: f145 is concave to f39, since p2(v43) is 0.04048 above QH6115 qhull precision error: f149 is concave to f106, since p18(v44) is 0.009672 above QH6113 qhull precision error: f152 is flipped(interior point is outside) QH6113 qhull precision error: f155 is flipped(interior point is outside) QH6113 qhull precision error: f161 is flipped(interior point is outside) QH6113 qhull precision error: f164 is flipped(interior point is outside) QH6115 qhull precision error: f166 is concave to f170, since p16(v10) is 0.04552 above QH6113 qhull precision error: f170 is flipped(interior point is outside) precision problems (corrected unless 'Q0' or an error) 37 concave half ridges in output 7 flipped facets 82 coplanar horizon facets for new vertices rbox 100 s D5 | qhull Q0 R1e-2 Tc Po Convex hull of 100 points in 5-d: Number of vertices: 37 Number of facets: 500 Statistics for: rbox 100 s D5 | qhull Q0 R1e-2 Tc Po Number of points processed: 37 Number of hyperplanes created: 1198 Number of distance tests for qhull: 2764 QH6107 qhull precision error: facets f1150, f1191 and f1152 meet at a ridge with more than 2 neighbors. Can not continue. ERRONEOUS FACET: - f1150 - flags: top simplicial new - normal: -0.7563 0.3207 -0.3738 0.2956 0.3133 - offset: -0.2362615 - vertices: p70(v37) p59(v25) p47(v17) p33(v15) p6(v9) - neighboring facets: f519 f1148 f1151 f1152 f1153 ERRONEOUS OTHER FACET: - f1191 - flags: top simplicial new - normal: 0.7615 -0.2592 0.3014 -0.3662 -0.3577 - offset: 0.27682 - vertices: p70(v37) p59(v25) p47(v17) p6(v9) p54(v0) - neighboring facets: f519 f1148 ERRONEOUS and NEIGHBORING FACETS to output While executing: rbox 100 s D5 | qhull Q0 R1e-2 Tc Po Options selected for Qhull 2012.1 2012/01/22: run-id 315466858 Q0-no-premerge Random_perturb 0.01 Tcheck-frequently Poutput-forced _max-width 0.88 Error-roundoff 0.0045 Visible-distance 0.0045 U-coplanar-distance 0.0045 Width-outside 0.009 _wide-facet 0.027 Last point added to hull was p70. precision problems (corrected unless 'Q0' or an error) 50 coplanar horizon facets for new vertices Precision problems were detected during construction of the convex hull. This occurs because convex hull algorithms assume that calculations are exact, but floating-point arithmetic has roundoff errors. To correct for precision problems, do not use 'Q0'. By default, Qhull selects 'C-0' or 'Qx' and merges non-convex facets. With option 'QJ', Qhull joggles the input to prevent precision problems. See "Imprecision in Qhull" (qh-impre.htm). If you use 'Q0', the output may include coplanar ridges, concave ridges, and flipped facets. In 4-d and higher, Qhull may produce a ridge with four neighbors or two facets with the same vertices. Qhull reports these events when they occur. It stops when a concave ridge, flipped facet, or duplicate facet occurs. If you need triangular output: - use option 'Qt' to triangulate the output - use option 'QJ' to joggle the input points and remove precision errors - use option 'Ft'. It triangulates non-simplicial facets with added points. If you must use 'Q0', try one or more of the following options. They can not guarantee an output. - use 'QbB' to scale the input to a cube. - use 'Po' to produce output and prevent partitioning for flipped facets - use 'V0' to set min. distance to visible facet as 0 instead of roundoff - use 'En' to specify a maximum roundoff error less than 0.0045. - options 'Qf', 'Qbb', and 'QR0' may also help To guarantee simplicial output: - use option 'Qt' to triangulate the output - use option 'QJ' to joggle the input points and remove precision errors - use option 'Ft' to triangulate the output by adding points - use exact arithmetic (see "Imprecision in Qhull", qh-impre.htm) qhull qhull- compute convex hulls and related structures. Qhull 2012.1 2012/01/22 input (stdin): dimension, n, point coordinates comments start with a non-numeric character halfspace: use dim+1 and put offsets after coefficients options (qh-quick.htm): d - Delaunay triangulation by lifting points to a paraboloid d Qu - furthest-site Delaunay triangulation (upper convex hull) v - Voronoi diagram as the dual of the Delaunay triangulation v Qu - furthest-site Voronoi diagram H1,1 - Halfspace intersection about [1,1,0,...] via polar duality Qt - triangulated output QJ - joggled input instead of merged facets Tv - verify result: structure, convexity, and point inclusion . - concise list of all options - - one-line description of each option Output options (subset): s - summary of results (default) i - vertices incident to each facet n - normals with offsets p - vertex coordinates (if 'Qc', includes coplanar points) if 'v', Voronoi vertices Fp - halfspace intersections Fx - extreme points (convex hull vertices) FA - compute total area and volume o - OFF format (if 'v', outputs Voronoi regions) G - Geomview output (2-d, 3-d and 4-d) m - Mathematica output (2-d and 3-d) QVn - print facets that include point n, -n if not TO file- output results to file, may be enclosed in single quotes examples: rbox c d D2 | qhull Qc s f Fx | more rbox 1000 s | qhull Tv s FA rbox 10 D2 | qhull d QJ s i TO result rbox 10 D2 | qhull v Qbb Qt p rbox 10 D2 | qhull d Qu QJ m rbox 10 D2 | qhull v Qu QJ o rbox c | qhull n rbox c | qhull FV n | qhull H Fp rbox d D12 | qhull QR0 FA rbox c D7 | qhull FA TF1000 rbox y 1000 W0 | qhull rbox 10 | qhull v QJ o Fv qhull . Qhull 2012.1 2012/01/22. Except for 'F.' and 'PG', upper-case options take an argument. delaunay voronoi Geomview Halfspace facet_dump incidences mathematica normals OFF_format points summary Farea FArea-total Fcoplanars FCentrums Fd-cdd-in FD-cdd-out FF-dump-xridge Finner FIDs Fmerges Fneighbors FNeigh-vertex Fouter FOptions Fpoint-intersect FPoint_near FQhull Fsummary FSize Ftriangles Fvertices Fvoronoi FVertex-ave Fxtremes FMaple Gvertices Gpoints Gall_points Gno_planes Ginner Gcentrums Ghyperplanes Gridges Gouter GDrop_dim Gtransparent PArea-keep Pdrop d0:0D0 Pgood PFacet_area_keep PGood_neighbors PMerge-keep Poutput_forced Pprecision_not QbBound 0:0.5 Qbk:0Bk:0_drop QbB-scale-box Qbb-scale-last Qcoplanar Qfurthest Qgood_only QGood_point Qinterior Qmax_out QJoggle Qrandom QRotate Qsearch_1st Qtriangulate QupperDelaunay QVertex_good Qvneighbors Qxact_merge Qzinfinite Q0_no_premerge Q1_no_angle Q2_no_independ Q3_no_redundant Q4_no_old Q5_no_check_out Q6_no_concave Q7_depth_first Q8_no_near_in Q9_pick_furthest Q10_no_narrow Q11_trinormals T4_trace Tannotate Tcheck_often Tstatistics Tverify Tz_stdout TFacet_log TInput_file TPoint_trace TMerge_trace TOutput_file TRerun TWide_trace TVertex_stop TCone_stop Angle_max Centrum_size Error_round Random_dist Visible_min Ucoplanar_max Wide_outside qhull - qhull- compute convex hulls and related structures. http://www.qhull.org 2012.1 2012/01/22 input (stdin): first lines: dimension and number of points (or vice-versa). other lines: point coordinates, best if one point per line comments: start with a non-numeric character halfspaces: use dim plus one and put offset after coefficients. May be preceeded by a single interior point ('H'). options: d - Delaunay triangulation by lifting points to a paraboloid d Qu - furthest-site Delaunay triangulation (upper convex hull) v - Voronoi diagram (dual of the Delaunay triangulation) v Qu - furthest-site Voronoi diagram Hn,n,... - halfspace intersection about point [n,n,0,...] Qt - triangulated output QJ - joggled input instead of merged facets Qc - keep coplanar points with nearest facet Qi - keep interior points with nearest facet Qhull control options: Qbk:n - scale coord k so that low bound is n QBk:n - scale coord k so that upper bound is n (QBk is 0.5) QbB - scale input to unit cube centered at the origin Qbb - scale last coordinate to [0,m] for Delaunay triangulations Qbk:0Bk:0 - remove k-th coordinate from input QJn - randomly joggle input in range [-n,n] QRn - random rotation (n=seed, n=0 time, n=-1 time/no rotate) Qf - partition point to furthest outside facet Qg - only build good facets (needs 'QGn', 'QVn', or 'PdD') Qm - only process points that would increase max_outside Qr - process random outside points instead of furthest ones Qs - search all points for the initial simplex Qu - for 'd' or 'v', compute upper hull without point at-infinity returns furthest-site Delaunay triangulation Qv - test vertex neighbors for convexity Qx - exact pre-merges (skips coplanar and angle-coplanar facets) Qz - add point-at-infinity to Delaunay triangulation QGn - good facet if visible from point n, -n for not visible QVn - good facet if it includes point n, -n if not Q0 - turn off default premerge with 'C-0'/'Qx' Q1 - sort merges by type instead of angle Q2 - merge all non-convex at once instead of independent sets Q3 - do not merge redundant vertices Q4 - avoid old->new merges Q5 - do not correct outer planes at end of qhull Q6 - do not pre-merge concave or coplanar facets Q7 - depth-first processing instead of breadth-first Q8 - do not process near-inside points Q9 - process furthest of furthest points Q10 - no special processing for narrow distributions Q11 - copy normals and recompute centrums for tricoplanar facets Topts- Trace options: T4 - trace at level n, 4=all, 5=mem/gauss, -1= events Ta - annotate output with message codes Tc - check frequently during execution Ts - print statistics Tv - verify result: structure, convexity, and point inclusion Tz - send all output to stdout TFn - report summary when n or more facets created TI file - input data from file, no spaces or single quotes TO file - output results to file, may be enclosed in single quotes TPn - turn on tracing when point n added to hull TMn - turn on tracing at merge n TWn - trace merge facets when width > n TRn - rerun qhull n times. Use with 'QJn' TVn - stop qhull after adding point n, -n for before (see TCn) TCn - stop qhull after building cone for point n (see TVn) Precision options: Cn - radius of centrum (roundoff added). Merge facets if non-convex An - cosine of maximum angle. Merge facets if cosine > n or non-convex C-0 roundoff, A-0.99/C-0.01 pre-merge, A0.99/C0.01 post-merge En - max roundoff error for distance computation Rn - randomly perturb computations by a factor of [1-n,1+n] Vn - min distance above plane for a visible facet (default 3C-n or En) Un - max distance below plane for a new, coplanar point (default Vn) Wn - min facet width for outside point (before roundoff, default 2Vn) Output formats (may be combined; if none, produces a summary to stdout): f - facet dump G - Geomview output (see below) i - vertices incident to each facet m - Mathematica output (2-d and 3-d) o - OFF format (dim, points and facets; Voronoi regions) n - normals with offsets p - vertex coordinates or Voronoi vertices (coplanar points if 'Qc') s - summary (stderr) More formats: Fa - area for each facet FA - compute total area and volume for option 's' Fc - count plus coplanar points for each facet use 'Qc' (default) for coplanar and 'Qi' for interior FC - centrum or Voronoi center for each facet Fd - use cdd format for input (homogeneous with offset first) FD - use cdd format for numeric output (offset first) FF - facet dump without ridges Fi - inner plane for each facet for 'v', separating hyperplanes for bounded Voronoi regions FI - ID of each facet Fm - merge count for each facet (511 max) FM - Maple output (2-d and 3-d) Fn - count plus neighboring facets for each facet FN - count plus neighboring facets for each point Fo - outer plane (or max_outside) for each facet for 'v', separating hyperplanes for unbounded Voronoi regions FO - options and precision constants Fp - dim, count, and intersection coordinates (halfspace only) FP - nearest vertex and distance for each coplanar point FQ - command used for qhull Fs - summary: #int (8), dimension, #points, tot vertices, tot facets, output: #vertices, #facets, #coplanars, #nonsimplicial #real (2), max outer plane, min vertex FS - sizes: #int (0) #real (2) tot area, tot volume Ft - triangulation with centrums for non-simplicial facets (OFF format) Fv - count plus vertices for each facet for 'v', Voronoi diagram as Voronoi vertices for pairs of sites FV - average of vertices (a feasible point for 'H') Fx - extreme points (in order for 2-d) Geomview options (2-d, 3-d, and 4-d; 2-d Voronoi) Ga - all points as dots Gp - coplanar points and vertices as radii Gv - vertices as spheres Gi - inner planes only Gn - no planes Go - outer planes only Gc - centrums Gh - hyperplane intersections Gr - ridges GDn - drop dimension n in 3-d and 4-d output Gt - for 3-d 'd', transparent outer ridges Print options: PAn - keep n largest facets by area Pdk:n - drop facet if normal[k] <= n (default 0.0) PDk:n - drop facet if normal[k] >= n Pg - print good facets (needs 'QGn' or 'QVn') PFn - keep facets whose area is at least n PG - print neighbors of good facets PMn - keep n facets with most merges Po - force output. If error, output neighborhood of facet Pp - do not report precision problems . - list of all options - - one line descriptions of all options rbox -rbox- generate various point distributions. Default is random in cube. args (any order, space separated): Version: 2001/06/24 3000 number of random points in cube, lens, spiral, sphere or grid D3 dimension 3-d c add a unit cube to the output ('c G2.0' sets size) d add a unit diamond to the output ('d G2.0' sets size) l generate a regular 3-d spiral r generate a regular polygon, ('r s Z1 G0.1' makes a cone) s generate cospherical points x generate random points in simplex, may use 'r' or 'Wn' y same as 'x', plus simplex Pn,m,r add point [n,m,r] first, pads with 0 Ln lens distribution of radius n. Also 's', 'r', 'G', 'W'. Mn,m,r lattice(Mesh) rotated by [n,-m,0], [m,n,0], [0,0,r], ... '27 M1,0,1' is {0,1,2} x {0,1,2} x {0,1,2}. Try 'M3,4 z'. W0.1 random distribution within 0.1 of the cube's or sphere's surface Z0.5 s random points in a 0.5 disk projected to a sphere Z0.5 s G0.6 same as Z0.5 within a 0.6 gap Bn bounding box coordinates, default 0.5 h output as homogeneous coordinates for cdd n remove command line from the first line of output On offset coordinates by n t use time as the random number seed(default is command line) tn use n as the random number seed z print integer coordinates, default 'Bn' is 1e+006 cat html/qhull.txt html/rbox.txt qhull(1) qhull(1) NAME qhull - convex hull, Delaunay triangulation, Voronoi dia- gram, halfspace intersection about a point, hull volume, facet area SYNOPSIS qhull- compute convex hulls and related structures input (stdin): dimension, #points, point coordinates first comment (non-numeric) is listed in the summary halfspace: use dim plus one with offsets after coefficients options (qh-quick.htm): d - Delaunay triangulation by lifting points to a paraboloid v - Voronoi diagram via the Delaunay triangulation H1,1 - Halfspace intersection about [1,1,0,...] d Qu - Furthest-site Delaunay triangulation (upper convex hull) v Qu - Furthest-site Voronoi diagram QJ - Joggle the input to avoid precision problems . - concise list of all options - - one-line description of all options Output options (subset): FA - compute total area and volume Fx - extreme points (convex hull vertices) G - Geomview output (2-d, 3-d and 4-d) Fp - halfspace intersection coordinates m - Mathematica output (2-d and 3-d) n - normals with offsets o - OFF file format (if Voronoi, outputs regions) TO file- output results to file, may be enclosed in single quotes f - print all fields of all facets s - summary of results (default) Tv - verify result: structure, convexity, and point inclusion p - vertex coordinates i - vertices incident to each facet example: rbox 1000 s | qhull Tv s FA - html manual: index.htm - installation: README.txt - see also: COPYING.txt, REGISTER.txt, Changes.txt - WWW: - GIT: - mirror: - news: - Geomview: - news group: - FAQ: - email: qhull@qhull.org - bug reports: qhull_bug@qhull.org Geometry Center 2003/12/30 1 qhull(1) qhull(1) The sections are: - INTRODUCTION - DESCRIPTION, a description of Qhull - IMPRECISION, how Qhull handles imprecision - OPTIONS - Input and output options - Additional input/output formats - Precision options - Geomview options - Print options - Qhull options - Trace options - BUGS - E-MAIL - SEE ALSO - AUTHORS - ACKNOWLEGEMENTS This man page briefly describes all Qhull options. Please report any mismatches with Qhull's html manual (qh- man.htm). INTRODUCTION Qhull is a general dimension code for computing convex hulls, Delaunay triangulations, Voronoi diagram, furthest- site Voronoi diagram, furthest-site Delaunay triangula- tions, and halfspace intersections about a point. It implements the Quickhull algorithm for computing the con- vex hull. Qhull handles round-off errors from floating point arithmetic. It can approximate a convex hull. The program includes options for hull volume, facet area, partial hulls, input transformations, randomization, trac- ing, multiple output formats, and execution statistics. The program can be called from within your application. You can view the results in 2-d, 3-d and 4-d with Geomview. DESCRIPTION The format of input is the following: first line contains the dimension, second line contains the number of input points, and point coordinates follow. The dimension and number of points can be reversed. Comments and line breaks are ignored. A comment starts with a non-numeric character and continues to the end of line. The first comment is reported in summaries and statistics. Error reporting is better if there is one point per line. The default printout option is a short summary. There are many other output formats. Geometry Center 2003/12/30 2 qhull(1) qhull(1) Qhull implements the Quickhull algorithm for convex hull. This algorithm combines the 2-d Quickhull algorithm with the n-d beneath-beyond algorithm [c.f., Preparata & Shamos '85]. It is similar to the randomized algorithms of Clarkson and others [Clarkson et al. '93]. The main advantages of Quickhull are output sensitive performance, reduced space requirements, and automatic handling of pre- cision problems. The data structure produced by Qhull consists of vertices, ridges, and facets. A vertex is a point of the input set. A ridge is a set of d vertices and two neighboring facets. For example in 3-d, a ridge is an edge of the polyhedron. A facet is a set of ridges, a set of neighboring facets, a set of incident vertices, and a hyperplane equation. For simplicial facets, the ridges are defined by the vertices and neighboring facets. When Qhull merges two facets, it produces a non-simplicial facet. A non-simplicial facet has more than d neighbors and may share more than one ridge with a neighbor. IMPRECISION Since Qhull uses floating point arithmetic, roundoff error may occur for each calculation. This causes problems for most geometric algorithms. Qhull automatically sets option 'C-0' in 2-d, 3-d, and 4-d, or option 'Qx' in 5-d and higher. These options han- dle precision problems by merging facets. Alternatively, use option 'QJ' to joggle the input. With 'C-0', Qhull merges non-convex facets while con- structing the hull. The remaining facets are clearly con- vex. With 'Qx', Qhull merges coplanar horizon facets, flipped facets, concave facets and duplicated ridges. It merges coplanar facets after constructing the hull. With 'Qx', coplanar points may be missed, but it appears to be unlikely. To guarantee triangular output, joggle the input with option 'QJ'. Facet merging will not occur. OPTIONS To get a list of the most important options, execute 'qhull' by itself. To get a complete list of options, execute 'qhull -'. To get a complete, concise list of options, execute 'qhull .'. Options can be in any order. Capitalized options take an argument (except 'PG' and 'F' options). Single letters are used for output formats and precision constants. The other options are grouped into menus for other output for- mats ('F'), Geomview output ('G'), printing ('P'), Qhull Geometry Center 2003/12/30 3 qhull(1) qhull(1) control ('Q'), and tracing ('T'). Main options: default Compute the convex hull of the input points. Report a summary of the result. d Compute the Delaunay triangulation by lifting the input points to a paraboloid. The 'o' option prints the input points and facets. The 'QJ' option guarantees triangular output. The 'Ft' option prints a triangulation. It adds points (the centrums) to non-simplicial facets. v Compute the Voronoi diagram from the Delaunay tri- angulation. The 'p' option prints the Voronoi ver- tices. The 'o' option prints the Voronoi vertices and the vertices in each Voronoi region. It lists regions in site id order. The 'Fv' option prints each ridge of the Voronoi diagram. The first or zero'th vertex indicates the infinity vertex. Its coordinates are qh_INFINITE (-10.101). It indi- cates unbounded Voronoi regions or degenerate Delaunay triangles. Hn,n,... Compute halfspace intersection about [n,n,0,...]. The input is a set of halfspaces defined in the same format as 'n', 'Fo', and 'Fi'. Use 'Fp' to print the intersection points. Use 'Fv' to list the intersection points for each halfspace. The other output formats display the dual convex hull. The point [n,n,n,...] is a feasible point for the halfspaces, i.e., a point that is inside all of the halfspaces (Hx+b <= 0). The default coordinate value is 0. The input may start with a feasible point. If so, use 'H' by itself. The input starts with a feasi- ble point when the first number is the dimension, the second number is "1", and the coordinates com- plete a line. The 'FV' option produces a feasible point for a convex hull. d Qu Compute the furthest-site Delaunay triangulation from the upper convex hull. The 'o' option prints the input points and facets. The 'QJ' option guar- antees triangular otuput. You can also use facets. v Qu Compute the furthest-site Voronoi diagram. The 'p' option prints the Voronoi vertices. The 'o' option prints the Voronoi vertices and the vertices in Geometry Center 2003/12/30 4 qhull(1) qhull(1) each Voronoi region. The 'Fv' option prints each ridge of the Voronoi diagram. The first or zero'th vertex indicates the infinity vertex at infinity. Its coordinates are qh_INFINITE (-10.101). It indicates unbounded Voronoi regions and degenerate Delaunay triangles. Qt Triangulated output. Input/Output options: f Print out all facets and all fields of each facet. G Output the hull in Geomview format. For imprecise hulls, Geomview displays the inner and outer hull. Geomview can also display points, ridges, vertices, coplanar points, and facet intersections. See below for a list of options. For Delaunay triangulations, 'G' displays the cor- responding paraboloid. For halfspace intersection, 'G' displays the dual polytope. i Output the incident vertices for each facet. Qhull prints the number of facets followed by the ver- tices of each facet. One facet is printed per line. The numbers are the 0-relative indices of the corresponding input points. The facets are oriented. In 4-d and higher, Qhull triangulates non-simpli- cial facets. Each apex (the first vertex) is a created point that corresponds to the facet's cen- trum. Its index is greater than the indices of the input points. Each base corresponds to a simpli- cial ridge between two facets. To print the ver- tices without triangulation, use option 'Fv'. m Output the hull in Mathematica format. Qhull writes a Mathematica file for 2-d and 3-d convex hulls and for 2-d Delaunay triangulations. Qhull produces a list of objects that you can assign to a variable in Mathematica, for example: "list= << ". If the object is 2-d, it can be visualized by "Show[Graphics[list]] ". For 3-d objects the command is "Show[Graphics3D[list]]". n Output the normal equation for each facet. Qhull prints the dimension (plus one), the number of facets, and the normals for each facet. The facet's offset follows its normal coefficients. o Output the facets in OFF file format. Qhull prints the dimension, number of points, number of facets, and number of ridges. Then it prints the Geometry Center 2003/12/30 5 qhull(1) qhull(1) coordinates of the input points and the vertices for each facet. Each facet is on a separate line. The first number is the number of vertices. The remainder are the indices of the corresponding points. The vertices are oriented in 2-d, 3-d, and in simplicial facets. For 2-d Voronoi diagrams, the vertices are sorted by adjacency, but not oriented. In 3-d and higher, the Voronoi vertices are sorted by index. See the 'v' option for more information. p Output the coordinates of each vertex point. Qhull prints the dimension, the number of points, and the coordinates for each vertex. With the 'Gc' and 'Gi' options, it also prints coplanar and interior points. For Voronoi diagrams, it prints the coor- dinates of each Voronoi vertex. s Print a summary to stderr. If no output options are specified at all, a summary goes to stdout. The summary lists the number of input points, the dimension, the number of vertices in the convex hull, the number of facets in the convex hull, the number of good facets (if 'Pg'), and statistics. The last two statistics (if needed) measure the maximum distance from a point or vertex to a facet. The number in parenthesis (e.g., 2.1x) is the ratio between the maximum distance and the worst-case distance due to merging two simplicial facets. Precision options An Maximum angle given as a cosine. If the angle between a pair of facet normals is greater than n, Qhull merges one of the facets into a neighbor. If 'n' is negative, Qhull tests angles after adding each point to the hull (pre-merging). If 'n' is posi- tive, Qhull tests angles after constructing the hull (post-merging). Both pre- and post-merging can be defined. Option 'C0' or 'C-0' is set if the corresponding 'Cn' or 'C-n' is not set. If 'Qx' is set, then 'A- n' and 'C-n' are checked after the hull is con- structed and before 'An' and 'Cn' are checked. Cn Centrum radius. If a centrum is less than n below a neighboring facet, Qhull merges one of the facets. If 'n' is negative or '-0', Qhull tests and merges facets after adding each point to the hull. This is called "pre-merging". If 'n' is Geometry Center 2003/12/30 6 qhull(1) qhull(1) positive, Qhull tests for convexity after con- structing the hull ("post-merging"). Both pre- and post-merging can be defined. For 5-d and higher, 'Qx' should be used instead of 'C-n'. Otherwise, most or all facets may be merged together. En Maximum roundoff error for distance computations. Rn Randomly perturb distance computations up to +/- n * max_coord. This option perturbs every distance, hyperplane, and angle computation. To use time as the random number seed, use option 'QR-1'. Vn Minimum distance for a facet to be visible. A facet is visible if the distance from the point to the facet is greater than 'Vn'. Without merging, the default value for 'Vn' is the round-off error ('En'). With merging, the default value is the pre-merge centrum ('C-n') in 2-d or 3--d, or three times that in other dimensions. If the outside width is specified ('Wn'), the maximum, default value for 'Vn' is 'Wn'. Un Maximum distance below a facet for a point to be coplanar to the facet. The default value is 'Vn'. Wn Minimum outside width of the hull. Points are added to the convex hull only if they are clearly outside of a facet. A point is outside of a facet if its distance to the facet is greater than 'Wn'. The normal value for 'Wn' is 'En'. If the user specifies pre-merging and does not set 'Wn', than 'Wn' is set to the premerge 'Cn' and maxco- ord*(1-An). Additional input/output formats Fa Print area for each facet. For Delaunay triangula- tions, the area is the area of the triangle. For Voronoi diagrams, the area is the area of the dual facet. Use 'PAn' for printing the n largest facets, and option 'PFn' for printing facets larger than 'n'. The area for non-simplicial facets is the sum of the areas for each ridge to the centrum. Vertices far below the facet's hyperplane are ignored. The reported area may be significantly less than the actual area. Geometry Center 2003/12/30 7 qhull(1) qhull(1) FA Compute the total area and volume for option 's'. It is an approximation for non-simplicial facets (see 'Fa'). Fc Print coplanar points for each facet. The output starts with the number of facets. Then each facet is printed one per line. Each line is the number of coplanar points followed by the point ids. Option 'Qi' includes the interior points. Each coplanar point (interior point) is assigned to the facet it is furthest above (resp., least below). FC Print centrums for each facet. The output starts with the dimension followed by the number of facets. Then each facet centrum is printed, one per line. Fd Read input in cdd format with homogeneous points. The input starts with comments. The first comment is reported in the summary. Data starts after a "begin" line. The next line is the number of points followed by the dimension+1 and "real" or "integer". Then the points are listed with a leading "1" or "1.0". The data ends with an "end" line. For halfspaces ('Fd Hn,n,...'), the input format is the same. Each halfspace starts with its offset. The sign of the offset is the opposite of Qhull's convention. FD Print normals ('n', 'Fo', 'Fi') or points ('p') in cdd format. The first line is the command line that invoked Qhull. Data starts with a "begin" line. The next line is the number of normals or points followed by the dimension+1 and "real". Then the normals or points are listed with the offset before the coefficients. The offset for points is 1.0. The offset for normals has the opposite sign. The data ends with an "end" line. FF Print facets (as in 'f') without printing the ridges. Fi Print inner planes for each facet. The inner plane is below all vertices. Fi Print separating hyperplanes for bounded, inner regions of the Voronoi diagram. The first line is the number of ridges. Then each hyperplane is printed, one per line. A line starts with the num- ber of indices and floats. The first pair lists adjacent input sites, the next d floats are the normalized coefficients for the hyperplane, and the Geometry Center 2003/12/30 8 qhull(1) qhull(1) last float is the offset. The hyperplane is ori- ented toward verify that the hyperplanes are per- pendicular bisectors. Use 'Fo' for unbounded regions, and 'Fv' for the corresponding Voronoi vertices. FI Print facet identifiers. Fm Print number of merges for each facet. At most 511 merges are reported for a facet. See 'PMn' for printing the facets with the most merges. FM Output the hull in Maple format. See 'm' Fn Print neighbors for each facet. The output starts with the number of facets. Then each facet is printed one per line. Each line is the number of neighbors followed by an index for each neighbor. The indices match the other facet output formats. A negative index indicates an unprinted facet due to printing only good facets ('Pg'). It is the negation of the facet's id (option 'FI'). For example, negative indices are used for facets "at infinity" in the Delaunay triangulation. FN Print vertex neighbors or coplanar facet for each point. The first line is the number of points. Then each point is printed, one per line. If the point is coplanar, the line is "1" followed by the facet's id. If the point is not a selected vertex, the line is "0". Otherwise, each line is the num- ber of neighbors followed by the corresponding facet indices (see 'Fn'). Fo Print outer planes for each facet in the same for- mat as 'n'. The outer plane is above all points. Fo Print separating hyperplanes for unbounded, outer regions of the Voronoi diagram. The first line is the number of ridges. Then each hyperplane is printed, one per line. A line starts with the num- ber of indices and floats. The first pair lists adjacent input sites, the next d floats are the normalized coefficients for the hyperplane, and the last float is the offset. The hyperplane is ori- ented toward verify that the hyperplanes are per- pendicular bisectors. Use 'Fi' for bounded regions, and 'Fv' for the corresponding Voronoi vertices. FO List all options to stderr, including the default values. Additional 'FO's are printed to stdout. Fp Print points for halfspace intersections (option 'Hn,n,...'). Each intersection corresponds to a Geometry Center 2003/12/30 9 qhull(1) qhull(1) facet of the dual polytope. The "infinity" point [-10.101,-10.101,...] indicates an unbounded intersection. FP For each coplanar point ('Qc') print the point id of the nearest vertex, the point id, the facet id, and the distance. FQ Print command used for qhull and input. Fs Print a summary. The first line consists of the number of integers ("7"), followed by the dimen- sion, the number of points, the number of vertices, the number of facets, the number of vertices selected for output, the number of facets selected for output, the number of coplanar points selected for output. The second line consists of the number of reals ("2"), followed by the maxmimum offset to an outer plane and and minimum offset to an inner plane. Roundoff is included. Later versions of Qhull may produce additional integers or reals. FS Print the size of the hull. The first line con- sists of the number of integers ("0"). The second line consists of the number of reals ("2"), fol- lowed by the total facet area, and the total vol- ume. Later versions of Qhull may produce addi- tional integers or reals. The total volume measures the volume of the inter- section of the halfspaces defined by each facet. Both area and volume are approximations for non- simplicial facets. See option 'Fa'. Ft Print a triangulation with added points for non- simplicial facets. The first line is the dimension and the second line is the number of points and the number of facets. The points follow, one per line, then the facets follow as a list of point indices. With option points include the point-at-infinity. Fv Print vertices for each facet. The first line is the number of facets. Then each facet is printed, one per line. Each line is the number of vertices followed by the corresponding point ids. Vertices are listed in the order they were added to the hull (the last one is first). Fv Print all ridges of a Voronoi diagram. The first line is the number of ridges. Then each ridge is printed, one per line. A line starts with the num- ber of indices. The first pair lists adjacent Geometry Center 2003/12/30 10 qhull(1) qhull(1) input sites, the remaining indices list Voronoi vertices. Vertex '0' indicates the vertex-at- infinity (i.e., an unbounded ray). In 3-d, the vertices are listed in order. See 'Fi' and 'Fo' for separating hyperplanes. FV Print average vertex. The average vertex is a fea- sible point for halfspace intersection. Fx List extreme points (vertices) of the convex hull. The first line is the number of points. The other lines give the indices of the corresponding points. The first point is '0'. In 2-d, the points occur in counter-clockwise order; otherwise they occur in input order. For Delaunay triangulations, 'Fx' lists the extreme points of the input sites. The points are unordered. Geomview options G Produce a file for viewing with Geomview. Without other options, Qhull displays edges in 2-d, outer planes in 3-d, and ridges in 4-d. A ridge can be explicit or implicit. An explicit ridge is a dim-1 dimensional simplex between two facets. In 4-d, the explicit ridges are triangles. When displaying a ridge in 4-d, Qhull projects the ridge's vertices to one of its facets' hyperplanes. Use 'Gh' to project ridges to the intersection of both hyper- planes. Ga Display all input points as dots. Gc Display the centrum for each facet in 3-d. The centrum is defined by a green radius sitting on a blue plane. The plane corresponds to the facet's hyperplane. The radius is defined by 'C-n' or 'Cn'. GDn Drop dimension n in 3-d or 4-d. The result is a 2-d or 3-d object. Gh Display hyperplane intersections in 3-d and 4-d. In 3-d, the intersection is a black line. It lies on two neighboring hyperplanes (c.f., the blue squares associated with centrums ('Gc')). In 4-d, the ridges are projected to the intersection of both hyperplanes. Gi Display inner planes in 2-d and 3-d. The inner plane of a facet is below all of its vertices. It is parallel to the facet's hyperplane. The inner plane's color is the opposite (1-r,1-g,1-b) of the Geometry Center 2003/12/30 11 qhull(1) qhull(1) outer plane. Its edges are determined by the ver- tices. Gn Do not display inner or outer planes. By default, Geomview displays the precise plane (no merging) or both inner and output planes (merging). Under merging, Geomview does not display the inner plane if the the difference between inner and outer is too small. Go Display outer planes in 2-d and 3-d. The outer plane of a facet is above all input points. It is parallel to the facet's hyperplane. Its color is determined by the facet's normal, and its edges are determined by the vertices. Gp Display coplanar points and vertices as radii. A radius defines a ball which corresponds to the imprecision of the point. The imprecision is the maximum of the roundoff error, the centrum radius, and maxcoord * (1-An). It is at least 1/20'th of the maximum coordinate, and ignores post-merging if pre-merging is done. Gr Display ridges in 3-d. A ridge connects the two vertices that are shared by neighboring facets. Ridges are always displayed in 4-d. Gt A 3-d Delaunay triangulation looks like a convex hull with interior facets. Option 'Gt' removes the outside ridges to reveal the outermost facets. It automatically sets options 'Gr' and 'GDn'. Gv Display vertices as spheres. The radius of the sphere corresponds to the imprecision of the data. See 'Gp' for determining the radius. Print options PAn Only the n largest facets are marked good for printing. Unless 'PG' is set, 'Pg' is automati- cally set. Pdk:n Drop facet from output if normal[k] <= n. The option 'Pdk' uses the default value of 0 for n. PDk:n Drop facet from output if normal[k] >= n. The option 'PDk' uses the default value of 0 for n. PFn Only facets with area at least 'n' are marked good for printing. Unless 'PG' is set, 'Pg' is automat- ically set. Geometry Center 2003/12/30 12 qhull(1) qhull(1) Pg Print only good facets. A good facet is either visible from a point (the 'QGn' option) or includes a point (the 'QVn' option). It also meets the requirements of 'Pdk' and 'PDk' options. Option 'Pg' is automatically set for options 'PAn' and 'PFn'. PG Print neighbors of good facets. PMn Only the n facets with the most merges are marked good for printing. Unless 'PG' is set, 'Pg' is automatically set. Po Force output despite precision problems. Verify ('Tv') does not check coplanar points. Flipped facets are reported and concave facets are counted. If 'Po' is used, points are not partitioned into flipped facets and a flipped facet is always visible to a point. Also, if an error occurs before the completion of Qhull and tracing is not active, 'Po' outputs a neighborhood of the erroneous facets (if any). Pp Do not report precision problems. Qhull control options Qbk:0Bk:0 Drop dimension k from the input points. This allows the user to take convex hulls of sub-dimen- sional objects. It happens before the Delaunay and Voronoi transformation. QbB Scale the input points to fit the unit cube. After scaling, the lower bound will be -0.5 and the upper bound +0.5 in all dimensions. For Delaunay and Voronoi diagrams, scaling happens after projection to the paraboloid. Under precise arithmetic, scal- ing does not change the topology of the convex hull. Qbb Scale the last coordinate to [0, m] where m is the maximum absolute value of the other coordinates. For Delaunay and Voronoi diagrams, scaling happens after projection to the paraboloid. It reduces roundoff error for inputs with integer coordinates. Under precise arithmetic, scaling does not change the topology of the convex hull. Qbk:n Scale the k'th coordinate of the input points. After scaling, the lower bound of the input points will be n. 'Qbk' scales to -0.5. Geometry Center 2003/12/30 13 qhull(1) qhull(1) QBk:n Scale the k'th coordinate of the input points. After scaling, the upper bound will be n. 'QBk' scales to +0.5. Qc Keep coplanar points with the nearest facet. Out- put formats 'p', 'f', 'Gp', 'Fc', 'FN', and 'FP' will print the points. Qf Partition points to the furthest outside facet. Qg Only build good facets. With the 'Qg' option, Qhull will only build those facets that it needs to determine the good facets in the output. See 'QGn', 'QVn', and 'PdD' for defining good facets, and 'Pg' and 'PG' for printing good facets and their neighbors. QGn A facet is good (see 'Qg' and 'Pg') if it is visi- ble from point n. If n < 0, a facet is good if it is not visible from point n. Point n is not added to the hull (unless 'TCn' or 'TPn'). With rbox, use the 'Pn,m,r' option to define your point; it will be point 0 (QG0). Qi Keep interior points with the nearest facet. Out- put formats 'p', 'f', 'Gp', 'FN', 'FP', and 'Fc' will print the points. QJn Joggle each input coordinate by adding a random number in [-n,n]. If a precision error occurs, then qhull increases n and tries again. It does not increase n beyond a certain value, and it stops after a certain number of attempts [see user.h]. Option 'QJ' selects a default value for n. The output will be simplicial. For Delaunay triangula- tions, 'QJn' sets 'Qbb' to scale the last coordi- nate (not if 'Qbk:n' or 'QBk:n' is set). 'QJn' is deprecated for Voronoi diagrams. See also 'Qt'. Qm Only process points that would otherwise increase max_outside. Other points are treated as coplanar or interior points. Qr Process random outside points instead of furthest ones. This makes Qhull equivalent to the random- ized incremental algorithms. CPU time is not reported since the randomization is inefficient. QRn Randomly rotate the input points. If n=0, use time as the random number seed. If n>0, use n as the random number seed. If n=-1, don't rotate but use time as the random number seed. For Delaunay tri- angulations ('d' and 'v'), rotate about the last axis. Geometry Center 2003/12/30 14 qhull(1) qhull(1) Qs Search all points for the initial simplex. Qt Triangulated output. Triangulate non-simplicial facets. 'Qt' is deprecated for Voronoi diagrams. See also 'QJn' Qv Test vertex neighbors for convexity after post- merging. To use the 'Qv' option, you also need to set a merge option (e.g., 'Qx' or 'C-0'). QVn A good facet (see 'Qg' and 'Pg') includes point n. If n<0, then a good facet does not include point n. The point is either in the initial simplex or it is the first point added to the hull. Option 'QVn' may not be used with merging. Qx Perform exact merges while building the hull. The "exact" merges are merging a point into a coplanar facet (defined by 'Vn', 'Un', and 'C-n'), merging concave facets, merging duplicate ridges, and merg- ing flipped facets. Coplanar merges and angle coplanar merges ('A-n') are not performed. Concav- ity testing is delayed until a merge occurs. After the hull is built, all coplanar merges are performed (defined by 'C-n' and 'A-n'), then post- merges are performed (defined by 'Cn' and 'An'). Qz Add a point "at infinity" that is above the paraboloid for Delaunay triangulations and Voronoi diagrams. This reduces precision problems and allows the triangulation of cospherical points. Qhull experiments and speedups Q0 Turn off pre-merging as a default option. With 'Q0'/'Qx' and without explicit pre-merge options, Qhull ignores precision issues while constructing the convex hull. This may lead to precision errors. If so, a descriptive warning is generated. Q1 With 'Q1', Qhull sorts merges by type (coplanar, angle coplanar, concave) instead of by angle. Q2 With 'Q2', Qhull merges all facets at once instead of using independent sets of merges and then retesting. Q3 With 'Q3', Qhull does not remove redundant ver- tices. Q4 With 'Q4', Qhull avoids merges of an old facet into a new facet. Q5 With 'Q5', Qhull does not correct outer planes at the end. The maximum outer plane is used instead. Geometry Center 2003/12/30 15 qhull(1) qhull(1) Q6 With 'Q6', Qhull does not pre-merge concave or coplanar facets. Q7 With 'Q7', Qhull processes facets in depth-first order instead of breadth-first order. Q8 With 'Q8' and merging, Qhull does not retain near- interior points for adjusting outer planes. 'Qc' will probably retain all points that adjust outer planes. Q9 With 'Q9', Qhull processes the furthest of all out- side sets at each iteration. Q10 With 'Q10', Qhull does not use special processing for narrow distributions. Q11 With 'Q11', Qhull copies normals and recomputes centrums for tricoplanar facets. Trace options Tn Trace at level n. Qhull includes full execution tracing. 'T-1' traces events. 'T1' traces the overall execution of the program. 'T2' and 'T3' trace overall execution and geometric and topologi- cal events. 'T4' traces the algorithm. 'T5' includes information about memory allocation and Gaussian elimination. Ta Annotate output with codes that identify the corresponding qh_fprintf() statement. Tc Check frequently during execution. This will catch most inconsistency errors. TCn Stop Qhull after building the cone of new facets for point n. The output for 'f' includes the cone and the old hull. See also 'TVn'. TFn Report progress whenever more than n facets are created During post-merging, 'TFn' reports progress after more than n/2 merges. TI file Input data from 'file'. The filename may not include spaces or quotes. TO file Output results to 'file'. The name may be enclosed in single quotes. TPn Turn on tracing when point n is added to the hull. Trace partitions of point n. If used with TWn, turn off tracing after adding point n to the hull. TRn Rerun qhull n times. Usually used with 'QJn' to determine the probability that a given joggle will fail. Ts Collect statistics and print to stderr at the end of execution. Tv Verify the convex hull. This checks the topologi- cal structure, facet convexity, and point inclu- sion. If precision problems occurred, facet con- vexity is tested whether or not 'Tv' is selected. Option 'Tv' does not check point inclusion if Geometry Center 2003/12/30 16 qhull(1) qhull(1) forcing output with 'Po', or if 'Q5' is set. For point inclusion testing, Qhull verifies that all points are below all outer planes (facet->max- outside). Point inclusion is exhaustive if merging or if the facet-point product is small enough; oth- erwise Qhull verifies each point with a directed search (qh_findbest). Point inclusion testing occurs after producing out- put. It prints a message to stderr unless option 'Pp' is used. This allows the user to interrupt Qhull without changing the output. TVn Stop Qhull after adding point n. If n < 0, stop Qhull before adding point n. Output shows the hull at this time. See also 'TCn' TMn Turn on tracing at n'th merge. TWn Trace merge facets when the width is greater than n. Tz Redirect stderr to stdout. BUGS Please report bugs to Brad Barber at qhull_bug@qhull.org. If Qhull does not compile, it is due to an incompatibility between your system and ours. The first thing to check is that your compiler is ANSI standard. If it is, check the man page for the best options, or find someone to help you. If you locate the cause of your problem, please send email since it might help others. If Qhull compiles but crashes on the test case (rbox D4), there's still incompatibility between your system and ours. Typically it's been due to mem.c and memory align- ment. You can use qh_NOmem in mem.h to turn off memory management. Please let us know if you figure out how to fix these problems. If you do find a problem, try to simplify it before reporting the error. Try different size inputs to locate the smallest one that causes an error. You're welcome to hunt through the code using the execution trace as a guide. This is especially true if you're incorporating Qhull into your own program. When you do report an error, please attach a data set to the end of your message. This allows us to see the error for ourselves. Qhull is maintained part-time. Geometry Center 2003/12/30 17 qhull(1) qhull(1) E-MAIL Please send correspondence to qhull@qhull.org and report bugs to qhull_bug@qhull.org. Let us know how you use Qhull. If you mention it in a paper, please send the reference and an abstract. If you would like to get Qhull announcements (e.g., a new version) and news (any bugs that get fixed, etc.), let us know and we will add you to our mailing list. If you would like to communicate with other Qhull users, we will add you to the qhull_users alias. For Internet news about geometric algorithms and convex hulls, look at comp.graph- ics.algorithms and sci.math.num-analysis SEE ALSO rbox(1) Barber, C. B., D.P. Dobkin, and H.T. Huhdanpaa, "The Quickhull Algorithm for Convex Hulls," ACM Trans. on Math- ematical Software, 22(4):469-483, Dec. 1996. http://portal.acm.org/citation.cfm?doid=235815.235821 http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.117.405 Clarkson, K.L., K. Mehlhorn, and R. Seidel, "Four results on randomized incremental construction," Computational Geometry: Theory and Applications, vol. 3, p. 185-211, 1993. Preparata, F. and M. Shamos, Computational Geometry, Springer-Verlag, New York, 1985. AUTHORS C. Bradford Barber Hannu Huhdanpaa bradb@shore.net hannu@qhull.org ACKNOWLEDGEMENTS A special thanks to Albert Marden, Victor Milenkovic, the Geometry Center, Harvard University, and Endocardial Solu- tions, Inc. for supporting this work. Qhull 1.0 and 2.0 were developed under National Science Foundation grants NSF/DMS-8920161 and NSF-CCR-91-15793 750-7504. David Dobkin Geometry Center 2003/12/30 18 qhull(1) qhull(1) guided the original work at Princeton University. If you find it useful, please let us know. The Geometry Center was supported by grant DMS-8920161 from the National Science Foundation, by grant DOE/DE-FG02-92ER25137 from the Department of Energy, by the University of Minnesota, and by Minnesota Technology, Inc. Qhull is available from http://www.qhull.org Geometry Center 2003/12/30 19 rbox(1) rbox(1) NAME rbox - generate point distributions for qhull SYNOPSIS Command "rbox" (w/o arguments) lists the options. DESCRIPTION rbox generates random or regular points according to the options given, and outputs the points to stdout. The points are generated in a cube, unless 's' or given. The format of the output is the following: first line contains the dimension and a comment, second line contains the num- ber of points, and the following lines contain the points, one point per line. Points are represented by their coor- dinate values. EXAMPLES rbox 10 10 random points in the unit cube centered at the origin. rbox 10 s D2 10 random points on a 2-d circle. rbox 100 W0 100 random points on the surface of a cube. rbox 1000 s D4 1000 random points on a 4-d sphere. rbox c D5 O0.5 a 5-d hypercube with one corner at the origin. rbox d D10 a 10-d diamond. rbox x 1000 r W0 100 random points on the surface of a fixed simplex rbox y D12 a 12-d simplex. rbox l 10 10 random points along a spiral rbox l 10 r 10 regular points along a spiral plus two end points rbox 1000 L10000 D4 s 1000 random points on the surface of a narrow lens. rbox c G2 d G3 a cube with coordinates +2/-2 and a diamond with Geometry Center August 10, 1998 1 rbox(1) rbox(1) coordinates +3/-3. rbox 64 M3,4 z a rotated, {0,1,2,3} x {0,1,2,3} x {0,1,2,3} lat- tice (Mesh) of integer points. rbox P0 P0 P0 P0 P0 5 copies of the origin in 3-d. Try 'rbox P0 P0 P0 P0 P0 | qhull QJ'. r 100 s Z1 G0.1 two cospherical 100-gons plus another cospherical point. 100 s Z1 a cone of points. 100 s Z1e-7 a narrow cone of points with many precision errors. OPTIONS n number of points Dn dimension n-d (default 3-d) Bn bounding box coordinates (default 0.5) l spiral distribution, available only in 3-d Ln lens distribution of radius n. May be used with 's', 'r', 'G', and 'W'. Mn,m,r lattice (Mesh) rotated by {[n,-m,0], [m,n,0], [0,0,r], ...}. Use 'Mm,n' for a rigid rotation with r = sqrt(n^2+m^2). 'M1,0' is an orthogonal lattice. For example, '27 M1,0' is {0,1,2} x {0,1,2} x {0,1,2}. s cospherical points randomly generated in a cube and projected to the unit sphere x simplicial distribution. It is fixed for option 'r'. May be used with 'W'. y simplicial distribution plus a simplex. Both 'x' and 'y' generate the same points. Wn restrict points to distance n of the surface of a sphere or a cube c add a unit cube to the output c Gm add a cube with all combinations of +m and -m to the output Geometry Center August 10, 1998 2 rbox(1) rbox(1) d add a unit diamond to the output. d Gm add a diamond made of 0, +m and -m to the output Pn,m,r add point [n,m,r] to the output first. Pad coordi- nates with 0.0. n Remove the command line from the first line of out- put. On offset the data by adding n to each coordinate. t use time in seconds as the random number seed (default is command line). tn set the random number seed to n. z generate integer coordinates. Use 'Bn' to change the range. The default is 'B1e6' for six-digit coordinates. In R^4, seven-digit coordinates will overflow hyperplane normalization. Zn s restrict points to a disk about the z+ axis and the sphere (default Z1.0). Includes the opposite pole. 'Z1e-6' generates degenerate points under single precision. Zn Gm s same as Zn with an empty center (default G0.5). r s D2 generate a regular polygon r s Z1 G0.1 generate a regular cone BUGS Some combinations of arguments generate odd results. Report bugs to qhull_bug@qhull.org, other correspon- dence to qhull@qhull.org SEE ALSO qhull(1) AUTHOR C. Bradford Barber bradb@shore.net Geometry Center August 10, 1998 3 # end of q_test qhull-2012.1/eg/q_test.bat0000755000076400010400000007431311665301514016503 0ustar bbarberAdministratorsecho Run q_test for Windows from the bin/ directory. >q_test.x echo === errors if 'user_eg' and 'user_eg2' not found === echo === check user_eg === >>q_test.x echo "user_eg 'QR1 p n Qt' 'v p' Fp" >>q_test.x user_eg "QR1 p n Qt" "v p" Fp >>q_test.x echo "user_eg2 'QR1 p' 'v p' Fp" >>q_test.x user_eg2 "QR1 p" "v p" Fp >>q_test.x echo 'user_eg3 rbox "10 D2" "2 D2" qhull "p"' >>q_test.x user_eg3 rbox "10 D2" "2 D2" qhull "p" >>q_test.x echo === check front ends ========================================================== >>q_test.x echo "qconvex -" >>q_test.x qconvex - >>q_test.x echo "qconvex ." >>q_test.x qconvex . >>q_test.x echo "qconvex" >>q_test.x qconvex >>q_test.x echo "rbox c D3 | qconvex s n Qt" >>q_test.x rbox c D3 | qconvex s n Qt >>q_test.x echo "rbox c D2 | qconvex i Qt " >>q_test.x rbox c D2 | qconvex i Qt >>q_test.x echo "rbox c D2 | qconvex o" >>q_test.x rbox c D2 | qconvex o >>q_test.x echo "rbox 1000 s | qconvex s Tv FA" >>q_test.x rbox 1000 s | qconvex s Tv FA >>q_test.x echo "rbox c d D2 | qconvex s Qc Fx" >>q_test.x rbox c d D2 | qconvex s Qc Fx >>q_test.x echo "rbox y 1000 W0 | qconvex s n " >>q_test.x rbox y 1000 W0 | qconvex s n >>q_test.x echo "rbox y 1000 W0 | qconvex s QJ" >>q_test.x rbox y 1000 W0 | qconvex s QJ >>q_test.x echo "rbox d G1 D12 | qconvex QR0 FA" >>q_test.x rbox d G1 D12 | qconvex QR0 FA >>q_test.x echo "rbox c D6 | qconvex FA TF500" >>q_test.x rbox c D6 | qconvex FA TF500 >>q_test.x echo "rbox c P0 d D2 | qconvex p Fa Fc FP FI Fn FN FS Fv Fx" >>q_test.x rbox c P0 d D2 | qconvex p Fa Fc FP FI Fn FN FS Fv Fx >>q_test.x echo "rbox c d D2 | qconvex s i QV0" >>q_test.x rbox c d D2 | qconvex s i QV0 >>q_test.x echo "rbox c | qconvex Q0" >>q_test.x rbox c | qconvex Q0 >>q_test.x echo "qvoronoi -" >>q_test.x qvoronoi - >>q_test.x echo "qvoronoi ." >>q_test.x qvoronoi . >>q_test.x echo "qvoronoi" >>q_test.x qvoronoi >>q_test.x echo "rbox c P0 D2 | qvoronoi s o" >>q_test.x rbox c P0 D2 | qvoronoi s o >>q_test.x echo "rbox c P0 D2 | qvoronoi Fi" >>q_test.x rbox c P0 D2 | qvoronoi Fi >>q_test.x echo "rbox c P0 D2 | qvoronoi Fo" >>q_test.x rbox c P0 D2 | qvoronoi Fo >>q_test.x echo "rbox c P0 D2 | qvoronoi Fv" >>q_test.x rbox c P0 D2 | qvoronoi Fv >>q_test.x echo "rbox c P0 D2 | qvoronoi s Qu Qt Fv" >>q_test.x rbox c P0 D2 | qvoronoi s Qu Qt Fv >>q_test.x echo "rbox c P0 D2 | qvoronoi Qu Fo" >>q_test.x rbox c P0 D2 | qvoronoi Qu Fo >>q_test.x echo "rbox c G1 d D2 | qvoronoi s p " >>q_test.x rbox c G1 d D2 | qvoronoi s p >>q_test.x echo "rbox c G1 d D2 | qvoronoi QJ p " >>q_test.x rbox c G1 d D2 | qvoronoi QJ p >>q_test.x echo "rbox c P-0.1 P+0.1 P+0.1 D2 | qvoronoi s Fc FP FQ Fn FN " >>q_test.x rbox c P-0.1 P+0.1 P+0.1 D2 | qvoronoi s Fc FP FQ Fn FN >>q_test.x echo "rbox P0 c D2 | qvoronoi s Fv QV0" >>q_test.x rbox P0 c D2 | qvoronoi s Fv QV0 >>q_test.x echo "qdelaunay -" >>q_test.x qdelaunay - >>q_test.x echo "qdelaunay ." >>q_test.x qdelaunay . >>q_test.x echo "qdelaunay" >>q_test.x qdelaunay >>q_test.x echo "rbox c P0 D2 | qdelaunay s o" >>q_test.x rbox c P0 D2 | qdelaunay s o >>q_test.x echo "rbox c P0 D2 | qdelaunay i" >>q_test.x rbox c P0 D2 | qdelaunay i >>q_test.x echo "rbox c P0 D2 | qdelaunay Fv" >>q_test.x rbox c P0 D2 | qdelaunay Fv >>q_test.x echo "rbox c P0 D2 | qdelaunay s Qu Qt Fv" >>q_test.x rbox c P0 D2 | qdelaunay s Qu Qt Fv >>q_test.x echo "rbox c G1 d D2 | qdelaunay s i" >>q_test.x rbox c G1 d D2 | qdelaunay s i >>q_test.x echo "rbox c G1 d D2 | qdelaunay Ft" >>q_test.x rbox c G1 d D2 | qdelaunay Ft >>q_test.x echo "rbox c G1 d D2 | qdelaunay QJ s Ft" >>q_test.x rbox c G1 d D2 | qdelaunay QJ s Ft >>q_test.x echo "rbox M3,4 z 100 D2 | qdelaunay s" >>q_test.x rbox M3,4 z 100 D2 | qdelaunay s >>q_test.x echo "rbox c P-0.1 P+0.1 P+0.1 D2 | qdelaunay s Fx Fa Fc FP FQ Fn FN" >>q_test.x rbox c P-0.1 P+0.1 P+0.1 D2 | qdelaunay s Fx Fa Fc FP FQ Fn FN >>q_test.x echo "rbox P0 P0 c D2 | qdelaunay s FP QV0" >>q_test.x rbox P0 P0 c D2 | qdelaunay s FP QV0 >>q_test.x echo "qhalf -" >>q_test.x qhalf - >>q_test.x echo "qhalf ." >>q_test.x qhalf . >>q_test.x echo "qhalf" >>q_test.x qhalf >>q_test.x echo "rbox d | qhull FQ n | qhalf s Qt H0,0,0 Fp" >>q_test.x rbox d | qhull FQ n | qhalf s H0,0,0 Fp >>q_test.x echo "rbox c | qhull FQ FV n | qhalf s i" >>q_test.x rbox c | qhull FQ FV n | qhalf s i >>q_test.x echo "rbox c | qhull FQ FV n | qhalf o" >>q_test.x rbox c | qhull FQ FV n | qhalf o >>q_test.x echo "rbox d D2 | qhull FQ n | qhalf s H0 Fc FP Fn FN FQ Fv Fx" >>q_test.x rbox d D2 | qhull FQ n | qhalf s H0 Fc FP Fn FN FQ Fv Fx >>q_test.x echo === check quality of merges for ${d:-`hostname`} ${d:-`date`} >>q_test.x echo "rbox 1000 W0 t | qhull QR2 QJ s Fs Tv" >>q_test.x rbox 1000 W0 t | qhull QR2 QJ s Fs Tv >>q_test.x echo "rbox 1000 W0 t | qhull QR2 s Fs Tv" >>q_test.x rbox 1000 W0 t | qhull QR2 s Fs Tv >>q_test.x echo "rbox 1000 s t | qhull C0.02 Qc Tv" >>q_test.x rbox 1000 s t | qhull C0.02 Qc Tv >>q_test.x echo "rbox 500 s D4 t | qhull C0.01 Qc Tv" >>q_test.x rbox 500 s D4 t | qhull C0.01 Qc Tv >>q_test.x echo "rbox 1000 s t | qhull C-0.02 Qc Tv" >>q_test.x rbox 1000 s t | qhull C-0.02 Qc Tv >>q_test.x echo "rbox 1000 s D4 t | qhull C-0.01 Qc Tv" >>q_test.x rbox 1000 s D4 t | qhull C-0.01 Qc Tv >>q_test.x echo "rbox 200 s D5 t | qhull C-0.01 Qx Qc Tv" >>q_test.x rbox 200 s D5 t | qhull C-0.01 Qx Qc Tv >>q_test.x echo "rbox 100 s D6 t | qhull C-0.001 Qx Qc Tv" >>q_test.x rbox 100 s D6 t | qhull C-0.001 Qx Qc Tv >>q_test.x echo "rbox 1000 W1e-4 t | qhull C-1e-6 Qc Tv" >>q_test.x rbox 1000 W1e-4 t | qhull C-1e-6 Qc Tv >>q_test.x echo "rbox 1000 W5e-4 D4 t | qhull C-1e-5 Qc Tv" >>q_test.x rbox 1000 W5e-4 D4 t | qhull C-1e-5 Qc Tv >>q_test.x echo "rbox 400 W1e-3 D5 t | qhull C-1e-5 Qx Qc Tv" >>q_test.x rbox 400 W1e-3 D5 t | qhull C-1e-5 Qx Qc Tv >>q_test.x echo === check input format etc. ${d:-`date`} >>q_test.x echo "rbox d h | qhull Fd FV n FD Tcv | qhull Fd H Fp Tcv" >>q_test.x rbox d h | qhull Fd FV n FD Tcv | qhull Fd H Fp Tcv >>q_test.x echo "rbox 10 h | qhull Fd FD p Tcv | qhull Fd d Tcv " >>q_test.x rbox 10 h | qhull Fd FD p Tcv | qhull Fd d Tcv >>q_test.x echo === check rbox ${d:-`date`} >>q_test.x echo "rbox 3 n D2" >>q_test.x rbox 3 n D2 >>q_test.x echo "rbox 3 D2" >>q_test.x rbox 3 D2 >>q_test.x echo "rbox 3 h D2" >>q_test.x rbox 3 h D2 >>q_test.x echo "rbox 3 z D2" >>q_test.x rbox 3 z D2 >>q_test.x echo "rbox 3 z h D2" >>q_test.x rbox 3 z h D2 >>q_test.x echo "rbox 3 B10 D2" >>q_test.x rbox 3 B10 D2 >>q_test.x echo "rbox 3 z B10 D2" >>q_test.x rbox 3 z B10 D2 >>q_test.x echo "rbox 4 L2 r D2" >>q_test.x rbox 4 L2 r D2 >>q_test.x echo "rbox 8 L2 D2" >>q_test.x rbox 8 L2 D2 >>q_test.x echo "rbox 4 L4 r D3" >>q_test.x rbox 4 L4 r D3 >>q_test.x echo "rbox y" >>q_test.x rbox y >>q_test.x echo "rbox 10 M3,4" >>q_test.x rbox 10 M3,4 >>q_test.x echo "rbox 4 L4 s D5 W1e-3 " >>q_test.x rbox 4 L4 s D5 W1e-3 >>q_test.x echo "rbox 10 L2 s D3 | qhull Tcv" >>q_test.x rbox 10 L2 s D3 | qhull Tcv >>q_test.x echo "rbox 10 L4 s W1e-3 D3 | qhull Tcv" >>q_test.x rbox 10 L4 s W1e-3 D3 | qhull Tcv >>q_test.x echo "rbox 10 L6 D3 | qhull Tcv" >>q_test.x rbox 10 L6 D3 | qhull Tcv >>q_test.x echo "rbox 10 L1.1 s D4 | qhull Tcv" >>q_test.x rbox 10 L1.1 s D4 | qhull Tcv >>q_test.x echo "rbox y r 100 W0 O0.5 | qhull s p Tcv" >>q_test.x rbox y r 100 W0 O0.5 | qhull s p Tcv >>q_test.x echo "rbox x r 100 W0 O0.5 | qhull s p Tcv" >>q_test.x rbox x r 100 W0 O0.5 | qhull s p Tcv >>q_test.x echo "rbox 12 D8 | qhull Tcv" >>q_test.x rbox 12 D8 | qhull Tcv >>q_test.x echo "rbox 12 D9 | qhull Tcv" >>q_test.x rbox 12 D9 | qhull Tcv >>q_test.x echo "rbox 1000 D4 | qhull s i A-0.97 C0.2 A0.7 Tcv" >>q_test.x rbox 1000 D4 | qhull s i A-0.97 C0.2 A0.7 Tcv >>q_test.x echo "rbox 3 D2 | qhull Qb0B1:-2 p " >>q_test.x rbox 3 D2 | qhull Qb0B1:-2 p >>q_test.x echo "rbox 100 r D2 | qhull Pd0:0.7 PD0:0.8 n Tcv" >>q_test.x rbox 100 r D2 | qhull Pd0:0.7 PD0:0.8 n Tcv >>q_test.x echo "rbox 1000 s | qhull C0.05 Tcv" >>q_test.x rbox 1000 s | qhull C0.05 Tcv >>q_test.x echo "rbox 1000 s t | qhull Qm C0.05 Tcv" >>q_test.x rbox 1000 s t | qhull Qm C0.05 Tcv >>q_test.x echo "rbox 500 D2 | qhull n A-0.95 C0.1 Tcv" >>q_test.x rbox 500 D2 | qhull n A-0.95 C0.1 Tcv >>q_test.x echo "rbox 500 s P1,1,1 | qhull QgG0 Pp Tcv" >>q_test.x rbox 500 s P1,1,1 | qhull QgG0 Pp Tcv >>q_test.x echo "rbox d | qhull m" >>q_test.x rbox d | qhull m >>q_test.x echo "rbox d | qhull FM" >>q_test.x rbox d | qhull FM >>q_test.x echo "rbox c D2 | qhull Q0 Tcv" >>q_test.x rbox c D2 | qhull Q0 Tcv >>q_test.x echo "rbox d D2 | qhull Tcv" >>q_test.x rbox d D2 | qhull Tcv >>q_test.x echo "rbox c D3 | qhull Q0 Tcv" >>q_test.x rbox c D3 | qhull Q0 Tcv >>q_test.x echo "rbox d D3 | qhull Tcv" >>q_test.x rbox d D3 | qhull Tcv >>q_test.x echo "rbox c D4 | qhull Q0 Tcv" >>q_test.x rbox c D4 | qhull Q0 Tcv >>q_test.x echo "rbox d D4 | qhull Tcv" >>q_test.x rbox d D4 | qhull Tcv >>q_test.x echo "rbox c D5 | qhull Q0 Tcv" >>q_test.x rbox c D5 | qhull Q0 Tcv >>q_test.x echo "rbox d D5 | qhull Tcv" >>q_test.x rbox d D5 | qhull Tcv >>q_test.x echo "rbox c D6 | qhull Q0 Tcv" >>q_test.x rbox c D6 | qhull Q0 Tcv >>q_test.x echo "rbox d D6 | qhull Tcv" >>q_test.x rbox d D6 | qhull Tcv >>q_test.x echo "rbox d D7 | qhull Tcv" >>q_test.x rbox d D7 | qhull Tcv >>q_test.x echo "rbox c D2 | qhull Tcv C-0" >>q_test.x rbox c D2 | qhull Tcv C-0 >>q_test.x echo "rbox c D3 | qhull Tcv C-0" >>q_test.x rbox c D3 | qhull Tcv C-0 >>q_test.x echo "rbox c D4 | qhull Tcv C-0" >>q_test.x rbox c D4 | qhull Tcv C-0 >>q_test.x echo "rbox c D5 | qhull Tcv C-0" >>q_test.x rbox c D5 | qhull Tcv C-0 >>q_test.x echo "rbox c D6 | qhull Tcv C-0" >>q_test.x rbox c D6 | qhull Tcv C-0 >>q_test.x echo "rbox c D7 | qhull Tv C-0" >>q_test.x rbox c D7 | qhull Tv C-0 >>q_test.x echo "rbox 20 l D3 | qhull Tcv" >>q_test.x rbox 20 l D3 | qhull Tcv >>q_test.x echo "rbox 100 s D2 | qhull Tcv" >>q_test.x rbox 100 s D2 | qhull Tcv >>q_test.x echo "rbox 100 s D3 | qhull Tcv" >>q_test.x rbox 100 s D3 | qhull Tcv >>q_test.x echo "rbox 100 s D4 | qhull Tcv" >>q_test.x rbox 100 s D4 | qhull Tcv >>q_test.x echo "rbox 100 s c D4 | qhull Tcv" >>q_test.x rbox 100 s c D4 | qhull Tcv >>q_test.x echo "rbox 100 s d G1.5 D4 | qhull Tcv" >>q_test.x rbox 100 s d G1.5 D4 | qhull Tcv >>q_test.x echo "rbox 100 s W1e-2 | qhull Tcv" >>q_test.x rbox 100 s W1e-2 | qhull Tcv >>q_test.x echo "rbox 100 | qhull Tcv" >>q_test.x rbox 100 | qhull Tcv >>q_test.x echo "rbox 100 W1e-3 | qhull Tcv" >>q_test.x rbox 100 W1e-3 | qhull Tcv >>q_test.x echo "rbox 100 r D2 | qhull Tcv" >>q_test.x rbox 100 r D2 | qhull Tcv >>q_test.x echo "rbox 100 r s Z1 | qhull Tcv" >>q_test.x rbox 100 r s Z1 | qhull Tcv >>q_test.x echo "rbox 100 r s Z1 G0.1 | qhull Tcv C-0" >>q_test.x rbox 100 r s Z1 G0.1 | qhull Tcv C-0 >>q_test.x echo "rbox 100 s Z1 G0.1 | qhull Tcv " >>q_test.x rbox 100 s Z1 G0.1 | qhull Tcv >>q_test.x echo "rbox 100 s Z1e-5 G0.1 | qhull Tc Pp" >>q_test.x rbox 100 s Z1e-5 G0.1 | qhull Tc Pp >>q_test.x echo === check qhull output formats ${d:-`date`} >>q_test.x echo "rbox 5 r s D2 | qhull Tcv" >>q_test.x rbox 5 r s D2 | qhull Tcv >>q_test.x echo "rbox 5 r s D2 | qhull s " >>q_test.x rbox 5 r s D2 | qhull s >>q_test.x echo "rbox 5 r s D2 | qhull s o " >>q_test.x rbox 5 r s D2 | qhull s o >>q_test.x echo "rbox 5 r s D2 | qhull f" >>q_test.x rbox 5 r s D2 | qhull f >>q_test.x echo "rbox 5 r s D2 | qhull i " >>q_test.x rbox 5 r s D2 | qhull i >>q_test.x echo "rbox 5 r s D2 | qhull m " >>q_test.x rbox 5 r s D2 | qhull m >>q_test.x echo "rbox 5 r s D2 | qhull FM " >>q_test.x rbox 5 r s D2 | qhull FM >>q_test.x echo "rbox 5 r s D2 | qhull n " >>q_test.x rbox 5 r s D2 | qhull n >>q_test.x echo "rbox 5 r s D2 | qhull p " >>q_test.x rbox 5 r s D2 | qhull p >>q_test.x echo "rbox 5 r s D2 | qhull o " >>q_test.x rbox 5 r s D2 | qhull o >>q_test.x echo "rbox 5 r s D2 | qhull Fx" >>q_test.x rbox 5 r s D2 | qhull Fx >>q_test.x echo "rbox 5 r s D2 | qhull p n i p p" >>q_test.x rbox 5 r s D2 | qhull p n i p p >>q_test.x echo "rbox 10 D3 | qhull f Tcv" >>q_test.x rbox 10 D3 | qhull f Tcv >>q_test.x echo "rbox 10 D3 | qhull i" >>q_test.x rbox 10 D3 | qhull i >>q_test.x echo "rbox 10 D3 | qhull p " >>q_test.x rbox 10 D3 | qhull p >>q_test.x echo "rbox 10 D3 | qhull o " >>q_test.x rbox 10 D3 | qhull o >>q_test.x echo "rbox 10 D3 | qhull Fx " >>q_test.x rbox 10 D3 | qhull Fx >>q_test.x echo "rbox 27 M1,0,1 | qhull Qc" >>q_test.x rbox 27 M1,0,1 | qhull Qc >>q_test.x echo "rbox 50 D3 s | qhull C0.1 Qc Pd0d1d2 s p Tcv" >>q_test.x rbox 50 D3 s | qhull C0.1 Qc Pd0d1d2 s p Tcv >>q_test.x echo "rbox 10 D2 P0 P1e-15 | qhull d Qc FP s Tcv" >>q_test.x rbox 10 D2 P0 P1e-15 | qhull d Qc FP s Tcv >>q_test.x echo "rbox 100 s | qhull C-0.003 Qc FP s" >>q_test.x rbox 100 s | qhull C-0.003 Qc FP s >>q_test.x echo "rbox 100 s D2 | qhull C0.1 i Fx Tcv" >>q_test.x rbox 100 s D2 | qhull C0.1 i Fx Tcv >>q_test.x echo "rbox 4 s D3 | qhull Qc Ghipv Tcv " >>q_test.x rbox 4 s D3 | qhull Qc Ghipv Tcv >>q_test.x echo "rbox 6 D4 | qhull f Tcv" >>q_test.x rbox 6 D4 | qhull f Tcv >>q_test.x echo "rbox 6 D4 | qhull i" >>q_test.x rbox 6 D4 | qhull i >>q_test.x echo "rbox 6 D4 | qhull p " >>q_test.x rbox 6 D4 | qhull p >>q_test.x echo "rbox 6 D4 | qhull o" >>q_test.x rbox 6 D4 | qhull o >>q_test.x echo "rbox 1000 s D2 | qhull FA Tcv" >>q_test.x rbox 1000 s D2 | qhull FA Tcv >>q_test.x echo "rbox 1000 s | qhull FA Tcv" >>q_test.x rbox 1000 s | qhull FA Tcv >>q_test.x echo "rbox c D4 | qhull FA Tcv" >>q_test.x rbox c D4 | qhull FA Tcv >>q_test.x echo "rbox c D5 | qhull FA Tcv" >>q_test.x rbox c D5 | qhull FA Tcv >>q_test.x echo "rbox 10 D2 | qhull d FA Tcv" >>q_test.x rbox 10 D2 | qhull d FA Tcv >>q_test.x echo "rbox 10 D2 | qhull d Qu FA Tcv" >>q_test.x rbox 10 D2 | qhull d Qu FA Tcv >>q_test.x echo "rbox 10 D2 | qhull FA Tcv" >>q_test.x rbox 10 D2 | qhull FA Tcv >>q_test.x echo "rbox 10 c D2 | qhull Fx Tcv" >>q_test.x rbox 10 c D2 | qhull Fx Tcv >>q_test.x echo "rbox 1000 s | qhull FS Tcv" >>q_test.x rbox 1000 s | qhull FS Tcv >>q_test.x echo "rbox 10 W0 D2 | qhull p Qc FcC Tcv" >>q_test.x rbox 10 W0 D2 | qhull p Qc FcC Tcv >>q_test.x echo "rbox 4 z h s D2 | qhull Fd s n FD Tcv" >>q_test.x rbox 4 z h s D2 | qhull Fd s n FD Tcv >>q_test.x echo "rbox 6 s D3 | qhull C-0.1 Qc FF s FQ Fi n Fo FQ FI Fm Fn FN FO FO FQ Fs FS FV Fv Tcv" >>q_test.x rbox 6 s D3 | qhull C-0.1 Qc FF s FQ Fi n Fo FQ FI Fm Fn FN FO FO FQ Fs FS FV Fv Tcv >>q_test.x echo "rbox P0.5,0.5 P0.5,0.5 W0 5 D2 | qhull d FN Qc" >>q_test.x rbox P0.5,0.5 P0.5,0.5 W0 5 D2 | qhull d FN Qc >>q_test.x echo "rbox 10 D3 | qhull Fa PA5" >>q_test.x rbox 10 D3 | qhull Fa PA5 >>q_test.x echo "rbox 10 D3 | qhull Fa PF0.4" >>q_test.x rbox 10 D3 | qhull Fa PF0.4 >>q_test.x echo === test Qt >>q_test.x echo "rbox c | qhull Qt s o Tcv" >>q_test.x rbox c | qhull Qt s o Tcv >>q_test.x echo "rbox c | qhull Qt f i" >>q_test.x rbox c | qhull Qt f i >>q_test.x echo "rbox c | qhull Qt m FM n" >>q_test.x rbox c | qhull Qt m FM n >>q_test.x echo "rbox c | qhull Qt p o" >>q_test.x rbox c | qhull Qt p o >>q_test.x echo "rbox c | qhull Qt Fx" >>q_test.x rbox c | qhull Qt Fx >>q_test.x echo "rbox c | qhull Qt FA s Fa" >>q_test.x rbox c | qhull Qt FA s Fa >>q_test.x echo "rbox 6 r s c G0.1 D2 | qhull Qt d FA Tcv" >>q_test.x rbox 6 r s c G0.1 D2 | qhull Qt d FA Tcv >>q_test.x echo "rbox 6 r s c G0.1 D2 | qhull d FA Tcv" >>q_test.x rbox 6 r s c G0.1 D2 | qhull d FA Tcv >>q_test.x echo "rbox 6 r s c G0.1 D2 | qhull Qt v p Tcv" >>q_test.x rbox 6 r s c G0.1 D2 | qhull Qt v p Tcv >>q_test.x echo "rbox c | qhull Qt C-0.1 Qc FF s FQ Fi n Fo FQ FI Fm Fn FN FO FO FQ Fs FS FV Fv Tcv" >>q_test.x rbox c | qhull Qt C-0.1 Qc FF s FQ Fi n Fo FQ FI Fm Fn FN FO FO FQ Fs FS FV Fv Tcv >>q_test.x echo "rbox 6 r s c G0.1 D2 P0.1,0.1 | qhull s FP d FO Qt" >>q_test.x rbox 6 r s c G0.1 D2 P0.1,0.1 | qhull s FP d FO Qt >>q_test.x echo "RBOX 100 W0 | QHULL Tv Q11 FO" >>q_test.x RBOX 100 W0 | QHULL Tv Q11 FO >>q_test.x echo === test unbounded intersection >>q_test.x echo "rbox c | qhull PD0:0.5 n | qhull H0 Fp Tcv" >>q_test.x rbox c | qhull PD0:0.5 n | qhull H0 Fp Tcv >>q_test.x echo "rbox 1000 W1e-3 D3 | qhull PA8 Fa FS s n Tcv " >>q_test.x rbox 1000 W1e-3 D3 | qhull PA8 Fa FS s n Tcv >>q_test.x echo "rbox 1000 W1e-3 D3 | qhull C-0.01 PM10 Fm n Tcv Qc" >>q_test.x rbox 1000 W1e-3 D3 | qhull C-0.01 PM10 Fm n Tcv Qc >>q_test.x echo "rbox 1000 W1e-3 D3 | qhull C-0.01 PA8 PG n Tcv Qc" >>q_test.x rbox 1000 W1e-3 D3 | qhull C-0.01 PA8 PG n Tcv Qc >>q_test.x rbox 10 | qhull FO Tz TO q_test.log.1 echo "type q_test.log.1" >>q_test.x type q_test.log.1 >>q_test.x echo === check Delaunay/Voronoi ${d:-`date`} >>q_test.x echo "rbox 10 D2 | qhull d Tcv" >>q_test.x rbox 10 D2 | qhull d Tcv >>q_test.x echo "rbox 10 D2 | qhull d Qz Tcv" >>q_test.x rbox 10 D2 | qhull d Qz Tcv >>q_test.x echo "rbox 10 D3 | qhull d Tcv" >>q_test.x rbox 10 D3 | qhull d Tcv >>q_test.x echo "rbox c | qhull d Qz Ft Tcv" >>q_test.x rbox c | qhull d Qz Ft Tcv >>q_test.x echo "rbox 10 s D2 c | qhull d Tcv" >>q_test.x rbox 10 s D2 c | qhull d Tcv >>q_test.x echo "rbox 10 s D2 | qhull d Tcv Qz Q8" >>q_test.x rbox 10 s D2 | qhull d Tcv Qz Q8 >>q_test.x echo "rbox 10 D2 | qhull d Tcv p" >>q_test.x rbox 10 D2 | qhull d Tcv p >>q_test.x echo "rbox 10 D2 | qhull d Tcv i" >>q_test.x rbox 10 D2 | qhull d Tcv i >>q_test.x echo "rbox 10 D2 | qhull d Tcv o" >>q_test.x rbox 10 D2 | qhull d Tcv o >>q_test.x echo "rbox 10 D2 | qhull v Tcv o" >>q_test.x rbox 10 D2 | qhull v Tcv o >>q_test.x echo "rbox 10 D2 | qhull v Tcv p" >>q_test.x rbox 10 D2 | qhull v Tcv p >>q_test.x echo "rbox 10 D2 | qhull v Tcv G" >>q_test.x rbox 10 D2 | qhull v Tcv G >>q_test.x echo "rbox 10 D2 | qhull v Tcv Fv" >>q_test.x rbox 10 D2 | qhull v Tcv Fv >>q_test.x echo "rbox 10 D2 | qhull v Tcv Fi" >>q_test.x rbox 10 D2 | qhull v Tcv Fi >>q_test.x echo "rbox 10 D2 | qhull v Tcv Fo" >>q_test.x rbox 10 D2 | qhull v Tcv Fo >>q_test.x echo "rbox 10 D2 | qhull v Qu Tcv o Fv Fi Fo" >>q_test.x rbox 10 D2 | qhull v Qu Tcv o Fv Fi Fo >>q_test.x echo "rbox 10 D3 | qhull v Tcv Fv" >>q_test.x rbox 10 D3 | qhull v Tcv Fv >>q_test.x echo "rbox 10 D3 | qhull v Tcv Fi" >>q_test.x rbox 10 D3 | qhull v Tcv Fi >>q_test.x echo "rbox 10 D3 | qhull v Tcv Fo" >>q_test.x rbox 10 D3 | qhull v Tcv Fo >>q_test.x echo "rbox 10 D3 | qhull v Qu Tcv o Fv Fi Fo" >>q_test.x rbox 10 D3 | qhull v Qu Tcv o Fv Fi Fo >>q_test.x echo "rbox 5 D2 | qhull v f FnN o" >>q_test.x rbox 5 D2 | qhull v f FnN o >>q_test.x echo === check Halfspace ${d:-`date`} >>q_test.x echo "rbox 100 s D4 | qhull FA FV n s Tcv | qhull H Fp Tcv | qhull FA Tcv" >>q_test.x rbox 100 s D4 | qhull FA s Tcv >>q_test.x rbox 100 s D4 | qhull FA FV n s Tcv | qhull H Fp Tcv | qhull FA Tcv >>q_test.x echo "rbox d D3 | qhull FQ n s FD Tcv | qhull Fd H0.1,0.1 Fp FQ Tcv" >>q_test.x rbox d D3 | qhull s >>q_test.x rbox d D3 | qhull FQ n FD Tcv | qhull Fd H0.1,0.1 Fp FQ Tcv >>q_test.x echo "rbox 5 r D2 | qhull s n Tcv | qhull H0 Fp Tcv" >>q_test.x rbox 5 r D2 | qhull >>q_test.x rbox 5 r D2 | qhull n Tcv | qhull H0 Fp Tcv >>q_test.x echo === check qhull ${d:-`date`} >>q_test.x echo "rbox 10 s D3 | qhull Tcv" >>q_test.x rbox 10 s D3 | qhull Tcv >>q_test.x echo "rbox 10 s D3 | qhull f Pd0:0.5 Pd2 Tcv" >>q_test.x rbox 10 s D3 | qhull f Pd0:0.5 Pd2 Tcv >>q_test.x echo "rbox 10 s D3 | qhull f Tcv PD2:-0.5" >>q_test.x rbox 10 s D3 | qhull f Tcv PD2:-0.5 >>q_test.x echo "rbox 10 s D3 | qhull QR-1" >>q_test.x rbox 10 s D3 | qhull QR-1 >>q_test.x echo "rbox 10 s D3 | qhull QR-40" >>q_test.x rbox 10 s D3 | qhull QR-40 >>q_test.x echo "rbox 1000 D3 | qhull Tcvs" >>q_test.x rbox 1000 D3 | qhull Tcvs >>q_test.x echo "rbox 100 s D3 | qhull TcvV-2" >>q_test.x rbox 100 s D3 | qhull TcvV-2 >>q_test.x echo "rbox 100 s D3 | qhull TcvC2" >>q_test.x rbox 100 s D3 | qhull TcvC2 >>q_test.x echo "rbox 100 s D3 | qhull TcvV2" >>q_test.x rbox 100 s D3 | qhull TcvV2 >>q_test.x echo "rbox 100 s D3 | qhull T1cvV2P2" >>q_test.x rbox 100 s D3 | qhull T1cvV2P2 >>q_test.x echo "rbox 100 s D3 | qhull TcvF100" >>q_test.x rbox 100 s D3 | qhull TcvF100 >>q_test.x echo "rbox 100 s D3 | qhull Qf Tcv" >>q_test.x rbox 100 s D3 | qhull Qf Tcv >>q_test.x echo "rbox 100 D3 | qhull Tcv" >>q_test.x rbox 100 D3 | qhull Tcv >>q_test.x echo "rbox 100 D3 | qhull Qs Tcv" >>q_test.x rbox 100 D3 | qhull Qs Tcv >>q_test.x echo "rbox 100 D5 | qhull Qs Tcv" >>q_test.x rbox 100 D5 | qhull Qs Tcv >>q_test.x echo "rbox 100 D3 | qhull Qr Tcv" >>q_test.x rbox 100 D3 | qhull Qr Tcv >>q_test.x echo "rbox 100 D3 | qhull Qxv Tcv" >>q_test.x rbox 100 D3 | qhull Qxv Tcv >>q_test.x echo "rbox 100 D3 | qhull Qi f Pd0 Pd1 Pd2 Tcv" >>q_test.x rbox 100 D3 | qhull Qi f Pd0 Pd1 Pd2 Tcv >>q_test.x echo "rbox c d | qhull Qc f Tcv" >>q_test.x rbox c d | qhull Qc f Tcv >>q_test.x echo "rbox c d | qhull Qc p Tcv" >>q_test.x rbox c d | qhull Qc p Tcv >>q_test.x echo "rbox 100 D3 | qhull QbB FO Tcv" >>q_test.x rbox 100 D3 | qhull QbB FO Tcv >>q_test.x echo "rbox 1000 D2 B1e6 | qhull d Qbb FO Tcv" >>q_test.x rbox 1000 D2 B1e6 | qhull d Qbb FO Tcv >>q_test.x echo "rbox 10 D3 | qhull QbB p Tcv" >>q_test.x rbox 10 D3 | qhull QbB p Tcv >>q_test.x echo "rbox 10 D3 | qhull Qbb p Tcv" >>q_test.x rbox 10 D3 | qhull Qbb p Tcv >>q_test.x echo "rbox 10 D3 | qhull Qb0:-10B2:20 p Tcv" >>q_test.x rbox 10 D3 | qhull Qb0:-10B2:20 p Tcv >>q_test.x echo "rbox 10 D3 | qhull Qb0:-10B2:20 p Tcv | qhull QbB p Tcv" >>q_test.x rbox 10 D3 | qhull Qb0:-10B2:20 p Tcv | qhull QbB p Tcv >>q_test.x echo "rbox 10 D3 | qhull Qb1:0B1:0 d Tcv Q8" >>q_test.x rbox 10 D3 | qhull Qb1:0B1:0 d Tcv Q8 >>q_test.x echo "rbox 10 D3 | qhull Qb1:0B1:0B2:0 d Tcv Q8" >>q_test.x rbox 10 D3 | qhull Qb1:0B1:0B2:0 d Tcv Q8 >>q_test.x echo "rbox 10 D3 | qhull Qb1:0 d Tcv " >>q_test.x rbox 10 D3 | qhull Qb1:0 d Tcv >>q_test.x echo "rbox 10 D3 | qhull Qb1:0B1:0 Tcv" >>q_test.x rbox 10 D3 | qhull Qb1:0B1:0 Tcv >>q_test.x echo "== next command will error ==" >>q_test.x echo "rbox 10 D2 | qhull Qb1:1B1:1 Tcv" >>q_test.x rbox 10 D2 | qhull Qb1:1B1:1 Tcv >>q_test.x echo "rbox 200 L20 D2 t | qhull FO Tcv C-0" >>q_test.x rbox 200 L20 D2 t | qhull FO Tcv C-0 >>q_test.x echo "rbox 1000 L20 t | qhull FO Tcv C-0" >>q_test.x rbox 1000 L20 t | qhull FO Tcv C-0 >>q_test.x echo "rbox 200 L20 D4 t | qhull FO Tcv C-0" >>q_test.x rbox 200 L20 D4 t | qhull FO Tcv C-0 >>q_test.x echo "rbox 200 L20 D5 t | qhull FO Tcv Qx" >>q_test.x rbox 200 L20 D5 t | qhull FO Tcv Qx >>q_test.x echo "rbox 1000 W1e-3 s D2 t | qhull d FO Tcv Qu Q0" >>q_test.x rbox 1000 W1e-3 s D2 t | qhull d FO Tcv Qu Q0 >>q_test.x echo "rbox 1000 W1e-3 s D2 t | qhull d FO Tcv Qu C-0" >>q_test.x rbox 1000 W1e-3 s D2 t | qhull d FO Tcv Qu C-0 >>q_test.x echo === check joggle and TRn ${d:-`date`} >>q_test.x echo "rbox 100 W0 | qhull QJ1e-14 Qc TR100 Tv" >>q_test.x rbox 100 W0 | qhull QJ1e-14 Qc TR100 Tv >>q_test.x echo "rbox 100 W0 | qhull QJ1e-13 Qc TR100 Tv" >>q_test.x rbox 100 W0 | qhull QJ1e-13 Qc TR100 Tv >>q_test.x echo "rbox 100 W0 | qhull QJ1e-12 Qc TR100 Tv" >>q_test.x rbox 100 W0 | qhull QJ1e-12 Qc TR100 Tv >>q_test.x echo "rbox 100 W0 | qhull QJ1e-11 Qc TR100 Tv" >>q_test.x rbox 100 W0 | qhull QJ1e-11 Qc TR100 Tv >>q_test.x echo "rbox 100 W0 | qhull QJ1e-10 Qc TR100 Tv" >>q_test.x rbox 100 W0 | qhull QJ1e-10 Qc TR100 Tv >>q_test.x echo "rbox 100 | qhull d QJ Qb0:1e4 QB0:1e5 Qb1:1e4 QB1:1e6 Qb2:1e5 QB2:1e7 FO Tv" >>q_test.x rbox 100 | qhull d QJ Qb0:1e4 QB0:1e5 Qb1:1e4 QB1:1e6 Qb2:1e5 QB2:1e7 FO Tv >>q_test.x echo === check precision options ${d:-`date`} >>q_test.x echo "rbox 100 D3 s | qhull E0.01 Qx Tcv FO" >>q_test.x rbox 100 D3 s | qhull E0.01 Qx Tcv FO >>q_test.x echo "rbox 100 D3 W1e-1 | qhull W1e-3 Tcv" >>q_test.x rbox 100 D3 W1e-1 | qhull W1e-3 Tcv >>q_test.x echo "rbox 100 D3 W1e-1 | qhull W1e-2 Tcv Q0" >>q_test.x rbox 100 D3 W1e-1 | qhull W1e-2 Tcv Q0 >>q_test.x echo "rbox 100 D3 W1e-1 | qhull W1e-2 Tcv" >>q_test.x rbox 100 D3 W1e-1 | qhull W1e-2 Tcv >>q_test.x echo "rbox 100 D3 W1e-1 | qhull W1e-1 Tcv" >>q_test.x rbox 100 D3 W1e-1 | qhull W1e-1 Tcv >>q_test.x echo "rbox 15 D2 P0 P1e-14,1e-14 | qhull d Quc Tcv" >>q_test.x rbox 15 D2 P0 P1e-14,1e-14 | qhull d Quc Tcv >>q_test.x echo "rbox 15 D3 P0 P1e-12,1e-14,1e-14 | qhull d Qcu Tcv" >>q_test.x rbox 15 D3 P0 P1e-12,1e-14,1e-14 | qhull d Qcu Tcv >>q_test.x echo "rbox 1000 s D3 | qhull C-0.01 Tcv Qc" >>q_test.x rbox 1000 s D3 | qhull C-0.01 Tcv Qc >>q_test.x echo "rbox 1000 s D3 | qhull C-0.01 V0 Qc Tcv" >>q_test.x rbox 1000 s D3 | qhull C-0.01 V0 Qc Tcv >>q_test.x echo "rbox 1000 s D3 | qhull C-0.01 U0 Qc Tcv" >>q_test.x rbox 1000 s D3 | qhull C-0.01 U0 Qc Tcv >>q_test.x echo "rbox 1000 s D3 | qhull C-0.01 V0 Qcm Tcv" >>q_test.x rbox 1000 s D3 | qhull C-0.01 V0 Qcm Tcv >>q_test.x echo "rbox 1000 s D3 | qhull C-0.01 Qcm Tcv" >>q_test.x rbox 1000 s D3 | qhull C-0.01 Qcm Tcv >>q_test.x echo "rbox 1000 s D3 | qhull C-0.01 Q1 FO Tcv Qc" >>q_test.x rbox 1000 s D3 | qhull C-0.01 Q1 FO Tcv Qc >>q_test.x echo "rbox 1000 s D3 | qhull C-0.01 Q2 FO Tcv Qc" >>q_test.x rbox 1000 s D3 | qhull C-0.01 Q2 FO Tcv Qc >>q_test.x echo "rbox 1000 s D3 | qhull C-0.01 Q3 FO Tcv Qc" >>q_test.x rbox 1000 s D3 | qhull C-0.01 Q3 FO Tcv Qc >>q_test.x echo "rbox 1000 s D3 | qhull C-0.01 Q4 FO Tcv Qc" >>q_test.x rbox 1000 s D3 | qhull C-0.01 Q4 FO Tcv Qc >>q_test.x echo === this may generate an error ${d:-`date`} >>q_test.x echo "rbox 1000 s D3 | qhull C-0.01 Q5 FO Tcv " >>q_test.x rbox 1000 s D3 | qhull C-0.01 Q5 FO Tcv >>q_test.x echo === this should generate an error ${d:-`date`} >>q_test.x echo "rbox 1000 s D3 | qhull C-0.01 Q6 FO Po Tcv Qc" >>q_test.x rbox 1000 s D3 | qhull C-0.01 Q6 FO Po Tcv Qc >>q_test.x echo "rbox 1000 s D3 | qhull C-0.01 Q7 FO Tcv Qc" >>q_test.x rbox 1000 s D3 | qhull C-0.01 Q7 FO Tcv Qc >>q_test.x echo "rbox 1000 s D3 | qhull C-0.01 Qx Tcv Qc" >>q_test.x rbox 1000 s D3 | qhull C-0.01 Qx Tcv Qc >>q_test.x echo "rbox 100 s D3 t | qhull R1e-3 Tcv Qc" >>q_test.x rbox 100 s D3 t | qhull R1e-3 Tcv Qc >>q_test.x echo "rbox 100 s D3 t | qhull R1e-2 Tcv Qc" >>q_test.x rbox 100 s D3 t | qhull R1e-2 Tcv Qc >>q_test.x echo "rbox 500 s D3 t | qhull R0.05 A-1 Tcv Qc" >>q_test.x rbox 500 s D3 t | qhull R0.05 A-1 Tcv Qc >>q_test.x echo "rbox 100 W0 D3 t | qhull R1e-3 Tcv Qc" >>q_test.x rbox 100 W0 D3 t | qhull R1e-3 Tcv Qc >>q_test.x echo "rbox 100 W0 D3 t | qhull R1e-3 Qx Tcv Qc" >>q_test.x rbox 100 W0 D3 t | qhull R1e-3 Qx Tcv Qc >>q_test.x echo "rbox 100 W0 D3 t | qhull R1e-2 Tcv Qc" >>q_test.x rbox 100 W0 D3 t | qhull R1e-2 Tcv Qc >>q_test.x echo "rbox 100 W0 D3 t | qhull R1e-2 Qx Tcv Qc" >>q_test.x rbox 100 W0 D3 t | qhull R1e-2 Qx Tcv Qc >>q_test.x echo "rbox 500 W0 D3 t | qhull R0.05 A-1 Tcv Qc" >>q_test.x rbox 500 W0 D3 t | qhull R0.05 A-1 Tcv Qc >>q_test.x echo "rbox 500 W0 D3 t | qhull R0.05 Qx Tcv Qc" >>q_test.x rbox 500 W0 D3 t | qhull R0.05 Qx Tcv Qc >>q_test.x echo "rbox 1000 W1e-20 t | qhull Tcv Qc" >>q_test.x rbox 1000 W1e-20 t | qhull Tcv Qc >>q_test.x echo "rbox 1000 W1e-20 D4 t | qhull Tcv Qc" >>q_test.x rbox 1000 W1e-20 D4 t | qhull Tcv Qc >>q_test.x echo "rbox 500 W1e-20 D5 t | qhull Tv Qc" >>q_test.x rbox 500 W1e-20 D5 t | qhull Tv Qc >>q_test.x echo "rbox 100 W1e-20 D6 t | qhull Tv Qc" >>q_test.x rbox 100 W1e-20 D6 t | qhull Tv Qc >>q_test.x echo "rbox 50 W1e-20 D6 t | qhull Qv Tv Qc" >>q_test.x rbox 50 W1e-20 D6 t | qhull Qv Tv Qc >>q_test.x echo "rbox 10000 D4 t | qhull QR0 Qc C-0.01 A0.3 Tv" >>q_test.x rbox 10000 D4 t | qhull QR0 Qc C-0.01 A0.3 Tv >>q_test.x echo "rbox 1000 D2 t | qhull d QR0 Qc C-1e-8 Qu Tv" >>q_test.x rbox 1000 D2 t | qhull d QR0 Qc C-1e-8 Qu Tv >>q_test.x echo "rbox 300 D5 t |qhull A-0.999 Qc Tcv" >>q_test.x rbox 300 D5 t |qhull A-0.999 Qc Tcv >>q_test.x echo "rbox 100 D6 t |qhull A-0.9999 Qc Tcv" >>q_test.x rbox 100 D6 t |qhull A-0.9999 Qc Tcv >>q_test.x echo "rbox 50 D7 t |qhull A-0.99999 Qc Tcv W0.1" >>q_test.x rbox 50 D7 t |qhull A-0.99999 Qc Tcv W0.1 >>q_test.x echo === check bad cases for Qhull. May cause errors ${d:-`date`} >>q_test.x echo "RBOX 1000 L100000 s G1e-6 t | QHULL Tv" >>q_test.x RBOX 1000 L100000 s G1e-6 t | QHULL Tv >>q_test.x echo "RBOX 1000 L100000 s G1e-6 t | QHULL Tv Q10" >>q_test.x RBOX 1000 L100000 s G1e-6 t | QHULL Tv Q10 >>q_test.x echo "rbox 1000 s Z1 G1e-13 t | qhull Tv" >>q_test.x rbox 1000 s Z1 G1e-13 t | qhull Tv >>q_test.x echo "RBOX 1000 s W1e-13 P0 t | QHULL d Qbb Qc Tv" >>q_test.x RBOX 1000 s W1e-13 P0 t | QHULL d Qbb Qc Tv >>q_test.x echo "RBOX 1000 s W1e-13 t | QHULL d Tv" >>q_test.x RBOX 1000 s W1e-13 t | QHULL d Tv >>q_test.x echo "RBOX 1000 s W1e-13 t D2 | QHULL d Tv" >>q_test.x RBOX 1000 s W1e-13 t D2 | QHULL d Tv >>q_test.x echo ======================================================= >>q_test.x echo ======================================================= >>q_test.x echo === The following commands may cause errors =========== >>q_test.x echo ======================================================= >>q_test.x echo ======================================================= >>q_test.x echo "rbox c D7 | qhull Q0 Tcv" >>q_test.x rbox c D7 | qhull Q0 Tcv >>q_test.x echo "rbox 100 s D3 | qhull Q0 E1e-3 Tc Po" >>q_test.x rbox 100 s D3 | qhull Q0 E1e-3 Tc Po >>q_test.x echo "rbox 100 s D3 | qhull Q0 E1e-2 Tc Po" >>q_test.x rbox 100 s D3 | qhull Q0 E1e-2 Tc Po >>q_test.x echo "rbox 100 s D3 | qhull Q0 E1e-1 Tc Po" >>q_test.x rbox 100 s D3 | qhull Q0 E1e-1 Tc Po >>q_test.x echo "rbox 100 s D3 | qhull Q0 R1e-3 Tc Po" >>q_test.x rbox 100 s D3 | qhull Q0 R1e-3 Tc Po >>q_test.x echo "rbox 100 s D3 | qhull Q0 R1e-2 Tc Po" >>q_test.x rbox 100 s D3 | qhull Q0 R1e-2 Tc Po >>q_test.x echo "rbox 100 s D3 | qhull Q0 R0.05 Tc" >>q_test.x rbox 100 s D3 | qhull Q0 R0.05 Tc >>q_test.x echo "rbox 100 s D3 | qhull Q0 R0.05 Tc Po" >>q_test.x rbox 100 s D3 | qhull Q0 R0.05 Tc Po >>q_test.x echo "rbox 1000 W1e-7 | qhull Q0 Tc Po" >>q_test.x rbox 1000 W1e-7 | qhull Q0 Tc Po >>q_test.x echo "rbox 50 s | qhull Q0 V0.05 W0.01 Tc Po" >>q_test.x rbox 50 s | qhull Q0 V0.05 W0.01 Tc Po >>q_test.x echo "rbox 100 s D5 | qhull Q0 R1e-2 Tc Po" >>q_test.x rbox 100 s D5 | qhull Q0 R1e-2 Tc Po >>q_test.x echo "qhull" >>q_test.x qhull >>q_test.x echo "qhull ." >>q_test.x qhull . >>q_test.x echo "qhull -" >>q_test.x qhull - >>q_test.x echo "rbox" >>q_test.x rbox >>q_test.x echo "# end of q_test" >>q_test.x qhull-2012.1/File_id.diz0000644000076400010400000000064511720340460016151 0ustar bbarberAdministratorsQhull 2012.1 - Qhull computes convex hulls, Delaunay triangulations, halfspace inter- sections about a point, Voronoi diagrams, furthest-site Delaunay triangulations, and furthest-site Voronoi diagrams. Qhull works with 2-d, 3-d, 4-d, 5-d, and higher dimensions. It computes volumes, surface areas, and approximations. It runs in a command window under Windows 95/NT/XP/7. www.qhull.org, freeware. qhull-2012.1/html/0000755000076400010400000000000011721063454015053 5ustar bbarberAdministratorsqhull-2012.1/html/index.htm0000644000076400010400000007771311711011266016704 0ustar bbarberAdministrators Qhull manual

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[random-fixed] Qhull manual

Qhull is a general dimension code for computing convex hulls, Delaunay triangulations, halfspace intersections about a point, Voronoi diagrams, furthest-site Delaunay triangulations, and furthest-site Voronoi diagrams. These structures have applications in science, engineering, statistics, and mathematics. See Fukuda's introduction to convex hulls, Delaunay triangulations, Voronoi diagrams, and linear programming. For a detailed introduction, see O'Rourke ['94], Computational Geometry in C.

There are six programs. Except for rbox, they use the same code.

  • qconvex -- convex hulls
  • qdelaunay -- Delaunay triangulations and furthest-site Delaunay triangulations
  • qhalf -- halfspace intersections about a point
  • qhull -- all structures with additional options
  • qvoronoi -- Voronoi diagrams and furthest-site Voronoi diagrams
  • rbox -- generate point distributions for qhull

Qhull implements the Quickhull algorithm for computing the convex hull. Qhull includes options for hull volume, facet area, multiple output formats, and graphical output. It can approximate a convex hull.

Qhull handles roundoff errors from floating point arithmetic. It generates a convex hull with "thick" facets. A facet's outer plane is clearly above all of the points; its inner plane is clearly below the facet's vertices. Any exact convex hull must lie between the inner and outer plane.

Qhull uses merged facets, triangulated output, or joggled input. Triangulated output triangulates non-simplicial, merged facets. Joggled input also guarantees simplicial output, but it is less accurate than merged facets. For merged facets, Qhull reports the maximum outer and inner plane.

Brad Barber, Arlington, MA

Copyright © 1995-2012 C.B. Barber

»Qhull manual: Table of Contents

»When to use Qhull

Qhull constructs convex hulls, Delaunay triangulations, halfspace intersections about a point, Voronoi diagrams, furthest-site Delaunay triangulations, and furthest-site Voronoi diagrams.

For convex hulls and halfspace intersections, Qhull may be used for 2-d upto 8-d. For Voronoi diagrams and Delaunay triangulations, Qhull may be used for 2-d upto 7-d. In higher dimensions, the size of the output grows rapidly and Qhull does not work well with virtual memory. If n is the size of the input and d is the dimension (d>=3), the size of the output and execution time grows by n^(floor(d/2) [see Performance]. For example, do not try to build a 16-d convex hull of 1000 points. It will have on the order of 1,000,000,000,000,000,000,000,000 facets.

On a 600 MHz Pentium 3, Qhull computes the 2-d convex hull of 300,000 cocircular points in 11 seconds. It computes the 2-d Delaunay triangulation and 3-d convex hull of 120,000 points in 12 seconds. It computes the 3-d Delaunay triangulation and 4-d convex hull of 40,000 points in 18 seconds. It computes the 4-d Delaunay triangulation and 5-d convex hull of 6,000 points in 12 seconds. It computes the 5-d Delaunay triangulation and 6-d convex hull of 1,000 points in 12 seconds. It computes the 6-d Delaunay triangulation and 7-d convex hull of 300 points in 15 seconds. It computes the 7-d Delaunay triangulation and 8-d convex hull of 120 points in 15 seconds. It computes the 8-d Delaunay triangulation and 9-d convex hull of 70 points in 15 seconds. It computes the 9-d Delaunay triangulation and 10-d convex hull of 50 points in 17 seconds. The 10-d convex hull of 50 points has about 90,000 facets.

Qhull does not support constrained Delaunay triangulations, triangulation of non-convex surfaces, mesh generation of non-convex objects, or medium-sized inputs in 9-D and higher.

This is a big package with many options. It is one of the fastest available. It is the only 3-d code that handles precision problems due to floating point arithmetic. For example, it implements the identity function for extreme points (see Imprecision in Qhull).

If you need a short code for convex hull, Delaunay triangulation, or Voronoi volumes consider Clarkson's hull program. If you need 2-d Delaunay triangulations consider Shewchuk's triangle program. It is much faster than Qhull and it allows constraints. Both programs use exact arithmetic. They are in http://www.netlib.org/voronoi/. Qhull version 1.0 may also meet your needs. It detects precision problems, but does not handle them.

Leda is a library for writing computational geometry programs and other combinatorial algorithms. It includes routines for computing 3-d convex hulls, 2-d Delaunay triangulations, and 3-d Delaunay triangulations. It provides rational arithmetic and graphical output. It runs on most platforms.

If your problem is in high dimensions with a few, non-simplicial facets, try Fukuda's cdd. It is much faster than Qhull for these distributions.

Custom software for 2-d and 3-d convex hulls may be faster than Qhull. Custom software should use less memory. Qhull uses general-dimension data structures and code. The data structures support non-simplicial facets.

Qhull is not suitable for mesh generation or triangulation of arbitrary surfaces. You may use Qhull if the surface is convex or completely visible from an interior point (e.g., a star-shaped polyhedron). First, project each site to a sphere that is centered at the interior point. Then, compute the convex hull of the projected sites. The facets of the convex hull correspond to a triangulation of the surface. For mesh generation of arbitrary surfaces, see Schneiders' Finite Element Mesh Generation.

Qhull is not suitable for constrained Delaunay triangulations. With a lot of work, you can write a program that uses Qhull to add constraints by adding additional points to the triangulation.

Qhull is not suitable for the subdivision of arbitrary objects. Use qdelaunay to subdivide a convex object.

»Description of Qhull

»definition

The convex hull of a point set P is the smallest convex set that contains P. If P is finite, the convex hull defines a matrix A and a vector b such that for all x in P, Ax+b <= [0,...].

Qhull computes the convex hull in 2-d, 3-d, 4-d, and higher dimensions. Qhull represents a convex hull as a list of facets. Each facet has a set of vertices, a set of neighboring facets, and a halfspace. A halfspace is defined by a unit normal and an offset (i.e., a row of A and an element of b).

Qhull accounts for round-off error. It returns "thick" facets defined by two parallel hyperplanes. The outer planes contain all input points. The inner planes exclude all output vertices. See Imprecise convex hulls.

Qhull may be used for the Delaunay triangulation or the Voronoi diagram of a set of points. It may be used for the intersection of halfspaces.

»input format

The input data on stdin consists of:

  • first line contains the dimension
  • second line contains the number of input points
  • remaining lines contain point coordinates

For example: 

    3  #sample 3-d input
    5
    0.4 -0.5 1.0
    1000 -1e-5 -100
    0.3 0.2 0.1
    1.0 1.0 1.0
    0 0 0

Input may be entered by hand. End the input with a control-D (^D) character.

To input data from a file, use I/O redirection or 'TI file'. The filename may not include spaces or quotes.

A comment starts with a non-numeric character and continues to the end of line. The first comment is reported in summaries and statistics. With multiple qhull commands, use option 'FQ' to place a comment in the output.

The dimension and number of points can be reversed. Comments and line breaks are ignored. Error reporting is better if there is one point per line.

»option format

Use options to specify the output formats and control Qhull. The qhull program takes all options. The other programs use a subset of the options. They disallow experimental and inappropriate options.

  • qconvex == qhull
  • qdelaunay == qhull d Qbb
  • qhalf == qhull H
  • qvoronoi == qhull v Qbb

Single letters are used for output formats and precision constants. The other options are grouped into menus for formats ('F'), Geomview ('G '), printing ('P'), Qhull control ('Q '), and tracing ('T'). The menu options may be listed together (e.g., 'GrD3' for 'Gr' and 'GD3'). Options may be in any order. Capitalized options take a numeric argument (except for 'PG' and 'F' options). Use option 'FO' to print the selected options.

Qhull uses zero-relative indexing. If there are n points, the index of the first point is 0 and the index of the last point is n-1.

The default options are:

  • summary output ('s')
  • merged facets ('C-0' in 2-d, 3-d, 4-d; 'Qx' in 5-d and up)

Except for bounding box ('Qbk:n', etc.), drop facets ('Pdk:n', etc.), and Qhull command ('FQ'), only the last occurence of an option counts. Bounding box and drop facets may be repeated for each dimension. Option 'FQ' may be repeated any number of times.

The Unix tcsh and ksh shells make it easy to try out different options. In Windows 95, use a command window with doskey and a window scroller (e.g., peruse).

»output format

To write the results to a file, use I/O redirection or 'TO file'. Windows 95 users should use 'TO file' or the console. If a filename is surrounded by single quotes, it may include spaces.

The default output option is a short summary ('s') to stdout. There are many others (see output and formats). You can list vertex incidences, vertices and facets, vertex coordinates, or facet normals. You can view Qhull objects with Geomview, Mathematica, or Maple. You can print the internal data structures. You can call Qhull from your application (see Qhull library).

For example, 'qhull o' lists the vertices and facets of the convex hull.

Error messages and additional summaries ('s') go to stderr. Unless redirected, stderr is the console.

»algorithm

Qhull implements the Quickhull algorithm for convex hull [Barber et al. '96]. This algorithm combines the 2-d Quickhull algorithm with the n-d beneath-beyond algorithm [c.f., Preparata & Shamos '85]. It is similar to the randomized algorithms of Clarkson and others [Clarkson & Shor '89; Clarkson et al. '93; Mulmuley '94]. For a demonstration, see How Qhull adds a point. The main advantages of Quickhull are output sensitive performance (in terms of the number of extreme points), reduced space requirements, and floating-point error handling.

»data structures

Qhull produces the following data structures for dimension d:

  • A coordinate is a real number in floating point format.
  • A point is an array of d coordinates. With option 'QJ', the coordinates are joggled by a small amount.
  • A vertex is an input point.
  • A hyperplane is d normal coefficients and an offset. The length of the normal is one. The hyperplane defines a halfspace. If V is a normal, b is an offset, and x is a point inside the convex hull, then Vx+b <0.
  • An outer plane is a positive offset from a hyperplane. When Qhull is done, all points will be below all outer planes.
  • An inner plane is a negative offset from a hyperplane. When Qhull is done, all vertices will be above the corresponding inner planes.
  • An orientation is either 'top' or 'bottom'. It is the topological equivalent of a hyperplane's geometric orientation.
  • A simplicial facet is a set of d neighboring facets, a set of d vertices, a hyperplane equation, an inner plane, an outer plane, and an orientation. For example in 3-d, a simplicial facet is a triangle.
  • A centrum is a point on a facet's hyperplane. A centrum is the average of a facet's vertices. Neighboring facets are convex if each centrum is below the neighbor facet's hyperplane.
  • A ridge is a set of d-1 vertices, two neighboring facets, and an orientation. For example in 3-d, a ridge is a line segment.
  • A non-simplicial facet is a set of ridges, a hyperplane equation, a centrum, an outer plane, and an inner plane. The ridges determine a set of neighboring facets, a set of vertices, and an orientation. Qhull produces a non-simplicial facet when it merges two facets together. For example, a cube has six non-simplicial facets.

For examples, use option 'f'. See polyhedron operations for further design documentation.

»Imprecision in Qhull

See Imprecision in Qhull.

»Geomview, Qhull's graphical viewer

Geomview is an interactive geometry viewing program for Linux, SGI workstations, Sun workstations, AIX workstations, NeXT workstations, and X-windows. It is an open source project under SourceForge. Besides a 3-d viewer, it includes a 4-d viewer, an n-d viewer and many features for viewing mathematical objects. You may need to ftp ndview from the newpieces directory.

»Description of Qhull examples

See Examples. Some of the examples have pictures .

»Options for using Qhull

See Options.

»Qhull internals

See Internals.

»What to do if something goes wrong

Please report bugs to qhull_bug@qhull.org . Please report if Qhull crashes. Please report if Qhull generates an "internal error". Please report if Qhull produces a poor approximate hull in 2-d, 3-d or 4-d. Please report documentation errors. Please report missing or incorrect links.

If you do not understand something, try a small example. The rbox program is an easy way to generate test cases. The Geomview program helps to visualize the output from Qhull.

If Qhull does not compile, it is due to an incompatibility between your system and ours. The first thing to check is that your compiler is ANSI standard. Qhull produces a compiler error if __STDC__ is not defined. You may need to set a flag (e.g., '-A' or '-ansi').

If Qhull compiles but crashes on the test case (rbox D4), there's still incompatibility between your system and ours. Sometimes it is due to memory management. This can be turned off with qh_NOmem in mem.h. Please let us know if you figure out how to fix these problems.

If you doubt the output from Qhull, add option 'Tv'. It checks that every point is inside the outer planes of the convex hull. It checks that every facet is convex with its neighbors. It checks the topology of the convex hull.

Qhull should work on all inputs. It may report precision errors if you turn off merged facets with option 'Q0'. This can get as bad as facets with flipped orientation or two facets with the same vertices. You'll get a long help message if you run into such a case. They are easy to generate with rbox.

If you do find a problem, try to simplify it before reporting the error. Try different size inputs to locate the smallest one that causes an error. You're welcome to hunt through the code using the execution trace ('T4') as a guide. This is especially true if you're incorporating Qhull into your own program.

When you report an error, please attach a data set to the end of your message. Include the options that you used with Qhull, the results of option 'FO', and any messages generated by Qhull. This allows me to see the error for myself. Qhull is maintained part-time.

»Email

Please send correspondence to Brad Barber at qhull@qhull.org and report bugs to qhull_bug@qhull.org . Let me know how you use Qhull. If you mention it in a paper, please send a reference and abstract.

If you would like to get Qhull announcements (e.g., a new version) and news (any bugs that get fixed, etc.), let us know and we will add you to our mailing list. If you would like to communicate with other Qhull users, I will add you to the qhull_users alias. For Internet news about geometric algorithms and convex hulls, look at comp.graphics.algorithms and sci.math.num-analysis. For Qhull news look at qhull-news.html.

»Authors

   C. Bradford Barber                    Hannu Huhdanpaa
   bradb@shore.net                       hannu@qhull.org

»Acknowledgments

A special thanks to David Dobkin for his guidance. A special thanks to Albert Marden, Victor Milenkovic, the Geometry Center, and Harvard University for supporting this work.

A special thanks to Mark Phillips, Robert Miner, and Stuart Levy for running the Geometry Center web site long after the Geometry Center closed. Stuart moved the web site to the University of Illinois at Champaign-Urbana. Mark and Robert are founders of Geometry Technologies. Mark, Stuart, and Tamara Munzner are the original authors of Geomview.

A special thanks to Endocardial Solutions, Inc. of St. Paul, Minnesota for their support of the internal documentation (src/libqhull/index.htm). They use Qhull to build 3-d models of heart chambers.

Qhull 1.0 and 2.0 were developed under National Science Foundation grants NSF/DMS-8920161 and NSF-CCR-91-15793 750-7504. If you find it useful, please let us know.

The Geometry Center was supported by grant DMS-8920161 from the National Science Foundation, by grant DOE/DE-FG02-92ER25137 from the Department of Energy, by the University of Minnesota, and by Minnesota Technology, Inc.

»References

Aurenhammer, F., "Voronoi diagrams -- A survey of a fundamental geometric data structure," ACM Computing Surveys, 1991, 23:345-405.

Barber, C. B., D.P. Dobkin, and H.T. Huhdanpaa, "The Quickhull Algorithm for Convex Hulls," ACM Transactions on Mathematical Software, 22(4):469-483, Dec 1996, www.qhull.org [http://portal.acm.org; http://citeseerx.ist.psu.edu].

Clarkson, K.L. and P.W. Shor, "Applications of random sampling in computational geometry, II", Discrete Computational Geometry, 4:387-421, 1989

Clarkson, K.L., K. Mehlhorn, and R. Seidel, "Four results on randomized incremental construction," Computational Geometry: Theory and Applications, vol. 3, p. 185-211, 1993.

Devillers, et. al., "Walking in a triangulation," ACM Symposium on Computational Geometry, June 3-5,2001, Medford MA.

Dobkin, D.P. and D.G. Kirkpatrick, "Determining the separation of preprocessed polyhedra--a unified approach," in Proc. 17th Inter. Colloq. Automata Lang. Program., in Lecture Notes in Computer Science, Springer-Verlag, 443:400-413, 1990.

Edelsbrunner, H, Geometry and Topology for Mesh Generation, Cambridge University Press, 2001.

Gartner, B., "Fast and robust smallest enclosing balls", Algorithms - ESA '99, LNCS 1643.

Fortune, S., "Computational geometry," in R. Martin, editor, Directions in Geometric Computation, Information Geometers, 47 Stockers Avenue, Winchester, SO22 5LB, UK, ISBN 1-874728-02-X, 1993.

Milenkovic, V., "Robust polygon modeling," Computer-Aided Design, vol. 25, p. 546-566, September 1993.

Mucke, E.P., I. Saias, B. Zhu, Fast randomized point location without preprocessing in Two- and Three-dimensional Delaunay Triangulations, ACM Symposium on Computational Geometry, p. 274-283, 1996 [GeomDir].

Mulmuley, K., Computational Geometry, An Introduction Through Randomized Algorithms, Prentice-Hall, NJ, 1994.

O'Rourke, J., Computational Geometry in C, Cambridge University Press, 1994.

Preparata, F. and M. Shamos, Computational Geometry, Springer-Verlag, New York, 1985.

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The Geometry Center Home Page

Comments to: qhull@qhull.org
Created: Sept. 25, 1995 --- Last modified: see top

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[cone]qconvex -- convex hull

The convex hull of a set of points is the smallest convex set containing the points. See the detailed introduction by O'Rourke ['94]. See Description of Qhull and How Qhull adds a point.

Example: rbox 10 D3 | qconvex s o TO result
Compute the 3-d convex hull of 10 random points. Write a summary to the console and the points and facets to 'result'.
 
Example: rbox c | qconvex n
Print the normals for each facet of a cube.
 
Example: rbox c | qconvex i Qt
Print the triangulated facets of a cube.
 
Example: rbox y 500 W0 | qconvex
Compute the convex hull of a simplex with 500 points on its surface.
 
Example: rbox x W1e-12 1000 | qconvex QR0
Compute the convex hull of 1000 points near the surface of a randomly rotated simplex. Report the maximum thickness of a facet.
 
Example: rbox 1000 s | qconvex s FA
Compute the convex hull of 1000 cospherical points. Verify the results and print a summary with the total area and volume.
 
Example: rbox d D12 | qconvex QR0 FA
Compute the convex hull of a 12-d diamond. Randomly rotate the input. Note the large number of facets and the small volume.
 
Example: rbox c D7 | qconvex FA TF1000
Compute the convex hull of the 7-d hypercube. Report on progress every 1000 facets. Computing the convex hull of the 9-d hypercube takes too much time and space.
 
Example: rbox c d D2 | qconvex Qc s f Fx | more
Dump all fields of all facets for a square and a diamond. Also print a summary and a list of vertices. Note the coplanar points.
 

Except for rbox, all of the qhull programs compute a convex hull.

By default, Qhull merges coplanar facets. For example, the convex hull of a cube's vertices has six facets.

If you use 'Qt' (triangulated output), all facets will be simplicial (e.g., triangles in 2-d). For the cube example, it will have 12 facets. Some facets may be degenerate and have zero area.

If you use 'QJ' (joggled input), all facets will be simplicial. The corresponding vertices will be slightly perturbed and identical points will be joggled apart. Joggled input is less accurate that triangulated output.See Merged facets or joggled input.

The output for 4-d convex hulls may be confusing if the convex hull contains non-simplicial facets (e.g., a hypercube). See Why are there extra points in a 4-d or higher convex hull?

The 'qconvex' program is equivalent to 'qhull' in 2-d to 4-d, and 'qhull Qx' in 5-d and higher. It disables the following Qhull options: d v H Qbb Qf Qg Qm Qr Qu Qv Qx Qz TR E V Fp Gt Q0,etc.

Copyright © 1995-2012 C.B. Barber

»qconvex synopsis

qconvex- compute the convex hull.
    input (stdin): dimension, number of points, point coordinates
    comments start with a non-numeric character

options (qconvex.htm):
    Qt   - triangulated output
    QJ   - joggle input instead of merging facets
    Tv   - verify result: structure, convexity, and point inclusion
    .    - concise list of all options
    -    - one-line description of all options

output options (subset):
    s    - summary of results (default)
    i    - vertices incident to each facet
    n    - normals with offsets
    p    - vertex coordinates (includes coplanar points if 'Qc')
    Fx   - extreme points (convex hull vertices)
    FA   - compute total area and volume
    o    - OFF format (dim, n, points, facets)
    G    - Geomview output (2-d, 3-d, and 4-d)
    m    - Mathematica output (2-d and 3-d)
    QVn  - print facets that include point n, -n if not
    TO file- output results to file, may be enclosed in single quotes

examples:
    rbox c D2 | qconvex s n                    rbox c D2 | qconvex i
    rbox c D2 | qconvex o                      rbox 1000 s | qconvex s Tv FA
    rbox c d D2 | qconvex s Qc Fx              rbox y 1000 W0 | qconvex s n
    rbox y 1000 W0 | qconvex s QJ              rbox d G1 D12 | qconvex QR0 FA Pp
    rbox c D7 | qconvex FA TF1000

»qconvex input

The input data on stdin consists of:

  • dimension
  • number of points
  • point coordinates

Use I/O redirection (e.g., qconvex < data.txt), a pipe (e.g., rbox 10 | qconvex), or the 'TI' option (e.g., qconvex TI data.txt).

Comments start with a non-numeric character. Error reporting is simpler if there is one point per line. Dimension and number of points may be reversed.

Here is the input for computing the convex hull of the unit cube. The output is the normals, one per facet.

rbox c > data 

3 RBOX c
8
  -0.5   -0.5   -0.5
  -0.5   -0.5    0.5
  -0.5    0.5   -0.5
  -0.5    0.5    0.5
   0.5   -0.5   -0.5
   0.5   -0.5    0.5
   0.5    0.5   -0.5
   0.5    0.5    0.5

qconvex s n < data


Convex hull of 8 points in 3-d:

  Number of vertices: 8
  Number of facets: 6
  Number of non-simplicial facets: 6

Statistics for: RBOX c | QCONVEX s n

  Number of points processed: 8
  Number of hyperplanes created: 11
  Number of distance tests for qhull: 35
  Number of merged facets: 6
  Number of distance tests for merging: 84
  CPU seconds to compute hull (after input): 0.081

4
6
     0      0     -1   -0.5
     0     -1      0   -0.5
     1      0      0   -0.5
    -1      0      0   -0.5
     0      1      0   -0.5
     0      0      1   -0.5

»qconvex outputs

These options control the output of qconvex. They may be used individually or together.

 
Vertices
Fx
list extreme points (i.e., vertices). The first line is the number of extreme points. Each point is listed, one per line. The cube example has eight vertices.
Fv
list vertices for each facet. The first line is the number of facets. Each remaining line starts with the number of vertices. For the cube example, each facet has four vertices.
i
list vertices for each facet. The first line is the number of facets. The remaining lines list the vertices for each facet. In 3-d and higher, report cospherical sites by adding extra points.
 
 
Coordinates
o
print vertices and facets of the convex hull in OFF format. The first line is the dimension. The second line is the number of vertices, facets, and ridges. The vertex coordinates are next, followed by the facets. Each facet starts with the number of vertices. The cube example has four vertices per facet.
Ft
print a triangulation of the convex hull in OFF format. The first line is the dimension. The second line is the number of vertices and added points, followed by the number of facets and the number of ridges. The vertex coordinates are next, followed by the centrum coordinates. There is one centrum for each non-simplicial facet. The cube example has six centrums, one per square. Each facet starts with the number of vertices or centrums. In the cube example, each facet uses two vertices and one centrum.
p
print vertex coordinates. The first line is the dimension and the second line is the number of vertices. The following lines are the coordinates of each vertex. The cube example has eight vertices.
Qc p
print coordinates of vertices and coplanar points. The first line is the dimension. The second line is the number of vertices and coplanar points. The coordinates are next, one line per point. Use 'Qc Qi p' to print the coordinates of all points.
 
 
Facets
Fn
list neighboring facets for each facet. The first line is the number of facets. Each remaining line starts with the number of neighboring facets. The cube example has four neighbors per facet.
FN
list neighboring facets for each point. The first line is the total number of points. Each remaining line starts with the number of neighboring facets. Each vertex of the cube example has three neighboring facets. Use 'Qc Qi FN' to include coplanar and interior points.
Fa
print area for each facet. The first line is the number of facets. Facet area follows, one line per facet. For the cube example, each facet has area one.
FI
list facet IDs. The first line is the number of facets. The IDs follow, one per line.
 
 
Coplanar and interior points
Fc
list coplanar points for each facet. The first line is the number of facets. The remaining lines start with the number of coplanar points. A coplanar point is assigned to one facet.
Qi Fc
list interior points for each facet. The first line is the number of facets. The remaining lines start with the number of interior points. A coplanar point is assigned to one facet.
FP
print distance to nearest vertex for coplanar points. The first line is the number of coplanar points. Each remaining line starts with the point ID of a vertex, followed by the point ID of a coplanar point, its facet, and distance. Use 'Qc Qi FP' for coplanar and interior points.
 
 
Hyperplanes
n
print hyperplane for each facet. The first line is the dimension. The second line is the number of facets. Each remaining line is the hyperplane's coefficients followed by its offset.
Fo
print outer plane for each facet. The output plane is above all points. The first line is the dimension. The second line is the number of facets. Each remaining line is the outer plane's coefficients followed by its offset.
Fi
print inner plane for each facet. The inner plane of a facet is below its vertices. The first line is the dimension. The second line is the number of facets. Each remaining line is the inner plane's coefficients followed by its offset.
 
 
General
s
print summary for the convex hull. Use 'Fs' and 'FS' if you need numeric data.
FA
compute total area and volume for 's' and 'FS'
m
Mathematica output for the convex hull in 2-d or 3-d.
FM
Maple output for the convex hull in 2-d or 3-d.
G
Geomview output for the convex hull in 2-d, 3-d, or 4-d.
 
 
Scaling and rotation
Qbk:n
scale k'th coordinate to lower bound.
QBk:n
scale k'th coordinate to upper bound.
QbB
scale input to unit cube centered at the origin.
QRn
randomly rotate the input with a random seed of n. If n=0, the seed is the time. If n=-1, use time for the random seed, but do not rotate the input.
Qbk:0Bk:0
remove k'th coordinate from input. This computes the convex hull in one lower dimension.

»qconvex controls

These options provide additional control:

Qt
triangulated output. Qhull triangulates non-simplicial facets. It may produce degenerate facets of zero area.
QJ
joggle the input instead of merging facets. This guarantees simplicial facets (e.g., triangles in 3-d). It is less accurate than triangulated output ('Qt').
Qc
keep coplanar points
Qi
keep interior points
f
facet dump. Print the data structure for each facet.
QVn
select facets containing point n as a vertex,
QGn
select facets that are visible from point n (marked 'good'). Use -n for the remainder.
PDk:0
select facets with a negative coordinate for dimension k
TFn
report progress after constructing n facets
Tv
verify result
TI file
input data from file. The filename may not use spaces or quotes.
TO file
output results to file. Use single quotes if the filename contains spaces (e.g., TO 'file with spaces.txt'
Qs
search all points for the initial simplex. If Qhull can not construct an initial simplex, it reports a descriptive message. Usually, the point set is degenerate and one or more dimensions should be removed ('Qbk:0Bk:0'). If not, use option 'Qs'. It performs an exhaustive search for the best initial simplex. This is expensive is high dimensions.

»qconvex graphics

Display 2-d, 3-d, and 4-d convex hulls with Geomview ('G').

Display 2-d and 3-d convex hulls with Mathematica ('m').

To view 4-d convex hulls in 3-d, use 'Pd0d1d2d3' to select the positive octant and 'GrD2' to drop dimension 2.

»qconvex notes

Qhull always computes a convex hull. The convex hull may be used for other geometric structures. The general technique is to transform the structure into an equivalent convex hull problem. For example, the Delaunay triangulation is equivalent to the convex hull of the input sites after lifting the points to a paraboloid.

»qconvex conventions

The following terminology is used for convex hulls in Qhull. See Qhull's data structures.

  • point - d coordinates
  • vertex - extreme point of the input set
  • ridge - d-1 vertices between two neighboring facets
  • hyperplane - halfspace defined by a unit normal and offset
  • coplanar point - a nearly incident point to a hyperplane
  • centrum - a point on the hyperplane for testing convexity
  • facet - a facet with vertices, ridges, coplanar points, neighboring facets, and hyperplane
  • simplicial facet - a facet with d vertices, d ridges, and d neighbors
  • non-simplicial facet - a facet with more than d vertices
  • good facet - a facet selected by 'QVn', etc.

»qconvex options

qconvex- compute the convex hull
    http://www.qhull.org

input (stdin):
    first lines: dimension and number of points (or vice-versa).
    other lines: point coordinates, best if one point per line
    comments:    start with a non-numeric character

options:
    Qt   - triangulated output
    QJ   - joggle input instead of merging facets
    Qc   - keep coplanar points with nearest facet
    Qi   - keep interior points with nearest facet

Qhull control options:
    Qbk:n   - scale coord k so that low bound is n
      QBk:n - scale coord k so that upper bound is n (QBk is 0.5)
    QbB  - scale input to unit cube centered at the origin
    Qbk:0Bk:0 - remove k-th coordinate from input
    QJn  - randomly joggle input in range [-n,n]
    QRn  - random rotation (n=seed, n=0 time, n=-1 time/no rotate)
    Qs   - search all points for the initial simplex
    QGn  - good facet if visible from point n, -n for not visible
    QVn  - good facet if it includes point n, -n if not

Trace options:
    T4   - trace at level n, 4=all, 5=mem/gauss, -1= events
    Tc   - check frequently during execution
    Ts   - print statistics
    Tv   - verify result: structure, convexity, and point inclusion
    Tz   - send all output to stdout
    TFn  - report summary when n or more facets created
    TI file - input data from file, no spaces or single quotes
    TO file - output results to file, may be enclosed in single quotes
    TPn  - turn on tracing when point n added to hull
     TMn - turn on tracing at merge n
     TWn - trace merge facets when width > n
    TVn  - stop qhull after adding point n, -n for before (see TCn)
     TCn - stop qhull after building cone for point n (see TVn)

Precision options:
    Cn   - radius of centrum (roundoff added).  Merge facets if non-convex
     An  - cosine of maximum angle.  Merge facets if cosine > n or non-convex
           C-0 roundoff, A-0.99/C-0.01 pre-merge, A0.99/C0.01 post-merge
    Rn   - randomly perturb computations by a factor of [1-n,1+n]
    Un   - max distance below plane for a new, coplanar point
    Wn   - min facet width for outside point (before roundoff)

Output formats (may be combined; if none, produces a summary to stdout):
    f    - facet dump
    G    - Geomview output (see below)
    i    - vertices incident to each facet
    m    - Mathematica output (2-d and 3-d)
    n    - normals with offsets
    o    - OFF file format (dim, points and facets; Voronoi regions)
    p    - point coordinates
    s    - summary (stderr)

More formats:
    Fa   - area for each facet
    FA   - compute total area and volume for option 's'
    Fc   - count plus coplanar points for each facet
           use 'Qc' (default) for coplanar and 'Qi' for interior
    FC   - centrum for each facet
    Fd   - use cdd format for input (homogeneous with offset first)
    FD   - use cdd format for numeric output (offset first)
    FF   - facet dump without ridges
    Fi   - inner plane for each facet
    FI   - ID for each facet
    Fm   - merge count for each facet (511 max)
    FM   - Maple output (2-d and 3-d)
    Fn   - count plus neighboring facets for each facet
    FN   - count plus neighboring facets for each point
    Fo   - outer plane (or max_outside) for each facet
    FO   - options and precision constants
    FP   - nearest vertex for each coplanar point
    FQ   - command used for qconvex
    Fs   - summary: #int (8), dimension, #points, tot vertices, tot facets,
                      for output: #vertices, #facets,
                                  #coplanar points, #non-simplicial facets
                    #real (2), max outer plane, min vertex
    FS   - sizes:   #int (0)
                    #real(2) tot area, tot volume
    Ft   - triangulation with centrums for non-simplicial facets (OFF format)
    Fv   - count plus vertices for each facet
    FV   - average of vertices (a feasible point for 'H')
    Fx   - extreme points (in order for 2-d)

Geomview output (2-d, 3-d, and 4-d)
    Ga   - all points as dots
     Gp  -  coplanar points and vertices as radii
     Gv  -  vertices as spheres
    Gi   - inner planes only
     Gn  -  no planes
     Go  -  outer planes only
    Gc   - centrums
    Gh   - hyperplane intersections
    Gr   - ridges
    GDn  - drop dimension n in 3-d and 4-d output

Print options:
    PAn  - keep n largest facets by area
    Pdk:n - drop facet if normal[k] <= n (default 0.0)
    PDk:n - drop facet if normal[k] >= n
    Pg   - print good facets (needs 'QGn' or 'QVn')
    PFn  - keep facets whose area is at least n
    PG   - print neighbors of good facets
    PMn  - keep n facets with most merges
    Po   - force output.  If error, output neighborhood of facet
    Pp   - do not report precision problems

    .    - list of all options
    -    - one line descriptions of all options

Up: Home page for Qhull
Up: Qhull manual: Table of Contents
To: Programs •Options • Output • Formats • Geomview • Print • Qhull • Precision • Trace
To: synopsis • input • outputs • controls • graphics • notes • conventions • options

The Geometry Center Home Page

Comments to: qhull@qhull.org
Created: Sept. 25, 1995 --- Last modified: see top

qhull-2012.1/html/qdelaun.htm0000644000076400010400000006511511720316127017223 0ustar bbarberAdministrators qdelaunay -- Delaunay triangulation Up: Home page for Qhull
Up: Qhull manual: Table of Contents
To: Programs • Options • Output • Formats • Geomview • Print • Qhull • Precision • Trace
To: synopsis • input • outputs • controls • graphics • notes • conventions • options

[delaunay]qdelaunay -- Delaunay triangulation

The Delaunay triangulation is the triangulation with empty circumspheres. It has many useful properties and applications. See the survey article by Aurenhammer ['91] and the detailed introduction by O'Rourke ['94].

Example: rbox r y c G0.1 D2 | qdelaunay s Fv TO result
Compute the 2-d Delaunay triangulation of a triangle and a small square. Write a summary to the console and unoriented regions to 'result'. Merge regions for cocircular input sites (i.e., the square).
 
Example: rbox r y c G0.1 D2 | qdelaunay s Fv Qt
Compute the 2-d Delaunay triangulation of a triangle and a small square. Write a summary and unoriented regions to the console. Produce triangulated output.
 
Example: rbox 10 D2 | qdelaunay QJ s i TO result
Compute the 2-d Delaunay triangulation of 10 random points. Joggle the input to guarantee triangular output. Write a summary to the console and the regions to 'result'.

Qhull computes the Delaunay triangulation by computing a convex hull. It lifts the input sites to a paraboloid by adding the sum of the squares of the coordinates. It scales the height of the paraboloid to improve numeric precision ('Qbb'). It computes the convex hull of the lifted sites, and projects the lower convex hull to the input.

Each region of the Delaunay triangulation corresponds to a facet of the lower half of the convex hull. Facets of the upper half of the convex hull correspond to the furthest-site Delaunay triangulation. See the examples, Delaunay and Voronoi diagrams.

See Qhull FAQ - Delaunay and Voronoi diagram questions.

By default, qdelaunay merges cocircular and cospherical regions. For example, the Delaunay triangulation of a square inside a diamond ('rbox D2 c d G4 | qdelaunay') contains one region for the square.

Use option 'Qz' if the input is circular, cospherical, or nearly so. It improves precision by adding a point "at infinity," above the corresponding paraboloid.

If you use 'Qt' (triangulated output), all Delaunay regions will be simplicial (e.g., triangles in 2-d). Some regions may be degenerate and have zero area. Triangulated output identifies coincident points.

If you use 'QJ' (joggled input), all Delaunay regions will be simplicial (e.g., triangles in 2-d). Coincident points will create small regions since the points are joggled apart. Joggled input is less accurate than triangulated output ('Qt'). See Merged facets or joggled input.

The output for 3-d Delaunay triangulations may be confusing if the input contains cospherical data. See the FAQ item Why are there extra points in a 4-d or higher convex hull? Avoid these problems with triangulated output ('Qt') or joggled input ('QJ').

The 'qdelaunay' program is equivalent to 'qhull d Qbb' in 2-d to 3-d, and 'qhull d Qbb Qx' in 4-d and higher. It disables the following Qhull options: d n v H U Qb QB Qc Qf Qg Qi Qm Qr QR Qv Qx TR E V FC Fi Fo Fp Ft FV Q0,etc.

Copyright © 1995-2012 C.B. Barber

»qdelaunay synopsis

qdelaunay- compute the Delaunay triangulation.
    input (stdin): dimension, number of points, point coordinates
    comments start with a non-numeric character

options (qdelaun.htm):
    Qt   - triangulated output
    QJ   - joggle input instead of merging facets
    Qu   - furthest-site Delaunay triangulation
    Tv   - verify result: structure, convexity, and in-circle test
    .    - concise list of all options
    -    - one-line description of all options

output options (subset):
    s    - summary of results (default)
    i    - vertices incident to each Delaunay region
    Fx   - extreme points (vertices of the convex hull)
    o    - OFF format (shows the points lifted to a paraboloid)
    G    - Geomview output (2-d and 3-d points lifted to a paraboloid)
    m    - Mathematica output (2-d inputs lifted to a paraboloid)
    QVn  - print Delaunay regions that include point n, -n if not
    TO file- output results to file, may be enclosed in single quotes

examples:
    rbox c P0 D2 | qdelaunay s o          rbox c P0 D2 | qdelaunay i
    rbox c P0 D3 | qdelaunay Fv Qt        rbox c P0 D2 | qdelaunay s Qu Fv
    rbox c G1 d D2 | qdelaunay s i        rbox c G1 d D2 | qdelaunay s i Qt
    rbox M3,4 z 100 D2 | qdelaunay s      rbox M3,4 z 100 D2 | qdelaunay s Qt

»qdelaunay input

The input data on stdin consists of:

  • dimension
  • number of points
  • point coordinates

Use I/O redirection (e.g., qdelaunay < data.txt), a pipe (e.g., rbox 10 | qdelaunay), or the 'TI' option (e.g., qdelaunay TI data.txt).

For example, this is four cocircular points inside a square. Its Delaunay triangulation contains 8 triangles and one four-sided figure.

rbox s 4 W0 c G1 D2 > data 
2 RBOX s 4 W0 c D2
8
-0.4941988586954018 -0.07594397977563715
-0.06448037284989526 0.4958248496365813
0.4911154367094632 0.09383830681375946
-0.348353580869097 -0.3586778257652367
    -1     -1
    -1      1
     1     -1
     1      1

qdelaunay s i < data 


Delaunay triangulation by the convex hull of 8 points in 3-d

  Number of input sites: 8
  Number of Delaunay regions: 9
  Number of non-simplicial Delaunay regions: 1

Statistics for: RBOX s 4 W0 c D2 | QDELAUNAY s i

  Number of points processed: 8
  Number of hyperplanes created: 18
  Number of facets in hull: 10
  Number of distance tests for qhull: 33
  Number of merged facets: 2
  Number of distance tests for merging: 102
  CPU seconds to compute hull (after input): 0.028

9
1 7 5
6 3 4
2 3 6
7 2 6
2 7 1
0 5 4
3 0 4
0 1 5
1 0 3 2

»qdelaunay outputs

These options control the output of Delaunay triangulations:

Delaunay regions
i
list input sites for each Delaunay region. The first line is the number of regions. The remaining lines list the input sites for each region. The regions are oriented. In 3-d and higher, report cospherical sites by adding extra points. Use triangulated output ('Qt') to avoid non-simpicial regions. For the circle-in-square example, eight Delaunay regions are triangular and the ninth has four input sites.
Fv
list input sites for each Delaunay region. The first line is the number of regions. Each remaining line starts with the number of input sites. The regions are unoriented. For the circle-in-square example, eight Delaunay regions are triangular and the ninth has four input sites.
Fn
list neighboring regions for each Delaunay region. The first line is the number of regions. Each remaining line starts with the number of neighboring regions. Negative indices (e.g., -1) indicate regions outside of the Delaunay triangulation. For the circle-in-square example, the four regions on the square are neighbors to the region-at-infinity.
FN
list the Delaunay regions for each input site. The first line is the total number of input sites. Each remaining line starts with the number of Delaunay regions. Negative indices (e.g., -1) indicate regions outside of the Delaunay triangulation. For the circle-in-square example, each point on the circle belongs to four Delaunay regions. Use 'Qc FN' to include coincident input sites and deleted vertices.
Fa
print area for each Delaunay region. The first line is the number of regions. The areas follow, one line per region. For the circle-in-square example, the cocircular region has area 0.4.
 
 
Input sites
Fc
list coincident input sites for each Delaunay region. The first line is the number of regions. The remaining lines start with the number of coincident sites and deleted vertices. Deleted vertices indicate highly degenerate input (see'Fs'). A coincident site is assigned to one Delaunay region. Do not use 'QJ' with 'Fc'; the joggle will separate coincident sites.
FP
print coincident input sites with distance to nearest site (i.e., vertex). The first line is the number of coincident sites. Each remaining line starts with the point ID of an input site, followed by the point ID of a coincident point, its region, and distance. Includes deleted vertices which indicate highly degenerate input (see'Fs'). Do not use 'QJ' with 'FP'; the joggle will separate coincident sites.
Fx
list extreme points of the input sites. These points are on the boundary of the convex hull. The first line is the number of extreme points. Each point is listed, one per line. The circle-in-square example has four extreme points.
 
 
General
FA
compute total area for 's' and 'FS'
o
print lower facets of the corresponding convex hull (a paraboloid)
m
Mathematica output for the lower facets of the paraboloid (2-d triangulations).
FM
Maple output for the lower facets of the paraboloid (2-d triangulations).
G
Geomview output for the paraboloid (2-d or 3-d triangulations).
s
print summary for the Delaunay triangulation. Use 'Fs' and 'FS' for numeric data.

»qdelaunay controls

These options provide additional control:

Qt
triangulated output. Qhull triangulates non-simplicial facets. It may produce degenerate facets of zero area.
QJ
joggle the input to avoid cospherical and coincident sites. It is less accurate than triangulated output ('Qt').
Qu
compute the furthest-site Delaunay triangulation.
Qz
add a point above the paraboloid to reduce precision errors. Use it for nearly cocircular/cospherical input (e.g., 'rbox c | qdelaunay Qz'). The point is printed for options 'Ft' and 'o'.
QVn
select facets adjacent to input site n (marked 'good').
Tv
verify result.
TI file
input data from file. The filename may not use spaces or quotes.
TO file
output results to file. Use single quotes if the filename contains spaces (e.g., TO 'file with spaces.txt'
TFn
report progress after constructing n facets
PDk:1
include upper and lower facets in the output. Set k to the last dimension (e.g., 'PD2:1' for 2-d inputs).
f
facet dump. Print the data structure for each facet (i.e., Delaunay region).

»qdelaunay graphics

For 2-d and 3-d Delaunay triangulations, Geomview ('qdelaunay G') displays the corresponding convex hull (a paraboloid).

To view a 2-d Delaunay triangulation, use 'qdelaunay GrD2' to drop the last dimension. This is the same as viewing the hull without perspective (see Geomview's 'cameras' menu).

To view a 3-d Delaunay triangulation, use 'qdelaunay GrD3' to drop the last dimension. You may see extra edges. These are interior edges that Geomview moves towards the viewer (see 'lines closer' in Geomview's camera options). Use option 'Gt' to make the outer ridges transparent in 3-d. See Delaunay and Voronoi examples.

For 2-d Delaunay triangulations, Mathematica ('m') and Maple ('FM') output displays the lower facets of the corresponding convex hull (a paraboloid).

For 2-d, furthest-site Delaunay triangulations, Maple and Mathematica output ('Qu m') displays the upper facets of the corresponding convex hull (a paraboloid).

»qdelaunay notes

You can simplify the Delaunay triangulation by enclosing the input sites in a large square or cube. This is particularly recommended for cocircular or cospherical input data.

A non-simplicial Delaunay region indicates nearly cocircular or cospherical input sites. To avoid non-simplicial regions either triangulate the output ('Qt') or joggle the input ('QJ'). Triangulated output is more accurate than joggled input. Alternatively, use an exact arithmetic code.

Delaunay triangulations do not include facets that are coplanar with the convex hull of the input sites. A facet is coplanar if the last coefficient of its normal is nearly zero (see qh_ZEROdelaunay).

See Imprecision issues :: Delaunay triangulations for a discussion of precision issues. Deleted vertices indicate highly degenerate input. They are listed in the summary output and option 'Fs'.

To compute the Delaunay triangulation of points on a sphere, compute their convex hull. If the sphere is the unit sphere at the origin, the facet normals are the Voronoi vertices of the input. The points may be restricted to a hemisphere. [S. Fortune]

The 3-d Delaunay triangulation of regular points on a half spiral (e.g., 'rbox 100 l | qdelaunay') has quadratic size, while the Delaunay triangulation of random 3-d points is approximately linear for reasonably sized point sets.

With the Qhull library, you can use qh_findbestfacet in poly2.c to locate the facet that contains a point. You should first lift the point to the paraboloid (i.e., the last coordinate is the sum of the squares of the point's coordinates -- qh_setdelaunay). Do not use options 'Qbb', 'QbB', 'Qbk:n', or 'QBk:n' since these scale the last coordinate.

If a point is interior to the convex hull of the input set, it is interior to the adjacent vertices of the Delaunay triangulation. This is demonstrated by the following pipe for point 0: 

    qdelaunay <data s FQ QV0 p | qconvex s Qb3:0B3:0 p

The first call to qdelaunay returns the neighboring points of point 0 in the Delaunay triangulation. The second call to qconvex returns the vertices of the convex hull of these points (after dropping the lifted coordinate). If point 0 is interior to the original point set, it is interior to the reduced point set.

»qdelaunay conventions

The following terminology is used for Delaunay triangulations in Qhull for dimension d. The underlying structure is the lower facets of a convex hull in dimension d+1. For further information, see data structures and convex hull conventions.

  • input site - a point in the input (one dimension lower than a point on the convex hull)
  • point - a point has d+1 coordinates. The last coordinate is the sum of the squares of the input site's coordinates
  • coplanar point - a coincident input site or a deleted vertex. Deleted vertices indicate highly degenerate input.
  • vertex - a point on the paraboloid. It corresponds to a unique input site.
  • point-at-infinity - a point added above the paraboloid by option 'Qz'
  • lower facet - a facet corresponding to a Delaunay region. The last coefficient of its normal is clearly negative.
  • upper facet - a facet corresponding to a furthest-site Delaunay region. The last coefficient of its normal is clearly positive.
  • Delaunay region - a lower facet projected to the input sites
  • upper Delaunay region - an upper facet projected to the input sites
  • non-simplicial facet - more than d input sites are cocircular or cospherical
  • good facet - a Delaunay region with optional restrictions by 'QVn', etc.

»qdelaunay options

qdelaunay- compute the Delaunay triangulation
    http://www.qhull.org

input (stdin):
    first lines: dimension and number of points (or vice-versa).
    other lines: point coordinates, best if one point per line
    comments:    start with a non-numeric character

options:
    Qt   - triangulated output
    QJ   - joggle input instead of merging facets
    Qu   - compute furthest-site Delaunay triangulation

Qhull control options:
    QJn  - randomly joggle input in range [-n,n]
    Qs   - search all points for the initial simplex
    Qz   - add point-at-infinity to Delaunay triangulation
    QGn  - print Delaunay region if visible from point n, -n if not
    QVn  - print Delaunay regions that include point n, -n if not

Trace options:
    T4   - trace at level n, 4=all, 5=mem/gauss, -1= events
    Tc   - check frequently during execution
    Ts   - print statistics
    Tv   - verify result: structure, convexity, and in-circle test
    Tz   - send all output to stdout
    TFn  - report summary when n or more facets created
    TI file - input data from file, no spaces or single quotes
    TO file - output results to file, may be enclosed in single quotes
    TPn  - turn on tracing when point n added to hull
     TMn - turn on tracing at merge n
     TWn - trace merge facets when width > n
    TVn  - stop qhull after adding point n, -n for before (see TCn)
     TCn - stop qhull after building cone for point n (see TVn)

Precision options:
    Cn   - radius of centrum (roundoff added).  Merge facets if non-convex
     An  - cosine of maximum angle.  Merge facets if cosine > n or non-convex
           C-0 roundoff, A-0.99/C-0.01 pre-merge, A0.99/C0.01 post-merge
    Rn   - randomly perturb computations by a factor of [1-n,1+n]
    Wn   - min facet width for outside point (before roundoff)

Output formats (may be combined; if none, produces a summary to stdout):
    f    - facet dump
    G    - Geomview output (see below)
    i    - vertices incident to each Delaunay region
    m    - Mathematica output (2-d only, lifted to a paraboloid)
    o    - OFF format (dim, points, and facets as a paraboloid)
    p    - point coordinates (lifted to a paraboloid)
    s    - summary (stderr)

More formats:
    Fa   - area for each Delaunay region
    FA   - compute total area for option 's'
    Fc   - count plus coincident points for each Delaunay region
    Fd   - use cdd format for input (homogeneous with offset first)
    FD   - use cdd format for numeric output (offset first)
    FF   - facet dump without ridges
    FI   - ID of each Delaunay region
    Fm   - merge count for each Delaunay region (511 max)
    FM   - Maple output (2-d only, lifted to a paraboloid)
    Fn   - count plus neighboring region for each Delaunay region
    FN   - count plus neighboring region for each point
    FO   - options and precision constants
    FP   - nearest point and distance for each coincident point
    FQ   - command used for qdelaunay
    Fs   - summary: #int (8), dimension, #points, tot vertices, tot facets,
                    for output: #vertices, #Delaunay regions,
                                #coincident points, #non-simplicial regions
                    #real (2), max outer plane, min vertex
    FS   - sizes:   #int (0)
                    #real (2), tot area, 0
    Fv   - count plus vertices for each Delaunay region
    Fx   - extreme points of Delaunay triangulation (on convex hull)

Geomview options (2-d and 3-d)
    Ga   - all points as dots
     Gp  -  coplanar points and vertices as radii
     Gv  -  vertices as spheres
    Gi   - inner planes only
     Gn  -  no planes
     Go  -  outer planes only
    Gc     - centrums
    Gh   - hyperplane intersections
    Gr   - ridges
    GDn  - drop dimension n in 3-d and 4-d output
    Gt   - transparent outer ridges to view 3-d Delaunay

Print options:
    PAn  - keep n largest Delaunay regions by area
    Pdk:n - drop facet if normal[k] <= n (default 0.0)
    PDk:n - drop facet if normal[k] >= n
    Pg   - print good Delaunay regions (needs 'QGn' or 'QVn')
    PFn  - keep Delaunay regions whose area is at least n
    PG   - print neighbors of good regions (needs 'QGn' or 'QVn')
    PMn  - keep n Delaunay regions with most merges
    Po   - force output.  If error, output neighborhood of facet
    Pp   - do not report precision problems

    .    - list of all options
    -    - one line descriptions of all options

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[delaunay]qdelaunay Qu -- furthest-site Delaunay triangulation

The furthest-site Delaunay triangulation corresponds to the upper facets of the Delaunay construction. Its vertices are the extreme points of the input sites. It is the dual of the furthest-site Voronoi diagram.

Example: rbox 10 D2 | qdelaunay Qu Qt s i TO result
Compute the 2-d, furthest-site Delaunay triangulation of 10 random points. Triangulate the output. Write a summary to the console and the regions to 'result'.
 
Example: rbox 10 D2 | qdelaunay Qu QJ s i TO result
Compute the 2-d, furthest-site Delaunay triangulation of 10 random points. Joggle the input to guarantee triangular output. Write a summary to the console and the regions to 'result'.
 
Example: rbox r y c G1 D2 | qdelaunay Qu s Fv TO result
Compute the 2-d, furthest-site Delaunay triangulation of a triangle inside a square. Write a summary to the console and unoriented regions to 'result'. Merge regions for cocircular input sites (e.g., the square). The square is the only furthest-site Delaunay region.

As with the Delaunay triangulation, Qhull computes the furthest-site Delaunay triangulation by lifting the input sites to a paraboloid. The lower facets correspond to the Delaunay triangulation while the upper facets correspond to the furthest-site triangulation. Neither triangulation includes "vertical" facets (i.e., facets whose last hyperplane coefficient is nearly zero). Vertical facets correspond to input sites that are coplanar to the convex hull of the input. An example is points on the boundary of a lattice.

By default, qdelaunay merges cocircular and cospherical regions. For example, the furthest-site Delaunay triangulation of a square inside a diamond ('rbox D2 c d G4 | qdelaunay Qu') consists of one region (the diamond).

If you use 'Qt' (triangulated output), all furthest-site Delaunay regions will be simplicial (e.g., triangles in 2-d). Some regions may be degenerate and have zero area.

If you use 'QJ' (joggled input), all furthest-site Delaunay regions will be simplicial (e.g., triangles in 2-d). Joggled input is less accurate than triangulated output ('Qt'). See Merged facets or joggled input.

The output for 3-d, furthest-site Delaunay triangulations may be confusing if the input contains cospherical data. See the FAQ item Why are there extra points in a 4-d or higher convex hull? Avoid these problems with triangulated output ('Qt') or joggled input ('QJ').

The 'qdelaunay' program is equivalent to 'qhull d Qbb' in 2-d to 3-d, and 'qhull d Qbb Qx' in 4-d and higher. It disables the following Qhull options: d n v H U Qb QB Qc Qf Qg Qi Qm Qr QR Qv Qx TR E V FC Fi Fo Fp FV Q0,etc.

Copyright © 1995-2012 C.B. Barber

»furthest-site qdelaunay synopsis

See qdelaunay synopsis. The same program is used for both constructions. Use option 'Qu' for furthest-site Delaunay triangulations.

»furthest-site qdelaunay input

The input data on stdin consists of:

  • dimension
  • number of points
  • point coordinates

Use I/O redirection (e.g., qdelaunay Qu < data.txt), a pipe (e.g., rbox 10 | qdelaunay Qu), or the 'TI' option (e.g., qdelaunay Qu TI data.txt).

For example, this is a square containing four random points. Its furthest-site Delaunay triangulation contains one square.

rbox c 4 D2 > data 
2 RBOX c 4 D2
8
-0.4999921736307369 -0.3684622117955817
0.2556053225468894 -0.0413498678629751
0.0327672376602583 -0.2810408135699488
-0.452955383763607 0.17886471718444
  -0.5   -0.5
  -0.5    0.5
   0.5   -0.5
   0.5    0.5

qdelaunay Qu i < data 


Furthest-site Delaunay triangulation by the convex hull of 8 points in 3-d:

  Number of input sites: 8
  Number of Delaunay regions: 1
  Number of non-simplicial Delaunay regions: 1

Statistics for: RBOX c 4 D2 | QDELAUNAY s Qu i

  Number of points processed: 8
  Number of hyperplanes created: 20
  Number of facets in hull: 11
  Number of distance tests for qhull: 34
  Number of merged facets: 1
  Number of distance tests for merging: 107
  CPU seconds to compute hull (after input): 0.02

1
7 6 4 5

»furthest-site qdelaunay outputs

These options control the output of furthest-site Delaunay triangulations:

furthest-site Delaunay regions
i
list input sites for each furthest-site Delaunay region. The first line is the number of regions. The remaining lines list the input sites for each region. The regions are oriented. In 3-d and higher, report cospherical sites by adding extra points. For the points-in-square example, the square is the only furthest-site Delaunay region.
Fv
list input sites for each furthest-site Delaunay region. The first line is the number of regions. Each remaining line starts with the number of input sites. The regions are unoriented. For the points-in-square example, the square is the only furthest-site Delaunay region.
Ft
print a triangulation of the furthest-site Delaunay regions in OFF format. The first line is the dimension. The second line is the number of input sites and added points, followed by the number of simplices and the number of ridges. The input coordinates are next, followed by the centrum coordinates. There is one centrum for each non-simplicial furthest-site Delaunay region. Each remaining line starts with dimension+1. The simplices are oriented. For the points-in-square example, the square has a centrum at the origin. It splits the square into four triangular regions.
Fn
list neighboring regions for each furthest-site Delaunay region. The first line is the number of regions. Each remaining line starts with the number of neighboring regions. Negative indices (e.g., -1) indicate regions outside of the furthest-site Delaunay triangulation. For the points-in-square example, the four neighboring regions are outside of the triangulation. They belong to the regular Delaunay triangulation.
FN
list the furthest-site Delaunay regions for each input site. The first line is the total number of input sites. Each remaining line starts with the number of furthest-site Delaunay regions. Negative indices (e.g., -1) indicate regions outside of the furthest-site Delaunay triangulation. For the points-in-square example, the four random points belong to no region while the square's vertices belong to region 0 and three regions outside of the furthest-site Delaunay triangulation.
Fa
print area for each furthest-site Delaunay region. The first line is the number of regions. The areas follow, one line per region. For the points-in-square example, the square has unit area.
 
 
Input sites
Fx
list extreme points of the input sites. These points are vertices of the furthest-point Delaunay triangulation. They are on the boundary of the convex hull. The first line is the number of extreme points. Each point is listed, one per line. The points-in-square example has four extreme points.
 
 
General
FA
compute total area for 's' and 'FS'. This is the same as the area of the convex hull.
o
print upper facets of the corresponding convex hull (a paraboloid)
m
Mathematica output for the upper facets of the paraboloid (2-d triangulations).
FM
Maple output for the upper facets of the paraboloid (2-d triangulations).
G
Geomview output for the paraboloid (2-d or 3-d triangulations).
s
print summary for the furthest-site Delaunay triangulation. Use 'Fs' and 'FS' for numeric data.

»furthest-site qdelaunay controls

These options provide additional control:

Qu
must be used for furthest-site Delaunay triangulation.
Qt
triangulated output. Qhull triangulates non-simplicial facets. It may produce degenerate facets of zero area.
QJ
joggle the input to avoid cospherical and coincident sites. It is less accurate than triangulated output ('Qt').
QVn
select facets adjacent to input site n (marked 'good').
Tv
verify result.
TI file
input data from file. The filename may not use spaces or quotes.
TO file
output results to file. Use single quotes if the filename contains spaces (e.g., TO 'file with spaces.txt'
TFn
report progress after constructing n facets
PDk:1
include upper and lower facets in the output. Set k to the last dimension (e.g., 'PD2:1' for 2-d inputs).
f
facet dump. Print the data structure for each facet (i.e., furthest-site Delaunay region).

»furthest-site qdelaunay graphics

See Delaunay graphics. They are the same except for Mathematica and Maple output.

»furthest-site qdelaunay notes

The furthest-site Delaunay triangulation does not record coincident input sites. Use qdelaunay instead.

qdelaunay Qu does not work for purely cocircular or cospherical points (e.g., rbox c | qdelaunay Qu). Instead, use qdelaunay Qz -- when all points are vertices of the convex hull of the input sites, the Delaunay triangulation is the same as the furthest-site Delaunay triangulation.

A non-simplicial, furthest-site Delaunay region indicates nearly cocircular or cospherical input sites. To avoid non-simplicial regions triangulate the output ('Qt') or joggle the input ('QJ'). Joggled input is less accurate than triangulated output. You may also triangulate non-simplicial regions with option 'Ft'. It adds the centrum to non-simplicial regions. Alternatively, use an exact arithmetic code.

Furthest-site Delaunay triangulations do not include facets that are coplanar with the convex hull of the input sites. A facet is coplanar if the last coefficient of its normal is nearly zero (see qh_ZEROdelaunay).

»furthest-site qdelaunay conventions

The following terminology is used for furthest-site Delaunay triangulations in Qhull. The underlying structure is the upper facets of a convex hull in one higher dimension. See convex hull conventions, Delaunay conventions, and Qhull's data structures

  • input site - a point in the input (one dimension lower than a point on the convex hull)
  • point - d+1 coordinates. The last coordinate is the sum of the squares of the input site's coordinates
  • vertex - a point on the paraboloid. It corresponds to a unique input site.
  • furthest-site Delaunay facet - an upper facet of the paraboloid. The last coefficient of its normal is clearly positive.
  • furthest-site Delaunay region - a furthest-site Delaunay facet projected to the input sites
  • non-simplicial facet - more than d points are cocircular or cospherical
  • good facet - a furthest-site Delaunay facet with optional restrictions by 'QVn', etc.

»furthest-site qdelaunay options

See qdelaunay options. The same program is used for both constructions. Use option 'Qu' for furthest-site Delaunay triangulations.

Up: Home page for Qhull
Up: Qhull manual: Table of Contents
To: Programs • Options • Output • Formats • Geomview • Print • Qhull • Precision • Trace
To: synopsis • input • outputs • controls • graphics • notes • conventions • options

The Geometry Center Home Page

Comments to: qhull@qhull.org
Created: Sept. 25, 1995 --- Last modified: see top

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[4-d cube] Qhull code

This section discusses the code for Qhull.

Copyright © 1995-2012 C.B. Barber

»Qhull code: Table of Contents

»Performance of Qhull

Empirically, Qhull's performance is balanced in the sense that the average case happens on average. This may always be true if the precision of the input is limited to at most O(log n) bits. Empirically, the maximum number of vertices occurs at the end of constructing the hull.

Let n be the number of input points, v be the number of output vertices, and f_v be the maximum number of facets for a convex hull of v vertices. If both conditions hold, Qhull runs in O(n log v) in 2-d and 3-d and O(n f_v/v) otherwise. The function f_v increases rapidly with dimension. It is O(v^floor(d/2) / floor(d/2)!).

The time complexity for merging is unknown. Options 'C-0' and 'Qx' (defaults) handle precision problems due to floating-point arithmetic. They are optimized for simplicial outputs.

When running large data sets, you should monitor Qhull's performance with the 'TFn' option. The time per facet is approximately constant. In high-d with many merged facets, the size of the ridge sets grows rapidly. For example the product of 8-d simplices contains 18 facets and 500,000 ridges. This will increase the time needed per facet.

As dimension increases, the number of facets and ridges in a convex hull grows rapidly for the same number of vertices. For example, the convex hull of 300 cospherical points in 6-d has 30,000 facets.

If Qhull appears to stop processing facets, check the memory usage of Qhull. If more than 5-10% of Qhull is in virtual memory, its performance will degrade rapidly.

When building hulls in 20-d and higher, you can follow the progress of Qhull with option 'T1'. It reports each major event in processing a point.

To reduce memory requirements, recompile Qhull for single-precision reals (REALfloat in user.h). Single-precision does not work with joggle ('QJ'). Check qh_MEMalign in user.h and the match between free list sizes and data structure sizes (see the end of the statistics report from 'Ts'). If free list sizes do not match, you may be able to use a smaller qh_MEMalign. Setting qh_COMPUTEfurthest saves a small amount of memory, as does clearing qh_MAXoutside (both in user.h).

Shewchuk is working on a 3-d version of his triangle program. It is optimized for 3-d simplicial Delaunay triangulation and uses less memory than Qhull.

To reduce the size of the Qhull executable, consider qh_NOtrace and qh_KEEPstatistics 0 in user.h. By changing user.c you can also remove the input/output code in io.c. If you don't need facet merging, then version 1.01 of Qhull is much smaller. It contains some bugs that prevent Qhull from initializing in simple test cases. It is slower in high dimensions.

The precision options, 'Vn', 'Wn', 'Un'. 'A-n', 'C-n', 'An', 'Cn', and 'Qx', may have large effects on Qhull performance. You will need to experiment to find the best combination for your application.

The verify option ('Tv') checks every point after the hull is complete. If facet merging is used, it checks that every point is inside every facet. This can take a very long time if there are many points and many facets. You can interrupt the verify without losing your output. If facet merging is not used and there are many points and facets, Qhull uses a directed search instead of an exhaustive search. This should be fast enough for most point sets. Directed search is not used for facet merging because directed search was already used for updating the facets' outer planes.

The check-frequently option ('Tc') becomes expensive as the dimension increases. The verify option ('Tv') performs many of the same checks before outputting the results.

Options 'Q0' (no pre-merging), 'Q3' (no checks for redundant vertices), 'Q5' (no updates for outer planes), and 'Q8' (no near-interior points) increase Qhull's speed. The corresponding operations may not be needed in your application.

In 2-d and 3-d, a partial hull may be faster to produce. Option 'QgGn' only builds facets visible to point n. Option 'QgVn' only builds facets that contain point n. In higher-dimensions, this does not reduce the number of facets.

User.h includes a number of performance-related constants. Changes may improve Qhull performance on your data sets. To understand their effect on performance, you will need to read the corresponding code.

GNU gprof reports that the dominate cost for 3-d convex hull of cosperical points is qh_distplane(), mainly called from qh_findbestnew(). The dominate cost for 3-d Delaunay triangulation is creating new facets in qh_addpoint(), while qh_distplane() remains the most expensive function.

»Calling Qhull from C++ programs

Warning: The C++ interface to Qhull is new and incomplete. You will need to extend the interface for all but the simplest applications. You will need to understand the data structures and read the code. Most users will find it easier to call Qhull as a program.

Note: Please download the 'next' branch from git://gitorious.org/qhull/qhull.git

Qhull's C++ interface provides wrapper classes for Qhull and Rbox. It provides access to Qhull's data structures. Most of the classes derive from the corresponding qhull data structure. For example, QhullFacet is an instance of Qhull's facetT.

The main methods are
  • RboxPoints.appendRandomPoints -- append random points according to rbox options.
  • Qhull.runQhull -- construct the convex hull of the input points
  • Qhull.outputQhull -- write output according to Qhull options
The sample program, user_eg3.cpp, duplicates Qhull's facet dump (option 'f'). Example (c.f., user_eg3 eg-100) 
    RboxPoints rbox;
    rbox.appendRandomPoints("100");
    Qhull qhull;
    qhull.runQhull("", rbox);
    QhullFacetList facets(qhull);
    cout<< facets;

The C++ iterface for RboxPoints redefines the fprintf() calls in rboxlib.c. Instead of writing its output to stdout, RboxPoints appends the output to a std::vector. The same technique may be used for calling Qhull from C++.

  • Run Qhull with option 'Ta' to annotate the output with qh_fprintf() identifiers.
  • Redefine qh_fprintf() for these identifiers.
  • See RboxPoints.cpp for an example.

A more flexible approach extends Qhull's classes. For example, to access the vertices of a QhullFacet, define a constructor of QhullVertexSet that takes a QhullFacet as a parameter.

With care, you may create multiple Qhull instances, but only one thread may use qh_qh, qh_qhstat, and qhmem at a time (i.e., most of libqhull, the original C program). only one instance may be active at time. The global pointer qh_qh points to Qhull's data structure, QhullQh. The class UsingLibQhull checks that qh_qh is correct.

Qhull objects have the entire qhull data structure, so they can explore this data structure independent of libqhull. You can use any method that does not refer to UsingLibQhull, or invoke methods that refer to UsingLibQhull. You may also use any method in libqhull that does not reference qh_qh, qh_qhstat (i.e., does not include the macro 'qh', zinc_, etc) and does not allocate or deallocate memory via mem.c. In particular, you can call most of the qset macros and functions, allowing you to explore the data structure with 'foreachFacet_(), etc.' You can call all of the qset.h functions if you turn off Qhull's memory manager (qh_NOmem in mem.h)

»Cpp questions for Qhull

Developing C++ code requires many conventions, idioms, and technical details. The following questions have either mystified the author or do not have a clear answer. See also C++ and Perl Guidelines, C++ interface to Qhull. and FIXUP in the code. Please add notes to Gitorious wiki.
  • FIXUP QH11026 Should return reference, but get reference to temporary 
    iterator Coordinates::operator++() { return iterator(++i); }
  • size() as size_t, size_type, or int
  • Should all containers have a reserve()?
  • Qhull.feasiblePoint interface
  • How to avoid copy constructor while logging, maybeThrowQhullMessage()
  • How to configure Qhull output. Trace and results should go to stdout/stderr
  • Qhull and RboxPoints messaging. e.g., ~Qhull, hasQhullMessage(). Rename them as QhullErrorMessage?
  • How to add additional output to an error message, e.g., qh_setprint
  • Is idx the best name for an index? It's rather cryptic, but BSD strings.h defines index().
  • Qhull::feasiblePoint Qhull::useOutputStream as field or getter?
  • Define virtual functions for user customization of Qhull (e.g., qh_fprintf, qh_memfree,etc.)
  • Figure out RoadError::global_log. clearQhullMessage currently clearGlobalLog
  • Should the false QhullFacet be NULL or empty? e.g., QhullFacet::tricoplanarOwner() and QhullFacetSet::end()
  • Should output format for floats be predefined (qh_REAL_1, 2.2g, 10.7g) or as currently set for stream
  • Should cout << !point.defined() be blank or 'undefined'
  • Interface for UsingLibQhull::globalAngleEpsilon(), globalDistanceEpsilon, etc.
  • Interface for UsingLibQhull::globalDimension
  • Set up globals for thread-private storage (redefine macros qh, qhstat, etc)
  • Is Q_GLOBAL_STATIC non-threaded/threaded, needed for Qhull?
  • Infinite point as !defined()
  • qlist and qlinkedlist define pointer, reference, size_type, difference_type, const_pointer, const_reference for the class but not for iterator and const_iterator vector.h -- 
    reference operator[](difference_type _Off) const
  • When forwarding an implementation is base() an approriate name (e.g., Coordinates::iterator::base() as std::vector::iterator).
  • When forwarding an implementation, does not work "returning address of temporary"
  • Also --, +=, and -= 
    iterator       &operator++() { return iterator(i++); }
  • if vector inheritance is bad, is QhullVertexSet OK?
  • Should QhullPointSet define pointer and reference data types?
  • Allow UsingQhullLib to work with static allocation of qh_qh

»CoordinateIterator

A CoordinateIterator or ConstCoordinateIterator [RboxPoints.cpp] is a std::vector<realT>::iterator for Rbox and Qhull coordinates. It is the result type of RboxPoints.coordinates().

Qhull does not use CoordinateIterator for its data structures. A point in Qhull is an array of reals instead of a std::vector. See QhullPoint.

»Qhull

Qhull is the top-level class for running Qhull. It initializes Qhull, runs the computation, and records errors. It provides access to the global data structure QhullQh, Qhull's facets, and vertices.

»QhullError

QhullError is derived from std::exception. It reports errors from Qhull and captures the output to stderr.

If error handling is not set up, Qhull exits with a code from 1 to 5 [qh_ERR* in libqhull.h via qh_exit() in usermem.c]. The C++ interface does not report the captured output in QhullError. Call Qhull::setErrorStream to send output to cerr instead.

»QhullFacet

A QhullFacet is a facet of the convex hull, a region of the Delaunay triangulation, a vertex of a Voronoi diagram, or an intersection of the halfspace intersection about a point. A QhullFacet has a set of QhullVertex, a set of QhullRidge, and a set of neighboring QhullFacets.

»QhullFacetList

A QhullFacetList is a linked list of QhullFacet. The result of Qhull.runQhull is a QhullFacetList stored in QhullQh.

»QhullFacetSet

A QhullFacetSet is a QhullSet of QhullFacet. QhullFacetSet may be ordered or unordered. The neighboring facets of a QhullFacet is a QhullFacetSet. The neighbors of a QhullFacet is a QhullFacetSet. The neighbors are ordered for simplicial facets, matching the opposite vertex of the facet.

»QhullIterator

QhullIterator contains macros for defining Java-style iterator templates from a STL-style iterator template.

»QhullLinkedList

A QhullLinkedLIst is a template for linked lists with next and previous pointers. QhullFacetList and QhullVertexList are QhullLinkedLists.

»QhullPoint

A QhullPoint is an array of point coordinates, typically doubles. The length of the array is QhullQh.hull_dim. The identifier of a QhullPoint is its 0-based index from QhullQh.first_point followed by QhullQh.other_points.

»QhullPointSet

A QhullPointSet is a QhullSet of QhullPoint. The QhullPointSet of a QhullFacet is its coplanar points.

»QhullQh

QhullQh is the root of Qhull's data structure. It contains initialized constants, sets, buffers, and variables. It contains an array and a set of QhullPoint, a list of QhullFacet, and a list of QhullVertex. The points are the input to Qhull. The facets and vertices are the result of running Qhull.

Qhull's functions access QhullQh through the global variable, qh_qh. The global data structures, qh_stat and qh_mem, record statistics and manage memory respectively.

»QhullRidge

A QhullRidge represents the edge between two QhullFacet's. It is always simplicial with qh.hull_dim-1 QhullVertex)'s.

»QhullRidgeSet

A QhullRidgeSet is a QhullSet of QhullRidge. Each QhullFacet contains a QhullRidgeSet.

»QhullSet

A QhullSet is a set of pointers to objects. QhullSets may be ordered or unordered. They are the core data structure for Qhull.

»QhullVertex

A QhullVertex is a vertex of the convex hull. A simplicial QhullFacet has qh.hull_dim-1 vertices. A QhullVertex contains a QhullPoint. It may list its neighboring QhullFacet's.

»QhullVertexList

A QhullVertexList is a QhullLinkedList of QhullVertex. The global data structure, QhullQh contains a QhullVertexList of all the vertices.

»QhullVertexSet

A QhullVertexSet is a QhullSet of QhullVertex. The QhullVertexSet of a QhullFacet is the vertices of the facet. It is ordered for simplicial facets and unordered for non-simplicial facets.

»RboxPoints

RboxPoints is a std::vector of point coordinates (QhullPoint). It's iterator is CoordinateIterator.

RboxPoints.appendRandomPoints() appends points from a variety of distributions such as uniformly distributed within a cube and random points on a sphere. It can also append a cube's vertices or specific points.

»UsingLibQhull

UsingLibQhull checks that the current thread owns Qhull's global data structure, QhullQh. It is required while calling the Qhull library. Otherwise two threads may be updating and reading the same data structure.

»Calling Qhull from C programs

Warning: Qhull was not designed for calling from C programs. You may find the C++ interface easier to use. You will need to understand the data structures and read the code. Most users will find it easier to call Qhull as an external command.

For examples of calling Qhull, see GNU Octave's computational geometry code, and Qhull's user_eg.c, user_eg2.c, and user.c. To see how Qhull calls its library, read unix.c, qconvex.c, qdelaun.c, qhalf.c, and qvoronoi.c.

The BGL Boost Graph Library [aka GGCL] provides C++ classes for graph data structures and algorithms [Dr. Dobb's 9/00 p. 29-38; OOPSLA '99 p. 399-414]. It is modelled after the Standard Template Library. It would provide a good interface to Qhull. If you are interested in adapting BGL to Qhull, please contact bradb@shore.net.

See Qhull functions, macros, and data structures for internal documentation of Qhull. The documentation provides an overview and index. To use the library you will need to read and understand the code. For most users, it is better to write data to a file, call the qhull program, and read the results from the output file.

When you read the code, be aware of the macros "qh" and "qhstat", e.g., "qh hull_dim". They are defined in libqhull.h. They allow the global data structures to be pre-allocated (faster access) or dynamically allocated (allows multiple copies).

Qhull's Makefile produces a library, libqhull.a, for inclusion in your programs. First review libqhull.h. This defines the data structures used by Qhull and provides prototypes for the top-level functions. Most users will only need libqhull.h in their programs. For example, the Qhull program is defined with libqhull.h and unix.c. To access all functions, use qhull_a.h. Include the file with "#include <qhull/qhull_a.h>". This avoids potential name conflicts.

If you use the Qhull library, you are on your own as far as bugs go. Start with small examples for which you know the output. If you get a bug, try to duplicate it with the Qhull program. The 'Tc' option will catch many problems as they occur. When an error occurs, use 'T4 TPn' to trace from the last point added to the hull. Compare your trace with the trace output from the Qhull program.

Errors in the Qhull library are more likely than errors in the Qhull program. These are usually due to feature interactions that do not occur in the Qhull program. Please report all errors that you find in the Qhull library. Please include suggestions for improvement.

»sets and quick memory allocation

You can use mem.c and qset.c individually. Mem.c implements quick-fit memory allocation. It is faster than malloc/free in applications that allocate and deallocate lots of memory.

Qset.c implements sets and related collections. It's the inner loop of Qhull, so speed is more important than abstraction. Set iteration is particularly fast. qset.c just includes the functions needed for Qhull.

»Delaunay triangulations and point indices

Here some unchecked code to print the point indices of each Delaunay triangle. Use option 'QJ' if you want to avoid non-simplicial facets. Note that upper Delaunay regions are skipped. These facets correspond to the furthest-site Delaunay triangulation. 

  facetT *facet;
  vertexT *vertex, **vertexp;

  FORALLfacets {
    if (!facet->upperdelaunay) {
      printf ("%d", qh_setsize (facet->vertices);
      FOREACHvertex_(facet->vertices)
        printf (" %d", qh_pointid (vertex->point));
      printf ("\n");
    }
  }

»locate a facet with qh_findbestfacet()

The routine qh_findbestfacet in poly2.c is particularly useful. It uses a directed search to locate the facet that is furthest below a point. For Delaunay triangulations, this facet is the Delaunay triangle that contains the lifted point. For convex hulls, the distance of a point to the convex hull is either the distance to this facet or the distance to a subface of the facet.

Warning: If triangulated output ('Qt') and the best facet is triangulated, qh_findbestfacet() returns one of the corresponding 'tricoplanar' facets. The actual best facet may be a different tricoplanar facet.

See qh_nearvertex() in poly2.c for sample code to visit each tricoplanar facet. To identify the correct tricoplanar facet, see Devillers, et. al., ['01] and Mucke, et al ['96]. If you implement this test in general dimension, please notify qhull@qhull.org.

qh_findbestfacet performs an exhaustive search if its directed search returns a facet that is above the point. This occurs when the point is inside the hull or if the curvature of the convex hull is less than the curvature of a sphere centered at the point (e.g., a point near a lens-shaped convex hull). When the later occurs, the distance function is bimodal and a directed search may return a facet on the far side of the convex hull.

Algorithms that retain the previously constructed hulls usually avoid an exhaustive search for the best facet. You may use a hierarchical decomposition of the convex hull [Dobkin and Kirkpatrick '90].

To use qh_findbestfacet with Delaunay triangulations, lift the point to a paraboloid by summing the squares of its coordinates (see qh_setdelaunay in geom2.c). Do not scale the input with options 'Qbk', 'QBk', 'QbB' or 'Qbb'. See Mucke, et al ['96] for a good point location algorithm.

The intersection of a ray with the convex hull may be found by locating the facet closest to a distant point on the ray. Intersecting the ray with the facet's hyperplane gives a new point to test.

»on-line construction with qh_addpoint()

The Qhull library may be used for the on-line construction of convex hulls, Delaunay triangulations, and halfspace intersections about a point. It may be slower than implementations that retain intermediate convex hulls (e.g., Clarkson's hull program). These implementations always use a directed search. For the on-line construction of convex hulls and halfspace intersections, Qhull may use an exhaustive search (qh_findbestfacet).

You may use qh_findbestfacet and qh_addpoint (libqhull.c) to add a point to a convex hull. Do not modify the point's coordinates since qh_addpoint does not make a copy of the coordinates. For Delaunay triangulations, you need to lift the point to a paraboloid by summing the squares of the coordinates (see qh_setdelaunay in geom2.c). Do not scale the input with options 'Qbk', 'QBk', 'QbB' or 'Qbb'. Do not deallocate the point's coordinates. You need to provide a facet that is below the point (qh_findbestfacet).

You can not delete points. Another limitation is that Qhull uses the initial set of points to determine the maximum roundoff error (via the upper and lower bounds for each coordinate).

For many applications, it is better to rebuild the hull from scratch for each new point. This is especially true if the point set is small or if many points are added at a time.

Calling qh_addpoint from your program may be slower than recomputing the convex hull with qh_qhull. This is especially true if the added points are not appended to the qh first_point array. In this case, Qhull must search a set to determine a point's ID. [R. Weber]

See user_eg.c for examples of the on-line construction of convex hulls, Delaunay triangulations, and halfspace intersections. The outline is: 

initialize qhull with an initial set of points
qh_qhull();

for each additional point p
   append p to the end of the point array or allocate p separately
   lift p to the paraboloid by calling qh_setdelaunay
   facet= qh_findbestfacet (p, !qh_ALL, &bestdist, &isoutside);
   if (isoutside)
      if (!qh_addpoint (point, facet, False))
         break;  /* user requested an early exit with 'TVn' or 'TCn' */

call qh_check_maxout() to compute outer planes
terminate qhull

»Constrained Delaunay triangulation

With a fair amount of work, Qhull is suitable for constrained Delaunay triangulation. See Shewchuk, ACM Symposium on Computational Geometry, Minneapolis 1998.

Here's a quick way to add a constraint to a Delaunay triangulation: subdivide the constraint into pieces shorter than the minimum feature separation. You will need an independent check of the constraint in the output since the minimum feature separation may be incorrect. [H. Geron]

»Tricoplanar facets and option 'Qt'

Option 'Qt' triangulates non-simplicial facets (e.g., a square facet in 3-d or a cubical facet in 4-d). All facets share the same apex (i.e., the first vertex in facet->vertices). For each triangulated facet, Qhull sets facet->tricoplanar true and copies facet->center, facet->normal, facet->offset, and facet->maxoutside. One of the facets owns facet->normal; its facet->keepcentrum is true. If facet->isarea is false, facet->triowner points to the owning facet.

Qhull sets facet->degenerate if the facet's vertices belong to the same ridge of the non-simplicial facet.

To visit each tricoplanar facet of a non-simplicial facet, either visit all neighbors of the apex or recursively visit all neighbors of a tricoplanar facet. The tricoplanar facets will have the same facet->center.

See qh_detvridge for an example of ignoring tricoplanar facets.

»Voronoi vertices of a region

The following code iterates over all Voronoi vertices for each Voronoi region. Qhull computes Voronoi vertices from the convex hull that corresponds to a Delaunay triangulation. An input site corresponds to a vertex of the convex hull and a Voronoi vertex corresponds to an adjacent facet. A facet is "upperdelaunay" if it corresponds to a Voronoi vertex "at-infinity". Qhull uses qh_printvoronoi in io.c for 'qvoronoi o' 

/* please review this code for correctness */
qh_setvoronoi_all();
FORALLvertices {
   site_id = qh_pointid (vertex->point);
   if (qh hull_dim == 3)
      qh_order_vertexneighbors(vertex);
   infinity_seen = 0;
   FOREACHneighbor_(vertex) {
      if (neighbor->upperdelaunay) {
        if (!infinity_seen) {
          infinity_seen = 1;
          ... process a Voronoi vertex "at infinity" ...
        }
      }else {
        voronoi_vertex = neighbor->center;
        ... your code goes here ...
      }
   }
}

»Voronoi vertices of a ridge

Qhull uses qh_printvdiagram() in io.c to print the ridges of a Voronoi diagram for option 'Fv'. The helper function qh_eachvoronoi() does the real work. It calls the callback 'printvridge' for each ridge of the Voronoi diagram.

You may call qh_printvdiagram2(), qh_eachvoronoi(), or qh_eachvoronoi_all() with your own function. If you do not need the total number of ridges, you can skip the first call to qh_printvdiagram2(). See qh_printvridge() and qh_printvnorm() in io.c for examples.

»vertex neighbors of a vertex

To visit all of the vertices that share an edge with a vertex:

  • Generate neighbors for each vertex with qh_vertexneighbors in poly2.c.
  • For simplicial facets, visit the vertices of each neighbor
  • For non-simplicial facets,
    • Generate ridges for neighbors with qh_makeridges in merge.c.
    • Generate ridges for a vertex with qh_vertexridges in merge.c.
    • Visit the vertices of these ridges.

For non-simplicial facets, the ridges form a simplicial decomposition of the (d-2)-faces between each pair of facets -- if you need 1-faces, you probably need to generate the full face graph of the convex hull.

»Enhancements to Qhull

There are many ways in which Qhull can be improved. 

[Jan 2010] Suggestions
 - Generate vcproj from qtpro files
   cd qtpro && qmake -spec win32-msvc2005 -tp vc -recursive
   sed -i 's/C\:\/bash\/local\/qhull\/qtpro\///' qhull-all.sln
   Change qhullcpp to libqhull.dll
   Allow both builds on same host (keep /tmp separate)
 - Make distribution -- remove tmp, news, .git, leftovers from project, change CRLF
     search for 2010.1, Dates
     qhulltest --all added to output
     Add md5sum
     Add test of user_eg3, etc.
 - C++ class for access to statistics, accumulate vs. add
 - Add dialog box to RoadError-- a virtual function?
 - Option 'Gt' does not make visible all facets of the mesh example, rbox 32 M1,0,1 | qhull d Gt
 - Option to select bounded Voronoi regions [A. Uzunovic]
 - Merge small volume boundary cells into unbounded regions [Dominik Szczerba]
 - Postmerge with merge options
 - Add const to C code
 - Add modify operators and MutablePointCoordinateIterator to PointCoordinates
 - Add Qtest::toString() functions for QhullPoint and others.  QByteArray and qstrdup()
 - Fix option Qt for conformant triangulations of merged facets
 - Investigate flipped facet -- rbox 100 s D3 t1263080158 | qhull R1e-3 Tcv Qc
 - Add doc comments to c++ code
 - Measure performance of Qhull, seconds per point by dimension
 - Report potential wraparound of 64-bit ints -- e.g., a large set or points

Documentation
- Qhull::addPoint().  Problems with qh_findbestfacet and otherpoints see
   qh-code.htm#inc on-line construction with qh_addpoint()
- How to handle 64-bit possible loss of data.  WARN64, ptr_intT, size_t/int
- Show custom of qh_fprintf
- grep 'qh_mem ' x | sort | awk '{ print $2; }' | uniq -c | grep -vE ' (2|4|6|8|10|12|14|16|20|64|162)[^0-9]'
- qtpro/qhulltest contains .pro and Makefile.  Remove Makefiles by setting shadow directory to ../../tmp/projectname
- Rules for use of qh_qh and multi processes
    UsingQhull
    errorIfAnotherUser
    ~QhullPoints() needs ownership of qh_qh
    Does !qh_pointer work?
    When is qh_qh required?  Minimize the time.
   qhmem, qhstat.ferr
   qhull_inuse==1 when qhull globals active [not useful?]
   rbox_inuse==1 when rbox globals active
   - Multithreaded -- call largest dimension for infinityPoint() and origin()
 - Better documentation for qhmem totshort, freesize, etc.
 - how to change .h, .c, and .cpp to text/html.  OK in Opera
 - QhullVertex.dimension() is not quite correct, epensive
 - Check globalAngleEpsilon
 - Deprecate save_qhull()

[Dec 2003] Here is a partial list:
 - fix finddelaunay() in user_eg.c for tricoplanar facets
 - write a BGL, C++ interface to Qhull
     http://www.boost.org/libs/graph/doc/table_of_contents.html
 - change qh_save_qhull to swap the qhT structure instead of using pointers
 - change error handling and tracing to be independent of 'qh ferr'
 - determine the maximum width for a given set of parameters
 - prove that directed search locates all coplanar facets
 - in high-d merging, can a loop of facets become disconnected?
 - find a way to improve inner hulls in 5-d and higher
 - determine the best policy for facet visibility ('Vn')
 - determine the limitations of 'Qg'

Precision improvements:
 - For 'Qt', resolve cross-linked, butterfly ridges.
     May allow retriangulation in qh_addpoint().
 - for Delaunay triangulations ('d' or 'v') under joggled input ('QJ'),
     remove vertical facets whose lowest vertex may be coplanar with convex hull
 - review use of 'Qbb' with 'd QJ'.  Is MAXabs_coord better than MAXwidth?
 - check Sugihara and Iri's better in-sphere test [Canadian
     Conf. on Comp. Geo., 1989; Univ. of Tokyo RMI 89-05]
 - replace centrum with center of mass and facet area
 - handle numeric overflow in qh_normalize and elsewhere
 - merge flipped facets into non-flipped neighbors.
     currently they merge into best neighbor (appears ok)
 - determine min norm for Cramer's rule (qh_sethyperplane_det).  It looks high.
 - improve facet width for very narrow distributions

New features:
 - implement Matlab's tsearch() using Qhull
 - compute volume of Voronoi regions.  You need to determine the dual face
   graph in all dimensions [see Clarkson's hull program]
 - compute alpha shapes [see Clarkson's hull program]
 - implement deletion of Delaunay vertices
      see Devillers, ACM Symposium on Computational Geometry, Minneapolis 1999.
 - compute largest empty circle [see O'Rourke, chapter 5.5.3] [Hase]
 - list redundant (i.e., coincident) vertices [Spitz]
 - implement Mucke, et al, ['96] for point location in Delaunay triangulations
 - implement convex hull of moving points
 - implement constrained Delaunay diagrams
      see Shewchuk, ACM Symposium on Computational Geometry, Minneapolis 1998.
 - estimate outer volume of hull
 - automatically determine lower dimensional hulls
 - allow "color" data for input points
      need to insert a coordinate for Delaunay triangulations

Input/output improvements:
 - Support the VTK Visualization Toolkit, http://www.kitware.com/vtk.html
 - generate output data array for Qhull library [Gautier]
 - need improved DOS window with screen fonts, scrollbar, cut/paste
 - generate Geomview output for Voronoi ridges and unbounded rays
 - generate Geomview output for halfspace intersection
 - generate Geomview display of furthest-site Voronoi diagram
 - use 'GDn' to view 5-d facets in 4-d
 - convert Geomview output for other 3-d viewers
 - add interactive output option to avoid recomputing a hull
 - orient vertex neighbors for 'Fv' in 3-d and 2-d
 - track total number of ridges for summary and logging

Performance improvements:
 - optimize Qhull for 2-d Delaunay triangulations
 -   use O'Rourke's '94 vertex->duplicate_edge
 -   add bucketing
 -   better to specialize all of the code (ca. 2-3x faster w/o merging)
 - use updated LU decomposition to speed up hyperplane construction
 -        [Gill et al. 1974, Math. Comp. 28:505-35]
 - construct hyperplanes from the corresponding horizon/visible facets
 - for merging in high d, do not use vertex->neighbors

Please let us know about your applications and improvements.

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[halfspace] Examples of Qhull

This section of the Qhull manual will introduce you to Qhull and its options. Each example is a file for viewing with Geomview. You will need to use a Unix computer with a copy of Geomview.

If you are not running Unix, you can view pictures for some of the examples. To understand Qhull without Geomview, try the examples in Programs and Programs/input. You can also try small examples that you compute by hand. Use rbox to generate examples.

To generate the Geomview examples, execute the shell script eg/q_eg. It uses rbox. The shell script eg/q_egtest generates test examples, and eg/q_test exercises the code. If you find yourself viewing the inside of a 3-d example, use Geomview's normalization option on the 'obscure' menu.

Copyright © 1995-2012 C.B. Barber

»Qhull examples: Table of Contents

»2-d and 3-d examples

»rbox c D3 | qconvex G >eg.01.cube

The first example is a cube in 3-d. The color of each facet indicates its normal. For example, normal [0,0,1] along the Z axis is (r=0.5, g=0.5, b=1.0). With the 'Dn' option in rbox, you can generate hypercubes in any dimension. Above 7-d the number of intermediate facets grows rapidly. Use 'TFn' to track qconvex's progress. Note that each facet is a square that qconvex merged from coplanar triangles.

»rbox c d G3.0 | qconvex G >eg.02.diamond.cube

The second example is a cube plus a diamond ('d') scaled by rbox's 'G' option. In higher dimensions, diamonds are much simpler than hypercubes.

»rbox s 100 D3 | qconvex G >eg.03.sphere

The rbox s option generates random points and projects them to the d-sphere. All points should be on the convex hull. Notice that random points look more clustered than you might expect. You can get a smoother distribution by merging facets and printing the vertices, e.g., rbox 1000 s | qconvex A-0.95 p | qconvex G >eg.99.

»rbox s 100 D2 | qconvex G >eg.04.circle

In 2-d, there are many ways to generate a convex hull. One of the earliest algorithms, and one of the fastest, is the 2-d Quickhull algorithm [c.f., Preparata & Shamos '85]. It was the model for Qhull.

»rbox 10 l | qconvex G >eg.05.spiral

One rotation of a spiral.

»rbox 1000 D2 | qconvex C-0.03 Qc Gapcv >eg.06.merge.square

This demonstrates how Qhull handles precision errors. Option 'C-0.03' requires a clearly convex angle between adjacent facets. Otherwise, Qhull merges the facets.

This is the convex hull of random points in a square. The facets have thickness because they must be outside all points and must include their vertices. The colored lines represent the original points and the spheres represent the vertices. Floating in the middle of each facet is the centrum. Each centrum is at least 0.03 below the planes of its neighbors. This guarantees that the facets are convex.

»rbox 1000 D3 | qconvex G >eg.07.box

Here's the same distribution but in 3-d with Qhull handling machine roundoff errors. Note the large number of facets.

»rbox c G0.4 s 500 | qconvex G >eg.08a.cube.sphere

The sphere is just barely poking out of the cube. Try the same distribution with randomization turned on ('Qr'). This turns Qhull into a randomized incremental algorithm. To compare Qhull and randomization, look at the number of hyperplanes created and the number of points partitioned. Don't compare CPU times since Qhull's implementation of randomization is inefficient. The number of hyperplanes and partitionings indicate the dominant costs for Qhull. With randomization, you'll notice that the number of facets created is larger than before. This is especially true as you increase the number of points. It is because the randomized algorithm builds most of the sphere before it adds the cube's vertices.

»rbox d G0.6 s 500 | qconvex G >eg.08b.diamond.sphere

This is a combination of the diamond distribution and the sphere.

»rbox 100 L3 G0.5 s | qconvex G >eg.09.lens

Each half of the lens distribution lies on a sphere of radius three. A directed search for the furthest facet below a point (e.g., qh_findbest in geom.c) may fail if started from an arbitrary facet. For example, if the first facet is on the opposite side of the lens, a directed search will report that the point is inside the convex hull even though it is outside. This problem occurs whenever the curvature of the convex hull is less than a sphere centered at the test point.

To prevent this problem, Qhull does not use directed search all the time. When Qhull processes a point on the edge of the lens, it partitions the remaining points with an exhaustive search instead of a directed search (see qh_findbestnew in geom2.c).

»How Qhull adds a point

»rbox 100 s P0.5,0.5,0.5 | qconvex Ga QG0 >eg.10a.sphere.visible

The next 4 examples show how Qhull adds a point. The point [0.5,0.5,0.5] is at one corner of the bounding box. Qhull adds a point using the beneath-beyond algorithm. First Qhull finds all of the facets that are visible from the point. Qhull will replace these facets with new facets.

»rbox 100 s P0.5,0.5,0.5|qconvex Ga QG-0 >eg.10b.sphere.beyond

These are the facets that are not visible from the point. Qhull will keep these facets.

»rbox 100 s P0.5,0.5,0.5 | qconvex PG Ga QG0 >eg.10c.sphere.horizon

These facets are the horizon facets; they border the visible facets. The inside edges are the horizon ridges. Each horizon ridge will form the base for a new facet.

»rbox 100 s P0.5,0.5,0.5 | qconvex Ga QV0 PgG >eg.10d.sphere.cone

This is the cone of points from the new point to the horizon facets. Try combining this image with eg.10c.sphere.horizon and eg.10a.sphere.visible.

»rbox 100 s P0.5,0.5,0.5 | qconvex Ga >eg.10e.sphere.new

This is the convex hull after [0.5,0.5,0.5] has been added. Note that in actual practice, the above sequence would never happen. Unlike the randomized algorithms, Qhull always processes a point that is furthest in an outside set. A point like [0.5,0.5,0.5] would be one of the first points processed.

»rbox 100 s P0.5,0.5,0.5 | qhull Ga QV0g Q0 >eg.14.sphere.corner

The 'QVn', 'QGn ' and 'Pdk' options define good facets for Qhull. In this case 'QV0' defines the 0'th point [0.5,0.5,0.5] as the good vertex, and 'Qg' tells Qhull to only build facets that might be part of a good facet. This technique reduces output size in low dimensions. It does not work with facet merging.

»Triangulated output or joggled input

»rbox 500 W0 | qconvex QR0 Qc Gvp >eg.15a.surface

This is the convex hull of 500 points on the surface of a cube. Note the large, non-simplicial facet for each face. Qhull merges non-convex facets.

If the facets were not merged, Qhull would report precision problems. For example, turn off facet merging with option 'Q0'. Qhull may report concave facets, flipped facets, or other precision errors:

rbox 500 W0 | qhull QR0 Q0

»rbox 500 W0 | qconvex QR0 Qt Qc Gvp >eg.15b.triangle

Like the previous examples, this is the convex hull of 500 points on the surface of a cube. Option 'Qt' triangulates the non-simplicial facets. Triangulated output is particularly helpful for Delaunay triangulations.

»rbox 500 W0 | qconvex QR0 QJ5e-2 Qc Gvp >eg.15c.joggle

This is the convex hull of 500 joggled points on the surface of a cube. The option 'QJ5e-2' sets a very large joggle to make the effect visible. Notice that all of the facets are triangles. If you rotate the cube, you'll see red-yellow lines for coplanar points.

With option 'QJ', Qhull joggles the input to avoid precision problems. It adds a small random number to each input coordinate. If a precision error occurs, it increases the joggle and tries again. It repeats this process until no precision problems occur.

Joggled input is a simple solution to precision problems in computational geometry. Qhull can also merge facets to handle precision problems. See Merged facets or joggled input.

»Delaunay and Voronoi diagrams

»qdelaunay Qt <eg.data.17 GnraD2 >eg.17a.delaunay.2

The input file, eg.data.17, consists of a square, 15 random points within the outside half of the square, and 6 co-circular points centered on the square.

The Delaunay triangulation is the triangulation with empty circumcircles. The input for this example is unusual because it includes six co-circular points. Every triangular subset of these points has the same circumcircle. Option 'Qt' triangulates the co-circular facet.

»qdelaunay <eg.data.17 GnraD2 >eg.17b.delaunay.2i

This is the same example without triangulated output ('Qt'). qdelaunay merges the non-unique Delaunay triangles into a hexagon.

»qdelaunay <eg.data.17 Ga >eg.17c.delaunay.2-3

This is how Qhull generated both diagrams. Use Geomview's 'obscure' menu to turn off normalization, and Geomview's 'cameras' menu to turn off perspective. Then load this object with one of the previous diagrams.

The points are lifted to a paraboloid by summing the squares of each coordinate. These are the light blue points. Then the convex hull is taken. That's what you see here. If you look up the Z-axis, you'll see that points and edges coincide.

»qvoronoi QJ <eg.data.17 Gna >eg.17d.voronoi.2

The Voronoi diagram is the dual of the Delaunay triangulation. Here you see the original sites and the Voronoi vertices. Notice the each vertex is equidistant from three sites. The edges indicate the Voronoi region for a site. Qhull does not draw the unbounded edges. Instead, it draws extra edges to close the unbounded Voronoi regions. You may find it helpful to enclose the input points in a square. You can compute the unbounded rays from option 'Fo'.

Instead of triangulated output ('Qt'), this example uses joggled input ('QJ'). Normally, you should use neither 'QJ' nor 'Qt' for Voronoi diagrams.

»qvoronoi <eg.data.17 Gna >eg.17e.voronoi.2i

This looks the same as the previous diagrams, but take a look at the data. Run 'qvoronoi p <eg/eg.data.17'. This prints the Voronoi vertices.

With 'QJ', there are four nearly identical Voronoi vertices within 10^-11 of the origin. Option 'QJ' joggled the input. After the joggle, the cocircular input sites are no longer cocircular. The corresponding Voronoi vertices are similar but not identical.

This example does not use options 'Qt' or 'QJ'. The cocircular input sites define one Voronoi vertex near the origin.

Option 'Qt' would triangulate the corresponding Delaunay region into four triangles. Each triangle is assigned the same Voronoi vertex.

» rbox c G0.1 d | qdelaunay Gt Qz <eg.17f.delaunay.3

This is the 3-d Delaunay triangulation of a small cube inside a prism. Since the outside ridges are transparent, it shows the interior of the outermost facets. If you slice open the triangulation with Geomview's ginsu, you will see that the innermost facet is a cube. Note the use of 'Qz' to add a point "at infinity". This avoids a degenerate input due to cospherical points.

»rbox 10 D2 d | qdelaunay Qu G >eg.18a.furthest.2-3

The furthest-site Voronoi diagram contains Voronoi regions for points that are furthest from an input site. It is the dual of the furthest-site Delaunay triangulation. You can determine the furthest-site Delaunay triangulation from the convex hull of the lifted points (eg.17c.delaunay.2-3). The upper convex hull (blue) generates the furthest-site Delaunay triangulation.

»rbox 10 D2 d | qdelaunay Qu Pd2 G >eg.18b.furthest-up.2-3

This is the upper convex hull of the preceding example. The furthest-site Delaunay triangulation is the projection of the upper convex hull back to the input points. The furthest-site Voronoi vertices are the circumcenters of the furthest-site Delaunay triangles.

»rbox 10 D2 d | qvoronoi Qu Gv >eg.18c.furthest.2

This shows an incomplete furthest-site Voronoi diagram. It only shows regions with more than two vertices. The regions are artificially truncated. The actual regions are unbounded. You can print the regions' vertices with 'qvoronoi Qu o'.

Use Geomview's 'obscure' menu to turn off normalization, and Geomview's 'cameras' menu to turn off perspective. Then load this with the upper convex hull.

»rbox 10 D3 | qvoronoi QV5 p | qconvex G >eg.19.voronoi.region.3

This shows the Voronoi region for input site 5 of a 3-d Voronoi diagram.

»Facet merging for imprecision

»rbox r s 20 Z1 G0.2 | qconvex G >eg.20.cone

There are two things unusual about this cone. One is the large flat disk at one end and the other is the rectangles about the middle. That's how the points were generated, and if those points were exact, this is the correct hull. But rbox used floating point arithmetic to generate the data. So the precise convex hull should have been triangles instead of rectangles. By requiring convexity, Qhull has recovered the original design.

»rbox 200 s | qhull Q0 R0.01 Gav Po >eg.21a.roundoff.errors

This is the convex hull of 200 cospherical points with precision errors ignored ('Q0'). To demonstrate the effect of roundoff error, we've added a random perturbation ('R0.01') to every distance and hyperplane calculation. Qhull, like all other convex hull algorithms with floating point arithmetic, makes inconsistent decisions and generates wildly wrong results. In this case, one or more facets are flipped over. These facets have the wrong color. You can also turn on 'normals' in Geomview's appearances menu and turn off 'facing normals'. There should be some white lines pointing in the wrong direction. These correspond to flipped facets.

Different machines may not produce this picture. If your machine generated a long error message, decrease the number of points or the random perturbation ('R0.01'). If it did not report flipped facets, increase the number of points or perturbation.

»rbox 200 s | qconvex Qc R0.01 Gpav >eg.21b.roundoff.fixed

Qhull handles the random perturbations and returns an imprecise sphere. In this case, the output is a weak approximation to the points. This is because a random perturbation of 'R0.01 ' is equivalent to losing all but 1.8 digits of precision. The outer planes float above the points because Qhull needs to allow for the maximum roundoff error.

If you start with a smaller random perturbation, you can use joggle ('QJn') to avoid precision problems. You need to set n significantly larger than the random perturbation. For example, try 'rbox 200 s | qconvex Qc R1e-4 QJ1e-1'.

»rbox 1000 s| qconvex C0.01 Qc Gcrp >eg.22a.merge.sphere.01

»rbox 1000 s| qconvex C-0.01 Qc Gcrp >eg.22b.merge.sphere.-01

»rbox 1000 s| qconvex C0.05 Qc Gcrpv >eg.22c.merge.sphere.05

»rbox 1000 s| qconvex C-0.05 Qc Gcrpv >eg.22d.merge.sphere.-05

The next four examples compare post-merging and pre-merging ('Cn' vs. 'C-n'). Qhull uses '-' as a flag to indicate pre-merging.

Post-merging happens after the convex hull is built. During post-merging, Qhull repeatedly merges an independent set of non-convex facets. For a given set of parameters, the result is about as good as one can hope for.

Pre-merging does the same thing as post-merging, except that it happens after adding each point to the convex hull. With pre-merging, Qhull guarantees a convex hull, but the facets are wider than those from post-merging. If a pre-merge option is not specified, Qhull handles machine round-off errors.

You may see coplanar points appearing slightly outside the facets of the last example. This is becomes Geomview moves line segments forward toward the viewer. You can avoid the effect by setting 'lines closer' to '0' in Geomview's camera menu.

»rbox 1000 | qconvex s Gcprvah C0.1 Qc >eg.23.merge.cube

Here's the 3-d imprecise cube with all of the Geomview options. There's spheres for the vertices, radii for the coplanar points, dots for the interior points, hyperplane intersections, centrums, and inner and outer planes. The radii are shorter than the spheres because this uses post-merging ('C0.1') instead of pre-merging.

»4-d objects

With Qhull and Geomview you can develop an intuitive sense of 4-d surfaces. When you get into trouble, think of viewing the surface of a 3-d sphere in a 2-d plane.

»rbox 5000 D4 | qconvex s GD0v Pd0:0.5 C-0.02 C0.1 >eg.24.merge.cube.4d-in-3d

Here's one facet of the imprecise cube in 4-d. It's projected into 3-d (the 'GDn' option drops dimension n). Each ridge consists of two triangles between this facet and the neighboring facet. In this case, Geomview displays the topological ridges, i.e., as triangles between three vertices. That is why the cube looks lopsided.

»rbox 5000 D4 | qconvex s C-0.02 C0.1 Gh >eg.30.4d.merge.cube

Here is the equivalent in 4-d of the imprecise square and imprecise cube. It's the imprecise convex hull of 5000 random points in a hypercube. It's a full 4-d object so Geomview's ginsu does not work. If you view it in Geomview, you'll be inside the hypercube. To view 4-d objects directly, either load the 4dview module or the ndview module. For 4dview, you must have started Geomview in the same directory as the object. For ndview, initialize a set of windows with the prefab menu, and load the object through Geomview. The 4dview module includes an option for slicing along any hyperplane. If you do this in the x, y, or z plane, you'll see the inside of a hypercube.

The 'Gh' option prints the geometric intersections between adjacent facets. Note the strong convexity constraint for post-merging ('C0.1'). It deletes the small facets.

»rbox 20 D3 | qdelaunay G >eg.31.4d.delaunay

The Delaunay triangulation of 3-d sites corresponds to a 4-d convex hull. You can't see 4-d directly but each facet is a 3-d object that you can project to 3-d. This is exactly the same as projecting a 2-d facet of a soccer ball onto a plane.

Here we see all of the facets together. You can use Geomview's ndview to look at the object from several directions. Try turning on edges in the appearance menu. You'll notice that some edges seem to disappear. That's because the object is actually two sets of overlapping facets.

You can slice the object apart using Geomview's 4dview. With 4dview, try slicing along the w axis to get a single set of facets and then slice along the x axis to look inside. Another interesting picture is to slice away the equator in the w dimension.

»rbox 30 s D4 | qconvex s G Pd0d1d2D3

This is the positive octant of the convex hull of 30 4-d points. When looking at 4-d, it's easier to look at just a few facets at once. If you picked a facet that was directly above you, then that facet looks exactly the same in 3-d as it looks in 4-d. If you pick several facets, then you need to imagine that the space of a facet is rotated relative to its neighbors. Try Geomview's ndview on this example.

»Halfspace intersections

»rbox 10 r s Z1 G0.3 | qconvex G >eg.33a.cone

»rbox 10 r s Z1 G0.3 | qconvex FV n | qhalf G >eg.33b.cone.dual

»rbox 10 r s Z1 G0.3 | qconvex FV n | qhalf Fp | qconvex G >eg.33c.cone.halfspace

These examples illustrate halfspace intersection. The first picture is the convex hull of two 20-gons plus an apex. The second picture is the dual of the first. Try loading both at once. Each vertex of the second picture corresponds to a facet or halfspace of the first. The vertices with four edges correspond to a facet with four neighbors. Similarly the facets correspond to vertices. A facet's normal coefficients divided by its negative offset is the vertice's coordinates. The coordinates are the intersection of the original halfspaces.

The third picture shows how Qhull can go back and forth between equivalent representations. It starts with a cone, generates the halfspaces that define each facet of the cone, and then intersects these halfspaces. Except for roundoff error, the third picture is a duplicate of the first.

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[4-d cube] Frequently Asked Questions about Qhull

If your question does not appear here, see:

Qhull is a general dimension code for computing convex hulls, Delaunay triangulations, halfspace intersections about a point, Voronoi diagrams, furthest-site Delaunay triangulations, and furthest-site Voronoi diagrams. These structures have applications in science, engineering, statistics, and mathematics. For a detailed introduction, see O'Rourke ['94], Computational Geometry in C.

There are separate programs for each application of Qhull. These programs disable experimental and inappropriate options. If you prefer, you may use Qhull directly. All programs run the same code.

Version 3.1 added triangulated output ('Qt'). It should be used for Delaunay triangulations instead of using joggled input ('QJ').

Brad Barber, Arlington MA, 2010/01/09

Copyright © 1998-2012 C.B. Barber

»FAQ: Table of Contents

Within each category, the most recently asked questions are first.

  • Startup questions
    • How do I run Qhull from Windows?
    • How do I enter points for Qhull?
    • How do I learn to use Qhull?
  • Convex hull questions
    • How do I report just the area and volume of a convex hull?
    • Why are there extra points in a 4-d or higher convex hull?
    • How do I report duplicate vertices?
  • Delaunay triangulation questions
    • How do I get rid of nearly flat Delaunay triangles?
    • How do I find the Delaunay triangle or Voronoi region that is closest to a point?
    • How do I compute the Delaunay triangulation of a non-convex object?
    • How do I mesh a volume from a set of triangulated surface points?
    • Can Qhull produce a triangular mesh for an object?
    • For 3-d Delaunay triangulations, how do I report the triangles of each tetrahedron?
    • How do I construct a 3-d Delaunay triangulation?
    • How do I get the triangles for a 2-d Delaunay triangulation and the vertices of its Voronoi diagram?
    • Can Qhull triangulate a hundred 16-d points?
  • Voronoi diagram questions
    • See also "Delaunay diagram questions". Qhull computes the Voronoi diagram from the Delaunay triagulation.
    • How do I compute the volume of a Voronoi region?
    • How do I get the radii of the empty spheres for each Voronoi vertex?
    • What is the Voronoi diagram of a square?
    • How do I construct the Voronoi diagram of cospherical points?
    • Can Qhull compute the unbounded rays of the Voronoi diagram?
  • Approximation questions
    • How do I approximate data with a simplex?
  • Halfspace questions
    • How do I compute the intersection of halfspaces with Qhull?
  • Qhull library questions
    • Is Qhull available for Mathematica, Matlab, or Maple?
    • Why are there too few ridges?
    • Can Qhull use coordinates without placing them in a data file?
    • How large are Qhull's data structures?
    • Can Qhull construct convex hulls and Delaunay triangulations one point at a time?
    • How do I visit the ridges of a Delaunay triangulation?
    • How do I visit the Delaunay facets?
    • When is a point outside or inside a facet?
    • How do I find the facet that is closest to a point?
    • How do I find the Delaunay triangle or Voronoi region that is closest to a point?
    • How do I list the vertices?
    • How do I test code that uses the Qhull library?
    • When I compute a plane equation from a facet, I sometimes get an outward-pointing normal and sometimes an inward-pointing normal

»Startup questions

»How do I run Qhull from Windows?

Qhull is a console program. You will first need a command window (i.e., a "command prompt"). You can double click on 'eg\Qhull-go.bat'.

  • Type 'qconvex', 'qdelaunay', 'qhalf', 'qvoronoi, 'qhull', and 'rbox' for a synopsis of each program.
  • Type 'rbox c D2 | qconvex s i' to compute the convex hull of a square.
  • Type 'rbox c D2 | qconvex s i TO results.txt' to write the results to the file 'results.txt'. A summary is still printed on the the console.
  • Type 'rbox c D2' to see the input format for qconvex.
  • Type 'qconvex < data.txt s i TO results.txt' to read input data from 'data.txt'.
  • If you want to enter data by hand, type 'qconvex s i TO results.txt' to read input data from the console. Type in the numbers and end with a ctrl-D.

»How do I enter points for Qhull?

Qhull takes its data from standard input. For example, create a file named 'data.txt' with the following contents: 

2  #sample 2-d input
5  #number of points
1 2  #coordinates of points
-1.1 3
3 2.2
4 5
-10 -10

Then call qconvex with 'qconvex < data.txt'. It will print a summary of the convex hull. Use 'qconvex < data.txt o' to print the vertices and edges. See also input format.

You can generate sample data with rbox, e.g., 'rbox 10' generates 10 random points in 3-d. Use a pipe ('|') to run rbox and qhull together, e.g.,

rbox c | qconvex o

computes the convex hull of a cube.

»How do I learn to use Qhull?

First read:

Look at Qhull's on-line documentation:

  • 'qconvex' gives a synopsis of qconvex and its options
  • 'rbox' lists all of the options for generating point sets
  • 'qconvex - | more' lists the options for qconvex
  • 'qconvex .' gives a concise list of options
  • 'qdelaunay', 'qhalf', 'qvoronoi', and 'qhull' also have a synopsis and option list

Then try out the Qhull programs on small examples.

  • 'rbox c' lists the vertices of a cube
  • 'rbox c | qconvex' is the convex hull of a cube
  • 'rbox c | qconvex o' lists the vertices and facets of a cube
  • 'rbox c | qconvex Qt o' triangulates the cube
  • 'rbox c | qconvex QJ o' joggles the input and triangulates the cube
  • 'rbox c D2 | qconvex' generates the convex hull of a square
  • 'rbox c D4 | qconvex' generates the convex hull of a hypercube
  • 'rbox 6 s D2 | qconvex p Fx' lists 6 random points in a circle and lists the vertices of their convex hull in order
  • 'rbox c D2 c G2 | qdelaunay' computes the Delaunay triangulation of two embedded squares. It merges the cospherical facets.
  • 'rbox c D2 c G2 | qdelaunay Qt' computes the Delaunay triangulation of two embedded squares. It triangulates the cospherical facets.
  • 'rbox c D2 c G2 | qvoronoi o' computes the corresponding Voronoi vertices and regions.
  • 'rbox c D2 c G2 | qvoronio Fv' shows the Voronoi diagram for the previous example. Each line is one edge of the diagram. The first number is 4, the next two numbers list a pair of input sites, and the last two numbers list the corresponding pair of Voronoi vertices.

Install Geomview if you are running SGI Irix, Solaris, SunOS, Linux, HP, IBM RS/6000, DEC Alpha, or Next. You can then visualize the output of Qhull. Qhull comes with Geomview examples.

Then try Qhull with a small example of your application. Work out the results by hand. Then experiment with Qhull's options to find the ones that you need.

You will need to decide how Qhull should handle precision problems. It can triangulate the output ('Qt'), joggle the input ('QJ'), or merge facets (the default).

  • With joggle, Qhull produces simplicial (i.e., triangular) output by joggling the input. After joggle, no points are cocircular or cospherical.
  • With facet merging, Qhull produces a better approximation and does not modify the input.
  • With triangulated output, Qhull merges facets and triangulates the result.
  • See Merged facets or joggled input.

»Convex hull questions

»How do I report just the area and volume of a convex hull?

Use option 'FS'. For example, 
C:\qhull>rbox 10 | qconvex FS
0
2 2.192915621644613 0.2027867899638665

C:\qhull>rbox 10 | qconvex FA

Convex hull of 10 points in 3-d:

  Number of vertices: 10
  Number of facets: 16

Statistics for: RBOX 10 | QCONVEX FA

  Number of points processed: 10
  Number of hyperplanes created: 28
  Number of distance tests for qhull: 44
  CPU seconds to compute hull (after input):  0
  Total facet area:   2.1929156
  Total volume:       0.20278679

»Why are there extra points in a 4-d or higher convex hull?

You may see extra points if you use options 'i' or 'Ft' without using triangulated output ('Qt'). The extra points occur when a facet is non-simplicial (i.e., a facet with more than d vertices). For example, Qhull reports the following for one facet of the convex hull of a hypercube. Option 'Pd0:0.5' returns the facet along the positive-x axis: 

rbox c D4 | qconvex i Pd0:0.5
12
17 13 14 15
17 13 12 14
17 11 13 15
17 14 11 15
17 10 11 14
17 14 12 8
17 12 13 8
17 10 14 8
17 11 10 8
17 13 9 8
17 9 11 8
17 11 9 13

The 4-d hypercube has 16 vertices; so point "17" was added by qconvex. Qhull adds the point in order to report a simplicial decomposition of the facet. The point corresponds to the "centrum" which Qhull computes to test for convexity.

Triangulate the output ('Qt') to avoid the extra points. Since the hypercube is 4-d, each simplicial facet is a tetrahedron. 

C:\qhull3.1>rbox c D4 | qconvex i Pd0:0.5 Qt
9
9 13 14 15
12 9 13 14
9 11 13 15
11 9 14 15
9 10 11 14
12 9 14 8
9 12 13 8
9 10 14 8
10 9 11 8

Use the 'Fv' option to print the vertices of simplicial and non-simplicial facets. For example, here is the same hypercube facet with option 'Fv' instead of 'i': 

C:\qhull>rbox c D4 | qconvex Pd0:0.5 Fv
1
8 9 10 12 11 13 14 15 8

The coordinates of the extra point are printed with the 'Ft' option. 

rbox c D4 | qconvex Pd0:0.5 Ft
4
17 12 3
  -0.5   -0.5   -0.5   -0.5
  -0.5   -0.5   -0.5    0.5
  -0.5   -0.5    0.5   -0.5
  -0.5   -0.5    0.5    0.5
  -0.5    0.5   -0.5   -0.5
  -0.5    0.5   -0.5    0.5
  -0.5    0.5    0.5   -0.5
  -0.5    0.5    0.5    0.5
   0.5   -0.5   -0.5   -0.5
   0.5   -0.5   -0.5    0.5
   0.5   -0.5    0.5   -0.5
   0.5   -0.5    0.5    0.5
   0.5    0.5   -0.5   -0.5
   0.5    0.5   -0.5    0.5
   0.5    0.5    0.5   -0.5
   0.5    0.5    0.5    0.5
   0.5      0      0      0
4 16 13 14 15
4 16 13 12 14
4 16 11 13 15
4 16 14 11 15
4 16 10 11 14
4 16 14 12 8
4 16 12 13 8
4 16 10 14 8
4 16 11 10 8
4 16 13 9 8
4 16 9 11 8
4 16 11 9 13

»How do I report duplicate vertices?

There's no direct way. You can use option 'FP' to report the distance to the nearest vertex for coplanar input points. Select the minimum distance for a duplicated vertex, and locate all input sites less than this distance.

For Delaunay triangulations, all coplanar points are nearly incident to a vertex. If you want a report of coincident input sites, do not use option 'QJ'. By adding a small random quantity to each input coordinate, it prevents coincident input sites.

»Delaunay triangulation questions

»How do I get rid of nearly flat Delaunay triangles?

Nearly flat triangles occur when boundary points are nearly collinear or coplanar. They also occur for nearly coincident points. Both events can easily occur when using joggle. For example (rbox 10 W0 D2 | qdelaunay QJ Fa) lists the areas of the Delaunay triangles of 10 points on the boundary of a square. Some of these triangles are nearly flat. This occurs when one point is joggled inside of two other points. In this case, nearly flat triangles do not occur with triangulated output (rbox 10 W0 D2 | qdelaunay Qt Fa).

Another example, (rbox c P0 P0 D2 | qdelaunay QJ Fa), computes the areas of the Delaunay triangles for the unit square and two instances of the origin. Four of the triangles have an area of 0.25 while two have an area of 2.0e-11. The later are due to the duplicated origin. With triangulated output (rbox c P0 P0 D2 | qdelaunay Qt Fa) there are four triangles of equal area.

Nearly flat triangles also occur without using joggle. For example, (rbox c P0 P0,0.4999999999 | qdelaunay Fa), computes the areas of the Delaunay triangles for the unit square, a nearly collinear point, and the origin. One triangle has an area of 3.3e-11.

Unfortunately, none of Qhull's merging options remove nearly flat Delaunay triangles due to nearly collinear or coplanar boundary points. The merging options concern the empty circumsphere property of Delaunay triangles. This is independent of the area of the Delaunay triangles. Qhull does handle nearly coincident points.

You can handle collinear or coplanar boundary points by enclosing the points in a box. For example, (rbox c P0 P0,0.4999999999 c G1 | qdelaunay Fa), surrounds the previous points with [(1,1), (1,-1), (-1,-1), (-1, 1)]. Its Delaunay triangulation does not include a nearly flat triangle. The box also simplifies the graphical output from Qhull.

Without joggle, Qhull lists coincident points as "coplanar" points. For example, (rbox c P0 P0 D2 | qdelaunay Fa), ignores the duplicated origin and lists four triangles of size 0.25. Use 'Fc' to list the coincident points (e.g., rbox c P0 P0 D2 | qdelaunay Fc).

There is no easy way to determine coincident points with joggle. Joggle removes all coincident, cocircular, and cospherical points before running Qhull. Instead use facet merging (the default) or triangulated output ('Qt').

»How do I compute the Delaunay triangulation of a non-convex object?

A similar question is "How do I mesh a volume from a set of triangulated surface points?"

This is an instance of the constrained Delaunay Triangulation problem. Qhull does not handle constraints. The boundary of the Delaunay triangulation is always convex. But if the input set contains enough points, the triangulation will include the boundary. The number of points needed depends on the input.

Shewchuk has developed a theory of constrained Delaunay triangulations. See his paper at the 1998 Computational Geometry Conference. Using these ideas, constraints could be added to Qhull. They would have many applications.

There is a large literature on mesh generation and many commercial offerings. For pointers see Owen's Meshing Research Corner and Schneiders' Finite Element Mesh Generation page.

»Can Qhull produce a triangular mesh for an object?

Yes for convex objects, no for non-convex objects. For non-convex objects, it triangulates the concavities. Unless the object has many points on its surface, triangles may cross the surface.

»For 3-d Delaunay triangulations, how do I report the triangles of each tetrahedron?

For points in general position, a 3-d Delaunay triangulation generates tetrahedron. Each face of a tetrahedron is a triangle. For example, the 3-d Delaunay triangulation of random points on the surface of a cube, is a cellular structure of tetrahedron.

Use triangulated output ('qdelaunay Qt i') or joggled input ('qdelaunay QJ i') to generate the Delaunay triangulation. Option 'i' reports each tetrahedron. The triangles are every combination of 3 vertices. Each triangle is a "ridge" of the Delaunay triangulation.

For example, 

        rbox 10 | qdelaunay Qt i
        14
        9 5 8 7
        0 9 8 7
        5 3 8 7
        3 0 8 7
        5 4 8 1
        4 6 8 1
        2 9 5 8
        4 2 5 8
        4 2 9 5
        6 2 4 8
        9 2 0 8
        2 6 0 8
        2 4 9 1
        2 6 4 1

is the Delaunay triangulation of 10 random points. Ridge 9-5-8 occurs twice. Once for tetrahedron 9 5 8 7 and the other for tetrahedron 2 9 5 8.

You can also use the Qhull library to generate the triangles. See "How do I visit the ridges of a Delaunay triangulation?"

»How do I construct a 3-d Delaunay triangulation?

For 3-d Delaunay triangulations with cospherical input sites, use triangulated output ('Qt') or joggled input ('QJ'). Otherwise option 'i' will triangulate non-simplicial facets by adding a point to the facet.

If you want non-simplicial output for cospherical sites, use option 'Fv' or 'o'. For option 'o', ignore the last coordinate. It is the lifted coordinate for the corresponding convex hull in 4-d.

The following example is a cube inside a tetrahedron. The 8-vertex facet is the cube. Ignore the last coordinates. 

C:\qhull>rbox r y c G0.1 | qdelaunay Fv
4
12 20 44
   0.5      0      0 0.3055555555555555
   0    0.5      0 0.3055555555555555
   0      0    0.5 0.3055555555555555
  -0.5   -0.5   -0.5 0.9999999999999999
  -0.1   -0.1   -0.1 -6.938893903907228e-018
  -0.1   -0.1    0.1 -6.938893903907228e-018
  -0.1    0.1   -0.1 -6.938893903907228e-018
  -0.1    0.1    0.1 -6.938893903907228e-018
   0.1   -0.1   -0.1 -6.938893903907228e-018
   0.1   -0.1    0.1 -6.938893903907228e-018
   0.1    0.1   -0.1 -6.938893903907228e-018
   0.1    0.1    0.1 -6.938893903907228e-018
4 2 11 1 0
4 10 1 0 3
4 11 10 1 0
4 2 9 0 3
4 9 11 2 0
4 7 2 1 3
4 11 7 2 1
4 8 10 0 3
4 9 8 0 3
5 8 9 10 11 0
4 10 6 1 3
4 6 7 1 3
5 6 8 10 4 3
5 6 7 10 11 1
4 5 9 2 3
4 7 5 2 3
5 5 8 9 4 3
5 5 6 7 4 3
8 5 6 8 7 9 10 11 4
5 5 7 9 11 2

If you want simplicial output use options 'Qt i' or 'QJ i', e.g., 

rbox r y c G0.1 | qdelaunay Qt i
31
2 11 1 0
11 10 1 0
9 11 2 0
11 7 2 1
8 10 0 3
9 8 0 3
10 6 1 3
6 7 1 3
5 9 2 3
7 5 2 3
9 8 10 11
8 10 11 0
9 8 11 0
6 8 10 4
8 6 10 3
6 8 4 3
6 7 10 11
10 6 11 1
6 7 11 1
8 5 4 3
5 8 9 3
5 6 4 3
6 5 7 3
5 9 10 11
8 5 9 10
7 5 10 11
5 6 7 10
8 5 10 4
5 6 10 4
5 9 11 2
7 5 11 2

»How do I get the triangles for a 2-d Delaunay triangulation and the vertices of its Voronoi diagram?

To compute the Delaunay triangles indexed by the indices of the input sites, use

rbox 10 D2 | qdelaunay Qt i

To compute the Voronoi vertices and the Voronoi region for each input site, use

rbox 10 D2 | qvoronoi o

To compute each edge ("ridge") of the Voronoi diagram for each pair of adjacent input sites, use

rbox 10 D2 | qvoronoi Fv

To compute the area and volume of the Voronoi region for input site 5 (site 0 is the first one), use

rbox 10 D2 | qvoronoi QV5 p | qconvex s FS

To compute the lines ("hyperplanes") that define the Voronoi region for input site 5, use

rbox 10 D2 | qvoronoi QV5 p | qconvex n

or

rbox 10 D2 | qvoronoi QV5 Fi Fo

To list the extreme points of the input sites use

rbox 10 D2 | qdelaunay Fx

You will get the same point ids with

rbox 10 D2 | qconvex Fx

»Can Qhull triangulate a hundred 16-d points?

No. This is an immense structure. A triangulation of 19, 16-d points has 43 simplices. If you add one point at a time, the triangulation increased as follows: 43, 189, 523, 1289, 2830, 6071, 11410, 20487. The last triangulation for 26 points used 13 megabytes of memory. When Qhull uses virtual memory, it becomes too slow to use.

»Voronoi diagram questions

»How do I compute the volume of a Voronoi region?

For each Voronoi region, compute the convex hull of the region's Voronoi vertices. The volume of each convex hull is the volume of the corresponding Vornoi region.

For example, to compute the volume of the bounded Voronoi region about [0,0,0]: output the origin's Voronoi vertices and compute the volume of their convex hull. The last number from option 'FS' is the volume.

rbox P0 10 | qvoronoi QV0 p | qhull FS
0
2 1.448134756744281 0.1067973560800857

For another example, see How do I get the triangles for a 2-d Delaunay triangulation and the vertices of its Voronoi diagram?

This approach is slow if you are using the command line. A faster approcach is to call Qhull from a program. The fastest method is Clarkson's hull program. It computes the volume for all Voronoi regions.

An unbounded Voronoi region does not have a volume.

»How do I get the radii of the empty spheres for each Voronoi vertex?

Use option 'Fi' to list each bisector (i.e. Delaunay ridge). Then compute the minimum distance for each Voronoi vertex.

There's other ways to get the same information. Let me know if you find a better method.

»What is the Voronoi diagram of a square?

Consider a square, 

C:\qhull>rbox c D2
2 RBOX c D2
4
  -0.5   -0.5
  -0.5    0.5
   0.5   -0.5
   0.5    0.5

There's two ways to compute the Voronoi diagram: with facet merging or with joggle. With facet merging, the result is: 

C:\qhull>rbox c D2 | qvoronoi Qz

Voronoi diagram by the convex hull of 5 points in 3-d:

  Number of Voronoi regions and at-infinity: 5
  Number of Voronoi vertices: 1
  Number of facets in hull: 5

Statistics for: RBOX c D2 | QVORONOI Qz

  Number of points processed: 5
  Number of hyperplanes created: 7
  Number of distance tests for qhull: 8
  Number of merged facets: 1
  Number of distance tests for merging: 29
  CPU seconds to compute hull (after input):  0

C:\qhull>rbox c D2 | qvoronoi Qz o
2
2 5 1
-10.101 -10.101
     0      0
2 0 1
2 0 1
2 0 1
2 0 1
0

C:\qhull>rbox c D2 | qvoronoi Qz Fv
4
4 0 1 0 1
4 0 2 0 1
4 1 3 0 1
4 2 3 0 1

There is one Voronoi vertex at the origin and rays from the origin along each of the coordinate axes. The last line '4 2 3 0 1' means that there is a ray that bisects input points #2 and #3 from infinity (vertex 0) to the origin (vertex 1). Option 'Qz' adds an artificial point since the input is cocircular. Coordinates -10.101 indicate the vertex at infinity.

With triangulated output, the Voronoi vertex is duplicated: 

C:\qhull3.1>rbox c D2 | qvoronoi Qt Qz

Voronoi diagram by the convex hull of 5 points in 3-d:

  Number of Voronoi regions and at-infinity: 5
  Number of Voronoi vertices: 2
  Number of triangulated facets: 1

Statistics for: RBOX c D2 | QVORONOI Qt Qz

  Number of points processed: 5
  Number of hyperplanes created: 7
  Number of facets in hull: 6
  Number of distance tests for qhull: 8
  Number of distance tests for merging: 33
  Number of distance tests for checking: 30
  Number of merged facets: 1
  CPU seconds to compute hull (after input): 0.05

C:\qhull3.1>rbox c D2 | qvoronoi Qt Qz o
2
3 5 1
-10.101 -10.101
     0      0
     0      0
3 2 0 1
2 1 0
2 2 0
3 2 0 1
0

C:\qhull3.1>rbox c D2 | qvoronoi Qt Qz Fv
4
4 0 2 0 2
4 0 1 0 1
4 1 3 0 1
4 2 3 0 2

With joggle, the input is no longer cocircular and the Voronoi vertex is split into two: 

C:\qhull>rbox c D2 | qvoronoi Qt Qz

C:\qhull>rbox c D2 | qvoronoi QJ o
2
3 4 1
-10.101 -10.101
-4.71511718558304e-012 -1.775812830118184e-011
9.020340030474472e-012 -4.02267108512433e-012
2 0 1
3 2 1 0
3 2 0 1
2 2 0

C:\qhull>rbox c D2 | qvoronoi QJ Fv
5
4 0 2 0 1
4 0 1 0 1
4 1 2 1 2
4 1 3 0 2
4 2 3 0 2

Note that the Voronoi diagram includes the same rays as before plus a short edge between the two vertices.

»How do I construct the Voronoi diagram of cospherical points?

Three-d terrain data can be approximated with cospherical points. The Delaunay triangulation of cospherical points is the same as their convex hull. If the points lie on the unit sphere, the facet normals are the Voronoi vertices [via S. Fortune].

For example, consider the points {[1,0,0], [-1,0,0], [0,1,0], ...}. Their convex hull is: 

rbox d G1 | qconvex o
3
6 8 12
     0      0     -1
     0      0      1
     0     -1      0
     0      1      0
    -1      0      0
     1      0      0
3 3 1 4
3 1 3 5
3 0 3 4
3 3 0 5
3 2 1 5
3 1 2 4
3 2 0 4
3 0 2 5

The facet normals are: 

rbox d G1 | qconvex n
4
8
-0.5773502691896258  0.5773502691896258  0.5773502691896258 -0.5773502691896258
 0.5773502691896258  0.5773502691896258  0.5773502691896258 -0.5773502691896258
-0.5773502691896258  0.5773502691896258 -0.5773502691896258 -0.5773502691896258
 0.5773502691896258  0.5773502691896258 -0.5773502691896258 -0.5773502691896258
 0.5773502691896258 -0.5773502691896258  0.5773502691896258 -0.5773502691896258
-0.5773502691896258 -0.5773502691896258  0.5773502691896258 -0.5773502691896258
-0.5773502691896258 -0.5773502691896258 -0.5773502691896258 -0.5773502691896258
 0.5773502691896258 -0.5773502691896258 -0.5773502691896258 -0.5773502691896258

If you drop the offset from each line (the last number), each line is the Voronoi vertex for the corresponding facet. The neighboring facets for each point define the Voronoi region for each point. For example: 

rbox d G1 | qconvex FN
6
4 7 3 2 6
4 5 0 1 4
4 7 4 5 6
4 3 1 0 2
4 6 2 0 5
4 7 3 1 4

The Voronoi vertices {7, 3, 2, 6} define the Voronoi region for point 0. Point 0 is [0,0,-1]. Its Voronoi vertices are 

-0.5773502691896258  0.5773502691896258 -0.5773502691896258
 0.5773502691896258  0.5773502691896258 -0.5773502691896258
-0.5773502691896258 -0.5773502691896258 -0.5773502691896258
 0.5773502691896258 -0.5773502691896258 -0.5773502691896258

In this case, the Voronoi vertices are oriented, but in general they are unordered.

By taking the dual of the Delaunay triangulation, you can construct the Voronoi diagram. For cospherical points, the convex hull vertices for each facet, define the input sites for each Voronoi vertex. In 3-d, the input sites are oriented. For example: 

rbox d G1 | qconvex i
8
3 1 4
1 3 5
0 3 4
3 0 5
2 1 5
1 2 4
2 0 4
0 2 5

The convex hull vertices for facet 0 are {3, 1, 4}. So Voronoi vertex 0 (i.e., [-0.577, 0.577, 0.577]) is the Voronoi vertex for input sites {3, 1, 4} (i.e., {[0,1,0], [0,0,1], [-1,0,0]}).

»Can Qhull compute the unbounded rays of the Voronoi diagram?

Use 'Fo' to compute the separating hyperplanes for unbounded Voronoi regions. The corresponding ray goes to infinity from the Voronoi vertices. If you enclose the input sites in a large enough box, the outermost bounded regions will represent the unbounded regions of the original points.

If you do not box the input sites, you can identify the unbounded regions. They list '0' as a vertex. Vertex 0 represents "infinity". Each unbounded ray includes vertex 0 in option 'Fv. See Voronoi graphics and Voronoi notes.

»Approximation questions

»How do I approximate data with a simplex

Qhull may be used to help select a simplex that approximates a data set. It will take experimentation. Geomview will help to visualize the results. This task may be difficult to do in 5-d and higher. Use rbox options 'x' and 'y' to produce random distributions within a simplex. Your methods work if you can recover the simplex.

Use Qhull's precision options to get a first approximation to the hull, say with 10 to 50 facets. For example, try 'C0.05' to remove small facets after constructing the hull. Use 'W0.05' to ignore points within 0.05 of a facet. Use 'PA5' to print the five largest facets by area.

Then use other methods to fit a simplex to this data. Remove outlying vertices with few nearby points. Look for large facets in different quadrants. You can use option 'Pd0d1d2' to print all the facets in a quadrant.

In 4-d and higher, use the outer planes (option 'Fo' or 'facet->maxoutside') since the hyperplane of an approximate facet may be below many of the input points.

For example, consider fitting a cube to 1000 uniformly random points in the unit cube. In this case, the first try was good: 

rbox 1000 | qconvex W0.05 C0.05 PA6 Fo
4
6
0.35715408374381 0.08706467018177928 -0.9299788727015564 -0.5985514741284483
0.995841591359023 -0.02512604712761577 0.08756829720435189 -0.5258834069202866
0.02448099521570909 -0.02685210459017302 0.9993396046151313 -0.5158104982631999
-0.9990223929415094 -0.01261133513150079 0.04236994958247349 -0.509218270408407
-0.0128069014364698 -0.9998380680115362 0.01264203427283151 -0.5002512653670584
0.01120895057872914 0.01803671994177704 -0.9997744926535512 -0.5056824072956361

»Halfspace questions

»How do I compute the intersection of halfspaces with Qhull?

Qhull computes the halfspace intersection about a point. The point must be inside all of the halfspaces. Given a point, a duality turns a halfspace intersection problem into a convex hull problem.

Use linear programming if you do not know a point in the interior of the halfspaces. See the manual. You will need a linear programming code. This may require a fair amount of work to implement.

»Qhull library questions

»Is Qhull available for Mathematica, Matlab, or Maple?

MATLAB

Z. You of MathWorks added qhull to MATLAB 6. See functions convhulln, delaunayn, griddata3, griddatan, tsearch, tsearchn, and voronoin. V. Brumberg update MATLAB R14 for Qhull 2003.1 and triangulated output.

Engwirda wrote mesh2d for unstructured mesh generation in MATLAB. It is based on the iterative method of Persson and generally results in better quality meshes than delaunay refinement.

Mathematica and Maple

See qh-math for a Delaunay interface to Mathematica. It includes projects for CodeWarrior on the Macintosh and Visual C++ on Win32 PCs.

See Mathematica ('m') and Maple ('FM') output options.

»Why are there too few ridges?

The following sample code may produce fewer ridges than expected: 
  facetT *facetp;
  ridgeT *ridge, **ridgep;

  FORALLfacets {
    printf("facet f%d\n", facet->id);
    FOREACHridge_(facet->ridges) {
      printf("   ridge r%d between f%d and f%d\n", ridge->id, ridge->top->id, ridge->bottom->id);
    }
  }

Qhull does not create ridges for simplicial facets. Instead it computes ridges from facet->neighbors. To make ridges for a simplicial facet, use qh_makeridges() in merge.c. Usefacet->visit_id to visit each ridge once (instead of twice). For example, 

  facetT *facet, *neighbor;
  ridgeT *ridge, **ridgep;

  qh visit_id++;
  FORALLfacets {
    printf("facet f%d\n", facet->id);
    qh_makeridges(facet);
    facet->visitId= qh visit_id;
    FOREACHridge_(facet->ridges) {
        neighbor= otherfacet_(ridge, visible);
        if (neighbor->visitid != qh visit_id)
            printf("   ridge r%d between f%d and f%d\n", ridge->id, ridge->top->id, ridge->bottom->id);
    }
  }

»Can Qhull use coordinates without placing them in a data file?

Use qh_call_qhull(). See user_eg.c for an example. See the manual for an introduction to the Qhull library.

Start with a small example for which you know the answer.

»How large are Qhull's data structures?

Qhull uses a general-dimension data structure. The size depends on the dimension. Use option 'Ts' to print out the memory statistics [e.g., 'rbox D2 10 | qconvex Ts'].

»Can Qhull construct convex hulls and Delaunay triangulations one point at a time?

The Qhull library may be used to construct convex hulls and Delaunay triangulations one point at a time. It may not be used for deleting points or moving points.

Qhull is designed for batch processing. Neither Clarkson's randomized incremental algorithm nor Qhull are designed for on-line operation. For many applications, it is better to reconstruct the convex hull or Delaunay triangulation from scratch for each new point.

With random point sets and on-line processing, Clarkson's algorithm should run faster than Qhull. Clarkson uses the intermediate facets to reject new, interior points, while Qhull, when used on-line, visits every facet to reject such points. If used on-line for n points, Clarkson may take O(n) times as much memory as the average off-line case, while Qhull's space requirement does not change.

If you triangulate the output before adding all the points (option 'Qt' and procedure qh_triangulate), you must set option 'Q11'. It duplicates the normals of triangulated facets and recomputes the centrums. This should be avoided for regular use since triangulated facets are not clearly convex with their neighbors. It appears to work most of the time, but fails for cases that Qhull normally handles well [see the test call to qh_triangulate in qh_addpoint].

»How do I visit the ridges of a Delaunay triangulation?

To visit the ridges of a Delaunay triangulation, visit each facet. Each ridge will appear twice since it belongs to two facets. In pseudo-code: 

    for each facet of the triangulation
        if the facet is Delaunay (i.e., part of the lower convex hull)
            for each ridge of the facet
                if the ridge's neighboring facet has not been visited
                    ... process a ridge of the Delaunay triangulation ...

In undebugged, C code: 

    qh visit_id++;
    FORALLfacets_(facetlist)
        if (!facet->upperdelaunay) {
            facet->visitid= qh visit_id;
            qh_makeridges(facet);
            FOREACHridge_(facet->ridges) {
                neighbor= otherfacet_(ridge, facet);
                if (neighbor->visitid != qh visit_id) {
                    /* Print ridge here with facet-id and neighbor-id */
                    /*fprintf(fp, "f%d\tf%d\t",facet->id,neighbor->ID);*/
                    FOREACHvertex_(ridge->vertices)
                        fprintf(fp,"%d ",qh_pointid (vertex->point) );
                    qh_printfacetNvertex_simplicial (fp, facet, format);
                    fprintf(fp," ");
                    if(neighbor->upperdelaunay)
                        fprintf(fp," -1 -1 -1 -1 ");
                    else
                        qh_printfacetNvertex_simplicial (fp, neighbor, format);
                    fprintf(fp,"\n");
                }
            }
        }
    }

Qhull should be redesigned as a class library, or at least as an API. It currently provides everything needed, but the programmer has to do a lot of work. Hopefully someone will write C++ wrapper classes or a Python module for Qhull.

»How do I visit the Delaunay regions?

Qhull constructs a Delaunay triangulation by lifting the input sites to a paraboloid. The Delaunay triangulation corresponds to the lower convex hull of the lifted points. To visit each facet of the lower convex hull, use: 

    facetT *facet;

    ...
    FORALLfacets {
        if (!facet->upperdelaunay) {
            ... only facets for Delaunay regions ...
        }
    }

»When is a point outside or inside a facet?

A point is outside of a facet if it is clearly outside the facet's outer plane. The outer plane is defined by an offset (facet->maxoutside) from the facet's hyperplane. 

    facetT *facet;
    pointT *point;
    realT dist;

    ...
    qh_distplane(point, facet, &dist);
    if (dist > facet->maxoutside + 2 * qh DISTround) {
        /* point is clearly outside of facet */
    }

A point is inside of a facet if it is clearly inside the facet's inner plane. The inner plane is computed as the maximum distance of a vertex to the facet. It may be computed for an individual facet, or you may use the maximum over all facets. For example: 

    facetT *facet;
    pointT *point;
    realT dist;

    ...
    qh_distplane(point, facet, &dist);
    if (dist < qh min_vertex - 2 * qh DISTround) {
        /* point is clearly inside of facet */
    }

Both tests include two qh.DISTrounds because the computation of the furthest point from a facet may be off by qh.DISTround and the computation of the current distance to the facet may be off by qh.DISTround.

»How do I find the facet that is closest to a point?

Use qh_findbestfacet(). For example, 

    coordT point[ DIM ];
    boolT isoutside;
    realT bestdist;
    facetT *facet;

    ... set coordinates for point ...

    facet= qh_findbestfacet (point, qh_ALL, &bestdist, &isoutside);

    /* 'facet' is the closest facet to 'point' */

qh_findbestfacet() performs a directed search for the facet furthest below the point. If the point lies inside this facet, qh_findbestfacet() performs an exhaustive search of all facets. An exhaustive search may be needed because a facet on the far side of a lens-shaped distribution may be closer to a point than all of the facet's neighbors. The exhaustive search may be skipped for spherical distributions.

Also see, "How do I find the Delaunay triangle that is closest to a point?"

»How do I find the Delaunay triangle or Voronoi region that is closest to a point?

A Delaunay triangulation subdivides the plane, or in general dimension, subdivides space. Given a point, how do you determine the subdivision containing the point? Or, given a set of points, how do you determine the subdivision containing each point of the set? Efficiency is important -- an exhaustive search of the subdivision is too slow.

First compute the Delaunay triangle with qh_call_qhull(). Lift the point to the paraboloid by summing the squares of the coordinates. Use qh_findbestfacet() [poly2.c] to find the closest Delaunay triangle. Determine the closest vertex to find the corresponding Voronoi region. Do not use options 'Qbb', 'QbB', 'Qbk:n', or 'QBk:n' since these scale the last coordinate. Optimizations of qh_findbestfacet() should be possible for Delaunay triangulations.

You first need to lift the point to the paraboloid (i.e., the last coordinate is the sum of the squares of the point's coordinates). The routine, qh_setdelaunay() [geom2.c], lifts an array of points to the paraboloid. The following excerpt is from findclosest() in user_eg.c. 

    coordT point[ DIM + 1];  /* one extra coordinate for lifting the point */
    boolT isoutside;
    realT bestdist;
    facetT *facet;

    ... set coordinates for point[] ...

    qh_setdelaunay (DIM+1, 1, point);
    facet= qh_findbestfacet (point, qh_ALL, &bestdist, &isoutside);
    /* 'facet' is the closest Delaunay triangle to 'point' */

The returned facet either contains the point or it is the closest Delaunay triangle along the convex hull of the input set.

Point location is an active research area in Computational Geometry. For a practical approach, see Mucke, et al, "Fast randomized point location without preprocessing in two- and three-dimensional Delaunay triangulations," Computational Geometry '96, p. 274-283, May 1996. For an introduction to planar point location see [O'Rourke '93]. Also see, "How do I find the facet that is closest to a point?"

To locate the closest Voronoi region, determine the closest vertex of the closest Delaunay triangle. 

    realT dist, bestdist= REALmax;
        vertexT *bestvertex= NULL, *vertex, **vertexp;

    /* 'facet' is the closest Delaunay triangle to 'point' */

    FOREACHvertex_( facet->vertices ) {
        dist= qh_pointdist( point, vertex->point, DIM );
        if (dist < bestdist) {
            bestdist= dist;
            bestvertex= vertex;
        }
    }
    /* 'bestvertex' represents the Voronoi region closest to 'point'.  The corresponding
       input site is 'bestvertex->point' */

»How do I list the vertices?

To list the vertices (i.e., extreme points) of the convex hull use 

    vertexT *vertex;

    FORALLvertices {
      ...
      // vertex->point is the coordinates of the vertex
      // qh_pointid(vertex->point) is the point ID of the vertex
      ...
    }

»How do I test code that uses the Qhull library?

Compare the output from your program with the output from the Qhull program. Use option 'T1' or 'T4' to trace what Qhull is doing. Prepare a small example for which you know the output. Run the example through the Qhull program and your code. Compare the trace outputs. If you do everything right, the two trace outputs should be almost the same. The trace output will also guide you to the functions that you need to review.

»When I compute a plane equation from a facet, I sometimes get an outward-pointing normal and sometimes an inward-pointing normal

Qhull orients simplicial facets, and prints oriented output for 'i', 'Ft', and other options. The orientation depends on both the vertex order and the flag facet->toporient.

Qhull does not orient non-simplicial facets. Instead it orients the facet's ridges. These are printed with the 'Qt' and 'Ft' option. The facet's hyperplane is oriented.

Up: Home page for Qhull
Up: Qhull manual: Table of Contents
To: Programs • Options • Output • Formats • Geomview • Print • Qhull • Precision • Trace
To: FAQ: Table of Contents

The Geometry Center Home Page

Comments to: qhull@qhull.org
Created: Sept. 25, 1995 --- Last modified: see top

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  • Qhull Home Page

    Qhull computes the convex hull, Delaunay triangulation, Voronoi diagram, halfspace intersection about a point, furthest-site Delaunay triangulation, and furthest-site Voronoi diagram. It runs in 2-d, 3-d, 4-d, and higher dimensions. It implements the Quickhull algorithm for computing the convex hull. Qhull handles roundoff errors from floating point arithmetic. It can approximate a convex hull.

    Visit Qhull News for news, bug reports, change history, and users. If you use Qhull 2003.1 or 2009.1, please upgrade to 2012.1 or apply poly.c-qh_gethash.patch.

  • Download: Qhull 2012.1 for Windows (2.1 Mbytes, readme, md5sum, contents)

    Type: console programs for Windows

    Includes executables, documentation, and sources files. It runs in a command window.

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    Type: C/C++ source code for 32-bit and 64-bit architectures

    Includes documentation, source files, two Makefile's, CMakeLists.txt, DevStudio projects, and Qt projects. Includes preliminary C++ support and a preliminary Debian/autoconf build.

    Debian, rpm, and Autoconf distributions are needed.

  • Gitorious Qhull (git://gitorious.org/qhull/qhull.git)

    Type: git repository for Qhull. See Changes.txt

    Includes documentation, source files, C++ interface, and test programs. It builds with gcc, mingw, CMake, DevStudio, and Qt Creator.

  • Download: Article about Qhull (307K)

    Type: PDF on ACM Digital Library (from this page only)

    Barber, C.B., Dobkin, D.P., and Huhdanpaa, H.T., "The Quickhull algorithm for convex hulls," ACM Transactions on Mathematical Software, 22(4):469-483, Dec 1996 [abstract].

  • Download: Qhull version 1.0 (92K)

    Type: C source code for 32-bit architectures

    Version 1.0 is a fifth the size of version 2.4. It computes convex hulls and Delaunay triangulations. If a precision error occurs, it stops with an error message. It reports an initialization error for inputs made with 0/1 coordinates.

    Version 1.0 compiles on a PC with Borland C++ 4.02 for Win32 and DOS Power Pack. The options for rbox are "bcc32 -WX -w- -O2-e -erbox -lc rbox.c". The options for qhull are the same. [D. Zwick]

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[4-d cube] Imprecision in Qhull

This section of the Qhull manual discusses the problems caused by coplanar points and why Qhull uses options 'C-0' or 'Qx' by default. If you ignore precision issues with option 'Q0', the output from Qhull can be arbitrarily bad. Qhull avoids precision problems if you merge facets (the default) or joggle the input ('QJ').

Use option 'Tv' to verify the output from Qhull. It verifies that adjacent facets are clearly convex. It verifies that all points are on or below all facets.

Qhull automatically tests for convexity if it detects precision errors while constructing the hull.

Copyright © 1995-2012 C.B. Barber

»Qhull imprecision: Table of Contents

»Precision problems

Since Qhull uses floating point arithmetic, roundoff error occurs with each calculation. This causes problems for geometric algorithms. Other floating point codes for convex hulls, Delaunay triangulations, and Voronoi diagrams also suffer from these problems. Qhull handles most of them.

There are several kinds of precision errors:

  • Representation error occurs when there are not enough digits to represent a number, e.g., 1/3.
  • Measurement error occurs when the input coordinates are from measurements.
  • Roundoff error occurs when a calculation is rounded to a fixed number of digits, e.g., a floating point calculation.
  • Approximation error occurs when the user wants an approximate result because the exact result contains too much detail.

Under imprecision, calculations may return erroneous results. For example, roundoff error can turn a small, positive number into a small, negative number. See Milenkovic ['93] for a discussion of strict robust geometry. Qhull does not meet Milenkovic's criterion for accuracy. Qhull's error bound is empirical instead of theoretical.

Qhull 1.0 checked for precision errors but did not handle them. The output could contain concave facets, facets with inverted orientation ("flipped" facets), more than two facets adjacent to a ridge, and two facets with exactly the same set of vertices.

Qhull 2.4 and later automatically handles errors due to machine round-off. Option 'C-0' or 'Qx' is set by default. In 5-d and higher, the output is clearly convex but an input point could be outside of the hull. This may be corrected by using option 'C-0', but then the output may contain wide facets.

Qhull 2.5 and later provides option 'QJ' to joggled input. Each input coordinate is modified by a small, random quantity. If a precision error occurs, a larger modification is tried. When no precision errors occur, Qhull is done.

Qhull 3.1 and later provides option 'Qt' for triangulated output. This removes the need for joggled input ('QJ'). Non-simplicial facets are triangulated. The facets may have zero area. Triangulated output is particularly useful for Delaunay triangulations.

By handling round-off errors, Qhull can provide a variety of output formats. For example, it can return the halfspace that defines each facet ('n'). The halfspaces include roundoff error. If the halfspaces were exact, their intersection would return the original extreme points. With imprecise halfspaces and exact arithmetic, nearly incident points may be returned for an original extreme point. By handling roundoff error, Qhull returns one intersection point for each of the original extreme points. Qhull may split or merge an extreme point, but this appears to be unlikely.

The following pipe implements the identity function for extreme points (with roundoff):

qconvex FV n | qhalf Fp

Bernd Gartner published his Miniball algorithm ["Fast and robust smallest enclosing balls", Algorithms - ESA '99, LNCS 1643]. It uses floating point arithmetic and a carefully designed primitive operation. It is practical to 20-D or higher, and identifies at least two points on the convex hull of the input set. Like Qhull, it is an incremental algorithm that processes points furthest from the intermediate result and ignores points that are close to the intermediate result.

»Merged facets or joggled input

This section discusses the choice between merged facets and joggled input. By default, Qhull uses merged facets to handle precision problems. With option 'QJ', the input is joggled. See examples of joggled input and triangulated output.

  • Use merged facets (the default) when you want non-simplicial output (e.g., the faces of a cube).
  • Use merged facets and triangulated output ('Qt') when you want simplicial output and coplanar facets (e.g., triangles for a Delaunay triangulation).
  • Use joggled input ('QJ') when you need clearly-convex, simplicial output.

The choice between merged facets and joggled input depends on the application. Both run about the same speed. Joggled input may be faster if the initial joggle is sufficiently large to avoid precision errors.

Most applications should used merged facets with triangulated output.

Use merged facets (the default, 'C-0') or triangulated output ('Qt') if

  • Your application supports non-simplicial facets, or it allows degenerate, simplicial facets (option 'Qt').
  • You do not want the input modified.
  • You want to set additional options for approximating the hull.
  • You use single precision arithmetic (realT).

Use joggled input ('QJ') if

  • Your application needs clearly convex, simplicial output
  • Your application supports perturbed input points and narrow triangles.
  • Seven significant digits is sufficient accuracy.

You may use both techniques or combine joggle with post-merging ('Cn').

Other researchers have used techniques similar to joggled input. Sullivan and Beichel [ref?] randomly perturb the input before computing the Delaunay triangulation. Corkum and Wyllie [news://comp.graphics, 1990] randomly rotate a polytope before testing point inclusion. Edelsbrunner and Mucke [Symp. Comp. Geo., 1988] and Yap [J. Comp. Sys. Sci., 1990] symbolically perturb the input to remove singularities.

Merged facets ('C-0') handles precision problems directly. If a precision problem occurs, Qhull merges one of the offending facets into one of its neighbors. Since all precision problems in Qhull are associated with one or more facets, Qhull will either fix the problem or attempt to merge the last remaining facets.

»Delaunay triangulations

Programs that use Delaunay triangulations traditionally assume a triangulated input. By default, qdelaunay merges regions with cocircular or cospherical input sites. If you want a simplicial triangulation use triangulated output ('Qt') or joggled input ('QJ').

For Delaunay triangulations, triangulated output should produce good results. All points are within roundoff error of a paraboloid. If two points are nearly incident, one will be a coplanar point. So all points are clearly separated and convex. If qhull reports deleted vertices, the triangulation may contain serious precision faults. Deleted vertices are reported in the summary ('s', 'Fs'

You should use option 'Qbb' with Delaunay triangulations. It scales the last coordinate and may reduce roundoff error. It is automatically set for qdelaunay, qvoronoi, and option 'QJ'.

Edelsbrunner, H, Geometry and Topology for Mesh Generation, Cambridge University Press, 2001. Good mathematical treatise on Delaunay triangulation and mesh generation for 2-d and 3-d surfaces. The chapter on surface simplification is particularly interesting. It is similar to facet merging in Qhull.

Veron and Leon published an algorithm for shape preserving polyhedral simplification with bounded error [Computers and Graphics, 22.5:565-585, 1998]. It remove nodes using front propagation and multiple remeshing.

»Halfspace intersection

The identity pipe for Qhull reveals some precision questions for halfspace intersections. The identity pipe creates the convex hull of a set of points and intersects the facets' hyperplanes. It should return the input points, but narrow distributions may drop points while offset distributions may add points. It may be better to normalize the input set about the origin. For example, compare the first results with the later two results: [T. Abraham]

rbox 100 s t | tee r | qconvex FV n | qhalf Fp | cat - r | /bin/sort -n | tail
rbox 100 L1e5 t | tee r | qconvex FV n | qhalf Fp | cat - r | /bin/sort -n | tail
rbox 100 s O10 t | tee r | qconvex FV n | qhalf Fp | cat - r | /bin/sort -n | tail

»Merged facets

Qhull detects precision problems when computing distances. A precision problem occurs if the distance computation is less than the maximum roundoff error. Qhull treats the result of a hyperplane computation as if it were exact.

Qhull handles precision problems by merging non-convex facets. The result of merging two facets is a thick facet defined by an inner plane and an outer plane. The inner and outer planes are offsets from the facet's hyperplane. The inner plane is clearly below the facet's vertices. At the end of Qhull, the outer planes are clearly above all input points. Any exact convex hull must lie between the inner and outer planes.

Qhull tests for convexity by computing a point for each facet. This point is called the facet's centrum. It is the arithmetic center of the facet's vertices projected to the facet's hyperplane. For simplicial facets with d vertices, the centrum is equivalent to the centroid or center of gravity.

Two neighboring facets are convex if each centrum is clearly below the other hyperplane. The 'Cn' or 'C-n' options sets the centrum's radius to n . A centrum is clearly below a hyperplane if the computed distance from the centrum to the hyperplane is greater than the centrum's radius plus two maximum roundoff errors. Two are required because the centrum can be the maximum roundoff error above its hyperplane and the distance computation can be high by the maximum roundoff error.

With the 'C-n' or 'A-n ' options, Qhull merges non-convex facets while constructing the hull. The remaining facets are clearly convex. With the 'Qx ' option, Qhull merges coplanar facets after constructing the hull. While constructing the hull, it merges coplanar horizon facets, flipped facets, concave facets and duplicated ridges. With 'Qx', coplanar points may be missed, but it appears to be unlikely.

If the user sets the 'An' or 'A-n' option, then all neighboring facets are clearly convex and the maximum (exact) cosine of an angle is n.

If 'C-0' or 'Qx' is used without other precision options (default), Qhull tests vertices instead of centrums for adjacent simplices. In 3-d, if simplex abc is adjacent to simplex bcd, Qhull tests that vertex a is clearly below simplex bcd , and vertex d is clearly below simplex abc. When building the hull, Qhull tests vertices if the horizon is simplicial and no merges occur.

»How Qhull merges facets

If two facets are not clearly convex, then Qhull removes one or the other facet by merging the facet into a neighbor. It selects the merge which minimizes the distance from the neighboring hyperplane to the facet's vertices. Qhull also performs merges when a facet has fewer than d neighbors (called a degenerate facet), when a facet's vertices are included in a neighboring facet's vertices (called a redundant facet), when a facet's orientation is flipped, or when a ridge occurs between more than two facets.

Qhull performs merges in a series of passes sorted by merge angle. Each pass merges those facets which haven't already been merged in that pass. After a pass, Qhull checks for redundant vertices. For example, if a vertex has only two neighbors in 3-d, the vertex is redundant and Qhull merges it into an adjacent vertex.

Merging two simplicial facets creates a non-simplicial facet of d+1 vertices. Additional merges create larger facets. When merging facet A into facet B, Qhull retains facet B's hyperplane. It merges the vertices, neighbors, and ridges of both facets. It recomputes the centrum if a wide merge has not occurred (qh_WIDEcoplanar) and the number of extra vertices is smaller than a constant (qh_MAXnewcentrum).

»Limitations of merged facets

  • Uneven dimensions -- If one coordinate has a larger absolute value than other coordinates, it may dominate the effect of roundoff errors on distance computations. You may use option 'QbB' to scale points to the unit cube. For Delaunay triangulations and Voronoi diagrams, qdelaunay and qvoronoi always set option 'Qbb'. It scales the last coordinate to [0,m] where m is the maximum width of the other coordinates. Option 'Qbb' is needed for Delaunay triangulations of integer coordinates and nearly cocircular points.

    For example, compare 

            rbox 1000 W0 t | qconvex Qb2:-1e-14B2:1e-14
    with 
            rbox 1000 W0 t | qconvex
    The distributions are the same but the first is compressed to a 2e-14 slab.

  • Post-merging of coplanar facets -- In 5-d and higher, option 'Qx' (default) delays merging of coplanar facets until post-merging. This may allow "dents" to occur in the intermediate convex hulls. A point may be poorly partitioned and force a poor approximation. See option 'Qx' for further discussion.

    This is difficult to produce in 5-d and higher. Option 'Q6' turns off merging of concave facets. This is similar to 'Qx'. It may lead to serious precision errors, for example, 

            rbox 10000 W1e-13  | qhull Q6  Tv

  • Maximum facet width -- Qhull reports the maximum outer plane and inner planes (if more than roundoff error apart). There is no upper bound for either figure. This is an area for further research. Qhull does a good job of post-merging in all dimensions. Qhull does a good job of pre-merging in 2-d, 3-d, and 4-d. With the 'Qx' option, it does a good job in higher dimensions. In 5-d and higher, Qhull does poorly at detecting redundant vertices.

    In the summary ('s'), look at the ratio between the maximum facet width and the maximum width of a single merge, e.g., "(3.4x)". Qhull usually reports a ratio of four or lower in 3-d and six or lower in 4-d. If it reports a ratio greater than 10, this may indicate an implementation error. Narrow distributions (see following) may produce wide facets.

    For example, if special processing for narrow distributions is turned off ('Q10'), qhull may produce a wide facet:

             RBOX 1000 L100000 s G1e-16 t1002074964 | QHULL Tv Q10

  • Narrow distribution -- In 3-d, a narrow distribution may result in a poor approximation. For example, if you do not use qdelaunay nor option 'Qbb', the furthest-site Delaunay triangulation of nearly cocircular points may produce a poor approximation: 
             RBOX s 5000 W1e-13 D2 t1002151341 | QHULL d Qt
         RBOX 1000 s W1e-13 t1002231672 | QHULL d Tv

    During construction of the hull, a point may be above two facets with opposite orientations that span the input set. Even though the point may be nearly coplanar with both facets, and can be distant from the precise convex hull of the input sites. Additional facets leave the point distant from a facet. To fix this problem, add option 'Qbb' (it scales the last coordinate). Option 'Qbb' is automatically set for qdelaunay and qvoronoi.

    Qhull generates a warning if the initial simplex is narrow. For narrow distributions, Qhull changes how it processes coplanar points -- it does not make a point coplanar until the hull is finished. Use option 'Q10' to try Qhull without special processing for narrow distributions. For example, special processing is needed for: 

             RBOX 1000 L100000 s G1e-16 t1002074964 | QHULL Tv Q10

    You may turn off the warning message by reducing qh_WARNnarrow in user.h or by setting option 'Pp'.

    Similar problems occur for distributions with a large flat facet surrounded with many small facet at a sharp angle to the large facet. Qhull 3.1 fixes most of these problems, but a poor approximation can occur. A point may be left outside of the convex hull ('Tv'). Examples include the furthest-site Delaunay triangulation of nearly cocircular points plus the origin, and the convex hull of a cone of nearly cocircular points. The width of the band is 10^-13. 

            rbox s 1000 W1e-13 P0 D2 t996799242 | qhull d Tv
        rbox 1000 s Z1 G1e-13 t1002152123 | qhull Tv
        RBOX 1000 s Z1 G1e-13 t1002231668 | QHULL Tv

  • Quadratic running time -- If the output contains large, non-simplicial facets, the running time for Qhull may be quadratic in the size of the triangulated output. For example, RBOX 1000 s W1e-13 c G2 | QHULL d is 4 times faster for 500 points. The convex hull contains two large nearly spherical facets and many nearly coplanar facets. Each new point retriangulates the spherical facet and repartitions the remaining points into all of the nearly coplanar facets. In this case, quadratic running time is avoided if you use qdelaunay, add option 'Qbb', or add the origin ('P0') to the input.

  • Facet with zero-area -- It is possible for a zero-area facet to be convex with its neighbors. This can occur if the hyperplanes of neighboring facets are above the facet's centrum, and the facet's hyperplane is above the neighboring centrums. Qhull computes the facet's hyperplane so that it passes through the facet's vertices. The vertices can be collinear.

  • No more facets -- Qhull reports an error if there are d+1 facets left and two of the facets are not clearly convex. This typically occurs when the convexity constraints are too strong or the input points are degenerate. The former is more likely in 5-d and higher -- especially with option 'C-n'.

  • Deleted cone -- Lots of merging can end up deleting all of the new facets for a point. This is a rare event that has only been seen while debugging the code.

  • Triangulated output leads to precision problems -- With sufficient merging, the ridges of a non-simplicial facet may have serious topological and geometric problems. A ridge may be between more than two neighboring facets. If so, their triangulation ('Qt') will fail since two facets have the same vertex set. Furthermore, a triangulated facet may have flipped orientation compared to its neighbors.

    • The triangulation process detects degenerate facets with only two neighbors. These are marked degenerate. They have zero area.

  • Coplanar points -- Option 'Qc' is determined by qh_check_maxout() after constructing the hull. Qhull needs to retain all possible coplanar points in the facets' coplanar sets. This depends on qh_RATIOnearInside in user.h. Furthermore, the cutoff for a coplanar point is arbitrarily set at the minimum vertex. If coplanar points are important to your application, remove the interior points by hand (set 'Qc Qi') or make qh_RATIOnearInside sufficiently large.

  • Maximum roundoff error -- Qhull computes the maximum roundoff error from the maximum coordinates of the point set. Usually the maximum roundoff error is a reasonable choice for all distance computations. The maximum roundoff error could be computed separately for each point or for each distance computation. This is expensive and it conflicts with option 'C-n'.

  • All flipped or upper Delaunay -- When a lot of merging occurs for Delaunay triangulations, a new point may lead to no good facets. For example, try a strong convexity constraint: 
            rbox 1000 s t993602376 | qdelaunay C-1e-3

»Joggled input

Joggled input is a simple work-around for precision problems in computational geometry ["joggle: to shake or jar slightly," Amer. Heritage Dictionary]. Other names are jostled input or random perturbation. Qhull joggles the input by modifying each coordinate by a small random quantity. If a precision problem occurs, Qhull joggles the input with a larger quantity and the algorithm is restarted. This process continues until no precision problems occur. Unless all inputs incur precision problems, Qhull will terminate. Qhull adjusts the inner and outer planes to account for the joggled input.

Neither joggle nor merged facets has an upper bound for the width of the output facets, but both methods work well in practice. Joggled input is easier to justify. Precision errors occur when the points are nearly singular. For example, four points may be coplanar or three points may be collinear. Consider a line and an incident point. A precision error occurs if the point is within some epsilon of the line. Now joggle the point away from the line by a small, uniformly distributed, random quantity. If the point is changed by more than epsilon, the precision error is avoided. The probability of this event depends on the maximum joggle. Once the maximum joggle is larger than epsilon, doubling the maximum joggle will halve the probability of a precision error.

With actual data, an analysis would need to account for each point changing independently and other computations. It is easier to determine the probabilities empirically ('TRn') . For example, consider computing the convex hull of the unit cube centered on the origin. The arithmetic has 16 significant decimal digits.

Convex hull of unit cube

joggle error prob.
1.0e-15 0.983
2.0e-15 0.830
4.0e-15 0.561
8.0e-15 0.325
1.6e-14 0.185
3.2e-14 0.099
6.4e-14 0.051
1.3e-13 0.025
2.6e-13 0.010
5.1e-13 0.004
1.0e-12 0.002
2.0e-12 0.001

A larger joggle is needed for multiple points. Since the number of potential singularities increases, the probability of one or more precision errors increases. Here is an example.

Convex hull of 1000 points on unit cube

joggle error prob.
1.0e-12 0.870
2.0e-12 0.700
4.0e-12 0.450
8.0e-12 0.250
1.6e-11 0.110
3.2e-11 0.065
6.4e-11 0.030
1.3e-10 0.010
2.6e-10 0.008
5.1e-09 0.003

Other distributions behave similarly. No distribution should behave significantly worse. In Euclidean space, the probability measure of all singularities is zero. With floating point numbers, the probability of a singularity is non-zero. With sufficient digits, the probability of a singularity is extremely small for random data. For a sufficiently large joggle, all data is nearly random data.

Qhull uses an initial joggle of 30,000 times the maximum roundoff error for a distance computation. This avoids most potential singularities. If a failure occurs, Qhull retries at the initial joggle (in case bad luck occurred). If it occurs again, Qhull increases the joggle by ten-fold and tries again. This process repeats until the joggle is a hundredth of the width of the input points. Qhull reports an error after 100 attempts. This should never happen with double-precision arithmetic. Once the probability of success is non-zero, the probability of success increases about ten-fold at each iteration. The probability of repeated failures becomes extremely small.

Merged facets produces a significantly better approximation. Empirically, the maximum separation between inner and outer facets is about 30 times the maximum roundoff error for a distance computation. This is about 2,000 times better than joggled input. Most applications though will not notice the difference.

»Exact arithmetic

Exact arithmetic may be used instead of floating point. Singularities such as coplanar points can either be handled directly or the input can be symbolically perturbed. Using exact arithmetic is slower than using floating point arithmetic and the output may take more space. Chaining a sequence of operations increases the time and space required. Some operations are difficult to do.

Clarkson's hull program and Shewchuk's triangle program are practical implementations of exact arithmetic.

Clarkson limits the input precision to about fifteen digits. This reduces the number of nearly singular computations. When a determinant is nearly singular, he uses exact arithmetic to compute a precise result.

»Approximating a convex hull

Qhull may be used for approximating a convex hull. This is particularly valuable in 5-d and higher where hulls can be immense. You can use 'Qx C-n' to merge facets as the hull is being constructed. Then use 'Cn' and/or 'An' to merge small facets during post-processing. You can print the n largest facets with option 'PAn'. You can print facets whose area is at least n with option 'PFn'. You can output the outer planes and an interior point with 'FV Fo' and then compute their intersection with 'qhalf'.

To approximate a convex hull in 6-d and higher, use post-merging with 'Wn' (e.g., qhull W1e-1 C1e-2 TF2000). Pre-merging with a convexity constraint (e.g., qhull Qx C-1e-2) often produces a poor approximation or terminates with a simplex. Option 'QbB' may help to spread out the data.

You will need to experiment to determine a satisfactory set of options. Use rbox to generate test sets quickly and Geomview to view the results. You will probably want to write your own driver for Qhull using the Qhull library. For example, you could select the largest facet in each quadrant.

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[delaunay] Qhull precision options

This section lists the precision options for Qhull. These options are indicated by an upper-case letter followed by a number.

Copyright © 1995-2012 C.B. Barber

» Programs • Options • Output • Formats • Geomview • Print • Qhull • Precision • Trace

Precision options

Most users will not need to set these options. They are best used for approximating a convex hull. They may also be used for testing Qhull's handling of precision errors.

By default, Qhull uses options 'C-0' for 2-d, 3-d and 4-d, and 'Qx' for 5-d and higher. These options use facet merging to handle precision errors. You may also use joggled input 'QJ' to avoid precision problems. For more information see Imprecision in Qhull.

 
General
Cn
centrum radius for post-merging
C-n
centrum radius for pre-merging
An
cosine of maximum angle for post-merging
A-n
cosine of maximum angle for pre-merging
Qx
exact pre-merges (allows coplanar facets)
C-0
handle all precision errors
Wn
min distance above plane for outside points
 
Experimental
Un
max distance below plane for a new, coplanar point
En
max roundoff error for distance computation
Vn
min distance above plane for a visible facet
Rn
randomly perturb computations by a factor of [1-n,1+n]

»A-n - cosine of maximum angle for pre-merging.

Pre-merging occurs while Qhull constructs the hull. It is indicated by 'C-n', 'A-n', or 'Qx'.

If the angle between a pair of facet normals is greater than n, Qhull merges one of the facets into a neighbor. It selects the facet that is closest to a neighboring facet.

For example, option 'A-0.99' merges facets during the construction of the hull. If the cosine of the angle between facets is greater than 0.99, one or the other facet is merged. Qhull accounts for the maximum roundoff error.

If 'A-n' is set without 'C-n', then 'C-0' is automatically set.

In 5-d and higher, you should set 'Qx' along with 'A-n'. It skips merges of coplanar facets until after the hull is constructed and before 'An' and 'Cn' are checked.

»An - cosine of maximum angle for post-merging.

Post merging occurs after the hull is constructed. For example, option 'A0.99' merges a facet if the cosine of the angle between facets is greater than 0.99. Qhull accounts for the maximum roundoff error.

If 'An' is set without 'Cn', then 'C0' is automatically set.

»C-0 - handle all precision errors

Qhull handles precision errors by merging facets. The 'C-0' option handles all precision errors in 2-d, 3-d, and 4-d. It is set by default. It may be used in higher dimensions, but sometimes the facet width grows rapidly. It is usually better to use 'Qx' in 5-d and higher. Use 'QJ' to joggle the input instead of merging facets. Use 'Q0' to turn both options off.

Qhull optimizes 'C-0' ("_zero-centrum") by testing vertices instead of centrums for adjacent simplices. This may be slower in higher dimensions if merges decrease the number of processed points. The optimization may be turned off by setting a small value such as 'C-1e-30'. See How Qhull handles imprecision.

»C-n - centrum radius for pre-merging

Pre-merging occurs while Qhull constructs the hull. It is indicated by 'C-n', 'A-n', or 'Qx'.

The centrum of a facet is a point on the facet for testing facet convexity. It is the average of the vertices projected to the facet's hyperplane. Two adjacent facets are convex if each centrum is clearly below the other facet.

If adjacent facets are non-convex, one of the facets is merged into a neighboring facet. Qhull merges the facet that is closest to a neighboring facet.

For option 'C-n', n is the centrum radius. For example, 'C-0.001' merges facets whenever the centrum is less than 0.001 from a neighboring hyperplane. Qhull accounts for roundoff error when testing the centrum.

In 5-d and higher, you should set 'Qx' along with 'C-n'. It skips merges of coplanar facets until after the hull is constructed and before 'An' and 'Cn' are checked.

»Cn - centrum radius for post-merging

Post-merging occurs after Qhull constructs the hull. It is indicated by 'Cn' or 'An'.

For option 'Cn', n is the centrum radius. For example, 'C0.001' merges facets when the centrum is less than 0.001 from a neighboring hyperplane. Qhull accounts for roundoff error when testing the centrum.

Both pre-merging and post-merging may be defined. If only post-merging is used ('Q0' with 'Cn'), Qhull may fail to produce a hull due to precision errors during the hull's construction.

»En - max roundoff error for distance computations

This allows the user to change the maximum roundoff error computed by Qhull. The value computed by Qhull may be overly pessimistic. If 'En' is set too small, then the output may not be convex. The statistic "max. distance of a new vertex to a facet" (from option 'Ts') is a reasonable upper bound for the actual roundoff error.

»Rn - randomly perturb computations

This option perturbs every distance, hyperplane, and angle computation by up to (+/- n * max_coord). It simulates the effect of roundoff errors. Unless 'En' is explicitly set, it is adjusted for 'Rn'. The command 'qhull Rn' will generate a convex hull despite the perturbations. See the Examples section for an example.

Options 'Rn C-n' have the effect of 'W2n' and 'C-2n'. To use time as the random number seed, use option 'QR-1'.

»Un - max distance for a new, coplanar point

This allows the user to set coplanarity. When pre-merging ('C-n ', 'A-n' or 'Qx'), Qhull merges a new point into any coplanar facets. The default value for 'Un' is 'Vn'.

»Vn - min distance for a visible facet

This allows the user to set facet visibility. When adding a point to the convex hull, Qhull determines all facets that are visible from the point. A facet is visible if the distance from the point to the facet is greater than 'Vn'.

Without merging, the default value for 'Vn' is the roundoff error ('En'). With merging, the default value is the pre-merge centrum ('C-n') in 2-d or 3-d, or three times that in other dimensions. If the outside width is specified with option 'Wn ', the maximum, default value for 'Vn' is 'Wn'.

Qhull warns if 'Vn' is greater than 'Wn' and furthest outside ('Qf') is not selected; this combination usually results in flipped facets (i.e., reversed normals).

»Wn - min distance above plane for outside points

Points are added to the convex hull only if they are clearly outside of a facet. A point is outside of a facet if its distance to the facet is greater than 'Wn'. Without pre-merging, the default value for 'Wn' is 'En '. If the user specifies pre-merging and does not set 'Wn', than 'Wn' is set to the maximum of 'C-n' and maxcoord*(1 - A-n).

This option is good for approximating a convex hull.

Options 'Qc' and 'Qi' use the minimum vertex to distinguish coplanar points from interior points.

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[delaunay] Qhull format options (F)

This section lists the format options for Qhull. These options are indicated by 'F' followed by a letter. See Output, Print, and Geomview for other output options.

Copyright © 1995-2012 C.B. Barber

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Additional input & output formats

These options allow for automatic processing of Qhull output. Options 'i', 'o', 'n', and 'p' may also be used.

Summary and control
FA
compute total area and volume for option 's'
FV
print average vertex (interior point for 'qhalf')
FQ
print command for qhull and input
FO
print options to stderr or stdout
FS
print sizes: total area and volume
Fs
print summary: dim, #points, total vertices and facets, #vertices, #facets, max outer and inner plane
Fd
use format for input (offset first)
FD
use cdd format for normals (offset first)
FM
print Maple output (2-d and 3-d)
Facets, points, and vertices
Fa
print area for each facet
FC
print centrum for each facet
Fc
print coplanar points for each facet
Fx
print extreme points (i.e., vertices) of convex hull.
FF
print facets w/o ridges
FI
print ID for each facet
Fi
print inner planes for each facet
Fm
print merge count for each facet (511 max)
FP
print nearest vertex for coplanar points
Fn
print neighboring facets for each facet
FN
print neighboring facets for each point
Fo
print outer planes for each facet
Ft
print triangulation with added points
Fv
print vertices for each facet
Delaunay, Voronoi, and halfspace
Fx
print extreme input sites of Delaunay triangulation or Voronoi diagram.
Fp
print points at halfspace intersections
Fi
print separating hyperplanes for inner, bounded Voronoi regions
Fo
print separating hyperplanes for outer, unbounded Voronoi regions
Fv
print Voronoi diagram as ridges for each input pair
FC
print Voronoi vertex ("center") for each facet

»Fa - print area for each facet

The first line is the number of facets. The remaining lines are the area for each facet, one facet per line. See 'FA' and 'FS' for computing the total area and volume.

Use 'PAn' for printing the n largest facets. Use option 'PFn' for printing facets larger than n.

For Delaunay triangulations, the area is the area of each Delaunay triangle. For Voronoi vertices, the area is the area of the dual facet to each vertex.

Qhull uses the centrum and ridges to triangulate non-simplicial facets. The area for non-simplicial facets is the sum of the areas for each triangle. It is an approximation of the actual area. The ridge's vertices are projected to the facet's hyperplane. If a vertex is far below a facet (qh_WIDEcoplanar in user.h), the corresponding triangles are ignored.

For non-simplicial facets, vertices are often below the facet's hyperplane. If so, the approximation is less than the actual value and it may be significantly less.

»FA - compute total area and volume for option 's'

With option 'FA', Qhull includes the total area and volume in the summary ('s'). Option 'FS' also includes the total area and volume. If facets are merged, the area and volume are approximations. Option 'FA' is automatically set for options 'Fa', 'PAn', and 'PFn'.

With 'qdelaunay s FA', Qhull computes the total area of the Delaunay triangulation. This equals the volume of the convex hull of the data points. With options 'qdelaunay Qu s FA', Qhull computes the total area of the furthest-site Delaunay triangulation. This equals of the total area of the Delaunay triangulation.

See 'Fa' for further details. Option 'FS' also computes the total area and volume.

»Fc - print coplanar points for each facet

The output starts with the number of facets. Then each facet is printed one per line. Each line is the number of coplanar points followed by the point ids.

By default, option 'Fc' reports coplanar points ('Qc'). You may also use option 'Qi'. Options 'Qi Fc' prints interior points while 'Qci Fc' prints both coplanar and interior points.

Each coplanar point or interior point is assigned to the facet it is furthest above (resp., least below).

Use 'Qc p' to print vertex and coplanar point coordinates. Use 'Fv' to print vertices.

»FC - print centrum or Voronoi vertex for each facet

The output starts with the dimension followed by the number of facets. Then each facet centrum is printed, one per line. For qvoronoi, Voronoi vertices are printed instead.

»Fd - use cdd format for input

The input starts with comments. The first comment is reported in the summary. Data starts after a "begin" line. The next line is the number of points followed by the dimension plus one and "real" or "integer". Then the points are listed with a leading "1" or "1.0". The data ends with an "end" line.

For halfspaces ('qhalf Fd'), the input format is the same. Each halfspace starts with its offset. The signs of the offset and coefficients are the opposite of Qhull's convention. The first two lines of the input may be an interior point in 'FV' format.

»FD - use cdd format for normals

Option 'FD' prints normals ('n', 'Fo', 'Fi') or points ('p') in cdd format. The first line is the command line that invoked Qhull. Data starts with a "begin" line. The next line is the number of normals or points followed by the dimension plus one and "real". Then the normals or points are listed with the offset before the coefficients. The offset for points is 1.0. For normals, the offset and coefficients use the opposite sign from Qhull. The data ends with an "end" line.

»FF - print facets w/o ridges

Option 'FF' prints all fields of all facets (as in 'f') without printing the ridges. This is useful in higher dimensions where a facet may have many ridges. For simplicial facets, options 'FF' and 'f ' are equivalent.

»Fi - print inner planes for each facet

The first line is the dimension plus one. The second line is the number of facets. The remainder is one inner plane per line. The format is the same as option 'n'.

The inner plane is a plane that is below the facet's vertices. It is an offset from the facet's hyperplane. It includes a roundoff error for computing the vertex distance.

Note that the inner planes for Geomview output ('Gi') include an additional offset for vertex visualization and roundoff error.

»Fi - print separating hyperplanes for inner, bounded Voronoi regions

With qvoronoi, 'Fi' prints the separating hyperplanes for inner, bounded regions of the Voronoi diagram. The first line is the number of ridges. Then each hyperplane is printed, one per line. A line starts with the number of indices and floats. The first pair of indices indicates an adjacent pair of input sites. The next d floats are the normalized coefficients for the hyperplane, and the last float is the offset. The hyperplane is oriented toward 'QVn' (if defined), or the first input site of the pair.

Use 'Fo' for unbounded regions, and 'Fv' for the corresponding Voronoi vertices.

Use 'Tv' to verify that the hyperplanes are perpendicular bisectors. It will list relevant statistics to stderr. The hyperplane is a perpendicular bisector if the midpoint of the input sites lies on the plane, all Voronoi vertices in the ridge lie on the plane, and the angle between the input sites and the plane is ninety degrees. This is true if all statistics are zero. Roundoff and computation errors make these non-zero. The deviations appear to be largest when the corresponding Delaunay triangles are large and thin; for example, the Voronoi diagram of nearly cospherical points.

»FI - print ID for each facet

Print facet identifiers. These are used internally and listed with options 'f' and 'FF'. Options 'Fn ' and 'FN' use facet identifiers for negative indices.

»Fm - print merge count for each facet

The first line is the number of facets. The remainder is the number of merges for each facet, one per line. At most 511 merges are reported for a facet. See 'PMn' for printing the facets with the most merges.

»FM - print Maple output

Qhull writes a Maple file for 2-d and 3-d convex hulls, 2-d and 3-d halfspace intersections, and 2-d Delaunay triangulations. Qhull produces a 2-d or 3-d plot.

Warning: This option has not been tested in Maple.

[From T. K. Abraham with help from M. R. Feinberg and N. Platinova.] The following steps apply while working within the Maple worksheet environment :

  1. Generate the data and store it as an array . For example, in 3-d, data generated in Maple is of the form : x[i],y[i],z[i]

  2. Create a single variable and assign the entire array of data points to this variable. Use the "seq" command within square brackets as shown in the following example. (The square brackets are essential for the rest of the steps to work.)

    >data:=[seq([x[i],y[i],z[i]],i=1..n)]:# here n is the number of data points

  3. Next we need to write the data to a file to be read by qhull. Before writing the data to a file, make sure that the qhull executable files and the data file lie in the same subdirectory. If the executable files are stored in the "C:\qhull3.1\" subdirectory, then save the file in the same subdirectory, say "C:\qhull3.1\datafile.txt". For the sake of integrity of the data file , it is best to first ensure that the data file does not exist before writing into the data file. This can be done by running a delete command first . To write the data to the file, use the "writedata" and the "writedata[APPEND]" commands as illustrated in the following example :

    >system("del c:\\qhull3.1\\datafile.txt");#To erase any previous versions of the file
    >writedata("c:\\qhull3.1\\datafile.txt ",[3, nops(data)]);#writing in qhull format
    >writedata[APPEND]("c:\\ qhull3.1\\datafile.txt ", data);#writing the data points

  4. Use the 'FM' option to produce Maple output. Store the output as a ".mpl" file. For example, using the file we created above, we type the following (in DOS environment)

    qconvex s FM <datafile.txt >dataplot.mpl

  5. To read 3-d output in Maple, we use the 'read' command followed by a 'display3d' command. For example (in Maple environment):

    >with (plots):
    >read `c:\\qhull3.1\\dataplot.mpl`:#IMPORTANT - Note that the punctuation mark used is ' and NOT '. The correct punctuation mark is the one next to the key for "1" (not the punctuation mark near the enter key)
    > qhullplot:=%:
    > display3d(qhullplot);

For Delaunay triangulation orthogonal projection is better.

For halfspace intersections, Qhull produces the dual convex hull.

See Is Qhull available for Maple? for other URLs.

»Fn - print neighboring facets for each facet

The output starts with the number of facets. Then each facet is printed one per line. Each line is the number of neighbors followed by an index for each neighbor. The indices match the other facet output formats.

For simplicial facets, each neighbor is opposite the corresponding vertex (option 'Fv'). Do not compare to option 'i'. Option 'i' orients facets by reversing the order of two vertices. For non-simplicial facets, the neighbors are unordered.

A negative index indicates an unprinted facet due to printing only good facets ('Pg', qdelaunay, qvoronoi). It is the negation of the facet's ID (option 'FI'). For example, negative indices are used for facets "at infinity" in the Delaunay triangulation.

»FN - print neighboring facets for each point

The first line is the number of points. Then each point is printed, one per line. For unassigned points (either interior or coplanar), the line is "0". For assigned coplanar points ('Qc'), the line is "1" followed by the index of the facet that is furthest below the point. For assigned interior points ('Qi'), the line is "1" followed by the index of the facet that is least above the point. For vertices that do not belong to good facet, the line is "0"

For vertices of good facets, the line is the number of neighboring facets followed by the facet indices. The indices correspond to the other 'F' formats. In 4-d and higher, the facets are sorted by index. In 3-d, the facets are in adjacency order (not oriented).

A negative index indicates an unprinted facet due to printing only good facets (qdelaunay, qvoronoi, 'Pdk', 'Pg'). It is the negation of the facet's ID (' FI'). For example, negative indices are used for facets "at infinity" in the Delaunay triangulation.

For Voronoi vertices, option 'FN' lists the vertices of the Voronoi region for each input site. Option 'FN' lists the regions in site ID order. Option 'FN' corresponds to the second half of option 'o'. To convert from 'FN' to 'o', replace negative indices with zero and increment non-negative indices by one.

If you are using the Qhull library or C++ interface, option 'FN' has the side effect of reordering the neighbors for a vertex

»Fo - print outer planes for each facet

The first line is the dimension plus one. The second line is the number of facets. The remainder is one outer plane per line. The format is the same as option 'n'.

The outer plane is a plane that is above all points. It is an offset from the facet's hyperplane. It includes a roundoff error for computing the point distance. When testing the outer plane (e.g., 'Tv'), another roundoff error should be added for the tested point.

If outer planes are not checked ('Q5') or not computed (!qh_MAXoutside), the maximum, computed outside distance is used instead. This can be much larger than the actual outer planes.

Note that the outer planes for Geomview output ('G') include an additional offset for vertex/point visualization, 'lines closer,' and roundoff error.

»Fo - print separating hyperplanes for outer, unbounded Voronoi regions

With qvoronoi, 'Fo' prints the separating hyperplanes for outer, unbounded regions of the Voronoi diagram. The first line is the number of ridges. Then each hyperplane is printed, one per line. A line starts with the number of indices and floats. The first pair of indices indicates an adjacent pair of input sites. The next d floats are the normalized coefficients for the hyperplane, and the last float is the offset. The hyperplane is oriented toward 'QVn' (if defined), or the first input site of the pair.

Option 'Fo' gives the hyperplanes for the unbounded rays of the unbounded regions of the Voronoi diagram. Each hyperplane goes through the midpoint of the corresponding input sites. The rays are directed away from the input sites.

Use 'Fi' for bounded regions, and 'Fv' for the corresponding Voronoi vertices. Use 'Tv' to verify that the corresponding Voronoi vertices lie on the hyperplane.

»FO - print list of selected options

Lists selected options and default values to stderr. Additional 'FO's are printed to stdout.

»Fp - print points at halfspace intersections

The first line is the number of intersection points. The remainder is one intersection point per line. A intersection point is the intersection of d or more halfspaces from 'qhalf'. It corresponds to a facet of the dual polytope. The "infinity" point [-10.101,-10.101,...] indicates an unbounded intersection.

If [x,y,z] are the dual facet's normal coefficients and b<0 is its offset, the halfspace intersection occurs at [x/-b,y/-b,z/-b] plus the interior point. If b>=0, the halfspace intersection is unbounded.

»FP - print nearest vertex for coplanar points

The output starts with the number of coplanar points. Then each coplanar point is printed one per line. Each line is the point ID of the closest vertex, the point ID of the coplanar point, the corresponding facet ID, and the distance. Sort the lines to list the coplanar points nearest to each vertex.

Use options 'Qc' and/or 'Qi' with 'FP'. Options 'Qc FP' prints coplanar points while 'Qci FP' prints coplanar and interior points. Option 'Qc' is automatically selected if 'Qi' is not selected.

For Delaunay triangulations (qdelaunay or qvoronoi), a coplanar point is nearly incident to a vertex. The distance is the distance in the original point set.

If imprecision problems are severe, Qhull will delete input sites when constructing the Delaunay triangulation. Option 'FP' will list these points along with coincident points.

If there are many coplanar or coincident points and non-simplicial facets are triangulated ('Qt'), option 'FP' may be inefficient. It redetermines the original vertex set for each coplanar point.

»FQ - print command for qhull and input

Prints qhull and input command, e.g., "rbox 10 s | qhull FQ". Option 'FQ' may be repeated multiple times.

»Fs - print summary

The first line consists of number of integers ("10") followed by the:

  • dimension
  • number of points
  • number of vertices
  • number of facets
  • number of vertices selected for output
  • number of facets selected for output
  • number of coplanar points for selected facets
  • number of nonsimplicial or merged facets selected for output
  • number of deleted vertices
  • number of triangulated facets ('Qt')

The second line consists of the number of reals ("2") followed by the:

  • maximum offset to an outer plane
  • minimum offset to an inner plane.
Roundoff and joggle are included.

For Delaunay triangulations and Voronoi diagrams, the number of deleted vertices should be zero. If greater than zero, then the input is highly degenerate and coplanar points are not necessarily coincident points. For example, 'RBOX 1000 s W1e-13 t995138628 | QHULL d Qbb' reports deleted vertices; the input is nearly cospherical.

Later versions of Qhull may produce additional integers or reals.

»FS - print sizes

The first line consists of the number of integers ("0"). The second line consists of the number of reals ("2"), followed by the total facet area, and the total volume. Later versions of Qhull may produce additional integers or reals.

The total volume measures the volume of the intersection of the halfspaces defined by each facet. It is computed from the facet area. Both area and volume are approximations for non-simplicial facets. See option 'Fa ' for further notes. Option 'FA ' also computes the total area and volume.

»Ft - print triangulation

Prints a triangulation with added points for non-simplicial facets. The output is

  • The first line is the dimension
  • The second line is the number of points, the number of facets, and the number of ridges.
  • All of the input points follow, one per line.
  • The centrums follow, one per non-simplicial facet
  • Then the facets follow as a list of point indices preceded by the number of points. The simplices are oriented.

For convex hulls with simplicial facets, the output is the same as option 'o'.

The added points are the centrums of the non-simplicial facets. Except for large facets, the centrum is the average vertex coordinate projected to the facet's hyperplane. Large facets may use an old centrum to avoid recomputing the centrum after each merge. In either case, the centrum is clearly below neighboring facets. See Precision issues.

The new simplices will not be clearly convex with their neighbors and they will not satisfy the Delaunay property. They may even have a flipped orientation. Use triangulated input ('Qt') for Delaunay triangulations.

For Delaunay triangulations with simplicial facets, the output is the same as option 'o' without the lifted coordinate. Since 'Ft' is invalid for merged Delaunay facets, option 'Ft' is not available for qdelaunay or qvoronoi. It may be used with joggled input ('QJ') or triangulated output ('Qt'), for example, rbox 10 c G 0.01 | qhull d QJ Ft

If you add a point-at-infinity with 'Qz', it is printed after the input sites and before any centrums. It will not be used in a Delaunay facet.

»Fv - print vertices for each facet

The first line is the number of facets. Then each facet is printed, one per line. Each line is the number of vertices followed by the corresponding point ids. Vertices are listed in the order they were added to the hull (the last one added is the first listed).

Option 'i' also lists the vertices, but it orients facets by reversing the order of two vertices. Option 'i' triangulates non-simplicial, 4-d and higher facets by adding vertices for the centrums.

»Fv - print Voronoi diagram

With qvoronoi, 'Fv' prints the Voronoi diagram or furthest-site Voronoi diagram. The first line is the number of ridges. Then each ridge is printed, one per line. The first number is the count of indices. The second pair of indices indicates a pair of input sites. The remaining indices list the corresponding ridge of Voronoi vertices. Vertex 0 is the vertex-at-infinity. It indicates an unbounded ray.

All vertices of a ridge are coplanar. If the ridge is unbounded, add the midpoint of the pair of input sites. The unbounded ray is directed from the Voronoi vertices to infinity.

Use 'Fo' for separating hyperplanes of outer, unbounded regions. Use 'Fi' for separating hyperplanes of inner, bounded regions.

Option 'Fv' does not list ridges that require more than one midpoint. For example, the Voronoi diagram of cospherical points lists zero ridges (e.g., 'rbox 10 s | qvoronoi Fv Qz'). Other examples are the Voronoi diagrams of a rectangular mesh (e.g., 'rbox 27 M1,0 | qvoronoi Fv') or a point set with a rectangular corner (e.g., 'rbox P4,4,4 P4,2,4 P2,4,4 P4,4,2 10 | qvoronoi Fv'). Both cases miss unbounded rays at the corners. To determine these ridges, surround the points with a large cube (e.g., 'rbox 10 s c G2.0 | qvoronoi Fv Qz'). The cube needs to be large enough to bound all Voronoi regions of the original point set. Please report any other cases that are missed. If you can formally describe these cases or write code to handle them, please send email to qhull@qhull.org.

»FV - print average vertex

The average vertex is the average of all vertex coordinates. It is an interior point for halfspace intersection. The first line is the dimension and "1"; the second line is the coordinates. For example,

qconvex FV n | qhalf Fp

prints the extreme points of the original point set (roundoff included).

»Fx - print extreme points (vertices) of convex hulls and Delaunay triangulations

The first line is the number of points. The following lines give the index of the corresponding points. The first point is '0'.

In 2-d, the extreme points (vertices) are listed in counterclockwise order (by qh_ORIENTclock in user.h).

In 3-d and higher convex hulls, the extreme points (vertices) are sorted by index. This is the same order as option 'p' when it doesn't include coplanar or interior points.

For Delaunay triangulations, 'Fx' lists the extreme points of the input sites (i.e., the vertices of their convex hull). The points are unordered.

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[delaunay] Qhull Geomview options (G)

This section lists the Geomview options for Qhull. These options are indicated by 'G' followed by a letter. See Output, Print, and Format for other output options.

Copyright © 1995-2012 C.B. Barber

» Programs • Options • Output • Formats • Geomview • Print • Qhull • Precision • Trace

Geomview output options

Geomview is the graphical viewer for visualizing Qhull output in 2-d, 3-d and 4-d.

Geomview displays each facet of the convex hull. The color of a facet is determined by the coefficients of the facet's normal equation. For imprecise hulls, Geomview displays the inner and outer hull. Geomview can also display points, ridges, vertices, coplanar points, and facet intersections.

For 2-d Delaunay triangulations, Geomview displays the corresponding paraboloid. Geomview displays the 2-d Voronoi diagram. For halfspace intersections, it displays the dual convex hull.

 
General
G
display Geomview output
Gt
display transparent 3-d Delaunay triangulation
GDn
drop dimension n in 3-d and 4-d output
 
 
Specific
Ga
display all points as dots
Gc
display centrums (2-d, 3-d)
Gp
display coplanar points and vertices as radii
Gh
display hyperplane intersections
Gi
display inner planes only (2-d, 3-d)
Go
display outer planes only (2-d, 3-d)
Gr
display ridges (3-d)
Gv
display vertices as spheres
Gn
do not display planes

»G - produce output for viewing with Geomview

By default, option 'G' displays edges in 2-d, outer planes in 3-d, and ridges in 4-d.

A ridge can be explicit or implicit. An explicit ridge is a (d-1)-dimensional simplex between two facets. In 4-d, the explicit ridges are triangles. An implicit ridge is the topological intersection of two neighboring facets. It is the union of explicit ridges.

For non-simplicial 4-d facets, the explicit ridges can be quite complex. When displaying a ridge in 4-d, Qhull projects the ridge's vertices to one of its facets' hyperplanes. Use 'Gh' to project ridges to the intersection of both hyperplanes. This usually results in a cleaner display.

For 2-d Delaunay triangulations, Geomview displays the corresponding paraboloid. Geomview displays the 2-d Voronoi diagram. For halfspace intersections, it displays the dual convex hull.

»Ga - display all points as dots

Each input point is displayed as a green dot.

»Gc - display centrums (3-d)

The centrum is defined by a green radius sitting on a blue plane. The plane corresponds to the facet's hyperplane. If you sight along a facet's hyperplane, you will see that all neighboring centrums are below the facet. The radius is defined by 'C-n' or 'Cn'.

»GDn - drop dimension n in 3-d and 4-d output

The result is a 2-d or 3-d object. In 4-d, this corresponds to viewing the 4-d object from the nth axis without perspective. It's best to view 4-d objects in pieces. Use the 'Pdk' 'Pg' 'PG' 'QGn' and 'QVn' options to select a few facets. If one of the facets is perpendicular to an axis, then projecting along that axis will show the facet exactly as it is in 4-d. If you generate many facets, use Geomview's ginsu module to view the interior

To view multiple 4-d dimensions at once, output the object without 'GDn' and read it with Geomview's ndview. As you rotate the object in one set of dimensions, you can see how it changes in other sets of dimensions.

For additional control over 4-d objects, output the object without 'GDn' and read it with Geomview's 4dview. You can slice the object along any 4-d plane. You can also flip the halfspace that's deleted when slicing. By combining these features, you can get some interesting cross sections.

»Gh - display hyperplane intersections (3-d, 4-d)

In 3-d, the intersection is a black line. It lies on two neighboring hyperplanes, c.f., the blue squares associated with centrums ('Gc '). In 4-d, the ridges are projected to the intersection of both hyperplanes. If you turn on edges (Geomview's 'appearances' menu), each triangle corresponds to one ridge. The ridges may overlap each other.

»Gi - display inner planes only (2-d, 3-d)

The inner plane of a facet is below all of its vertices. It is parallel to the facet's hyperplane. The inner plane's color is the opposite of the outer plane's color, i.e., [1-r,1-g,1-b] . Its edges are determined by the vertices.

»Gn - do not display planes

By default, Geomview displays the precise plane (no merging) or both inner and output planes (if merging). If merging, Geomview does not display the inner plane if the the difference between inner and outer is too small.

»Go - display outer planes only (2-d, 3-d)

The outer plane of a facet is above all input points. It is parallel to the facet's hyperplane. Its color is determined by the facet's normal, and its edges are determined by the vertices.

»Gp - display coplanar points and vertices as radii

Coplanar points ('Qc'), interior points ('Qi'), outside points ('TCn' or 'TVn'), and vertices are displayed as red and yellow radii. The radii are perpendicular to the corresponding facet. Vertices are aligned with an interior point. The radii define a ball which corresponds to the imprecision of the point. The imprecision is the maximum of the roundoff error, the centrum radius, and maxcoord * (1 - A-n). It is at least 1/20'th of the maximum coordinate, and ignores post merging if pre-merging is done.

If 'Gv' (print vertices as spheres) is also selected, option 'Gp' displays coplanar points as radii. Select options Qc' and/or 'Qi'. Options 'Qc Gpv' displays coplanar points while 'Qci Gpv' displays coplanar and interior points. Option 'Qc' is automatically selected if 'Qi' is not selected with options 'Gpv'.

»Gr - display ridges (3-d)

A ridge connects the two vertices that are shared by neighboring facets. It is displayed in green. A ridge is the topological edge between two facets while the hyperplane intersection is the geometric edge between two facets. Ridges are always displayed in 4-d.

»Gt - transparent 3-d Delaunay

A 3-d Delaunay triangulation looks like a convex hull with interior facets. Option 'Gt' removes the outside ridges to reveal the outermost facets. It automatically sets options 'Gr' and 'GDn'. See example eg.17f.delaunay.3.

»Gv - display vertices as spheres (2-d, 3-d)

The radius of the sphere corresponds to the imprecision of the data. See 'Gp' for determining the radius.

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[delaunay] Qhull output options

This section lists the output options for Qhull. These options are indicated by lower case characters. See Formats, Print, and Geomview for other output options.

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Output options

Qhull prints its output to standard out. All output is printed text. The default output is a summary (option 's'). Other outputs may be specified as follows.

f
print all fields of all facets
n
print hyperplane normals with offsets
m
print Mathematica output (2-d and 3-d)
o
print OFF file format (dim, points and facets)
s
print summary to stderr
p
print vertex and point coordinates
i
print vertices incident to each facet
 
 
Related options
F
additional input/output formats
G
Geomview output
P
Print options
Ft
print triangulation with added points
 

»f - print all fields of all facets

Print all fields of all facets. The facet is the primary data structure for Qhull.

Option 'f' is for debugging. Most of the fields are available via the 'F' options. If you need specialized information from Qhull, you can use the Qhull library or C++ interface.

Use the 'FF' option to print the facets but not the ridges.

»i - print vertices incident to each facet

The first line is the number of facets. The remaining lines list the vertices for each facet, one facet per line. The indices are 0-relative indices of the corresponding input points. The facets are oriented. Option 'Fv' displays an unoriented list of vertices with a vertex count per line. Options 'o' and 'Ft' displays coordinates for each vertex prior to the vertices for each facet.

Simplicial facets (e.g., triangles in 3-d) consist of d vertices. Non-simplicial facets in 3-d consist of 4 or more vertices. For example, a facet of a cube consists of 4 vertices. Use option 'Qt' to triangulate non-simplicial facets.

For 4-d and higher convex hulls and 3-d and higher Delaunay triangulations, d vertices are listed for all facets. A non-simplicial facet is triangulated with its centrum and each ridge. The index of the centrum is higher than any input point. Use option 'Fv' to list the vertices of non-simplicial facets as is. Use option 'Ft' to print the coordinates of the centrums as well as those of the input points.

»m - print Mathematica output

Qhull writes a Mathematica file for 2-d and 3-d convex hulls, 2-d and 3-d halfspace intersections, and 2-d Delaunay triangulations. Qhull produces a list of objects that you can assign to a variable in Mathematica, for example: "list= << <outputfilename> ". If the object is 2-d, it can be visualized by "Show[Graphics[list]] ". For 3-d objects the command is "Show[Graphics3D[list]] ". Now the object can be manipulated by commands of the form "Show[%, <parametername> -> <newvalue>]".

For Delaunay triangulation orthogonal projection is better. This can be specified, for example, by "BoxRatios: Show[%, BoxRatios -> {1, 1, 1e-8}]". To see the meaningful side of the 3-d object used to visualize 2-d Delaunay, you need to change the viewpoint: "Show[%, ViewPoint -> {0, 0, -1}]". By specifying different viewpoints you can slowly rotate objects.

For halfspace intersections, Qhull produces the dual convex hull.

See Is Qhull available for Mathematica? for URLs.

»n - print hyperplane normals with offsets

The first line is the dimension plus one. The second line is the number of facets. The remaining lines are the normals for each facet, one normal per line. The facet's offset follows its normal coefficients.

The normals point outward, i.e., the convex hull satisfies Ax <= -b where A is the matrix of coefficients and b is the vector of offsets.

If cdd output is specified ('FD'), Qhull prints the command line, the keyword "begin", the number of facets, the dimension (plus one), the keyword "real", and the normals for each facet. The facet's negative offset precedes its normal coefficients (i.e., if the origin is an interior point, the offset is positive). Qhull ends the output with the keyword "end".

»o - print OFF file format

The output is:

  • The first line is the dimension
  • The second line is the number of points, the number of facets, and the number of ridges.
  • All of the input points follow, one per line.
  • Then Qhull prints the vertices for each facet. Each facet is on a separate line. The first number is the number of vertices. The remainder is the indices of the corresponding points. The vertices are oriented in 2-d, 3-d, and in simplicial facets.

Option 'Ft' prints the same information with added points for non-simplicial facets.

Option 'i' displays vertices without the point coordinates. Option 'p' displays the point coordinates without vertex and facet information.

In 3-d, Geomview can load the file directly if you delete the first line (e.g., by piping through 'tail +2').

For Voronoi diagrams (qvoronoi), option 'o' prints Voronoi vertices and Voronoi regions instead of input points and facets. The first vertex is the infinity vertex [-10.101, -10.101, ...]. Then, option 'o' lists the vertices in the Voronoi region for each input site. The regions appear in site ID order. In 2-d, the vertices of a Voronoi region are sorted by adjacency (non-oriented). In 3-d and higher, the Voronoi vertices are sorted by index. See the 'FN' option for listing Voronoi regions without listing Voronoi vertices.

If you are using the Qhull library, options 'v o' have the side effect of reordering the neighbors for a vertex.

»p - print vertex and point coordinates

The first line is the dimension. The second line is the number of vertices. The remaining lines are the vertices, one vertex per line. A vertex consists of its point coordinates

With the 'Gc' and 'Gi' options, option 'p' also prints coplanar and interior points respectively.

For qvoronoi, it prints the coordinates of each Voronoi vertex.

For qdelaunay, it prints the input sites as lifted to a paraboloid. For qhalf it prints the dual points. For both, option 'p' is the same as the first section of option 'o'.

Use 'Fx' to list the point ids of the extreme points (i.e., vertices).

If a subset of the facets is selected ('Pdk', 'PDk', 'Pg' options), option 'p' only prints vertices and points associated with those facets.

If cdd-output format is selected ('FD'), the first line is "begin". The second line is the number of vertices, the dimension plus one, and "real". The vertices follow with a leading "1". Output ends with "end".

»s - print summary to stderr

The default output of Qhull is a summary to stderr. Options 'FS' and 'Fs' produce the same information for programs. Note: Windows 95 and 98 treats stderr the same as stdout. Use option 'TO file' to separate stderr and stdout.

The summary lists the number of input points, the dimension, the number of vertices in the convex hull, and the number of facets in the convex hull. It lists the number of selected ("good") facets for options 'Pg', 'Pdk', qdelaunay, or qvoronoi (Delaunay triangulations only use the lower half of a convex hull). It lists the number of coplanar points. For Delaunay triangulations without 'Qc', it lists the total number of coplanar points. It lists the number of simplicial facets in the output.

The terminology depends on the output structure.

The summary lists these statistics:

  • number of points processed by Qhull
  • number of hyperplanes created
  • number of distance tests (not counting statistics, summary, and checking)
  • number of merged facets (if any)
  • number of distance tests for merging (if any)
  • CPU seconds to compute the hull
  • the maximum joggle for 'QJ'
    or, the probability of precision errors for 'QJ TRn'
  • total area and volume (if computed, see 'FS' 'FA' 'Fa' 'PAn')
  • max. distance of a point above a facet (if non-zero)
  • max. distance of a vertex below a facet (if non-zero)

The statistics include intermediate hulls. For example 'rbox d D4 | qhull' reports merged facets even though the final hull is simplicial.

Qhull starts counting CPU seconds after it has read and projected the input points. It stops counting before producing output. In the code, CPU seconds measures the execution time of function qhull() in libqhull.c. If the number of CPU seconds is clearly wrong, check qh_SECticks in user.h.

The last two figures measure the maximum distance from a point or vertex to a facet. They are not printed if less than roundoff or if not merging. They account for roundoff error in computing the distance (c.f., option 'Rn'). Use 'Fs' to report the maximum outer and inner plane.

A number may appear in parentheses after the maximum distance (e.g., 2.1x). It is the ratio between the maximum distance and the worst-case distance due to merging two simplicial facets. It should be small for 2-d, 3-d, and 4-d, and for higher dimensions with 'Qx'. It is not printed if less than 0.05.

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[delaunay] Qhull print options (P)

This section lists the print options for Qhull. These options are indicated by 'P' followed by a letter. See Output, Geomview, and Format for other output options.

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Print options

 
General
Pp
do not report precision problems
Po
force output despite precision problems
Po
if error, output neighborhood of facet
 
 
Select
Pdk:n
print facets with normal[k] >= n (default 0.0)
PDk:n
print facets with normal[k] <= n
PFn
print facets whose area is at least n
Pg
print good facets only (needs 'QGn' or 'QVn ')
PMn
print n facets with most merges
PAn
print n largest facets by area
PG
print neighbors of good facets

»PAn - keep n largest facets by area

The n largest facets are marked good for printing. This may be useful for approximating a hull. Unless 'PG' is set, 'Pg' is automatically set.

»Pdk:n - print facet if normal[k] >= n

For a given output, print only those facets with normal[k] >= n and drop the others. For example, 'Pd0:0.5' prints facets with normal[0] >= 0.5 . The default value of n is zero. For example in 3-d, 'Pd0d1d2' prints facets in the positive octant.

If no facets match, the closest facet is returned.

On Windows 95, do not combine multiple options. A 'd' is considered part of a number. For example, use 'Pd0:0.5 Pd1:0.5' instead of 'Pd0:0.5d1:0.5'.

»PDk:n - print facet if normal[k] <= n

For a given output, print only those facets with normal[k] <= n and drop the others. For example, 'PD0:0.5' prints facets with normal[0] <= 0.5 . The default value of n is zero. For example in 3-d, 'PD0D1D2' displays facets in the negative octant.

If no facets match, the closest facet is returned.

In 2-d, 'd G PD2' displays the Delaunay triangulation instead of the corresponding paraboloid.

Be careful of placing 'Dk' or 'dk' immediately after a real number. Some compilers treat the 'D' as a double precision exponent.

»PFn - keep facets whose area is at least n

The facets with area at least n are marked good for printing. This may be useful for approximating a hull. Unless 'PG' is set, 'Pg' is automatically set.

»Pg - print good facets

Qhull can mark facets as "good". This is used to

  • mark the lower convex hull for Delaunay triangulations and Voronoi diagrams
  • mark the facets that are visible from a point (the 'QGn ' option)
  • mark the facets that contain a point (the 'QVn' option).
  • indicate facets with a large enough area (options 'PAn' and 'PFn')

Option 'Pg' only prints good facets that also meet 'Pdk' and 'PDk' options. It is automatically set for options 'PAn', 'PFn ', 'QGn', and 'QVn'.

»PG - print neighbors of good facets

Option 'PG' can be used with or without option 'Pg' to print the neighbors of good facets. For example, options 'QGn' and 'QVn' print the horizon facets for point n.

»PMn - keep n facets with most merges

The n facets with the most merges are marked good for printing. This may be useful for approximating a hull. Unless 'PG' is set, 'Pg' is automatically set.

Use option 'Fm' to print merges per facet.

»Po - force output despite precision problems

Use options 'Po' and 'Q0' if you can not merge facets, triangulate the output ('Qt'), or joggle the input (QJ).

Option 'Po' can not force output when duplicate ridges or duplicate facets occur. It may produce erroneous results. For these reasons, merged facets, joggled input, or exact arithmetic are better.

If you need a simplicial Delaunay triangulation, use joggled input 'QJ' or triangulated output 'Ft'.

Option 'Po' may be used without 'Q0' to remove some steps from Qhull or to output the neighborhood of an error.

Option 'Po' may be used with option 'Q5') to skip qh_check_maxout (i.e., do not determine the maximum outside distance). This can save a significant amount of time.

If option 'Po' is used,

  • most precision errors allow Qhull to continue.
  • verify ('Tv') does not check coplanar points.
  • points are not partitioned into flipped facets and a flipped facet is always visible to a point. This may delete flipped facets from the output.

»Po - if error, output neighborhood of facet

If an error occurs before the completion of Qhull and tracing is not active, 'Po' outputs a neighborhood of the erroneous facets (if any). It uses the current output options.

See 'Po' - force output despite precision problems.

»Pp - do not report precision problems

With option 'Pp', Qhull does not print statistics about precision problems, and it removes some of the warnings. It removes the narrow hull warning.

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[delaunay] Qhull control options (Q)

This section lists the control options for Qhull. These options are indicated by 'Q' followed by a letter.

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Qhull control options

 
General
Qu
compute upper hull for furthest-site Delaunay triangulation
Qc
keep coplanar points with nearest facet
Qi
keep interior points with nearest facet
QJ
joggled input to avoid precision problems
Qt
triangulated output
 
 
Precision handling
Qz
add a point-at-infinity for Delaunay triangulations
Qx
exact pre-merges (allows coplanar facets)
Qs
search all points for the initial simplex
Qbb
scale last coordinate to [0,m] for Delaunay
Qv
test vertex neighbors for convexity
 
 
Transform input
Qbk:0Bk:0
drop dimension k from input
QRn
random rotation (n=seed, n=0 time, n=-1 time/no rotate)
Qbk:n
scale coord[k] to low bound of n (default -0.5)
QBk:n
scale coord[k] to upper bound of n (default 0.5)
QbB
scale input to fit the unit cube
 
 
Select facets
QVn
good facet if it includes point n, -n if not
QGn
good facet if visible from point n, -n for not visible
Qg
only build good facets (needs 'QGn', 'QVn ', or 'Pdk')
 
 
Experimental
Q4
avoid merging old facets into new facets
Q5
do not correct outer planes at end of qhull
Q3
do not merge redundant vertices
Q6
do not pre-merge concave or coplanar facets
Q0
do not pre-merge facets with 'C-0' or 'Qx'
Q8
ignore near-interior points
Q2
merge all non-convex at once instead of independent sets
Qf
partition point to furthest outside facet
Q7
process facets depth-first instead of breadth-first
Q9
process furthest of furthest points
Q10
no special processing for narrow distributions
Q11
copy normals and recompute centrums for tricoplanar facets
Qm
process points only if they would increase the max. outer plane
Qr
process random outside points instead of furthest one
Q1
sort merges by type instead of angle

»Qbb - scale the last coordinate to [0,m] for Delaunay

After scaling with option 'Qbb', the lower bound of the last coordinate will be 0 and the upper bound will be the maximum width of the other coordinates. Scaling happens after projecting the points to a paraboloid and scaling other coordinates.

Option 'Qbb' is automatically set for qdelaunay and qvoronoi. Option 'Qbb' is automatically set for joggled input 'QJ'.

Option 'Qbb' should be used for Delaunay triangulations with integer coordinates. Since the last coordinate is the sum of squares, it may be much larger than the other coordinates. For example, rbox 10000 D2 B1e8 | qhull d has precision problems while rbox 10000 D2 B1e8 | qhull d Qbb is OK.

»QbB - scale the input to fit the unit cube

After scaling with option 'QbB', the lower bound will be -0.5 and the upper bound +0.5 in all dimensions. For different bounds change qh_DEFAULTbox in user.h (0.5 is best for Geomview).

For Delaunay and Voronoi diagrams, scaling happens after projection to the paraboloid. Under precise arithmetic, scaling does not change the topology of the convex hull. Scaling may reduce precision errors if coordinate values vary widely.

»Qbk:n - scale coord[k] to low bound

After scaling, the lower bound for dimension k of the input points will be n. 'Qbk' scales coord[k] to -0.5.

»QBk:n - scale coord[k] to upper bound

After scaling, the upper bound for dimension k of the input points will be n. 'QBk' scales coord[k] to 0.5.

»Qbk:0Bk:0 - drop dimension k from the input points

Drop dimension k from the input points. For example, 'Qb1:0B1:0' deletes the y-coordinate from all input points. This allows the user to take convex hulls of sub-dimensional objects. It happens before the Delaunay and Voronoi transformation. It happens after the halfspace transformation for both the data and the feasible point.

»Qc - keep coplanar points with nearest facet

During construction of the hull, a point is coplanar if it is between 'Wn' above and 'Un' below a facet's hyperplane. A different definition is used for output from Qhull.

For output, a coplanar point is above the minimum vertex (i.e., above the inner plane). With joggle ('QJ'), a coplanar point includes points within one joggle of the inner plane.

With option 'Qc', output formats 'p ', 'f', 'Gp', 'Fc', 'FN', and 'FP' will print the coplanar points. With options 'Qc Qi' these outputs include the interior points.

For Delaunay triangulations (qdelaunay or qvoronoi), a coplanar point is a point that is nearly incident to a vertex. All input points are either vertices of the triangulation or coplanar.

Qhull stores coplanar points with a facet. While constructing the hull, it retains all points within qh_RATIOnearInside (user.h) of a facet. In qh_check_maxout(), it uses these points to determine the outer plane for each facet. With option 'Qc', qh_check_maxout() retains points above the minimum vertex for the hull. Other points are removed. If qh_RATIOnearInside is wrong or if options 'Q5 Q8' are set, a coplanar point may be missed in the output (see Qhull limitations).

»Qf - partition point to furthest outside facet

After adding a new point to the convex hull, Qhull partitions the outside points and coplanar points of the old, visible facets. Without the 'f ' option and merging, it assigns a point to the first facet that it is outside ('Wn'). When merging, it assigns a point to the first facet that is more than several times outside (see qh_DISToutside in user.h).

If option 'Qf' is selected, Qhull performs a directed search (no merging) or an exhaustive search (merging) of new facets. Option 'Qf' may reduce precision errors if pre-merging does not occur.

Option 'Q9' processes the furthest of all furthest points.

»Qg - only build good facets (needs 'QGn' 'QVn' or 'Pdk')

Qhull has several options for defining and printing good facets. With the 'Qg' option, Qhull will only build those facets that it needs to determine the good facets in the output. This may speed up Qhull in 2-d and 3-d. It is useful for furthest-site Delaunay triangulations (qdelaunay Qu, invoke with 'qhull d Qbb Qu Qg'). It is not effective in higher dimensions because many facets see a given point and contain a given vertex. It is not guaranteed to work for all combinations.

See 'QGn', 'QVn', and 'Pdk' for defining good facets, and 'Pg' and 'PG' for printing good facets and their neighbors. If pre-merging ('C-n') is not used and there are coplanar facets, then 'Qg Pg' may produce a different result than 'Pg'.

»QGn - good facet if visible from point n, -n for not visible

With option 'QGn', a facet is good (see 'Qg' and 'Pg') if it is visible from point n. If n < 0, a facet is good if it is not visible from point n. Point n is not added to the hull (unless 'TCn' or 'TPn').

With rbox, use the 'Pn,m,r' option to define your point; it will be point 0 ('QG0').

»Qi - keep interior points with nearest facet

Normally Qhull ignores points that are clearly interior to the convex hull. With option 'Qi', Qhull treats interior points the same as coplanar points. Option 'Qi' does not retain coplanar points. You will probably want 'Qc ' as well.

Option 'Qi' is automatically set for 'qdelaunay Qc' and 'qvoronoi Qc'. If you use 'qdelaunay Qi' or 'qvoronoi Qi', option 's' reports all nearly incident points while option 'Fs' reports the number of interior points (should always be zero).

With option 'Qi', output formats 'p', 'f','Gp', 'Fc', 'FN', and 'FP' include interior points.

»QJ or QJn - joggled input to avoid precision errors

Option 'QJ' or 'QJn' joggles each input coordinate by adding a random number in the range [-n,n]. If a precision error occurs, It tries again. If precision errors still occur, Qhull increases n ten-fold and tries again. The maximum value for increasing n is 0.01 times the maximum width of the input. Option 'QJ' selects a default value for n. User.h defines these parameters and a maximum number of retries. See Merged facets or joggled input.

Users of joggled input should consider converting to triangulated output ('Qt'). Triangulated output is approximately 1000 times more accurate than joggled input.

Option 'QJ' also sets 'Qbb' for Delaunay triangulations and Voronoi diagrams. It does not set 'Qbb' if 'Qbk:n' or 'QBk:n' are set.

If 'QJn' is set, Qhull does not merge facets unless requested to. All facets are simplicial (triangular in 2-d). This may be important for your application. You may also use triangulated output ('Qt') or Option 'Ft'.

Qhull adjusts the outer and inner planes for 'QJn' ('Fs'). They are increased by sqrt(d)*n to account for the maximum distance between a joggled point and the corresponding input point. Coplanar points ('Qc') require an additional sqrt(d)*n since vertices and coplanar points may be joggled in opposite directions.

For Delaunay triangulations (qdelaunay), joggle happens before lifting the input sites to a paraboloid. Instead of 'QJ', you may use triangulated output ('Qt')

This option is deprecated for Voronoi diagrams (qvoronoi). It triangulates cospherical points, leading to duplicated Voronoi vertices.

By default, 'QJn' uses a fixed random number seed. To use time as the random number seed, select 'QR-1'. The summary ('s') will show the selected seed as 'QR-n'.

With 'QJn', Qhull does not error on degenerate hyperplane computations. Except for Delaunay and Voronoi computations, Qhull does not error on coplanar points.

Use option 'FO' to display the selected options. Option 'FO' displays the joggle and the joggle seed. If Qhull restarts, it will redisplay the options.

Use option 'TRn' to estimate the probability that Qhull will fail for a given 'QJn'.

»Qm - only process points that increase the maximum outer plane

Qhull reports the maximum outer plane in its summary ('s'). With option 'Qm', Qhull does not process points that are below the current, maximum outer plane. This is equivalent to always adjusting 'Wn ' to the maximum distance of a coplanar point to a facet. It is ignored for points above the upper convex hull of a Delaunay triangulation. Option 'Qm' is no longer important for merging.

»Qr - process random outside points instead of furthest ones

Normally, Qhull processes the furthest point of a facet's outside points. Option 'Qr' instead selects a random outside point for processing. This makes Qhull equivalent to the randomized incremental algorithms.

The original randomization algorithm by Clarkson and Shor ['89] used a conflict list which is equivalent to Qhull's outside set. Later randomized algorithms retained the previously constructed facets.

To compare Qhull to the randomized algorithms with option 'Qr', compare "hyperplanes constructed" and "distance tests". Qhull does not report CPU time because the randomization is inefficient.

»QRn - random rotation

Option 'QRn' randomly rotates the input. For Delaunay triangulations (qdelaunay or qvoronoi), it rotates the lifted points about the last axis.

If n=0, use time as the random number seed. If n>0, use n as the random number seed. If n=-1, don't rotate but use time as the random number seed. If n<-1, don't rotate but use n as the random number seed.

»Qs - search all points for the initial simplex

Qhull constructs an initial simplex from d+1 points. It selects points with the maximum and minimum coordinates and non-zero determinants. If this fails, it searches all other points. In 8-d and higher, Qhull selects points with the minimum x or maximum coordinate (see qh_initialvertices in poly2.c ). It rejects points with nearly zero determinants. This should work for almost all input sets.

If Qhull can not construct an initial simplex, it reports a descriptive message. Usually, the point set is degenerate and one or more dimensions should be removed ('Qbk:0Bk:0'). If not, use option 'Qs'. It performs an exhaustive search for the best initial simplex. This is expensive is high dimensions.

»Qt - triangulated output

By default, qhull merges facets to handle precision errors. This produces non-simplicial facets (e.g., the convex hull of a cube has 6 square facets). Each facet is non-simplicial because it has four vertices.

Use option 'Qt' to triangulate all non-simplicial facets before generating results. Alternatively, use joggled input ('QJ') to prevent non-simplical facets. Unless 'Pp' is set, qhull produces a warning if 'QJ' and 'Qt' are used together.

For Delaunay triangulations (qdelaunay), triangulation occurs after lifting the input sites to a paraboloid and computing the convex hull.

Option 'Qt' is deprecated for Voronoi diagrams (qvoronoi). It triangulates cospherical points, leading to duplicated Voronoi vertices.

Option 'Qt' may produce degenerate facets with zero area.

Facet area and hull volumes may differ with and without 'Qt'. The triangulations are different and different triangles may be ignored due to precision errors.

With sufficient merging, the ridges of a non-simplicial facet may share more than two neighboring facets. If so, their triangulation ('Qt') will fail since two facets have the same vertex set.

»Qu - compute upper hull for furthest-site Delaunay triangulation

When computing a Delaunay triangulation (qdelaunay or qvoronoi), Qhull computes both the the convex hull of points on a paraboloid. It normally prints facets of the lower hull. These correspond to the Delaunay triangulation. With option 'Qu', Qhull prints facets of the upper hull. These correspond to the furthest-site Delaunay triangulation and the furthest-site Voronoi diagram.

Option 'qhull d Qbb Qu Qg' may improve the speed of option 'Qu'. If you use the Qhull library, a faster method is 1) use Qhull to compute the convex hull of the input sites; 2) take the extreme points (vertices) of the convex hull; 3) add one interior point (e.g., 'FV', the average of d extreme points); 4) run 'qhull d Qbb Qu' or 'qhull v Qbb Qu' on these points.

»Qv - test vertex neighbors for convexity

Normally, Qhull tests all facet neighbors for convexity. Non-neighboring facets which share a vertex may not satisfy the convexity constraint. This occurs when a facet undercuts the centrum of another facet. They should still be convex. Option 'Qv' extends Qhull's convexity testing to all neighboring facets of each vertex. The extra testing occurs after the hull is constructed..

»QVn - good facet if it includes point n, -n if not

With option 'QVn', a facet is good ('Qg', 'Pg') if one of its vertices is point n. If n<0, a good facet does not include point n.

If options 'PG' and 'Qg' are not set, option 'Pg' (print only good) is automatically set.

Option 'QVn' behaves oddly with options 'Fx' and 'qvoronoi Fv'.

If used with option 'Qg' (only process good facets), point n is either in the initial simplex or it is the first point added to the hull. Options 'QVn Qg' require either 'QJ' or 'Q0' (no merging).

»Qx - exact pre-merges (allows coplanar facets)

Option 'Qx' performs exact merges while building the hull. Option 'Qx' is set by default in 5-d and higher. Use option 'Q0' to not use 'Qx' by default. Unless otherwise specified, option 'Qx' sets option 'C-0'.

The "exact" merges are merging a point into a coplanar facet (defined by 'Vn ', 'Un', and 'C-n'), merging concave facets, merging duplicate ridges, and merging flipped facets. Coplanar merges and angle coplanar merges ('A-n') are not performed. Concavity testing is delayed until a merge occurs.

After the hull is built, all coplanar merges are performed (defined by 'C-n' and 'A-n'), then post-merges are performed (defined by 'Cn' and 'An'). If facet progress is logged ('TFn'), Qhull reports each phase and prints intermediate summaries and statistics ('Ts').

Without 'Qx' in 5-d and higher, options 'C-n' and 'A-n' may merge too many facets. Since redundant vertices are not removed effectively, facets become increasingly wide.

Option 'Qx' may report a wide facet. With 'Qx', coplanar facets are not merged. This can produce a "dent" in an intermediate hull. If a point is partitioned into a dent and it is below the surrounding facets but above other facets, one or more wide facets will occur. In practice, this is unlikely. To observe this effect, run Qhull with option 'Q6' which doesn't pre-merge concave facets. A concave facet makes a large dent in the intermediate hull.

Option 'Qx' may set an outer plane below one of the input points. A coplanar point may be assigned to the wrong facet because of a "dent" in an intermediate hull. After constructing the hull, Qhull double checks all outer planes with qh_check_maxout in poly2.c . If a coplanar point is assigned to the wrong facet, qh_check_maxout may reach a local maximum instead of locating all coplanar facets. This appears to be unlikely.

»Qz - add a point-at-infinity for Delaunay triangulations

Option 'Qz' adds a point above the paraboloid of lifted sites for a Delaunay triangulation. It allows the Delaunay triangulation of cospherical sites. It reduces precision errors for nearly cospherical sites.

»Q0 - no merging with C-0 and Qx

Turn off default merge options 'C-0' and 'Qx'.

With 'Q0' and without other pre-merge options, Qhull ignores precision issues while constructing the convex hull. This may lead to precision errors. If so, a descriptive warning is generated. See Precision issues.

»Q1 - sort merges by type instead of angle

Qhull sorts the coplanar facets before picking a subset of the facets to merge. It merges concave and flipped facets first. Then it merges facets that meet at a steep angle. With 'Q1', Qhull sorts merges by type (coplanar, angle coplanar, concave) instead of by angle. This may make the facets wider.

»Q2 - merge all non-convex at once instead of independent sets

With 'Q2', Qhull merges all facets at once instead of performing merges in independent sets. This may make the facets wider.

»Q3 - do not merge redundant vertices

With 'Q3', Qhull does not remove redundant vertices. In 6-d and higher, Qhull never removes redundant vertices (since vertices are highly interconnected). Option 'Q3' may be faster, but it may result in wider facets. Its effect is easiest to see in 3-d and 4-d.

»Q4 - avoid merging old facets into new facets

With 'Q4', Qhull avoids merges of an old facet into a new facet. This sometimes improves facet width and sometimes makes it worse.

»Q5 - do not correct outer planes at end of qhull

When merging facets or approximating a hull, Qhull tests coplanar points and outer planes after constructing the hull. It does this by performing a directed search (qh_findbest in geom.c). It includes points that are just inside the hull.

With options 'Q5' or 'Po', Qhull does not test outer planes. The maximum outer plane is used instead. Coplanar points ('Qc') are defined by 'Un'. An input point may be outside of the maximum outer plane (this appears to be unlikely). An interior point may be above 'Un' from a hyperplane.

Option 'Q5' may be used if outer planes are not needed. Outer planes are needed for options 's', 'G', 'Go ', 'Fs', 'Fo', 'FF', and 'f'.

»Q6 - do not pre-merge concave or coplanar facets

With 'Q6', Qhull does not pre-merge concave or coplanar facets. This demonstrates the effect of "dents" when using 'Qx'.

»Q7 - depth-first processing instead of breadth-first

With 'Q7', Qhull processes facets in depth-first order instead of breadth-first order. This may increase the locality of reference in low dimensions. If so, Qhull may be able to use virtual memory effectively.

In 5-d and higher, many facets are visible from each unprocessed point. So each iteration may access a large proportion of allocated memory. This makes virtual memory ineffectual. Once real memory is used up, Qhull will spend most of its time waiting for I/O.

Under 'Q7', Qhull runs slower and the facets may be wider.

»Q8 - ignore near-interior points

With 'Q8' and merging, Qhull does not process interior points that are near to a facet (as defined by qh_RATIOnearInside in user.h). This avoids partitioning steps. It may miss a coplanar point when adjusting outer hulls in qh_check_maxout(). The best value for qh_RATIOnearInside is not known. Options 'Q8 Qc' may be sufficient.

»Q9 - process furthest of furthest points

With 'Q9', Qhull processes the furthest point of all outside sets. This may reduce precision problems. The furthest point of all outside sets is not necessarily the furthest point from the convex hull.

»Q10 - no special processing for narrow distributions

With 'Q10', Qhull does not special-case narrow distributions. See Limitations of merged facets for more information.

»Q11 - copy normals and recompute centrums for tricoplanar facets

Option 'Qt' triangulates non-simplicial facets into "tricoplanar" facets. Normally tricoplanar facets share the same normal, centrum, and Voronoi vertex. They can not be merged or replaced. With option 'Q11', Qhull duplicates the normal and Voronoi vertex. It recomputes the centrum.

Use 'Q11' if you use the Qhull library to add points incrementally and call qh_triangulate() after each point. Otherwise, Qhull will report an error when it tries to merge and replace a tricoplanar facet.

With sufficient merging and new points, option 'Q11' may lead to precision problems such as duplicate ridges and concave facets. For example, if qh_triangulate() is added to qh_addpoint(), RBOX 1000 s W1e-12 t1001813667 P0 | QHULL d Q11 Tv, reports an error due to a duplicate ridge.

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[delaunay] Qhull trace options (T)

This section lists the trace options for Qhull. These options are indicated by 'T' followed by a letter.

Copyright © 1995-2012 C.B. Barber

» Programs • Options • Output • Formats • Geomview • Print • Qhull • Precision • Trace

Trace options

 
General
Tz
output error information to stdout instead of stderr
TI file
input data from a file
TO file
output results to a file
Ts
print statistics
TFn
report progress whenever n or more facets created
TRn
rerun qhull n times
Tv
verify result: structure, convexity, and point inclusion
 
 
Debugging
Tc
check frequently during execution
TVn
stop qhull after adding point n
TCn
stop qhull after building cone for point n
TV-n
stop qhull before adding point n
T4
trace at level n, 4=all, 5=mem/gauss, -1= events
TWn
trace merge facets when width > n
TMn
turn on tracing at merge n
TPn
turn on tracing when point n added to hull

»Tc - check frequently during execution

Qhull includes frequent checks of its data structures. Option 'Tc' will catch most inconsistency errors. It is slow and should not be used for production runs. Option 'Tv' performs the same checks after the hull is constructed.

»TCn - stop qhull after building cone for point n

Qhull builds a cone from the point to its horizon facets. Option 'TCn' stops Qhull just after building the cone. The output for 'f' includes the cone and the old hull.'.

»TFn - report summary whenever n or more facets created

Option 'TFn' reports progress whenever more than n facets are created. The test occurs just before adding a new point to the hull. During post-merging, 'TFn' reports progress after more than n/2 merges.

»TI file - input data from file

Input data from 'file' instead of stdin. The filename may not contain spaces or use single quotes. You may use I/O redirection instead (e.g., 'rbox 10 | qdelaunay >results').

»TMn - turn on tracing at merge n

Turn on tracing at n'th merge.

»Tn - trace at level n

Qhull includes full execution tracing. 'T-1' traces events. 'T1' traces the overall execution of the program. 'T2' and 'T3' trace overall execution and geometric and topological events. 'T4' traces the algorithm. 'T5' includes information about memory allocation and Gaussian elimination. 'T1' is useful for logging progress of Qhull in high dimensions.

Option 'Tn' can produce large amounts of output. Use options 'TPn', 'TWn', and 'TMn' to selectively turn on tracing. Since all errors report the last processed point, option 'TPn' is particularly useful.

Different executions of the same program may produce different traces and different results. The reason is that Qhull uses hashing to match ridges of non-simplicial facets. For performance reasons, the hash computation uses memory addresses which may change across executions.

»TO file - output results to file

Redirect stdout to 'file'. The filename may be enclosed in single quotes. Unix and Windows NT users may use I/O redirection instead (e.g., 'rbox 10 | qdelaunay >results').

Windows95 users should always use 'TO file'. If they use I/O redirection, error output is not sent to the console. Qhull uses single quotes instead of double quotes because a missing double quote can freeze Windows95 (e.g., do not run, rbox 10 | qhull TO "x)

»TPn - turn on tracing when point n added to hull

Option 'TPn' turns on tracing when point n is added to the hull. It also traces partitions of point n. This option reduces the output size when tracing. It is the normal method to determine the cause of a Qhull error. All Qhull errors report the last point added.

Use options 'TPn TVn' to trace the addition of point n to the convex hull and stop when done.

If used with option 'TWn', 'TPn' turns off tracing after adding point n to the hull. Use options 'TPn TWn' to trace the addition of point n to the convex hull, partitions of point n, and wide merges.

»TRn - rerun qhull n times

Option 'TRn' reruns Qhull n times. It is usually used with 'QJn' to determine the probability that a given joggle will fail. The summary ('s') lists the failure rate and the precision errors that occurred. Option 'Ts' will report statistics for all of the runs. Trace and output options only apply to the last run. An event trace, 'T-1' reports events for all runs.

Tracing applies to the last run of Qhull. If an error is reported, the options list the run number as "_run". To trace this run, set 'TRn' to the same value.

»Ts - print statistics

Option 'Ts' collects statistics and prints them to stderr. For Delaunay triangulations, the angle statistics are restricted to the lower or upper envelope.

»Tv - verify result: structure, convexity, and point inclusion

Option 'Tv' checks the topological structure, convexity, and point inclusion. If precision problems occurred, facet convexity is tested whether or not 'Tv' is selected. Option 'Tv' does not check point inclusion if forcing output with 'Po', or if 'Q5' is set.

The convex hull of a set of points is the smallest polytope that includes the points. Option 'Tv' tests point inclusion. Qhull verifies that all points are below all outer planes (facet->maxoutside). Point inclusion is exhaustive if merging or if the facet-point product is small enough; otherwise Qhull verifies each point with a directed search (qh_findbest). To force an exhaustive test when using option 'C-0' (default), use 'C-1e-30' instead.

Point inclusion testing occurs after producing output. It prints a message to stderr unless option 'Pp' is used. This allows the user to interrupt Qhull without changing the output.

With 'qvoronoi Fi' and 'qvoronoi Fo', option 'Tv' collects statistics that verify all Voronoi vertices lie on the separating hyperplane, and for bounded regions, all separating hyperplanes are perpendicular bisectors.

»TV-n - stop qhull before adding point n

Qhull adds one point at a time to the convex hull. See how Qhull adds a point. Option 'TV-n' stops Qhull just before adding a new point. Output shows the hull at this time.

»TVn - stop qhull after adding point n

Option 'TVn' stops Qhull after it has added point n. Output shows the hull at this time.

»TWn - trace merge facets when width > n

Along with TMn, this option allows the user to determine the cause of a wide merge.

»Tz - send all output to stdout

Redirect stderr to stdout.

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[cone] Qhull quick reference

This section lists all programs and options in Qhull.

Copyright © 1995-2012 C.B. Barber

 

Qhull programs

» Programs • Options • Output • Formats • Geomview • Print • Qhull • Precision • Trace

qconvex -- convex hull
synopsis • input • outputs • controls • graphics • notes • conventions • options
 
qdelaunay -- Delaunay triangulation
synopsis • input • outputs • controls • graphics • notes • conventions • options
 
qdelaunay Qu -- furthest-site Delaunay triangulation
synopsis • input • outputs • controls • graphics • notes • conventions • options
 
qhalf -- halfspace intersection about a point
synopsis • input • outputs • controls • graphics • notes • conventions • options
 
qvoronoi -- Voronoi diagram
synopsis • input • outputs • controls • graphics • notes • conventions • options
 
qvoronoi Qu -- furthest-site Voronoi diagram
synopsis • input • outputs • controls • graphics • notes • conventions • options
 
rbox -- generate point distributions for qhull
synopsis • outputs • examples • notes • options
 
qhull -- convex hull and related structures
synopsis • input • outputs • controls • options
 
Qhull options

» Programs • Options • Output • Formats • Geomview • Print • Qhull • Precision • Trace

'Fa' Farea 'FA' FArea-total 'Fc' Fcoplanars 'FC' FCentrums
'Fd' Fd-cdd-in 'FD' FD-cdd-out 'FF' FF-dump-xridge 'Fi' Finner
'Fi' Finner_bounded 'FI' FIDs 'Fm' Fmerges 'FM' FMaple
'Fn' Fneighbors 'FN' FNeigh-vertex 'Fo' Fouter 'Fo' Fouter_unbounded
'FO' FOptions 'Fp' Fpoint-intersect 'FP' FPoint_near 'FQ' FQhull
'Fs' Fsummary 'FS' FSize 'Ft' Ftriangles 'Fv' Fvertices
'Fv' Fvoronoi 'FV' FVertex-ave 'Fx' Fxtremes Merged facets or joggled input
 
'PAn' PArea-keep 'Pdk:n' Pdrop_low 'PDk:n' Pdrop_high 'Pg' Pgood
'PFn' PFacet_area_keep 'PG' PGood_neighbors 'PMn' PMerge-keep 'Po' Poutput_forced
'Po' Poutput_error 'Pp' Pprecision_not
 
'd' delaunay 'v' voronoi 'G' Geomview 'H' Halfspace
'f' facet_dump 'i' incidences 'm' mathematica 'n' normals
'o' OFF_format 'p' points 's' summary
 
'Gv' Gvertices 'Gp' Gpoints 'Ga' Gall_points 'Gn' Gno_planes
'Gi' Ginner 'Gc' Gcentrums 'Gh' Ghyperplanes 'Gr' Gridges
'Go' Gouter 'GDn' GDrop_dim 'Gt' Gtransparent
 
'T4' T4_trace 'Tc' Tcheck_often 'Ts' Tstatistics 'Tv' Tverify
'Tz' Tz_stdout 'TFn' TFacet_log 'TI file' TInput_file 'TPn' TPoint_trace
'TMn' TMerge_trace 'TO file' TOutput_file 'TRn' TRerun 'TWn' TWide_trace
'TV-n' TVertex_stop_before
'TVn' TVertex_stop_after 'TCn' TCone_stop_after
 
'A-n' Angle_max_pre 'An' Angle_max_post 'C-0' Centrum_roundoff 'C-n' Centrum_size_pre
'Cn' Centrum_size_post 'En' Error_round 'Rn' Random_dist 'Vn' Visible_min
'Un' Ucoplanar_max 'Wn' Wide_outside
 
'Qbk:n' Qbound_low 'QBk:n' QBound_high 'Qbk:0Bk:0' Qbound_drop 'QbB' QbB-scale-box
'Qbb' Qbb-scale-last 'Qc' Qcoplanar 'Qf' Qfurthest 'Qg' Qgood_only
'QGn' QGood_point 'Qi' Qinterior 'Qm' Qmax_out 'QJn' QJoggle
'Qr' Qrandom 'QRn' QRotate 'Qs' Qsearch_1st 'Qt' Qtriangulate
'Qu' QupperDelaunay 'QVn' QVertex_good 'Qv' Qvneighbors 'Qx' Qxact_merge
'Qz' Qzinfinite
 
'Q0' Q0_no_premerge 'Q1' Q1_no_angle 'Q2' Q2_no_independ 'Q3' Q3_no_redundant
'Q4' Q4_no_old 'Q5' Q5_no_check_out 'Q6' Q6_no_concave 'Q7' Q7_depth_first
'Q8' Q8_no_near_in 'Q9' Q9_pick_furthest 'Q10' Q10_no_narrow 'Q11' Q11_trinormals

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[halfspace]qhalf -- halfspace intersection about a point

The intersection of a set of halfspaces is a polytope. The polytope may be unbounded. See Preparata & Shamos ['85] for a discussion. In low dimensions, halfspace intersection may be used for linear programming.

Example: rbox c | qconvex FQ FV n | qhalf Fp
Print the intersection of the facets of a cube. rbox c generates the vertices of a cube. qconvex FV n returns of average of the cube's vertices (in this case, the origin) and the halfspaces that define the cube. qhalf Fp computes the intersection of the halfspaces about the origin. The intersection is the vertices of the original cube.

Example: rbox c d G0.55 | qconvex FQ FV n | qhalf Fp

Print the intersection of the facets of a cube and a diamond. There are 24 facets and 14 intersection points. Four facets define each diamond vertex. Six facets define each cube vertex.

Example: rbox c d G0.55 | qconvex FQ FV n | qhalf Fp Qt

Same as above except triangulate before computing the intersection points. Three facets define each intersection point. There are two duplicates of the diamond and four duplicates of the cube.

Qhull computes a halfspace intersection by the geometric duality between points and halfspaces. See halfspace examples, qhalf notes, and option 'p' of qhalf outputs.

By default, halfspace intersections may be defined by more than d halfspaces. See the previous cube and diamond example. This is the expected output for halfspace intersection.

You can try triangulated output and joggled input. It demonstrates that triangulated output is more accurate than joggled input.

If you use 'Qt' (triangulated output), all halfspace intersections are simplicial (e.g., three halfspaces per intersection in 3-d). In 3-d, if more than three halfspaces intersect at the same point, triangulated output will produce duplicate intersections, one for each additional halfspace. See the previous cube and diamond example.

If you use 'QJ' (joggled input), all halfspace intersections are simplicial. This may lead to nearly identical intersections. For example, replace 'Qt' with 'QJ' above and compare the duplicated intersections. See Merged facets or joggled input.

The 'qhalf' program is equivalent to 'qhull H' in 2-d to 4-d, and 'qhull H Qx' in 5-d and higher. It disables the following Qhull options: d n v Qbb QbB Qf Qg Qm Qr QR Qv Qx Qz TR E V Fa FA FC FD FS Ft FV Gt Q0,etc.

Copyright © 1995-2012 C.B. Barber

»qhalf synopsis

qhalf- halfspace intersection about a point.
    input (stdin): [dim, 1, interior point]
                   dim+1, n
                   halfspace coefficients + offset
    comments start with a non-numeric character

options (qhalf.htm):
    Hn,n - specify coordinates of interior point
    Qt   - triangulated output
    QJ   - joggle input instead of merging facets
    Tv   - verify result: structure, convexity, and redundancy
    .    - concise list of all options
    -    - one-line description of all options

output options (subset):
    s    - summary of results (default)
    Fp   - intersection coordinates
    Fv   - non-redundant halfspaces incident to each intersection
    Fx   - non-redundant halfspaces
    o    - OFF file format (dual convex hull)
    G    - Geomview output (dual convex hull)
    m    - Mathematica output (dual convex hull)
    QVn  - print intersections for halfspace n, -n if not
    TO file - output results to file, may be enclosed in single quotes

examples:
    rbox d | qconvex n | qhalf s H0,0,0 Fp
    rbox c | qconvex FV n | qhalf s i
    rbox c | qconvex FV n | qhalf s o

»qhalf input

The input data on stdin consists of:

  • [optional] interior point
    • dimension
    • 1
    • coordinates of interior point
  • dimension + 1
  • number of halfspaces
  • halfspace coefficients followed by offset

Use I/O redirection (e.g., qhalf < data.txt), a pipe (e.g., rbox c | qconvex FV n | qhalf), or the 'TI' option (e.g., qhalf TI data.txt).

Qhull needs an interior point to compute the halfspace intersection. An interior point is inside all of the halfspaces Hx+b <= 0. The interior point may be in the input. If not, option 'Hn,n' defines the interior point as [n,n,0,...] where 0 is the default coordinate (e.g., 'H0' is the origin). Use linear programming if you do not know the interior point (see halfspace notes),

The input to qhalf is a set of halfspaces. Each halfspace is defined by d coefficients followed by a signed offset. This defines a linear inequality. The coefficients define a vector that is normal to the halfspace. The vector may have any length. If it has length one, the offset is the distance from the origin to the halfspace's boundary.

This is the same format used for output options 'n', 'Fo', and 'Fi'. Use option 'Fd' to use cdd format for the halfspaces.

For example, here is the input for computing the intersection of halfplanes that form a cube.

rbox c | qconvex FQ FV n TO data 

RBOX c | QCONVEX FQ FV n
3 1
     0      0      0
4
6
     0      0     -1   -0.5
     0     -1      0   -0.5
     1      0      0   -0.5
    -1      0      0   -0.5
     0      1      0   -0.5
     0      0      1   -0.5

qhalf s Fp < data 


Halfspace intersection by the convex hull of 6 points in 3-d:

  Number of halfspaces: 6
  Number of non-redundant halfspaces: 6
  Number of intersection points: 8

Statistics for: RBOX c | QCONVEX FQ FV n | QHALF s Fp

  Number of points processed: 6
  Number of hyperplanes created: 11
  Number of distance tests for qhull: 11
  Number of merged facets: 1
  Number of distance tests for merging: 45
  CPU seconds to compute hull (after input):  0

3
3
8
  -0.5    0.5    0.5
   0.5    0.5    0.5
  -0.5    0.5   -0.5
   0.5    0.5   -0.5
   0.5   -0.5    0.5
  -0.5   -0.5    0.5
  -0.5   -0.5   -0.5
   0.5   -0.5   -0.5

»qhalf outputs

The following options control the output for halfspace intersection.

 
Intersections
FN
list intersection points for each non-redundant halfspace. The first line is the number of non-redundant halfspaces. Each remaining lines starts with the number of intersection points. For the cube example, each halfspace has four intersection points.
Fn
list neighboring intersections for each intersection point. The first line is the number of intersection points. Each remaining line starts with the number of neighboring intersections. For the cube example, each intersection point has three neighboring intersections. In 3-d, a non-simplicial intersection has more than three neighboring intersections. Use option 'QJ' to avoid non-simplicial intersections.
Fp
print intersection coordinates. The first line is the dimension and the second line is the number of intersection points. The following lines are the coordinates of each intersection.
FI
list intersection IDs. The first line is the number of intersections. The IDs follow, one per line.
 
 
Halfspaces
Fx
list non-redundant halfspaces. The first line is the number of non-redundant halfspaces. The other lines list one halfspace per line. A halfspace is non-redundant if it defines a facet of the intersection. Redundant halfspaces are ignored. For the cube example, all of the halfspaces are non-redundant.
Fv
list non-redundant halfspaces incident to each intersection point. The first line is the number of non-redundant halfspaces. Each remaining line starts with the number of non-redundant halfspaces. For the cube example, each intersection is incident to three halfspaces.
i
list non-redundant halfspaces incident to each intersection point. The first line is the number of intersection points. Each remaining line lists the incident, non-redundant halfspaces. For the cube example, each intersection is incident to three halfspaces.
Fc
list coplanar halfspaces for each intersection point. The first line is the number of intersection points. Each remaining line starts with the number of coplanar halfspaces. A coplanar halfspace is listed for one intersection point even though it is coplanar to multiple intersection points.
Qi Fc
list redundant halfspaces for each intersection point. The first line is the number of intersection points. Each remaining line starts with the number of redundant halfspaces. Use options 'Qc Qi Fc' to list coplanar and redundant halfspaces.
 
 
General
s
print summary for the halfspace intersection. Use 'Fs' if you need numeric data.
o
print vertices and facets of the dual convex hull. The first line is the dimension. The second line is the number of vertices, facets, and ridges. The vertex coordinates are next, followed by the facets, one per line.
p
print vertex coordinates of the dual convex hull. Each vertex corresponds to a non-redundant halfspace. Its coordinates are the negative of the hyperplane's coefficients divided by the offset plus the inner product of the coefficients and the interior point (-c/(b+a.p). Options 'p Qc' includes coplanar halfspaces. Options 'p Qi' includes redundant halfspaces.
m
Mathematica output for the dual convex hull in 2-d or 3-d.
FM
Maple output for the dual convex hull in 2-d or 3-d.
G
Geomview output for the dual convex hull in 2-d, 3-d, or 4-d.

»qhalf controls

These options provide additional control:

Qt
triangulated output. If a 3-d intersection is defined by more than three hyperplanes, Qhull produces duplicate intersections -- one for each extra hyperplane.
QJ
joggle the input instead of merging facets. In 3-d, this guarantees that each intersection is defined by three hyperplanes.
f
facet dump. Print the data structure for each intersection (i.e., facet)
TFn
report summary after constructing n intersections
QVn
select intersection points for halfspace n (marked 'good')
QGn
select intersection points that are visible to halfspace n (marked 'good'). Use -n for the remainder.
Qbk:0Bk:0
remove the k-th coordinate from the input. This computes the halfspace intersection in one lower dimension.
Tv
verify result
TI file
input data from file. The filename may not use spaces or quotes.
TO file
output results to file. Use single quotes if the filename contains spaces (e.g., TO 'file with spaces.txt'
Qs
search all points for the initial simplex. If Qhull can not construct an initial simplex, it reports a descriptive message. Usually, the point set is degenerate and one or more dimensions should be removed ('Qbk:0Bk:0'). If not, use option 'Qs'. It performs an exhaustive search for the best initial simplex. This is expensive is high dimensions.

»qhalf graphics

To view the results with Geomview, compute the convex hull of the intersection points ('qhull FQ H0 Fp | qhull G'). See Halfspace examples.

»qhalf notes

See halfspace intersection for precision issues related to qhalf.

If you do not know an interior point for the halfspaces, use linear programming to find one. Assume, n halfspaces defined by: aj*x1+bj*x2+cj*x3+dj>=0, j=1..n. Perform the following linear program:

max(x5) aj*x1+bj*x2+cj*x3+dj*x4-x5>=0, j=1..n

Then, if [x1,x2,x3,x4,x5] is an optimal solution with x4,x5>0 we get:

aj*(x1/x4)+bj*(x2/x4)+cj*(x3/x4)+dj>=(x5/x4)>0, j=1..n

and conclude that the point [x1/x4,x2/x4,x3/x4] is in the interior of all the halfspaces. Note that x5 is optimal, so this point is "way in" the interior (good for precision errors).

After finding an interior point, the rest of the intersection algorithm is from Preparata & Shamos ['85, p. 316, "A simple case ..."]. Translate the halfspaces so that the interior point is the origin. Calculate the dual polytope. The dual polytope is the convex hull of the vertices dual to the original faces in regard to the unit sphere (i.e., halfspaces at distance d from the origin are dual to vertices at distance 1/d). Then calculate the resulting polytope, which is the dual of the dual polytope, and translate the origin back to the interior point [S. Spitz and S. Teller].

»qhalf conventions

The following terminology is used for halfspace intersection in Qhull. This is the hardest structure to understand. The underlying structure is a convex hull with one vertex per non-redundant halfspace. See convex hull conventions and Qhull's data structures.

  • interior point - a point in the intersection of the halfspaces. Qhull needs an interior point to compute the intersection. See halfspace input.
  • halfspace - d coordinates for the normal and a signed offset. The distance to an interior point is negative.
  • non-redundant halfspace - a halfspace that defines an output facet
  • vertex - a dual vertex in the convex hull corresponding to a non-redundant halfspace
  • coplanar point - the dual point corresponding to a similar halfspace
  • interior point - the dual point corresponding to a redundant halfspace
  • intersection point- the intersection of d or more non-redundant halfspaces
  • facet - a dual facet in the convex hull corresponding to an intersection point
  • non-simplicial facet - more than d halfspaces intersect at a point
  • good facet - an intersection point that satisfies restriction 'QVn', etc.

»qhalf options

qhalf- compute the intersection of halfspaces about a point
    http://www.qhull.org

input (stdin):
    optional interior point: dimension, 1, coordinates
    first lines: dimension+1 and number of halfspaces
    other lines: halfspace coefficients followed by offset
    comments:    start with a non-numeric character

options:
    Hn,n - specify coordinates of interior point
    Qt   - triangulated ouput
    QJ   - joggle input instead of merging facets
    Qc   - keep coplanar halfspaces
    Qi   - keep other redundant halfspaces

Qhull control options:
    QJn  - randomly joggle input in range [-n,n]
    Qbk:0Bk:0 - remove k-th coordinate from input
    Qs   - search all halfspaces for the initial simplex
    QGn  - print intersection if redundant to halfspace n, -n for not
    QVn  - print intersections for halfspace n, -n if not

Trace options:
    T4   - trace at level n, 4=all, 5=mem/gauss, -1= events
    Tc   - check frequently during execution
    Ts   - print statistics
    Tv   - verify result: structure, convexity, and redundancy
    Tz   - send all output to stdout
    TFn  - report summary when n or more facets created
    TI file - input data from file, no spaces or single quotes
    TO file - output results to file, may be enclosed in single quotes
    TPn  - turn on tracing when halfspace n added to intersection
    TMn  - turn on tracing at merge n
    TWn  - trace merge facets when width > n
    TVn  - stop qhull after adding halfspace n, -n for before (see TCn)
    TCn  - stop qhull after building cone for halfspace n (see TVn)

Precision options:
    Cn   - radius of centrum (roundoff added).  Merge facets if non-convex
     An  - cosine of maximum angle.  Merge facets if cosine > n or non-convex
           C-0 roundoff, A-0.99/C-0.01 pre-merge, A0.99/C0.01 post-merge
    Rn   - randomly perturb computations by a factor of [1-n,1+n]
    Un   - max distance below plane for a new, coplanar halfspace
    Wn   - min facet width for outside halfspace (before roundoff)

Output formats (may be combined; if none, produces a summary to stdout):
    f    - facet dump
    G    - Geomview output (dual convex hull)
    i    - non-redundant halfspaces incident to each intersection
    m    - Mathematica output (dual convex hull)
    o    - OFF format (dual convex hull: dimension, points, and facets)
    p    - vertex coordinates of dual convex hull (coplanars if 'Qc' or 'Qi')
    s    - summary (stderr)

More formats:
    Fc   - count plus redundant halfspaces for each intersection
         -   Qc (default) for coplanar and Qi for other redundant
    Fd   - use cdd format for input (homogeneous with offset first)
    FF   - facet dump without ridges
    FI   - ID of each intersection
    Fm   - merge count for each intersection (511 max)
    FM   - Maple output (dual convex hull)
    Fn   - count plus neighboring intersections for each intersection
    FN   - count plus intersections for each non-redundant halfspace
    FO   - options and precision constants
    Fp   - dim, count, and intersection coordinates
    FP   - nearest halfspace and distance for each redundant halfspace
    FQ   - command used for qhalf
    Fs   - summary: #int (8), dim, #halfspaces, #non-redundant, #intersections
                      for output: #non-redundant, #intersections, #coplanar
                                  halfspaces, #non-simplicial intersections
                    #real (2), max outer plane, min vertex
    Fv   - count plus non-redundant halfspaces for each intersection
    Fx   - non-redundant halfspaces

Geomview output (2-d, 3-d and 4-d; dual convex hull)
    Ga   - all points (i.e., transformed halfspaces) as dots
     Gp  -  coplanar points and vertices as radii
     Gv  -  vertices (i.e., non-redundant halfspaces) as spheres
    Gi   - inner planes (i.e., halfspace intersections) only
     Gn  -  no planes
     Go  -  outer planes only
    Gc   - centrums
    Gh   - hyperplane intersections
    Gr   - ridges
    GDn  - drop dimension n in 3-d and 4-d output

Print options:
    PAn  - keep n largest facets (i.e., intersections) by area
    Pdk:n- drop facet if normal[k] <= n (default 0.0)
    PDk:n- drop facet if normal[k] >= n
    Pg   - print good facets (needs 'QGn' or 'QVn')
    PFn  - keep facets whose area is at least n
    PG   - print neighbors of good facets
    PMn  - keep n facets with most merges
    Po   - force output.  If error, output neighborhood of facet
    Pp   - do not report precision problems

    .    - list of all options
    -    - one line descriptions of all options

Up: Home page for Qhull
Up: Qhull manual: Table of Contents
To: Programs • Options • Output • Formats • Geomview • Print • Qhull • Precision • Trace
To: synopsis • input • outputs • controls • graphics • notes • conventions • options

The Geometry Center Home Page

Comments to: qhull@qhull.org
Created: Sept. 25, 1995 --- Last modified: see top

qhull-2012.1/html/qhull-cpp.xml0000644000076400010400000002671611710144470017512 0ustar bbarberAdministrators

Qhull C++ -- C++ interface to Qhull

Copyright (c) 2009-2012, C.B. Barber

This document records Please send comments and suggestions to bradb@shore.net

Help
.
Qhull's collection APIs are modeled on Qt's collection API (QList, QVector, QHash). They support STL and Qt programming. Some of Qhull's collection classes derive from STL classes. If so, please avoid additional STL functions and operators added by inheritance. These collection classes may be rewritten to derive from Qt classes instead. See . Qhull's collection API (where applicable). For documentation, see Qt's QList, QMap, QListIterator, QMapIterator, QMutableListIterator, and QMutableMapIterator
  • STL types [list, qlinkedlist, qlist, qvector, vector] -- const_iterator, iterator
  • STL types describing iterators [list, qlinkedlist, qlist, qvector, vector] -- const_pointer, const_reference, difference_type, pointer, reference, size_type, value_type. Pointer and reference types not defined if unavailable (not needed for <algorithm>)
  • const_iterator, iterator types -- difference_type, iterator_category, pointer, reference, value_type
  • Qt types [qlinkedlist, qlist, qvector] -- ConstIterator, Iterator, QhullclassIterator, MutableQhullclassIterator. Qt's foreach requires const_iterator.
  • Types for sets/maps [hash_map, QHash] -- key_compare, key_type, mapped_type
  • Constructor -- default constructor, copy constructor, assignment operator, destructor
  • Conversion -- to/from/as corresponding C, STL, and Qt constructs. Include toQList and toStdVector (may be filtered, e.g., QhullFacetSet). Do not define fromStdList and fromQList if container is not reference counted (i.e., acts like a value)
  • Get/set -- configuration options for class
  • STL-style iterator - begin, constBegin, constEnd, end, key, value, =, *, [], ->, ++, --, +, -, ==, !=, <, <=, >, >=, const_iterator(iterator), iterator COMPARE const_iterator. An iterator is an abstraction of a pointer. It is not aware of its container.
  • Java-style iterator [qiterator.h] - countRemaining, findNext, findPrevious, hasNext, hasPrevious, next, peekNext, peekPrevious, previous, toBack, toFront, = Coordinates
  • Mutable Java-style iterator adds - insert, remove, setValue, value
  • Element access -- back, first, front, last
  • Element access w/ index -- [], at (const& only), constData, data, mid, value
  • Read-only - (int)count, empty, isEmpty, (size_t)size. Count() and size() may be filtered. If so, they may be zero when !empty().
  • Read-only for sets/maps - capacity, key, keys, reserve, resize, values
  • Operator - ==, !=, +, +=, <<
  • Read-write -- append, clear, erase, insert, move, prepend, pop_back, pop_front, push_back, push_front, removeAll, removeAt, removeFirst, removeLast, replace, swap, takeAt, takeFirst, takeLast
  • Read-write for sets/maps -- insertMulti, squeeze, take, unite
  • Search -- contains(const T &), count(const T &), indexOf, lastIndexOf
  • Search for sets/maps -- constFind, lowerBound, upperBound
  • Stream I/O -- stream <<
STL list and vector -- For unfiltered access to each element.
  • Apache: Creating your own containers -- requirements for STL containers. Iterators should define the types from 'iterator_traits'.
  • STL types -- allocator_type, const_iterator, const_pointer, const_reference, const_reverse_iterator, difference_type, iterator, iterator_category, pointer, reference, reverse_iterator, size_type, value_type
  • STL constructors -- MyType(), MyType(count), MyType(count, value), MyType(first, last), MyType(MyType&),
  • STL getter/setters -- at (random_access only), back, begin, capacity, end, front, rbegin, rend, size, max_size
  • STL predicates -- empty
  • STL iterator types -- const_pointer, const_reference, difference_type, iterator_category, pointer, reference, value_type
  • STL iterator operators -- *, -<, ++, --, +=, -=, +, -, [], ==, !=, <, >, >=, <=
  • STL operators -- =, [] (random_access only), ==, !=, <, >, <=, >=
  • STL modifiers -- assign, clear, erase, insert, pop_back, push_back, reserve, resize, swap
Qt Qlist -- For unfiltered access to each element
  • Additional Qt types -- ConstIterator, Iterator, QListIterator, QMutableListIterator
  • Additional Qt get/set -- constBegin, constEnd, count, first, last, value (random_access only)
  • Additional Qt predicates -- isEmpty
  • Additional Qt -- mid (random_access only)
  • Additional Qt search -- contains, count(T&), indexOf (random_access only), lastIndeOf (random_access only)
  • Additional Qt modifiers -- append, insert(index,value) (random_access only), move (random_access only), pop_front, prepend, push_front, removeAll, removeAt (random_access only), removeFirst, removeLast, replace, swap by index, takeAt, takeFirst, takeLast
  • Additional Qt operators -- +, <<, +=, stream << and >>
  • Unsupported types by Qt -- allocator_type, const_reverse_iterator, reverse_iterator
  • Unsupported accessors by Qt -- max_size, rbegin, rend
  • Unsupported constructors by Qt -- multi-value constructors
  • unsupported modifiers by Qt -- assign, muli-value inserts, STL's swaps
STL map and Qt QMap. These use nearly the same API as list and vector classes. They add the following.
  • STL types -- key_compare, key_type, mapped_type
  • STL search -- equal_range, find, lower_bound, upper_bound
  • Qt removes -- equal_range, key_compare
  • Qt renames -- lowerBound, upperBound
  • Qt adds -- constFind, insertMulti, key, keys, take, uniqueKeys, unite, values
  • Not applicable to map and QMap -- at, back, pop_back, pop_front, push_back, push_front, swap
  • Not applicable to QMap -- append, first, last, lastIndexOf, mid, move, prepend, removeAll, removeAt, removeFirst, removeLast, replace, squeeze, takeAt, takeFirst, takeLast
  • Not applicable to map -- assign
Qt QHash. STL extensions provide similar classes, e.g., Microsoft's stdext::hash_set. THey are nearly the same as QMap
  • Not applicable to Qhash -- lowerBound, unite, upperBound,
  • Qt adds -- squeeze
  • check... -- Throw error on failure
  • try... -- Return false on failure. Do not throw errors.
  • ...Temporarily -- lifetime depends on source. e.g., toByteArrayTemporarily
  • ...p -- indicates pointer-to.
  • end... -- points to one beyond the last available
  • private functions -- No syntactic indication. They may become public later on.
  • Error messages -- Preceed error messages with the name of the class throwing the error (e.g. "ClassName: ..."). If this is an internal error, use "ClassName inconsistent: ..."
  • parameter order -- qhRunId, dimension, coordinates, count.
  • toClass -- Convert into a Class object (makes a deep copy)
  • qRunId -- Requires Qh installed. Some routines allow 0 for limited info (e.g., operator<<)
  • Disable methods in derived classes -- If the default constructor, copy constructor, or copy assignment is disabled, it should be also disabled in derived classes (better error messages).
  • Constructor order -- default constructor, other constructors, copy constructor, copy assignment, destructor
qhull-2012.1/html/qhull.htm0000644000076400010400000004465411720062203016715 0ustar bbarberAdministrators qhull -- convex hull and related structures

Up: Home page for Qhull
Up: Qhull manual: Table of Contents
To: Programs • Options • Output • Formats • Geomview • Print • Qhull • Precision • Trace
To: synopsis • input • outputs • controls • options

[cone]qhull -- convex hull and related structures

The convex hull of a set of points is the smallest convex set containing the points. The Delaunay triangulation and furthest-site Delaunay triangulation are equivalent to a convex hull in one higher dimension. Halfspace intersection about a point is equivalent to a convex hull by polar duality.

The qhull program provides options to build these structures and to experiment with the process. Use the qconvex, qdelaunay, qhalf, and qvoronoi programs to build specific structures. You may use qhull instead. It takes the same options and uses the same code.

Example: rbox 1000 D3 | qhull C-1e-4 FO Ts
Compute the 3-d convex hull of 1000 random points. Centrums must be 10^-4 below neighboring hyperplanes. Print the options and precision constants. When done, print statistics. These options may be used with any of the Qhull programs.
 
Example: rbox 1000 D3 | qhull d Qbb R1e-4 Q0
Compute the 3-d Delaunay triangulation of 1000 random points. Randomly perturb all calculations by [0.9999,1.0001]. Do not correct precision problems. This leads to serious precision errors.

Use the following equivalences when calling qhull in 2-d to 4-d (a 3-d Delaunay triangulation is a 4-d convex hull):

Use the following equivalences when calling qhull in 5-d and higher (a 4-d Delaunay triangulation is a 5-d convex hull):

By default, Qhull merges coplanar facets. For example, the convex hull of a cube's vertices has six facets.

If you use 'Qt' (triangulated output), all facets will be simplicial (e.g., triangles in 2-d). For the cube example, it will have 12 facets. Some facets may be degenerate and have zero area.

If you use 'QJ' (joggled input), all facets will be simplicial. The corresponding vertices will be slightly perturbed. Joggled input is less accurate that triangulated output.See Merged facets or joggled input.

The output for 4-d convex hulls may be confusing if the convex hull contains non-simplicial facets (e.g., a hypercube). See Why are there extra points in a 4-d or higher convex hull?

Copyright © 1995-2012 C.B. Barber

»qhull synopsis

qhull- compute convex hulls and related structures.
    input (stdin): dimension, n, point coordinates
    comments start with a non-numeric character
    halfspace: use dim+1 and put offsets after coefficients

options (qh-quick.htm):
    d    - Delaunay triangulation by lifting points to a paraboloid
    d Qu - furthest-site Delaunay triangulation (upper convex hull)
    v    - Voronoi diagram as the dual of the Delaunay triangulation
    v Qu - furthest-site Voronoi diagram
    H1,1 - Halfspace intersection about [1,1,0,...] via polar duality
    Qt   - triangulated output
    QJ   - joggle input instead of merging facets
    Tv   - verify result: structure, convexity, and point inclusion
    .    - concise list of all options
    -    - one-line description of all options

Output options (subset):
    s    - summary of results (default)
    i    - vertices incident to each facet
    n    - normals with offsets
    p    - vertex coordinates (if 'Qc', includes coplanar points)
           if 'v', Voronoi vertices
    Fp   - halfspace intersections
    Fx   - extreme points (convex hull vertices)
    FA   - compute total area and volume
    o    - OFF format (if 'v', outputs Voronoi regions)
    G    - Geomview output (2-d, 3-d and 4-d)
    m    - Mathematica output (2-d and 3-d)
    QVn  - print facets that include point n, -n if not
    TO file- output results to file, may be enclosed in single quotes

examples:
    rbox c d D2 | qhull Qc s f Fx | more      rbox 1000 s | qhull Tv s FA
    rbox 10 D2 | qhull d QJ s i TO result     rbox 10 D2 | qhull v Qbb Qt p
    rbox 10 D2 | qhull d Qu QJ m              rbox 10 D2 | qhull v Qu QJ o
    rbox c | qhull n                          rbox c | qhull FV n | qhull H Fp
    rbox d D12 | qhull QR0 FA                 rbox c D7 | qhull FA TF1000
    rbox y 1000 W0 | qhull                    rbox 10 | qhull v QJ o Fv

»qhull input

The input data on stdin consists of:

  • dimension
  • number of points
  • point coordinates

Use I/O redirection (e.g., qhull < data.txt), a pipe (e.g., rbox 10 | qhull), or the 'TI' option (e.g., qhull TI data.txt).

Comments start with a non-numeric character. Error reporting is simpler if there is one point per line. Dimension and number of points may be reversed. For halfspace intersection, an interior point may be prepended (see qhalf input).

Here is the input for computing the convex hull of the unit cube. The output is the normals, one per facet.

rbox c > data 

3 RBOX c
8
  -0.5   -0.5   -0.5
  -0.5   -0.5    0.5
  -0.5    0.5   -0.5
  -0.5    0.5    0.5
   0.5   -0.5   -0.5
   0.5   -0.5    0.5
   0.5    0.5   -0.5
   0.5    0.5    0.5

qhull s n < data


Convex hull of 8 points in 3-d:

  Number of vertices: 8
  Number of facets: 6
  Number of non-simplicial facets: 6

Statistics for: RBOX c | QHULL s n

  Number of points processed: 8
  Number of hyperplanes created: 11
  Number of distance tests for qhull: 35
  Number of merged facets: 6
  Number of distance tests for merging: 84
  CPU seconds to compute hull (after input): 0.081

4
6
     0      0     -1   -0.5
     0     -1      0   -0.5
     1      0      0   -0.5
    -1      0      0   -0.5
     0      1      0   -0.5
     0      0      1   -0.5

»qhull outputs

These options control the output of qhull. They may be used individually or together.

 
General
qhull
compute the convex hull of the input points. See qconvex.
qhull d Qbb
compute the Delaunay triangulation by lifting the points to a paraboloid. Use option 'Qbb' to scale the paraboloid and improve numeric precision. See qdelaunay.
qhull v Qbb
compute the Voronoi diagram by computing the Delaunay triangulation. Use option 'Qbb' to scale the paraboloid and improve numeric precision. See qvoronoi.
qhull H
compute the halfspace intersection about a point via polar duality. See qhalf.

For a full list of output options see

»qhull controls

For a full list of control options see

»qhull options

qhull- compute convex hulls and related structures.
    http://www.qhull.org

input (stdin):
    first lines: dimension and number of points (or vice-versa).
    other lines: point coordinates, best if one point per line
    comments:    start with a non-numeric character
    halfspaces:  use dim plus one and put offset after coefficients.
                 May be preceded by a single interior point ('H').

options:
    d    - Delaunay triangulation by lifting points to a paraboloid
    d Qu - furthest-site Delaunay triangulation (upper convex hull)
    v    - Voronoi diagram (dual of the Delaunay triangulation)
    v Qu - furthest-site Voronoi diagram
    Hn,n,... - halfspace intersection about point [n,n,0,...]
    Qt   - triangulated output
    QJ   - joggle input instead of merging facets
    Qc   - keep coplanar points with nearest facet
    Qi   - keep interior points with nearest facet

Qhull control options:
    Qbk:n   - scale coord k so that low bound is n
      QBk:n - scale coord k so that upper bound is n (QBk is 0.5)
    QbB  - scale input to unit cube centered at the origin
    Qbb  - scale last coordinate to [0,m] for Delaunay triangulations
    Qbk:0Bk:0 - remove k-th coordinate from input
    QJn  - randomly joggle input in range [-n,n]
    QRn  - random rotation (n=seed, n=0 time, n=-1 time/no rotate)
    Qf   - partition point to furthest outside facet
    Qg   - only build good facets (needs 'QGn', 'QVn', or 'PdD')
    Qm   - only process points that would increase max_outside
    Qr   - process random outside points instead of furthest ones
    Qs   - search all points for the initial simplex
    Qu   - for 'd' or 'v', compute upper hull without point at-infinity
              returns furthest-site Delaunay triangulation
    Qv   - test vertex neighbors for convexity
    Qx   - exact pre-merges (skips coplanar and anglomaniacs facets)
    Qz   - add point-at-infinity to Delaunay triangulation
    QGn  - good facet if visible from point n, -n for not visible
    QVn  - good facet if it includes point n, -n if not
    Q0   - turn off default p remerge with 'C-0'/'Qx'
    Q1     - sort merges by type instead of angle
    Q2   - merge all non-convex at once instead of independent sets
    Q3   - do not merge redundant vertices
    Q4   - avoid old>new merges
    Q5   - do not correct outer planes at end of qhull
    Q6   - do not pre-merge concave or coplanar facets
    Q7   - depth-first processing instead of breadth-first
    Q8   - do not process near-inside points
    Q9   - process furthest of furthest points
    Q10  - no special processing for narrow distributions
        Q11  - copy normals and recompute centrums for tricoplanar facets

Towpaths Trace options:
    T4   - trace at level n, 4=all, 5=mem/gauss, -1= events
    Tc   - check frequently during execution
    Ts   - print statistics
    Tv   - verify result: structure, convexity, and point inclusion
    Tz   - send all output to stdout
    TFn  - report summary when n or more facets created
    TI file - input data from file, no spaces or single quotes
    TO file - output results to file, may be enclosed in single quotes
    TPn  - turn on tracing when point n added to hull
     TMn - turn on tracing at merge n
     TWn - trace merge facets when width > n
    TRn  - rerun qhull n times.  Use with 'QJn'
    TVn  - stop qhull after adding point n, -n for before (see TCn)
     TCn - stop qhull after building cone for point n (see TVn)

Precision options:
    Cn   - radius of centrum (roundoff added).  Merge facets if non-convex
     An  - cosine of maximum angle.  Merge facets if cosine > n or non-convex
           C-0 roundoff, A-0.99/C-0.01 pre-merge, A0.99/C0.01 post-merge
    En   - max roundoff error for distance computation
    Rn   - randomly perturb computations by a factor of [1-n,1+n]
    Vn   - min distance above plane for a visible facet (default 3C-n or En)
    Un   - max distance below plane for a new, coplanar point (default Vn)
    Wn   - min facet width for outside point (before roundoff, default 2Vn)

Output formats (may be combined; if none, produces a summary to stdout):
    f    - facet dump
    G    - Geomview output (see below)
    i    - vertices incident to each facet
    m    - Mathematica output (2-d and 3-d)
    o    - OFF format (dim, points and facets; Voronoi regions)
    n    - normals with offsets
    p    - vertex coordinates or Voronoi vertices (coplanar points if 'Qc')
    s    - summary (stderr)

More formats:
    Fa   - area for each facet
    FA   - compute total area and volume for option 's'
    Fc   - count plus coplanar points for each facet
           use 'Qc' (default) for coplanar and 'Qi' for interior
    FC   - centrum or Voronoi center for each facet
    Fd   - use cdd format for input (homogeneous with offset first)
    FD   - use cdd format for numeric output (offset first)
    FF   - facet dump without ridges
    Fi   - inner plane for each facet
           for 'v', separating hyperplanes for bounded Voronoi regions
    FI   - ID of each facet
    Fm   - merge count for each facet (511 max)
    FM   - Maple output (2-d and 3-d)
    Fn   - count plus neighboring facets for each facet
    FN   - count plus neighboring facets for each point
    Fo   - outer plane (or max_outside) for each facet
           for 'v', separating hyperplanes for unbounded Voronoi regions
    FO   - options and precision constants
    Fp   - dim, count, and intersection coordinates (halfspace only)
    FP   - nearest vertex and distance for each coplanar point
    FQ   - command used for qhull
    Fs   - summary: #int (8), dimension, #points, tot vertices, tot facets,
                      output: #vertices, #facets, #coplanars, #nonsimplicial
                    #real (2), max outer plane, min vertex
    FS   - sizes:   #int (0)
                    #real(2) tot area, tot volume
    Ft   - triangulation with centrums for non-simplicial facets (OFF format)
    Fv   - count plus vertices for each facet
           for 'v', Voronoi diagram as Voronoi vertices for pairs of sites
    FV   - average of vertices (a feasible point for 'H')
    Fx   - extreme points (in order for 2-d)

Geomview options (2-d, 3-d, and 4-d; 2-d Voronoi)
    Ga   - all points as dots
     Gp  -  coplanar points and vertices as radii
     Gv  -  vertices as spheres
    Gi   - inner planes only
     Gn  -  no planes
     Go  -  outer planes only
    Gc   - centrums
    Gh   - hyperplane intersections
    Gr   - ridges
    GDn  - drop dimension n in 3-d and 4-d output
    Gt   - for 3-d 'd', transparent outer ridges

Print options:
    PAn  - keep n largest facets by area
    Pdk:n - drop facet if normal[k] <= n (default 0.0)
    PDk:n - drop facet if normal[k] >= n
    Pg   - print good facets (needs 'QGn' or 'QVn')
    PFn  - keep facets whose area is at least n
    PG   - print neighbors of good facets
    PMn  - keep n facets with most merges
    Po   - force output.  If error, output neighborhood of facet
    Pp   - do not report precision problems

    .    - list of all options
    -    - one line descriptions of all options

Up: Home page for Qhull
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To: synopsis • input • outputs • controls • options

The Geometry Center Home Page

Comments to: qhull@qhull.org
Created: Sept. 25, 1995 --- Last modified: see top

qhull-2012.1/html/qhull.man0000644000076400010400000011216211545627033016703 0ustar bbarberAdministrators.\" This is the Unix manual page for qhull, written in nroff, the standard .\" manual formatter for Unix systems. To format it, type .\" .\" nroff -man qhull.man .\" .\" This will print a formatted copy to standard output. If you want .\" to ensure that the output is plain ASCII, free of any control .\" characters that nroff uses for underlining etc, pipe the output .\" through "col -b": .\" .\" nroff -man qhull.man | col -b .\" .\" Warning: a leading quote "'" or dot "." will not format correctly .\" .TH qhull 1 "2003/12/30" "Geometry Center" .SH NAME qhull \- convex hull, Delaunay triangulation, Voronoi diagram, halfspace intersection about a point, hull volume, facet area .SH SYNOPSIS .nf qhull- compute convex hulls and related structures input (stdin): dimension, #points, point coordinates first comment (non-numeric) is listed in the summary halfspace: use dim plus one with offsets after coefficients options (qh-quick.htm): d - Delaunay triangulation by lifting points to a paraboloid v - Voronoi diagram via the Delaunay triangulation H1,1 - Halfspace intersection about [1,1,0,...] d Qu - Furthest-site Delaunay triangulation (upper convex hull) v Qu - Furthest-site Voronoi diagram Qt - triangulated output QJ - Joggle the input to avoid precision problems . - concise list of all options - - one-line description of all options Output options (subset): FA - compute total area and volume Fx - extreme points (convex hull vertices) G - Geomview output (2-d, 3-d and 4-d) Fp - halfspace intersection coordinates m - Mathematica output (2-d and 3-d) n - normals with offsets o - OFF file format (if Voronoi, outputs regions) TO file- output results to file, may be enclosed in single quotes f - print all fields of all facets s - summary of results (default) Tv - verify result: structure, convexity, and point inclusion p - vertex coordinates (centers for Voronoi) i - vertices incident to each facet example: rbox 1000 s | qhull Tv s FA .fi - html manual: index.htm - installation: README.txt - see also: COPYING.txt, REGISTER.txt, Changes.txt - WWW: - GIT: - mirror: - news: - Geomview: - news group: - FAQ: - email: qhull@qhull.org - bug reports: qhull_bug@qhull.org The sections are: - INTRODUCTION - DESCRIPTION, a description of Qhull - IMPRECISION, how Qhull handles imprecision - OPTIONS - Input and output options - Additional input/output formats - Precision options - Geomview options - Print options - Qhull options - Trace options - BUGS - E-MAIL - SEE ALSO - AUTHORS - ACKNOWLEGEMENTS This man page briefly describes all Qhull options. Please report any mismatches with Qhull's html manual (index.htm). .PP .SH INTRODUCTION Qhull is a general dimension code for computing convex hulls, Delaunay triangulations, Voronoi diagram, furthest\[hy]site Voronoi diagram, furthest\[hy]site Delaunay triangulations, and halfspace intersections about a point. It implements the Quickhull algorithm for computing the convex hull. Qhull handles round\[hy]off errors from floating point arithmetic. It can approximate a convex hull. The program includes options for hull volume, facet area, partial hulls, input transformations, randomization, tracing, multiple output formats, and execution statistics. The program can be called from within your application. You can view the results in 2\[hy]d, 3\[hy]d and 4\[hy]d with Geomview. .PP .SH DESCRIPTION .PP The format of input is the following: first line contains the dimension, second line contains the number of input points, and point coordinates follow. The dimension and number of points can be reversed. Comments and line breaks are ignored. A comment starts with a non\[hy]numeric character and continues to the end of line. The first comment is reported in summaries and statistics. Error reporting is better if there is one point per line. .PP The default printout option is a short summary. There are many other output formats. .PP Qhull implements the Quickhull algorithm for convex hull. This algorithm combines the 2\[hy]d Quickhull algorithm with the n\[hy]d beneath\[hy]beyond algorithm [c.f., Preparata & Shamos '85]. It is similar to the randomized algorithms of Clarkson and others [Clarkson et al. '93]. The main advantages of Quickhull are output sensitive performance, reduced space requirements, and automatic handling of precision problems. .PP The data structure produced by Qhull consists of vertices, ridges, and facets. A vertex is a point of the input set. A ridge is a set of d vertices and two neighboring facets. For example in 3\[hy]d, a ridge is an edge of the polyhedron. A facet is a set of ridges, a set of neighboring facets, a set of incident vertices, and a hyperplane equation. For simplicial facets, the ridges are defined by the vertices and neighboring facets. When Qhull merges two facets, it produces a non\[hy]simplicial facet. A non\[hy]simplicial facet has more than d neighbors and may share more than one ridge with a neighbor. .PP .SH IMPRECISION .PP Since Qhull uses floating point arithmetic, roundoff error may occur for each calculation. This causes problems for most geometric algorithms. .PP Qhull automatically sets option 'C\-0' in 2\[hy]d, 3\[hy]d, and 4\[hy]d, or option 'Qx' in 5\[hy]d and higher. These options handle precision problems by merging facets. Alternatively, use option 'QJ' to joggle the input. .PP With 'C\-0', Qhull merges non\[hy]convex facets while constructing the hull. The remaining facets are clearly convex. With 'Qx', Qhull merges coplanar horizon facets, flipped facets, concave facets and duplicated ridges. It merges coplanar facets after constructing the hull. With 'Qx', coplanar points may be missed, but it appears to be unlikely. .PP To guarantee triangular output, joggle the input with option 'QJ'. Facet merging will not occur. .SH OPTIONS .PP To get a list of the most important options, execute 'qhull' by itself. To get a complete list of options, execute 'qhull \-'. To get a complete, concise list of options, execute 'qhull .'. Options can be in any order. Capitalized options take an argument (except 'PG' and 'F' options). Single letters are used for output formats and precision constants. The other options are grouped into menus for other output formats ('F'), Geomview output ('G'), printing ('P'), Qhull control ('Q'), and tracing ('T'). .TP Main options: .TP default Compute the convex hull of the input points. Report a summary of the result. .TP d Compute the Delaunay triangulation by lifting the input points to a paraboloid. The 'o' option prints the input points and facets. The 'QJ' option guarantees triangular output. The 'Ft' option prints a triangulation. It adds points (the centrums) to non\[hy]simplicial facets. .TP v Compute the Voronoi diagram from the Delaunay triangulation. The 'p' option prints the Voronoi vertices. The 'o' option prints the Voronoi vertices and the vertices in each Voronoi region. It lists regions in site ID order. The 'Fv' option prints each ridge of the Voronoi diagram. The first or zero'th vertex indicates the infinity vertex. Its coordinates are qh_INFINITE (\-10.101). It indicates unbounded Voronoi regions or degenerate Delaunay triangles. .TP Hn,n,... Compute halfspace intersection about [n,n,0,...]. The input is a set of halfspaces defined in the same format as 'n', 'Fo', and 'Fi'. Use 'Fp' to print the intersection points. Use 'Fv' to list the intersection points for each halfspace. The other output formats display the dual convex hull. The point [n,n,n,...] is a feasible point for the halfspaces, i.e., a point that is inside all of the halfspaces (Hx+b <= 0). The default coordinate value is 0. The input may start with a feasible point. If so, use 'H' by itself. The input starts with a feasible point when the first number is the dimension, the second number is "1", and the coordinates complete a line. The 'FV' option produces a feasible point for a convex hull. .TP d Qu Compute the furthest\[hy]site Delaunay triangulation from the upper convex hull. The 'o' option prints the input points and facets. The 'QJ' option guarantees triangular otuput. You can also use 'Ft' to triangulate via the centrums of non\[hy]simplicial facets. .TP v Qu Compute the furthest\[hy]site Voronoi diagram. The 'p' option prints the Voronoi vertices. The 'o' option prints the Voronoi vertices and the vertices in each Voronoi region. The 'Fv' option prints each ridge of the Voronoi diagram. The first or zero'th vertex indicates the infinity vertex at infinity. Its coordinates are qh_INFINITE (\-10.101). It indicates unbounded Voronoi regions and degenerate Delaunay triangles. .PP .TP Input/Output options: .TP f Print out all facets and all fields of each facet. .TP G Output the hull in Geomview format. For imprecise hulls, Geomview displays the inner and outer hull. Geomview can also display points, ridges, vertices, coplanar points, and facet intersections. See below for a list of options. For Delaunay triangulations, 'G' displays the corresponding paraboloid. For halfspace intersection, 'G' displays the dual polytope. .TP i Output the incident vertices for each facet. Qhull prints the number of facets followed by the vertices of each facet. One facet is printed per line. The numbers are the 0\[hy]relative indices of the corresponding input points. The facets are oriented. In 4d and higher, Qhull triangulates non\[hy]simplicial facets. Each apex (the first vertex) is a created point that corresponds to the facet's centrum. Its index is greater than the indices of the input points. Each base corresponds to a simplicial ridge between two facets. To print the vertices without triangulation, use option 'Fv'. .TP m Output the hull in Mathematica format. Qhull writes a Mathematica file for 2\[hy]d and 3\[hy]d convex hulls and for 2\[hy]d Delaunay triangulations. Qhull produces a list of objects that you can assign to a variable in Mathematica, for example: "list= << ". If the object is 2\[hy]d, it can be visualized by "Show[Graphics[list]] ". For 3\[hy]d objects the command is "Show[Graphics3D[list]]". .TP n Output the normal equation for each facet. Qhull prints the dimension (plus one), the number of facets, and the normals for each facet. The facet's offset follows its normal coefficients. .TP o Output the facets in OFF file format. Qhull prints the dimension, number of points, number of facets, and number of ridges. Then it prints the coordinates of the input points and the vertices for each facet. Each facet is on a separate line. The first number is the number of vertices. The remainder are the indices of the corresponding points. The vertices are oriented in 2\[hy]d, 3\[hy]d, and in simplicial facets. For 2\[hy]d Voronoi diagrams, the vertices are sorted by adjacency, but not oriented. In 3\[hy]d and higher, the Voronoi vertices are sorted by index. See the 'v' option for more information. .TP p Output the coordinates of each vertex point. Qhull prints the dimension, the number of points, and the coordinates for each vertex. With the 'Gc' and 'Gi' options, it also prints coplanar and interior points. For Voronoi diagrams, it prints the coordinates of each Voronoi vertex. .TP s Print a summary to stderr. If no output options are specified at all, a summary goes to stdout. The summary lists the number of input points, the dimension, the number of vertices in the convex hull, the number of facets in the convex hull, the number of good facets (if 'Pg'), and statistics. The last two statistics (if needed) measure the maximum distance from a point or vertex to a facet. The number in parenthesis (e.g., 2.1x) is the ratio between the maximum distance and the worst\[hy]case distance due to merging two simplicial facets. .PP .TP Precision options .TP An Maximum angle given as a cosine. If the angle between a pair of facet normals is greater than n, Qhull merges one of the facets into a neighbor. If 'n' is negative, Qhull tests angles after adding each point to the hull (pre\[hy]merging). If 'n' is positive, Qhull tests angles after constructing the hull (post\[hy]merging). Both pre\[hy] and post\[hy]merging can be defined. Option 'C0' or 'C\-0' is set if the corresponding 'Cn' or 'C\-n' is not set. If 'Qx' is set, then 'A\-n' and 'C\-n' are checked after the hull is constructed and before 'An' and 'Cn' are checked. .TP Cn Centrum radius. If a centrum is less than n below a neighboring facet, Qhull merges one of the facets. If 'n' is negative or '\-0', Qhull tests and merges facets after adding each point to the hull. This is called "pre\[hy]merging". If 'n' is positive, Qhull tests for convexity after constructing the hull ("post\[hy]merging"). Both pre\[hy] and post\[hy]merging can be defined. For 5\[hy]d and higher, 'Qx' should be used instead of 'C\-n'. Otherwise, most or all facets may be merged together. .TP En Maximum roundoff error for distance computations. .TP Rn Randomly perturb distance computations up to +/\- n * max_coord. This option perturbs every distance, hyperplane, and angle computation. To use time as the random number seed, use option 'QR\-1'. .TP Vn Minimum distance for a facet to be visible. A facet is visible if the distance from the point to the facet is greater than 'Vn'. Without merging, the default value for 'Vn' is the round\[hy]off error ('En'). With merging, the default value is the pre\[hy]merge centrum ('C\-n') in 2\[hy]d or 3\[hy]d, or three times that in other dimensions. If the outside width is specified ('Wn'), the maximum, default value for 'Vn' is 'Wn'. .TP Un Maximum distance below a facet for a point to be coplanar to the facet. The default value is 'Vn'. .TP Wn Minimum outside width of the hull. Points are added to the convex hull only if they are clearly outside of a facet. A point is outside of a facet if its distance to the facet is greater than 'Wn'. The normal value for 'Wn' is 'En'. If the user specifies pre\[hy]merging and does not set 'Wn', than 'Wn' is set to the premerge 'Cn' and maxcoord*(1\-An). .PP .TP Additional input/output formats .TP Fa Print area for each facet. For Delaunay triangulations, the area is the area of the triangle. For Voronoi diagrams, the area is the area of the dual facet. Use 'PAn' for printing the n largest facets, and option 'PFn' for printing facets larger than 'n'. The area for non\[hy]simplicial facets is the sum of the areas for each ridge to the centrum. Vertices far below the facet's hyperplane are ignored. The reported area may be significantly less than the actual area. .TP FA Compute the total area and volume for option 's'. It is an approximation for non\[hy]simplicial facets (see 'Fa'). .TP Fc Print coplanar points for each facet. The output starts with the number of facets. Then each facet is printed one per line. Each line is the number of coplanar points followed by the point ids. Option 'Qi' includes the interior points. Each coplanar point (interior point) is assigned to the facet it is furthest above (resp., least below). .TP FC Print centrums for each facet. The output starts with the dimension followed by the number of facets. Then each facet centrum is printed, one per line. .TP Fd Read input in cdd format with homogeneous points. The input starts with comments. The first comment is reported in the summary. Data starts after a "begin" line. The next line is the number of points followed by the dimension+1 and "real" or "integer". Then the points are listed with a leading "1" or "1.0". The data ends with an "end" line. For halfspaces ('Fd Hn,n,...'), the input format is the same. Each halfspace starts with its offset. The sign of the offset is the opposite of Qhull's convention. .TP FD Print normals ('n', 'Fo', 'Fi') or points ('p') in cdd format. The first line is the command line that invoked Qhull. Data starts with a "begin" line. The next line is the number of normals or points followed by the dimension+1 and "real". Then the normals or points are listed with the offset before the coefficients. The offset for points is 1.0. The offset for normals has the opposite sign. The data ends with an "end" line. .TP FF Print facets (as in 'f') without printing the ridges. .TP Fi Print inner planes for each facet. The inner plane is below all vertices. .TP Fi Print separating hyperplanes for bounded, inner regions of the Voronoi diagram. The first line is the number of ridges. Then each hyperplane is printed, one per line. A line starts with the number of indices and floats. The first pair lists adjacent input sites, the next d floats are the normalized coefficients for the hyperplane, and the last float is the offset. The hyperplane is oriented toward 'QVn' (if defined), or the first input site of the pair. Use 'Tv' to verify that the hyperplanes are perpendicular bisectors. Use 'Fo' for unbounded regions, and 'Fv' for the corresponding Voronoi vertices. .TP FI Print facet identifiers. .TP Fm Print number of merges for each facet. At most 511 merges are reported for a facet. See 'PMn' for printing the facets with the most merges. .TP FM Output the hull in Maple format. Qhull writes a Maple file for 2\[hy]d and 3\[hy]d convex hulls and for 2\[hy]d Delaunay triangulations. Qhull produces a '.mpl' file for displaying with display3d(). .TP Fn Print neighbors for each facet. The output starts with the number of facets. Then each facet is printed one per line. Each line is the number of neighbors followed by an index for each neighbor. The indices match the other facet output formats. A negative index indicates an unprinted facet due to printing only good facets ('Pg'). It is the negation of the facet's ID (option 'FI'). For example, negative indices are used for facets "at infinity" in the Delaunay triangulation. .TP FN Print vertex neighbors or coplanar facet for each point. The first line is the number of points. Then each point is printed, one per line. If the point is coplanar, the line is "1" followed by the facet's ID. If the point is not a selected vertex, the line is "0". Otherwise, each line is the number of neighbors followed by the corresponding facet indices (see 'Fn'). .TP Fo Print outer planes for each facet in the same format as 'n'. The outer plane is above all points. .TP Fo Print separating hyperplanes for unbounded, outer regions of the Voronoi diagram. The first line is the number of ridges. Then each hyperplane is printed, one per line. A line starts with the number of indices and floats. The first pair lists adjacent input sites, the next d floats are the normalized coefficients for the hyperplane, and the last float is the offset. The hyperplane is oriented toward 'QVn' (if defined), or the first input site of the pair. Use 'Tv' to verify that the hyperplanes are perpendicular bisectors. Use 'Fi' for bounded regions, and 'Fv' for the corresponding Voronoi vertices. .TP FO List all options to stderr, including the default values. Additional 'FO's are printed to stdout. .TP Fp Print points for halfspace intersections (option 'Hn,n,...'). Each intersection corresponds to a facet of the dual polytope. The "infinity" point [\-10.101,\-10.101,...] indicates an unbounded intersection. .TP FP For each coplanar point ('Qc') print the point ID of the nearest vertex, the point ID, the facet ID, and the distance. .TP FQ Print command used for qhull and input. .TP Fs Print a summary. The first line consists of the number of integers ("8"), followed by the dimension, the number of points, the number of vertices, the number of facets, the number of vertices selected for output, the number of facets selected for output, the number of coplanar points selected for output, number of simplicial, unmerged facets in output The second line consists of the number of reals ("2"), followed by the maxmimum offset to an outer plane and and minimum offset to an inner plane. Roundoff is included. Later versions of Qhull may produce additional integers or reals. .TP FS Print the size of the hull. The first line consists of the number of integers ("0"). The second line consists of the number of reals ("2"), followed by the total facet area, and the total volume. Later versions of Qhull may produce additional integers or reals. The total volume measures the volume of the intersection of the halfspaces defined by each facet. Both area and volume are approximations for non\[hy]simplicial facets. See option 'Fa'. .TP Ft Print a triangulation with added points for non\[hy]simplicial facets. The first line is the dimension and the second line is the number of points and the number of facets. The points follow, one per line, then the facets follow as a list of point indices. With option 'Qz', the points include the point\[hy]at\[hy]infinity. .TP Fv Print vertices for each facet. The first line is the number of facets. Then each facet is printed, one per line. Each line is the number of vertices followed by the corresponding point ids. Vertices are listed in the order they were added to the hull (the last one is first). .TP Fv Print all ridges of a Voronoi diagram. The first line is the number of ridges. Then each ridge is printed, one per line. A line starts with the number of indices. The first pair lists adjacent input sites, the remaining indices list Voronoi vertices. Vertex '0' indicates the vertex\[hy]at\[hy]infinity (i.e., an unbounded ray). In 3\[hy]d, the vertices are listed in order. See 'Fi' and 'Fo' for separating hyperplanes. .TP FV Print average vertex. The average vertex is a feasible point for halfspace intersection. .TP Fx List extreme points (vertices) of the convex hull. The first line is the number of points. The other lines give the indices of the corresponding points. The first point is '0'. In 2\[hy]d, the points occur in counter\[hy]clockwise order; otherwise they occur in input order. For Delaunay triangulations, 'Fx' lists the extreme points of the input sites. The points are unordered. .PP .TP Geomview options .TP G Produce a file for viewing with Geomview. Without other options, Qhull displays edges in 2\[hy]d, outer planes in 3\[hy]d, and ridges in 4\[hy]d. A ridge can be explicit or implicit. An explicit ridge is a dim\-1 dimensional simplex between two facets. In 4\[hy]d, the explicit ridges are triangles. When displaying a ridge in 4\[hy]d, Qhull projects the ridge's vertices to one of its facets' hyperplanes. Use 'Gh' to project ridges to the intersection of both hyperplanes. .TP Ga Display all input points as dots. .TP Gc Display the centrum for each facet in 3\[hy]d. The centrum is defined by a green radius sitting on a blue plane. The plane corresponds to the facet's hyperplane. The radius is defined by 'C\-n' or 'Cn'. .TP GDn Drop dimension n in 3\[hy]d or 4\[hy]d. The result is a 2\[hy]d or 3\[hy]d object. .TP Gh Display hyperplane intersections in 3\[hy]d and 4\[hy]d. In 3\[hy]d, the intersection is a black line. It lies on two neighboring hyperplanes (c.f., the blue squares associated with centrums ('Gc')). In 4\[hy]d, the ridges are projected to the intersection of both hyperplanes. .TP Gi Display inner planes in 2\[hy]d and 3\[hy]d. The inner plane of a facet is below all of its vertices. It is parallel to the facet's hyperplane. The inner plane's color is the opposite (1\-r,1\-g,1\-b) of the outer plane. Its edges are determined by the vertices. .TP Gn Do not display inner or outer planes. By default, Geomview displays the precise plane (no merging) or both inner and output planes (merging). Under merging, Geomview does not display the inner plane if the the difference between inner and outer is too small. .TP Go Display outer planes in 2\[hy]d and 3\[hy]d. The outer plane of a facet is above all input points. It is parallel to the facet's hyperplane. Its color is determined by the facet's normal, and its edges are determined by the vertices. .TP Gp Display coplanar points and vertices as radii. A radius defines a ball which corresponds to the imprecision of the point. The imprecision is the maximum of the roundoff error, the centrum radius, and maxcoord * (1\-An). It is at least 1/20'th of the maximum coordinate, and ignores post\[hy]merging if pre\[hy]merging is done. .TP Gr Display ridges in 3\[hy]d. A ridge connects the two vertices that are shared by neighboring facets. Ridges are always displayed in 4\[hy]d. .TP Gt A 3\[hy]d Delaunay triangulation looks like a convex hull with interior facets. Option 'Gt' removes the outside ridges to reveal the outermost facets. It automatically sets options 'Gr' and 'GDn'. .TP Gv Display vertices as spheres. The radius of the sphere corresponds to the imprecision of the data. See 'Gp' for determining the radius. .PP .TP Print options .TP PAn Only the n largest facets are marked good for printing. Unless 'PG' is set, 'Pg' is automatically set. .TP Pdk:n Drop facet from output if normal[k] <= n. The option 'Pdk' uses the default value of 0 for n. .TP PDk:n Drop facet from output if normal[k] >= n. The option 'PDk' uses the default value of 0 for n. .TP PFn Only facets with area at least 'n' are marked good for printing. Unless 'PG' is set, 'Pg' is automatically set. .TP Pg Print only good facets. A good facet is either visible from a point (the 'QGn' option) or includes a point (the 'QVn' option). It also meets the requirements of 'Pdk' and 'PDk' options. Option 'Pg' is automatically set for options 'PAn' and 'PFn'. .TP PG Print neighbors of good facets. .TP PMn Only the n facets with the most merges are marked good for printing. Unless 'PG' is set, 'Pg' is automatically set. .TP Po Force output despite precision problems. Verify ('Tv') does not check coplanar points. Flipped facets are reported and concave facets are counted. If 'Po' is used, points are not partitioned into flipped facets and a flipped facet is always visible to a point. Also, if an error occurs before the completion of Qhull and tracing is not active, 'Po' outputs a neighborhood of the erroneous facets (if any). .TP Pp Do not report precision problems. .PP .TP Qhull control options .TP Qbk:0Bk:0 Drop dimension k from the input points. This allows the user to take convex hulls of sub\[hy]dimensional objects. It happens before the Delaunay and Voronoi transformation. .TP QbB Scale the input points to fit the unit cube. After scaling, the lower bound will be \-0.5 and the upper bound +0.5 in all dimensions. For Delaunay and Voronoi diagrams, scaling happens after projection to the paraboloid. Under precise arithmetic, scaling does not change the topology of the convex hull. .TP Qbb Scale the last coordinate to [0, m] where m is the maximum absolute value of the other coordinates. For Delaunay and Voronoi diagrams, scaling happens after projection to the paraboloid. It reduces roundoff error for inputs with integer coordinates. Under precise arithmetic, scaling does not change the topology of the convex hull. .TP Qbk:n Scale the k'th coordinate of the input points. After scaling, the lower bound of the input points will be n. 'Qbk' scales to \-0.5. .TP QBk:n Scale the k'th coordinate of the input points. After scaling, the upper bound will be n. 'QBk' scales to +0.5. .TP Qc Keep coplanar points with the nearest facet. Output formats 'p', 'f', 'Gp', 'Fc', 'FN', and 'FP' will print the points. .TP Qf Partition points to the furthest outside facet. .TP Qg Only build good facets. With the 'Qg' option, Qhull will only build those facets that it needs to determine the good facets in the output. See 'QGn', 'QVn', and 'PdD' for defining good facets, and 'Pg' and 'PG' for printing good facets and their neighbors. .TP QGn A facet is good (see 'Qg' and 'Pg') if it is visible from point n. If n < 0, a facet is good if it is not visible from point n. Point n is not added to the hull (unless 'TCn' or 'TPn'). With rbox, use the 'Pn,m,r' option to define your point; it will be point 0 (QG0). .TP Qi Keep interior points with the nearest facet. Output formats 'p', 'f', 'Gp', 'FN', 'FP', and 'Fc' will print the points. .TP QJn Joggle each input coordinate by adding a random number in [\-n,n]. If a precision error occurs, then qhull increases n and tries again. It does not increase n beyond a certain value, and it stops after a certain number of attempts [see user.h]. Option 'QJ' selects a default value for n. The output will be simplicial. For Delaunay triangulations, 'QJn' sets 'Qbb' to scale the last coordinate (not if 'Qbk:n' or 'QBk:n' is set). 'QJn' is deprecated for Voronoi diagrams. See also 'Qt'. .TP Qm Only process points that would otherwise increase max_outside. Other points are treated as coplanar or interior points. .TP Qr Process random outside points instead of furthest ones. This makes Qhull equivalent to the randomized incremental algorithms. CPU time is not reported since the randomization is inefficient. .TP QRn Randomly rotate the input points. If n=0, use time as the random number seed. If n>0, use n as the random number seed. If n=\-1, don't rotate but use time as the random number seed. For Delaunay triangulations ('d' and 'v'), rotate about the last axis. .TP Qs Search all points for the initial simplex. .TP Qt Triangulated output. Triangulate all non\[hy]simplicial facets. 'Qt' is deprecated for Voronoi diagrams. See also 'Qt'. .TP Qv Test vertex neighbors for convexity after post\[hy]merging. To use the 'Qv' option, you also need to set a merge option (e.g., 'Qx' or 'C\-0'). .TP QVn A good facet (see 'Qg' and 'Pg') includes point n. If n<0, then a good facet does not include point n. The point is either in the initial simplex or it is the first point added to the hull. Option 'QVn' may not be used with merging. .TP Qx Perform exact merges while building the hull. The "exact" merges are merging a point into a coplanar facet (defined by 'Vn', 'Un', and 'C\-n'), merging concave facets, merging duplicate ridges, and merging flipped facets. Coplanar merges and angle coplanar merges ('A\-n') are not performed. Concavity testing is delayed until a merge occurs. After the hull is built, all coplanar merges are performed (defined by 'C\-n' and 'A\-n'), then post\[hy]merges are performed (defined by 'Cn' and 'An'). .TP Qz Add a point "at infinity" that is above the paraboloid for Delaunay triangulations and Voronoi diagrams. This reduces precision problems and allows the triangulation of cospherical points. .PP .TP Qhull experiments and speedups .TP Q0 Turn off pre\[hy]merging as a default option. With 'Q0'/'Qx' and without explicit pre\[hy]merge options, Qhull ignores precision issues while constructing the convex hull. This may lead to precision errors. If so, a descriptive warning is generated. .TP Q1 With 'Q1', Qhull sorts merges by type (coplanar, angle coplanar, concave) instead of by angle. .TP Q2 With 'Q2', Qhull merges all facets at once instead of using independent sets of merges and then retesting. .TP Q3 With 'Q3', Qhull does not remove redundant vertices. .TP Q4 With 'Q4', Qhull avoids merges of an old facet into a new facet. .TP Q5 With 'Q5', Qhull does not correct outer planes at the end. The maximum outer plane is used instead. .TP Q6 With 'Q6', Qhull does not pre\[hy]merge concave or coplanar facets. .TP Q7 With 'Q7', Qhull processes facets in depth\[hy]first order instead of breadth\[hy]first order. .TP Q8 With 'Q8' and merging, Qhull does not retain near\[hy]interior points for adjusting outer planes. 'Qc' will probably retain all points that adjust outer planes. .TP Q9 With 'Q9', Qhull processes the furthest of all outside sets at each iteration. .TP Q10 With 'Q10', Qhull does not use special processing for narrow distributions. .TP Q11 With 'Q11', Qhull copies normals and recompute centrums for tricoplanar facets. .PP .TP Trace options .TP Tn Trace at level n. Qhull includes full execution tracing. 'T\-1' traces events. 'T1' traces the overall execution of the program. 'T2' and 'T3' trace overall execution and geometric and topological events. 'T4' traces the algorithm. 'T5' includes information about memory allocation and Gaussian elimination. .TP Ta Annotate output with codes that identify the corresponding qh_fprintf() statement. .TP Tc Check frequently during execution. This will catch most inconsistency errors. .TP TCn Stop Qhull after building the cone of new facets for point n. The output for 'f' includes the cone and the old hull. See also 'TVn'. .TP TFn Report progress whenever more than n facets are created During post\[hy]merging, 'TFn' reports progress after more than n/2 merges. .TP TI file Input data from 'file'. The filename may not include spaces or quotes. .TP TO file Output results to 'file'. The name may be enclosed in single quotes. .TP TPn Turn on tracing when point n is added to the hull. Trace partitions of point n. If used with TWn, turn off tracing after adding point n to the hull. .TP TRn Rerun qhull n times. Usually used with 'QJn' to determine the probability that a given joggle will fail. .TP Ts Collect statistics and print to stderr at the end of execution. .TP Tv Verify the convex hull. This checks the topological structure, facet convexity, and point inclusion. If precision problems occurred, facet convexity is tested whether or not 'Tv' is selected. Option 'Tv' does not check point inclusion if forcing output with 'Po', or if 'Q5' is set. For point inclusion testing, Qhull verifies that all points are below all outer planes (facet\->maxoutside). Point inclusion is exhaustive if merging or if the facet\[hy]point product is small enough; otherwise Qhull verifies each point with a directed search (qh_findbest). Point inclusion testing occurs after producing output. It prints a message to stderr unless option 'Pp' is used. This allows the user to interrupt Qhull without changing the output. .TP TVn Stop Qhull after adding point n. If n < 0, stop Qhull before adding point n. Output shows the hull at this time. See also 'TCn' .TP TMn Turn on tracing at n'th merge. .TP TWn Trace merge facets when the width is greater than n. .TP Tz Redirect stderr to stdout. .PP .SH BUGS Please report bugs to Brad Barber at qhull_bug@qhull.org. If Qhull does not compile, it is due to an incompatibility between your system and ours. The first thing to check is that your compiler is ANSI standard. If it is, check the man page for the best options, or find someone to help you. If you locate the cause of your problem, please send email since it might help others. If Qhull compiles but crashes on the test case (rbox D4), there's still incompatibility between your system and ours. Typically it's been due to mem.c and memory alignment. You can use qh_NOmem in mem.h to turn off memory management. Please let us know if you figure out how to fix these problems. If you do find a problem, try to simplify it before reporting the error. Try different size inputs to locate the smallest one that causes an error. You're welcome to hunt through the code using the execution trace as a guide. This is especially true if you're incorporating Qhull into your own program. When you do report an error, please attach a data set to the end of your message. This allows us to see the error for ourselves. Qhull is maintained part\[hy]time. .PP .SH E\[hy]MAIL Please send correspondence to qhull@qhull.org and report bugs to qhull_bug@qhull.org. Let us know how you use Qhull. If you mention it in a paper, please send the reference and an abstract. If you would like to get Qhull announcements (e.g., a new version) and news (any bugs that get fixed, etc.), let us know and we will add you to our mailing list. If you would like to communicate with other Qhull users, we will add you to the qhull_users alias. For Internet news about geometric algorithms and convex hulls, look at comp.graphics.algorithms and sci.math.num\-analysis .SH SEE ALSO rbox(1) Barber, C. B., D.P. Dobkin, and H.T. Huhdanpaa, "The Quickhull Algorithm for Convex Hulls," ACM Trans. on Mathematical Software, 22(4):469\[en]483, Dec. 1996. http://portal.acm.org/citation.cfm?doid=235815.235821 http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.117.405 Clarkson, K.L., K. Mehlhorn, and R. Seidel, "Four results on randomized incremental construction," Computational Geometry: Theory and Applications, vol. 3, p. 185\[en]211, 1993. Preparata, F. and M. Shamos, Computational Geometry, Springer\[hy]Verlag, New York, 1985. .PP .SH AUTHORS .nf C. Bradford Barber Hannu Huhdanpaa bradb@shore.net hannu@qhull.org .fi .SH ACKNOWLEDGEMENTS A special thanks to Albert Marden, Victor Milenkovic, the Geometry Center, Harvard University, and Endocardial Solutions, Inc. for supporting this work. Qhull 1.0 and 2.0 were developed under National Science Foundation grants NSF/DMS\[hy]8920161 and NSF\[hy]CCR\[hy]91\[hy]15793 750\[hy]7504. David Dobkin guided the original work at Princeton University. If you find it useful, please let us know. The Geometry Center is supported by grant DMS\[hy]8920161 from the National Science Foundation, by grant DOE/DE\[hy]FG02\[hy]92ER25137 from the Department of Energy, by the University of Minnesota, and by Minnesota Technology, Inc. Qhull is available from http://www.qhull.org qhull-2012.1/html/qhull.txt0000644000076400010400000014030011545626745016753 0ustar bbarberAdministrators qhull(1) qhull(1) NAME qhull - convex hull, Delaunay triangulation, Voronoi dia- gram, halfspace intersection about a point, hull volume, facet area SYNOPSIS qhull- compute convex hulls and related structures input (stdin): dimension, #points, point coordinates first comment (non-numeric) is listed in the summary halfspace: use dim plus one with offsets after coefficients options (qh-quick.htm): d - Delaunay triangulation by lifting points to a paraboloid v - Voronoi diagram via the Delaunay triangulation H1,1 - Halfspace intersection about [1,1,0,...] d Qu - Furthest-site Delaunay triangulation (upper convex hull) v Qu - Furthest-site Voronoi diagram QJ - Joggle the input to avoid precision problems . - concise list of all options - - one-line description of all options Output options (subset): FA - compute total area and volume Fx - extreme points (convex hull vertices) G - Geomview output (2-d, 3-d and 4-d) Fp - halfspace intersection coordinates m - Mathematica output (2-d and 3-d) n - normals with offsets o - OFF file format (if Voronoi, outputs regions) TO file- output results to file, may be enclosed in single quotes f - print all fields of all facets s - summary of results (default) Tv - verify result: structure, convexity, and point inclusion p - vertex coordinates i - vertices incident to each facet example: rbox 1000 s | qhull Tv s FA - html manual: index.htm - installation: README.txt - see also: COPYING.txt, REGISTER.txt, Changes.txt - WWW: - GIT: - mirror: - news: - Geomview: - news group: - FAQ: - email: qhull@qhull.org - bug reports: qhull_bug@qhull.org Geometry Center 2003/12/30 1 qhull(1) qhull(1) The sections are: - INTRODUCTION - DESCRIPTION, a description of Qhull - IMPRECISION, how Qhull handles imprecision - OPTIONS - Input and output options - Additional input/output formats - Precision options - Geomview options - Print options - Qhull options - Trace options - BUGS - E-MAIL - SEE ALSO - AUTHORS - ACKNOWLEGEMENTS This man page briefly describes all Qhull options. Please report any mismatches with Qhull's html manual (qh- man.htm). INTRODUCTION Qhull is a general dimension code for computing convex hulls, Delaunay triangulations, Voronoi diagram, furthest- site Voronoi diagram, furthest-site Delaunay triangula- tions, and halfspace intersections about a point. It implements the Quickhull algorithm for computing the con- vex hull. Qhull handles round-off errors from floating point arithmetic. It can approximate a convex hull. The program includes options for hull volume, facet area, partial hulls, input transformations, randomization, trac- ing, multiple output formats, and execution statistics. The program can be called from within your application. You can view the results in 2-d, 3-d and 4-d with Geomview. DESCRIPTION The format of input is the following: first line contains the dimension, second line contains the number of input points, and point coordinates follow. The dimension and number of points can be reversed. Comments and line breaks are ignored. A comment starts with a non-numeric character and continues to the end of line. The first comment is reported in summaries and statistics. Error reporting is better if there is one point per line. The default printout option is a short summary. There are many other output formats. Geometry Center 2003/12/30 2 qhull(1) qhull(1) Qhull implements the Quickhull algorithm for convex hull. This algorithm combines the 2-d Quickhull algorithm with the n-d beneath-beyond algorithm [c.f., Preparata & Shamos '85]. It is similar to the randomized algorithms of Clarkson and others [Clarkson et al. '93]. The main advantages of Quickhull are output sensitive performance, reduced space requirements, and automatic handling of pre- cision problems. The data structure produced by Qhull consists of vertices, ridges, and facets. A vertex is a point of the input set. A ridge is a set of d vertices and two neighboring facets. For example in 3-d, a ridge is an edge of the polyhedron. A facet is a set of ridges, a set of neighboring facets, a set of incident vertices, and a hyperplane equation. For simplicial facets, the ridges are defined by the vertices and neighboring facets. When Qhull merges two facets, it produces a non-simplicial facet. A non-simplicial facet has more than d neighbors and may share more than one ridge with a neighbor. IMPRECISION Since Qhull uses floating point arithmetic, roundoff error may occur for each calculation. This causes problems for most geometric algorithms. Qhull automatically sets option 'C-0' in 2-d, 3-d, and 4-d, or option 'Qx' in 5-d and higher. These options han- dle precision problems by merging facets. Alternatively, use option 'QJ' to joggle the input. With 'C-0', Qhull merges non-convex facets while con- structing the hull. The remaining facets are clearly con- vex. With 'Qx', Qhull merges coplanar horizon facets, flipped facets, concave facets and duplicated ridges. It merges coplanar facets after constructing the hull. With 'Qx', coplanar points may be missed, but it appears to be unlikely. To guarantee triangular output, joggle the input with option 'QJ'. Facet merging will not occur. OPTIONS To get a list of the most important options, execute 'qhull' by itself. To get a complete list of options, execute 'qhull -'. To get a complete, concise list of options, execute 'qhull .'. Options can be in any order. Capitalized options take an argument (except 'PG' and 'F' options). Single letters are used for output formats and precision constants. The other options are grouped into menus for other output for- mats ('F'), Geomview output ('G'), printing ('P'), Qhull Geometry Center 2003/12/30 3 qhull(1) qhull(1) control ('Q'), and tracing ('T'). Main options: default Compute the convex hull of the input points. Report a summary of the result. d Compute the Delaunay triangulation by lifting the input points to a paraboloid. The 'o' option prints the input points and facets. The 'QJ' option guarantees triangular output. The 'Ft' option prints a triangulation. It adds points (the centrums) to non-simplicial facets. v Compute the Voronoi diagram from the Delaunay tri- angulation. The 'p' option prints the Voronoi ver- tices. The 'o' option prints the Voronoi vertices and the vertices in each Voronoi region. It lists regions in site id order. The 'Fv' option prints each ridge of the Voronoi diagram. The first or zero'th vertex indicates the infinity vertex. Its coordinates are qh_INFINITE (-10.101). It indi- cates unbounded Voronoi regions or degenerate Delaunay triangles. Hn,n,... Compute halfspace intersection about [n,n,0,...]. The input is a set of halfspaces defined in the same format as 'n', 'Fo', and 'Fi'. Use 'Fp' to print the intersection points. Use 'Fv' to list the intersection points for each halfspace. The other output formats display the dual convex hull. The point [n,n,n,...] is a feasible point for the halfspaces, i.e., a point that is inside all of the halfspaces (Hx+b <= 0). The default coordinate value is 0. The input may start with a feasible point. If so, use 'H' by itself. The input starts with a feasi- ble point when the first number is the dimension, the second number is "1", and the coordinates com- plete a line. The 'FV' option produces a feasible point for a convex hull. d Qu Compute the furthest-site Delaunay triangulation from the upper convex hull. The 'o' option prints the input points and facets. The 'QJ' option guar- antees triangular otuput. You can also use facets. v Qu Compute the furthest-site Voronoi diagram. The 'p' option prints the Voronoi vertices. The 'o' option prints the Voronoi vertices and the vertices in Geometry Center 2003/12/30 4 qhull(1) qhull(1) each Voronoi region. The 'Fv' option prints each ridge of the Voronoi diagram. The first or zero'th vertex indicates the infinity vertex at infinity. Its coordinates are qh_INFINITE (-10.101). It indicates unbounded Voronoi regions and degenerate Delaunay triangles. Qt Triangulated output. Input/Output options: f Print out all facets and all fields of each facet. G Output the hull in Geomview format. For imprecise hulls, Geomview displays the inner and outer hull. Geomview can also display points, ridges, vertices, coplanar points, and facet intersections. See below for a list of options. For Delaunay triangulations, 'G' displays the cor- responding paraboloid. For halfspace intersection, 'G' displays the dual polytope. i Output the incident vertices for each facet. Qhull prints the number of facets followed by the ver- tices of each facet. One facet is printed per line. The numbers are the 0-relative indices of the corresponding input points. The facets are oriented. In 4-d and higher, Qhull triangulates non-simpli- cial facets. Each apex (the first vertex) is a created point that corresponds to the facet's cen- trum. Its index is greater than the indices of the input points. Each base corresponds to a simpli- cial ridge between two facets. To print the ver- tices without triangulation, use option 'Fv'. m Output the hull in Mathematica format. Qhull writes a Mathematica file for 2-d and 3-d convex hulls and for 2-d Delaunay triangulations. Qhull produces a list of objects that you can assign to a variable in Mathematica, for example: "list= << ". If the object is 2-d, it can be visualized by "Show[Graphics[list]] ". For 3-d objects the command is "Show[Graphics3D[list]]". n Output the normal equation for each facet. Qhull prints the dimension (plus one), the number of facets, and the normals for each facet. The facet's offset follows its normal coefficients. o Output the facets in OFF file format. Qhull prints the dimension, number of points, number of facets, and number of ridges. Then it prints the Geometry Center 2003/12/30 5 qhull(1) qhull(1) coordinates of the input points and the vertices for each facet. Each facet is on a separate line. The first number is the number of vertices. The remainder are the indices of the corresponding points. The vertices are oriented in 2-d, 3-d, and in simplicial facets. For 2-d Voronoi diagrams, the vertices are sorted by adjacency, but not oriented. In 3-d and higher, the Voronoi vertices are sorted by index. See the 'v' option for more information. p Output the coordinates of each vertex point. Qhull prints the dimension, the number of points, and the coordinates for each vertex. With the 'Gc' and 'Gi' options, it also prints coplanar and interior points. For Voronoi diagrams, it prints the coor- dinates of each Voronoi vertex. s Print a summary to stderr. If no output options are specified at all, a summary goes to stdout. The summary lists the number of input points, the dimension, the number of vertices in the convex hull, the number of facets in the convex hull, the number of good facets (if 'Pg'), and statistics. The last two statistics (if needed) measure the maximum distance from a point or vertex to a facet. The number in parenthesis (e.g., 2.1x) is the ratio between the maximum distance and the worst-case distance due to merging two simplicial facets. Precision options An Maximum angle given as a cosine. If the angle between a pair of facet normals is greater than n, Qhull merges one of the facets into a neighbor. If 'n' is negative, Qhull tests angles after adding each point to the hull (pre-merging). If 'n' is posi- tive, Qhull tests angles after constructing the hull (post-merging). Both pre- and post-merging can be defined. Option 'C0' or 'C-0' is set if the corresponding 'Cn' or 'C-n' is not set. If 'Qx' is set, then 'A- n' and 'C-n' are checked after the hull is con- structed and before 'An' and 'Cn' are checked. Cn Centrum radius. If a centrum is less than n below a neighboring facet, Qhull merges one of the facets. If 'n' is negative or '-0', Qhull tests and merges facets after adding each point to the hull. This is called "pre-merging". If 'n' is Geometry Center 2003/12/30 6 qhull(1) qhull(1) positive, Qhull tests for convexity after con- structing the hull ("post-merging"). Both pre- and post-merging can be defined. For 5-d and higher, 'Qx' should be used instead of 'C-n'. Otherwise, most or all facets may be merged together. En Maximum roundoff error for distance computations. Rn Randomly perturb distance computations up to +/- n * max_coord. This option perturbs every distance, hyperplane, and angle computation. To use time as the random number seed, use option 'QR-1'. Vn Minimum distance for a facet to be visible. A facet is visible if the distance from the point to the facet is greater than 'Vn'. Without merging, the default value for 'Vn' is the round-off error ('En'). With merging, the default value is the pre-merge centrum ('C-n') in 2-d or 3--d, or three times that in other dimensions. If the outside width is specified ('Wn'), the maximum, default value for 'Vn' is 'Wn'. Un Maximum distance below a facet for a point to be coplanar to the facet. The default value is 'Vn'. Wn Minimum outside width of the hull. Points are added to the convex hull only if they are clearly outside of a facet. A point is outside of a facet if its distance to the facet is greater than 'Wn'. The normal value for 'Wn' is 'En'. If the user specifies pre-merging and does not set 'Wn', than 'Wn' is set to the premerge 'Cn' and maxco- ord*(1-An). Additional input/output formats Fa Print area for each facet. For Delaunay triangula- tions, the area is the area of the triangle. For Voronoi diagrams, the area is the area of the dual facet. Use 'PAn' for printing the n largest facets, and option 'PFn' for printing facets larger than 'n'. The area for non-simplicial facets is the sum of the areas for each ridge to the centrum. Vertices far below the facet's hyperplane are ignored. The reported area may be significantly less than the actual area. Geometry Center 2003/12/30 7 qhull(1) qhull(1) FA Compute the total area and volume for option 's'. It is an approximation for non-simplicial facets (see 'Fa'). Fc Print coplanar points for each facet. The output starts with the number of facets. Then each facet is printed one per line. Each line is the number of coplanar points followed by the point ids. Option 'Qi' includes the interior points. Each coplanar point (interior point) is assigned to the facet it is furthest above (resp., least below). FC Print centrums for each facet. The output starts with the dimension followed by the number of facets. Then each facet centrum is printed, one per line. Fd Read input in cdd format with homogeneous points. The input starts with comments. The first comment is reported in the summary. Data starts after a "begin" line. The next line is the number of points followed by the dimension+1 and "real" or "integer". Then the points are listed with a leading "1" or "1.0". The data ends with an "end" line. For halfspaces ('Fd Hn,n,...'), the input format is the same. Each halfspace starts with its offset. The sign of the offset is the opposite of Qhull's convention. FD Print normals ('n', 'Fo', 'Fi') or points ('p') in cdd format. The first line is the command line that invoked Qhull. Data starts with a "begin" line. The next line is the number of normals or points followed by the dimension+1 and "real". Then the normals or points are listed with the offset before the coefficients. The offset for points is 1.0. The offset for normals has the opposite sign. The data ends with an "end" line. FF Print facets (as in 'f') without printing the ridges. Fi Print inner planes for each facet. The inner plane is below all vertices. Fi Print separating hyperplanes for bounded, inner regions of the Voronoi diagram. The first line is the number of ridges. Then each hyperplane is printed, one per line. A line starts with the num- ber of indices and floats. The first pair lists adjacent input sites, the next d floats are the normalized coefficients for the hyperplane, and the Geometry Center 2003/12/30 8 qhull(1) qhull(1) last float is the offset. The hyperplane is ori- ented toward verify that the hyperplanes are per- pendicular bisectors. Use 'Fo' for unbounded regions, and 'Fv' for the corresponding Voronoi vertices. FI Print facet identifiers. Fm Print number of merges for each facet. At most 511 merges are reported for a facet. See 'PMn' for printing the facets with the most merges. FM Output the hull in Maple format. See 'm' Fn Print neighbors for each facet. The output starts with the number of facets. Then each facet is printed one per line. Each line is the number of neighbors followed by an index for each neighbor. The indices match the other facet output formats. A negative index indicates an unprinted facet due to printing only good facets ('Pg'). It is the negation of the facet's id (option 'FI'). For example, negative indices are used for facets "at infinity" in the Delaunay triangulation. FN Print vertex neighbors or coplanar facet for each point. The first line is the number of points. Then each point is printed, one per line. If the point is coplanar, the line is "1" followed by the facet's id. If the point is not a selected vertex, the line is "0". Otherwise, each line is the num- ber of neighbors followed by the corresponding facet indices (see 'Fn'). Fo Print outer planes for each facet in the same for- mat as 'n'. The outer plane is above all points. Fo Print separating hyperplanes for unbounded, outer regions of the Voronoi diagram. The first line is the number of ridges. Then each hyperplane is printed, one per line. A line starts with the num- ber of indices and floats. The first pair lists adjacent input sites, the next d floats are the normalized coefficients for the hyperplane, and the last float is the offset. The hyperplane is ori- ented toward verify that the hyperplanes are per- pendicular bisectors. Use 'Fi' for bounded regions, and 'Fv' for the corresponding Voronoi vertices. FO List all options to stderr, including the default values. Additional 'FO's are printed to stdout. Fp Print points for halfspace intersections (option 'Hn,n,...'). Each intersection corresponds to a Geometry Center 2003/12/30 9 qhull(1) qhull(1) facet of the dual polytope. The "infinity" point [-10.101,-10.101,...] indicates an unbounded intersection. FP For each coplanar point ('Qc') print the point id of the nearest vertex, the point id, the facet id, and the distance. FQ Print command used for qhull and input. Fs Print a summary. The first line consists of the number of integers ("7"), followed by the dimen- sion, the number of points, the number of vertices, the number of facets, the number of vertices selected for output, the number of facets selected for output, the number of coplanar points selected for output. The second line consists of the number of reals ("2"), followed by the maxmimum offset to an outer plane and and minimum offset to an inner plane. Roundoff is included. Later versions of Qhull may produce additional integers or reals. FS Print the size of the hull. The first line con- sists of the number of integers ("0"). The second line consists of the number of reals ("2"), fol- lowed by the total facet area, and the total vol- ume. Later versions of Qhull may produce addi- tional integers or reals. The total volume measures the volume of the inter- section of the halfspaces defined by each facet. Both area and volume are approximations for non- simplicial facets. See option 'Fa'. Ft Print a triangulation with added points for non- simplicial facets. The first line is the dimension and the second line is the number of points and the number of facets. The points follow, one per line, then the facets follow as a list of point indices. With option points include the point-at-infinity. Fv Print vertices for each facet. The first line is the number of facets. Then each facet is printed, one per line. Each line is the number of vertices followed by the corresponding point ids. Vertices are listed in the order they were added to the hull (the last one is first). Fv Print all ridges of a Voronoi diagram. The first line is the number of ridges. Then each ridge is printed, one per line. A line starts with the num- ber of indices. The first pair lists adjacent Geometry Center 2003/12/30 10 qhull(1) qhull(1) input sites, the remaining indices list Voronoi vertices. Vertex '0' indicates the vertex-at- infinity (i.e., an unbounded ray). In 3-d, the vertices are listed in order. See 'Fi' and 'Fo' for separating hyperplanes. FV Print average vertex. The average vertex is a fea- sible point for halfspace intersection. Fx List extreme points (vertices) of the convex hull. The first line is the number of points. The other lines give the indices of the corresponding points. The first point is '0'. In 2-d, the points occur in counter-clockwise order; otherwise they occur in input order. For Delaunay triangulations, 'Fx' lists the extreme points of the input sites. The points are unordered. Geomview options G Produce a file for viewing with Geomview. Without other options, Qhull displays edges in 2-d, outer planes in 3-d, and ridges in 4-d. A ridge can be explicit or implicit. An explicit ridge is a dim-1 dimensional simplex between two facets. In 4-d, the explicit ridges are triangles. When displaying a ridge in 4-d, Qhull projects the ridge's vertices to one of its facets' hyperplanes. Use 'Gh' to project ridges to the intersection of both hyper- planes. Ga Display all input points as dots. Gc Display the centrum for each facet in 3-d. The centrum is defined by a green radius sitting on a blue plane. The plane corresponds to the facet's hyperplane. The radius is defined by 'C-n' or 'Cn'. GDn Drop dimension n in 3-d or 4-d. The result is a 2-d or 3-d object. Gh Display hyperplane intersections in 3-d and 4-d. In 3-d, the intersection is a black line. It lies on two neighboring hyperplanes (c.f., the blue squares associated with centrums ('Gc')). In 4-d, the ridges are projected to the intersection of both hyperplanes. Gi Display inner planes in 2-d and 3-d. The inner plane of a facet is below all of its vertices. It is parallel to the facet's hyperplane. The inner plane's color is the opposite (1-r,1-g,1-b) of the Geometry Center 2003/12/30 11 qhull(1) qhull(1) outer plane. Its edges are determined by the ver- tices. Gn Do not display inner or outer planes. By default, Geomview displays the precise plane (no merging) or both inner and output planes (merging). Under merging, Geomview does not display the inner plane if the the difference between inner and outer is too small. Go Display outer planes in 2-d and 3-d. The outer plane of a facet is above all input points. It is parallel to the facet's hyperplane. Its color is determined by the facet's normal, and its edges are determined by the vertices. Gp Display coplanar points and vertices as radii. A radius defines a ball which corresponds to the imprecision of the point. The imprecision is the maximum of the roundoff error, the centrum radius, and maxcoord * (1-An). It is at least 1/20'th of the maximum coordinate, and ignores post-merging if pre-merging is done. Gr Display ridges in 3-d. A ridge connects the two vertices that are shared by neighboring facets. Ridges are always displayed in 4-d. Gt A 3-d Delaunay triangulation looks like a convex hull with interior facets. Option 'Gt' removes the outside ridges to reveal the outermost facets. It automatically sets options 'Gr' and 'GDn'. Gv Display vertices as spheres. The radius of the sphere corresponds to the imprecision of the data. See 'Gp' for determining the radius. Print options PAn Only the n largest facets are marked good for printing. Unless 'PG' is set, 'Pg' is automati- cally set. Pdk:n Drop facet from output if normal[k] <= n. The option 'Pdk' uses the default value of 0 for n. PDk:n Drop facet from output if normal[k] >= n. The option 'PDk' uses the default value of 0 for n. PFn Only facets with area at least 'n' are marked good for printing. Unless 'PG' is set, 'Pg' is automat- ically set. Geometry Center 2003/12/30 12 qhull(1) qhull(1) Pg Print only good facets. A good facet is either visible from a point (the 'QGn' option) or includes a point (the 'QVn' option). It also meets the requirements of 'Pdk' and 'PDk' options. Option 'Pg' is automatically set for options 'PAn' and 'PFn'. PG Print neighbors of good facets. PMn Only the n facets with the most merges are marked good for printing. Unless 'PG' is set, 'Pg' is automatically set. Po Force output despite precision problems. Verify ('Tv') does not check coplanar points. Flipped facets are reported and concave facets are counted. If 'Po' is used, points are not partitioned into flipped facets and a flipped facet is always visible to a point. Also, if an error occurs before the completion of Qhull and tracing is not active, 'Po' outputs a neighborhood of the erroneous facets (if any). Pp Do not report precision problems. Qhull control options Qbk:0Bk:0 Drop dimension k from the input points. This allows the user to take convex hulls of sub-dimen- sional objects. It happens before the Delaunay and Voronoi transformation. QbB Scale the input points to fit the unit cube. After scaling, the lower bound will be -0.5 and the upper bound +0.5 in all dimensions. For Delaunay and Voronoi diagrams, scaling happens after projection to the paraboloid. Under precise arithmetic, scal- ing does not change the topology of the convex hull. Qbb Scale the last coordinate to [0, m] where m is the maximum absolute value of the other coordinates. For Delaunay and Voronoi diagrams, scaling happens after projection to the paraboloid. It reduces roundoff error for inputs with integer coordinates. Under precise arithmetic, scaling does not change the topology of the convex hull. Qbk:n Scale the k'th coordinate of the input points. After scaling, the lower bound of the input points will be n. 'Qbk' scales to -0.5. Geometry Center 2003/12/30 13 qhull(1) qhull(1) QBk:n Scale the k'th coordinate of the input points. After scaling, the upper bound will be n. 'QBk' scales to +0.5. Qc Keep coplanar points with the nearest facet. Out- put formats 'p', 'f', 'Gp', 'Fc', 'FN', and 'FP' will print the points. Qf Partition points to the furthest outside facet. Qg Only build good facets. With the 'Qg' option, Qhull will only build those facets that it needs to determine the good facets in the output. See 'QGn', 'QVn', and 'PdD' for defining good facets, and 'Pg' and 'PG' for printing good facets and their neighbors. QGn A facet is good (see 'Qg' and 'Pg') if it is visi- ble from point n. If n < 0, a facet is good if it is not visible from point n. Point n is not added to the hull (unless 'TCn' or 'TPn'). With rbox, use the 'Pn,m,r' option to define your point; it will be point 0 (QG0). Qi Keep interior points with the nearest facet. Out- put formats 'p', 'f', 'Gp', 'FN', 'FP', and 'Fc' will print the points. QJn Joggle each input coordinate by adding a random number in [-n,n]. If a precision error occurs, then qhull increases n and tries again. It does not increase n beyond a certain value, and it stops after a certain number of attempts [see user.h]. Option 'QJ' selects a default value for n. The output will be simplicial. For Delaunay triangula- tions, 'QJn' sets 'Qbb' to scale the last coordi- nate (not if 'Qbk:n' or 'QBk:n' is set). 'QJn' is deprecated for Voronoi diagrams. See also 'Qt'. Qm Only process points that would otherwise increase max_outside. Other points are treated as coplanar or interior points. Qr Process random outside points instead of furthest ones. This makes Qhull equivalent to the random- ized incremental algorithms. CPU time is not reported since the randomization is inefficient. QRn Randomly rotate the input points. If n=0, use time as the random number seed. If n>0, use n as the random number seed. If n=-1, don't rotate but use time as the random number seed. For Delaunay tri- angulations ('d' and 'v'), rotate about the last axis. Geometry Center 2003/12/30 14 qhull(1) qhull(1) Qs Search all points for the initial simplex. Qt Triangulated output. Triangulate non-simplicial facets. 'Qt' is deprecated for Voronoi diagrams. See also 'QJn' Qv Test vertex neighbors for convexity after post- merging. To use the 'Qv' option, you also need to set a merge option (e.g., 'Qx' or 'C-0'). QVn A good facet (see 'Qg' and 'Pg') includes point n. If n<0, then a good facet does not include point n. The point is either in the initial simplex or it is the first point added to the hull. Option 'QVn' may not be used with merging. Qx Perform exact merges while building the hull. The "exact" merges are merging a point into a coplanar facet (defined by 'Vn', 'Un', and 'C-n'), merging concave facets, merging duplicate ridges, and merg- ing flipped facets. Coplanar merges and angle coplanar merges ('A-n') are not performed. Concav- ity testing is delayed until a merge occurs. After the hull is built, all coplanar merges are performed (defined by 'C-n' and 'A-n'), then post- merges are performed (defined by 'Cn' and 'An'). Qz Add a point "at infinity" that is above the paraboloid for Delaunay triangulations and Voronoi diagrams. This reduces precision problems and allows the triangulation of cospherical points. Qhull experiments and speedups Q0 Turn off pre-merging as a default option. With 'Q0'/'Qx' and without explicit pre-merge options, Qhull ignores precision issues while constructing the convex hull. This may lead to precision errors. If so, a descriptive warning is generated. Q1 With 'Q1', Qhull sorts merges by type (coplanar, angle coplanar, concave) instead of by angle. Q2 With 'Q2', Qhull merges all facets at once instead of using independent sets of merges and then retesting. Q3 With 'Q3', Qhull does not remove redundant ver- tices. Q4 With 'Q4', Qhull avoids merges of an old facet into a new facet. Q5 With 'Q5', Qhull does not correct outer planes at the end. The maximum outer plane is used instead. Geometry Center 2003/12/30 15 qhull(1) qhull(1) Q6 With 'Q6', Qhull does not pre-merge concave or coplanar facets. Q7 With 'Q7', Qhull processes facets in depth-first order instead of breadth-first order. Q8 With 'Q8' and merging, Qhull does not retain near- interior points for adjusting outer planes. 'Qc' will probably retain all points that adjust outer planes. Q9 With 'Q9', Qhull processes the furthest of all out- side sets at each iteration. Q10 With 'Q10', Qhull does not use special processing for narrow distributions. Q11 With 'Q11', Qhull copies normals and recomputes centrums for tricoplanar facets. Trace options Tn Trace at level n. Qhull includes full execution tracing. 'T-1' traces events. 'T1' traces the overall execution of the program. 'T2' and 'T3' trace overall execution and geometric and topologi- cal events. 'T4' traces the algorithm. 'T5' includes information about memory allocation and Gaussian elimination. Ta Annotate output with codes that identify the corresponding qh_fprintf() statement. Tc Check frequently during execution. This will catch most inconsistency errors. TCn Stop Qhull after building the cone of new facets for point n. The output for 'f' includes the cone and the old hull. See also 'TVn'. TFn Report progress whenever more than n facets are created During post-merging, 'TFn' reports progress after more than n/2 merges. TI file Input data from 'file'. The filename may not include spaces or quotes. TO file Output results to 'file'. The name may be enclosed in single quotes. TPn Turn on tracing when point n is added to the hull. Trace partitions of point n. If used with TWn, turn off tracing after adding point n to the hull. TRn Rerun qhull n times. Usually used with 'QJn' to determine the probability that a given joggle will fail. Ts Collect statistics and print to stderr at the end of execution. Tv Verify the convex hull. This checks the topologi- cal structure, facet convexity, and point inclu- sion. If precision problems occurred, facet con- vexity is tested whether or not 'Tv' is selected. Option 'Tv' does not check point inclusion if Geometry Center 2003/12/30 16 qhull(1) qhull(1) forcing output with 'Po', or if 'Q5' is set. For point inclusion testing, Qhull verifies that all points are below all outer planes (facet->max- outside). Point inclusion is exhaustive if merging or if the facet-point product is small enough; oth- erwise Qhull verifies each point with a directed search (qh_findbest). Point inclusion testing occurs after producing out- put. It prints a message to stderr unless option 'Pp' is used. This allows the user to interrupt Qhull without changing the output. TVn Stop Qhull after adding point n. If n < 0, stop Qhull before adding point n. Output shows the hull at this time. See also 'TCn' TMn Turn on tracing at n'th merge. TWn Trace merge facets when the width is greater than n. Tz Redirect stderr to stdout. BUGS Please report bugs to Brad Barber at qhull_bug@qhull.org. If Qhull does not compile, it is due to an incompatibility between your system and ours. The first thing to check is that your compiler is ANSI standard. If it is, check the man page for the best options, or find someone to help you. If you locate the cause of your problem, please send email since it might help others. If Qhull compiles but crashes on the test case (rbox D4), there's still incompatibility between your system and ours. Typically it's been due to mem.c and memory align- ment. You can use qh_NOmem in mem.h to turn off memory management. Please let us know if you figure out how to fix these problems. If you do find a problem, try to simplify it before reporting the error. Try different size inputs to locate the smallest one that causes an error. You're welcome to hunt through the code using the execution trace as a guide. This is especially true if you're incorporating Qhull into your own program. When you do report an error, please attach a data set to the end of your message. This allows us to see the error for ourselves. Qhull is maintained part-time. Geometry Center 2003/12/30 17 qhull(1) qhull(1) E-MAIL Please send correspondence to qhull@qhull.org and report bugs to qhull_bug@qhull.org. Let us know how you use Qhull. If you mention it in a paper, please send the reference and an abstract. If you would like to get Qhull announcements (e.g., a new version) and news (any bugs that get fixed, etc.), let us know and we will add you to our mailing list. If you would like to communicate with other Qhull users, we will add you to the qhull_users alias. For Internet news about geometric algorithms and convex hulls, look at comp.graph- ics.algorithms and sci.math.num-analysis SEE ALSO rbox(1) Barber, C. B., D.P. Dobkin, and H.T. Huhdanpaa, "The Quickhull Algorithm for Convex Hulls," ACM Trans. on Math- ematical Software, 22(4):469-483, Dec. 1996. http://portal.acm.org/citation.cfm?doid=235815.235821 http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.117.405 Clarkson, K.L., K. Mehlhorn, and R. Seidel, "Four results on randomized incremental construction," Computational Geometry: Theory and Applications, vol. 3, p. 185-211, 1993. Preparata, F. and M. Shamos, Computational Geometry, Springer-Verlag, New York, 1985. AUTHORS C. Bradford Barber Hannu Huhdanpaa bradb@shore.net hannu@qhull.org ACKNOWLEDGEMENTS A special thanks to Albert Marden, Victor Milenkovic, the Geometry Center, Harvard University, and Endocardial Solu- tions, Inc. for supporting this work. Qhull 1.0 and 2.0 were developed under National Science Foundation grants NSF/DMS-8920161 and NSF-CCR-91-15793 750-7504. David Dobkin Geometry Center 2003/12/30 18 qhull(1) qhull(1) guided the original work at Princeton University. If you find it useful, please let us know. The Geometry Center was supported by grant DMS-8920161 from the National Science Foundation, by grant DOE/DE-FG02-92ER25137 from the Department of Energy, by the University of Minnesota, and by Minnesota Technology, Inc. Qhull is available from http://www.qhull.org Geometry Center 2003/12/30 19 qhull-2012.1/html/qvoronoi.htm0000644000076400010400000006651011720316254017447 0ustar bbarberAdministrators qvoronoi -- Voronoi diagram Up: Home page for Qhull
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[voronoi]qvoronoi -- Voronoi diagram

The Voronoi diagram is the nearest-neighbor map for a set of points. Each region contains those points that are nearer one input site than any other input site. It has many useful properties and applications. See the survey article by Aurenhammer ['91] and the detailed introduction by O'Rourke ['94]. The Voronoi diagram is the dual of the Delaunay triangulation.

Example: rbox 10 D3 | qvoronoi s o TO result
Compute the 3-d Voronoi diagram of 10 random points. Write a summary to the console and the Voronoi vertices and regions to 'result'. The first vertex of the result indicates unbounded regions.
 
Example: rbox r y c G0.1 D2 | qvoronoi s o TO result
Compute the 2-d Voronoi diagram of a triangle and a small square. Write a summary to the console and Voronoi vertices and regions to 'result'. Report a single Voronoi vertex for cocircular input sites. The first vertex of the result indicates unbounded regions. The origin is the Voronoi vertex for the square.
 
Example: rbox r y c G0.1 D2 | qvoronoi Fv TO result
Compute the 2-d Voronoi diagram of a triangle and a small square. Write a summary to the console and the Voronoi ridges to 'result'. Each ridge is the perpendicular bisector of a pair of input sites. Vertex "0" indicates unbounded ridges. Vertex "8" is the Voronoi vertex for the square.
 
Example: rbox r y c G0.1 D2 | qvoronoi Fi
Print the bounded, separating hyperplanes for the 2-d Voronoi diagram of a triangle and a small square. Note the four hyperplanes (i.e., lines) for Voronoi vertex "8". It is at the origin.

Qhull computes the Voronoi diagram via the Delaunay triangulation. Each Voronoi vertex is the circumcenter of a facet of the Delaunay triangulation. Each Voronoi region corresponds to a vertex (i.e., input site) of the Delaunay triangulation.

Qhull outputs the Voronoi vertices for each Voronoi region. With option 'Fv', it lists all ridges of the Voronoi diagram with the corresponding pairs of input sites. With options 'Fi' and 'Fo', it lists the bounded and unbounded separating hyperplanes. You can also output a single Voronoi region for further processing [see graphics].

Use option 'Qz' if the input is circular, cospherical, or nearly so. It improves precision by adding a point "at infinity," above the corresponding paraboloid.

See Qhull FAQ - Delaunay and Voronoi diagram questions.

The 'qvonoroi' program is equivalent to 'qhull v Qbb' in 2-d to 3-d, and 'qhull v Qbb Qx' in 4-d and higher. It disables the following Qhull options: d n v Qbb QbB Qf Qg Qm Qr QR Qv Qx Qz TR E V Fa FA FC FD FS Ft FV Gt Q0,etc.

Copyright © 1995-2012 C.B. Barber

Voronoi image by KOOK Architecture, Silvan Oesterle and Michael Knauss.

»qvoronoi synopsis

qvoronoi- compute the Voronoi diagram.
    input (stdin): dimension, number of points, point coordinates
    comments start with a non-numeric character

options (qh-voron.htm):
    Qu   - compute furthest-site Voronoi diagram
    Tv   - verify result: structure, convexity, and in-circle test
    .    - concise list of all options
    -    - one-line description of all options

output options (subset):
    s    - summary of results (default)
    p    - Voronoi vertices
    o    - OFF file format (dim, Voronoi vertices, and Voronoi regions)
    FN   - count and Voronoi vertices for each Voronoi region
    Fv   - Voronoi diagram as Voronoi vertices between adjacent input sites
    Fi   - separating hyperplanes for bounded regions, 'Fo' for unbounded
    G    - Geomview output (2-d only)
    QVn  - Voronoi vertices for input point n, -n if not
    TO file- output results to file, may be enclosed in single quotes

examples:
rbox c P0 D2 | qvoronoi s o         rbox c P0 D2 | qvoronoi Fi
rbox c P0 D2 | qvoronoi Fo          rbox c P0 D2 | qvoronoi Fv
rbox c P0 D2 | qvoronoi s Qu Fv     rbox c P0 D2 | qvoronoi Qu Fo
rbox c G1 d D2 | qvoronoi s p       rbox c P0 D2 | qvoronoi s Fv QV0

»qvoronoi input

The input data on stdin consists of:
  • dimension
  • number of points
  • point coordinates

Use I/O redirection (e.g., qvoronoi < data.txt), a pipe (e.g., rbox 10 | qvoronoi), or the 'TI' option (e.g., qvoronoi TI data.txt).

For example, this is four cocircular points inside a square. Their Voronoi diagram has nine vertices and eight regions. Notice the Voronoi vertex at the origin, and the Voronoi vertices (on each axis) for the four sides of the square.

rbox s 4 W0 c G1 D2 > data 
2 RBOX s 4 W0 c D2
8
-0.4941988586954018 -0.07594397977563715
-0.06448037284989526 0.4958248496365813
0.4911154367094632 0.09383830681375946
-0.348353580869097 -0.3586778257652367
    -1     -1
    -1      1
     1     -1
     1      1

qvoronoi s p < data 


Voronoi diagram by the convex hull of 8 points in 3-d:

  Number of Voronoi regions: 8
  Number of Voronoi vertices: 9
  Number of non-simplicial Voronoi vertices: 1

Statistics for: RBOX s 4 W0 c D2 | QVORONOI s p

  Number of points processed: 8
  Number of hyperplanes created: 18
  Number of facets in hull: 10
  Number of distance tests for qhull: 33
  Number of merged facets: 2
  Number of distance tests for merging: 102
  CPU seconds to compute hull (after input): 0.094

2
9
4.217546450968612e-17 1.735507986399734
-8.402566836762659e-17 -1.364368854147395
0.3447488772716865 -0.6395484723719818
1.719446929853986 2.136555906154247e-17
0.4967882915039657 0.68662371396699
-1.729928876283549 1.343733067524222e-17
-0.8906163241424728 -0.4594150543829102
-0.6656840313875723 0.5003013793414868
-7.318364664277155e-19 -1.188217818408333e-16

» qvoronoi outputs

These options control the output of Voronoi diagrams.

 
Voronoi vertices
p
print the coordinates of the Voronoi vertices. The first line is the dimension. The second line is the number of vertices. Each remaining line is a Voronoi vertex.
Fn
list the neighboring Voronoi vertices for each Voronoi vertex. The first line is the number of Voronoi vertices. Each remaining line starts with the number of neighboring vertices. Negative vertices (e.g., -1) indicate vertices outside of the Voronoi diagram. In the circle-in-box example, the Voronoi vertex at the origin has four neighbors.
FN
list the Voronoi vertices for each Voronoi region. The first line is the number of Voronoi regions. Each remaining line starts with the number of Voronoi vertices. Negative indices (e.g., -1) indicate vertices outside of the Voronoi diagram. In the circle-in-box example, the four bounded regions are defined by four Voronoi vertices.
 
 
Voronoi regions
o
print the Voronoi regions in OFF format. The first line is the dimension. The second line is the number of vertices, the number of input sites, and "1". The third line represents the vertex-at-infinity. Its coordinates are "-10.101". The next lines are the coordinates of the Voronoi vertices. Each remaining line starts with the number of Voronoi vertices in a Voronoi region. In 2-d, the vertices are listed in adjacency order (unoriented). In 3-d and higher, the vertices are listed in numeric order. In the circle-in-square example, each bounded region includes the Voronoi vertex at the origin. Lines consisting of 0 indicate coplanar input sites or 'Qz'.
Fi
print separating hyperplanes for inner, bounded Voronoi regions. The first number is the number of separating hyperplanes. Each remaining line starts with 3+dim. The next two numbers are adjacent input sites. The next dim numbers are the coefficients of the separating hyperplane. The last number is its offset. Use 'Tv' to verify that the hyperplanes are perpendicular bisectors. It will list relevant statistics to stderr.
Fo
print separating hyperplanes for outer, unbounded Voronoi regions. The first number is the number of separating hyperplanes. Each remaining line starts with 3+dim. The next two numbers are adjacent input sites on the convex hull. The next dim numbers are the coefficients of the separating hyperplane. The last number is its offset. Use 'Tv' to verify that the hyperplanes are perpendicular bisectors. It will list relevant statistics to stderr,
 
 
Input sites
Fv
list ridges of Voronoi vertices for pairs of input sites. The first line is the number of ridges. Each remaining line starts with two plus the number of Voronoi vertices in the ridge. The next two numbers are two adjacent input sites. The remaining numbers list the Voronoi vertices. As with option 'o', a 0 indicates the vertex-at-infinity and an unbounded, separating hyperplane. The perpendicular bisector (separating hyperplane) of the input sites is a flat through these vertices. In the circle-in-square example, the ridge for each edge of the square is unbounded.
Fc
list coincident input sites for each Voronoi vertex. The first line is the number of vertices. The remaining lines start with the number of coincident sites and deleted vertices. Deleted vertices indicate highly degenerate input (see'Fs'). A coincident site is assigned to one Voronoi vertex. Do not use 'QJ' with 'Fc'; the joggle will separate coincident sites.
FP
print coincident input sites with distance to nearest site (i.e., vertex). The first line is the number of coincident sites. Each remaining line starts with the point ID of an input site, followed by the point ID of a coincident point, its vertex, and distance. Includes deleted vertices which indicate highly degenerate input (see'Fs'). Do not use 'QJ' with 'FP'; the joggle will separate coincident sites.
 
 
General
s
print summary of the Voronoi diagram. Use 'Fs' for numeric data.
i
list input sites for each Delaunay region. Use option 'Pp' to avoid the warning. The first line is the number of regions. The remaining lines list the input sites for each region. The regions are oriented. In the circle-in-square example, the cocircular region has four edges. In 3-d and higher, report cospherical sites by adding extra points.
G
Geomview output for 2-d Voronoi diagrams.

» qvoronoi controls

These options provide additional control:

Qu
compute the furthest-site Voronoi diagram.
QVn
select Voronoi vertices for input site n
Qz
add a point above the paraboloid to reduce precision errors. Use it for nearly cocircular/cospherical input (e.g., 'rbox c | qvoronoi Qz').
Tv
verify result
TI file
input data from file. The filename may not use spaces or quotes.
TO file
output results to file. Use single quotes if the filename contains spaces (e.g., TO 'file with spaces.txt'
TFn
report progress after constructing n facets
PDk:1
include upper and lower facets in the output. Set k to the last dimension (e.g., 'PD2:1' for 2-d inputs).
f
facet dump. Print the data structure for each facet (i.e., Voronoi vertex).

» qvoronoi graphics

In 2-d, Geomview output ('G') displays a Voronoi diagram with extra edges to close the unbounded Voronoi regions. To view the unbounded rays, enclose the input points in a square.

You can also view individual Voronoi regions in 3-d. To view the Voronoi region for site 3 in Geomview, execute

qvoronoi <data QV3 p | qconvex s G >output

The qvoronoi command returns the Voronoi vertices for input site 3. The qconvex command computes their convex hull. This is the Voronoi region for input site 3. Its hyperplane normals (qconvex 'n') are the same as the separating hyperplanes from options 'Fi' and 'Fo' (up to roundoff error).

See the Delaunay and Voronoi examples for 2-d and 3-d examples. Turn off normalization (on Geomview's 'obscure' menu) when comparing the Voronoi diagram with the corresponding Delaunay triangulation.

»qvoronoi notes

You can simplify the Voronoi diagram by enclosing the input sites in a large square or cube. This is particularly recommended for cocircular or cospherical input data.

See Voronoi graphics for computing the convex hull of a Voronoi region.

Voronoi diagrams do not include facets that are coplanar with the convex hull of the input sites. A facet is coplanar if the last coefficient of its normal is nearly zero (see qh_ZEROdelaunay).

Unbounded regions can be confusing. For example, 'rbox c | qvoronoi Qz o' produces the Voronoi regions for the vertices of a cube centered at the origin. All regions are unbounded. The output is 

3
2 9 1
-10.101 -10.101 -10.101
     0      0      0
2 0 1
2 0 1
2 0 1
2 0 1
2 0 1
2 0 1
2 0 1
2 0 1
0

The first line is the dimension. The second line is the number of vertices and the number of regions. There is one region per input point plus a region for the point-at-infinity added by option 'Qz'. The next two lines lists the Voronoi vertices. The first vertex is the infinity vertex. It is indicate by the coordinates -10.101. The second vertex is the origin. The next nine lines list the regions. Each region lists two vertices -- the infinity vertex and the origin. The last line is "0" because no region is associated with the point-at-infinity. A "0" would also be listed for nearly incident input sites.

To use option 'Fv', add an interior point. For example, 

rbox c P0 | qvoronoi Fv
20
5 0 7 1 3 5
5 0 3 1 4 5
5 0 5 1 2 3
5 0 1 1 2 4
5 0 6 2 3 6
5 0 2 2 4 6
5 0 4 4 5 6
5 0 8 5 3 6
5 1 2 0 2 4
5 1 3 0 1 4
5 1 5 0 1 2
5 2 4 0 4 6
5 2 6 0 2 6
5 3 4 0 4 5
5 3 7 0 1 5
5 4 8 0 6 5
5 5 6 0 2 3
5 5 7 0 1 3
5 6 8 0 6 3
5 7 8 0 3 5

The output consists of 20 ridges and each ridge lists a pair of input sites and a triplet of Voronoi vertices. The first eight ridges connect the origin ('P0'). The remainder list the edges of the cube. Each edge generates an unbounded ray through the midpoint. The corresponding separating planes ('Fo') follow each pair of coordinate axes.

Options 'Qt' (triangulated output) and 'QJ' (joggled input) are deprecated. They may produce unexpected results. If you use these options, cocircular and cospherical input sites will produce duplicate or nearly duplicate Voronoi vertices. See also Merged facets or joggled input.

»qvoronoi conventions

The following terminology is used for Voronoi diagrams in Qhull. The underlying structure is a Delaunay triangulation from a convex hull in one higher dimension. Facets of the Delaunay triangulation correspond to vertices of the Voronoi diagram. Vertices of the Delaunay triangulation correspond to input sites. They also correspond to regions of the Voronoi diagram. See convex hull conventions, Delaunay conventions, and Qhull's data structures.

  • input site - a point in the input (one dimension lower than a point on the convex hull)
  • point - a point has d+1 coordinates. The last coordinate is the sum of the squares of the input site's coordinates
  • coplanar point - a nearly incident input site
  • vertex - a point on the paraboloid. It corresponds to a unique input site.
  • point-at-infinity - a point added above the paraboloid by option 'Qz'
  • Delaunay facet - a lower facet of the paraboloid. The last coefficient of its normal is clearly negative.
  • Voronoi vertex - the circumcenter of a Delaunay facet
  • Voronoi region - the Voronoi vertices for an input site. The region of Euclidean space nearest to an input site.
  • Voronoi diagram - the graph of the Voronoi regions. It includes the ridges (i.e., edges) between the regions.
  • vertex-at-infinity - the Voronoi vertex that indicates unbounded Voronoi regions in 'o' output format. Its coordinates are -10.101.
  • good facet - a Voronoi vertex with optional restrictions by 'QVn', etc.

»qvoronoi options

qvoronoi- compute the Voronoi diagram
    http://www.qhull.org

input (stdin):
    first lines: dimension and number of points (or vice-versa).
    other lines: point coordinates, best if one point per line
    comments:    start with a non-numeric character

options:
    Qu   - compute furthest-site Voronoi diagram

Qhull control options:
    QJn  - randomly joggle input in range [-n,n]
    Qs   - search all points for the initial simplex
    Qz   - add point-at-infinity to Voronoi diagram
    QGn  - Voronoi vertices if visible from point n, -n if not
    QVn  - Voronoi vertices for input point n, -n if not

Trace options:
    T4   - trace at level n, 4=all, 5=mem/gauss, -1= events
    Tc   - check frequently during execution
    Ts   - statistics
    Tv   - verify result: structure, convexity, and in-circle test
    Tz   - send all output to stdout
    TFn  - report summary when n or more facets created
    TI file - input data from file, no spaces or single quotes
    TO file - output results to file, may be enclosed in single quotes
    TPn  - turn on tracing when point n added to hull
     TMn - turn on tracing at merge n
     TWn - trace merge facets when width > n
    TVn  - stop qhull after adding point n, -n for before (see TCn)
     TCn - stop qhull after building cone for point n (see TVn)

Precision options:
    Cn   - radius of centrum (roundoff added).  Merge facets if non-convex
     An  - cosine of maximum angle.  Merge facets if cosine > n or non-convex
           C-0 roundoff, A-0.99/C-0.01 pre-merge, A0.99/C0.01 post-merge
    Rn   - randomly perturb computations by a factor of [1-n,1+n]
    Wn   - min facet width for non-coincident point (before roundoff)

Output formats (may be combined; if none, produces a summary to stdout):
    s    - summary to stderr
    p    - Voronoi vertices
    o    - OFF format (dim, Voronoi vertices, and Voronoi regions)
    i    - Delaunay regions (use 'Pp' to avoid warning)
    f    - facet dump

More formats:
    Fc   - count plus coincident points (by Voronoi vertex)
    Fd   - use cdd format for input (homogeneous with offset first)
    FD   - use cdd format for output (offset first)
    FF   - facet dump without ridges
    Fi   - separating hyperplanes for bounded Voronoi regions
    FI   - ID for each Voronoi vertex
    Fm   - merge count for each Voronoi vertex (511 max)
    Fn   - count plus neighboring Voronoi vertices for each Voronoi vertex
    FN   - count and Voronoi vertices for each Voronoi region
    Fo   - separating hyperplanes for unbounded Voronoi regions
    FO   - options and precision constants
    FP   - nearest point and distance for each coincident point
    FQ   - command used for qvoronoi
    Fs   - summary: #int (8), dimension, #points, tot vertices, tot facets,
                    for output: #Voronoi regions, #Voronoi vertices,
                                #coincident points, #non-simplicial regions
                    #real (2), max outer plane and min vertex
    Fv   - Voronoi diagram as Voronoi vertices between adjacent input sites
    Fx   - extreme points of Delaunay triangulation (on convex hull)

Geomview options (2-d only)
    Ga   - all points as dots
     Gp  -  coplanar points and vertices as radii
     Gv  -  vertices as spheres
    Gi   - inner planes only
     Gn  -  no planes
     Go  -  outer planes only
    Gc   - centrums
    Gh   - hyperplane intersections
    Gr   - ridges
    GDn  - drop dimension n in 3-d and 4-d output

Print options:
    PAn  - keep n largest Voronoi vertices by 'area'
    Pdk:n - drop facet if normal[k] <= n (default 0.0)
    PDk:n - drop facet if normal[k] >= n
    Pg   - print good Voronoi vertices (needs 'QGn' or 'QVn')
    PFn  - keep Voronoi vertices whose 'area' is at least n
    PG   - print neighbors of good Voronoi vertices
    PMn  - keep n Voronoi vertices with most merges
    Po   - force output.  If error, output neighborhood of facet
    Pp   - do not report precision problems

    .    - list of all options
    -    - one line descriptions of all options

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[delaunay]qvoronoi Qu -- furthest-site Voronoi diagram

The furthest-site Voronoi diagram is the furthest-neighbor map for a set of points. Each region contains those points that are further from one input site than any other input site. See the survey article by Aurenhammer ['91] and the brief introduction by O'Rourke ['94]. The furthest-site Voronoi diagram is the dual of the furthest-site Delaunay triangulation.

Example: rbox 10 D2 | qvoronoi Qu s o TO result
Compute the 2-d, furthest-site Voronoi diagram of 10 random points. Write a summary to the console and the Voronoi regions and vertices to 'result'. The first vertex of the result indicates unbounded regions. Almost all regions are unbounded.
Example: rbox r y c G1 D2 | qvoronoi Qu s Fn TO result
Compute the 2-d furthest-site Voronoi diagram of a square and a small triangle. Write a summary to the console and the Voronoi vertices for each input site to 'result'. The origin is the only furthest-site Voronoi vertex. The negative indices indicate vertices-at-infinity.

Qhull computes the furthest-site Voronoi diagram via the furthest-site Delaunay triangulation. Each furthest-site Voronoi vertex is the circumcenter of an upper facet of the Delaunay triangulation. Each furthest-site Voronoi region corresponds to a vertex of the Delaunay triangulation (i.e., an input site).

See Qhull FAQ - Delaunay and Voronoi diagram questions.

The 'qvonoroi' program is equivalent to 'qhull v Qbb' in 2-d to 3-d, and 'qhull v Qbb Qx' in 4-d and higher. It disables the following Qhull options: d n m v H U Qb QB Qc Qf Qg Qi Qm Qr QR Qv Qx TR E V Fa FA FC Fp FS Ft FV Gt Q0,etc.

Copyright © 1995-2012 C.B. Barber

»furthest-site qvoronoi synopsis

See qvoronoi synopsis. The same program is used for both constructions. Use option 'Qu' for furthest-site Voronoi diagrams.

»furthest-site qvoronoi input

The input data on stdin consists of:

  • dimension
  • number of points
  • point coordinates

Use I/O redirection (e.g., qvoronoi Qu < data.txt), a pipe (e.g., rbox 10 | qvoronoi Qu), or the 'TI' option (e.g., qvoronoi TI data.txt Qu).

For example, this is a square containing four random points. Its furthest-site Voronoi diagram has on vertex and four unbounded, separating hyperplanes (i.e., the coordinate axes)

rbox c 4 D2 > data 
2 RBOX c 4 D2
8
-0.4999921736307369 -0.3684622117955817
0.2556053225468894 -0.0413498678629751
0.0327672376602583 -0.2810408135699488
-0.452955383763607 0.17886471718444
  -0.5   -0.5
  -0.5    0.5
   0.5   -0.5
   0.5    0.5

qvoronoi Qu s Fo < data 


Furthest-site Voronoi vertices by the convex hull of 8 points in 3-d:

  Number of Voronoi regions: 8
  Number of Voronoi vertices: 1
  Number of non-simplicial Voronoi vertices: 1

Statistics for: RBOX c 4 D2 | QVORONOI Qu s Fo

  Number of points processed: 8
  Number of hyperplanes created: 20
  Number of facets in hull: 11
  Number of distance tests for qhull: 34
  Number of merged facets: 1
  Number of distance tests for merging: 107
  CPU seconds to compute hull (after input):  0

4
5 4 5      0      1      0
5 4 6      1      0      0
5 5 7      1      0      0
5 6 7      0      1      0

» furthest-site qvoronoi outputs

These options control the output of furthest-site Voronoi diagrams.

 
furthest-site Voronoi vertices
p
print the coordinates of the furthest-site Voronoi vertices. The first line is the dimension. The second line is the number of vertices. Each remaining line is a furthest-site Voronoi vertex. The points-in-square example has one furthest-site Voronoi vertex at the origin.
Fn
list the neighboring furthest-site Voronoi vertices for each furthest-site Voronoi vertex. The first line is the number of Voronoi vertices. Each remaining line starts with the number of neighboring vertices. Negative indices (e.g., -1) indicate vertices outside of the Voronoi diagram. In the points-in-square example, the Voronoi vertex at the origin has four neighbors-at-infinity.
FN
list the furthest-site Voronoi vertices for each furthest-site Voronoi region. The first line is the number of Voronoi regions. Each remaining line starts with the number of Voronoi vertices. Negative indices (e.g., -1) indicate vertices outside of the Voronoi diagram. In the points-in-square example, all regions share the Voronoi vertex at the origin.
 
 
furthest-site Voronoi regions
o
print the furthest-site Voronoi regions in OFF format. The first line is the dimension. The second line is the number of vertices, the number of input sites, and "1". The third line represents the vertex-at-infinity. Its coordinates are "-10.101". The next lines are the coordinates of the furthest-site Voronoi vertices. Each remaining line starts with the number of Voronoi vertices in a Voronoi region. In 2-d, the vertices are listed in adjacency order (unoriented). In 3-d and higher, the vertices are listed in numeric order. In the points-in-square example, each unbounded region includes the Voronoi vertex at the origin. Lines consisting of 0 indicate interior input sites.
Fi
print separating hyperplanes for inner, bounded furthest-site Voronoi regions. The first number is the number of separating hyperplanes. Each remaining line starts with 3+dim. The next two numbers are adjacent input sites. The next dim numbers are the coefficients of the separating hyperplane. The last number is its offset. The are no bounded, separating hyperplanes for the points-in-square example.
Fo
print separating hyperplanes for outer, unbounded furthest-site Voronoi regions. The first number is the number of separating hyperplanes. Each remaining line starts with 3+dim. The next two numbers are adjacent input sites on the convex hull. The next dim numbers are the coefficients of the separating hyperplane. The last number is its offset. The points-in-square example has four unbounded, separating hyperplanes.
 
 
Input sites
Fv
list ridges of furthest-site Voronoi vertices for pairs of input sites. The first line is the number of ridges. Each remaining line starts with two plus the number of Voronoi vertices in the ridge. The next two numbers are two adjacent input sites. The remaining numbers list the Voronoi vertices. As with option 'o', a 0 indicates the vertex-at-infinity and an unbounded, separating hyperplane. The perpendicular bisector (separating hyperplane) of the input sites is a flat through these vertices. In the points-in-square example, the ridge for each edge of the square is unbounded.
 
 
General
s
print summary of the furthest-site Voronoi diagram. Use 'Fs' for numeric data.
i
list input sites for each furthest-site Delaunay region. Use option 'Pp' to avoid the warning. The first line is the number of regions. The remaining lines list the input sites for each region. The regions are oriented. In the points-in-square example, the square region has four input sites. In 3-d and higher, report cospherical sites by adding extra points.
G
Geomview output for 2-d furthest-site Voronoi diagrams.

» furthest-site qvoronoi controls

These options provide additional control:

Qu
must be used.
QVn
select furthest-site Voronoi vertices for input site n
Tv
verify result
TI file
input data from file. The filename may not use spaces or quotes.
TO file
output results to file. Use single quotes if the filename contains spaces (e.g., TO 'file with spaces.txt'
TFn
report progress after constructing n facets
PDk:1
include upper and lower facets in the output. Set k to the last dimension (e.g., 'PD2:1' for 2-d inputs).
f
facet dump. Print the data structure for each facet (i.e., furthest-site Voronoi vertex).

» furthest-site qvoronoi graphics

In 2-d, Geomview output ('G') displays a furthest-site Voronoi diagram with extra edges to close the unbounded furthest-site Voronoi regions. All regions will be unbounded. Since the points-in-box example has only one furthest-site Voronoi vertex, the Geomview output is one point.

See the Delaunay and Voronoi examples for a 2-d example. Turn off normalization (on Geomview's 'obscure' menu) when comparing the furthest-site Voronoi diagram with the corresponding Voronoi diagram.

»furthest-site qvoronoi notes

See Voronoi notes.

»furthest-site qvoronoi conventions

The following terminology is used for furthest-site Voronoi diagrams in Qhull. The underlying structure is a furthest-site Delaunay triangulation from a convex hull in one higher dimension. Upper facets of the Delaunay triangulation correspond to vertices of the furthest-site Voronoi diagram. Vertices of the furthest-site Delaunay triangulation correspond to input sites. They also define regions of the furthest-site Voronoi diagram. All vertices are extreme points of the input sites. See qconvex conventions, furthest-site delaunay conventions, and Qhull's data structures.

  • input site - a point in the input (one dimension lower than a point on the convex hull)
  • point - a point has d+1 coordinates. The last coordinate is the sum of the squares of the input site's coordinates
  • vertex - a point on the upper facets of the paraboloid. It corresponds to a unique input site.
  • furthest-site Delaunay facet - an upper facet of the paraboloid. The last coefficient of its normal is clearly positive.
  • furthest-site Voronoi vertex - the circumcenter of a furthest-site Delaunay facet
  • furthest-site Voronoi region - the region of Euclidean space further from an input site than any other input site. Qhull lists the furthest-site Voronoi vertices that define each furthest-site Voronoi region.
  • furthest-site Voronoi diagram - the graph of the furthest-site Voronoi regions with the ridges (edges) between the regions.
  • infinity vertex - the Voronoi vertex for unbounded furthest-site Voronoi regions in 'o' output format. Its coordinates are -10.101.
  • good facet - an furthest-site Voronoi vertex with optional restrictions by 'QVn', etc.

»furthest-site qvoronoi options

See qvoronoi options. The same program is used for both constructions. Use option 'Qu' for furthest-site Voronoi diagrams.

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[CONE]rbox -- generate point distributions

rbox generates random or regular points according to the options given, and outputs the points to stdout. The points are generated in a cube, unless 's', 'x', or 'y' are given.

»rbox synopsis

rbox- generate various point distributions.  Default is random in cube.

args (any order, space separated):
  3000    number of random points in cube, lens, spiral, sphere or grid
  D3      dimension 3-d
  c       add a unit cube to the output ('c G2.0' sets size)
  d       add a unit diamond to the output ('d G2.0' sets size)
  l       generate a regular 3-d spiral
  r       generate a regular polygon, ('r s Z1 G0.1' makes a cone)
  s       generate cospherical points
  x       generate random points in simplex, may use 'r' or 'Wn'
  y       same as 'x', plus simplex
  Pn,m,r  add point [n,m,r] first, pads with 0

  Ln      lens distribution of radius n.  Also 's', 'r', 'G', 'W'.
  Mn,m,r  lattice (Mesh) rotated by [n,-m,0], [m,n,0], [0,0,r], ...
          '27 M1,0,1' is {0,1,2} x {0,1,2} x {0,1,2}.  Try 'M3,4 z'.
  W0.1    random distribution within 0.1 of the cube's or sphere's surface
  Z0.5 s  random points in a 0.5 disk projected to a sphere
  Z0.5 s G0.6 same as Z0.5 within a 0.6 gap

  Bn      bounding box coordinates, default 0.5
  h       output as homogeneous coordinates for cdd
  n       remove command line from the first line of output
  On      offset coordinates by n
  t       use time as the random number seed (default is command line)
  tn      use n as the random number seed
  z       print integer coordinates, default 'Bn' is 1e+06

»rbox outputs

The format of the output is the following: first line contains the dimension and a comment, second line contains the number of points, and the following lines contain the points, one point per line. Points are represented by their coordinate values.

For example, rbox c 10 D2 generates 

2 RBOX c 10 D2
14
-0.4999921736307369 -0.3684622117955817
0.2556053225468894 -0.0413498678629751
0.0327672376602583 -0.2810408135699488
-0.452955383763607 0.17886471718444
0.1792964061529342 0.4346928963760779
-0.1164979223315585 0.01941637230982666
0.3309653464993139 -0.4654278894564396
-0.4465383649305798 0.02970019358182344
0.1711493843897706 -0.4923018137852678
-0.1165843490665633 -0.433157762450313
  -0.5   -0.5
  -0.5    0.5
   0.5   -0.5
   0.5    0.5

»rbox examples

       rbox 10
              10 random points in the unit cube centered  at  the
              origin.

       rbox 10 s D2
              10 random points on a 2-d circle.

       rbox 100 W0
              100 random points on the surface of a cube.

       rbox 1000 s D4
              1000 random points on a 4-d sphere.

       rbox c D5 O0.5
              a 5-d hypercube with one corner at the origin.

       rbox d D10
              a 10-d diamond.

       rbox x 1000 r W0
              100 random points on the surface of a fixed simplex

       rbox y D12
              a 12-d simplex.

       rbox l 10
              10 random points along a spiral

       rbox l 10 r
              10 regular points  along  a  spiral  plus  two  end
              points

       rbox 1000 L10000 D4 s
              1000 random points on the surface of a narrow lens.

           rbox 1000 L100000 s G1e-6
                  1000 random points near the edge of a narrow lens

       rbox c G2 d G3
              a cube with coordinates +2/-2 and  a  diamond  with
              coordinates +3/-3.

       rbox 64 M3,4 z
              a  rotated,  {0,1,2,3} x {0,1,2,3} x {0,1,2,3} lat-
              tice (Mesh) of integer points.

       rbox P0 P0 P0 P0 P0
              5 copies of the origin in 3-d.  Try 'rbox P0 P0  P0
              P0 P0 | qhull QJ'.

       r 100 s Z1 G0.1
              two  cospherical  100-gons plus another cospherical
              point.

       100 s Z1
              a cone of points.

       100 s Z1e-7
              a narrow cone of points with many precision errors.

»rbox notes

Some combinations of arguments generate odd results.

»rbox options

       n      number of points

       Dn     dimension n-d (default 3-d)

       Bn     bounding box coordinates (default 0.5)

       l      spiral distribution, available only in 3-d

       Ln     lens  distribution  of  radius n.  May be used with
              's', 'r', 'G', and 'W'.

       Mn,m,r lattice  (Mesh)  rotated  by  {[n,-m,0],   [m,n,0],
              [0,0,r],  ...}.   Use  'Mm,n'  for a rigid rotation
              with r = sqrt(n^2+m^2).  'M1,0'  is  an  orthogonal
              lattice.   For  example,  '27  M1,0'  is  {0,1,2} x
              {0,1,2} x {0,1,2}.

       s      cospherical points randomly generated in a cube and
              projected to the unit sphere

       x      simplicial  distribution.   It  is fixed for option
              'r'.  May be used with 'W'.

       y      simplicial distribution plus a simplex.   Both  'x'
              and 'y' generate the same points.

       Wn     restrict  points  to distance n of the surface of a
              sphere or a cube

       c      add a unit cube to the output

       c Gm   add a cube with all combinations of +m  and  -m  to
              the output

       d      add a unit diamond to the output.

       d Gm   add a diamond made of 0, +m and -m to the output

       Pn,m,r add point [n,m,r] to the output first.  Pad coordi-
              nates with 0.0.

       n      Remove the command line from the first line of out-
              put.

       On     offset the data by adding n to each coordinate.

       t      use  time  in  seconds  as  the  random number seed
              (default is command line).

       tn     set the random number seed to n.

       z      generate integer coordinates.  Use 'Bn'  to  change
              the  range.   The  default  is 'B1e6' for six-digit
              coordinates.  In R^4, seven-digit coordinates  will
              overflow hyperplane normalization.

       Zn s   restrict points to a disk about the z+ axis and the
              sphere (default Z1.0).  Includes the opposite pole.
              'Z1e-6'  generates  degenerate  points under single
              precision.

       Zn Gm s
              same as Zn with an empty center (default G0.5).

       r s D2 generate a regular polygon

       r s Z1 G0.1
              generate a regular cone

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The Geometry Center Home Page

Comments to: qhull@qhull.org
Created: Sept. 25, 1995 --- Last modified: August 12, 1998

qhull-2012.1/html/rbox.man0000644000076400010400000001033511313566220016520 0ustar bbarberAdministrators.\" This is the Unix manual page for rbox, written in nroff, the standard .\" manual formatter for Unix systems. To format it, type .\" .\" nroff -man rbox.man .\" .\" This will print a formatted copy to standard output. If you want .\" to ensure that the output is plain ascii, free of any control .\" characters that nroff uses for underlining etc, pipe the output .\" through "col -b": .\" .\" nroff -man rbox.man | col -b .\" .TH rbox 1 "August 10, 1998" "Geometry Center" .SH NAME rbox \- generate point distributions for qhull .SH SYNOPSIS Command "rbox" (w/o arguments) lists the options. .SH DESCRIPTION .PP rbox generates random or regular points according to the options given, and outputs the points to stdout. The points are generated in a cube, unless 's' or 'k' option is given. The format of the output is the following: first line contains the dimension and a comment, second line contains the number of points, and the following lines contain the points, one point per line. Points are represented by their coordinate values. .SH EXAMPLES .TP rbox 10 10 random points in the unit cube centered at the origin. .TP rbox 10 s D2 10 random points on a 2\[hy]d circle. .TP rbox 100 W0 100 random points on the surface of a cube. .TP rbox 1000 s D4 1000 random points on a 4\[hy]d sphere. .TP rbox c D5 O0.5 a 5\[hy]d hypercube with one corner at the origin. .TP rbox d D10 a 10\[hy]d diamond. .TP rbox x 1000 r W0 100 random points on the surface of a fixed simplex .TP rbox y D12 a 12\[hy]d simplex. .TP rbox l 10 10 random points along a spiral .TP rbox l 10 r 10 regular points along a spiral plus two end points .TP rbox 1000 L10000 D4 s 1000 random points on the surface of a narrow lens. .TP rbox c G2 d G3 a cube with coordinates +2/\-2 and a diamond with coordinates +3/\-3. .TP rbox 64 M3,4 z a rotated, {0,1,2,3} x {0,1,2,3} x {0,1,2,3} lattice (Mesh) of integer points. 'rbox 64 M1,0' is orthogonal. .TP rbox P0 P0 P0 P0 P0 5 copies of the origin in 3\-d. Try 'rbox P0 P0 P0 P0 P0 | qhull QJ'. .TP r 100 s Z1 G0.1 two cospherical 100\-gons plus another cospherical point. .TP 100 s Z1 a cone of points. .TP 100 s Z1e\-7 a narrow cone of points with many precision errors. .SH OPTIONS .TP n number of points .TP Dn dimension n\[hy]d (default 3\[hy]d) .TP Bn bounding box coordinates (default 0.5) .TP l spiral distribution, available only in 3\[hy]d .TP Ln lens distribution of radius n. May be used with 's', 'r', 'G', and 'W'. .TP Mn,m,r lattice (Mesh) rotated by {[n,\-m,0], [m,n,0], [0,0,r], ...}. Use 'Mm,n' for a rigid rotation with r = sqrt(n^2+m^2). 'M1,0' is an orthogonal lattice. For example, '27 M1,0' is {0,1,2} x {0,1,2} x {0,1,2}. '27 M3,4 z' is a rotated integer lattice. .TP s cospherical points randomly generated in a cube and projected to the unit sphere .TP x simplicial distribution. It is fixed for option 'r'. May be used with 'W'. .TP y simplicial distribution plus a simplex. Both 'x' and 'y' generate the same points. .TP Wn restrict points to distance n of the surface of a sphere or a cube .TP c add a unit cube to the output .TP c Gm add a cube with all combinations of +m and \-m to the output .TP d add a unit diamond to the output. .TP d Gm add a diamond made of 0, +m and \-m to the output .TP Pn,m,r add point [n,m,r] to the output first. Pad coordinates with 0.0. .TP n Remove the command line from the first line of output. .TP On offset the data by adding n to each coordinate. .TP t use time in seconds as the random number seed (default is command line). .TP tn set the random number seed to n. .TP z generate integer coordinates. Use 'Bn' to change the range. The default is 'B1e6' for six\[hy]digit coordinates. In R^4, seven\[hy]digit coordinates will overflow hyperplane normalization. .TP Zn s restrict points to a disk about the z+ axis and the sphere (default Z1.0). Includes the opposite pole. 'Z1e\-6' generates degenerate points under single precision. .TP Zn Gm s same as Zn with an empty center (default G0.5). .TP r s D2 generate a regular polygon .TP r s Z1 G0.1 generate a regular cone .SH BUGS Some combinations of arguments generate odd results. Report bugs to qhull_bug@qhull.org, other correspondence to qhull@qhull.org .SH SEE ALSO qhull(1) .SH AUTHOR .nf C. Bradford Barber bradb@shore.net .fi qhull-2012.1/html/rbox.txt0000644000076400010400000001202311313565352016565 0ustar bbarberAdministrators rbox(1) rbox(1) NAME rbox - generate point distributions for qhull SYNOPSIS Command "rbox" (w/o arguments) lists the options. DESCRIPTION rbox generates random or regular points according to the options given, and outputs the points to stdout. The points are generated in a cube, unless 's' or given. The format of the output is the following: first line contains the dimension and a comment, second line contains the num- ber of points, and the following lines contain the points, one point per line. Points are represented by their coor- dinate values. EXAMPLES rbox 10 10 random points in the unit cube centered at the origin. rbox 10 s D2 10 random points on a 2-d circle. rbox 100 W0 100 random points on the surface of a cube. rbox 1000 s D4 1000 random points on a 4-d sphere. rbox c D5 O0.5 a 5-d hypercube with one corner at the origin. rbox d D10 a 10-d diamond. rbox x 1000 r W0 100 random points on the surface of a fixed simplex rbox y D12 a 12-d simplex. rbox l 10 10 random points along a spiral rbox l 10 r 10 regular points along a spiral plus two end points rbox 1000 L10000 D4 s 1000 random points on the surface of a narrow lens. rbox c G2 d G3 a cube with coordinates +2/-2 and a diamond with Geometry Center August 10, 1998 1 rbox(1) rbox(1) coordinates +3/-3. rbox 64 M3,4 z a rotated, {0,1,2,3} x {0,1,2,3} x {0,1,2,3} lat- tice (Mesh) of integer points. rbox P0 P0 P0 P0 P0 5 copies of the origin in 3-d. Try 'rbox P0 P0 P0 P0 P0 | qhull QJ'. r 100 s Z1 G0.1 two cospherical 100-gons plus another cospherical point. 100 s Z1 a cone of points. 100 s Z1e-7 a narrow cone of points with many precision errors. OPTIONS n number of points Dn dimension n-d (default 3-d) Bn bounding box coordinates (default 0.5) l spiral distribution, available only in 3-d Ln lens distribution of radius n. May be used with 's', 'r', 'G', and 'W'. Mn,m,r lattice (Mesh) rotated by {[n,-m,0], [m,n,0], [0,0,r], ...}. Use 'Mm,n' for a rigid rotation with r = sqrt(n^2+m^2). 'M1,0' is an orthogonal lattice. For example, '27 M1,0' is {0,1,2} x {0,1,2} x {0,1,2}. s cospherical points randomly generated in a cube and projected to the unit sphere x simplicial distribution. It is fixed for option 'r'. May be used with 'W'. y simplicial distribution plus a simplex. Both 'x' and 'y' generate the same points. Wn restrict points to distance n of the surface of a sphere or a cube c add a unit cube to the output c Gm add a cube with all combinations of +m and -m to the output Geometry Center August 10, 1998 2 rbox(1) rbox(1) d add a unit diamond to the output. d Gm add a diamond made of 0, +m and -m to the output Pn,m,r add point [n,m,r] to the output first. Pad coordi- nates with 0.0. n Remove the command line from the first line of out- put. On offset the data by adding n to each coordinate. t use time in seconds as the random number seed (default is command line). tn set the random number seed to n. z generate integer coordinates. Use 'Bn' to change the range. The default is 'B1e6' for six-digit coordinates. In R^4, seven-digit coordinates will overflow hyperplane normalization. Zn s restrict points to a disk about the z+ axis and the sphere (default Z1.0). Includes the opposite pole. 'Z1e-6' generates degenerate points under single precision. Zn Gm s same as Zn with an empty center (default G0.5). r s D2 generate a regular polygon r s Z1 G0.1 generate a regular cone BUGS Some combinations of arguments generate odd results. Report bugs to qhull_bug@qhull.org, other correspon- dence to qhull@qhull.org SEE ALSO qhull(1) AUTHOR C. Bradford Barber bradb@shore.net Geometry Center August 10, 1998 3 qhull-2012.1/index.htm0000644000076400010400000003326011720041145015724 0ustar bbarberAdministrators Qhull code for Convex Hull, Delaunay Triangulation, Voronoi Diagram, and Halfspace Intersection about a Point URL: http://www.qhull.org
To: News • Download • CiteSeer • Images • Manual • FAQ • Programs • Options

Qhull

[CONE] 		Qhull computes the convex hull, Delaunay triangulation, Voronoi diagram, halfspace intersection about a point, furthest-site Delaunay triangulation, and furthest-site Voronoi diagram. The source code runs in 2-d, 3-d, 4-d, and higher dimensions. Qhull implements the Quickhull algorithm for computing the convex hull. It handles roundoff errors from floating point arithmetic. It computes volumes, surface areas, and approximations to the convex hull.

Qhull does not support triangulation of non-convex surfaces, mesh generation of non-convex objects, medium-sized inputs in 9-D and higher, alpha shapes, weighted Voronoi diagrams, Voronoi volumes, or constrained Delaunay triangulations,

Qhull 2012.1 fixes qhull-go for Windows 64-bit. If you use Qhull 2003.1. please upgrade to 2012.1 or apply poly.c-qh_gethash.patch.

Introduction

  • Fukuda's introduction to convex hulls, Delaunay triangulations, Voronoi diagrams, and linear programming
  • Lambert's Java visualization of convex hull algorithms
  • LEDA Guide to geometry algorithms
  • MathWorld's Computational Geometry from Wolfram Research
  • Skiena's Computational Geometry from his Algorithm Design Manual.
  • Stony Brook Algorithm Repository, computational geometry

Qhull Documentation and Support

Related URLs

FAQs and Newsgroups

The program includes options for input transformations, randomization, tracing, multiple output formats, and execution statistics. The program can be called from within your application.

You can view the results in 2-d, 3-d and 4-d with Geomview. An alternative is VTK.

For an article about Qhull, download from ACM or CiteSeer:

Barber, C.B., Dobkin, D.P., and Huhdanpaa, H.T., "The Quickhull algorithm for convex hulls," ACM Trans. on Mathematical Software, 22(4):469-483, Dec 1996, http://www.qhull.org

Abstract:

The convex hull of a set of points is the smallest convex set that contains the points. This article presents a practical convex hull algorithm that combines the two-dimensional Quickhull Algorithm with the general dimension Beneath-Beyond Algorithm. It is similar to the randomized, incremental algorithms for convex hull and Delaunay triangulation. We provide empirical evidence that the algorithm runs faster when the input contains non-extreme points, and that it uses less memory.

Computational geometry algorithms have traditionally assumed that input sets are well behaved. When an algorithm is implemented with floating point arithmetic, this assumption can lead to serious errors. We briefly describe a solution to this problem when computing the convex hull in two, three, or four dimensions. The output is a set of "thick" facets that contain all possible exact convex hulls of the input. A variation is effective in five or more dimensions.

Up: Past Software Projects of the Geometry Center
URL: http://www.qhull.org
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[HOME] The Geometry Center Home Page

Comments to: qhull@qhull.org
Created: May 17 1995 --- qhull-2012.1/Makefile0000644000076400010400000005521211720333075015552 0ustar bbarberAdministrators# Unix Makefile for qhull and rbox (default gcc/g++) # # see README.txt and 'make help' # For qhulltest, use Qt project file at src/qhull-all.pro # For static builds, an alternative is src/libqhull/Makefile # # Results # qhull Computes convex hull and related structures (libqhullstatic) # qconvex, qdelaunay, qhalf, qvoronoi # Specializations of qhull for each geometric structure # libqhull.so Shared library with a static qh_qh struct # libqhull_p.so ... with a malloc'd qh_qh struct with -Dqh_QHpointer # make SO=dll ... on Windows, use SO=dll. It compiles dlls # libqhullstatic.a Static library with a static qh_qh struct # ... called 'static' to avoid naming conflicts # libqhullstatic_p.a with a malloc'd qh_qh struct with -Dqh_QHpointer # libqhullcpp.a Static library using a malloc'd qh_qh struct # user_eg An example of using shared library qhull_p # ... compiled with -Dqh_QHpointer # user_eg2 An example of using shared library qhull # user_eg3 An example of the C++ interface to qhull # ... using libqhullcpp, libqhullstatic_p, -Dqh_QHpointer # testqset Standalone test program for qset.c with mem.c # # Make targets # make Produce all of the results # make qhullx Produce qhull, qconvex etc. without using library # make qtest Quick test of rbox and qhull (bin/rbox D4 | bin/qhull) # make qtestall Quick test of all programs except qhulltest # make test Test of rbox and qhull # make bin/qvoronoi Produce bin/qvoronoi (etc.) # make doc Print documentation # make install Copy qhull, rbox, qhull.1, rbox.1 to BINDIR, MANDIR # make new Rebuild qhull and rbox from source # # make printall Print all files # make clean Remove object files # make cleanall Remove generated files # # DESTDIR destination directory. Other directories are relative # BINDIR directory where to copy executables # DOCDIR directory where to copy html documentation # INCDIR directory where to copy headers # LIBDIR directory where to copy libraries # MANDIR directory where to copy manual pages # PRINTMAN command for printing manual pages # PRINTC command for printing C files # CC ANSI C or C++ compiler # CC_OPTS1 options used to compile .c files # CC_OPTS2 options used to link .o files # CC_OPTS3 options to build shared libraries # CXX ANSI C++ compiler # CXX_OPTS1 options used to compile .cpp files # CXX_OPTS2 options used to link .o files # CC_WARNINGS warnings for .c programs # CXX_WARNINGS warnings for .cpp programs # # LIBQHULLS_OBJS .o files for linking # LIBQHULL_HDRS .h files for printing # CFILES .c files for printing # CXXFILES .cpp files for printing # TESTFILES .cpp test files for printing # DOCFILES documentation files # FILES miscellaneous files for printing # HTMFILES documentation source files # TFILES .txt versions of html files # FILES all other files # LIBQHULLS_OBJS specifies the object files of libqhullstatic.a # # Do not replace tabs with spaces. Needed by 'make' for build rules # You may build the qhull programs without using a library # make qhullx DESTDIR = /usr/local BINDIR = $(DESTDIR)/bin INCDIR = $(DESTDIR)/include LIBDIR = $(DESTDIR)/lib DOCDIR = $(DESTDIR)/share/doc/qhull MANDIR = $(DESTDIR)/share/man/man1 # if you do not have enscript, try a2ps or just use lpr. The files are text. PRINTMAN = enscript -2rl PRINTC = enscript -2r # PRINTMAN = lpr # PRINTC = lpr #for Gnu's gcc compiler, -O2 for optimization, -g for debugging CC = gcc CC_OPTS1 = -O2 -fPIC -ansi -Isrc/libqhull $(CC_WARNINGS) CXX = g++ # libqhullcpp must be before libqhull CXX_OPTS1 = -O2 -Dqh_QHpointer -Isrc/ -Isrc/libqhullcpp -Isrc/libqhull $(CXX_WARNINGS) # for shared library link CC_OPTS3 = # Define qhull_VERSION in CMakeLists.txt, Makefile, and qhull-warn.pri # Truncated version in qhull-exports.def, qhull_p-exports.def, # qhull.so -- static qh_qhT global data structure (qh_QHpointer=0) # qhull_p.so -- allocated qh_qhT global data structure (qh_QHpointer=1). Required for libqhullcpp # qhull_m.so -- future version of Qhull with qh_qhT passed as an argument. qhull_SOVERSION=6 SO = so.6.3.1 # On MinGW, # make SO=dll # Copy lib/libqhull6_p.dll and lib/libqhull.dll to bin/ # for Sun's cc compiler, -fast or O2 for optimization, -g for debugging, -Xc for ANSI #CC = cc #CC_OPTS1 = -Xc -v -fast # for Silicon Graphics cc compiler, -O2 for optimization, -g for debugging #CC = cc #CC_OPTS1 = -ansi -O2 # for Next cc compiler with fat executable #CC = cc #CC_OPTS1 = -ansi -O2 -arch m68k -arch i386 -arch hppa # For loader, ld, CC_OPTS2 = $(CC_OPTS1) CXX_OPTS2 = $(CXX_OPTS1) # [gcc 4.4] Compiles without error (-Werror) CC_WARNINGS = -Wall -Wcast-qual -Wextra -Wwrite-strings -Wshadow CXX_WARNINGS = -Wall -Wcast-qual -Wextra -Wwrite-strings -Wno-sign-conversion -Wshadow -Wconversion # Compiles OK with all gcc warnings except for -Wno-sign-conversion and -Wconversion # Compiles OK with all g++ warnings except Qt source errors on -Wshadow and -Wconversion # -Waddress -Warray-bounds -Wchar-subscripts -Wclobbered -Wcomment -Wunused-variable # -Wempty-body -Wformat -Wignored-qualifiers -Wimplicit-function-declaration -Wimplicit-int # -Wmain -Wmissing-braces -Wmissing-field-initializers -Wmissing-parameter-type -Wnonnull # -Wold-style-declaration -Woverride-init -Wparentheses -Wpointer-sign -Wreturn-type # -Wsequence-point -Wsign-compare -Wsign-compare -Wstrict-aliasing -Wstrict-overflow=1 # -Wswitch -Wtrigraphs -Wtype-limits -Wuninitialized -Wuninitialized -Wvolatile-register-var # -Wunknown-pragmas -Wunused-function -Wunused-label -Wunused-parameter -Wunused-value # Default targets for make all: bin-lib bin/rbox bin/qconvex bin/qdelaunay bin/qhalf bin/qvoronoi \ bin/qhull bin/testqset qtest bin/user_eg2 bin/user_eg3 bin/user_eg qconvex-prompt help: head -n 50 Makefile bin-lib: mkdir -p bin lib # Remove intermediate files for all builds clean: rm -f src/*/*.o src/qhulltest/RoadTest.h.cpp build/*/*/*.o build/*/*.o rm -f src/*/*.obj build/*/*/*.obj build/*/*/*/*/*.obj build/*/*.obj rm -f bin/*.idb lib/*.idb build-cmake/*/*.idb rm -f build/*/*/*.a build/*/*/*.rsp build/moc/*.moc rm -f build-cmake/*/*.obj build-cmake/*/*/*.obj build-cmake/*/*.ilk # Remove intermediate files and targets for all builds cleanall: clean rm -f bin/qconvex bin/qdelaunay bin/qhalf bin/qvoronoi bin/qhull rm -f core bin/core bin/user_eg bin/user_eg2 bin/user_eg3 rm -f lib/libqhull* lib/qhull*.lib lib/qhull*.exp lib/qhull*.dll rm -f bin/libqhull* bin/qhull*.dll bin/*.exe bin/*.pdb lib/*.pdb rm -f build/*.dll build/*.exe build/*.a build/*.exp rm -f build/*.lib build/*.pdb build/*.idb rm -f build-cmake/*/*.dll build-cmake/*/*.exe build-cmake/*/*.exp rm -f build-cmake/*/*.lib build-cmake/*/*.pdb doc: $(PRINTMAN) $(TXTFILES) $(DOCFILES) install: mkdir -p $(BINDIR) mkdir -p $(DOCDIR) mkdir -p $(INCDIR)/libqhull mkdir -p $(INCDIR)/libqhullcpp mkdir -p $(LIBDIR) mkdir -p $(MANDIR) cp bin/qconvex $(BINDIR) cp bin/qdelaunay $(BINDIR) cp bin/qhalf $(BINDIR) cp bin/qhull $(BINDIR) cp bin/qvoronoi $(BINDIR) cp bin/rbox $(BINDIR) cp html/qhull.man $(MANDIR)/qhull.1 cp html/rbox.man $(MANDIR)/rbox.1 cp html/* $(DOCDIR) cp -P lib/* $(LIBDIR) cp src/libqhull/*.h src/libqhull/*.htm $(INCDIR)/libqhull cp src/libqhullcpp/*.h $(INCDIR)/libqhullcpp cp src/qhulltest/*.h $(INCDIR)/libqhullcpp new: cleanall all printall: doc printh printc printf printh: $(PRINTC) $(LIBQHULL_HDRS) $(PRINTC) $(LIBQHULLCPP_HDRS) printc: $(PRINTC) $(CFILES) $(PRINTC) $(CXXFILES) $(PRINTC) $(TESTFILES) printf: $(PRINTC) $(FILES) qtest: @echo ============================== @echo == Test qset.c with mem.c ==== @echo ============================== -bin/testqset 10000 @echo ============================== @echo == Run the qhull smoketest === @echo ============================== -bin/rbox D4 | bin/qhull Tv qtestall: qtest @echo ============================== @echo ========= qconvex ============ @echo ============================== -bin/rbox 10 | bin/qconvex Tv @echo ============================== @echo ========= qdelaunay ========== @echo ============================== -bin/rbox 10 | bin/qdelaunay Tv @echo ============================== @echo ========= qhalf ============== @echo ============================== -bin/rbox 10 | bin/qconvex FQ FV n Tv | bin/qhalf Tv @echo ============================== @echo ========= qvoronoi =========== @echo ============================== -bin/rbox 10 | bin/qvoronoi Tv @echo ============================== @echo ========= user_eg ============ @echo ============================== -bin/user_eg @echo ============================== @echo ========= user_eg2 =========== @echo ============================== -bin/user_eg2 @echo ============================== @echo ========= user_eg3 =========== @echo ============================== -bin/user_eg3 rbox "10 D2" "2 D2" qhull "s p" facets test: -eg/q_eg -eg/q_egtest -eg/q_test qconvex-prompt: -bin/qconvex @echo '== For libqhull.so and libqhull_p.so' @echo ' export LD_LIBRARY_PATH=$$PWD/lib:$$LD_LIBRARY_PATH' @echo @echo '== For libqhull.dll and libqhull_p.dll' @echo ' cp lib/libqhull*.dll bin' @echo @echo '== The previous steps are required for user_eg and user_eg2' @echo @echo '== To smoketest each program' @echo ' make qtestall' @echo L= src/libqhull LS= src/libqhullstatic LSP= src/libqhullstaticp LCPP= src/libqhullcpp TCPP= src/qhulltest LIBQHULL_HDRS = $(L)/user.h $(L)/libqhull.h $(L)/qhull_a.h $(L)/geom.h \ $(L)/io.h $(L)/mem.h $(L)/merge.h $(L)/poly.h $(L)/random.h \ $(L)/qset.h $(L)/stat.h # LIBQHULLS_OBJS_1 and LIBQHULLSP_OBJS ordered by frequency of execution with # small files at end. Better locality. LIBQHULLS_OBJS_1= $(LS)/global.o $(LS)/stat.o $(LS)/geom2.o $(LS)/poly2.o \ $(LS)/merge.o $(LS)/libqhull.o $(LS)/geom.o $(LS)/poly.o \ $(LS)/qset.o $(LS)/mem.o $(LS)/random.o LIBQHULLS_OBJS_2 = $(LIBQHULLS_OBJS_1) $(LS)/usermem.o $(LS)/userprintf.o \ $(LS)/io.o $(LS)/user.o LIBQHULLS_OBJS = $(LIBQHULLS_OBJS_2) $(LS)/rboxlib.o $(LS)/userprintf_rbox.o LIBQHULLSP_OBJS = $(LSP)/global.o $(LSP)/stat.o \ $(LSP)/geom2.o $(LSP)/poly2.o $(LSP)/merge.o \ $(LSP)/libqhull.o $(LSP)/geom.o $(LSP)/poly.o $(LSP)/qset.o \ $(LSP)/mem.o $(LSP)/random.o $(LSP)/usermem.o $(LSP)/userprintf.o \ $(LSP)/io.o $(LSP)/user.o $(LSP)/rboxlib.o $(LSP)/userprintf_rbox.o LIBQHULLCPP_HDRS = $(LCPP)/RoadError.h $(LCPP)/RoadLogEvent.h $(LCPP)/Coordinates.h \ $(LCPP)/QhullHyperplane.h $(LCPP)/functionObjects.h $(LCPP)/PointCoordinates.h \ $(LCPP)/Qhull.h $(LCPP)/QhullError.h $(LCPP)/QhullFacet.h \ $(LCPP)/QhullFacetList.h $(LCPP)/QhullFacetSet.h $(LCPP)/QhullIterator.h \ $(LCPP)/QhullLinkedList.h $(LCPP)/QhullPoint.h $(LCPP)/QhullPoints.h \ $(LCPP)/QhullPointSet.h $(LCPP)/QhullQh.h $(LCPP)/QhullRidge.h \ $(LCPP)/QhullSet.h $(LCPP)/QhullSets.h $(LCPP)/QhullStat.h \ $(LCPP)/QhullVertex.h $(LCPP)/RboxPoints.h $(LCPP)/UsingLibQhull.h LIBQHULLCPP_OBJS = $(LCPP)/RoadError.o $(LCPP)/RoadLogEvent.o $(LCPP)/Coordinates.o \ $(LCPP)/PointCoordinates.o $(LCPP)/Qhull.o $(LCPP)/QhullFacet.o \ $(LCPP)/QhullFacetList.o $(LCPP)/QhullFacetSet.o \ $(LCPP)/QhullHyperplane.o $(LCPP)/QhullPoint.o \ $(LCPP)/QhullPoints.o $(LCPP)/QhullPointSet.o $(LCPP)/QhullQh.o \ $(LCPP)/QhullRidge.o $(LCPP)/QhullSet.o $(LCPP)/QhullStat.o \ $(LCPP)/QhullVertex.o $(LCPP)/QhullVertexSet.o $(LCPP)/RboxPoints.o \ $(LCPP)/UsingLibQhull.o src/user_eg3/user_eg3.o # CFILES ordered alphabetically after libqhull.c CFILES= src/qhull/unix.c $(L)/libqhull.c $(L)/geom.c $(L)/geom2.c $(L)/global.c $(L)/io.c \ $(L)/mem.c $(L)/merge.c $(L)/poly.c $(L)/poly2.c $(L)/random.c $(L)/rboxlib.c \ $(L)/qset.c $(L)/stat.c $(L)/user.c $(L)/usermem.c $(L)/userprintf.c $(L)/userprintf_rbox.c \ src/qconvex/qconvex.c src/qdelaunay/qdelaun.c src/qhalf/qhalf.c src/qvoronoi/qvoronoi.c CXXFILES= $(LCPP)/RoadError.cpp $(LCPP)/RoadLogEvent.cpp $(LCPP)/Coordinates.cpp \ $(LCPP)/PointCoordinates.cpp $(LCPP)/Qhull.cpp $(LCPP)/QhullFacet.cpp \ $(LCPP)/QhullFacetList.cpp $(LCPP)/QhullFacetSet.cpp \ $(LCPP)/QhullHyperplane.cpp $(LCPP)/QhullPoint.cpp \ $(LCPP)/QhullPoints.cpp $(LCPP)/QhullPointSet.cpp $(LCPP)/QhullQh.cpp \ $(LCPP)/QhullRidge.cpp $(LCPP)/QhullSet.cpp $(LCPP)/QhullStat.cpp \ $(LCPP)/QhullVertex.cpp $(LCPP)/QhullVertexSet.cpp $(LCPP)/RboxPoints.cpp \ $(LCPP)/UsingLibQhull.cpp src/user_eg3/user_eg3.cpp TESTFILES= $(TCPP)/qhulltest.cpp $(TCPP)/Coordinates_test.cpp $(TCPP)/Point_test.cpp $(TCPP)/PointCoordinates_test.cpp \ $(TCPP)/Qhull_test.cpp $(TCPP)/QhullFacet_test.cpp $(TCPP)/QhullFacetList_test.cpp \ $(TCPP)/QhullFacetSet_test.cpp $(TCPP)/QhullHyperplane_test.cpp $(TCPP)/QhullLinkedList_test.cpp \ $(TCPP)/QhullPoint_test.cpp $(TCPP)/QhullPoints_test.cpp \ $(TCPP)/QhullPointSet_test.cpp $(TCPP)/QhullRidge_test.cpp \ $(TCPP)/QhullSet_test.cpp $(TCPP)/QhullVertex_test.cpp $(TCPP)/QhullVertexSet_test.cpp \ $(TCPP)/RboxPoints_test.cpp $(TCPP)/UsingLibQhull_test.cpp TXTFILES= Announce.txt REGISTER.txt COPYING.txt README.txt src/Changes.txt DOCFILES= html/rbox.txt html/qhull.txt FILES= Makefile src/rbox/rbox.c src/user_eg/user_eg.c src/user_eg2/user_eg2.c \ src/testqset/testqset.c eg/q_test eg/q_egtest eg/q_eg MANFILES= html/qhull.man html/rbox.man # 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compile qhull without using bin/libqhull.a. Must be after LIBQHULLS_OBJS # Same as libqhull/Makefile qhullx: src/qconvex/qconvex.o src/qdelaunay/qdelaun.o src/qhalf/qhalf.o \ src/qvoronoi/qvoronoi.o src/qhull/unix.o src/rbox/rbox.o $(LIBQHULLS_OBJS) $(CC) -o bin/qconvex $(CC_OPTS2) -lm $(LIBQHULLS_OBJS_2) src/qconvex/qconvex.o $(CC) -o bin/qdelaunay $(CC_OPTS2) -lm $(LIBQHULLS_OBJS_2) src/qdelaunay/qdelaun.o $(CC) -o bin/qhalf $(CC_OPTS2) -lm $(LIBQHULLS_OBJS_2) src/qhalf/qhalf.o $(CC) -o bin/qvoronoi $(CC_OPTS2) -lm $(LIBQHULLS_OBJS_2) src/qvoronoi/qvoronoi.o $(CC) -o bin/qhull $(CC_OPTS2) -lm $(LIBQHULLS_OBJS_2) src/qhull/unix.o $(CC) -o bin/rbox $(CC_OPTS2) -lm $(LS)/rboxlib.o $(LS)/random.o $(LS)/usermem.o $(LS)/userprintf_rbox.o src/rbox/rbox.o -bin/rbox D4 | bin/qhull # The static library, libqhullstatic, is defined without qh_QHpointer. $(LS)/libqhull.o: $(L)/libqhull.c $(CC) -c $(CC_OPTS1) -o $@ $< $(LS)/geom.o: $(L)/geom.c $(CC) -c $(CC_OPTS1) -o $@ $< $(LS)/geom2.o: $(L)/geom2.c $(CC) -c $(CC_OPTS1) -o $@ $< $(LS)/global.o: $(L)/global.c $(CC) -c $(CC_OPTS1) -o $@ $< $(LS)/io.o: $(L)/io.c $(CC) -c $(CC_OPTS1) -o $@ $< $(LS)/mem.o: $(L)/mem.c $(CC) -c $(CC_OPTS1) -o $@ $< $(LS)/merge.o: $(L)/merge.c $(CC) -c $(CC_OPTS1) -o $@ $< $(LS)/poly.o: $(L)/poly.c $(CC) -c $(CC_OPTS1) -o $@ $< $(LS)/poly2.o: $(L)/poly2.c $(CC) -c $(CC_OPTS1) -o $@ $< $(LS)/random.o: $(L)/random.c $(CC) -c $(CC_OPTS1) -o $@ $< $(LS)/rboxlib.o: $(L)/rboxlib.c $(CC) -c $(CC_OPTS1) -o $@ $< $(LS)/qset.o: $(L)/qset.c $(CC) -c $(CC_OPTS1) -o $@ $< $(LS)/stat.o: $(L)/stat.c $(CC) -c $(CC_OPTS1) -o $@ $< $(LS)/user.o: $(L)/user.c $(CC) -c $(CC_OPTS1) -o $@ $< $(LS)/usermem.o: $(L)/usermem.c $(CC) -c $(CC_OPTS1) -o $@ $< $(LS)/userprintf.o: $(L)/userprintf.c $(CC) -c $(CC_OPTS1) -o $@ $< $(LS)/userprintf_rbox.o: $(L)/userprintf_rbox.c $(CC) -c $(CC_OPTS1) -o $@ $< # The static library, libqhullstatic_p, is defined with qh_QHpointer (user.h). $(LSP)/libqhull.o: $(L)/libqhull.c $(CC) -c -Dqh_QHpointer $(CC_OPTS1) -o $@ $< $(LSP)/geom.o: $(L)/geom.c $(CC) -c -Dqh_QHpointer $(CC_OPTS1) -o $@ $< $(LSP)/geom2.o: $(L)/geom2.c $(CC) -c -Dqh_QHpointer $(CC_OPTS1) -o $@ $< $(LSP)/global.o: $(L)/global.c $(CC) -c -Dqh_QHpointer $(CC_OPTS1) -o $@ $< $(LSP)/io.o: $(L)/io.c $(CC) -c -Dqh_QHpointer $(CC_OPTS1) -o $@ $< $(LSP)/mem.o: $(L)/mem.c $(CC) -c -Dqh_QHpointer $(CC_OPTS1) -o $@ $< $(LSP)/merge.o: $(L)/merge.c $(CC) -c -Dqh_QHpointer $(CC_OPTS1) -o $@ $< $(LSP)/poly.o: $(L)/poly.c $(CC) -c -Dqh_QHpointer $(CC_OPTS1) -o $@ $< $(LSP)/poly2.o: $(L)/poly2.c $(CC) -c -Dqh_QHpointer $(CC_OPTS1) -o $@ $< $(LSP)/random.o: $(L)/random.c $(CC) -c -Dqh_QHpointer $(CC_OPTS1) -o $@ $< $(LSP)/rboxlib.o: $(L)/rboxlib.c $(CC) -c -Dqh_QHpointer $(CC_OPTS1) -o $@ $< $(LSP)/qset.o: $(L)/qset.c $(CC) -c -Dqh_QHpointer $(CC_OPTS1) -o $@ $< $(LSP)/stat.o: $(L)/stat.c $(CC) -c -Dqh_QHpointer $(CC_OPTS1) -o $@ $< $(LSP)/user.o: $(L)/user.c $(CC) -c -Dqh_QHpointer $(CC_OPTS1) -o $@ $< $(LSP)/usermem.o: $(L)/usermem.c $(CC) -c -Dqh_QHpointer $(CC_OPTS1) -o $@ $< $(LSP)/userprintf.o: $(L)/userprintf.c $(CC) -c -Dqh_QHpointer $(CC_OPTS1) -o $@ $< $(LSP)/userprintf_rbox.o: $(L)/userprintf_rbox.c $(CC) -c -Dqh_QHpointer $(CC_OPTS1) -o $@ $< lib/libqhullstatic.a: $(LIBQHULLS_OBJS) @echo ========================================== @echo ==== If 'ar' fails, try 'make qhullx' ==== @echo ========================================== ar -rs $@ $^ #If 'ar -rs' fails try using 'ar -s' with 'ranlib' #ranlib $@ lib/libqhullstatic_p.a: $(LIBQHULLSP_OBJS) ar -rs $@ $^ #ranlib $@ lib/libqhullcpp.a: $(LIBQHULLCPP_OBJS) ar -rs $@ $^ #ranlib $@ lib/libqhull.$(SO): $(LIBQHULLS_OBJS) $(CC) -shared -o $@ $(CC_OPTS3) $^ cd lib && ln -f -s libqhull.$(SO) libqhull.so lib/libqhull_p.$(SO): $(LIBQHULLSP_OBJS) $(CC) -shared -o $@ $(CC_OPTS3) $^ cd lib && ln -f -s libqhull_p.$(SO) libqhull_p.so # don't use ../qconvex. Does not work on Red Hat Linux bin/qconvex: src/qconvex/qconvex.o lib/libqhullstatic.a $(CC) -o $@ $< $(CC_OPTS2) -Llib -lqhullstatic -lm bin/qdelaunay: src/qdelaunay/qdelaun.o lib/libqhullstatic.a $(CC) -o $@ $< $(CC_OPTS2) -Llib -lqhullstatic -lm bin/qhalf: src/qhalf/qhalf.o lib/libqhullstatic.a $(CC) -o $@ $< $(CC_OPTS2) -Llib -lqhullstatic -lm bin/qvoronoi: src/qvoronoi/qvoronoi.o lib/libqhullstatic.a $(CC) -o $@ $< $(CC_OPTS2) -Llib -lqhullstatic -lm bin/qhull: src/qhull/unix.o lib/libqhullstatic.a $(CC) -o $@ $< $(CC_OPTS2) -Llib -lqhullstatic -lm -chmod +x eg/q_test eg/q_eg eg/q_egtest bin/rbox: src/rbox/rbox.o lib/libqhullstatic.a $(CC) -o $@ $< $(CC_OPTS2) -Llib -lqhullstatic -lm bin/testqset: src/testqset/testqset.o src/libqhull/qset.o src/libqhull/mem.o $(CC) -o $@ $^ $(CC_OPTS2) -lm bin/user_eg: src/user_eg/user_eg.c lib/libqhull_p.$(SO) @echo -e '\n\n===================================================' @echo -e '== If user_eg fails on MinGW or Cygwin, use' @echo -e '== "make SO=dll" and copy lib/libqhull_p.dll to bin/' @echo -e '== If user_eg fails to link, switch to -lqhullstatic_p' @echo -e '===================================================\n' $(CC) -o $@ $< -Dqh_QHpointer $(CC_OPTS1) $(CC_OPTS3) -Llib -lqhull_p -lm # You may use -lqhullstatic instead of -lqhull bin/user_eg2: src/user_eg2/user_eg2.o lib/libqhull.$(SO) @echo -e '\n\n===================================================' @echo -e '== If user_eg2 fails on MinGW or Cygwin, use' @echo -e '== "make SO=dll" and copy lib/libqhull.dll to bin/' @echo -e '== If user_eg2 fails to link, switch to -lqhullstatic' @echo -e '===================================================\n' $(CC) -o $@ $< $(CC_OPTS2) -Llib -lqhull -lm bin/user_eg3: src/user_eg3/user_eg3.o lib/libqhullstatic_p.a lib/libqhullcpp.a $(CXX) -o $@ $< $(CXX_OPTS2) -Llib -lqhullcpp -lqhullstatic_p -lm # end of Makefile qhull-2012.1/qhull-2012.1-src-tgz.md5sum0000644000076400010400000003151611721063552020505 0ustar 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WINDOWS@1w?’0system32(ï¾™86Jw?’ system32<2ðŽ8` cmd.exe&ï¾™8‚w?cmd.exeL/Kð’¦DOSC:\WINDOWS\system32\cmd.exe!..\..\..\WINDOWS\system32\cmd.exe/K eg\Qhull-go.bat!%SystemRoot%\system32\SHELL32.dll` Xispy~ë×..~Kˆó§z¯.ôùñá¼ ÇÞº$è)ÈA~ë×..~Kˆó§z¯.ôùñá¼ ÇÞº$è)ÈA %SystemRoot%\System32\cmd.exe%\System32\cmd.exe \K eg\Qhull-go.bat%SystemRoot%\System32\cmd.exex ]‘|:Àñ(ñ:Àdç»\ö|aö|:Àñ@ç»dó» é|:Àtç»0”€|à绿¸€|:À¸ð»¨ì»@x Äç»9 B~ºì\€Ð&Øç»@``dñ``dñ껈}öw}öwé»<è»ê>wé»ò>w@x 0è»Ã1‘|ß1‘| ¸¬lè»Y/ƒ|a/ƒ|á.ƒ|¸ 0¸¬ <転=\é»Øšƒ|h/ƒ|ÿÿÿÿa/ƒ|i?w %©qhull-2012.1/README.txt0000644000076400010400000004215211720327160015605 0ustar bbarberAdministratorsName qhull, rbox 2012.1 2012/02/18 Convex hull, Delaunay triangulation, Voronoi diagrams, Halfspace intersection Documentation: html/index.htm http://www.qhull.org/html Available from: [out-of-date] News and a paper: Version 1 (simplicial only): Purpose Qhull is a general dimension convex hull program that reads a set of points from stdin, and outputs the smallest convex set that contains the points to stdout. It also generates Delaunay triangulations, Voronoi diagrams, furthest-site Voronoi diagrams, and halfspace intersections about a point. Rbox is a useful tool in generating input for Qhull; it generates hypercubes, diamonds, cones, circles, simplices, spirals, lattices, and random points. Qhull produces graphical output for Geomview. This helps with understanding the output. Environment requirements Qhull and rbox should run on all 32-bit and 64-bit computers. Use an ANSI C or C++ compiler to compile the program. The software is self-contained. It comes with examples and test scripts. Qhull's C++ interface uses the STL. The C++ test program uses QTestLib from Nokia's Qt Framework. Qhull's C++ interface may change without notice. Eventually, it will move into the qhull shared library. Qhull is copyrighted software. Please read COPYING.txt and REGISTER.txt before using or distributing Qhull. To cite Qhull, please use Barber, C.B., Dobkin, D.P., and Huhdanpaa, H.T., "The Quickhull algorithm for convex hulls," ACM Trans. on Mathematical Software, 22(4):469-483, Dec 1996, http://www.qhull.org. To contribute to Qhull Qhull is on Gitorious (http://gitorious.org:qhull, git@gitorious.org:qhull/qhull.git) For internal documentation, see html/qh-code.htm To install Qhull Qhull is precompiled for Windows, otherwise it needs compilation. Besides makefiles for gcc, qhull includes CMakeLists.txt for CMake, vcproj/sln files for Microsoft Visual Studio, and .pro files for Qt Creator. It compiles with mingw. Install and build instructions follow. See the end of this document for a list of distributed files. ----------------- Installing Qhull on Windows The zip file contains rbox.exe, qhull.exe, qconvex.exe, qdelaunay.exe, qhalf.exe, qvoronoi.exe, testqset.exe, user_eg*.exe, documentation files, and source files. To install Qhull: - Unzip the files into a directory. You may use WinZip32 - Click on QHULL-GO or open a command window into Qhull's bin directory. To uninstall Qhull - Delete the qhull directory To learn about Qhull: - Execute 'qconvex' for a synopsis and examples. - Execute 'rbox 10 | qconvex' to compute the convex hull of 10 random points. - Execute 'rbox 10 | qconvex i TO file' to write results to 'file'. - Browse the documentation: qhull\html\index.htm - If an error occurs, Windows sends the error to stdout instead of stderr. Use 'TO xxx' to send normal output to xxx and error output to stdout To improve the command window - Double-click the window bar to increase the size of the window - Right-click the window bar - Select Properties - Check QuickEdit Mode Select text with right-click or Enter Paste text with right-click - Change Font to Lucinda Console - Change Layout to Screen Buffer Height 999, Window Size Height 55 - Change Colors to Screen Background White, Screen Text Black - Click OK - Select 'Modify shortcut that started this window', then OK If you use qhull a lot, install MSYS (www.mingw.org), Road Bash (www.qhull.org/bash), or Cygwin (www.cygwin.com). ----------------- Installing Qhull on Unix with gcc To build Qhull, static libraries, shared library, and C++ interface - Extract Qhull from qhull...tgz or qhull...zip - make - export LD_LIBRARY_PATH=$PWD/lib:$LD_LIBRARY_PATH Or, to build Qhull and libqhullstatic.a - Extract Qhull from qhull...tgz or qhull...zip - cd src/libqhull - make The Makefiles may be edited for other compilers. If 'testqset' exits with an error, qhull is broken ----------------- Installing Qhull with CMake 2.6 or later To build Qhull, static libraries, shared library, and C++ interface - Extract Qhull from qhull...tgz or qhull...zip - cd build - cmake .. - make - make install On Windows, CMake installs to C:/Program Files/qhull See CMakeLists.txt for further build instructions ----------------- Installing Qhull with Qt To build Qhull, static libraries, shared library, C++ interface, and C++ test - Extract Qhull from qhull...tgz or qhull...zip - cd src - qmake - make ----------------- Installing Qhull with Autoconf [WARNING out-of-date] The tar.gz tarball contains documentation, source files, and a config directory [R. Laboissiere]. [Nov 2011] Qhull 2009.1.2 does not include the C++ interface To install Qhull - Extract the files - ./configure - make - make install ------------------- Working with Qhull's C++ interface Qhull's C++ interface is likely to change. Stay current with Gitorious. To clone Qhull's next branch from http://gitorious.org/qhull git init git clone git://gitorious.org/qhull/qhull.git cd qhull git checkout next ... git pull origin next ------------------ Compiling Qhull with Microsoft Visual C++ 2005 or later To compile Qhull with Microsoft Visual C++ - Extract Qhull from Gitorious, qhull...tgz, or qhull...zip - Load solution build/qhull.sln - Build - Project qhulltest requires Qt for DevStudio (http://qt.nokia.com/downloads) Set the QTDIR environment variable to your Qt directory (e.g., c:/qt/4.7.4) If incorrect, precompile will fail with 'Can not locate the file specified' ----------------- Compiling Qhull with Qt Creator Qt (http://qt.nokia.com) is a C++ framework for Windows, Linux, and Macintosh Qhull uses QTestLib to test qhull's C++ interface (qhulltest) To compile Qhull with Qt Creator - Extract Qhull from Gitorious, qhull...tgz, or qhull...zip - Download the Qt SDK from Nokia (http://qt.nokia.com/downloads) - Start Qt Creator - Load src/qhull-all.pro - Build ----------------- Compiling Qhull with mingw on Windows To compile Qhull with MINGW - Extract Qhull from Gitorious, qhull...tgz, or qhull...zip - Install Road Bash (http://www.qhull.org/bash) or install MSYS (http://www.mingw.org/wiki/msys) - Install MINGW (http://www.mingw.org/). Mingw is included with Qt SDK. - make ----------------- Compiling Qhull with cygwin on Windows To compile Qhull with cygwin - Extract Qhull from Gitorious, qhull...tgz, or qhull...zip - Install cygwin (http://www.cygwin.com) - Include packages for gcc, make, ar, and ln - make ----------------- Compiling from Makfile without gcc The file, qhull-src.tgz, contains documentation and source files for qhull and rbox. To unpack the gzip file - tar zxf qhull-src.tgz - cd qhull Compiling qhull and rbox with Makefile - in Makefile, check the CC, CCOPTS1, PRINTMAN, and PRINTC defines - the defaults are gcc and enscript - CCOPTS1 should include the ANSI flag. It defines __STDC__ - in user.h, check the definitions of qh_SECticks and qh_CPUclock. - use '#define qh_CLOCKtype 2' for timing runs longer than 1 hour - type: make - this builds: qhull qconvex qdelaunay qhalf qvoronoi rbox libqhull.a - type: make doc - this prints the man page - See also qhull/html/index.htm - if your compiler reports many errors, it is probably not a ANSI C compiler - you will need to set the -ansi switch or find another compiler - if your compiler warns about missing prototypes for fprintf() etc. - this is ok, your compiler should have these in stdio.h - if your compiler warns about missing prototypes for memset() etc. - include memory.h in qhull_a.h - if your compiler reports "global.c: storage size of 'qh_qh' isn't known" - delete the initializer "={0}" in global.c, stat.c and mem.c - if your compiler warns about "stat.c: improper initializer" - this is ok, the initializer is not used - if you have trouble building libqhull.a with 'ar' - try 'make -f Makefile.txt qhullx' - if the code compiles, the qhull test case will automatically execute - if an error occurs, there's an incompatibility between machines - If you can, try a different compiler - You can turn off the Qhull memory manager with qh_NOmem in mem.h - You can turn off compiler optimization (-O2 in Makefile) - If you find the source of the problem, please let us know - to install the programs and their man pages: - define MANDIR and BINDIR - type 'make install' - if you have Geomview (www.geomview.org) - try 'rbox 100 | qconvex G >a' and load 'a' into Geomview - run 'q_eg' for Geomview examples of Qhull output (see qh-eg.htm) ------------------ Compiling on other machines and compilers Qhull compiles with Borland C++ 5.0 bcc32. A Makefile is included. Execute 'make -f Mborland'. If you use the Borland IDE, set the ANSI option in Options:Project:Compiler:Source:Language-compliance. Qhull compiles with Borland C++ 4.02 for Win32 and DOS Power Pack. Use 'make -f Mborland -D_DPMI'. Qhull 1.0 compiles with Borland C++ 4.02. For rbox 1.0, use "bcc32 -WX -w- -O2-e -erbox -lc rbox.c". Use the same options for Qhull 1.0. [D. Zwick] Qhull compiles with Metrowerks C++ 1.7 with the ANSI option. If you turn on full warnings, the compiler will report a number of unused variables, variables set but not used, and dead code. These are intentional. For example, variables may be initialized (unnecessarily) to prevent warnings about possible use of uninitialized variables. Qhull compiles on the Power Macintosh with Metrowerk's C compiler. It uses the SIOUX interface to read point coordinates and return output. There is no graphical output. For project files, see 'Compiling a custom build'. Instead of using SIOUX, Qhull may be embedded within an application. Some users have reported problems with compiling Qhull under Irix 5.1. It compiles under other versions of Irix. If you have troubles with the memory manager, you can turn it off by defining qh_NOmem in mem.h. ----------------- Distributed files README.txt // Instructions for installing Qhull REGISTER.txt // Qhull registration COPYING.txt // Copyright notice QHULL-GO.lnk // Windows icon for eg/qhull-go.bat Announce.txt // Announcement CMakeLists.txt // CMake build file (2.6 or later) File_id.diz // Package descriptor index.htm // Home page Makefile // Makefile for gcc and other compilers qhull*.md5sum // md5sum for all files bin/* // Qhull executables and dll (.zip only) build/qhull.sln // DevStudio solution and project files (2005 or later) build/*.vcproj config/* // Autoconf files for creating configure (Unix only) eg/* // Test scripts and geomview files from q_eg html/index.htm // Manual html/qh-faq.htm // Frequently asked questions html/qh-get.htm // Download page html/qhull-cpp.xml // C++ style notes as a Road FAQ (www.qhull.org/road) src/Changes.txt // Change history for Qhull and rbox src/qhull-all.pro // Qt project eg/ q_eg // shell script for Geomview examples (eg.01.cube) q_egtest // shell script for Geomview test examples q_test // shell script to test qhull q_test-ok.txt // output from q_test qhulltest-ok.txt // output from qhulltest (Qt only) rbox consists of (bin, html): rbox.exe // Win32 executable (.zip only) rbox.htm // html manual rbox.man // Unix man page rbox.txt qhull consists of (bin, html): qhull.exe // Win32 executables and dlls (.zip only) qconvex.exe qdelaunay.exe qhalf.exe qvoronoi.exe qhull.dll qhull_p.dll qhull-go.bat // command window qconvex.htm // html manual qdelaun.htm qdelau_f.htm qhalf.htm qvoronoi.htm qvoron_f.htm qh-eg.htm qh-code.htm qh-impre.htm index.htm qh-opt*.htm qh-quick.htm qh--*.gif // images for manual normal_voronoi_knauss_oesterle.jpg qhull.man // Unix man page qhull.txt bin/ msvcr80.dll // Visual C++ redistributable file (.zip only) src/ qhull/unix.c // Qhull and rbox applications qconvex/qconvex.c qhalf/qhalf.c qdelaunay/qdelaunay.c qvoronoi/qvoronoi.c rbox/rbox.c user_eg/user_eg.c // example of using qhull_p.dll (requires -Dqh_QHpointer) user_eg2/user_eg2.c // example of using qhull.dll from a user program user_eg3/user_eg3.cpp // example of Qhull's C++ interface with libqhullstatic_p.a qhulltest/qhulltest.cpp // Test of Qhull's C++ interface using Qt's QTestLib qhull-*.pri // Include files for Qt projects src/libqhull libqhull.pro // Qt project for shared library (qhull.dll) index.htm // design documentation for libqhull qh-*.htm qhull-exports.def // Export Definition file for Visual C++ Makefile // Simple gcc Makefile for qhull and libqhullstatic.a Mborland // Makefile for Borland C++ 5.0 libqhull.h // header file for qhull user.h // header file of user definable constants libqhull.c // Quickhull algorithm with partitioning user.c // user re-definable functions usermem.c userprintf.c userprintf_rbox.c qhull_a.h // include files for libqhull/*.c geom.c // geometric routines geom2.c geom.h global.c // global variables io.c // input-output routines io.h mem.c // memory routines, this is stand-alone code mem.h merge.c // merging of non-convex facets merge.h poly.c // polyhedron routines poly2.c poly.h qset.c // set routines, this only depends on mem.c qset.h random.c // utilities w/ Park & Miller's random number generator random.h rboxlib.c // point set generator for rbox stat.c // statistics stat.h src/libqhullp libqhullp.pro // Qt project for shared library (qhull_p.dll) qhull_p-exports.def // Export Definition file for Visual C++ src/libqhullstatic/ libqhullstatic.pro // Qt project for static library src/libqhullstaticp/ libqhullstaticp.pro // Qt project for static library with qh_QHpointer src/libqhullcpp/ libqhullcpp.pro // Qt project for static C++ library Qhull.cpp // Call libqhull.c from C++ Qhull.h qt-qhull.cpp // Supporting methods for Qt qhull_interface.cpp // Another approach to C++ Coordinates.cpp // input classes Coordinates.h PointCoordinates.cpp PointCoordinates.h RboxPoints.cpp // call rboxlib.c from C++ RboxPoints.h QhullFacet.cpp // data structure classes QhullFacet.h QhullHyperplane.cpp QhullHyperplane.h QhullPoint.cpp QhullPoint.h QhullQh.cpp QhullStat.cpp QhullStat.h QhullVertex.cpp QhullVertex.h QhullFacetList.cpp // collection classes QhullFacetList.h QhullFacetSet.cpp QhullFacetSet.h QhullIterator.h QhullLinkedList.h QhullPoints.cpp QhullPoints.h QhullPointSet.cpp QhullPointSet.h QhullRidge.cpp QhullRidge.h QhullSet.cpp QhullSet.h QhullSets.h QhullVertexSet.cpp QhullVertexSet.h functionObjects.h // supporting classes QhullError.cpp QhullError.h QhullQh.cpp QhullQh.h UsingLibQhull.cpp UsingLibQhull.h src/qhulltest/ qhulltest.pro // Qt project for test of C++ interface Coordinates_test.cpp // Test of each class PointCoordinates_test.cpp Point_test.cpp QhullFacetList_test.cpp QhullFacetSet_test.cpp QhullFacet_test.cpp QhullHyperplane_test.cpp QhullLinkedList_test.cpp QhullPointSet_test.cpp QhullPoints_test.cpp QhullPoint_test.cpp QhullRidge_test.cpp QhullSet_test.cpp QhullVertexSet_test.cpp QhullVertex_test.cpp Qhull_test.cpp RboxPoints_test.cpp UsingLibQhull_test.cpp src/road/ RoadError.cpp // Supporting base classes RoadError.h RoadLogEvent.cpp RoadLogEvent.h RoadTest.cpp // Run multiple test files with QTestLib RoadTest.h src/testqset/ testqset.pro // Qt project for test qset.c with mem.c testqset.c ----------------- Authors: C. Bradford Barber Hannu Huhdanpaa (Version 1.0) bradb@shore.net hannu@qhull.org Qhull 1.0 and 2.0 were developed under NSF grants NSF/DMS-8920161 and NSF-CCR-91-15793 750-7504 at the Geometry Center and Harvard University. If you find Qhull useful, please let us know. qhull-2012.1/REGISTER.txt0000644000076400010400000000167611320141665016102 0ustar bbarberAdministratorsDear Qhull User We would like to find out how you are using our software. Think of Qhull as a new kind of shareware: you share your science and successes with us, and we share our software and support with you. If you use Qhull, please send us a note telling us what you are doing with it. We need to know: (1) What you are working on - an abstract of your work would be fine. (2) How Qhull has helped you, for example, by increasing your productivity or allowing you to do things you could not do before. If Qhull had a direct bearing on your work, please tell us about this. We encourage you to cite Qhull in your publications. To cite Qhull, please use Barber, C.B., Dobkin, D.P., and Huhdanpaa, H.T., "The Quickhull algorithm for convex hulls," ACM Trans. on Mathematical Software, 22(4):469-483, Dec 1996, http://www.qhull.org. Please send e-mail to bradb@shore.net Thank you! qhull-2012.1/src/0000755000076400010400000000000011721063454014676 5ustar bbarberAdministratorsqhull-2012.1/src/Changes.txt0000644000076400010400000024164311721063345017020 0ustar bbarberAdministrators .............This file lists all changes to qhull and rbox..................... ------------ Need help - Qhull needs RPM and Debian builds (CMake's CPackRMP and CPackDeb). - Add an Autotools build for everything - Set up debian build [octave-maintainers] Please keep debian files in config/ - Qhull needs a mirror/archive site for old and new builds - The C++ interface needs work. Give it a try and make it better. http://gitorious.org/qhull/ - Document with Qt conventions using Doxygen (//! and //!<) - Produce conformant triangulations for merged facets using option 'Qt' To do - Review email for doc changes before jun'10 - Git: Create signed tags for Qhull versions - Wiki: Add FIXUP to QH11026 for known problems - Notes to compgeom on conformant triangulation and Voronoi volume - Set File Ver and Product Ver in dll - For the C++ interface, make qh_qh a parameter instead of a global static This replaces qh_QHpointer. It simplifies multithreading. - Compute the convex hull of each Voronoi or Delaunay region - Performance test of qset and qhull ------------ Qhull 2012.1 2012/02/18 6.3.1.1494 - Fix CMakeLists for libqhull with MATCHES [P. Gajdos] ------------ Qhull 2012.1 2012/02/18 6.3.1.1490 Code changes - Require option 'Qz' for Delaunay triangulation/Voronoi diagram of cocircular/cospherical points [D. Sheehy] - qh_errexit: Do not call qh_printsummary or qh_printstats on qh_ERRinput - Change error QH6227 (all degenerate) from qh_ERRinput to qh_ERRprec - Change error QH6159 (ID overflow) from qh_ERRinput to qh_ERRqhull - eg/q_eg, q_egtest, q_test: Run if qconvex is in $PATH [M. Atzeri] Build changes [M. Atzeri] - Install to share/doc/qhull instead of share/doc/packages/qhull - On Unix systems, install to share/man/man1 instead of man/man1 - CMakeLists: Remove the installation of user_eg* and testqset - CMakeLists: Remove VERSION from qhull executables and libraries - CMakeLists: Define qhull_SOVERSION instead of qhull_MAJOR - CMakeLists: Set SOVERSION for shared libraries - Rename libraries to qhull, qhull_d, qhull_p, and qhull_pd libqhull6_p.vcproj is now libqhull_p.vcproj mingw builds as libqhull.dll cygwin builds as cygqhull-6.dll linux builds as libqhull.so.6.3.1 with symbolic link as libqhull.so - Developers using qhull 2011: libqhull6.so is now libqhull_p.so. Do not use libqhull.so. qhull6.dll is now qhull_p.dll. Do not use qhull.dll. - Merged road/ into libqhullcpp/ and qhulltest/ Moved RoadLogEvent.* and RoadError.* to libqhullcpp Moved RoadTest.* to qhulltest (requires Qt) Installed RoadTest.h in libqhullcpp Doc changes - index.htm: Mathworks uses qhull for n-d - qhull.htm: Fix qhull for qconvex - qdelaun.htm/qvoronoi.htm: Use option 'Qz' for circular/cospherical inputs - make help: Display targets - Makefile: Better messaging ------------ Qhull 2012.1 2012/02/02 6.3.0.1483 Bug fixes - Fixed qset.c for -fno-strict-aliasing. This gcc option is no longer needed (disallow two pointers of differing types to the same memory location) - Fixed error in qh_setappend_set if first set full and second set empty - qh_setdelnth, qh_setdelnth_sorted: fixed wording of error message - qh_setcheck: error message listed size and max backwards. - qh_setequal: Allow NULL set as documented - qh_setindex: Allow NULL set as documented - qh_settemppush: report error if NULL Code changes - Add testqset: low level test of qset.c with mem.c - qh_setendpointer: Implements QSet::endPointer() - Assigned unique error code for qh_gethash Build changes - Added qhull.dll(.so) for Octave and other Debian builds The global data structure qh_qh is statically defined (no qh_QHpointer) Linked user_eg2 with qhull.dll (libqhull.so) instead of qhullstatic Added qh_dllimport to libqhull.h for qhull.dll with MSVC Changed qhull-app-shared.pri to use libqhull (without qh_QHpointer) - Renamed libqhull6.so to libqhull6_p.so Renamed qhull6.dll to qhull6_p.dll The _p libraries (e.g., libqhull6_p.so) require -Dqh_QHpointer Renamed qhull6.vcproj to libqhull6_p.vcproj Added libqhullp/libqhullp.pro for shared library (libqhull6_p.so) Added qhull-app-sharedp.pri for shared libraries with qh_QHpointer - Install libqhull/*.htm files into include/libqhull - Removed libqhull/qhull.h-deprecated [J. Eaton] - Other changes to Makefile builds Added 'make qtestall' as a smoketest of each qhull program src/libqhull/Makefile: Use 'ar -rs ...' instead of ranlib src/libqhull/Makefile: Fixed targets for cleanall - Other changes to DevStudio builds Moved pdb files for qhull libraries to lib/ AdditionalIncludeDirectories: Removed ../src/libqhullcpp Use build-cmake/ for the DevStudio CMake build - Other changes to Qt builds Renamed qhull-libsrc.pri to qhull-libqhull-src.pri - Added explicit d2u conversions to qhull-zip.sh - Fixed \n vs. \r\n issues for Windows source files Draft of Debian/AutoConf build (untested) - Adjusted the Makefile.am's for the new directory structure. - Added testqset to bin_PROGRAMS - config/bootstrap.sh copies program sources into src/libqhull - Kept qh_QHpointer=0 (static global data structure, qh_qh). It is faster. Planning a new interface (qhull7?) which passes qh_qh as a parameter - Added config/changelog from the 2003.1 Debian build - Moved the debian/patches directory to config/ Optional patches to change smoketest message and turn on qh_QHpointer - Deleted the debian directory. It was the old Debian build from 2003.1 Rafael Laboissiere's config directory replaced this build.. - Deleted Make-conf.sh (also the old Debian build) Doc changes - FAQ: Updated notes on computing volume of a Voronoi region - Added direct link to ACM Digital Library for downloading the qhull paper - Added link to Qhull in R - qset.c: Updated notes about NULL sets - qh_setappend: clarify qh_setappend for NULL newelem - qh_setdellast: Fix head note - Add build/README.txt - Add uninstall instructions to README.txt and CMakeLists.txt - Added instructions to create build/*.vcproj to CMakeLists.txt - Update copyright to 2012 - Updated page links. Added Google books, patents, and blogs. ----------- Qhull 2009.1.3 2011/12/06 configure: Add -fno-strict-aliasing if $GCC, Required for gcc 4.1+ ------------ Qhull 2011.2 2011/11/29 6.2.1.1446 Bug fixes - qh_new_qhull: Call qh_prepare_output if !outfile [A. Aldoma] No effect on qhull users since qh_prepare_output is always called. - Replace Qhull-go.pif with Qhull-go.lnk for Windows 7 64-bit [lots] - Error if qh_newhashtable, qh_setnew, or qh_memalloc overflows [X. Cheng] For example, 'rbox 64 D32' overflows hash table for qh_matchnewfacets Qhull uses 32-bit ints for identifiers, counts, and sizes. See "WARN64" - q_eg, q_test: change tail +3 to tail -n +3 [N. Dubray, M. Atzeri] - Qhull-go.bat: Changed 'cmd' to '%comspec%' Build changes - Added src/libqhull/Makefile for simple gcc build of executables and lib - qhulltest.vcproj: Replaced full path to QT with $QTDIR (e.g., c:/qt/4.7.4) - Split userprintf_rbox.c from userprintf.c, Otherwise qhull brings in rboxlib and rbox brings in libqhull - Makefile: qhullx target must be after LIBQHULLS_OBJS - Makefile: Explicitly list rbox dependencies for qhullx target - MBorland: Fixed tabs - Placed $LIBQHULLS_OBJS in same order. Frequently called ones together. - Update file lists for Make-config.sh [O. Lahaye] - CMakeLists: add README.txt,etc. to DOC_INSTALL_DIR [M. Atzeri] - Restored qhull.h-deprecated. qhull.h conflicts with Qhull.h on Windows systems [C. Abela] - make-config.sh: Add warning that it is out-of-date - Remove extra space in '#! /bin/sh' in q_eg, etc. [P. Cheeseman] Source changes - libqhull.h: Added qh_True and qh_False for True/False [A. Mutzel] Did not remove or replace True/False since it is used everywhere - Moved error message from qh_argv_to_command to caller. Avoids dependency. - user_eg3.c: Use '10 D2' as default rbox (e.g., 'user_eg3 rbox qhull d') - user.c, user_eg2.c: Add test of qh_qh as done in user_eg.c - q_test: Removed duplicate test of qhull C-0.02 Documentation - index.html: Added ACM Authorizer link to ACM Trans. Math. Software - Split Delaunay and Voronoi FAQs - FAQ: How to compute the volume of a Voronoi region [C, Brinch] - Add 'FS' to qconvex prompt (total area and volume) - Add clarification to 'Fv' about corner input sites [O. Can] - Qhull-go.bat: Removed out-of-date advice. Added title. - qh-code.htm: Updated the discussion of multi-threading for C++ [I. Pirwani] Qhull 2009.1.2 2011/11/21 - Revert to LF line endings [P. Cheeseman] - Remove out-of-date material from qhull-go.bat - Replaced QHULL-GO with a lnk file Qhull 2011.1 2011/05/23 6.2.0.1385 (exe/dll files unchanged) - delaunay.vcproj: Fixed qhullstatic_d.lib for debug and minrelsize builds - Did not redate the distribution Qhull 2011.1 2011/05/18 6.2.0.1385 (exe/dll files unchanged) - Add 'm' library to shared and static targets on Unix [A. Bouchard] Qhull 2011.1 2011/05/14 6.2.0.1383 (exe/dll files unchanged) - PointCoordinates.cpp: Add #include [R. Richter, S. Pasko] - Remove deprecated libqhull/qhull.h Use libqhull/libqhull.h instead. Avoids confusion with libqhullcpp/Qhull.h - Makefile: Add LIBDIR, INCDIR, and DESTDIR to install [L.H. de Mello] Separate MAN install from DOC install Create install directories Installs headers to include/libqhull, include/libqhullcpp, include/road - CMakeLists.txt: Add MAN_INSTALL_DIR for qhull.1 and rbox.1 man pages Add RoadTest.h to include/road for Qt users (road_HEADERS) - Renamed md5sum files to avoid two extensions - qh-get.htm: Add Readme links and 2009.1 note. - qh-optf.htm: Fix link - index.htm: Updated Google Scholar link - qhull-zip.sh: Improved error message. ------------ Qhull 2011.1 2011/04/17 6.2.0.1373 Changes to deliverables - qvoronoi: Deprecated 'Qt' and 'QJn'. Removed from documentation and prompts. These options produced duplicate Voronoi vertices for cospherical data. - Removed doskey from Qhull-go.bat. It is incompatible with Windows 7 - Added 'facets' argument to user_eg3.cpp - user_eg links with shared library - qhulltest.cpp: Add closing prompt. Changes to build system - Reorganized source directories - Moved executables to bin directory - Add CMake build for all targets (CMakeFiles.txt) [M. Moll assisted] - Add gcc build for all targets (Makefile) - Fixed location of qhull.man and rbox.man [M. Moll] - Add DevStudio builds for all targets (build/*.vcproj) - Added shared library (lib/qhull6.dll) Added qh_QHpointer_dllimport to work around problems with MSVC - Added static libraries with and without qh_QHpointer (lib/qhullstatic.lib) - Added eg/make-vcproj.sh to create vcproj/sln files from cmake and qmake - Document location of qh_QHpointer - Use shadow build directory - Made -fno-strict-aliasing conditional on gcc version - Added src/qhull-app-cpp.pri, src/qhull-app-c.pri, etc. for common settings - Add .gitignore with ignored files and directories. - Use .git/info/exclude for locally excluded files. - Fixed MBorland for new directory structure Changes to documentation - qvoronoi.htm: Remove quotes from qvoronoi example - qhull-cpp.xml: Add naming conventions - index.htm: Add Google Scholar references - qh-optf.htm: Add note about order of 'Fn' matching 'Fv' order [Q. Pan] - Add patch for old builds in qh-get.htm - Added C++ compiling instructions to README.txt - Add instructions for fixing the DOS window - Changed DOS window to command window - Fixed html links - qh-get.htm: Dropped the Spanish mirror site. It was disabled. Changes to C code - mem.h: Define ptr_intT as 'long long' for Microsoft Windows _win64 builds. On Linux and Mac, 'long' is 64-bits on a 64-bit host - Added qh_QHpointer_dllimport to work around MSVC problem - qconvex.c,etc.: Define prototype for _isatty - Define MSG_QHULL_ERROR in user.h - Move MSG_FIXUP to 11000 and updated FIXUP QH11... Changes to test code - Add note to q_test than R1e-3 may error (qh-code.htm, Enhancements) - Add test for executables to q_eg, etc. - Fixed Qhull-go.bat. QHULL-GO invokes it with command.com, Changes to C++ interface - QhullFacet: Added isSimplicial, isTopOrient, isTriCoplanar, isUpperDelaunay - Added Qhull::defineVertexFacetNeighbors() for facetNeighbors of vertices. Automatically called for facet merging and Voronoi diagrams Do not print QhullVertex::facetNeighbors is !facetNeighborsDefined() - Add Fixup identifiers - QhullError: Add copy constructor, assignment operator, and destructor - Add throw() specifiers to RoadError and QhullError - Renamed RoadError::defined() to RoadError::isDefined() - Add #error to Qhull.h if qh_QHpointer is not defined Changes to C++ code - Fixed bug reported by renangms. Vertex output throws error QH10034 and defineVertexNeighbors() does not exist. - Define QHULL_USES_QT for qt-qhull.cpp [renangms] - Reviewed all copy constructors and copy assignments. Updated comments. Defined Qhull copy constructor and copy assignment [G. Rivet-Sabourin] Disabled UsingQhullLib default constructor, copy construct, and copy assign - Merged changes from J. Obermayr in gitorious/jobermayrs-qhull:next - Fix strncat limit in rboxlib.c and global.c - Changes to CMakeLists.txt for openSUSE - Fixed additional uses of strncat - Fixed QhullFacet::PrintRidges to check hasNextRidge3d() - Removed gcc warnings for shadowing from code (src/qhull-warn.pri) - Removed semicolon after extern "C" {...} - Removed experimental QhullEvent/QhullLog - Use fabs() instead of abs() to avoid accidental conversions to int - Fixed type of vertex->neighbors in qh_printvoronoi [no effect on results] - Removed unnecessary if statement in qh_printvoronoi ------------ qhull 2010.1 2010/01/14 - Fixed quote for #include in qhull.h [U.Hergenhahn, K.Roland] - Add qt-qhull.cpp with Qt conditional code - Add libqhullp.proj - Add libqhull5 to Readme, Announce, download - Reviewed #pragma - Reviewed FIXUP and assigned QH tags - All projects compile with warnings enabled - Replaced 'up' glyphs with » - Moved cpp questions to qh-code.htm#questions-cpp - Moved suggestions to qh-code.htm#enhance - Moved documentation requests to qh-code.htm#enhance - Add md5sum file to distributions - Switched to DevStudio builds to avoid dependent libraries, 10% slower Removed user_eg3.exe and qhullcpp.dll from Windows build Fix qhull.sln and project files for qh_QHpointer - Add eg/qhull-zip.sh to build qhull distribution files ------------ qhull 2010.1 2010/01/10 - Test for NULL fp in qh_eachvoronoi [D. Szczerba] qhull 2010.1 2010/01/09 Changes to build and distribution - Use qh_QHpointer=0 for libqhull.a, qhull, rbox, etc. Use -Dqh_QHpointer for libqhullp.a, qhullcpp.dll, etc. qh_QHpointer [2010, gcc] 4% time 4% space, [2003, msvc] 8% time 2% space - Add config/ and project/debian/ for Autoconf build [R. Laboissiere] from debian branch in git and http://savannah.nongnu.org/cvs/?group=qhull - Add CMakeLists.txt [kwilliams] - Fix tabs in Makefile.txt [mschamschula] - Add -fno-strict-aliasing to Makefile for gcc 4.1, 4.2, and 4.3 qset segfault - Remove user_eg.exe and user_eg2.exe from Windows distribution - Order object files by frequency of execution for better locality. Changes to source - Remove ptr_intT from qh_matchvertices. It was int since the beginning. - user.h requires for CLOCKS_PER_SEC - Move ostream<

  ---------------------------------

   geom.c
   geometric routines of qhull

   see qh-geom.htm and geom.h

   Copyright (c) 1993-2012 The Geometry Center.
   $Id: //main/2011/qhull/src/libqhull/geom.c#3 $$Change: 1464 $
   $DateTime: 2012/01/25 22:58:41 $$Author: bbarber $

   infrequent code goes into geom2.c
*/

#include "qhull_a.h"

/*---------------------------------

  qh_distplane( point, facet, dist )
    return distance from point to facet

  returns:
    dist
    if qh.RANDOMdist, joggles result

  notes:
    dist > 0 if point is above facet (i.e., outside)
    does not error (for qh_sortfacets, qh_outerinner)

  see:
    qh_distnorm in geom2.c
    qh_distplane [geom.c], QhullFacet::distance, and QhullHyperplane::distance are copies
*/
void qh_distplane(pointT *point, facetT *facet, realT *dist) {
  coordT *normal= facet->normal, *coordp, randr;
  int k;

  switch (qh hull_dim){
  case 2:
    *dist= facet->offset + point[0] * normal[0] + point[1] * normal[1];
    break;
  case 3:
    *dist= facet->offset + point[0] * normal[0] + point[1] * normal[1] + point[2] * normal[2];
    break;
  case 4:
    *dist= facet->offset+point[0]*normal[0]+point[1]*normal[1]+point[2]*normal[2]+point[3]*normal[3];
    break;
  case 5:
    *dist= facet->offset+point[0]*normal[0]+point[1]*normal[1]+point[2]*normal[2]+point[3]*normal[3]+point[4]*normal[4];
    break;
  case 6:
    *dist= facet->offset+point[0]*normal[0]+point[1]*normal[1]+point[2]*normal[2]+point[3]*normal[3]+point[4]*normal[4]+point[5]*normal[5];
    break;
  case 7:
    *dist= facet->offset+point[0]*normal[0]+point[1]*normal[1]+point[2]*normal[2]+point[3]*normal[3]+point[4]*normal[4]+point[5]*normal[5]+point[6]*normal[6];
    break;
  case 8:
    *dist= facet->offset+point[0]*normal[0]+point[1]*normal[1]+point[2]*normal[2]+point[3]*normal[3]+point[4]*normal[4]+point[5]*normal[5]+point[6]*normal[6]+point[7]*normal[7];
    break;
  default:
    *dist= facet->offset;
    coordp= point;
    for (k=qh hull_dim; k--; )
      *dist += *coordp++ * *normal++;
    break;
  }
  zinc_(Zdistplane);
  if (!qh RANDOMdist && qh IStracing < 4)
    return;
  if (qh RANDOMdist) {
    randr= qh_RANDOMint;
    *dist += (2.0 * randr / qh_RANDOMmax - 1.0) *
      qh RANDOMfactor * qh MAXabs_coord;
  }
  if (qh IStracing >= 4) {
    qh_fprintf(qh ferr, 8001, "qh_distplane: ");
    qh_fprintf(qh ferr, 8002, qh_REAL_1, *dist);
    qh_fprintf(qh ferr, 8003, "from p%d to f%d\n", qh_pointid(point), facet->id);
  }
  return;
} /* distplane */


/*---------------------------------

  qh_findbest( point, startfacet, bestoutside, qh_ISnewfacets, qh_NOupper, dist, isoutside, numpart )
    find facet that is furthest below a point
    for upperDelaunay facets
      returns facet only if !qh_NOupper and clearly above

  input:
    starts search at 'startfacet' (can not be flipped)
    if !bestoutside(qh_ALL), stops at qh.MINoutside

  returns:
    best facet (reports error if NULL)
    early out if isoutside defined and bestdist > qh.MINoutside
    dist is distance to facet
    isoutside is true if point is outside of facet
    numpart counts the number of distance tests

  see also:
    qh_findbestnew()

  notes:
    If merging (testhorizon), searches horizon facets of coplanar best facets because
    after qh_distplane, this and qh_partitionpoint are the most expensive in 3-d
      avoid calls to distplane, function calls, and real number operations.
    caller traces result
    Optimized for outside points.   Tried recording a search set for qh_findhorizon.
    Made code more complicated.

  when called by qh_partitionvisible():
    indicated by qh_ISnewfacets
    qh.newfacet_list is list of simplicial, new facets
    qh_findbestnew set if qh_sharpnewfacets returns True (to use qh_findbestnew)
    qh.bestfacet_notsharp set if qh_sharpnewfacets returns False

  when called by qh_findfacet(), qh_partitionpoint(), qh_partitioncoplanar(),
                 qh_check_bestdist(), qh_addpoint()
    indicated by !qh_ISnewfacets
    returns best facet in neighborhood of given facet
      this is best facet overall if dist > -   qh.MAXcoplanar
        or hull has at least a "spherical" curvature

  design:
    initialize and test for early exit
    repeat while there are better facets
      for each neighbor of facet
        exit if outside facet found
        test for better facet
    if point is inside and partitioning
      test for new facets with a "sharp" intersection
      if so, future calls go to qh_findbestnew()
    test horizon facets
*/
facetT *qh_findbest(pointT *point, facetT *startfacet,
                     boolT bestoutside, boolT isnewfacets, boolT noupper,
                     realT *dist, boolT *isoutside, int *numpart) {
  realT bestdist= -REALmax/2 /* avoid underflow */;
  facetT *facet, *neighbor, **neighborp;
  facetT *bestfacet= NULL, *lastfacet= NULL;
  int oldtrace= qh IStracing;
  unsigned int visitid= ++qh visit_id;
  int numpartnew=0;
  boolT testhorizon = True; /* needed if precise, e.g., rbox c D6 | qhull Q0 Tv */

  zinc_(Zfindbest);
  if (qh IStracing >= 3 || (qh TRACElevel && qh TRACEpoint >= 0 && qh TRACEpoint == qh_pointid(point))) {
    if (qh TRACElevel > qh IStracing)
      qh IStracing= qh TRACElevel;
    qh_fprintf(qh ferr, 8004, "qh_findbest: point p%d starting at f%d isnewfacets? %d, unless %d exit if > %2.2g\n",
             qh_pointid(point), startfacet->id, isnewfacets, bestoutside, qh MINoutside);
    qh_fprintf(qh ferr, 8005, "  testhorizon? %d noupper? %d", testhorizon, noupper);
    qh_fprintf(qh ferr, 8006, "  Last point added was p%d.", qh furthest_id);
    qh_fprintf(qh ferr, 8007, "  Last merge was #%d.  max_outside %2.2g\n", zzval_(Ztotmerge), qh max_outside);
  }
  if (isoutside)
    *isoutside= True;
  if (!startfacet->flipped) {  /* test startfacet */
    *numpart= 1;
    qh_distplane(point, startfacet, dist);  /* this code is duplicated below */
    if (!bestoutside && *dist >= qh MINoutside
    && (!startfacet->upperdelaunay || !noupper)) {
      bestfacet= startfacet;
      goto LABELreturn_best;
    }
    bestdist= *dist;
    if (!startfacet->upperdelaunay) {
      bestfacet= startfacet;
    }
  }else
    *numpart= 0;
  startfacet->visitid= visitid;
  facet= startfacet;
  while (facet) {
    trace4((qh ferr, 4001, "qh_findbest: neighbors of f%d, bestdist %2.2g f%d\n",
                facet->id, bestdist, getid_(bestfacet)));
    lastfacet= facet;
    FOREACHneighbor_(facet) {
      if (!neighbor->newfacet && isnewfacets)
        continue;
      if (neighbor->visitid == visitid)
        continue;
      neighbor->visitid= visitid;
      if (!neighbor->flipped) {  /* code duplicated above */
        (*numpart)++;
        qh_distplane(point, neighbor, dist);
        if (*dist > bestdist) {
          if (!bestoutside && *dist >= qh MINoutside
          && (!neighbor->upperdelaunay || !noupper)) {
            bestfacet= neighbor;
            goto LABELreturn_best;
          }
          if (!neighbor->upperdelaunay) {
            bestfacet= neighbor;
            bestdist= *dist;
            break; /* switch to neighbor */
          }else if (!bestfacet) {
            bestdist= *dist;
            break; /* switch to neighbor */
          }
        } /* end of *dist>bestdist */
      } /* end of !flipped */
    } /* end of FOREACHneighbor */
    facet= neighbor;  /* non-NULL only if *dist>bestdist */
  } /* end of while facet (directed search) */
  if (isnewfacets) {
    if (!bestfacet) {
      bestdist= -REALmax/2;
      bestfacet= qh_findbestnew(point, startfacet->next, &bestdist, bestoutside, isoutside, &numpartnew);
      testhorizon= False; /* qh_findbestnew calls qh_findbesthorizon */
    }else if (!qh findbest_notsharp && bestdist < - qh DISTround) {
      if (qh_sharpnewfacets()) {
        /* seldom used, qh_findbestnew will retest all facets */
        zinc_(Zfindnewsharp);
        bestfacet= qh_findbestnew(point, bestfacet, &bestdist, bestoutside, isoutside, &numpartnew);
        testhorizon= False; /* qh_findbestnew calls qh_findbesthorizon */
        qh findbestnew= True;
      }else
        qh findbest_notsharp= True;
    }
  }
  if (!bestfacet)
    bestfacet= qh_findbestlower(lastfacet, point, &bestdist, numpart);
  if (testhorizon)
    bestfacet= qh_findbesthorizon(!qh_IScheckmax, point, bestfacet, noupper, &bestdist, &numpartnew);
  *dist= bestdist;
  if (isoutside && bestdist < qh MINoutside)
    *isoutside= False;
LABELreturn_best:
  zadd_(Zfindbesttot, *numpart);
  zmax_(Zfindbestmax, *numpart);
  (*numpart) += numpartnew;
  qh IStracing= oldtrace;
  return bestfacet;
}  /* findbest */


/*---------------------------------

  qh_findbesthorizon( qh_IScheckmax, point, startfacet, qh_NOupper, &bestdist, &numpart )
    search coplanar and better horizon facets from startfacet/bestdist
    ischeckmax turns off statistics and minsearch update
    all arguments must be initialized
  returns(ischeckmax):
    best facet
  returns(!ischeckmax):
    best facet that is not upperdelaunay
    allows upperdelaunay that is clearly outside
  returns:
    bestdist is distance to bestfacet
    numpart -- updates number of distance tests

  notes:
    no early out -- use qh_findbest() or qh_findbestnew()
    Searches coplanar or better horizon facets

  when called by qh_check_maxout() (qh_IScheckmax)
    startfacet must be closest to the point
      Otherwise, if point is beyond and below startfacet, startfacet may be a local minimum
      even though other facets are below the point.
    updates facet->maxoutside for good, visited facets
    may return NULL

    searchdist is qh.max_outside + 2 * DISTround
      + max( MINvisible('Vn'), MAXcoplanar('Un'));
    This setting is a guess.  It must be at least max_outside + 2*DISTround
    because a facet may have a geometric neighbor across a vertex

  design:
    for each horizon facet of coplanar best facets
      continue if clearly inside
      unless upperdelaunay or clearly outside
         update best facet
*/
facetT *qh_findbesthorizon(boolT ischeckmax, pointT* point, facetT *startfacet, boolT noupper, realT *bestdist, int *numpart) {
  facetT *bestfacet= startfacet;
  realT dist;
  facetT *neighbor, **neighborp, *facet;
  facetT *nextfacet= NULL; /* optimize last facet of coplanarfacetset */
  int numpartinit= *numpart, coplanarfacetset_size;
  unsigned int visitid= ++qh visit_id;
  boolT newbest= False; /* for tracing */
  realT minsearch, searchdist;  /* skip facets that are too far from point */

  if (!ischeckmax) {
    zinc_(Zfindhorizon);
  }else {
#if qh_MAXoutside
    if ((!qh ONLYgood || startfacet->good) && *bestdist > startfacet->maxoutside)
      startfacet->maxoutside= *bestdist;
#endif
  }
  searchdist= qh_SEARCHdist; /* multiple of qh.max_outside and precision constants */
  minsearch= *bestdist - searchdist;
  if (ischeckmax) {
    /* Always check coplanar facets.  Needed for RBOX 1000 s Z1 G1e-13 t996564279 | QHULL Tv */
    minimize_(minsearch, -searchdist);
  }
  coplanarfacetset_size= 0;
  facet= startfacet;
  while (True) {
    trace4((qh ferr, 4002, "qh_findbesthorizon: neighbors of f%d bestdist %2.2g f%d ischeckmax? %d noupper? %d minsearch %2.2g searchdist %2.2g\n",
                facet->id, *bestdist, getid_(bestfacet), ischeckmax, noupper,
                minsearch, searchdist));
    FOREACHneighbor_(facet) {
      if (neighbor->visitid == visitid)
        continue;
      neighbor->visitid= visitid;
      if (!neighbor->flipped) {
        qh_distplane(point, neighbor, &dist);
        (*numpart)++;
        if (dist > *bestdist) {
          if (!neighbor->upperdelaunay || ischeckmax || (!noupper && dist >= qh MINoutside)) {
            bestfacet= neighbor;
            *bestdist= dist;
            newbest= True;
            if (!ischeckmax) {
              minsearch= dist - searchdist;
              if (dist > *bestdist + searchdist) {
                zinc_(Zfindjump);  /* everything in qh.coplanarfacetset at least searchdist below */
                coplanarfacetset_size= 0;
              }
            }
          }
        }else if (dist < minsearch)
          continue;  /* if ischeckmax, dist can't be positive */
#if qh_MAXoutside
        if (ischeckmax && dist > neighbor->maxoutside)
          neighbor->maxoutside= dist;
#endif
      } /* end of !flipped */
      if (nextfacet) {
        if (!coplanarfacetset_size++) {
          SETfirst_(qh coplanarfacetset)= nextfacet;
          SETtruncate_(qh coplanarfacetset, 1);
        }else
          qh_setappend(&qh coplanarfacetset, nextfacet); /* Was needed for RBOX 1000 s W1e-13 P0 t996547055 | QHULL d Qbb Qc Tv
                                                 and RBOX 1000 s Z1 G1e-13 t996564279 | qhull Tv  */
      }
      nextfacet= neighbor;
    } /* end of EACHneighbor */
    facet= nextfacet;
    if (facet)
      nextfacet= NULL;
    else if (!coplanarfacetset_size)
      break;
    else if (!--coplanarfacetset_size) {
      facet= SETfirstt_(qh coplanarfacetset, facetT);
      SETtruncate_(qh coplanarfacetset, 0);
    }else
      facet= (facetT*)qh_setdellast(qh coplanarfacetset);
  } /* while True, for each facet in qh.coplanarfacetset */
  if (!ischeckmax) {
    zadd_(Zfindhorizontot, *numpart - numpartinit);
    zmax_(Zfindhorizonmax, *numpart - numpartinit);
    if (newbest)
      zinc_(Zparthorizon);
  }
  trace4((qh ferr, 4003, "qh_findbesthorizon: newbest? %d bestfacet f%d bestdist %2.2g\n", newbest, getid_(bestfacet), *bestdist));
  return bestfacet;
}  /* findbesthorizon */

/*---------------------------------

  qh_findbestnew( point, startfacet, dist, isoutside, numpart )
    find best newfacet for point
    searches all of qh.newfacet_list starting at startfacet
    searches horizon facets of coplanar best newfacets
    searches all facets if startfacet == qh.facet_list
  returns:
    best new or horizon facet that is not upperdelaunay
    early out if isoutside and not 'Qf'
    dist is distance to facet
    isoutside is true if point is outside of facet
    numpart is number of distance tests

  notes:
    Always used for merged new facets (see qh_USEfindbestnew)
    Avoids upperdelaunay facet unless (isoutside and outside)

    Uses qh.visit_id, qh.coplanarfacetset.
    If share visit_id with qh_findbest, coplanarfacetset is incorrect.

    If merging (testhorizon), searches horizon facets of coplanar best facets because
    a point maybe coplanar to the bestfacet, below its horizon facet,
    and above a horizon facet of a coplanar newfacet.  For example,
      rbox 1000 s Z1 G1e-13 | qhull
      rbox 1000 s W1e-13 P0 t992110337 | QHULL d Qbb Qc

    qh_findbestnew() used if
       qh_sharpnewfacets -- newfacets contains a sharp angle
       if many merges, qh_premerge found a merge, or 'Qf' (qh.findbestnew)

  see also:
    qh_partitionall() and qh_findbest()

  design:
    for each new facet starting from startfacet
      test distance from point to facet
      return facet if clearly outside
      unless upperdelaunay and a lowerdelaunay exists
         update best facet
    test horizon facets
*/
facetT *qh_findbestnew(pointT *point, facetT *startfacet,
           realT *dist, boolT bestoutside, boolT *isoutside, int *numpart) {
  realT bestdist= -REALmax/2;
  facetT *bestfacet= NULL, *facet;
  int oldtrace= qh IStracing, i;
  unsigned int visitid= ++qh visit_id;
  realT distoutside= 0.0;
  boolT isdistoutside; /* True if distoutside is defined */
  boolT testhorizon = True; /* needed if precise, e.g., rbox c D6 | qhull Q0 Tv */

  if (!startfacet) {
    if (qh MERGING)
      qh_fprintf(qh ferr, 6001, "qhull precision error (qh_findbestnew): merging has formed and deleted a cone of new facets.  Can not continue.\n");
    else
      qh_fprintf(qh ferr, 6002, "qhull internal error (qh_findbestnew): no new facets for point p%d\n",
              qh furthest_id);
    qh_errexit(qh_ERRqhull, NULL, NULL);
  }
  zinc_(Zfindnew);
  if (qh BESToutside || bestoutside)
    isdistoutside= False;
  else {
    isdistoutside= True;
    distoutside= qh_DISToutside; /* multiple of qh.MINoutside & qh.max_outside, see user.h */
  }
  if (isoutside)
    *isoutside= True;
  *numpart= 0;
  if (qh IStracing >= 3 || (qh TRACElevel && qh TRACEpoint >= 0 && qh TRACEpoint == qh_pointid(point))) {
    if (qh TRACElevel > qh IStracing)
      qh IStracing= qh TRACElevel;
    qh_fprintf(qh ferr, 8008, "qh_findbestnew: point p%d facet f%d. Stop? %d if dist > %2.2g\n",
             qh_pointid(point), startfacet->id, isdistoutside, distoutside);
    qh_fprintf(qh ferr, 8009, "  Last point added p%d visitid %d.",  qh furthest_id, visitid);
    qh_fprintf(qh ferr, 8010, "  Last merge was #%d.\n", zzval_(Ztotmerge));
  }
  /* visit all new facets starting with startfacet, maybe qh facet_list */
  for (i=0, facet=startfacet; i < 2; i++, facet= qh newfacet_list) {
    FORALLfacet_(facet) {
      if (facet == startfacet && i)
        break;
      facet->visitid= visitid;
      if (!facet->flipped) {
        qh_distplane(point, facet, dist);
        (*numpart)++;
        if (*dist > bestdist) {
          if (!facet->upperdelaunay || *dist >= qh MINoutside) {
            bestfacet= facet;
            if (isdistoutside && *dist >= distoutside)
              goto LABELreturn_bestnew;
            bestdist= *dist;
          }
        }
      } /* end of !flipped */
    } /* FORALLfacet from startfacet or qh newfacet_list */
  }
  if (testhorizon || !bestfacet)
    bestfacet= qh_findbesthorizon(!qh_IScheckmax, point, bestfacet ? bestfacet : startfacet,
                                        !qh_NOupper, &bestdist, numpart);
  *dist= bestdist;
  if (isoutside && *dist < qh MINoutside)
    *isoutside= False;
LABELreturn_bestnew:
  zadd_(Zfindnewtot, *numpart);
  zmax_(Zfindnewmax, *numpart);
  trace4((qh ferr, 4004, "qh_findbestnew: bestfacet f%d bestdist %2.2g\n", getid_(bestfacet), *dist));
  qh IStracing= oldtrace;
  return bestfacet;
}  /* findbestnew */

/* ============ hyperplane functions -- keep code together [?] ============ */

/*---------------------------------

  qh_backnormal( rows, numrow, numcol, sign, normal, nearzero )
    given an upper-triangular rows array and a sign,
    solve for normal equation x using back substitution over rows U

  returns:
     normal= x

     if will not be able to divzero() when normalized(qh.MINdenom_2 and qh.MINdenom_1_2),
       if fails on last row
         this means that the hyperplane intersects [0,..,1]
         sets last coordinate of normal to sign
       otherwise
         sets tail of normal to [...,sign,0,...], i.e., solves for b= [0...0]
         sets nearzero

  notes:
     assumes numrow == numcol-1

     see Golub & van Loan 4.4-9 for back substitution

     solves Ux=b where Ax=b and PA=LU
     b= [0,...,0,sign or 0]  (sign is either -1 or +1)
     last row of A= [0,...,0,1]

     1) Ly=Pb == y=b since P only permutes the 0's of   b

  design:
    for each row from end
      perform back substitution
      if near zero
        use qh_divzero for division
        if zero divide and not last row
          set tail of normal to 0
*/
void qh_backnormal(realT **rows, int numrow, int numcol, boolT sign,
        coordT *normal, boolT *nearzero) {
  int i, j;
  coordT *normalp, *normal_tail, *ai, *ak;
  realT diagonal;
  boolT waszero;
  int zerocol= -1;

  normalp= normal + numcol - 1;
  *normalp--= (sign ? -1.0 : 1.0);
  for (i=numrow; i--; ) {
    *normalp= 0.0;
    ai= rows[i] + i + 1;
    ak= normalp+1;
    for (j=i+1; j < numcol; j++)
      *normalp -= *ai++ * *ak++;
    diagonal= (rows[i])[i];
    if (fabs_(diagonal) > qh MINdenom_2)
      *(normalp--) /= diagonal;
    else {
      waszero= False;
      *normalp= qh_divzero(*normalp, diagonal, qh MINdenom_1_2, &waszero);
      if (waszero) {
        zerocol= i;
        *(normalp--)= (sign ? -1.0 : 1.0);
        for (normal_tail= normalp+2; normal_tail < normal + numcol; normal_tail++)
          *normal_tail= 0.0;
      }else
        normalp--;
    }
  }
  if (zerocol != -1) {
    zzinc_(Zback0);
    *nearzero= True;
    trace4((qh ferr, 4005, "qh_backnormal: zero diagonal at column %d.\n", i));
    qh_precision("zero diagonal on back substitution");
  }
} /* backnormal */

/*---------------------------------

  qh_gausselim( rows, numrow, numcol, sign )
    Gaussian elimination with partial pivoting

  returns:
    rows is upper triangular (includes row exchanges)
    flips sign for each row exchange
    sets nearzero if pivot[k] < qh.NEARzero[k], else clears it

  notes:
    if nearzero, the determinant's sign may be incorrect.
    assumes numrow <= numcol

  design:
    for each row
      determine pivot and exchange rows if necessary
      test for near zero
      perform gaussian elimination step
*/
void qh_gausselim(realT **rows, int numrow, int numcol, boolT *sign, boolT *nearzero) {
  realT *ai, *ak, *rowp, *pivotrow;
  realT n, pivot, pivot_abs= 0.0, temp;
  int i, j, k, pivoti, flip=0;

  *nearzero= False;
  for (k=0; k < numrow; k++) {
    pivot_abs= fabs_((rows[k])[k]);
    pivoti= k;
    for (i=k+1; i < numrow; i++) {
      if ((temp= fabs_((rows[i])[k])) > pivot_abs) {
        pivot_abs= temp;
        pivoti= i;
      }
    }
    if (pivoti != k) {
      rowp= rows[pivoti];
      rows[pivoti]= rows[k];
      rows[k]= rowp;
      *sign ^= 1;
      flip ^= 1;
    }
    if (pivot_abs <= qh NEARzero[k]) {
      *nearzero= True;
      if (pivot_abs == 0.0) {   /* remainder of column == 0 */
        if (qh IStracing >= 4) {
          qh_fprintf(qh ferr, 8011, "qh_gausselim: 0 pivot at column %d. (%2.2g < %2.2g)\n", k, pivot_abs, qh DISTround);
          qh_printmatrix(qh ferr, "Matrix:", rows, numrow, numcol);
        }
        zzinc_(Zgauss0);
        qh_precision("zero pivot for Gaussian elimination");
        goto LABELnextcol;
      }
    }
    pivotrow= rows[k] + k;
    pivot= *pivotrow++;  /* signed value of pivot, and remainder of row */
    for (i=k+1; i < numrow; i++) {
      ai= rows[i] + k;
      ak= pivotrow;
      n= (*ai++)/pivot;   /* divzero() not needed since |pivot| >= |*ai| */
      for (j= numcol - (k+1); j--; )
        *ai++ -= n * *ak++;
    }
  LABELnextcol:
    ;
  }
  wmin_(Wmindenom, pivot_abs);  /* last pivot element */
  if (qh IStracing >= 5)
    qh_printmatrix(qh ferr, "qh_gausselem: result", rows, numrow, numcol);
} /* gausselim */


/*---------------------------------

  qh_getangle( vect1, vect2 )
    returns the dot product of two vectors
    if qh.RANDOMdist, joggles result

  notes:
    the angle may be > 1.0 or < -1.0 because of roundoff errors

*/
realT qh_getangle(pointT *vect1, pointT *vect2) {
  realT angle= 0, randr;
  int k;

  for (k=qh hull_dim; k--; )
    angle += *vect1++ * *vect2++;
  if (qh RANDOMdist) {
    randr= qh_RANDOMint;
    angle += (2.0 * randr / qh_RANDOMmax - 1.0) *
      qh RANDOMfactor;
  }
  trace4((qh ferr, 4006, "qh_getangle: %2.2g\n", angle));
  return(angle);
} /* getangle */


/*---------------------------------

  qh_getcenter( vertices )
    returns arithmetic center of a set of vertices as a new point

  notes:
    allocates point array for center
*/
pointT *qh_getcenter(setT *vertices) {
  int k;
  pointT *center, *coord;
  vertexT *vertex, **vertexp;
  int count= qh_setsize(vertices);

  if (count < 2) {
    qh_fprintf(qh ferr, 6003, "qhull internal error (qh_getcenter): not defined for %d points\n", count);
    qh_errexit(qh_ERRqhull, NULL, NULL);
  }
  center= (pointT *)qh_memalloc(qh normal_size);
  for (k=0; k < qh hull_dim; k++) {
    coord= center+k;
    *coord= 0.0;
    FOREACHvertex_(vertices)
      *coord += vertex->point[k];
    *coord /= count;
  }
  return(center);
} /* getcenter */


/*---------------------------------

  qh_getcentrum( facet )
    returns the centrum for a facet as a new point

  notes:
    allocates the centrum
*/
pointT *qh_getcentrum(facetT *facet) {
  realT dist;
  pointT *centrum, *point;

  point= qh_getcenter(facet->vertices);
  zzinc_(Zcentrumtests);
  qh_distplane(point, facet, &dist);
  centrum= qh_projectpoint(point, facet, dist);
  qh_memfree(point, qh normal_size);
  trace4((qh ferr, 4007, "qh_getcentrum: for f%d, %d vertices dist= %2.2g\n",
          facet->id, qh_setsize(facet->vertices), dist));
  return centrum;
} /* getcentrum */


/*---------------------------------

  qh_getdistance( facet, neighbor, mindist, maxdist )
    returns the maxdist and mindist distance of any vertex from neighbor

  returns:
    the max absolute value

  design:
    for each vertex of facet that is not in neighbor
      test the distance from vertex to neighbor
*/
realT qh_getdistance(facetT *facet, facetT *neighbor, realT *mindist, realT *maxdist) {
  vertexT *vertex, **vertexp;
  realT dist, maxd, mind;

  FOREACHvertex_(facet->vertices)
    vertex->seen= False;
  FOREACHvertex_(neighbor->vertices)
    vertex->seen= True;
  mind= 0.0;
  maxd= 0.0;
  FOREACHvertex_(facet->vertices) {
    if (!vertex->seen) {
      zzinc_(Zbestdist);
      qh_distplane(vertex->point, neighbor, &dist);
      if (dist < mind)
        mind= dist;
      else if (dist > maxd)
        maxd= dist;
    }
  }
  *mindist= mind;
  *maxdist= maxd;
  mind= -mind;
  if (maxd > mind)
    return maxd;
  else
    return mind;
} /* getdistance */


/*---------------------------------

  qh_normalize( normal, dim, toporient )
    normalize a vector and report if too small
    does not use min norm

  see:
    qh_normalize2
*/
void qh_normalize(coordT *normal, int dim, boolT toporient) {
  qh_normalize2( normal, dim, toporient, NULL, NULL);
} /* normalize */

/*---------------------------------

  qh_normalize2( normal, dim, toporient, minnorm, ismin )
    normalize a vector and report if too small
    qh.MINdenom/MINdenom1 are the upper limits for divide overflow

  returns:
    normalized vector
    flips sign if !toporient
    if minnorm non-NULL,
      sets ismin if normal < minnorm

  notes:
    if zero norm
       sets all elements to sqrt(1.0/dim)
    if divide by zero (divzero())
       sets largest element to   +/-1
       bumps Znearlysingular

  design:
    computes norm
    test for minnorm
    if not near zero
      normalizes normal
    else if zero norm
      sets normal to standard value
    else
      uses qh_divzero to normalize
      if nearzero
        sets norm to direction of maximum value
*/
void qh_normalize2 (coordT *normal, int dim, boolT toporient,
            realT *minnorm, boolT *ismin) {
  int k;
  realT *colp, *maxp, norm= 0, temp, *norm1, *norm2, *norm3;
  boolT zerodiv;

  norm1= normal+1;
  norm2= normal+2;
  norm3= normal+3;
  if (dim == 2)
    norm= sqrt((*normal)*(*normal) + (*norm1)*(*norm1));
  else if (dim == 3)
    norm= sqrt((*normal)*(*normal) + (*norm1)*(*norm1) + (*norm2)*(*norm2));
  else if (dim == 4) {
    norm= sqrt((*normal)*(*normal) + (*norm1)*(*norm1) + (*norm2)*(*norm2)
               + (*norm3)*(*norm3));
  }else if (dim > 4) {
    norm= (*normal)*(*normal) + (*norm1)*(*norm1) + (*norm2)*(*norm2)
               + (*norm3)*(*norm3);
    for (k=dim-4, colp=normal+4; k--; colp++)
      norm += (*colp) * (*colp);
    norm= sqrt(norm);
  }
  if (minnorm) {
    if (norm < *minnorm)
      *ismin= True;
    else
      *ismin= False;
  }
  wmin_(Wmindenom, norm);
  if (norm > qh MINdenom) {
    if (!toporient)
      norm= -norm;
    *normal /= norm;
    *norm1 /= norm;
    if (dim == 2)
      ; /* all done */
    else if (dim == 3)
      *norm2 /= norm;
    else if (dim == 4) {
      *norm2 /= norm;
      *norm3 /= norm;
    }else if (dim >4) {
      *norm2 /= norm;
      *norm3 /= norm;
      for (k=dim-4, colp=normal+4; k--; )
        *colp++ /= norm;
    }
  }else if (norm == 0.0) {
    temp= sqrt(1.0/dim);
    for (k=dim, colp=normal; k--; )
      *colp++ = temp;
  }else {
    if (!toporient)
      norm= -norm;
    for (k=dim, colp=normal; k--; colp++) { /* k used below */
      temp= qh_divzero(*colp, norm, qh MINdenom_1, &zerodiv);
      if (!zerodiv)
        *colp= temp;
      else {
        maxp= qh_maxabsval(normal, dim);
        temp= ((*maxp * norm >= 0.0) ? 1.0 : -1.0);
        for (k=dim, colp=normal; k--; colp++)
          *colp= 0.0;
        *maxp= temp;
        zzinc_(Znearlysingular);
        trace0((qh ferr, 1, "qh_normalize: norm=%2.2g too small during p%d\n",
               norm, qh furthest_id));
        return;
      }
    }
  }
} /* normalize */


/*---------------------------------

  qh_projectpoint( point, facet, dist )
    project point onto a facet by dist

  returns:
    returns a new point

  notes:
    if dist= distplane(point,facet)
      this projects point to hyperplane
    assumes qh_memfree_() is valid for normal_size
*/
pointT *qh_projectpoint(pointT *point, facetT *facet, realT dist) {
  pointT *newpoint, *np, *normal;
  int normsize= qh normal_size;
  int k;
  void **freelistp; /* used !qh_NOmem */

  qh_memalloc_(normsize, freelistp, newpoint, pointT);
  np= newpoint;
  normal= facet->normal;
  for (k=qh hull_dim; k--; )
    *(np++)= *point++ - dist * *normal++;
  return(newpoint);
} /* projectpoint */


/*---------------------------------

  qh_setfacetplane( facet )
    sets the hyperplane for a facet
    if qh.RANDOMdist, joggles hyperplane

  notes:
    uses global buffers qh.gm_matrix and qh.gm_row
    overwrites facet->normal if already defined
    updates Wnewvertex if PRINTstatistics
    sets facet->upperdelaunay if upper envelope of Delaunay triangulation

  design:
    copy vertex coordinates to qh.gm_matrix/gm_row
    compute determinate
    if nearzero
      recompute determinate with gaussian elimination
      if nearzero
        force outside orientation by testing interior point
*/
void qh_setfacetplane(facetT *facet) {
  pointT *point;
  vertexT *vertex, **vertexp;
  int normsize= qh normal_size;
  int k,i, oldtrace= 0;
  realT dist;
  void **freelistp; /* used !qh_NOmem */
  coordT *coord, *gmcoord;
  pointT *point0= SETfirstt_(facet->vertices, vertexT)->point;
  boolT nearzero= False;

  zzinc_(Zsetplane);
  if (!facet->normal)
    qh_memalloc_(normsize, freelistp, facet->normal, coordT);
  if (facet == qh tracefacet) {
    oldtrace= qh IStracing;
    qh IStracing= 5;
    qh_fprintf(qh ferr, 8012, "qh_setfacetplane: facet f%d created.\n", facet->id);
    qh_fprintf(qh ferr, 8013, "  Last point added to hull was p%d.", qh furthest_id);
    if (zzval_(Ztotmerge))
      qh_fprintf(qh ferr, 8014, "  Last merge was #%d.", zzval_(Ztotmerge));
    qh_fprintf(qh ferr, 8015, "\n\nCurrent summary is:\n");
      qh_printsummary(qh ferr);
  }
  if (qh hull_dim <= 4) {
    i= 0;
    if (qh RANDOMdist) {
      gmcoord= qh gm_matrix;
      FOREACHvertex_(facet->vertices) {
        qh gm_row[i++]= gmcoord;
        coord= vertex->point;
        for (k=qh hull_dim; k--; )
          *(gmcoord++)= *coord++ * qh_randomfactor(qh RANDOMa, qh RANDOMb);
      }
    }else {
      FOREACHvertex_(facet->vertices)
       qh gm_row[i++]= vertex->point;
    }
    qh_sethyperplane_det(qh hull_dim, qh gm_row, point0, facet->toporient,
                facet->normal, &facet->offset, &nearzero);
  }
  if (qh hull_dim > 4 || nearzero) {
    i= 0;
    gmcoord= qh gm_matrix;
    FOREACHvertex_(facet->vertices) {
      if (vertex->point != point0) {
        qh gm_row[i++]= gmcoord;
        coord= vertex->point;
        point= point0;
        for (k=qh hull_dim; k--; )
          *(gmcoord++)= *coord++ - *point++;
      }
    }
    qh gm_row[i]= gmcoord;  /* for areasimplex */
    if (qh RANDOMdist) {
      gmcoord= qh gm_matrix;
      for (i=qh hull_dim-1; i--; ) {
        for (k=qh hull_dim; k--; )
          *(gmcoord++) *= qh_randomfactor(qh RANDOMa, qh RANDOMb);
      }
    }
    qh_sethyperplane_gauss(qh hull_dim, qh gm_row, point0, facet->toporient,
                facet->normal, &facet->offset, &nearzero);
    if (nearzero) {
      if (qh_orientoutside(facet)) {
        trace0((qh ferr, 2, "qh_setfacetplane: flipped orientation after testing interior_point during p%d\n", qh furthest_id));
      /* this is part of using Gaussian Elimination.  For example in 5-d
           1 1 1 1 0
           1 1 1 1 1
           0 0 0 1 0
           0 1 0 0 0
           1 0 0 0 0
           norm= 0.38 0.38 -0.76 0.38 0
         has a determinate of 1, but g.e. after subtracting pt. 0 has
         0's in the diagonal, even with full pivoting.  It does work
         if you subtract pt. 4 instead. */
      }
    }
  }
  facet->upperdelaunay= False;
  if (qh DELAUNAY) {
    if (qh UPPERdelaunay) {     /* matches qh_triangulate_facet and qh.lower_threshold in qh_initbuild */
      if (facet->normal[qh hull_dim -1] >= qh ANGLEround * qh_ZEROdelaunay)
        facet->upperdelaunay= True;
    }else {
      if (facet->normal[qh hull_dim -1] > -qh ANGLEround * qh_ZEROdelaunay)
        facet->upperdelaunay= True;
    }
  }
  if (qh PRINTstatistics || qh IStracing || qh TRACElevel || qh JOGGLEmax < REALmax) {
    qh old_randomdist= qh RANDOMdist;
    qh RANDOMdist= False;
    FOREACHvertex_(facet->vertices) {
      if (vertex->point != point0) {
        boolT istrace= False;
        zinc_(Zdiststat);
        qh_distplane(vertex->point, facet, &dist);
        dist= fabs_(dist);
        zinc_(Znewvertex);
        wadd_(Wnewvertex, dist);
        if (dist > wwval_(Wnewvertexmax)) {
          wwval_(Wnewvertexmax)= dist;
          if (dist > qh max_outside) {
            qh max_outside= dist;  /* used by qh_maxouter() */
            if (dist > qh TRACEdist)
              istrace= True;
          }
        }else if (-dist > qh TRACEdist)
          istrace= True;
        if (istrace) {
          qh_fprintf(qh ferr, 8016, "qh_setfacetplane: ====== vertex p%d(v%d) increases max_outside to %2.2g for new facet f%d last p%d\n",
                qh_pointid(vertex->point), vertex->id, dist, facet->id, qh furthest_id);
          qh_errprint("DISTANT", facet, NULL, NULL, NULL);
        }
      }
    }
    qh RANDOMdist= qh old_randomdist;
  }
  if (qh IStracing >= 3) {
    qh_fprintf(qh ferr, 8017, "qh_setfacetplane: f%d offset %2.2g normal: ",
             facet->id, facet->offset);
    for (k=0; k < qh hull_dim; k++)
      qh_fprintf(qh ferr, 8018, "%2.2g ", facet->normal[k]);
    qh_fprintf(qh ferr, 8019, "\n");
  }
  if (facet == qh tracefacet)
    qh IStracing= oldtrace;
} /* setfacetplane */


/*---------------------------------

  qh_sethyperplane_det( dim, rows, point0, toporient, normal, offset, nearzero )
    given dim X dim array indexed by rows[], one row per point,
        toporient(flips all signs),
        and point0 (any row)
    set normalized hyperplane equation from oriented simplex

  returns:
    normal (normalized)
    offset (places point0 on the hyperplane)
    sets nearzero if hyperplane not through points

  notes:
    only defined for dim == 2..4
    rows[] is not modified
    solves det(P-V_0, V_n-V_0, ..., V_1-V_0)=0, i.e. every point is on hyperplane
    see Bower & Woodworth, A programmer's geometry, Butterworths 1983.

  derivation of 3-d minnorm
    Goal: all vertices V_i within qh.one_merge of hyperplane
    Plan: exactly translate the facet so that V_0 is the origin
          exactly rotate the facet so that V_1 is on the x-axis and y_2=0.
          exactly rotate the effective perturbation to only effect n_0
             this introduces a factor of sqrt(3)
    n_0 = ((y_2-y_0)*(z_1-z_0) - (z_2-z_0)*(y_1-y_0)) / norm
    Let M_d be the max coordinate difference
    Let M_a be the greater of M_d and the max abs. coordinate
    Let u be machine roundoff and distround be max error for distance computation
    The max error for n_0 is sqrt(3) u M_a M_d / norm.  n_1 is approx. 1 and n_2 is approx. 0
    The max error for distance of V_1 is sqrt(3) u M_a M_d M_d / norm.  Offset=0 at origin
    Then minnorm = 1.8 u M_a M_d M_d / qh.ONEmerge
    Note that qh.one_merge is approx. 45.5 u M_a and norm is usually about M_d M_d

  derivation of 4-d minnorm
    same as above except rotate the facet so that V_1 on x-axis and w_2, y_3, w_3=0
     [if two vertices fixed on x-axis, can rotate the other two in yzw.]
    n_0 = det3_(...) = y_2 det2_(z_1, w_1, z_3, w_3) = - y_2 w_1 z_3
     [all other terms contain at least two factors nearly zero.]
    The max error for n_0 is sqrt(4) u M_a M_d M_d / norm
    Then minnorm = 2 u M_a M_d M_d M_d / qh.ONEmerge
    Note that qh.one_merge is approx. 82 u M_a and norm is usually about M_d M_d M_d
*/
void qh_sethyperplane_det(int dim, coordT **rows, coordT *point0,
          boolT toporient, coordT *normal, realT *offset, boolT *nearzero) {
  realT maxround, dist;
  int i;
  pointT *point;


  if (dim == 2) {
    normal[0]= dY(1,0);
    normal[1]= dX(0,1);
    qh_normalize2 (normal, dim, toporient, NULL, NULL);
    *offset= -(point0[0]*normal[0]+point0[1]*normal[1]);
    *nearzero= False;  /* since nearzero norm => incident points */
  }else if (dim == 3) {
    normal[0]= det2_(dY(2,0), dZ(2,0),
                     dY(1,0), dZ(1,0));
    normal[1]= det2_(dX(1,0), dZ(1,0),
                     dX(2,0), dZ(2,0));
    normal[2]= det2_(dX(2,0), dY(2,0),
                     dX(1,0), dY(1,0));
    qh_normalize2 (normal, dim, toporient, NULL, NULL);
    *offset= -(point0[0]*normal[0] + point0[1]*normal[1]
               + point0[2]*normal[2]);
    maxround= qh DISTround;
    for (i=dim; i--; ) {
      point= rows[i];
      if (point != point0) {
        dist= *offset + (point[0]*normal[0] + point[1]*normal[1]
               + point[2]*normal[2]);
        if (dist > maxround || dist < -maxround) {
          *nearzero= True;
          break;
        }
      }
    }
  }else if (dim == 4) {
    normal[0]= - det3_(dY(2,0), dZ(2,0), dW(2,0),
                        dY(1,0), dZ(1,0), dW(1,0),
                        dY(3,0), dZ(3,0), dW(3,0));
    normal[1]=   det3_(dX(2,0), dZ(2,0), dW(2,0),
                        dX(1,0), dZ(1,0), dW(1,0),
                        dX(3,0), dZ(3,0), dW(3,0));
    normal[2]= - det3_(dX(2,0), dY(2,0), dW(2,0),
                        dX(1,0), dY(1,0), dW(1,0),
                        dX(3,0), dY(3,0), dW(3,0));
    normal[3]=   det3_(dX(2,0), dY(2,0), dZ(2,0),
                        dX(1,0), dY(1,0), dZ(1,0),
                        dX(3,0), dY(3,0), dZ(3,0));
    qh_normalize2 (normal, dim, toporient, NULL, NULL);
    *offset= -(point0[0]*normal[0] + point0[1]*normal[1]
               + point0[2]*normal[2] + point0[3]*normal[3]);
    maxround= qh DISTround;
    for (i=dim; i--; ) {
      point= rows[i];
      if (point != point0) {
        dist= *offset + (point[0]*normal[0] + point[1]*normal[1]
               + point[2]*normal[2] + point[3]*normal[3]);
        if (dist > maxround || dist < -maxround) {
          *nearzero= True;
          break;
        }
      }
    }
  }
  if (*nearzero) {
    zzinc_(Zminnorm);
    trace0((qh ferr, 3, "qh_sethyperplane_det: degenerate norm during p%d.\n", qh furthest_id));
    zzinc_(Znearlysingular);
  }
} /* sethyperplane_det */


/*---------------------------------

  qh_sethyperplane_gauss( dim, rows, point0, toporient, normal, offset, nearzero )
    given(dim-1) X dim array of rows[i]= V_{i+1} - V_0 (point0)
    set normalized hyperplane equation from oriented simplex

  returns:
    normal (normalized)
    offset (places point0 on the hyperplane)

  notes:
    if nearzero
      orientation may be incorrect because of incorrect sign flips in gausselim
    solves [V_n-V_0,...,V_1-V_0, 0 .. 0 1] * N == [0 .. 0 1]
        or [V_n-V_0,...,V_1-V_0, 0 .. 0 1] * N == [0]
    i.e., N is normal to the hyperplane, and the unnormalized
        distance to [0 .. 1] is either 1 or   0

  design:
    perform gaussian elimination
    flip sign for negative values
    perform back substitution
    normalize result
    compute offset
*/
void qh_sethyperplane_gauss(int dim, coordT **rows, pointT *point0,
                boolT toporient, coordT *normal, coordT *offset, boolT *nearzero) {
  coordT *pointcoord, *normalcoef;
  int k;
  boolT sign= toporient, nearzero2= False;

  qh_gausselim(rows, dim-1, dim, &sign, nearzero);
  for (k=dim-1; k--; ) {
    if ((rows[k])[k] < 0)
      sign ^= 1;
  }
  if (*nearzero) {
    zzinc_(Znearlysingular);
    trace0((qh ferr, 4, "qh_sethyperplane_gauss: nearly singular or axis parallel hyperplane during p%d.\n", qh furthest_id));
    qh_backnormal(rows, dim-1, dim, sign, normal, &nearzero2);
  }else {
    qh_backnormal(rows, dim-1, dim, sign, normal, &nearzero2);
    if (nearzero2) {
      zzinc_(Znearlysingular);
      trace0((qh ferr, 5, "qh_sethyperplane_gauss: singular or axis parallel hyperplane at normalization during p%d.\n", qh furthest_id));
    }
  }
  if (nearzero2)
    *nearzero= True;
  qh_normalize2(normal, dim, True, NULL, NULL);
  pointcoord= point0;
  normalcoef= normal;
  *offset= -(*pointcoord++ * *normalcoef++);
  for (k=dim-1; k--; )
    *offset -= *pointcoord++ * *normalcoef++;
} /* sethyperplane_gauss */



qhull-2012.1/src/libqhull/geom.h0000644000076400010400000001603111710144466017614 0ustar  bbarberAdministrators/*
  ---------------------------------

  geom.h
    header file for geometric routines

   see qh-geom.htm and geom.c

   Copyright (c) 1993-2012 The Geometry Center.
   $Id: //main/2011/qhull/src/libqhull/geom.h#3 $$Change: 1464 $
   $DateTime: 2012/01/25 22:58:41 $$Author: bbarber $
*/

#ifndef qhDEFgeom
#define qhDEFgeom 1

#include "libqhull.h"

/* ============ -macros- ======================== */

/*----------------------------------

  fabs_(a)
    returns the absolute value of a
*/
#define fabs_( a ) ((( a ) < 0 ) ? -( a ):( a ))

/*----------------------------------

  fmax_(a,b)
    returns the maximum value of a and b
*/
#define fmax_( a,b )  ( ( a ) < ( b ) ? ( b ) : ( a ) )

/*----------------------------------

  fmin_(a,b)
    returns the minimum value of a and b
*/
#define fmin_( a,b )  ( ( a ) > ( b ) ? ( b ) : ( a ) )

/*----------------------------------

  maximize_(maxval, val)
    set maxval to val if val is greater than maxval
*/
#define maximize_( maxval, val ) { if (( maxval ) < ( val )) ( maxval )= ( val ); }

/*----------------------------------

  minimize_(minval, val)
    set minval to val if val is less than minval
*/
#define minimize_( minval, val ) { if (( minval ) > ( val )) ( minval )= ( val ); }

/*----------------------------------

  det2_(a1, a2,
        b1, b2)

    compute a 2-d determinate
*/
#define det2_( a1,a2,b1,b2 ) (( a1 )*( b2 ) - ( a2 )*( b1 ))

/*----------------------------------

  det3_(a1, a2, a3,
       b1, b2, b3,
       c1, c2, c3)

    compute a 3-d determinate
*/
#define det3_( a1,a2,a3,b1,b2,b3,c1,c2,c3 ) ( ( a1 )*det2_( b2,b3,c2,c3 ) \
                - ( b1 )*det2_( a2,a3,c2,c3 ) + ( c1 )*det2_( a2,a3,b2,b3 ) )

/*----------------------------------

  dX( p1, p2 )
  dY( p1, p2 )
  dZ( p1, p2 )

    given two indices into rows[],

    compute the difference between X, Y, or Z coordinates
*/
#define dX( p1,p2 )  ( *( rows[p1] ) - *( rows[p2] ))
#define dY( p1,p2 )  ( *( rows[p1]+1 ) - *( rows[p2]+1 ))
#define dZ( p1,p2 )  ( *( rows[p1]+2 ) - *( rows[p2]+2 ))
#define dW( p1,p2 )  ( *( rows[p1]+3 ) - *( rows[p2]+3 ))

/*============= prototypes in alphabetical order, infrequent at end ======= */

void    qh_backnormal(realT **rows, int numrow, int numcol, boolT sign, coordT *normal, boolT *nearzero);
void    qh_distplane(pointT *point, facetT *facet, realT *dist);
facetT *qh_findbest(pointT *point, facetT *startfacet,
                     boolT bestoutside, boolT isnewfacets, boolT noupper,
                     realT *dist, boolT *isoutside, int *numpart);
facetT *qh_findbesthorizon(boolT ischeckmax, pointT *point,
                     facetT *startfacet, boolT noupper, realT *bestdist, int *numpart);
facetT *qh_findbestnew(pointT *point, facetT *startfacet, realT *dist,
                     boolT bestoutside, boolT *isoutside, int *numpart);
void    qh_gausselim(realT **rows, int numrow, int numcol, boolT *sign, boolT *nearzero);
realT   qh_getangle(pointT *vect1, pointT *vect2);
pointT *qh_getcenter(setT *vertices);
pointT *qh_getcentrum(facetT *facet);
realT   qh_getdistance(facetT *facet, facetT *neighbor, realT *mindist, realT *maxdist);
void    qh_normalize(coordT *normal, int dim, boolT toporient);
void    qh_normalize2 (coordT *normal, int dim, boolT toporient,
            realT *minnorm, boolT *ismin);
pointT *qh_projectpoint(pointT *point, facetT *facet, realT dist);

void    qh_setfacetplane(facetT *newfacets);
void    qh_sethyperplane_det(int dim, coordT **rows, coordT *point0,
              boolT toporient, coordT *normal, realT *offset, boolT *nearzero);
void    qh_sethyperplane_gauss(int dim, coordT **rows, pointT *point0,
             boolT toporient, coordT *normal, coordT *offset, boolT *nearzero);
boolT   qh_sharpnewfacets(void);

/*========= infrequently used code in geom2.c =============*/

coordT *qh_copypoints(coordT *points, int numpoints, int dimension);
void    qh_crossproduct(int dim, realT vecA[3], realT vecB[3], realT vecC[3]);
realT   qh_determinant(realT **rows, int dim, boolT *nearzero);
realT   qh_detjoggle(pointT *points, int numpoints, int dimension);
void    qh_detroundoff(void);
realT   qh_detsimplex(pointT *apex, setT *points, int dim, boolT *nearzero);
realT   qh_distnorm(int dim, pointT *point, pointT *normal, realT *offsetp);
realT   qh_distround(int dimension, realT maxabs, realT maxsumabs);
realT   qh_divzero(realT numer, realT denom, realT mindenom1, boolT *zerodiv);
realT   qh_facetarea(facetT *facet);
realT   qh_facetarea_simplex(int dim, coordT *apex, setT *vertices,
          vertexT *notvertex,  boolT toporient, coordT *normal, realT *offset);
pointT *qh_facetcenter(setT *vertices);
facetT *qh_findgooddist(pointT *point, facetT *facetA, realT *distp, facetT **facetlist);
void    qh_getarea(facetT *facetlist);
boolT   qh_gram_schmidt(int dim, realT **rows);
boolT   qh_inthresholds(coordT *normal, realT *angle);
void    qh_joggleinput(void);
realT  *qh_maxabsval(realT *normal, int dim);
setT   *qh_maxmin(pointT *points, int numpoints, int dimension);
realT   qh_maxouter(void);
void    qh_maxsimplex(int dim, setT *maxpoints, pointT *points, int numpoints, setT **simplex);
realT   qh_minabsval(realT *normal, int dim);
int     qh_mindiff(realT *vecA, realT *vecB, int dim);
boolT   qh_orientoutside(facetT *facet);
void    qh_outerinner(facetT *facet, realT *outerplane, realT *innerplane);
coordT  qh_pointdist(pointT *point1, pointT *point2, int dim);
void    qh_printmatrix(FILE *fp, const char *string, realT **rows, int numrow, int numcol);
void    qh_printpoints(FILE *fp, const char *string, setT *points);
void    qh_projectinput(void);
void    qh_projectpoints(signed char *project, int n, realT *points,
             int numpoints, int dim, realT *newpoints, int newdim);
void    qh_rotateinput(realT **rows);
void    qh_rotatepoints(realT *points, int numpoints, int dim, realT **rows);
void    qh_scaleinput(void);
void    qh_scalelast(coordT *points, int numpoints, int dim, coordT low,
                   coordT high, coordT newhigh);
void    qh_scalepoints(pointT *points, int numpoints, int dim,
                realT *newlows, realT *newhighs);
boolT   qh_sethalfspace(int dim, coordT *coords, coordT **nextp,
              coordT *normal, coordT *offset, coordT *feasible);
coordT *qh_sethalfspace_all(int dim, int count, coordT *halfspaces, pointT *feasible);
pointT *qh_voronoi_center(int dim, setT *points);

#endif /* qhDEFgeom */



qhull-2012.1/src/libqhull/geom2.c0000644000076400010400000020002311710144466017665 0ustar  bbarberAdministrators/*
  ---------------------------------


   geom2.c
   infrequently used geometric routines of qhull

   see qh-geom.htm and geom.h

   Copyright (c) 1993-2012 The Geometry Center.
   $Id: //main/2011/qhull/src/libqhull/geom2.c#3 $$Change: 1464 $
   $DateTime: 2012/01/25 22:58:41 $$Author: bbarber $

   frequently used code goes into geom.c
*/

#include "qhull_a.h"

/*================== functions in alphabetic order ============*/

/*---------------------------------

  qh_copypoints( points, numpoints, dimension)
    return qh_malloc'd copy of points
*/
coordT *qh_copypoints(coordT *points, int numpoints, int dimension) {
  int size;
  coordT *newpoints;

  size= numpoints * dimension * (int)sizeof(coordT);
  if (!(newpoints=(coordT*)qh_malloc((size_t)size))) {
    qh_fprintf(qh ferr, 6004, "qhull error: insufficient memory to copy %d points\n",
        numpoints);
    qh_errexit(qh_ERRmem, NULL, NULL);
  }
  memcpy((char *)newpoints, (char *)points, (size_t)size);
  return newpoints;
} /* copypoints */

/*---------------------------------

  qh_crossproduct( dim, vecA, vecB, vecC )
    crossproduct of 2 dim vectors
    C= A x B

  notes:
    from Glasner, Graphics Gems I, p. 639
    only defined for dim==3
*/
void qh_crossproduct(int dim, realT vecA[3], realT vecB[3], realT vecC[3]){

  if (dim == 3) {
    vecC[0]=   det2_(vecA[1], vecA[2],
                     vecB[1], vecB[2]);
    vecC[1]= - det2_(vecA[0], vecA[2],
                     vecB[0], vecB[2]);
    vecC[2]=   det2_(vecA[0], vecA[1],
                     vecB[0], vecB[1]);
  }
} /* vcross */

/*---------------------------------

  qh_determinant( rows, dim, nearzero )
    compute signed determinant of a square matrix
    uses qh.NEARzero to test for degenerate matrices

  returns:
    determinant
    overwrites rows and the matrix
    if dim == 2 or 3
      nearzero iff determinant < qh NEARzero[dim-1]
      (!quite correct, not critical)
    if dim >= 4
      nearzero iff diagonal[k] < qh NEARzero[k]
*/
realT qh_determinant(realT **rows, int dim, boolT *nearzero) {
  realT det=0;
  int i;
  boolT sign= False;

  *nearzero= False;
  if (dim < 2) {
    qh_fprintf(qh ferr, 6005, "qhull internal error (qh_determinate): only implemented for dimension >= 2\n");
    qh_errexit(qh_ERRqhull, NULL, NULL);
  }else if (dim == 2) {
    det= det2_(rows[0][0], rows[0][1],
                 rows[1][0], rows[1][1]);
    if (fabs_(det) < qh NEARzero[1])  /* not really correct, what should this be? */
      *nearzero= True;
  }else if (dim == 3) {
    det= det3_(rows[0][0], rows[0][1], rows[0][2],
                 rows[1][0], rows[1][1], rows[1][2],
                 rows[2][0], rows[2][1], rows[2][2]);
    if (fabs_(det) < qh NEARzero[2])  /* not really correct, what should this be? */
      *nearzero= True;
  }else {
    qh_gausselim(rows, dim, dim, &sign, nearzero);  /* if nearzero, diagonal still ok*/
    det= 1.0;
    for (i=dim; i--; )
      det *= (rows[i])[i];
    if (sign)
      det= -det;
  }
  return det;
} /* determinant */

/*---------------------------------

  qh_detjoggle( points, numpoints, dimension )
    determine default max joggle for point array
      as qh_distround * qh_JOGGLEdefault

  returns:
    initial value for JOGGLEmax from points and REALepsilon

  notes:
    computes DISTround since qh_maxmin not called yet
    if qh SCALElast, last dimension will be scaled later to MAXwidth

    loop duplicated from qh_maxmin
*/
realT qh_detjoggle(pointT *points, int numpoints, int dimension) {
  realT abscoord, distround, joggle, maxcoord, mincoord;
  pointT *point, *pointtemp;
  realT maxabs= -REALmax;
  realT sumabs= 0;
  realT maxwidth= 0;
  int k;

  for (k=0; k < dimension; k++) {
    if (qh SCALElast && k == dimension-1)
      abscoord= maxwidth;
    else if (qh DELAUNAY && k == dimension-1) /* will qh_setdelaunay() */
      abscoord= 2 * maxabs * maxabs;  /* may be low by qh hull_dim/2 */
    else {
      maxcoord= -REALmax;
      mincoord= REALmax;
      FORALLpoint_(points, numpoints) {
        maximize_(maxcoord, point[k]);
        minimize_(mincoord, point[k]);
      }
      maximize_(maxwidth, maxcoord-mincoord);
      abscoord= fmax_(maxcoord, -mincoord);
    }
    sumabs += abscoord;
    maximize_(maxabs, abscoord);
  } /* for k */
  distround= qh_distround(qh hull_dim, maxabs, sumabs);
  joggle= distround * qh_JOGGLEdefault;
  maximize_(joggle, REALepsilon * qh_JOGGLEdefault);
  trace2((qh ferr, 2001, "qh_detjoggle: joggle=%2.2g maxwidth=%2.2g\n", joggle, maxwidth));
  return joggle;
} /* detjoggle */

/*---------------------------------

  qh_detroundoff()
    determine maximum roundoff errors from
      REALepsilon, REALmax, REALmin, qh.hull_dim, qh.MAXabs_coord,
      qh.MAXsumcoord, qh.MAXwidth, qh.MINdenom_1

    accounts for qh.SETroundoff, qh.RANDOMdist, qh MERGEexact
      qh.premerge_cos, qh.postmerge_cos, qh.premerge_centrum,
      qh.postmerge_centrum, qh.MINoutside,
      qh_RATIOnearinside, qh_COPLANARratio, qh_WIDEcoplanar

  returns:
    sets qh.DISTround, etc. (see below)
    appends precision constants to qh.qhull_options

  see:
    qh_maxmin() for qh.NEARzero

  design:
    determine qh.DISTround for distance computations
    determine minimum denominators for qh_divzero
    determine qh.ANGLEround for angle computations
    adjust qh.premerge_cos,... for roundoff error
    determine qh.ONEmerge for maximum error due to a single merge
    determine qh.NEARinside, qh.MAXcoplanar, qh.MINvisible,
      qh.MINoutside, qh.WIDEfacet
    initialize qh.max_vertex and qh.minvertex
*/
void qh_detroundoff(void) {

  qh_option("_max-width", NULL, &qh MAXwidth);
  if (!qh SETroundoff) {
    qh DISTround= qh_distround(qh hull_dim, qh MAXabs_coord, qh MAXsumcoord);
    if (qh RANDOMdist)
      qh DISTround += qh RANDOMfactor * qh MAXabs_coord;
    qh_option("Error-roundoff", NULL, &qh DISTround);
  }
  qh MINdenom= qh MINdenom_1 * qh MAXabs_coord;
  qh MINdenom_1_2= sqrt(qh MINdenom_1 * qh hull_dim) ;  /* if will be normalized */
  qh MINdenom_2= qh MINdenom_1_2 * qh MAXabs_coord;
                                              /* for inner product */
  qh ANGLEround= 1.01 * qh hull_dim * REALepsilon;
  if (qh RANDOMdist)
    qh ANGLEround += qh RANDOMfactor;
  if (qh premerge_cos < REALmax/2) {
    qh premerge_cos -= qh ANGLEround;
    if (qh RANDOMdist)
      qh_option("Angle-premerge-with-random", NULL, &qh premerge_cos);
  }
  if (qh postmerge_cos < REALmax/2) {
    qh postmerge_cos -= qh ANGLEround;
    if (qh RANDOMdist)
      qh_option("Angle-postmerge-with-random", NULL, &qh postmerge_cos);
  }
  qh premerge_centrum += 2 * qh DISTround;    /*2 for centrum and distplane()*/
  qh postmerge_centrum += 2 * qh DISTround;
  if (qh RANDOMdist && (qh MERGEexact || qh PREmerge))
    qh_option("Centrum-premerge-with-random", NULL, &qh premerge_centrum);
  if (qh RANDOMdist && qh POSTmerge)
    qh_option("Centrum-postmerge-with-random", NULL, &qh postmerge_centrum);
  { /* compute ONEmerge, max vertex offset for merging simplicial facets */
    realT maxangle= 1.0, maxrho;

    minimize_(maxangle, qh premerge_cos);
    minimize_(maxangle, qh postmerge_cos);
    /* max diameter * sin theta + DISTround for vertex to its hyperplane */
    qh ONEmerge= sqrt((realT)qh hull_dim) * qh MAXwidth *
      sqrt(1.0 - maxangle * maxangle) + qh DISTround;
    maxrho= qh hull_dim * qh premerge_centrum + qh DISTround;
    maximize_(qh ONEmerge, maxrho);
    maxrho= qh hull_dim * qh postmerge_centrum + qh DISTround;
    maximize_(qh ONEmerge, maxrho);
    if (qh MERGING)
      qh_option("_one-merge", NULL, &qh ONEmerge);
  }
  qh NEARinside= qh ONEmerge * qh_RATIOnearinside; /* only used if qh KEEPnearinside */
  if (qh JOGGLEmax < REALmax/2 && (qh KEEPcoplanar || qh KEEPinside)) {
    realT maxdist;             /* adjust qh.NEARinside for joggle */
    qh KEEPnearinside= True;
    maxdist= sqrt((realT)qh hull_dim) * qh JOGGLEmax + qh DISTround;
    maxdist= 2*maxdist;        /* vertex and coplanar point can joggle in opposite directions */
    maximize_(qh NEARinside, maxdist);  /* must agree with qh_nearcoplanar() */
  }
  if (qh KEEPnearinside)
    qh_option("_near-inside", NULL, &qh NEARinside);
  if (qh JOGGLEmax < qh DISTround) {
    qh_fprintf(qh ferr, 6006, "qhull error: the joggle for 'QJn', %.2g, is below roundoff for distance computations, %.2g\n",
         qh JOGGLEmax, qh DISTround);
    qh_errexit(qh_ERRinput, NULL, NULL);
  }
  if (qh MINvisible > REALmax/2) {
    if (!qh MERGING)
      qh MINvisible= qh DISTround;
    else if (qh hull_dim <= 3)
      qh MINvisible= qh premerge_centrum;
    else
      qh MINvisible= qh_COPLANARratio * qh premerge_centrum;
    if (qh APPROXhull && qh MINvisible > qh MINoutside)
      qh MINvisible= qh MINoutside;
    qh_option("Visible-distance", NULL, &qh MINvisible);
  }
  if (qh MAXcoplanar > REALmax/2) {
    qh MAXcoplanar= qh MINvisible;
    qh_option("U-coplanar-distance", NULL, &qh MAXcoplanar);
  }
  if (!qh APPROXhull) {             /* user may specify qh MINoutside */
    qh MINoutside= 2 * qh MINvisible;
    if (qh premerge_cos < REALmax/2)
      maximize_(qh MINoutside, (1- qh premerge_cos) * qh MAXabs_coord);
    qh_option("Width-outside", NULL, &qh MINoutside);
  }
  qh WIDEfacet= qh MINoutside;
  maximize_(qh WIDEfacet, qh_WIDEcoplanar * qh MAXcoplanar);
  maximize_(qh WIDEfacet, qh_WIDEcoplanar * qh MINvisible);
  qh_option("_wide-facet", NULL, &qh WIDEfacet);
  if (qh MINvisible > qh MINoutside + 3 * REALepsilon
  && !qh BESToutside && !qh FORCEoutput)
    qh_fprintf(qh ferr, 7001, "qhull input warning: minimum visibility V%.2g is greater than \nminimum outside W%.2g.  Flipped facets are likely.\n",
             qh MINvisible, qh MINoutside);
  qh max_vertex= qh DISTround;
  qh min_vertex= -qh DISTround;
  /* numeric constants reported in printsummary */
} /* detroundoff */

/*---------------------------------

  qh_detsimplex( apex, points, dim, nearzero )
    compute determinant of a simplex with point apex and base points

  returns:
     signed determinant and nearzero from qh_determinant

  notes:
     uses qh.gm_matrix/qh.gm_row (assumes they're big enough)

  design:
    construct qm_matrix by subtracting apex from points
    compute determinate
*/
realT qh_detsimplex(pointT *apex, setT *points, int dim, boolT *nearzero) {
  pointT *coorda, *coordp, *gmcoord, *point, **pointp;
  coordT **rows;
  int k,  i=0;
  realT det;

  zinc_(Zdetsimplex);
  gmcoord= qh gm_matrix;
  rows= qh gm_row;
  FOREACHpoint_(points) {
    if (i == dim)
      break;
    rows[i++]= gmcoord;
    coordp= point;
    coorda= apex;
    for (k=dim; k--; )
      *(gmcoord++)= *coordp++ - *coorda++;
  }
  if (i < dim) {
    qh_fprintf(qh ferr, 6007, "qhull internal error (qh_detsimplex): #points %d < dimension %d\n",
               i, dim);
    qh_errexit(qh_ERRqhull, NULL, NULL);
  }
  det= qh_determinant(rows, dim, nearzero);
  trace2((qh ferr, 2002, "qh_detsimplex: det=%2.2g for point p%d, dim %d, nearzero? %d\n",
          det, qh_pointid(apex), dim, *nearzero));
  return det;
} /* detsimplex */

/*---------------------------------

  qh_distnorm( dim, point, normal, offset )
    return distance from point to hyperplane at normal/offset

  returns:
    dist

  notes:
    dist > 0 if point is outside of hyperplane

  see:
    qh_distplane in geom.c
*/
realT qh_distnorm(int dim, pointT *point, pointT *normal, realT *offsetp) {
  coordT *normalp= normal, *coordp= point;
  realT dist;
  int k;

  dist= *offsetp;
  for (k=dim; k--; )
    dist += *(coordp++) * *(normalp++);
  return dist;
} /* distnorm */

/*---------------------------------

  qh_distround(dimension, maxabs, maxsumabs )
    compute maximum round-off error for a distance computation
      to a normalized hyperplane
    maxabs is the maximum absolute value of a coordinate
    maxsumabs is the maximum possible sum of absolute coordinate values

  returns:
    max dist round for REALepsilon

  notes:
    calculate roundoff error according to
    Lemma 3.2-1 of Golub and van Loan "Matrix Computation"
    use sqrt(dim) since one vector is normalized
      or use maxsumabs since one vector is < 1
*/
realT qh_distround(int dimension, realT maxabs, realT maxsumabs) {
  realT maxdistsum, maxround;

  maxdistsum= sqrt((realT)dimension) * maxabs;
  minimize_( maxdistsum, maxsumabs);
  maxround= REALepsilon * (dimension * maxdistsum * 1.01 + maxabs);
              /* adds maxabs for offset */
  trace4((qh ferr, 4008, "qh_distround: %2.2g maxabs %2.2g maxsumabs %2.2g maxdistsum %2.2g\n",
                 maxround, maxabs, maxsumabs, maxdistsum));
  return maxround;
} /* distround */

/*---------------------------------

  qh_divzero( numer, denom, mindenom1, zerodiv )
    divide by a number that's nearly zero
    mindenom1= minimum denominator for dividing into 1.0

  returns:
    quotient
    sets zerodiv and returns 0.0 if it would overflow

  design:
    if numer is nearly zero and abs(numer) < abs(denom)
      return numer/denom
    else if numer is nearly zero
      return 0 and zerodiv
    else if denom/numer non-zero
      return numer/denom
    else
      return 0 and zerodiv
*/
realT qh_divzero(realT numer, realT denom, realT mindenom1, boolT *zerodiv) {
  realT temp, numerx, denomx;


  if (numer < mindenom1 && numer > -mindenom1) {
    numerx= fabs_(numer);
    denomx= fabs_(denom);
    if (numerx < denomx) {
      *zerodiv= False;
      return numer/denom;
    }else {
      *zerodiv= True;
      return 0.0;
    }
  }
  temp= denom/numer;
  if (temp > mindenom1 || temp < -mindenom1) {
    *zerodiv= False;
    return numer/denom;
  }else {
    *zerodiv= True;
    return 0.0;
  }
} /* divzero */


/*---------------------------------

  qh_facetarea( facet )
    return area for a facet

  notes:
    if non-simplicial,
      uses centrum to triangulate facet and sums the projected areas.
    if (qh DELAUNAY),
      computes projected area instead for last coordinate
    assumes facet->normal exists
    projecting tricoplanar facets to the hyperplane does not appear to make a difference

  design:
    if simplicial
      compute area
    else
      for each ridge
        compute area from centrum to ridge
    negate area if upper Delaunay facet
*/
realT qh_facetarea(facetT *facet) {
  vertexT *apex;
  pointT *centrum;
  realT area= 0.0;
  ridgeT *ridge, **ridgep;

  if (facet->simplicial) {
    apex= SETfirstt_(facet->vertices, vertexT);
    area= qh_facetarea_simplex(qh hull_dim, apex->point, facet->vertices,
                    apex, facet->toporient, facet->normal, &facet->offset);
  }else {
    if (qh CENTERtype == qh_AScentrum)
      centrum= facet->center;
    else
      centrum= qh_getcentrum(facet);
    FOREACHridge_(facet->ridges)
      area += qh_facetarea_simplex(qh hull_dim, centrum, ridge->vertices,
                 NULL, (boolT)(ridge->top == facet),  facet->normal, &facet->offset);
    if (qh CENTERtype != qh_AScentrum)
      qh_memfree(centrum, qh normal_size);
  }
  if (facet->upperdelaunay && qh DELAUNAY)
    area= -area;  /* the normal should be [0,...,1] */
  trace4((qh ferr, 4009, "qh_facetarea: f%d area %2.2g\n", facet->id, area));
  return area;
} /* facetarea */

/*---------------------------------

  qh_facetarea_simplex( dim, apex, vertices, notvertex, toporient, normal, offset )
    return area for a simplex defined by
      an apex, a base of vertices, an orientation, and a unit normal
    if simplicial or tricoplanar facet,
      notvertex is defined and it is skipped in vertices

  returns:
    computes area of simplex projected to plane [normal,offset]
    returns 0 if vertex too far below plane (qh WIDEfacet)
      vertex can't be apex of tricoplanar facet

  notes:
    if (qh DELAUNAY),
      computes projected area instead for last coordinate
    uses qh gm_matrix/gm_row and qh hull_dim
    helper function for qh_facetarea

  design:
    if Notvertex
      translate simplex to apex
    else
      project simplex to normal/offset
      translate simplex to apex
    if Delaunay
      set last row/column to 0 with -1 on diagonal
    else
      set last row to Normal
    compute determinate
    scale and flip sign for area
*/
realT qh_facetarea_simplex(int dim, coordT *apex, setT *vertices,
        vertexT *notvertex,  boolT toporient, coordT *normal, realT *offset) {
  pointT *coorda, *coordp, *gmcoord;
  coordT **rows, *normalp;
  int k,  i=0;
  realT area, dist;
  vertexT *vertex, **vertexp;
  boolT nearzero;

  gmcoord= qh gm_matrix;
  rows= qh gm_row;
  FOREACHvertex_(vertices) {
    if (vertex == notvertex)
      continue;
    rows[i++]= gmcoord;
    coorda= apex;
    coordp= vertex->point;
    normalp= normal;
    if (notvertex) {
      for (k=dim; k--; )
        *(gmcoord++)= *coordp++ - *coorda++;
    }else {
      dist= *offset;
      for (k=dim; k--; )
        dist += *coordp++ * *normalp++;
      if (dist < -qh WIDEfacet) {
        zinc_(Znoarea);
        return 0.0;
      }
      coordp= vertex->point;
      normalp= normal;
      for (k=dim; k--; )
        *(gmcoord++)= (*coordp++ - dist * *normalp++) - *coorda++;
    }
  }
  if (i != dim-1) {
    qh_fprintf(qh ferr, 6008, "qhull internal error (qh_facetarea_simplex): #points %d != dim %d -1\n",
               i, dim);
    qh_errexit(qh_ERRqhull, NULL, NULL);
  }
  rows[i]= gmcoord;
  if (qh DELAUNAY) {
    for (i=0; i < dim-1; i++)
      rows[i][dim-1]= 0.0;
    for (k=dim; k--; )
      *(gmcoord++)= 0.0;
    rows[dim-1][dim-1]= -1.0;
  }else {
    normalp= normal;
    for (k=dim; k--; )
      *(gmcoord++)= *normalp++;
  }
  zinc_(Zdetsimplex);
  area= qh_determinant(rows, dim, &nearzero);
  if (toporient)
    area= -area;
  area *= qh AREAfactor;
  trace4((qh ferr, 4010, "qh_facetarea_simplex: area=%2.2g for point p%d, toporient %d, nearzero? %d\n",
          area, qh_pointid(apex), toporient, nearzero));
  return area;
} /* facetarea_simplex */

/*---------------------------------

  qh_facetcenter( vertices )
    return Voronoi center (Voronoi vertex) for a facet's vertices

  returns:
    return temporary point equal to the center

  see:
    qh_voronoi_center()
*/
pointT *qh_facetcenter(setT *vertices) {
  setT *points= qh_settemp(qh_setsize(vertices));
  vertexT *vertex, **vertexp;
  pointT *center;

  FOREACHvertex_(vertices)
    qh_setappend(&points, vertex->point);
  center= qh_voronoi_center(qh hull_dim-1, points);
  qh_settempfree(&points);
  return center;
} /* facetcenter */

/*---------------------------------

  qh_findgooddist( point, facetA, dist, facetlist )
    find best good facet visible for point from facetA
    assumes facetA is visible from point

  returns:
    best facet, i.e., good facet that is furthest from point
      distance to best facet
      NULL if none

    moves good, visible facets (and some other visible facets)
      to end of qh facet_list

  notes:
    uses qh visit_id

  design:
    initialize bestfacet if facetA is good
    move facetA to end of facetlist
    for each facet on facetlist
      for each unvisited neighbor of facet
        move visible neighbors to end of facetlist
        update best good neighbor
        if no good neighbors, update best facet
*/
facetT *qh_findgooddist(pointT *point, facetT *facetA, realT *distp,
               facetT **facetlist) {
  realT bestdist= -REALmax, dist;
  facetT *neighbor, **neighborp, *bestfacet=NULL, *facet;
  boolT goodseen= False;

  if (facetA->good) {
    zzinc_(Zcheckpart);  /* calls from check_bestdist occur after print stats */
    qh_distplane(point, facetA, &bestdist);
    bestfacet= facetA;
    goodseen= True;
  }
  qh_removefacet(facetA);
  qh_appendfacet(facetA);
  *facetlist= facetA;
  facetA->visitid= ++qh visit_id;
  FORALLfacet_(*facetlist) {
    FOREACHneighbor_(facet) {
      if (neighbor->visitid == qh visit_id)
        continue;
      neighbor->visitid= qh visit_id;
      if (goodseen && !neighbor->good)
        continue;
      zzinc_(Zcheckpart);
      qh_distplane(point, neighbor, &dist);
      if (dist > 0) {
        qh_removefacet(neighbor);
        qh_appendfacet(neighbor);
        if (neighbor->good) {
          goodseen= True;
          if (dist > bestdist) {
            bestdist= dist;
            bestfacet= neighbor;
          }
        }
      }
    }
  }
  if (bestfacet) {
    *distp= bestdist;
    trace2((qh ferr, 2003, "qh_findgooddist: p%d is %2.2g above good facet f%d\n",
      qh_pointid(point), bestdist, bestfacet->id));
    return bestfacet;
  }
  trace4((qh ferr, 4011, "qh_findgooddist: no good facet for p%d above f%d\n",
      qh_pointid(point), facetA->id));
  return NULL;
}  /* findgooddist */

/*---------------------------------

  qh_getarea( facetlist )
    set area of all facets in facetlist
    collect statistics
    nop if hasAreaVolume

  returns:
    sets qh totarea/totvol to total area and volume of convex hull
    for Delaunay triangulation, computes projected area of the lower or upper hull
      ignores upper hull if qh ATinfinity

  notes:
    could compute outer volume by expanding facet area by rays from interior
    the following attempt at perpendicular projection underestimated badly:
      qh.totoutvol += (-dist + facet->maxoutside + qh DISTround)
                            * area/ qh hull_dim;
  design:
    for each facet on facetlist
      compute facet->area
      update qh.totarea and qh.totvol
*/
void qh_getarea(facetT *facetlist) {
  realT area;
  realT dist;
  facetT *facet;

  if (qh hasAreaVolume)
    return;
  if (qh REPORTfreq)
    qh_fprintf(qh ferr, 8020, "computing area of each facet and volume of the convex hull\n");
  else
    trace1((qh ferr, 1001, "qh_getarea: computing volume and area for each facet\n"));
  qh totarea= qh totvol= 0.0;
  FORALLfacet_(facetlist) {
    if (!facet->normal)
      continue;
    if (facet->upperdelaunay && qh ATinfinity)
      continue;
    if (!facet->isarea) {
      facet->f.area= qh_facetarea(facet);
      facet->isarea= True;
    }
    area= facet->f.area;
    if (qh DELAUNAY) {
      if (facet->upperdelaunay == qh UPPERdelaunay)
        qh totarea += area;
    }else {
      qh totarea += area;
      qh_distplane(qh interior_point, facet, &dist);
      qh totvol += -dist * area/ qh hull_dim;
    }
    if (qh PRINTstatistics) {
      wadd_(Wareatot, area);
      wmax_(Wareamax, area);
      wmin_(Wareamin, area);
    }
  }
  qh hasAreaVolume= True;
} /* getarea */

/*---------------------------------

  qh_gram_schmidt( dim, row )
    implements Gram-Schmidt orthogonalization by rows

  returns:
    false if zero norm
    overwrites rows[dim][dim]

  notes:
    see Golub & van Loan Algorithm 6.2-2
    overflow due to small divisors not handled

  design:
    for each row
      compute norm for row
      if non-zero, normalize row
      for each remaining rowA
        compute inner product of row and rowA
        reduce rowA by row * inner product
*/
boolT qh_gram_schmidt(int dim, realT **row) {
  realT *rowi, *rowj, norm;
  int i, j, k;

  for (i=0; i < dim; i++) {
    rowi= row[i];
    for (norm= 0.0, k= dim; k--; rowi++)
      norm += *rowi * *rowi;
    norm= sqrt(norm);
    wmin_(Wmindenom, norm);
    if (norm == 0.0)  /* either 0 or overflow due to sqrt */
      return False;
    for (k=dim; k--; )
      *(--rowi) /= norm;
    for (j=i+1; j < dim; j++) {
      rowj= row[j];
      for (norm= 0.0, k=dim; k--; )
        norm += *rowi++ * *rowj++;
      for (k=dim; k--; )
        *(--rowj) -= *(--rowi) * norm;
    }
  }
  return True;
} /* gram_schmidt */


/*---------------------------------

  qh_inthresholds( normal, angle )
    return True if normal within qh.lower_/upper_threshold

  returns:
    estimate of angle by summing of threshold diffs
      angle may be NULL
      smaller "angle" is better

  notes:
    invalid if qh.SPLITthresholds

  see:
    qh.lower_threshold in qh_initbuild()
    qh_initthresholds()

  design:
    for each dimension
      test threshold
*/
boolT qh_inthresholds(coordT *normal, realT *angle) {
  boolT within= True;
  int k;
  realT threshold;

  if (angle)
    *angle= 0.0;
  for (k=0; k < qh hull_dim; k++) {
    threshold= qh lower_threshold[k];
    if (threshold > -REALmax/2) {
      if (normal[k] < threshold)
        within= False;
      if (angle) {
        threshold -= normal[k];
        *angle += fabs_(threshold);
      }
    }
    if (qh upper_threshold[k] < REALmax/2) {
      threshold= qh upper_threshold[k];
      if (normal[k] > threshold)
        within= False;
      if (angle) {
        threshold -= normal[k];
        *angle += fabs_(threshold);
      }
    }
  }
  return within;
} /* inthresholds */


/*---------------------------------

  qh_joggleinput()
    randomly joggle input to Qhull by qh.JOGGLEmax
    initial input is qh.first_point/qh.num_points of qh.hull_dim
      repeated calls use qh.input_points/qh.num_points

  returns:
    joggles points at qh.first_point/qh.num_points
    copies data to qh.input_points/qh.input_malloc if first time
    determines qh.JOGGLEmax if it was zero
    if qh.DELAUNAY
      computes the Delaunay projection of the joggled points

  notes:
    if qh.DELAUNAY, unnecessarily joggles the last coordinate
    the initial 'QJn' may be set larger than qh_JOGGLEmaxincrease

  design:
    if qh.DELAUNAY
      set qh.SCALElast for reduced precision errors
    if first call
      initialize qh.input_points to the original input points
      if qh.JOGGLEmax == 0
        determine default qh.JOGGLEmax
    else
      increase qh.JOGGLEmax according to qh.build_cnt
    joggle the input by adding a random number in [-qh.JOGGLEmax,qh.JOGGLEmax]
    if qh.DELAUNAY
      sets the Delaunay projection
*/
void qh_joggleinput(void) {
  int i, seed, size;
  coordT *coordp, *inputp;
  realT randr, randa, randb;

  if (!qh input_points) { /* first call */
    qh input_points= qh first_point;
    qh input_malloc= qh POINTSmalloc;
    size= qh num_points * qh hull_dim * sizeof(coordT);
    if (!(qh first_point=(coordT*)qh_malloc((size_t)size))) {
      qh_fprintf(qh ferr, 6009, "qhull error: insufficient memory to joggle %d points\n",
          qh num_points);
      qh_errexit(qh_ERRmem, NULL, NULL);
    }
    qh POINTSmalloc= True;
    if (qh JOGGLEmax == 0.0) {
      qh JOGGLEmax= qh_detjoggle(qh input_points, qh num_points, qh hull_dim);
      qh_option("QJoggle", NULL, &qh JOGGLEmax);
    }
  }else {                 /* repeated call */
    if (!qh RERUN && qh build_cnt > qh_JOGGLEretry) {
      if (((qh build_cnt-qh_JOGGLEretry-1) % qh_JOGGLEagain) == 0) {
        realT maxjoggle= qh MAXwidth * qh_JOGGLEmaxincrease;
        if (qh JOGGLEmax < maxjoggle) {
          qh JOGGLEmax *= qh_JOGGLEincrease;
          minimize_(qh JOGGLEmax, maxjoggle);
        }
      }
    }
    qh_option("QJoggle", NULL, &qh JOGGLEmax);
  }
  if (qh build_cnt > 1 && qh JOGGLEmax > fmax_(qh MAXwidth/4, 0.1)) {
      qh_fprintf(qh ferr, 6010, "qhull error: the current joggle for 'QJn', %.2g, is too large for the width\nof the input.  If possible, recompile Qhull with higher-precision reals.\n",
                qh JOGGLEmax);
      qh_errexit(qh_ERRqhull, NULL, NULL);
  }
  /* for some reason, using qh ROTATErandom and qh_RANDOMseed does not repeat the run. Use 'TRn' instead */
  seed= qh_RANDOMint;
  qh_option("_joggle-seed", &seed, NULL);
  trace0((qh ferr, 6, "qh_joggleinput: joggle input by %2.2g with seed %d\n",
    qh JOGGLEmax, seed));
  inputp= qh input_points;
  coordp= qh first_point;
  randa= 2.0 * qh JOGGLEmax/qh_RANDOMmax;
  randb= -qh JOGGLEmax;
  size= qh num_points * qh hull_dim;
  for (i=size; i--; ) {
    randr= qh_RANDOMint;
    *(coordp++)= *(inputp++) + (randr * randa + randb);
  }
  if (qh DELAUNAY) {
    qh last_low= qh last_high= qh last_newhigh= REALmax;
    qh_setdelaunay(qh hull_dim, qh num_points, qh first_point);
  }
} /* joggleinput */

/*---------------------------------

  qh_maxabsval( normal, dim )
    return pointer to maximum absolute value of a dim vector
    returns NULL if dim=0
*/
realT *qh_maxabsval(realT *normal, int dim) {
  realT maxval= -REALmax;
  realT *maxp= NULL, *colp, absval;
  int k;

  for (k=dim, colp= normal; k--; colp++) {
    absval= fabs_(*colp);
    if (absval > maxval) {
      maxval= absval;
      maxp= colp;
    }
  }
  return maxp;
} /* maxabsval */


/*---------------------------------

  qh_maxmin( points, numpoints, dimension )
    return max/min points for each dimension
    determine max and min coordinates

  returns:
    returns a temporary set of max and min points
      may include duplicate points. Does not include qh.GOODpoint
    sets qh.NEARzero, qh.MAXabs_coord, qh.MAXsumcoord, qh.MAXwidth
         qh.MAXlastcoord, qh.MINlastcoord
    initializes qh.max_outside, qh.min_vertex, qh.WAScoplanar, qh.ZEROall_ok

  notes:
    loop duplicated in qh_detjoggle()

  design:
    initialize global precision variables
    checks definition of REAL...
    for each dimension
      for each point
        collect maximum and minimum point
      collect maximum of maximums and minimum of minimums
      determine qh.NEARzero for Gaussian Elimination
*/
setT *qh_maxmin(pointT *points, int numpoints, int dimension) {
  int k;
  realT maxcoord, temp;
  pointT *minimum, *maximum, *point, *pointtemp;
  setT *set;

  qh max_outside= 0.0;
  qh MAXabs_coord= 0.0;
  qh MAXwidth= -REALmax;
  qh MAXsumcoord= 0.0;
  qh min_vertex= 0.0;
  qh WAScoplanar= False;
  if (qh ZEROcentrum)
    qh ZEROall_ok= True;
  if (REALmin < REALepsilon && REALmin < REALmax && REALmin > -REALmax
  && REALmax > 0.0 && -REALmax < 0.0)
    ; /* all ok */
  else {
    qh_fprintf(qh ferr, 6011, "qhull error: floating point constants in user.h are wrong\n\
REALepsilon %g REALmin %g REALmax %g -REALmax %g\n",
             REALepsilon, REALmin, REALmax, -REALmax);
    qh_errexit(qh_ERRinput, NULL, NULL);
  }
  set= qh_settemp(2*dimension);
  for (k=0; k < dimension; k++) {
    if (points == qh GOODpointp)
      minimum= maximum= points + dimension;
    else
      minimum= maximum= points;
    FORALLpoint_(points, numpoints) {
      if (point == qh GOODpointp)
        continue;
      if (maximum[k] < point[k])
        maximum= point;
      else if (minimum[k] > point[k])
        minimum= point;
    }
    if (k == dimension-1) {
      qh MINlastcoord= minimum[k];
      qh MAXlastcoord= maximum[k];
    }
    if (qh SCALElast && k == dimension-1)
      maxcoord= qh MAXwidth;
    else {
      maxcoord= fmax_(maximum[k], -minimum[k]);
      if (qh GOODpointp) {
        temp= fmax_(qh GOODpointp[k], -qh GOODpointp[k]);
        maximize_(maxcoord, temp);
      }
      temp= maximum[k] - minimum[k];
      maximize_(qh MAXwidth, temp);
    }
    maximize_(qh MAXabs_coord, maxcoord);
    qh MAXsumcoord += maxcoord;
    qh_setappend(&set, maximum);
    qh_setappend(&set, minimum);
    /* calculation of qh NEARzero is based on error formula 4.4-13 of
       Golub & van Loan, authors say n^3 can be ignored and 10 be used in
       place of rho */
    qh NEARzero[k]= 80 * qh MAXsumcoord * REALepsilon;
  }
  if (qh IStracing >=1)
    qh_printpoints(qh ferr, "qh_maxmin: found the max and min points(by dim):", set);
  return(set);
} /* maxmin */

/*---------------------------------

  qh_maxouter()
    return maximum distance from facet to outer plane
    normally this is qh.max_outside+qh.DISTround
    does not include qh.JOGGLEmax

  see:
    qh_outerinner()

  notes:
    need to add another qh.DISTround if testing actual point with computation

  for joggle:
    qh_setfacetplane() updated qh.max_outer for Wnewvertexmax (max distance to vertex)
    need to use Wnewvertexmax since could have a coplanar point for a high
      facet that is replaced by a low facet
    need to add qh.JOGGLEmax if testing input points
*/
realT qh_maxouter(void) {
  realT dist;

  dist= fmax_(qh max_outside, qh DISTround);
  dist += qh DISTround;
  trace4((qh ferr, 4012, "qh_maxouter: max distance from facet to outer plane is %2.2g max_outside is %2.2g\n", dist, qh max_outside));
  return dist;
} /* maxouter */

/*---------------------------------

  qh_maxsimplex( dim, maxpoints, points, numpoints, simplex )
    determines maximum simplex for a set of points
    starts from points already in simplex
    skips qh.GOODpointp (assumes that it isn't in maxpoints)

  returns:
    simplex with dim+1 points

  notes:
    assumes at least pointsneeded points in points
    maximizes determinate for x,y,z,w, etc.
    uses maxpoints as long as determinate is clearly non-zero

  design:
    initialize simplex with at least two points
      (find points with max or min x coordinate)
    for each remaining dimension
      add point that maximizes the determinate
        (use points from maxpoints first)
*/
void qh_maxsimplex(int dim, setT *maxpoints, pointT *points, int numpoints, setT **simplex) {
  pointT *point, **pointp, *pointtemp, *maxpoint, *minx=NULL, *maxx=NULL;
  boolT nearzero, maxnearzero= False;
  int k, sizinit;
  realT maxdet= -REALmax, det, mincoord= REALmax, maxcoord= -REALmax;

  sizinit= qh_setsize(*simplex);
  if (sizinit < 2) {
    if (qh_setsize(maxpoints) >= 2) {
      FOREACHpoint_(maxpoints) {
        if (maxcoord < point[0]) {
          maxcoord= point[0];
          maxx= point;
        }
        if (mincoord > point[0]) {
          mincoord= point[0];
          minx= point;
        }
      }
    }else {
      FORALLpoint_(points, numpoints) {
        if (point == qh GOODpointp)
          continue;
        if (maxcoord < point[0]) {
          maxcoord= point[0];
          maxx= point;
        }
        if (mincoord > point[0]) {
          mincoord= point[0];
          minx= point;
        }
      }
    }
    qh_setunique(simplex, minx);
    if (qh_setsize(*simplex) < 2)
      qh_setunique(simplex, maxx);
    sizinit= qh_setsize(*simplex);
    if (sizinit < 2) {
      qh_precision("input has same x coordinate");
      if (zzval_(Zsetplane) > qh hull_dim+1) {
        qh_fprintf(qh ferr, 6012, "qhull precision error (qh_maxsimplex for voronoi_center):\n%d points with the same x coordinate.\n",
                 qh_setsize(maxpoints)+numpoints);
        qh_errexit(qh_ERRprec, NULL, NULL);
      }else {
        qh_fprintf(qh ferr, 6013, "qhull input error: input is less than %d-dimensional since it has the same x coordinate\n", qh hull_dim);
        qh_errexit(qh_ERRinput, NULL, NULL);
      }
    }
  }
  for (k=sizinit; k < dim+1; k++) {
    maxpoint= NULL;
    maxdet= -REALmax;
    FOREACHpoint_(maxpoints) {
      if (!qh_setin(*simplex, point)) {
        det= qh_detsimplex(point, *simplex, k, &nearzero);
        if ((det= fabs_(det)) > maxdet) {
          maxdet= det;
          maxpoint= point;
          maxnearzero= nearzero;
        }
      }
    }
    if (!maxpoint || maxnearzero) {
      zinc_(Zsearchpoints);
      if (!maxpoint) {
        trace0((qh ferr, 7, "qh_maxsimplex: searching all points for %d-th initial vertex.\n", k+1));
      }else {
        trace0((qh ferr, 8, "qh_maxsimplex: searching all points for %d-th initial vertex, better than p%d det %2.2g\n",
                k+1, qh_pointid(maxpoint), maxdet));
      }
      FORALLpoint_(points, numpoints) {
        if (point == qh GOODpointp)
          continue;
        if (!qh_setin(*simplex, point)) {
          det= qh_detsimplex(point, *simplex, k, &nearzero);
          if ((det= fabs_(det)) > maxdet) {
            maxdet= det;
            maxpoint= point;
            maxnearzero= nearzero;
          }
        }
      }
    } /* !maxpoint */
    if (!maxpoint) {
      qh_fprintf(qh ferr, 6014, "qhull internal error (qh_maxsimplex): not enough points available\n");
      qh_errexit(qh_ERRqhull, NULL, NULL);
    }
    qh_setappend(simplex, maxpoint);
    trace1((qh ferr, 1002, "qh_maxsimplex: selected point p%d for %d`th initial vertex, det=%2.2g\n",
            qh_pointid(maxpoint), k+1, maxdet));
  } /* k */
} /* maxsimplex */

/*---------------------------------

  qh_minabsval( normal, dim )
    return minimum absolute value of a dim vector
*/
realT qh_minabsval(realT *normal, int dim) {
  realT minval= 0;
  realT maxval= 0;
  realT *colp;
  int k;

  for (k=dim, colp=normal; k--; colp++) {
    maximize_(maxval, *colp);
    minimize_(minval, *colp);
  }
  return fmax_(maxval, -minval);
} /* minabsval */


/*---------------------------------

  qh_mindif ( vecA, vecB, dim )
    return index of min abs. difference of two vectors
*/
int qh_mindiff(realT *vecA, realT *vecB, int dim) {
  realT mindiff= REALmax, diff;
  realT *vecAp= vecA, *vecBp= vecB;
  int k, mink= 0;

  for (k=0; k < dim; k++) {
    diff= *vecAp++ - *vecBp++;
    diff= fabs_(diff);
    if (diff < mindiff) {
      mindiff= diff;
      mink= k;
    }
  }
  return mink;
} /* mindiff */



/*---------------------------------

  qh_orientoutside( facet  )
    make facet outside oriented via qh.interior_point

  returns:
    True if facet reversed orientation.
*/
boolT qh_orientoutside(facetT *facet) {
  int k;
  realT dist;

  qh_distplane(qh interior_point, facet, &dist);
  if (dist > 0) {
    for (k=qh hull_dim; k--; )
      facet->normal[k]= -facet->normal[k];
    facet->offset= -facet->offset;
    return True;
  }
  return False;
} /* orientoutside */

/*---------------------------------

  qh_outerinner( facet, outerplane, innerplane  )
    if facet and qh.maxoutdone (i.e., qh_check_maxout)
      returns outer and inner plane for facet
    else
      returns maximum outer and inner plane
    accounts for qh.JOGGLEmax

  see:
    qh_maxouter(), qh_check_bestdist(), qh_check_points()

  notes:
    outerplaner or innerplane may be NULL
    facet is const
    Does not error (QhullFacet)

    includes qh.DISTround for actual points
    adds another qh.DISTround if testing with floating point arithmetic
*/
void qh_outerinner(facetT *facet, realT *outerplane, realT *innerplane) {
  realT dist, mindist;
  vertexT *vertex, **vertexp;

  if (outerplane) {
    if (!qh_MAXoutside || !facet || !qh maxoutdone) {
      *outerplane= qh_maxouter();       /* includes qh.DISTround */
    }else { /* qh_MAXoutside ... */
#if qh_MAXoutside
      *outerplane= facet->maxoutside + qh DISTround;
#endif

    }
    if (qh JOGGLEmax < REALmax/2)
      *outerplane += qh JOGGLEmax * sqrt((realT)qh hull_dim);
  }
  if (innerplane) {
    if (facet) {
      mindist= REALmax;
      FOREACHvertex_(facet->vertices) {
        zinc_(Zdistio);
        qh_distplane(vertex->point, facet, &dist);
        minimize_(mindist, dist);
      }
      *innerplane= mindist - qh DISTround;
    }else
      *innerplane= qh min_vertex - qh DISTround;
    if (qh JOGGLEmax < REALmax/2)
      *innerplane -= qh JOGGLEmax * sqrt((realT)qh hull_dim);
  }
} /* outerinner */

/*---------------------------------

  qh_pointdist( point1, point2, dim )
    return distance between two points

  notes:
    returns distance squared if 'dim' is negative
*/
coordT qh_pointdist(pointT *point1, pointT *point2, int dim) {
  coordT dist, diff;
  int k;

  dist= 0.0;
  for (k= (dim > 0 ? dim : -dim); k--; ) {
    diff= *point1++ - *point2++;
    dist += diff * diff;
  }
  if (dim > 0)
    return(sqrt(dist));
  return dist;
} /* pointdist */


/*---------------------------------

  qh_printmatrix( fp, string, rows, numrow, numcol )
    print matrix to fp given by row vectors
    print string as header

  notes:
    print a vector by qh_printmatrix(fp, "", &vect, 1, len)
*/
void qh_printmatrix(FILE *fp, const char *string, realT **rows, int numrow, int numcol) {
  realT *rowp;
  realT r; /*bug fix*/
  int i,k;

  qh_fprintf(fp, 9001, "%s\n", string);
  for (i=0; i < numrow; i++) {
    rowp= rows[i];
    for (k=0; k < numcol; k++) {
      r= *rowp++;
      qh_fprintf(fp, 9002, "%6.3g ", r);
    }
    qh_fprintf(fp, 9003, "\n");
  }
} /* printmatrix */


/*---------------------------------

  qh_printpoints( fp, string, points )
    print pointids to fp for a set of points
    if string, prints string and 'p' point ids
*/
void qh_printpoints(FILE *fp, const char *string, setT *points) {
  pointT *point, **pointp;

  if (string) {
    qh_fprintf(fp, 9004, "%s", string);
    FOREACHpoint_(points)
      qh_fprintf(fp, 9005, " p%d", qh_pointid(point));
    qh_fprintf(fp, 9006, "\n");
  }else {
    FOREACHpoint_(points)
      qh_fprintf(fp, 9007, " %d", qh_pointid(point));
    qh_fprintf(fp, 9008, "\n");
  }
} /* printpoints */


/*---------------------------------

  qh_projectinput()
    project input points using qh.lower_bound/upper_bound and qh DELAUNAY
    if qh.lower_bound[k]=qh.upper_bound[k]= 0,
      removes dimension k
    if halfspace intersection
      removes dimension k from qh.feasible_point
    input points in qh first_point, num_points, input_dim

  returns:
    new point array in qh first_point of qh hull_dim coordinates
    sets qh POINTSmalloc
    if qh DELAUNAY
      projects points to paraboloid
      lowbound/highbound is also projected
    if qh ATinfinity
      adds point "at-infinity"
    if qh POINTSmalloc
      frees old point array

  notes:
    checks that qh.hull_dim agrees with qh.input_dim, PROJECTinput, and DELAUNAY


  design:
    sets project[k] to -1 (delete), 0 (keep), 1 (add for Delaunay)
    determines newdim and newnum for qh hull_dim and qh num_points
    projects points to newpoints
    projects qh.lower_bound to itself
    projects qh.upper_bound to itself
    if qh DELAUNAY
      if qh ATINFINITY
        projects points to paraboloid
        computes "infinity" point as vertex average and 10% above all points
      else
        uses qh_setdelaunay to project points to paraboloid
*/
void qh_projectinput(void) {
  int k,i;
  int newdim= qh input_dim, newnum= qh num_points;
  signed char *project;
  int size= (qh input_dim+1)*sizeof(*project);
  pointT *newpoints, *coord, *infinity;
  realT paraboloid, maxboloid= 0;

  project= (signed char*)qh_memalloc(size);
  memset((char*)project, 0, (size_t)size);
  for (k=0; k < qh input_dim; k++) {   /* skip Delaunay bound */
    if (qh lower_bound[k] == 0 && qh upper_bound[k] == 0) {
      project[k]= -1;
      newdim--;
    }
  }
  if (qh DELAUNAY) {
    project[k]= 1;
    newdim++;
    if (qh ATinfinity)
      newnum++;
  }
  if (newdim != qh hull_dim) {
    qh_fprintf(qh ferr, 6015, "qhull internal error (qh_projectinput): dimension after projection %d != hull_dim %d\n", newdim, qh hull_dim);
    qh_errexit(qh_ERRqhull, NULL, NULL);
  }
  if (!(newpoints=(coordT*)qh_malloc(newnum*newdim*sizeof(coordT)))){
    qh_fprintf(qh ferr, 6016, "qhull error: insufficient memory to project %d points\n",
           qh num_points);
    qh_errexit(qh_ERRmem, NULL, NULL);
  }
  qh_projectpoints(project, qh input_dim+1, qh first_point,
                    qh num_points, qh input_dim, newpoints, newdim);
  trace1((qh ferr, 1003, "qh_projectinput: updating lower and upper_bound\n"));
  qh_projectpoints(project, qh input_dim+1, qh lower_bound,
                    1, qh input_dim+1, qh lower_bound, newdim+1);
  qh_projectpoints(project, qh input_dim+1, qh upper_bound,
                    1, qh input_dim+1, qh upper_bound, newdim+1);
  if (qh HALFspace) {
    if (!qh feasible_point) {
      qh_fprintf(qh ferr, 6017, "qhull internal error (qh_projectinput): HALFspace defined without qh.feasible_point\n");
      qh_errexit(qh_ERRqhull, NULL, NULL);
    }
    qh_projectpoints(project, qh input_dim, qh feasible_point,
                      1, qh input_dim, qh feasible_point, newdim);
  }
  qh_memfree(project, (qh input_dim+1)*sizeof(*project));
  if (qh POINTSmalloc)
    qh_free(qh first_point);
  qh first_point= newpoints;
  qh POINTSmalloc= True;
  if (qh DELAUNAY && qh ATinfinity) {
    coord= qh first_point;
    infinity= qh first_point + qh hull_dim * qh num_points;
    for (k=qh hull_dim-1; k--; )
      infinity[k]= 0.0;
    for (i=qh num_points; i--; ) {
      paraboloid= 0.0;
      for (k=0; k < qh hull_dim-1; k++) {
        paraboloid += *coord * *coord;
        infinity[k] += *coord;
        coord++;
      }
      *(coord++)= paraboloid;
      maximize_(maxboloid, paraboloid);
    }
    /* coord == infinity */
    for (k=qh hull_dim-1; k--; )
      *(coord++) /= qh num_points;
    *(coord++)= maxboloid * 1.1;
    qh num_points++;
    trace0((qh ferr, 9, "qh_projectinput: projected points to paraboloid for Delaunay\n"));
  }else if (qh DELAUNAY)  /* !qh ATinfinity */
    qh_setdelaunay( qh hull_dim, qh num_points, qh first_point);
} /* projectinput */


/*---------------------------------

  qh_projectpoints( project, n, points, numpoints, dim, newpoints, newdim )
    project points/numpoints/dim to newpoints/newdim
    if project[k] == -1
      delete dimension k
    if project[k] == 1
      add dimension k by duplicating previous column
    n is size of project

  notes:
    newpoints may be points if only adding dimension at end

  design:
    check that 'project' and 'newdim' agree
    for each dimension
      if project == -1
        skip dimension
      else
        determine start of column in newpoints
        determine start of column in points
          if project == +1, duplicate previous column
        copy dimension (column) from points to newpoints
*/
void qh_projectpoints(signed char *project, int n, realT *points,
        int numpoints, int dim, realT *newpoints, int newdim) {
  int testdim= dim, oldk=0, newk=0, i,j=0,k;
  realT *newp, *oldp;

  for (k=0; k < n; k++)
    testdim += project[k];
  if (testdim != newdim) {
    qh_fprintf(qh ferr, 6018, "qhull internal error (qh_projectpoints): newdim %d should be %d after projection\n",
      newdim, testdim);
    qh_errexit(qh_ERRqhull, NULL, NULL);
  }
  for (j=0; j= dim)
          continue;
        oldp= points+oldk;
      }else
        oldp= points+oldk++;
      for (i=numpoints; i--; ) {
        *newp= *oldp;
        newp += newdim;
        oldp += dim;
      }
    }
    if (oldk >= dim)
      break;
  }
  trace1((qh ferr, 1004, "qh_projectpoints: projected %d points from dim %d to dim %d\n",
    numpoints, dim, newdim));
} /* projectpoints */


/*---------------------------------

  qh_rotateinput( rows )
    rotate input using row matrix
    input points given by qh first_point, num_points, hull_dim
    assumes rows[dim] is a scratch buffer
    if qh POINTSmalloc, overwrites input points, else mallocs a new array

  returns:
    rotated input
    sets qh POINTSmalloc

  design:
    see qh_rotatepoints
*/
void qh_rotateinput(realT **rows) {

  if (!qh POINTSmalloc) {
    qh first_point= qh_copypoints(qh first_point, qh num_points, qh hull_dim);
    qh POINTSmalloc= True;
  }
  qh_rotatepoints(qh first_point, qh num_points, qh hull_dim, rows);
}  /* rotateinput */

/*---------------------------------

  qh_rotatepoints( points, numpoints, dim, row )
    rotate numpoints points by a d-dim row matrix
    assumes rows[dim] is a scratch buffer

  returns:
    rotated points in place

  design:
    for each point
      for each coordinate
        use row[dim] to compute partial inner product
      for each coordinate
        rotate by partial inner product
*/
void qh_rotatepoints(realT *points, int numpoints, int dim, realT **row) {
  realT *point, *rowi, *coord= NULL, sum, *newval;
  int i,j,k;

  if (qh IStracing >= 1)
    qh_printmatrix(qh ferr, "qh_rotatepoints: rotate points by", row, dim, dim);
  for (point= points, j= numpoints; j--; point += dim) {
    newval= row[dim];
    for (i=0; i < dim; i++) {
      rowi= row[i];
      coord= point;
      for (sum= 0.0, k= dim; k--; )
        sum += *rowi++ * *coord++;
      *(newval++)= sum;
    }
    for (k=dim; k--; )
      *(--coord)= *(--newval);
  }
} /* rotatepoints */


/*---------------------------------

  qh_scaleinput()
    scale input points using qh low_bound/high_bound
    input points given by qh first_point, num_points, hull_dim
    if qh POINTSmalloc, overwrites input points, else mallocs a new array

  returns:
    scales coordinates of points to low_bound[k], high_bound[k]
    sets qh POINTSmalloc

  design:
    see qh_scalepoints
*/
void qh_scaleinput(void) {

  if (!qh POINTSmalloc) {
    qh first_point= qh_copypoints(qh first_point, qh num_points, qh hull_dim);
    qh POINTSmalloc= True;
  }
  qh_scalepoints(qh first_point, qh num_points, qh hull_dim,
       qh lower_bound, qh upper_bound);
}  /* scaleinput */

/*---------------------------------

  qh_scalelast( points, numpoints, dim, low, high, newhigh )
    scale last coordinate to [0,m] for Delaunay triangulations
    input points given by points, numpoints, dim

  returns:
    changes scale of last coordinate from [low, high] to [0, newhigh]
    overwrites last coordinate of each point
    saves low/high/newhigh in qh.last_low, etc. for qh_setdelaunay()

  notes:
    when called by qh_setdelaunay, low/high may not match actual data

  design:
    compute scale and shift factors
    apply to last coordinate of each point
*/
void qh_scalelast(coordT *points, int numpoints, int dim, coordT low,
                   coordT high, coordT newhigh) {
  realT scale, shift;
  coordT *coord;
  int i;
  boolT nearzero= False;

  trace4((qh ferr, 4013, "qh_scalelast: scale last coordinate from [%2.2g, %2.2g] to [0,%2.2g]\n",
    low, high, newhigh));
  qh last_low= low;
  qh last_high= high;
  qh last_newhigh= newhigh;
  scale= qh_divzero(newhigh, high - low,
                  qh MINdenom_1, &nearzero);
  if (nearzero) {
    if (qh DELAUNAY)
      qh_fprintf(qh ferr, 6019, "qhull input error: can not scale last coordinate.  Input is cocircular\n   or cospherical.   Use option 'Qz' to add a point at infinity.\n");
    else
      qh_fprintf(qh ferr, 6020, "qhull input error: can not scale last coordinate.  New bounds [0, %2.2g] are too wide for\nexisting bounds [%2.2g, %2.2g] (width %2.2g)\n",
                newhigh, low, high, high-low);
    qh_errexit(qh_ERRinput, NULL, NULL);
  }
  shift= - low * newhigh / (high-low);
  coord= points + dim - 1;
  for (i=numpoints; i--; coord += dim)
    *coord= *coord * scale + shift;
} /* scalelast */

/*---------------------------------

  qh_scalepoints( points, numpoints, dim, newlows, newhighs )
    scale points to new lowbound and highbound
    retains old bound when newlow= -REALmax or newhigh= +REALmax

  returns:
    scaled points
    overwrites old points

  design:
    for each coordinate
      compute current low and high bound
      compute scale and shift factors
      scale all points
      enforce new low and high bound for all points
*/
void qh_scalepoints(pointT *points, int numpoints, int dim,
        realT *newlows, realT *newhighs) {
  int i,k;
  realT shift, scale, *coord, low, high, newlow, newhigh, mincoord, maxcoord;
  boolT nearzero= False;

  for (k=0; k < dim; k++) {
    newhigh= newhighs[k];
    newlow= newlows[k];
    if (newhigh > REALmax/2 && newlow < -REALmax/2)
      continue;
    low= REALmax;
    high= -REALmax;
    for (i=numpoints, coord=points+k; i--; coord += dim) {
      minimize_(low, *coord);
      maximize_(high, *coord);
    }
    if (newhigh > REALmax/2)
      newhigh= high;
    if (newlow < -REALmax/2)
      newlow= low;
    if (qh DELAUNAY && k == dim-1 && newhigh < newlow) {
      qh_fprintf(qh ferr, 6021, "qhull input error: 'Qb%d' or 'QB%d' inverts paraboloid since high bound %.2g < low bound %.2g\n",
               k, k, newhigh, newlow);
      qh_errexit(qh_ERRinput, NULL, NULL);
    }
    scale= qh_divzero(newhigh - newlow, high - low,
                  qh MINdenom_1, &nearzero);
    if (nearzero) {
      qh_fprintf(qh ferr, 6022, "qhull input error: %d'th dimension's new bounds [%2.2g, %2.2g] too wide for\nexisting bounds [%2.2g, %2.2g]\n",
              k, newlow, newhigh, low, high);
      qh_errexit(qh_ERRinput, NULL, NULL);
    }
    shift= (newlow * high - low * newhigh)/(high-low);
    coord= points+k;
    for (i=numpoints; i--; coord += dim)
      *coord= *coord * scale + shift;
    coord= points+k;
    if (newlow < newhigh) {
      mincoord= newlow;
      maxcoord= newhigh;
    }else {
      mincoord= newhigh;
      maxcoord= newlow;
    }
    for (i=numpoints; i--; coord += dim) {
      minimize_(*coord, maxcoord);  /* because of roundoff error */
      maximize_(*coord, mincoord);
    }
    trace0((qh ferr, 10, "qh_scalepoints: scaled %d'th coordinate [%2.2g, %2.2g] to [%.2g, %.2g] for %d points by %2.2g and shifted %2.2g\n",
      k, low, high, newlow, newhigh, numpoints, scale, shift));
  }
} /* scalepoints */


/*---------------------------------

  qh_setdelaunay( dim, count, points )
    project count points to dim-d paraboloid for Delaunay triangulation

    dim is one more than the dimension of the input set
    assumes dim is at least 3 (i.e., at least a 2-d Delaunay triangulation)

    points is a dim*count realT array.  The first dim-1 coordinates
    are the coordinates of the first input point.  array[dim] is
    the first coordinate of the second input point.  array[2*dim] is
    the first coordinate of the third input point.

    if qh.last_low defined (i.e., 'Qbb' called qh_scalelast)
      calls qh_scalelast to scale the last coordinate the same as the other points

  returns:
    for each point
      sets point[dim-1] to sum of squares of coordinates
    scale points to 'Qbb' if needed

  notes:
    to project one point, use
      qh_setdelaunay(qh hull_dim, 1, point)

    Do not use options 'Qbk', 'QBk', or 'QbB' since they scale
    the coordinates after the original projection.

*/
void qh_setdelaunay(int dim, int count, pointT *points) {
  int i, k;
  coordT *coordp, coord;
  realT paraboloid;

  trace0((qh ferr, 11, "qh_setdelaunay: project %d points to paraboloid for Delaunay triangulation\n", count));
  coordp= points;
  for (i=0; i < count; i++) {
    coord= *coordp++;
    paraboloid= coord*coord;
    for (k=dim-2; k--; ) {
      coord= *coordp++;
      paraboloid += coord*coord;
    }
    *coordp++ = paraboloid;
  }
  if (qh last_low < REALmax/2)
    qh_scalelast(points, count, dim, qh last_low, qh last_high, qh last_newhigh);
} /* setdelaunay */


/*---------------------------------

  qh_sethalfspace( dim, coords, nextp, normal, offset, feasible )
    set point to dual of halfspace relative to feasible point
    halfspace is normal coefficients and offset.

  returns:
    false if feasible point is outside of hull (error message already reported)
    overwrites coordinates for point at dim coords
    nextp= next point (coords)

  design:
    compute distance from feasible point to halfspace
    divide each normal coefficient by -dist
*/
boolT qh_sethalfspace(int dim, coordT *coords, coordT **nextp,
         coordT *normal, coordT *offset, coordT *feasible) {
  coordT *normp= normal, *feasiblep= feasible, *coordp= coords;
  realT dist;
  realT r; /*bug fix*/
  int k;
  boolT zerodiv;

  dist= *offset;
  for (k=dim; k--; )
    dist += *(normp++) * *(feasiblep++);
  if (dist > 0)
    goto LABELerroroutside;
  normp= normal;
  if (dist < -qh MINdenom) {
    for (k=dim; k--; )
      *(coordp++)= *(normp++) / -dist;
  }else {
    for (k=dim; k--; ) {
      *(coordp++)= qh_divzero(*(normp++), -dist, qh MINdenom_1, &zerodiv);
      if (zerodiv)
        goto LABELerroroutside;
    }
  }
  *nextp= coordp;
  if (qh IStracing >= 4) {
    qh_fprintf(qh ferr, 8021, "qh_sethalfspace: halfspace at offset %6.2g to point: ", *offset);
    for (k=dim, coordp=coords; k--; ) {
      r= *coordp++;
      qh_fprintf(qh ferr, 8022, " %6.2g", r);
    }
    qh_fprintf(qh ferr, 8023, "\n");
  }
  return True;
LABELerroroutside:
  feasiblep= feasible;
  normp= normal;
  qh_fprintf(qh ferr, 6023, "qhull input error: feasible point is not clearly inside halfspace\nfeasible point: ");
  for (k=dim; k--; )
    qh_fprintf(qh ferr, 8024, qh_REAL_1, r=*(feasiblep++));
  qh_fprintf(qh ferr, 8025, "\n     halfspace: ");
  for (k=dim; k--; )
    qh_fprintf(qh ferr, 8026, qh_REAL_1, r=*(normp++));
  qh_fprintf(qh ferr, 8027, "\n     at offset: ");
  qh_fprintf(qh ferr, 8028, qh_REAL_1, *offset);
  qh_fprintf(qh ferr, 8029, " and distance: ");
  qh_fprintf(qh ferr, 8030, qh_REAL_1, dist);
  qh_fprintf(qh ferr, 8031, "\n");
  return False;
} /* sethalfspace */

/*---------------------------------

  qh_sethalfspace_all( dim, count, halfspaces, feasible )
    generate dual for halfspace intersection with feasible point
    array of count halfspaces
      each halfspace is normal coefficients followed by offset
      the origin is inside the halfspace if the offset is negative

  returns:
    malloc'd array of count X dim-1 points

  notes:
    call before qh_init_B or qh_initqhull_globals
    unused/untested code: please email bradb@shore.net if this works ok for you
    If using option 'Fp', also set qh feasible_point. It is a malloc'd array
      that is freed by qh_freebuffers.

  design:
    see qh_sethalfspace
*/
coordT *qh_sethalfspace_all(int dim, int count, coordT *halfspaces, pointT *feasible) {
  int i, newdim;
  pointT *newpoints;
  coordT *coordp, *normalp, *offsetp;

  trace0((qh ferr, 12, "qh_sethalfspace_all: compute dual for halfspace intersection\n"));
  newdim= dim - 1;
  if (!(newpoints=(coordT*)qh_malloc(count*newdim*sizeof(coordT)))){
    qh_fprintf(qh ferr, 6024, "qhull error: insufficient memory to compute dual of %d halfspaces\n",
          count);
    qh_errexit(qh_ERRmem, NULL, NULL);
  }
  coordp= newpoints;
  normalp= halfspaces;
  for (i=0; i < count; i++) {
    offsetp= normalp + newdim;
    if (!qh_sethalfspace(newdim, coordp, &coordp, normalp, offsetp, feasible)) {
      qh_fprintf(qh ferr, 8032, "The halfspace was at index %d\n", i);
      qh_errexit(qh_ERRinput, NULL, NULL);
    }
    normalp= offsetp + 1;
  }
  return newpoints;
} /* sethalfspace_all */


/*---------------------------------

  qh_sharpnewfacets()

  returns:
    true if could be an acute angle (facets in different quadrants)

  notes:
    for qh_findbest

  design:
    for all facets on qh.newfacet_list
      if two facets are in different quadrants
        set issharp
*/
boolT qh_sharpnewfacets() {
  facetT *facet;
  boolT issharp = False;
  int *quadrant, k;

  quadrant= (int*)qh_memalloc(qh hull_dim * sizeof(int));
  FORALLfacet_(qh newfacet_list) {
    if (facet == qh newfacet_list) {
      for (k=qh hull_dim; k--; )
        quadrant[ k]= (facet->normal[ k] > 0);
    }else {
      for (k=qh hull_dim; k--; ) {
        if (quadrant[ k] != (facet->normal[ k] > 0)) {
          issharp= True;
          break;
        }
      }
    }
    if (issharp)
      break;
  }
  qh_memfree( quadrant, qh hull_dim * sizeof(int));
  trace3((qh ferr, 3001, "qh_sharpnewfacets: %d\n", issharp));
  return issharp;
} /* sharpnewfacets */

/*---------------------------------

  qh_voronoi_center( dim, points )
    return Voronoi center for a set of points
    dim is the orginal dimension of the points
    gh.gm_matrix/qh.gm_row are scratch buffers

  returns:
    center as a temporary point
    if non-simplicial,
      returns center for max simplex of points

  notes:
    from Bowyer & Woodwark, A Programmer's Geometry, 1983, p. 65

  design:
    if non-simplicial
      determine max simplex for points
    translate point0 of simplex to origin
    compute sum of squares of diagonal
    compute determinate
    compute Voronoi center (see Bowyer & Woodwark)
*/
pointT *qh_voronoi_center(int dim, setT *points) {
  pointT *point, **pointp, *point0;
  pointT *center= (pointT*)qh_memalloc(qh center_size);
  setT *simplex;
  int i, j, k, size= qh_setsize(points);
  coordT *gmcoord;
  realT *diffp, sum2, *sum2row, *sum2p, det, factor;
  boolT nearzero, infinite;

  if (size == dim+1)
    simplex= points;
  else if (size < dim+1) {
    qh_fprintf(qh ferr, 6025, "qhull internal error (qh_voronoi_center):\n  need at least %d points to construct a Voronoi center\n",
             dim+1);
    qh_errexit(qh_ERRqhull, NULL, NULL);
    simplex= points;  /* never executed -- avoids warning */
  }else {
    simplex= qh_settemp(dim+1);
    qh_maxsimplex(dim, points, NULL, 0, &simplex);
  }
  point0= SETfirstt_(simplex, pointT);
  gmcoord= qh gm_matrix;
  for (k=0; k < dim; k++) {
    qh gm_row[k]= gmcoord;
    FOREACHpoint_(simplex) {
      if (point != point0)
        *(gmcoord++)= point[k] - point0[k];
    }
  }
  sum2row= gmcoord;
  for (i=0; i < dim; i++) {
    sum2= 0.0;
    for (k=0; k < dim; k++) {
      diffp= qh gm_row[k] + i;
      sum2 += *diffp * *diffp;
    }
    *(gmcoord++)= sum2;
  }
  det= qh_determinant(qh gm_row, dim, &nearzero);
  factor= qh_divzero(0.5, det, qh MINdenom, &infinite);
  if (infinite) {
    for (k=dim; k--; )
      center[k]= qh_INFINITE;
    if (qh IStracing)
      qh_printpoints(qh ferr, "qh_voronoi_center: at infinity for ", simplex);
  }else {
    for (i=0; i < dim; i++) {
      gmcoord= qh gm_matrix;
      sum2p= sum2row;
      for (k=0; k < dim; k++) {
        qh gm_row[k]= gmcoord;
        if (k == i) {
          for (j=dim; j--; )
            *(gmcoord++)= *sum2p++;
        }else {
          FOREACHpoint_(simplex) {
            if (point != point0)
              *(gmcoord++)= point[k] - point0[k];
          }
        }
      }
      center[i]= qh_determinant(qh gm_row, dim, &nearzero)*factor + point0[i];
    }
#ifndef qh_NOtrace
    if (qh IStracing >= 3) {
      qh_fprintf(qh ferr, 8033, "qh_voronoi_center: det %2.2g factor %2.2g ", det, factor);
      qh_printmatrix(qh ferr, "center:", ¢er, 1, dim);
      if (qh IStracing >= 5) {
        qh_printpoints(qh ferr, "points", simplex);
        FOREACHpoint_(simplex)
          qh_fprintf(qh ferr, 8034, "p%d dist %.2g, ", qh_pointid(point),
                   qh_pointdist(point, center, dim));
        qh_fprintf(qh ferr, 8035, "\n");
      }
    }
#endif
  }
  if (simplex != points)
    qh_settempfree(&simplex);
  return center;
} /* voronoi_center */

qhull-2012.1/src/libqhull/global.c0000644000076400010400000021167511720041145020122 0ustar  bbarberAdministrators
/*
  ---------------------------------

   global.c
   initializes all the globals of the qhull application

   see README

   see libqhull.h for qh.globals and function prototypes

   see qhull_a.h for internal functions

   Copyright (c) 1993-2012 The Geometry Center.
   $Id: //main/2011/qhull/src/libqhull/global.c#15 $$Change: 1490 $
   $DateTime: 2012/02/19 20:27:01 $$Author: bbarber $
 */

#include "qhull_a.h"

/*========= qh definition -- globals defined in libqhull.h =======================*/

int qhull_inuse= 0; /* not used */

#if qh_QHpointer
qhT *qh_qh= NULL;       /* pointer to all global variables */
#else
qhT qh_qh;              /* all global variables.
                           Add "= {0}" if this causes a compiler error.
                           Also qh_qhstat in stat.c and qhmem in mem.c.  */
#endif

/*----------------------------------

  qh_version
    version string by year and date

    the revision increases on code changes only

  notes:
    change date:    Changes.txt, Announce.txt, index.htm, README.txt,
                    qhull-news.html, Eudora signatures, CMakeLists.txt
    change version: README.txt, qh-get.htm, File_id.diz, Makefile.txt
    change year:    Copying.txt
    check download size
    recompile user_eg.c, rbox.c, libqhull.c, qconvex.c, qdelaun.c qvoronoi.c, qhalf.c, testqset.c
*/

const char *qh_version = "2012.1 2012/02/18";

/*---------------------------------

  qh_appendprint( printFormat )
    append printFormat to qh.PRINTout unless already defined
*/
void qh_appendprint(qh_PRINT format) {
  int i;

  for (i=0; i < qh_PRINTEND; i++) {
    if (qh PRINTout[i] == format && format != qh_PRINTqhull)
      break;
    if (!qh PRINTout[i]) {
      qh PRINTout[i]= format;
      break;
    }
  }
} /* appendprint */

/*---------------------------------

  qh_checkflags( commandStr, hiddenFlags )
    errors if commandStr contains hiddenFlags
    hiddenFlags starts and ends with a space and is space deliminated (checked)

  notes:
    ignores first word (e.g., "qconvex i")
    use qh_strtol/strtod since strtol/strtod may or may not skip trailing spaces

  see:
    qh_initflags() initializes Qhull according to commandStr
*/
void qh_checkflags(char *command, char *hiddenflags) {
  char *s= command, *t, *chkerr; /* qh_skipfilename is non-const */
  char key, opt, prevopt;
  char chkkey[]= "   ";
  char chkopt[]=  "    ";
  char chkopt2[]= "     ";
  boolT waserr= False;

  if (*hiddenflags != ' ' || hiddenflags[strlen(hiddenflags)-1] != ' ') {
    qh_fprintf(qh ferr, 6026, "qhull error (qh_checkflags): hiddenflags must start and end with a space: \"%s\"", hiddenflags);
    qh_errexit(qh_ERRinput, NULL, NULL);
  }
  if (strpbrk(hiddenflags, ",\n\r\t")) {
    qh_fprintf(qh ferr, 6027, "qhull error (qh_checkflags): hiddenflags contains commas, newlines, or tabs: \"%s\"", hiddenflags);
    qh_errexit(qh_ERRinput, NULL, NULL);
  }
  while (*s && !isspace(*s))  /* skip program name */
    s++;
  while (*s) {
    while (*s && isspace(*s))
      s++;
    if (*s == '-')
      s++;
    if (!*s)
      break;
    key = *s++;
    chkerr = NULL;
    if (key == 'T' && (*s == 'I' || *s == 'O')) {  /* TI or TO 'file name' */
      s= qh_skipfilename(++s);
      continue;
    }
    chkkey[1]= key;
    if (strstr(hiddenflags, chkkey)) {
      chkerr= chkkey;
    }else if (isupper(key)) {
      opt= ' ';
      prevopt= ' ';
      chkopt[1]= key;
      chkopt2[1]= key;
      while (!chkerr && *s && !isspace(*s)) {
        opt= *s++;
        if (isalpha(opt)) {
          chkopt[2]= opt;
          if (strstr(hiddenflags, chkopt))
            chkerr= chkopt;
          if (prevopt != ' ') {
            chkopt2[2]= prevopt;
            chkopt2[3]= opt;
            if (strstr(hiddenflags, chkopt2))
              chkerr= chkopt2;
          }
        }else if (key == 'Q' && isdigit(opt) && prevopt != 'b'
              && (prevopt == ' ' || islower(prevopt))) {
            chkopt[2]= opt;
            if (strstr(hiddenflags, chkopt))
              chkerr= chkopt;
        }else {
          qh_strtod(s-1, &t);
          if (s < t)
            s= t;
        }
        prevopt= opt;
      }
    }
    if (chkerr) {
      *chkerr= '\'';
      chkerr[strlen(chkerr)-1]=  '\'';
      qh_fprintf(qh ferr, 6029, "qhull error: option %s is not used with this program.\n             It may be used with qhull.\n", chkerr);
      waserr= True;
    }
  }
  if (waserr)
    qh_errexit(qh_ERRinput, NULL, NULL);
} /* checkflags */

/*---------------------------------

  qh_clear_outputflags()
    Clear output flags for QhullPoints
*/
void qh_clear_outputflags(void) {
  int i,k;

  qh ANNOTATEoutput= False;
  qh DOintersections= False;
  qh DROPdim= -1;
  qh FORCEoutput= False;
  qh GETarea= False;
  qh GOODpoint= 0;
  qh GOODpointp= NULL;
  qh GOODthreshold= False;
  qh GOODvertex= 0;
  qh GOODvertexp= NULL;
  qh IStracing= 0;
  qh KEEParea= False;
  qh KEEPmerge= False;
  qh KEEPminArea= REALmax;
  qh PRINTcentrums= False;
  qh PRINTcoplanar= False;
  qh PRINTdots= False;
  qh PRINTgood= False;
  qh PRINTinner= False;
  qh PRINTneighbors= False;
  qh PRINTnoplanes= False;
  qh PRINToptions1st= False;
  qh PRINTouter= False;
  qh PRINTprecision= True;
  qh PRINTridges= False;
  qh PRINTspheres= False;
  qh PRINTstatistics= False;
  qh PRINTsummary= False;
  qh PRINTtransparent= False;
  qh SPLITthresholds= False;
  qh TRACElevel= 0;
  qh TRInormals= False;
  qh USEstdout= False;
  qh VERIFYoutput= False;
  for (k=qh input_dim+1; k--; ) {  /* duplicated in qh_initqhull_buffers and qh_clear_ouputflags */
    qh lower_threshold[k]= -REALmax;
    qh upper_threshold[k]= REALmax;
    qh lower_bound[k]= -REALmax;
    qh upper_bound[k]= REALmax;
  }

  for (i=0; i < qh_PRINTEND; i++) {
    qh PRINTout[i]= qh_PRINTnone;
  }

  if (!qh qhull_commandsiz2)
      qh qhull_commandsiz2= (int)strlen(qh qhull_command); /* WARN64 */
  else {
      qh qhull_command[qh qhull_commandsiz2]= '\0';
  }
  if (!qh qhull_optionsiz2)
    qh qhull_optionsiz2= (int)strlen(qh qhull_options);  /* WARN64 */
  else {
    qh qhull_options[qh qhull_optionsiz2]= '\0';
    qh qhull_optionlen= qh_OPTIONline;  /* start a new line */
  }
} /* clear_outputflags */

/*---------------------------------

  qh_clock()
    return user CPU time in 100ths (qh_SECtick)
    only defined for qh_CLOCKtype == 2

  notes:
    use first value to determine time 0
    from Stevens '92 8.15
*/
unsigned long qh_clock(void) {

#if (qh_CLOCKtype == 2)
  struct tms time;
  static long clktck;  /* initialized first call */
  double ratio, cpu;
  unsigned long ticks;

  if (!clktck) {
    if ((clktck= sysconf(_SC_CLK_TCK)) < 0) {
      qh_fprintf(qh ferr, 6030, "qhull internal error (qh_clock): sysconf() failed.  Use qh_CLOCKtype 1 in user.h\n");
      qh_errexit(qh_ERRqhull, NULL, NULL);
    }
  }
  if (times(&time) == -1) {
    qh_fprintf(qh ferr, 6031, "qhull internal error (qh_clock): times() failed.  Use qh_CLOCKtype 1 in user.h\n");
    qh_errexit(qh_ERRqhull, NULL, NULL);
  }
  ratio= qh_SECticks / (double)clktck;
  ticks= time.tms_utime * ratio;
  return ticks;
#else
  qh_fprintf(qh ferr, 6032, "qhull internal error (qh_clock): use qh_CLOCKtype 2 in user.h\n");
  qh_errexit(qh_ERRqhull, NULL, NULL); /* never returns */
  return 0;
#endif
} /* clock */

/*---------------------------------

  qh_freebuffers()
    free up global memory buffers

  notes:
    must match qh_initbuffers()
*/
void qh_freebuffers(void) {

  trace5((qh ferr, 5001, "qh_freebuffers: freeing up global memory buffers\n"));
  /* allocated by qh_initqhull_buffers */
  qh_memfree(qh NEARzero, qh hull_dim * sizeof(realT));
  qh_memfree(qh lower_threshold, (qh input_dim+1) * sizeof(realT));
  qh_memfree(qh upper_threshold, (qh input_dim+1) * sizeof(realT));
  qh_memfree(qh lower_bound, (qh input_dim+1) * sizeof(realT));
  qh_memfree(qh upper_bound, (qh input_dim+1) * sizeof(realT));
  qh_memfree(qh gm_matrix, (qh hull_dim+1) * qh hull_dim * sizeof(coordT));
  qh_memfree(qh gm_row, (qh hull_dim+1) * sizeof(coordT *));
  qh NEARzero= qh lower_threshold= qh upper_threshold= NULL;
  qh lower_bound= qh upper_bound= NULL;
  qh gm_matrix= NULL;
  qh gm_row= NULL;
  qh_setfree(&qh other_points);
  qh_setfree(&qh del_vertices);
  qh_setfree(&qh coplanarfacetset);
  if (qh line)                /* allocated by qh_readinput, freed if no error */
    qh_free(qh line);
  if (qh half_space)
    qh_free(qh half_space);
  if (qh temp_malloc)
    qh_free(qh temp_malloc);
  if (qh feasible_point)      /* allocated by qh_readfeasible */
    qh_free(qh feasible_point);
  if (qh feasible_string)     /* allocated by qh_initflags */
    qh_free(qh feasible_string);
  qh line= qh feasible_string= NULL;
  qh half_space= qh feasible_point= qh temp_malloc= NULL;
  /* usually allocated by qh_readinput */
  if (qh first_point && qh POINTSmalloc) {
    qh_free(qh first_point);
    qh first_point= NULL;
  }
  if (qh input_points && qh input_malloc) { /* set by qh_joggleinput */
    qh_free(qh input_points);
    qh input_points= NULL;
  }
  trace5((qh ferr, 5002, "qh_freebuffers: finished\n"));
} /* freebuffers */


/*---------------------------------

  qh_freebuild( allmem )
    free global memory used by qh_initbuild and qh_buildhull
    if !allmem,
      does not free short memory (e.g., facetT, freed by qh_memfreeshort)

  design:
    free centrums
    free each vertex
    mark unattached ridges
    for each facet
      free ridges
      free outside set, coplanar set, neighbor set, ridge set, vertex set
      free facet
    free hash table
    free interior point
    free merge set
    free temporary sets
*/
void qh_freebuild(boolT allmem) {
  facetT *facet;
  vertexT *vertex;
  ridgeT *ridge, **ridgep;
  mergeT *merge, **mergep;

  trace1((qh ferr, 1005, "qh_freebuild: free memory from qh_inithull and qh_buildhull\n"));
  if (qh del_vertices)
    qh_settruncate(qh del_vertices, 0);
  if (allmem) {
    while ((vertex= qh vertex_list)) {
      if (vertex->next)
        qh_delvertex(vertex);
      else {
        qh_memfree(vertex, (int)sizeof(vertexT));
        qh newvertex_list= qh vertex_list= NULL;
      }
    }
  }else if (qh VERTEXneighbors) {
    FORALLvertices
      qh_setfreelong(&(vertex->neighbors));
  }
  qh VERTEXneighbors= False;
  qh GOODclosest= NULL;
  if (allmem) {
    FORALLfacets {
      FOREACHridge_(facet->ridges)
        ridge->seen= False;
    }
    FORALLfacets {
      if (facet->visible) {
        FOREACHridge_(facet->ridges) {
          if (!otherfacet_(ridge, facet)->visible)
            ridge->seen= True;  /* an unattached ridge */
        }
      }
    }
    while ((facet= qh facet_list)) {
      FOREACHridge_(facet->ridges) {
        if (ridge->seen) {
          qh_setfree(&(ridge->vertices));
          qh_memfree(ridge, (int)sizeof(ridgeT));
        }else
          ridge->seen= True;
      }
      qh_setfree(&(facet->outsideset));
      qh_setfree(&(facet->coplanarset));
      qh_setfree(&(facet->neighbors));
      qh_setfree(&(facet->ridges));
      qh_setfree(&(facet->vertices));
      if (facet->next)
        qh_delfacet(facet);
      else {
        qh_memfree(facet, (int)sizeof(facetT));
        qh visible_list= qh newfacet_list= qh facet_list= NULL;
      }
    }
  }else {
    FORALLfacets {
      qh_setfreelong(&(facet->outsideset));
      qh_setfreelong(&(facet->coplanarset));
      if (!facet->simplicial) {
        qh_setfreelong(&(facet->neighbors));
        qh_setfreelong(&(facet->ridges));
        qh_setfreelong(&(facet->vertices));
      }
    }
  }
  qh_setfree(&(qh hash_table));
  qh_memfree(qh interior_point, qh normal_size);
  qh interior_point= NULL;
  FOREACHmerge_(qh facet_mergeset)  /* usually empty */
    qh_memfree(merge, (int)sizeof(mergeT));
  qh facet_mergeset= NULL;  /* temp set */
  qh degen_mergeset= NULL;  /* temp set */
  qh_settempfree_all();
} /* freebuild */

/*---------------------------------

  qh_freeqhull( allmem )
    see qh_freeqhull2
    if qh_QHpointer, frees qh_qh
*/
void qh_freeqhull(boolT allmem) {
    qh_freeqhull2(allmem);
#if qh_QHpointer
    qh_free(qh_qh);
    qh_qh= NULL;
#endif
}

/*---------------------------------

qh_freeqhull2( allmem )
  free global memory
  if !allmem,
    does not free short memory (freed by qh_memfreeshort)

notes:
  sets qh.NOerrexit in case caller forgets to

see:
  see qh_initqhull_start2()

design:
  free global and temporary memory from qh_initbuild and qh_buildhull
  free buffers
  free statistics
*/
void qh_freeqhull2(boolT allmem) {

  trace1((qh ferr, 1006, "qh_freeqhull2: free global memory\n"));
  qh NOerrexit= True;  /* no more setjmp since called at exit and ~QhullQh */
  qh_freebuild(allmem);
  qh_freebuffers();
  qh_freestatistics();
#if qh_QHpointer
  memset((char *)qh_qh, 0, sizeof(qhT));
  /* qh_qh freed by caller, qh_freeqhull() */
#else
  memset((char *)&qh_qh, 0, sizeof(qhT));
#endif
  qh NOerrexit= True;
} /* freeqhull2 */

/*---------------------------------

  qh_init_A( infile, outfile, errfile, argc, argv )
    initialize memory and stdio files
    convert input options to option string (qh.qhull_command)

  notes:
    infile may be NULL if qh_readpoints() is not called

    errfile should always be defined.  It is used for reporting
    errors.  outfile is used for output and format options.

    argc/argv may be 0/NULL

    called before error handling initialized
    qh_errexit() may not be used
*/
void qh_init_A(FILE *infile, FILE *outfile, FILE *errfile, int argc, char *argv[]) {
  qh_meminit(errfile);
  qh_initqhull_start(infile, outfile, errfile);
  qh_init_qhull_command(argc, argv);
} /* init_A */

/*---------------------------------

  qh_init_B( points, numpoints, dim, ismalloc )
    initialize globals for points array

    points has numpoints dim-dimensional points
      points[0] is the first coordinate of the first point
      points[1] is the second coordinate of the first point
      points[dim] is the first coordinate of the second point

    ismalloc=True
      Qhull will call qh_free(points) on exit or input transformation
    ismalloc=False
      Qhull will allocate a new point array if needed for input transformation

    qh.qhull_command
      is the option string.
      It is defined by qh_init_B(), qh_qhull_command(), or qh_initflags

  returns:
    if qh.PROJECTinput or (qh.DELAUNAY and qh.PROJECTdelaunay)
      projects the input to a new point array

        if qh.DELAUNAY,
          qh.hull_dim is increased by one
        if qh.ATinfinity,
          qh_projectinput adds point-at-infinity for Delaunay tri.

    if qh.SCALEinput
      changes the upper and lower bounds of the input, see qh_scaleinput()

    if qh.ROTATEinput
      rotates the input by a random rotation, see qh_rotateinput()
      if qh.DELAUNAY
        rotates about the last coordinate

  notes:
    called after points are defined
    qh_errexit() may be used
*/
void qh_init_B(coordT *points, int numpoints, int dim, boolT ismalloc) {
  qh_initqhull_globals(points, numpoints, dim, ismalloc);
  if (qhmem.LASTsize == 0)
    qh_initqhull_mem();
  /* mem.c and qset.c are initialized */
  qh_initqhull_buffers();
  qh_initthresholds(qh qhull_command);
  if (qh PROJECTinput || (qh DELAUNAY && qh PROJECTdelaunay))
    qh_projectinput();
  if (qh SCALEinput)
    qh_scaleinput();
  if (qh ROTATErandom >= 0) {
    qh_randommatrix(qh gm_matrix, qh hull_dim, qh gm_row);
    if (qh DELAUNAY) {
      int k, lastk= qh hull_dim-1;
      for (k=0; k < lastk; k++) {
        qh gm_row[k][lastk]= 0.0;
        qh gm_row[lastk][k]= 0.0;
      }
      qh gm_row[lastk][lastk]= 1.0;
    }
    qh_gram_schmidt(qh hull_dim, qh gm_row);
    qh_rotateinput(qh gm_row);
  }
} /* init_B */

/*---------------------------------

  qh_init_qhull_command( argc, argv )
    build qh.qhull_command from argc/argv

  returns:
    a space-delimited string of options (just as typed)

  notes:
    makes option string easy to input and output

    argc/argv may be 0/NULL
*/
void qh_init_qhull_command(int argc, char *argv[]) {

  if (!qh_argv_to_command(argc, argv, qh qhull_command, (int)sizeof(qh qhull_command))){
    /* Assumes qh.ferr is defined. */
    qh_fprintf(qh ferr, 6033, "qhull input error: more than %d characters in command line\n",
          (int)sizeof(qh qhull_command));
    qh_exit(qh_ERRinput);  /* error reported, can not use qh_errexit */
  }
} /* init_qhull_command */

/*---------------------------------

  qh_initflags( commandStr )
    set flags and initialized constants from commandStr

  returns:
    sets qh.qhull_command to command if needed

  notes:
    ignores first word (e.g., "qhull d")
    use qh_strtol/strtod since strtol/strtod may or may not skip trailing spaces

  see:
    qh_initthresholds() continues processing of 'Pdn' and 'PDn'
    'prompt' in unix.c for documentation

  design:
    for each space-deliminated option group
      if top-level option
        check syntax
        append approriate option to option string
        set appropriate global variable or append printFormat to print options
      else
        for each sub-option
          check syntax
          append approriate option to option string
          set appropriate global variable or append printFormat to print options
*/
void qh_initflags(char *command) {
  int k, i, lastproject;
  char *s= command, *t, *prev_s, *start, key;
  boolT isgeom= False, wasproject;
  realT r;

  if (command <= &qh qhull_command[0] || command > &qh qhull_command[0] + sizeof(qh qhull_command)) {
    if (command != &qh qhull_command[0]) {
      *qh qhull_command= '\0';
      strncat(qh qhull_command, command, sizeof(qh qhull_command)-strlen(qh qhull_command)-1);
    }
    while (*s && !isspace(*s))  /* skip program name */
      s++;
  }
  while (*s) {
    while (*s && isspace(*s))
      s++;
    if (*s == '-')
      s++;
    if (!*s)
      break;
    prev_s= s;
    switch (*s++) {
    case 'd':
      qh_option("delaunay", NULL, NULL);
      qh DELAUNAY= True;
      break;
    case 'f':
      qh_option("facets", NULL, NULL);
      qh_appendprint(qh_PRINTfacets);
      break;
    case 'i':
      qh_option("incidence", NULL, NULL);
      qh_appendprint(qh_PRINTincidences);
      break;
    case 'm':
      qh_option("mathematica", NULL, NULL);
      qh_appendprint(qh_PRINTmathematica);
      break;
    case 'n':
      qh_option("normals", NULL, NULL);
      qh_appendprint(qh_PRINTnormals);
      break;
    case 'o':
      qh_option("offFile", NULL, NULL);
      qh_appendprint(qh_PRINToff);
      break;
    case 'p':
      qh_option("points", NULL, NULL);
      qh_appendprint(qh_PRINTpoints);
      break;
    case 's':
      qh_option("summary", NULL, NULL);
      qh PRINTsummary= True;
      break;
    case 'v':
      qh_option("voronoi", NULL, NULL);
      qh VORONOI= True;
      qh DELAUNAY= True;
      break;
    case 'A':
      if (!isdigit(*s) && *s != '.' && *s != '-')
        qh_fprintf(qh ferr, 7002, "qhull warning: no maximum cosine angle given for option 'An'.  Ignored.\n");
      else {
        if (*s == '-') {
          qh premerge_cos= -qh_strtod(s, &s);
          qh_option("Angle-premerge-", NULL, &qh premerge_cos);
          qh PREmerge= True;
        }else {
          qh postmerge_cos= qh_strtod(s, &s);
          qh_option("Angle-postmerge", NULL, &qh postmerge_cos);
          qh POSTmerge= True;
        }
        qh MERGING= True;
      }
      break;
    case 'C':
      if (!isdigit(*s) && *s != '.' && *s != '-')
        qh_fprintf(qh ferr, 7003, "qhull warning: no centrum radius given for option 'Cn'.  Ignored.\n");
      else {
        if (*s == '-') {
          qh premerge_centrum= -qh_strtod(s, &s);
          qh_option("Centrum-premerge-", NULL, &qh premerge_centrum);
          qh PREmerge= True;
        }else {
          qh postmerge_centrum= qh_strtod(s, &s);
          qh_option("Centrum-postmerge", NULL, &qh postmerge_centrum);
          qh POSTmerge= True;
        }
        qh MERGING= True;
      }
      break;
    case 'E':
      if (*s == '-')
        qh_fprintf(qh ferr, 7004, "qhull warning: negative maximum roundoff given for option 'An'.  Ignored.\n");
      else if (!isdigit(*s))
        qh_fprintf(qh ferr, 7005, "qhull warning: no maximum roundoff given for option 'En'.  Ignored.\n");
      else {
        qh DISTround= qh_strtod(s, &s);
        qh_option("Distance-roundoff", NULL, &qh DISTround);
        qh SETroundoff= True;
      }
      break;
    case 'H':
      start= s;
      qh HALFspace= True;
      qh_strtod(s, &t);
      while (t > s)  {
        if (*t && !isspace(*t)) {
          if (*t == ',')
            t++;
          else
            qh_fprintf(qh ferr, 7006, "qhull warning: origin for Halfspace intersection should be 'Hn,n,n,...'\n");
        }
        s= t;
        qh_strtod(s, &t);
      }
      if (start < t) {
        if (!(qh feasible_string= (char*)calloc((size_t)(t-start+1), (size_t)1))) {
          qh_fprintf(qh ferr, 6034, "qhull error: insufficient memory for 'Hn,n,n'\n");
          qh_errexit(qh_ERRmem, NULL, NULL);
        }
        strncpy(qh feasible_string, start, (size_t)(t-start));
        qh_option("Halfspace-about", NULL, NULL);
        qh_option(qh feasible_string, NULL, NULL);
      }else
        qh_option("Halfspace", NULL, NULL);
      break;
    case 'R':
      if (!isdigit(*s))
        qh_fprintf(qh ferr, 7007, "qhull warning: missing random perturbation for option 'Rn'.  Ignored\n");
      else {
        qh RANDOMfactor= qh_strtod(s, &s);
        qh_option("Random_perturb", NULL, &qh RANDOMfactor);
        qh RANDOMdist= True;
      }
      break;
    case 'V':
      if (!isdigit(*s) && *s != '-')
        qh_fprintf(qh ferr, 7008, "qhull warning: missing visible distance for option 'Vn'.  Ignored\n");
      else {
        qh MINvisible= qh_strtod(s, &s);
        qh_option("Visible", NULL, &qh MINvisible);
      }
      break;
    case 'U':
      if (!isdigit(*s) && *s != '-')
        qh_fprintf(qh ferr, 7009, "qhull warning: missing coplanar distance for option 'Un'.  Ignored\n");
      else {
        qh MAXcoplanar= qh_strtod(s, &s);
        qh_option("U-coplanar", NULL, &qh MAXcoplanar);
      }
      break;
    case 'W':
      if (*s == '-')
        qh_fprintf(qh ferr, 7010, "qhull warning: negative outside width for option 'Wn'.  Ignored.\n");
      else if (!isdigit(*s))
        qh_fprintf(qh ferr, 7011, "qhull warning: missing outside width for option 'Wn'.  Ignored\n");
      else {
        qh MINoutside= qh_strtod(s, &s);
        qh_option("W-outside", NULL, &qh MINoutside);
        qh APPROXhull= True;
      }
      break;
    /************  sub menus ***************/
    case 'F':
      while (*s && !isspace(*s)) {
        switch (*s++) {
        case 'a':
          qh_option("Farea", NULL, NULL);
          qh_appendprint(qh_PRINTarea);
          qh GETarea= True;
          break;
        case 'A':
          qh_option("FArea-total", NULL, NULL);
          qh GETarea= True;
          break;
        case 'c':
          qh_option("Fcoplanars", NULL, NULL);
          qh_appendprint(qh_PRINTcoplanars);
          break;
        case 'C':
          qh_option("FCentrums", NULL, NULL);
          qh_appendprint(qh_PRINTcentrums);
          break;
        case 'd':
          qh_option("Fd-cdd-in", NULL, NULL);
          qh CDDinput= True;
          break;
        case 'D':
          qh_option("FD-cdd-out", NULL, NULL);
          qh CDDoutput= True;
          break;
        case 'F':
          qh_option("FFacets-xridge", NULL, NULL);
          qh_appendprint(qh_PRINTfacets_xridge);
          break;
        case 'i':
          qh_option("Finner", NULL, NULL);
          qh_appendprint(qh_PRINTinner);
          break;
        case 'I':
          qh_option("FIDs", NULL, NULL);
          qh_appendprint(qh_PRINTids);
          break;
        case 'm':
          qh_option("Fmerges", NULL, NULL);
          qh_appendprint(qh_PRINTmerges);
          break;
        case 'M':
          qh_option("FMaple", NULL, NULL);
          qh_appendprint(qh_PRINTmaple);
          break;
        case 'n':
          qh_option("Fneighbors", NULL, NULL);
          qh_appendprint(qh_PRINTneighbors);
          break;
        case 'N':
          qh_option("FNeighbors-vertex", NULL, NULL);
          qh_appendprint(qh_PRINTvneighbors);
          break;
        case 'o':
          qh_option("Fouter", NULL, NULL);
          qh_appendprint(qh_PRINTouter);
          break;
        case 'O':
          if (qh PRINToptions1st) {
            qh_option("FOptions", NULL, NULL);
            qh_appendprint(qh_PRINToptions);
          }else
            qh PRINToptions1st= True;
          break;
        case 'p':
          qh_option("Fpoint-intersect", NULL, NULL);
          qh_appendprint(qh_PRINTpointintersect);
          break;
        case 'P':
          qh_option("FPoint-nearest", NULL, NULL);
          qh_appendprint(qh_PRINTpointnearest);
          break;
        case 'Q':
          qh_option("FQhull", NULL, NULL);
          qh_appendprint(qh_PRINTqhull);
          break;
        case 's':
          qh_option("Fsummary", NULL, NULL);
          qh_appendprint(qh_PRINTsummary);
          break;
        case 'S':
          qh_option("FSize", NULL, NULL);
          qh_appendprint(qh_PRINTsize);
          qh GETarea= True;
          break;
        case 't':
          qh_option("Ftriangles", NULL, NULL);
          qh_appendprint(qh_PRINTtriangles);
          break;
        case 'v':
          /* option set in qh_initqhull_globals */
          qh_appendprint(qh_PRINTvertices);
          break;
        case 'V':
          qh_option("FVertex-average", NULL, NULL);
          qh_appendprint(qh_PRINTaverage);
          break;
        case 'x':
          qh_option("Fxtremes", NULL, NULL);
          qh_appendprint(qh_PRINTextremes);
          break;
        default:
          s--;
          qh_fprintf(qh ferr, 7012, "qhull warning: unknown 'F' output option %c, rest ignored\n", (int)s[0]);
          while (*++s && !isspace(*s));
          break;
        }
      }
      break;
    case 'G':
      isgeom= True;
      qh_appendprint(qh_PRINTgeom);
      while (*s && !isspace(*s)) {
        switch (*s++) {
        case 'a':
          qh_option("Gall-points", NULL, NULL);
          qh PRINTdots= True;
          break;
        case 'c':
          qh_option("Gcentrums", NULL, NULL);
          qh PRINTcentrums= True;
          break;
        case 'h':
          qh_option("Gintersections", NULL, NULL);
          qh DOintersections= True;
          break;
        case 'i':
          qh_option("Ginner", NULL, NULL);
          qh PRINTinner= True;
          break;
        case 'n':
          qh_option("Gno-planes", NULL, NULL);
          qh PRINTnoplanes= True;
          break;
        case 'o':
          qh_option("Gouter", NULL, NULL);
          qh PRINTouter= True;
          break;
        case 'p':
          qh_option("Gpoints", NULL, NULL);
          qh PRINTcoplanar= True;
          break;
        case 'r':
          qh_option("Gridges", NULL, NULL);
          qh PRINTridges= True;
          break;
        case 't':
          qh_option("Gtransparent", NULL, NULL);
          qh PRINTtransparent= True;
          break;
        case 'v':
          qh_option("Gvertices", NULL, NULL);
          qh PRINTspheres= True;
          break;
        case 'D':
          if (!isdigit(*s))
            qh_fprintf(qh ferr, 6035, "qhull input error: missing dimension for option 'GDn'\n");
          else {
            if (qh DROPdim >= 0)
              qh_fprintf(qh ferr, 7013, "qhull warning: can only drop one dimension.  Previous 'GD%d' ignored\n",
                   qh DROPdim);
            qh DROPdim= qh_strtol(s, &s);
            qh_option("GDrop-dim", &qh DROPdim, NULL);
          }
          break;
        default:
          s--;
          qh_fprintf(qh ferr, 7014, "qhull warning: unknown 'G' print option %c, rest ignored\n", (int)s[0]);
          while (*++s && !isspace(*s));
          break;
        }
      }
      break;
    case 'P':
      while (*s && !isspace(*s)) {
        switch (*s++) {
        case 'd': case 'D':  /* see qh_initthresholds() */
          key= s[-1];
          i= qh_strtol(s, &s);
          r= 0;
          if (*s == ':') {
            s++;
            r= qh_strtod(s, &s);
          }
          if (key == 'd')
            qh_option("Pdrop-facets-dim-less", &i, &r);
          else
            qh_option("PDrop-facets-dim-more", &i, &r);
          break;
        case 'g':
          qh_option("Pgood-facets", NULL, NULL);
          qh PRINTgood= True;
          break;
        case 'G':
          qh_option("PGood-facet-neighbors", NULL, NULL);
          qh PRINTneighbors= True;
          break;
        case 'o':
          qh_option("Poutput-forced", NULL, NULL);
          qh FORCEoutput= True;
          break;
        case 'p':
          qh_option("Pprecision-ignore", NULL, NULL);
          qh PRINTprecision= False;
          break;
        case 'A':
          if (!isdigit(*s))
            qh_fprintf(qh ferr, 6036, "qhull input error: missing facet count for keep area option 'PAn'\n");
          else {
            qh KEEParea= qh_strtol(s, &s);
            qh_option("PArea-keep", &qh KEEParea, NULL);
            qh GETarea= True;
          }
          break;
        case 'F':
          if (!isdigit(*s))
            qh_fprintf(qh ferr, 6037, "qhull input error: missing facet area for option 'PFn'\n");
          else {
            qh KEEPminArea= qh_strtod(s, &s);
            qh_option("PFacet-area-keep", NULL, &qh KEEPminArea);
            qh GETarea= True;
          }
          break;
        case 'M':
          if (!isdigit(*s))
            qh_fprintf(qh ferr, 6038, "qhull input error: missing merge count for option 'PMn'\n");
          else {
            qh KEEPmerge= qh_strtol(s, &s);
            qh_option("PMerge-keep", &qh KEEPmerge, NULL);
          }
          break;
        default:
          s--;
          qh_fprintf(qh ferr, 7015, "qhull warning: unknown 'P' print option %c, rest ignored\n", (int)s[0]);
          while (*++s && !isspace(*s));
          break;
        }
      }
      break;
    case 'Q':
      lastproject= -1;
      while (*s && !isspace(*s)) {
        switch (*s++) {
        case 'b': case 'B':  /* handled by qh_initthresholds */
          key= s[-1];
          if (key == 'b' && *s == 'B') {
            s++;
            r= qh_DEFAULTbox;
            qh SCALEinput= True;
            qh_option("QbBound-unit-box", NULL, &r);
            break;
          }
          if (key == 'b' && *s == 'b') {
            s++;
            qh SCALElast= True;
            qh_option("Qbbound-last", NULL, NULL);
            break;
          }
          k= qh_strtol(s, &s);
          r= 0.0;
          wasproject= False;
          if (*s == ':') {
            s++;
            if ((r= qh_strtod(s, &s)) == 0.0) {
              t= s;            /* need true dimension for memory allocation */
              while (*t && !isspace(*t)) {
                if (toupper(*t++) == 'B'
                 && k == qh_strtol(t, &t)
                 && *t++ == ':'
                 && qh_strtod(t, &t) == 0.0) {
                  qh PROJECTinput++;
                  trace2((qh ferr, 2004, "qh_initflags: project dimension %d\n", k));
                  qh_option("Qb-project-dim", &k, NULL);
                  wasproject= True;
                  lastproject= k;
                  break;
                }
              }
            }
          }
          if (!wasproject) {
            if (lastproject == k && r == 0.0)
              lastproject= -1;  /* doesn't catch all possible sequences */
            else if (key == 'b') {
              qh SCALEinput= True;
              if (r == 0.0)
                r= -qh_DEFAULTbox;
              qh_option("Qbound-dim-low", &k, &r);
            }else {
              qh SCALEinput= True;
              if (r == 0.0)
                r= qh_DEFAULTbox;
              qh_option("QBound-dim-high", &k, &r);
            }
          }
          break;
        case 'c':
          qh_option("Qcoplanar-keep", NULL, NULL);
          qh KEEPcoplanar= True;
          break;
        case 'f':
          qh_option("Qfurthest-outside", NULL, NULL);
          qh BESToutside= True;
          break;
        case 'g':
          qh_option("Qgood-facets-only", NULL, NULL);
          qh ONLYgood= True;
          break;
        case 'i':
          qh_option("Qinterior-keep", NULL, NULL);
          qh KEEPinside= True;
          break;
        case 'm':
          qh_option("Qmax-outside-only", NULL, NULL);
          qh ONLYmax= True;
          break;
        case 'r':
          qh_option("Qrandom-outside", NULL, NULL);
          qh RANDOMoutside= True;
          break;
        case 's':
          qh_option("Qsearch-initial-simplex", NULL, NULL);
          qh ALLpoints= True;
          break;
        case 't':
          qh_option("Qtriangulate", NULL, NULL);
          qh TRIangulate= True;
          break;
        case 'T':
          qh_option("QTestPoints", NULL, NULL);
          if (!isdigit(*s))
            qh_fprintf(qh ferr, 6039, "qhull input error: missing number of test points for option 'QTn'\n");
          else {
            qh TESTpoints= qh_strtol(s, &s);
            qh_option("QTestPoints", &qh TESTpoints, NULL);
          }
          break;
        case 'u':
          qh_option("QupperDelaunay", NULL, NULL);
          qh UPPERdelaunay= True;
          break;
        case 'v':
          qh_option("Qvertex-neighbors-convex", NULL, NULL);
          qh TESTvneighbors= True;
          break;
        case 'x':
          qh_option("Qxact-merge", NULL, NULL);
          qh MERGEexact= True;
          break;
        case 'z':
          qh_option("Qz-infinity-point", NULL, NULL);
          qh ATinfinity= True;
          break;
        case '0':
          qh_option("Q0-no-premerge", NULL, NULL);
          qh NOpremerge= True;
          break;
        case '1':
          if (!isdigit(*s)) {
            qh_option("Q1-no-angle-sort", NULL, NULL);
            qh ANGLEmerge= False;
            break;
          }
          switch (*s++) {
          case '0':
            qh_option("Q10-no-narrow", NULL, NULL);
            qh NOnarrow= True;
            break;
          case '1':
            qh_option("Q11-trinormals Qtriangulate", NULL, NULL);
            qh TRInormals= True;
            qh TRIangulate= True;
            break;
          default:
            s--;
            qh_fprintf(qh ferr, 7016, "qhull warning: unknown 'Q' qhull option 1%c, rest ignored\n", (int)s[0]);
            while (*++s && !isspace(*s));
            break;
          }
          break;
        case '2':
          qh_option("Q2-no-merge-independent", NULL, NULL);
          qh MERGEindependent= False;
          goto LABELcheckdigit;
          break; /* no warnings */
        case '3':
          qh_option("Q3-no-merge-vertices", NULL, NULL);
          qh MERGEvertices= False;
        LABELcheckdigit:
          if (isdigit(*s))
            qh_fprintf(qh ferr, 7017, "qhull warning: can not follow '1', '2', or '3' with a digit.  '%c' skipped.\n",
                     *s++);
          break;
        case '4':
          qh_option("Q4-avoid-old-into-new", NULL, NULL);
          qh AVOIDold= True;
          break;
        case '5':
          qh_option("Q5-no-check-outer", NULL, NULL);
          qh SKIPcheckmax= True;
          break;
        case '6':
          qh_option("Q6-no-concave-merge", NULL, NULL);
          qh SKIPconvex= True;
          break;
        case '7':
          qh_option("Q7-no-breadth-first", NULL, NULL);
          qh VIRTUALmemory= True;
          break;
        case '8':
          qh_option("Q8-no-near-inside", NULL, NULL);
          qh NOnearinside= True;
          break;
        case '9':
          qh_option("Q9-pick-furthest", NULL, NULL);
          qh PICKfurthest= True;
          break;
        case 'G':
          i= qh_strtol(s, &t);
          if (qh GOODpoint)
            qh_fprintf(qh ferr, 7018, "qhull warning: good point already defined for option 'QGn'.  Ignored\n");
          else if (s == t)
            qh_fprintf(qh ferr, 7019, "qhull warning: missing good point id for option 'QGn'.  Ignored\n");
          else if (i < 0 || *s == '-') {
            qh GOODpoint= i-1;
            qh_option("QGood-if-dont-see-point", &i, NULL);
          }else {
            qh GOODpoint= i+1;
            qh_option("QGood-if-see-point", &i, NULL);
          }
          s= t;
          break;
        case 'J':
          if (!isdigit(*s) && *s != '-')
            qh JOGGLEmax= 0.0;
          else {
            qh JOGGLEmax= (realT) qh_strtod(s, &s);
            qh_option("QJoggle", NULL, &qh JOGGLEmax);
          }
          break;
        case 'R':
          if (!isdigit(*s) && *s != '-')
            qh_fprintf(qh ferr, 7020, "qhull warning: missing random seed for option 'QRn'.  Ignored\n");
          else {
            qh ROTATErandom= i= qh_strtol(s, &s);
            if (i > 0)
              qh_option("QRotate-id", &i, NULL );
            else if (i < -1)
              qh_option("QRandom-seed", &i, NULL );
          }
          break;
        case 'V':
          i= qh_strtol(s, &t);
          if (qh GOODvertex)
            qh_fprintf(qh ferr, 7021, "qhull warning: good vertex already defined for option 'QVn'.  Ignored\n");
          else if (s == t)
            qh_fprintf(qh ferr, 7022, "qhull warning: no good point id given for option 'QVn'.  Ignored\n");
          else if (i < 0) {
            qh GOODvertex= i - 1;
            qh_option("QV-good-facets-not-point", &i, NULL);
          }else {
            qh_option("QV-good-facets-point", &i, NULL);
            qh GOODvertex= i + 1;
          }
          s= t;
          break;
        default:
          s--;
          qh_fprintf(qh ferr, 7023, "qhull warning: unknown 'Q' qhull option %c, rest ignored\n", (int)s[0]);
          while (*++s && !isspace(*s));
          break;
        }
      }
      break;
    case 'T':
      while (*s && !isspace(*s)) {
        if (isdigit(*s) || *s == '-')
          qh IStracing= qh_strtol(s, &s);
        else switch (*s++) {
        case 'a':
          qh_option("Tannotate-output", NULL, NULL);
          qh ANNOTATEoutput= True;
          break;
        case 'c':
          qh_option("Tcheck-frequently", NULL, NULL);
          qh CHECKfrequently= True;
          break;
        case 's':
          qh_option("Tstatistics", NULL, NULL);
          qh PRINTstatistics= True;
          break;
        case 'v':
          qh_option("Tverify", NULL, NULL);
          qh VERIFYoutput= True;
          break;
        case 'z':
          if (qh ferr == qh_FILEstderr) {
            /* The C++ interface captures the output in qh_fprint_qhull() */
            qh_option("Tz-stdout", NULL, NULL);
            qh USEstdout= True;
          }else if (!qh fout)
            qh_fprintf(qh ferr, 7024, "qhull warning: output file undefined(stdout).  Option 'Tz' ignored.\n");
          else {
            qh_option("Tz-stdout", NULL, NULL);
            qh USEstdout= True;
            qh ferr= qh fout;
            qhmem.ferr= qh fout;
          }
          break;
        case 'C':
          if (!isdigit(*s))
            qh_fprintf(qh ferr, 7025, "qhull warning: missing point id for cone for trace option 'TCn'.  Ignored\n");
          else {
            i= qh_strtol(s, &s);
            qh_option("TCone-stop", &i, NULL);
            qh STOPcone= i + 1;
          }
          break;
        case 'F':
          if (!isdigit(*s))
            qh_fprintf(qh ferr, 7026, "qhull warning: missing frequency count for trace option 'TFn'.  Ignored\n");
          else {
            qh REPORTfreq= qh_strtol(s, &s);
            qh_option("TFacet-log", &qh REPORTfreq, NULL);
            qh REPORTfreq2= qh REPORTfreq/2;  /* for tracemerging() */
          }
          break;
        case 'I':
          if (!isspace(*s))
            qh_fprintf(qh ferr, 7027, "qhull warning: missing space between 'TI' and filename, %s\n", s);
          while (isspace(*s))
            s++;
          t= qh_skipfilename(s);
          {
            char filename[qh_FILENAMElen];

            qh_copyfilename(filename, (int)sizeof(filename), s, (int)(t-s));   /* WARN64 */
            s= t;
            if (!freopen(filename, "r", stdin)) {
              qh_fprintf(qh ferr, 6041, "qhull error: could not open file \"%s\".", filename);
              qh_errexit(qh_ERRinput, NULL, NULL);
            }else {
              qh_option("TInput-file", NULL, NULL);
              qh_option(filename, NULL, NULL);
            }
          }
          break;
        case 'O':
            if (!isspace(*s))
                qh_fprintf(qh ferr, 7028, "qhull warning: missing space between 'TO' and filename, %s\n", s);
            while (isspace(*s))
                s++;
            t= qh_skipfilename(s);
            {
              char filename[qh_FILENAMElen];

              qh_copyfilename(filename, (int)sizeof(filename), s, (int)(t-s));  /* WARN64 */
              s= t;
              if (!freopen(filename, "w", stdout)) {
                qh_fprintf(qh ferr, 6044, "qhull error: could not open file \"%s\".", filename);
                qh_errexit(qh_ERRinput, NULL, NULL);
              }else {
                qh_option("TOutput-file", NULL, NULL);
              qh_option(filename, NULL, NULL);
            }
          }
          break;
        case 'P':
          if (!isdigit(*s))
            qh_fprintf(qh ferr, 7029, "qhull warning: missing point id for trace option 'TPn'.  Ignored\n");
          else {
            qh TRACEpoint= qh_strtol(s, &s);
            qh_option("Trace-point", &qh TRACEpoint, NULL);
          }
          break;
        case 'M':
          if (!isdigit(*s))
            qh_fprintf(qh ferr, 7030, "qhull warning: missing merge id for trace option 'TMn'.  Ignored\n");
          else {
            qh TRACEmerge= qh_strtol(s, &s);
            qh_option("Trace-merge", &qh TRACEmerge, NULL);
          }
          break;
        case 'R':
          if (!isdigit(*s))
            qh_fprintf(qh ferr, 7031, "qhull warning: missing rerun count for trace option 'TRn'.  Ignored\n");
          else {
            qh RERUN= qh_strtol(s, &s);
            qh_option("TRerun", &qh RERUN, NULL);
          }
          break;
        case 'V':
          i= qh_strtol(s, &t);
          if (s == t)
            qh_fprintf(qh ferr, 7032, "qhull warning: missing furthest point id for trace option 'TVn'.  Ignored\n");
          else if (i < 0) {
            qh STOPpoint= i - 1;
            qh_option("TV-stop-before-point", &i, NULL);
          }else {
            qh STOPpoint= i + 1;
            qh_option("TV-stop-after-point", &i, NULL);
          }
          s= t;
          break;
        case 'W':
          if (!isdigit(*s))
            qh_fprintf(qh ferr, 7033, "qhull warning: missing max width for trace option 'TWn'.  Ignored\n");
          else {
            qh TRACEdist= (realT) qh_strtod(s, &s);
            qh_option("TWide-trace", NULL, &qh TRACEdist);
          }
          break;
        default:
          s--;
          qh_fprintf(qh ferr, 7034, "qhull warning: unknown 'T' trace option %c, rest ignored\n", (int)s[0]);
          while (*++s && !isspace(*s));
          break;
        }
      }
      break;
    default:
      qh_fprintf(qh ferr, 7035, "qhull warning: unknown flag %c(%x)\n", (int)s[-1],
               (int)s[-1]);
      break;
    }
    if (s-1 == prev_s && *s && !isspace(*s)) {
      qh_fprintf(qh ferr, 7036, "qhull warning: missing space after flag %c(%x); reserved for menu. Skipped.\n",
               (int)*prev_s, (int)*prev_s);
      while (*s && !isspace(*s))
        s++;
    }
  }
  if (qh STOPcone && qh JOGGLEmax < REALmax/2)
    qh_fprintf(qh ferr, 7078, "qhull warning: 'TCn' (stopCone) ignored when used with 'QJn' (joggle)\n");
  if (isgeom && !qh FORCEoutput && qh PRINTout[1])
    qh_fprintf(qh ferr, 7037, "qhull warning: additional output formats are not compatible with Geomview\n");
  /* set derived values in qh_initqhull_globals */
} /* initflags */


/*---------------------------------

  qh_initqhull_buffers()
    initialize global memory buffers

  notes:
    must match qh_freebuffers()
*/
void qh_initqhull_buffers(void) {
  int k;

  qh TEMPsize= (qhmem.LASTsize - sizeof(setT))/SETelemsize;
  if (qh TEMPsize <= 0 || qh TEMPsize > qhmem.LASTsize)
    qh TEMPsize= 8;  /* e.g., if qh_NOmem */
  qh other_points= qh_setnew(qh TEMPsize);
  qh del_vertices= qh_setnew(qh TEMPsize);
  qh coplanarfacetset= qh_setnew(qh TEMPsize);
  qh NEARzero= (realT *)qh_memalloc(qh hull_dim * sizeof(realT));
  qh lower_threshold= (realT *)qh_memalloc((qh input_dim+1) * sizeof(realT));
  qh upper_threshold= (realT *)qh_memalloc((qh input_dim+1) * sizeof(realT));
  qh lower_bound= (realT *)qh_memalloc((qh input_dim+1) * sizeof(realT));
  qh upper_bound= (realT *)qh_memalloc((qh input_dim+1) * sizeof(realT));
  for (k=qh input_dim+1; k--; ) {  /* duplicated in qh_initqhull_buffers and qh_clear_ouputflags */
    qh lower_threshold[k]= -REALmax;
    qh upper_threshold[k]= REALmax;
    qh lower_bound[k]= -REALmax;
    qh upper_bound[k]= REALmax;
  }
  qh gm_matrix= (coordT *)qh_memalloc((qh hull_dim+1) * qh hull_dim * sizeof(coordT));
  qh gm_row= (coordT **)qh_memalloc((qh hull_dim+1) * sizeof(coordT *));
} /* initqhull_buffers */

/*---------------------------------

  qh_initqhull_globals( points, numpoints, dim, ismalloc )
    initialize globals
    if ismalloc
      points were malloc'd and qhull should free at end

  returns:
    sets qh.first_point, num_points, input_dim, hull_dim and others
    seeds random number generator (seed=1 if tracing)
    modifies qh.hull_dim if ((qh.DELAUNAY and qh.PROJECTdelaunay) or qh.PROJECTinput)
    adjust user flags as needed
    also checks DIM3 dependencies and constants

  notes:
    do not use qh_point() since an input transformation may move them elsewhere

  see:
    qh_initqhull_start() sets default values for non-zero globals

  design:
    initialize points array from input arguments
    test for qh.ZEROcentrum
      (i.e., use opposite vertex instead of cetrum for convexity testing)
    initialize qh.CENTERtype, qh.normal_size,
      qh.center_size, qh.TRACEpoint/level,
    initialize and test random numbers
    qh_initqhull_outputflags() -- adjust and test output flags
*/
void qh_initqhull_globals(coordT *points, int numpoints, int dim, boolT ismalloc) {
  int seed, pointsneeded, extra= 0, i, randi, k;
  realT randr;
  realT factorial;

  time_t timedata;

  trace0((qh ferr, 13, "qh_initqhull_globals: for %s | %s\n", qh rbox_command,
      qh qhull_command));
  qh POINTSmalloc= ismalloc;
  qh first_point= points;
  qh num_points= numpoints;
  qh hull_dim= qh input_dim= dim;
  if (!qh NOpremerge && !qh MERGEexact && !qh PREmerge && qh JOGGLEmax > REALmax/2) {
    qh MERGING= True;
    if (qh hull_dim <= 4) {
      qh PREmerge= True;
      qh_option("_pre-merge", NULL, NULL);
    }else {
      qh MERGEexact= True;
      qh_option("Qxact_merge", NULL, NULL);
    }
  }else if (qh MERGEexact)
    qh MERGING= True;
  if (!qh NOpremerge && qh JOGGLEmax > REALmax/2) {
#ifdef qh_NOmerge
    qh JOGGLEmax= 0.0;
#endif
  }
  if (qh TRIangulate && qh JOGGLEmax < REALmax/2 && qh PRINTprecision)
    qh_fprintf(qh ferr, 7038, "qhull warning: joggle('QJ') always produces simplicial output.  Triangulated output('Qt') does nothing.\n");
  if (qh JOGGLEmax < REALmax/2 && qh DELAUNAY && !qh SCALEinput && !qh SCALElast) {
    qh SCALElast= True;
    qh_option("Qbbound-last-qj", NULL, NULL);
  }
  if (qh MERGING && !qh POSTmerge && qh premerge_cos > REALmax/2
  && qh premerge_centrum == 0) {
    qh ZEROcentrum= True;
    qh ZEROall_ok= True;
    qh_option("_zero-centrum", NULL, NULL);
  }
  if (qh JOGGLEmax < REALmax/2 && REALepsilon > 2e-8 && qh PRINTprecision)
    qh_fprintf(qh ferr, 7039, "qhull warning: real epsilon, %2.2g, is probably too large for joggle('QJn')\nRecompile with double precision reals(see user.h).\n",
          REALepsilon);
#ifdef qh_NOmerge
  if (qh MERGING) {
    qh_fprintf(qh ferr, 6045, "qhull input error: merging not installed(qh_NOmerge + 'Qx', 'Cn' or 'An')\n");
    qh_errexit(qh_ERRinput, NULL, NULL);
  }
#endif
  if (qh DELAUNAY && qh KEEPcoplanar && !qh KEEPinside) {
    qh KEEPinside= True;
    qh_option("Qinterior-keep", NULL, NULL);
  }
  if (qh DELAUNAY && qh HALFspace) {
    qh_fprintf(qh ferr, 6046, "qhull input error: can not use Delaunay('d') or Voronoi('v') with halfspace intersection('H')\n");
    qh_errexit(qh_ERRinput, NULL, NULL);
  }
  if (!qh DELAUNAY && (qh UPPERdelaunay || qh ATinfinity)) {
    qh_fprintf(qh ferr, 6047, "qhull input error: use upper-Delaunay('Qu') or infinity-point('Qz') with Delaunay('d') or Voronoi('v')\n");
    qh_errexit(qh_ERRinput, NULL, NULL);
  }
  if (qh UPPERdelaunay && qh ATinfinity) {
    qh_fprintf(qh ferr, 6048, "qhull input error: can not use infinity-point('Qz') with upper-Delaunay('Qu')\n");
    qh_errexit(qh_ERRinput, NULL, NULL);
  }
  if (qh SCALElast && !qh DELAUNAY && qh PRINTprecision)
    qh_fprintf(qh ferr, 7040, "qhull input warning: option 'Qbb' (scale-last-coordinate) is normally used with 'd' or 'v'\n");
  qh DOcheckmax= (!qh SKIPcheckmax && qh MERGING );
  qh KEEPnearinside= (qh DOcheckmax && !(qh KEEPinside && qh KEEPcoplanar)
                          && !qh NOnearinside);
  if (qh MERGING)
    qh CENTERtype= qh_AScentrum;
  else if (qh VORONOI)
    qh CENTERtype= qh_ASvoronoi;
  if (qh TESTvneighbors && !qh MERGING) {
    qh_fprintf(qh ferr, 6049, "qhull input error: test vertex neighbors('Qv') needs a merge option\n");
    qh_errexit(qh_ERRinput, NULL ,NULL);
  }
  if (qh PROJECTinput || (qh DELAUNAY && qh PROJECTdelaunay)) {
    qh hull_dim -= qh PROJECTinput;
    if (qh DELAUNAY) {
      qh hull_dim++;
      if (qh ATinfinity)
        extra= 1;
    }
  }
  if (qh hull_dim <= 1) {
    qh_fprintf(qh ferr, 6050, "qhull error: dimension %d must be > 1\n", qh hull_dim);
    qh_errexit(qh_ERRinput, NULL, NULL);
  }
  for (k=2, factorial=1.0; k < qh hull_dim; k++)
    factorial *= k;
  qh AREAfactor= 1.0 / factorial;
  trace2((qh ferr, 2005, "qh_initqhull_globals: initialize globals.  dim %d numpoints %d malloc? %d projected %d to hull_dim %d\n",
        dim, numpoints, ismalloc, qh PROJECTinput, qh hull_dim));
  qh normal_size= qh hull_dim * sizeof(coordT);
  qh center_size= qh normal_size - sizeof(coordT);
  pointsneeded= qh hull_dim+1;
  if (qh hull_dim > qh_DIMmergeVertex) {
    qh MERGEvertices= False;
    qh_option("Q3-no-merge-vertices-dim-high", NULL, NULL);
  }
  if (qh GOODpoint)
    pointsneeded++;
#ifdef qh_NOtrace
  if (qh IStracing) {
    qh_fprintf(qh ferr, 6051, "qhull input error: tracing is not installed(qh_NOtrace in user.h)");
    qh_errexit(qh_ERRqhull, NULL, NULL);
  }
#endif
  if (qh RERUN > 1) {
    qh TRACElastrun= qh IStracing; /* qh_build_withrestart duplicates next conditional */
    if (qh IStracing != -1)
      qh IStracing= 0;
  }else if (qh TRACEpoint != -1 || qh TRACEdist < REALmax/2 || qh TRACEmerge) {
    qh TRACElevel= (qh IStracing? qh IStracing : 3);
    qh IStracing= 0;
  }
  if (qh ROTATErandom == 0 || qh ROTATErandom == -1) {
    seed= (int)time(&timedata);
    if (qh ROTATErandom  == -1) {
      seed= -seed;
      qh_option("QRandom-seed", &seed, NULL );
    }else
      qh_option("QRotate-random", &seed, NULL);
    qh ROTATErandom= seed;
  }
  seed= qh ROTATErandom;
  if (seed == INT_MIN)    /* default value */
    seed= 1;
  else if (seed < 0)
    seed= -seed;
  qh_RANDOMseed_(seed);
  randr= 0.0;
  for (i=1000; i--; ) {
    randi= qh_RANDOMint;
    randr += randi;
    if (randi > qh_RANDOMmax) {
      qh_fprintf(qh ferr, 8036, "\
qhull configuration error (qh_RANDOMmax in user.h):\n\
   random integer %d > qh_RANDOMmax(%.8g)\n",
               randi, qh_RANDOMmax);
      qh_errexit(qh_ERRinput, NULL, NULL);
    }
  }
  qh_RANDOMseed_(seed);
  randr = randr/1000;
  if (randr < qh_RANDOMmax * 0.1
  || randr > qh_RANDOMmax * 0.9)
    qh_fprintf(qh ferr, 8037, "\
qhull configuration warning (qh_RANDOMmax in user.h):\n\
   average of 1000 random integers (%.2g) is much different than expected (%.2g).\n\
   Is qh_RANDOMmax (%.2g) wrong?\n",
             randr, qh_RANDOMmax * 0.5, qh_RANDOMmax);
  qh RANDOMa= 2.0 * qh RANDOMfactor/qh_RANDOMmax;
  qh RANDOMb= 1.0 - qh RANDOMfactor;
  if (qh_HASHfactor < 1.1) {
    qh_fprintf(qh ferr, 6052, "qhull internal error (qh_initqhull_globals): qh_HASHfactor %d must be at least 1.1.  Qhull uses linear hash probing\n",
      qh_HASHfactor);
    qh_errexit(qh_ERRqhull, NULL, NULL);
  }
  if (numpoints+extra < pointsneeded) {
    qh_fprintf(qh ferr, 6214, "qhull input error: not enough points(%d) to construct initial simplex (need %d)\n",
            numpoints, pointsneeded);
    qh_errexit(qh_ERRinput, NULL, NULL);
  }
  qh_initqhull_outputflags();
} /* initqhull_globals */

/*---------------------------------

  qh_initqhull_mem(  )
    initialize mem.c for qhull
    qh.hull_dim and qh.normal_size determine some of the allocation sizes
    if qh.MERGING,
      includes ridgeT
    calls qh_user_memsizes() to add up to 10 additional sizes for quick allocation
      (see numsizes below)

  returns:
    mem.c already for qh_memalloc/qh_memfree (errors if called beforehand)

  notes:
    qh_produceoutput() prints memsizes

*/
void qh_initqhull_mem(void) {
  int numsizes;
  int i;

  numsizes= 8+10;
  qh_meminitbuffers(qh IStracing, qh_MEMalign, numsizes,
                     qh_MEMbufsize,qh_MEMinitbuf);
  qh_memsize((int)sizeof(vertexT));
  if (qh MERGING) {
    qh_memsize((int)sizeof(ridgeT));
    qh_memsize((int)sizeof(mergeT));
  }
  qh_memsize((int)sizeof(facetT));
  i= sizeof(setT) + (qh hull_dim - 1) * SETelemsize;  /* ridge.vertices */
  qh_memsize(i);
  qh_memsize(qh normal_size);        /* normal */
  i += SETelemsize;                 /* facet.vertices, .ridges, .neighbors */
  qh_memsize(i);
  qh_user_memsizes();
  qh_memsetup();
} /* initqhull_mem */

/*---------------------------------

  qh_initqhull_outputflags
    initialize flags concerned with output

  returns:
    adjust user flags as needed

  see:
    qh_clear_outputflags() resets the flags

  design:
    test for qh.PRINTgood (i.e., only print 'good' facets)
    check for conflicting print output options
*/
void qh_initqhull_outputflags(void) {
  boolT printgeom= False, printmath= False, printcoplanar= False;
  int i;

  trace3((qh ferr, 3024, "qh_initqhull_outputflags: %s\n", qh qhull_command));
  if (!(qh PRINTgood || qh PRINTneighbors)) {
    if (qh KEEParea || qh KEEPminArea < REALmax/2 || qh KEEPmerge || qh DELAUNAY
        || (!qh ONLYgood && (qh GOODvertex || qh GOODpoint))) {
      qh PRINTgood= True;
      qh_option("Pgood", NULL, NULL);
    }
  }
  if (qh PRINTtransparent) {
    if (qh hull_dim != 4 || !qh DELAUNAY || qh VORONOI || qh DROPdim >= 0) {
      qh_fprintf(qh ferr, 6215, "qhull input error: transparent Delaunay('Gt') needs 3-d Delaunay('d') w/o 'GDn'\n");
      qh_errexit(qh_ERRinput, NULL, NULL);
    }
    qh DROPdim = 3;
    qh PRINTridges = True;
  }
  for (i=qh_PRINTEND; i--; ) {
    if (qh PRINTout[i] == qh_PRINTgeom)
      printgeom= True;
    else if (qh PRINTout[i] == qh_PRINTmathematica || qh PRINTout[i] == qh_PRINTmaple)
      printmath= True;
    else if (qh PRINTout[i] == qh_PRINTcoplanars)
      printcoplanar= True;
    else if (qh PRINTout[i] == qh_PRINTpointnearest)
      printcoplanar= True;
    else if (qh PRINTout[i] == qh_PRINTpointintersect && !qh HALFspace) {
      qh_fprintf(qh ferr, 6053, "qhull input error: option 'Fp' is only used for \nhalfspace intersection('Hn,n,n').\n");
      qh_errexit(qh_ERRinput, NULL, NULL);
    }else if (qh PRINTout[i] == qh_PRINTtriangles && (qh HALFspace || qh VORONOI)) {
      qh_fprintf(qh ferr, 6054, "qhull input error: option 'Ft' is not available for Voronoi vertices or halfspace intersection\n");
      qh_errexit(qh_ERRinput, NULL, NULL);
    }else if (qh PRINTout[i] == qh_PRINTcentrums && qh VORONOI) {
      qh_fprintf(qh ferr, 6055, "qhull input error: option 'FC' is not available for Voronoi vertices('v')\n");
      qh_errexit(qh_ERRinput, NULL, NULL);
    }else if (qh PRINTout[i] == qh_PRINTvertices) {
      if (qh VORONOI)
        qh_option("Fvoronoi", NULL, NULL);
      else
        qh_option("Fvertices", NULL, NULL);
    }
  }
  if (printcoplanar && qh DELAUNAY && qh JOGGLEmax < REALmax/2) {
    if (qh PRINTprecision)
      qh_fprintf(qh ferr, 7041, "qhull input warning: 'QJ' (joggle) will usually prevent coincident input sites for options 'Fc' and 'FP'\n");
  }
  if (printmath && (qh hull_dim > 3 || qh VORONOI)) {
    qh_fprintf(qh ferr, 6056, "qhull input error: Mathematica and Maple output is only available for 2-d and 3-d convex hulls and 2-d Delaunay triangulations\n");
    qh_errexit(qh_ERRinput, NULL, NULL);
  }
  if (printgeom) {
    if (qh hull_dim > 4) {
      qh_fprintf(qh ferr, 6057, "qhull input error: Geomview output is only available for 2-d, 3-d and 4-d\n");
      qh_errexit(qh_ERRinput, NULL, NULL);
    }
    if (qh PRINTnoplanes && !(qh PRINTcoplanar + qh PRINTcentrums
     + qh PRINTdots + qh PRINTspheres + qh DOintersections + qh PRINTridges)) {
      qh_fprintf(qh ferr, 6058, "qhull input error: no output specified for Geomview\n");
      qh_errexit(qh_ERRinput, NULL, NULL);
    }
    if (qh VORONOI && (qh hull_dim > 3 || qh DROPdim >= 0)) {
      qh_fprintf(qh ferr, 6059, "qhull input error: Geomview output for Voronoi diagrams only for 2-d\n");
      qh_errexit(qh_ERRinput, NULL, NULL);
    }
    /* can not warn about furthest-site Geomview output: no lower_threshold */
    if (qh hull_dim == 4 && qh DROPdim == -1 &&
        (qh PRINTcoplanar || qh PRINTspheres || qh PRINTcentrums)) {
      qh_fprintf(qh ferr, 7042, "qhull input warning: coplanars, vertices, and centrums output not\n\
available for 4-d output(ignored).  Could use 'GDn' instead.\n");
      qh PRINTcoplanar= qh PRINTspheres= qh PRINTcentrums= False;
    }
  }
  if (!qh KEEPcoplanar && !qh KEEPinside && !qh ONLYgood) {
    if ((qh PRINTcoplanar && qh PRINTspheres) || printcoplanar) {
      if (qh QHULLfinished) {
        qh_fprintf(qh ferr, 7072, "qhull output warning: ignoring coplanar points, option 'Qc' was not set for the first run of qhull.\n");
      }else {
        qh KEEPcoplanar = True;
        qh_option("Qcoplanar", NULL, NULL);
      }
    }
  }
  qh PRINTdim= qh hull_dim;
  if (qh DROPdim >=0) {    /* after Geomview checks */
    if (qh DROPdim < qh hull_dim) {
      qh PRINTdim--;
      if (!printgeom || qh hull_dim < 3)
        qh_fprintf(qh ferr, 7043, "qhull input warning: drop dimension 'GD%d' is only available for 3-d/4-d Geomview\n", qh DROPdim);
    }else
      qh DROPdim= -1;
  }else if (qh VORONOI) {
    qh DROPdim= qh hull_dim-1;
    qh PRINTdim= qh hull_dim-1;
  }
} /* qh_initqhull_outputflags */

/*---------------------------------

  qh_initqhull_start( infile, outfile, errfile )
    allocate memory if needed and call qh_initqhull_start2()
*/
void qh_initqhull_start(FILE *infile, FILE *outfile, FILE *errfile) {

#if qh_QHpointer
  if (qh_qh) {
    qh_fprintf(errfile, 6205, "qhull error (qh_initqhull_start): qh_qh already defined.  Call qh_save_qhull() first\n");
    qh_exit(qh_ERRqhull);  /* no error handler */
  }
  if (!(qh_qh= (qhT *)qh_malloc(sizeof(qhT)))) {
    qh_fprintf(errfile, 6060, "qhull error (qh_initqhull_start): insufficient memory\n");
    qh_exit(qh_ERRmem);  /* no error handler */
  }
#endif
  qh_initstatistics();
  qh_initqhull_start2(infile, outfile, errfile);
} /* initqhull_start */

/*---------------------------------

  qh_initqhull_start2( infile, outfile, errfile )
    start initialization of qhull
    initialize statistics, stdio, default values for global variables
    assumes qh_qh is defined
  notes:
    report errors elsewhere, error handling and g_qhull_output [Qhull.cpp, QhullQh()] not in initialized
  see:
    qh_maxmin() determines the precision constants
    qh_freeqhull2()
*/
void qh_initqhull_start2(FILE *infile, FILE *outfile, FILE *errfile) {
  time_t timedata;
  int seed;

  qh_CPUclock; /* start the clock(for qh_clock).  One-shot. */
#if qh_QHpointer
  memset((char *)qh_qh, 0, sizeof(qhT));   /* every field is 0, FALSE, NULL */
#else
  memset((char *)&qh_qh, 0, sizeof(qhT));
#endif
  qh ANGLEmerge= True;
  qh DROPdim= -1;
  qh ferr= errfile;
  qh fin= infile;
  qh fout= outfile;
  qh furthest_id= -1;
  qh JOGGLEmax= REALmax;
  qh KEEPminArea = REALmax;
  qh last_low= REALmax;
  qh last_high= REALmax;
  qh last_newhigh= REALmax;
  qh max_outside= 0.0;
  qh max_vertex= 0.0;
  qh MAXabs_coord= 0.0;
  qh MAXsumcoord= 0.0;
  qh MAXwidth= -REALmax;
  qh MERGEindependent= True;
  qh MINdenom_1= fmax_(1.0/REALmax, REALmin); /* used by qh_scalepoints */
  qh MINoutside= 0.0;
  qh MINvisible= REALmax;
  qh MAXcoplanar= REALmax;
  qh outside_err= REALmax;
  qh premerge_centrum= 0.0;
  qh premerge_cos= REALmax;
  qh PRINTprecision= True;
  qh PRINTradius= 0.0;
  qh postmerge_cos= REALmax;
  qh postmerge_centrum= 0.0;
  qh ROTATErandom= INT_MIN;
  qh MERGEvertices= True;
  qh totarea= 0.0;
  qh totvol= 0.0;
  qh TRACEdist= REALmax;
  qh TRACEpoint= -1; /* recompile or use 'TPn' */
  qh tracefacet_id= UINT_MAX;  /* recompile to trace a facet */
  qh tracevertex_id= UINT_MAX; /* recompile to trace a vertex */
  seed= (int)time(&timedata);
  qh_RANDOMseed_(seed);
  qh run_id= qh_RANDOMint+1; /* disallow 0 [UsingLibQhull::NOqhRunId] */
  qh_option("run-id", &qh run_id, NULL);
  strcat(qh qhull, "qhull");
} /* initqhull_start2 */

/*---------------------------------

  qh_initthresholds( commandString )
    set thresholds for printing and scaling from commandString

  returns:
    sets qh.GOODthreshold or qh.SPLITthreshold if 'Pd0D1' used

  see:
    qh_initflags(), 'Qbk' 'QBk' 'Pdk' and 'PDk'
    qh_inthresholds()

  design:
    for each 'Pdn' or 'PDn' option
      check syntax
      set qh.lower_threshold or qh.upper_threshold
    set qh.GOODthreshold if an unbounded threshold is used
    set qh.SPLITthreshold if a bounded threshold is used
*/
void qh_initthresholds(char *command) {
  realT value;
  int idx, maxdim, k;
  char *s= command; /* non-const due to strtol */
  char key;

  maxdim= qh input_dim;
  if (qh DELAUNAY && (qh PROJECTdelaunay || qh PROJECTinput))
    maxdim++;
  while (*s) {
    if (*s == '-')
      s++;
    if (*s == 'P') {
      s++;
      while (*s && !isspace(key= *s++)) {
        if (key == 'd' || key == 'D') {
          if (!isdigit(*s)) {
            qh_fprintf(qh ferr, 7044, "qhull warning: no dimension given for Print option '%c' at: %s.  Ignored\n",
                    key, s-1);
            continue;
          }
          idx= qh_strtol(s, &s);
          if (idx >= qh hull_dim) {
            qh_fprintf(qh ferr, 7045, "qhull warning: dimension %d for Print option '%c' is >= %d.  Ignored\n",
                idx, key, qh hull_dim);
            continue;
          }
          if (*s == ':') {
            s++;
            value= qh_strtod(s, &s);
            if (fabs((double)value) > 1.0) {
              qh_fprintf(qh ferr, 7046, "qhull warning: value %2.4g for Print option %c is > +1 or < -1.  Ignored\n",
                      value, key);
              continue;
            }
          }else
            value= 0.0;
          if (key == 'd')
            qh lower_threshold[idx]= value;
          else
            qh upper_threshold[idx]= value;
        }
      }
    }else if (*s == 'Q') {
      s++;
      while (*s && !isspace(key= *s++)) {
        if (key == 'b' && *s == 'B') {
          s++;
          for (k=maxdim; k--; ) {
            qh lower_bound[k]= -qh_DEFAULTbox;
            qh upper_bound[k]= qh_DEFAULTbox;
          }
        }else if (key == 'b' && *s == 'b')
          s++;
        else if (key == 'b' || key == 'B') {
          if (!isdigit(*s)) {
            qh_fprintf(qh ferr, 7047, "qhull warning: no dimension given for Qhull option %c.  Ignored\n",
                    key);
            continue;
          }
          idx= qh_strtol(s, &s);
          if (idx >= maxdim) {
            qh_fprintf(qh ferr, 7048, "qhull warning: dimension %d for Qhull option %c is >= %d.  Ignored\n",
                idx, key, maxdim);
            continue;
          }
          if (*s == ':') {
            s++;
            value= qh_strtod(s, &s);
          }else if (key == 'b')
            value= -qh_DEFAULTbox;
          else
            value= qh_DEFAULTbox;
          if (key == 'b')
            qh lower_bound[idx]= value;
          else
            qh upper_bound[idx]= value;
        }
      }
    }else {
      while (*s && !isspace(*s))
        s++;
    }
    while (isspace(*s))
      s++;
  }
  for (k=qh hull_dim; k--; ) {
    if (qh lower_threshold[k] > -REALmax/2) {
      qh GOODthreshold= True;
      if (qh upper_threshold[k] < REALmax/2) {
        qh SPLITthresholds= True;
        qh GOODthreshold= False;
        break;
      }
    }else if (qh upper_threshold[k] < REALmax/2)
      qh GOODthreshold= True;
  }
} /* initthresholds */

/*---------------------------------

  qh_option( option, intVal, realVal )
    add an option description to qh.qhull_options

  notes:
    NOerrors -- qh_option can not call qh_errexit() [qh_initqhull_start2]
    will be printed with statistics ('Ts') and errors
    strlen(option) < 40
*/
void qh_option(const char *option, int *i, realT *r) {
  char buf[200];
  int len, maxlen;

  sprintf(buf, "  %s", option);
  if (i)
    sprintf(buf+strlen(buf), " %d", *i);
  if (r)
    sprintf(buf+strlen(buf), " %2.2g", *r);
  len= (int)strlen(buf);  /* WARN64 */
  qh qhull_optionlen += len;
  maxlen= sizeof(qh qhull_options) - len -1;
  maximize_(maxlen, 0);
  if (qh qhull_optionlen >= qh_OPTIONline && maxlen > 0) {
    qh qhull_optionlen= len;
    strncat(qh qhull_options, "\n", (size_t)(maxlen--));
  }
  strncat(qh qhull_options, buf, (size_t)maxlen);
} /* option */

#if qh_QHpointer
/*---------------------------------

  qh_restore_qhull( oldqh )
    restores a previously saved qhull
    also restores qh_qhstat and qhmem.tempstack
    Sets *oldqh to NULL
  notes:
    errors if current qhull hasn't been saved or freed
    uses qhmem for error reporting

  NOTE 1998/5/11:
    Freeing memory after qh_save_qhull and qh_restore_qhull
    is complicated.  The procedures will be redesigned.

  see:
    qh_save_qhull(), UsingLibQhull
*/
void qh_restore_qhull(qhT **oldqh) {

  if (*oldqh && strcmp((*oldqh)->qhull, "qhull")) {
    qh_fprintf(qhmem.ferr, 6061, "qhull internal error (qh_restore_qhull): %p is not a qhull data structure\n",
                  *oldqh);
    qh_errexit(qh_ERRqhull, NULL, NULL);
  }
  if (qh_qh) {
    qh_fprintf(qhmem.ferr, 6062, "qhull internal error (qh_restore_qhull): did not save or free existing qhull\n");
    qh_errexit(qh_ERRqhull, NULL, NULL);
  }
  if (!*oldqh || !(*oldqh)->old_qhstat) {
    qh_fprintf(qhmem.ferr, 6063, "qhull internal error (qh_restore_qhull): did not previously save qhull %p\n",
                  *oldqh);
    qh_errexit(qh_ERRqhull, NULL, NULL);
  }
  qh_qh= *oldqh;
  *oldqh= NULL;
  qh_qhstat= qh old_qhstat;
  qhmem.tempstack= qh old_tempstack;
  qh old_qhstat= 0;
  qh old_tempstack= 0;
  trace1((qh ferr, 1007, "qh_restore_qhull: restored qhull from %p\n", *oldqh));
} /* restore_qhull */

/*---------------------------------

  qh_save_qhull(  )
    saves qhull for a later qh_restore_qhull
    also saves qh_qhstat and qhmem.tempstack

  returns:
    qh_qh=NULL

  notes:
    need to initialize qhull or call qh_restore_qhull before continuing

  NOTE 1998/5/11:
    Freeing memory after qh_save_qhull and qh_restore_qhull
    is complicated.  The procedures will be redesigned.

  see:
    qh_restore_qhull()
*/
qhT *qh_save_qhull(void) {
  qhT *oldqh;

  trace1((qhmem.ferr, 1045, "qh_save_qhull: save qhull %p\n", qh_qh));
  if (!qh_qh) {
    qh_fprintf(qhmem.ferr, 6064, "qhull internal error (qh_save_qhull): qhull not initialized\n");
    qh_errexit(qh_ERRqhull, NULL, NULL);
  }
  qh old_qhstat= qh_qhstat;
  qh_qhstat= NULL;
  qh old_tempstack= qhmem.tempstack;
  qhmem.tempstack= NULL;
  oldqh= qh_qh;
  qh_qh= NULL;
  return oldqh;
} /* save_qhull */

#endif

qhull-2012.1/src/libqhull/index.htm0000644000076400010400000002502311710144470020331 0ustar  bbarberAdministrators



Qhull functions, macros, and data structures





Up: Home page for Qhull

Up: Qhull manual: Table of Contents 

Up: Programs
• Options
• Output
• Formats
• Geomview
• Print
• Qhull
• Precision
• Trace

Up: Qhull code

To: Qhull files

To: Geom • Global
• Io • Mem
• Merge • Poly
• Qhull • Set
• Stat • User






Qhull functions, macros, and data structures




The following sections provide an overview and index to
Qhull's functions, macros, and data structures. Each
section starts with an introduction. If you use Opera, the source code links back to this documentation.
See also Calling
Qhull from C programs and Calling Qhull from C++ programs.



Qhull uses the following conventions:





    

  • in code, global variables start with "qh "

  • in documentation, global variables start with 'qh.'

  • constants start with an upper case word

  • important globals include an '_'

  • functions, macros, and constants start with "qh_"
    • 

  • data types end in "T"
    • 

  • macros with arguments end in "_"
    • 

  • iterators are macros that use local variables
    • 

  • iterators for sets start with "FOREACH"
    • 

  • iterators for lists start with "FORALL"
    • 

  • qhull options are in single quotes (e.g., 'Pdn')
    • 

  • lists are sorted alphabetically
    • 

  • preprocessor directives on left margin for older compilers
    • 






When reading the code, please note that the
global data structure, 'qh', is a macro.  It
either expands to "qh_qh." or to
"qh_qh->". The later is used for
applications which run concurrent calls to qh_qhull().


When reading code with an editor, a search for
"procedure
will locate the header of qh_procedure.  A search for * procedure
will locate the tail of qh_procedure.


A useful starting point is libqhull.h.  It defines most
of Qhull data structures and top-level functions.  Search for 'PFn' to
determine the corresponding constant in Qhull.  Search for 'Fp' to
determine the corresponding qh_PRINT... constant.
Search io.c to learn how the print function is implemented.



If your web browser loads .c and .h files with an external application,
change the MIME type of .c and .h files to "text/html".
Opera does not always work since it treats '<' characters as HTML tags.


Please report documentation and link errors
to qhull-bug@qhull.org.




Copyright © 1997-2012 C.B. Barber






»Qhull files 





This sections lists the .c and .h files for Qhull. Please
refer to these files for detailed information.







Makefile, CMakeLists.txt


Makefile is preconfigured for gcc.  CMakeLists.txt supports multiple
platforms with CMake.
Qhull includes project files for Visual Studio and Qt.




 


libqhull.h 


Include file for the Qhull library (libqhull.so, qhull.dll, libqhullstatic.a).
Data structures are documented under Poly.
Global variables are documented under Global.
Other data structures and variables are documented under
Qhull or Geom.



 


Geom, 
geom.h, 
geom.c, 
geom2.c, 
random.c, 
random.h


Geometric routines. These routines implement mathematical
functions such as Gaussian elimination and geometric
routines needed for Qhull. Frequently used routines are
in geom.c while infrequent ones are in geom2.c.




 


Global, 
global.c, 
libqhull.h 


Global routines. Qhull uses a global data structure, qh,
to store globally defined constants, lists, sets, and
variables.
global.c initializes and frees these
structures. 



 


Io, io.h,
io.c 


Input and output routines. Qhull provides a wide range of
input and output options.



 


Mem, 
mem.h, 
mem.c 


Memory routines. Qhull provides memory allocation and
deallocation. It uses quick-fit allocation.



 


Merge, 
merge.h, 
merge.c 


Merge routines. Qhull handles precision problems by
merged facets or joggled input. These routines merge simplicial facets,
merge non-simplicial facets, merge cycles of facets, and
rename redundant vertices.



 


Poly, 
poly.h, 
poly.c, 
poly2.c, 
libqhull.h 


Polyhedral routines. Qhull produces a polyhedron as a
list of facets with vertices, neighbors, ridges, and
geometric information. libqhull.h defines the main
data structures. Frequently used routines are in poly.c
while infrequent ones are in poly2.c.



 


Qhull, 
libqhull.c, 
libqhull.h, 
qhull_a.h, 
unix.c , 
qconvex.c , 
qdelaun.c , 
qhalf.c , 
qvoronoi.c 


Top-level routines. The Quickhull algorithm is
implemented by libqhull.c. qhull_a.h
includes all header files. 



 


Set, 
qset.h, 
qset.c 


Set routines. Qhull implements its data structures as
sets. A set is an array of pointers that is expanded as
needed. This is a separate package that may be used in
other applications. 



 


Stat, 
stat.h, 
stat.c 


Statistical routines. Qhull maintains statistics about
its implementation. 



 


User, 
user.h, 
user.c, 
user_eg.c, 
user_eg2.c, 
user_eg3.cpp, 
qhull_interface.cpp


User-defined routines. Qhull allows the user to configure
the code with defined constants and specialized routines.










 




Up:
Home page for
Qhull 

Up: Qhull manual: Table of Contents 

Up: Programs
• Options
• Output
• Formats
• Geomview
• Print
• Qhull
• Precision
• Trace

Up: Qhull code: Table of Contents 

To: Qhull files

To: Geom •
Global • Io
• Mem • Merge
• Poly • Qhull
• Set • Stat
• User



 




The
Geometry Center Home Page 


Comments to: qhull@qhull.org


Created: May 2, 1997 ---  Last modified: see top  



qhull-2012.1/src/libqhull/io.c0000644000076400010400000040455611710144466017304 0ustar  bbarberAdministrators/*
  ---------------------------------

   io.c
   Input/Output routines of qhull application

   see qh-io.htm and io.h

   see user.c for qh_errprint and qh_printfacetlist

   unix.c calls qh_readpoints and qh_produce_output

   unix.c and user.c are the only callers of io.c functions
   This allows the user to avoid loading io.o from qhull.a

   Copyright (c) 1993-2012 The Geometry Center.
   $Id: //main/2011/qhull/src/libqhull/io.c#3 $$Change: 1464 $
   $DateTime: 2012/01/25 22:58:41 $$Author: bbarber $
*/

#include "qhull_a.h"

/*========= -functions in alphabetical order after qh_produce_output()  =====*/

/*---------------------------------

  qh_produce_output()
  qh_produce_output2()
    prints out the result of qhull in desired format
    qh_produce_output2() does not call qh_prepare_output()
    if qh.GETarea
      computes and prints area and volume
    qh.PRINTout[] is an array of output formats

  notes:
    prints output in qh.PRINTout order
*/
void qh_produce_output(void) {
    int tempsize= qh_setsize(qhmem.tempstack);

    qh_prepare_output();
    qh_produce_output2();
    if (qh_setsize(qhmem.tempstack) != tempsize) {
        qh_fprintf(qh ferr, 6206, "qhull internal error (qh_produce_output): temporary sets not empty(%d)\n",
            qh_setsize(qhmem.tempstack));
        qh_errexit(qh_ERRqhull, NULL, NULL);
    }
} /* produce_output */


void qh_produce_output2(void) {
  int i, tempsize= qh_setsize(qhmem.tempstack), d_1;

  if (qh PRINTsummary)
    qh_printsummary(qh ferr);
  else if (qh PRINTout[0] == qh_PRINTnone)
    qh_printsummary(qh fout);
  for (i=0; i < qh_PRINTEND; i++)
    qh_printfacets(qh fout, qh PRINTout[i], qh facet_list, NULL, !qh_ALL);
  qh_allstatistics();
  if (qh PRINTprecision && !qh MERGING && (qh JOGGLEmax > REALmax/2 || qh RERUN))
    qh_printstats(qh ferr, qhstat precision, NULL);
  if (qh VERIFYoutput && (zzval_(Zridge) > 0 || zzval_(Zridgemid) > 0))
    qh_printstats(qh ferr, qhstat vridges, NULL);
  if (qh PRINTstatistics) {
    qh_printstatistics(qh ferr, "");
    qh_memstatistics(qh ferr);
    d_1= sizeof(setT) + (qh hull_dim - 1) * SETelemsize;
    qh_fprintf(qh ferr, 8040, "\
    size in bytes: merge %d ridge %d vertex %d facet %d\n\
         normal %d ridge vertices %d facet vertices or neighbors %d\n",
            (int)sizeof(mergeT), (int)sizeof(ridgeT),
            (int)sizeof(vertexT), (int)sizeof(facetT),
            qh normal_size, d_1, d_1 + SETelemsize);
  }
  if (qh_setsize(qhmem.tempstack) != tempsize) {
    qh_fprintf(qh ferr, 6065, "qhull internal error (qh_produce_output2): temporary sets not empty(%d)\n",
             qh_setsize(qhmem.tempstack));
    qh_errexit(qh_ERRqhull, NULL, NULL);
  }
} /* produce_output2 */

/*---------------------------------

  dfacet( id )
    print facet by id, for debugging

*/
void dfacet(unsigned id) {
  facetT *facet;

  FORALLfacets {
    if (facet->id == id) {
      qh_printfacet(qh fout, facet);
      break;
    }
  }
} /* dfacet */


/*---------------------------------

  dvertex( id )
    print vertex by id, for debugging
*/
void dvertex(unsigned id) {
  vertexT *vertex;

  FORALLvertices {
    if (vertex->id == id) {
      qh_printvertex(qh fout, vertex);
      break;
    }
  }
} /* dvertex */


/*---------------------------------

  qh_compare_vertexpoint( p1, p2 )
    used by qsort() to order vertices by point id
*/
int qh_compare_vertexpoint(const void *p1, const void *p2) {
  const vertexT *a= *((vertexT *const*)p1), *b= *((vertexT *const*)p2);

  return((qh_pointid(a->point) > qh_pointid(b->point)?1:-1));
} /* compare_vertexpoint */

/*---------------------------------

  qh_compare_facetarea( p1, p2 )
    used by qsort() to order facets by area
*/
int qh_compare_facetarea(const void *p1, const void *p2) {
  const facetT *a= *((facetT *const*)p1), *b= *((facetT *const*)p2);

  if (!a->isarea)
    return -1;
  if (!b->isarea)
    return 1;
  if (a->f.area > b->f.area)
    return 1;
  else if (a->f.area == b->f.area)
    return 0;
  return -1;
} /* compare_facetarea */

/*---------------------------------

  qh_compare_facetmerge( p1, p2 )
    used by qsort() to order facets by number of merges
*/
int qh_compare_facetmerge(const void *p1, const void *p2) {
  const facetT *a= *((facetT *const*)p1), *b= *((facetT *const*)p2);

  return(a->nummerge - b->nummerge);
} /* compare_facetvisit */

/*---------------------------------

  qh_compare_facetvisit( p1, p2 )
    used by qsort() to order facets by visit id or id
*/
int qh_compare_facetvisit(const void *p1, const void *p2) {
  const facetT *a= *((facetT *const*)p1), *b= *((facetT *const*)p2);
  int i,j;

  if (!(i= a->visitid))
    i= 0 - a->id; /* do not convert to int, sign distinguishes id from visitid */
  if (!(j= b->visitid))
    j= 0 - b->id;
  return(i - j);
} /* compare_facetvisit */

/*---------------------------------

  qh_copyfilename( dest, size, source, length )
    copy filename identified by qh_skipfilename()

  notes:
    see qh_skipfilename() for syntax
*/
void qh_copyfilename(char *filename, int size, const char* source, int length) {
  char c= *source;

  if (length > size + 1) {
      qh_fprintf(qh ferr, 6040, "qhull error: filename is more than %d characters, %s\n",  size-1, source);
      qh_errexit(qh_ERRinput, NULL, NULL);
  }
  strncpy(filename, source, length);
  filename[length]= '\0';
  if (c == '\'' || c == '"') {
    char *s= filename + 1;
    char *t= filename;
    while (*s) {
      if (*s == c) {
          if (s[-1] == '\\')
              t[-1]= c;
      }else
          *t++= *s;
      s++;
    }
    *t= '\0';
  }
} /* copyfilename */

/*---------------------------------

  qh_countfacets( facetlist, facets, printall,
          numfacets, numsimplicial, totneighbors, numridges, numcoplanar, numtricoplanars  )
    count good facets for printing and set visitid
    if allfacets, ignores qh_skipfacet()

  notes:
    qh_printsummary and qh_countfacets must match counts

  returns:
    numfacets, numsimplicial, total neighbors, numridges, coplanars
    each facet with ->visitid indicating 1-relative position
      ->visitid==0 indicates not good

  notes
    numfacets >= numsimplicial
    if qh.NEWfacets,
      does not count visible facets (matches qh_printafacet)

  design:
    for all facets on facetlist and in facets set
      unless facet is skipped or visible (i.e., will be deleted)
        mark facet->visitid
        update counts
*/
void qh_countfacets(facetT *facetlist, setT *facets, boolT printall,
    int *numfacetsp, int *numsimplicialp, int *totneighborsp, int *numridgesp, int *numcoplanarsp, int *numtricoplanarsp) {
  facetT *facet, **facetp;
  int numfacets= 0, numsimplicial= 0, numridges= 0, totneighbors= 0, numcoplanars= 0, numtricoplanars= 0;

  FORALLfacet_(facetlist) {
    if ((facet->visible && qh NEWfacets)
    || (!printall && qh_skipfacet(facet)))
      facet->visitid= 0;
    else {
      facet->visitid= ++numfacets;
      totneighbors += qh_setsize(facet->neighbors);
      if (facet->simplicial) {
        numsimplicial++;
        if (facet->keepcentrum && facet->tricoplanar)
          numtricoplanars++;
      }else
        numridges += qh_setsize(facet->ridges);
      if (facet->coplanarset)
        numcoplanars += qh_setsize(facet->coplanarset);
    }
  }

  FOREACHfacet_(facets) {
    if ((facet->visible && qh NEWfacets)
    || (!printall && qh_skipfacet(facet)))
      facet->visitid= 0;
    else {
      facet->visitid= ++numfacets;
      totneighbors += qh_setsize(facet->neighbors);
      if (facet->simplicial){
        numsimplicial++;
        if (facet->keepcentrum && facet->tricoplanar)
          numtricoplanars++;
      }else
        numridges += qh_setsize(facet->ridges);
      if (facet->coplanarset)
        numcoplanars += qh_setsize(facet->coplanarset);
    }
  }
  qh visit_id += numfacets+1;
  *numfacetsp= numfacets;
  *numsimplicialp= numsimplicial;
  *totneighborsp= totneighbors;
  *numridgesp= numridges;
  *numcoplanarsp= numcoplanars;
  *numtricoplanarsp= numtricoplanars;
} /* countfacets */

/*---------------------------------

  qh_detvnorm( vertex, vertexA, centers, offset )
    compute separating plane of the Voronoi diagram for a pair of input sites
    centers= set of facets (i.e., Voronoi vertices)
      facet->visitid= 0 iff vertex-at-infinity (i.e., unbounded)

  assumes:
    qh_ASvoronoi and qh_vertexneighbors() already set

  returns:
    norm
      a pointer into qh.gm_matrix to qh.hull_dim-1 reals
      copy the data before reusing qh.gm_matrix
    offset
      if 'QVn'
        sign adjusted so that qh.GOODvertexp is inside
      else
        sign adjusted so that vertex is inside

    qh.gm_matrix= simplex of points from centers relative to first center

  notes:
    in io.c so that code for 'v Tv' can be removed by removing io.c
    returns pointer into qh.gm_matrix to avoid tracking of temporary memory

  design:
    determine midpoint of input sites
    build points as the set of Voronoi vertices
    select a simplex from points (if necessary)
      include midpoint if the Voronoi region is unbounded
    relocate the first vertex of the simplex to the origin
    compute the normalized hyperplane through the simplex
    orient the hyperplane toward 'QVn' or 'vertex'
    if 'Tv' or 'Ts'
      if bounded
        test that hyperplane is the perpendicular bisector of the input sites
      test that Voronoi vertices not in the simplex are still on the hyperplane
    free up temporary memory
*/
pointT *qh_detvnorm(vertexT *vertex, vertexT *vertexA, setT *centers, realT *offsetp) {
  facetT *facet, **facetp;
  int  i, k, pointid, pointidA, point_i, point_n;
  setT *simplex= NULL;
  pointT *point, **pointp, *point0, *midpoint, *normal, *inpoint;
  coordT *coord, *gmcoord, *normalp;
  setT *points= qh_settemp(qh TEMPsize);
  boolT nearzero= False;
  boolT unbounded= False;
  int numcenters= 0;
  int dim= qh hull_dim - 1;
  realT dist, offset, angle, zero= 0.0;

  midpoint= qh gm_matrix + qh hull_dim * qh hull_dim;  /* last row */
  for (k=0; k < dim; k++)
    midpoint[k]= (vertex->point[k] + vertexA->point[k])/2;
  FOREACHfacet_(centers) {
    numcenters++;
    if (!facet->visitid)
      unbounded= True;
    else {
      if (!facet->center)
        facet->center= qh_facetcenter(facet->vertices);
      qh_setappend(&points, facet->center);
    }
  }
  if (numcenters > dim) {
    simplex= qh_settemp(qh TEMPsize);
    qh_setappend(&simplex, vertex->point);
    if (unbounded)
      qh_setappend(&simplex, midpoint);
    qh_maxsimplex(dim, points, NULL, 0, &simplex);
    qh_setdelnth(simplex, 0);
  }else if (numcenters == dim) {
    if (unbounded)
      qh_setappend(&points, midpoint);
    simplex= points;
  }else {
    qh_fprintf(qh ferr, 6216, "qhull internal error (qh_detvnorm): too few points(%d) to compute separating plane\n", numcenters);
    qh_errexit(qh_ERRqhull, NULL, NULL);
  }
  i= 0;
  gmcoord= qh gm_matrix;
  point0= SETfirstt_(simplex, pointT);
  FOREACHpoint_(simplex) {
    if (qh IStracing >= 4)
      qh_printmatrix(qh ferr, "qh_detvnorm: Voronoi vertex or midpoint",
                              &point, 1, dim);
    if (point != point0) {
      qh gm_row[i++]= gmcoord;
      coord= point0;
      for (k=dim; k--; )
        *(gmcoord++)= *point++ - *coord++;
    }
  }
  qh gm_row[i]= gmcoord;  /* does not overlap midpoint, may be used later for qh_areasimplex */
  normal= gmcoord;
  qh_sethyperplane_gauss(dim, qh gm_row, point0, True,
                normal, &offset, &nearzero);
  if (qh GOODvertexp == vertexA->point)
    inpoint= vertexA->point;
  else
    inpoint= vertex->point;
  zinc_(Zdistio);
  dist= qh_distnorm(dim, inpoint, normal, &offset);
  if (dist > 0) {
    offset= -offset;
    normalp= normal;
    for (k=dim; k--; ) {
      *normalp= -(*normalp);
      normalp++;
    }
  }
  if (qh VERIFYoutput || qh PRINTstatistics) {
    pointid= qh_pointid(vertex->point);
    pointidA= qh_pointid(vertexA->point);
    if (!unbounded) {
      zinc_(Zdiststat);
      dist= qh_distnorm(dim, midpoint, normal, &offset);
      if (dist < 0)
        dist= -dist;
      zzinc_(Zridgemid);
      wwmax_(Wridgemidmax, dist);
      wwadd_(Wridgemid, dist);
      trace4((qh ferr, 4014, "qh_detvnorm: points %d %d midpoint dist %2.2g\n",
                 pointid, pointidA, dist));
      for (k=0; k < dim; k++)
        midpoint[k]= vertexA->point[k] - vertex->point[k];  /* overwrites midpoint! */
      qh_normalize(midpoint, dim, False);
      angle= qh_distnorm(dim, midpoint, normal, &zero); /* qh_detangle uses dim+1 */
      if (angle < 0.0)
        angle= angle + 1.0;
      else
        angle= angle - 1.0;
      if (angle < 0.0)
        angle -= angle;
      trace4((qh ferr, 4015, "qh_detvnorm: points %d %d angle %2.2g nearzero %d\n",
                 pointid, pointidA, angle, nearzero));
      if (nearzero) {
        zzinc_(Zridge0);
        wwmax_(Wridge0max, angle);
        wwadd_(Wridge0, angle);
      }else {
        zzinc_(Zridgeok)
        wwmax_(Wridgeokmax, angle);
        wwadd_(Wridgeok, angle);
      }
    }
    if (simplex != points) {
      FOREACHpoint_i_(points) {
        if (!qh_setin(simplex, point)) {
          facet= SETelemt_(centers, point_i, facetT);
          zinc_(Zdiststat);
          dist= qh_distnorm(dim, point, normal, &offset);
          if (dist < 0)
            dist= -dist;
          zzinc_(Zridge);
          wwmax_(Wridgemax, dist);
          wwadd_(Wridge, dist);
          trace4((qh ferr, 4016, "qh_detvnorm: points %d %d Voronoi vertex %d dist %2.2g\n",
                             pointid, pointidA, facet->visitid, dist));
        }
      }
    }
  }
  *offsetp= offset;
  if (simplex != points)
    qh_settempfree(&simplex);
  qh_settempfree(&points);
  return normal;
} /* detvnorm */

/*---------------------------------

  qh_detvridge( vertexA )
    determine Voronoi ridge from 'seen' neighbors of vertexA
    include one vertex-at-infinite if an !neighbor->visitid

  returns:
    temporary set of centers (facets, i.e., Voronoi vertices)
    sorted by center id
*/
setT *qh_detvridge(vertexT *vertex) {
  setT *centers= qh_settemp(qh TEMPsize);
  setT *tricenters= qh_settemp(qh TEMPsize);
  facetT *neighbor, **neighborp;
  boolT firstinf= True;

  FOREACHneighbor_(vertex) {
    if (neighbor->seen) {
      if (neighbor->visitid) {
        if (!neighbor->tricoplanar || qh_setunique(&tricenters, neighbor->center))
          qh_setappend(¢ers, neighbor);
      }else if (firstinf) {
        firstinf= False;
        qh_setappend(¢ers, neighbor);
      }
    }
  }
  qsort(SETaddr_(centers, facetT), (size_t)qh_setsize(centers),
             sizeof(facetT *), qh_compare_facetvisit);
  qh_settempfree(&tricenters);
  return centers;
} /* detvridge */

/*---------------------------------

  qh_detvridge3( atvertex, vertex )
    determine 3-d Voronoi ridge from 'seen' neighbors of atvertex and vertex
    include one vertex-at-infinite for !neighbor->visitid
    assumes all facet->seen2= True

  returns:
    temporary set of centers (facets, i.e., Voronoi vertices)
    listed in adjacency order (!oriented)
    all facet->seen2= True

  design:
    mark all neighbors of atvertex
    for each adjacent neighbor of both atvertex and vertex
      if neighbor selected
        add neighbor to set of Voronoi vertices
*/
setT *qh_detvridge3 (vertexT *atvertex, vertexT *vertex) {
  setT *centers= qh_settemp(qh TEMPsize);
  setT *tricenters= qh_settemp(qh TEMPsize);
  facetT *neighbor, **neighborp, *facet= NULL;
  boolT firstinf= True;

  FOREACHneighbor_(atvertex)
    neighbor->seen2= False;
  FOREACHneighbor_(vertex) {
    if (!neighbor->seen2) {
      facet= neighbor;
      break;
    }
  }
  while (facet) {
    facet->seen2= True;
    if (neighbor->seen) {
      if (facet->visitid) {
        if (!facet->tricoplanar || qh_setunique(&tricenters, facet->center))
          qh_setappend(¢ers, facet);
      }else if (firstinf) {
        firstinf= False;
        qh_setappend(¢ers, facet);
      }
    }
    FOREACHneighbor_(facet) {
      if (!neighbor->seen2) {
        if (qh_setin(vertex->neighbors, neighbor))
          break;
        else
          neighbor->seen2= True;
      }
    }
    facet= neighbor;
  }
  if (qh CHECKfrequently) {
    FOREACHneighbor_(vertex) {
      if (!neighbor->seen2) {
          qh_fprintf(qh ferr, 6217, "qhull internal error (qh_detvridge3): neighbors of vertex p%d are not connected at facet %d\n",
                 qh_pointid(vertex->point), neighbor->id);
        qh_errexit(qh_ERRqhull, neighbor, NULL);
      }
    }
  }
  FOREACHneighbor_(atvertex)
    neighbor->seen2= True;
  qh_settempfree(&tricenters);
  return centers;
} /* detvridge3 */

/*---------------------------------

  qh_eachvoronoi( fp, printvridge, vertex, visitall, innerouter, inorder )
    if visitall,
      visit all Voronoi ridges for vertex (i.e., an input site)
    else
      visit all unvisited Voronoi ridges for vertex
      all vertex->seen= False if unvisited
    assumes
      all facet->seen= False
      all facet->seen2= True (for qh_detvridge3)
      all facet->visitid == 0 if vertex_at_infinity
                         == index of Voronoi vertex
                         >= qh.num_facets if ignored
    innerouter:
      qh_RIDGEall--  both inner (bounded) and outer(unbounded) ridges
      qh_RIDGEinner- only inner
      qh_RIDGEouter- only outer

    if inorder
      orders vertices for 3-d Voronoi diagrams

  returns:
    number of visited ridges (does not include previously visited ridges)

    if printvridge,
      calls printvridge( fp, vertex, vertexA, centers)
        fp== any pointer (assumes FILE*)
        vertex,vertexA= pair of input sites that define a Voronoi ridge
        centers= set of facets (i.e., Voronoi vertices)
                 ->visitid == index or 0 if vertex_at_infinity
                 ordered for 3-d Voronoi diagram
  notes:
    uses qh.vertex_visit

  see:
    qh_eachvoronoi_all()

  design:
    mark selected neighbors of atvertex
    for each selected neighbor (either Voronoi vertex or vertex-at-infinity)
      for each unvisited vertex
        if atvertex and vertex share more than d-1 neighbors
          bump totalcount
          if printvridge defined
            build the set of shared neighbors (i.e., Voronoi vertices)
            call printvridge
*/
int qh_eachvoronoi(FILE *fp, printvridgeT printvridge, vertexT *atvertex, boolT visitall, qh_RIDGE innerouter, boolT inorder) {
  boolT unbounded;
  int count;
  facetT *neighbor, **neighborp, *neighborA, **neighborAp;
  setT *centers;
  setT *tricenters= qh_settemp(qh TEMPsize);

  vertexT *vertex, **vertexp;
  boolT firstinf;
  unsigned int numfacets= (unsigned int)qh num_facets;
  int totridges= 0;

  qh vertex_visit++;
  atvertex->seen= True;
  if (visitall) {
    FORALLvertices
      vertex->seen= False;
  }
  FOREACHneighbor_(atvertex) {
    if (neighbor->visitid < numfacets)
      neighbor->seen= True;
  }
  FOREACHneighbor_(atvertex) {
    if (neighbor->seen) {
      FOREACHvertex_(neighbor->vertices) {
        if (vertex->visitid != qh vertex_visit && !vertex->seen) {
          vertex->visitid= qh vertex_visit;
          count= 0;
          firstinf= True;
          qh_settruncate(tricenters, 0);
          FOREACHneighborA_(vertex) {
            if (neighborA->seen) {
              if (neighborA->visitid) {
                if (!neighborA->tricoplanar || qh_setunique(&tricenters, neighborA->center))
                  count++;
              }else if (firstinf) {
                count++;
                firstinf= False;
              }
            }
          }
          if (count >= qh hull_dim - 1) {  /* e.g., 3 for 3-d Voronoi */
            if (firstinf) {
              if (innerouter == qh_RIDGEouter)
                continue;
              unbounded= False;
            }else {
              if (innerouter == qh_RIDGEinner)
                continue;
              unbounded= True;
            }
            totridges++;
            trace4((qh ferr, 4017, "qh_eachvoronoi: Voronoi ridge of %d vertices between sites %d and %d\n",
                  count, qh_pointid(atvertex->point), qh_pointid(vertex->point)));
            if (printvridge && fp) {
              if (inorder && qh hull_dim == 3+1) /* 3-d Voronoi diagram */
                centers= qh_detvridge3 (atvertex, vertex);
              else
                centers= qh_detvridge(vertex);
              (*printvridge) (fp, atvertex, vertex, centers, unbounded);
              qh_settempfree(¢ers);
            }
          }
        }
      }
    }
  }
  FOREACHneighbor_(atvertex)
    neighbor->seen= False;
  qh_settempfree(&tricenters);
  return totridges;
} /* eachvoronoi */


/*---------------------------------

  qh_eachvoronoi_all( fp, printvridge, isUpper, innerouter, inorder )
    visit all Voronoi ridges

    innerouter:
      see qh_eachvoronoi()

    if inorder
      orders vertices for 3-d Voronoi diagrams

  returns
    total number of ridges

    if isUpper == facet->upperdelaunay  (i.e., a Vornoi vertex)
      facet->visitid= Voronoi vertex index(same as 'o' format)
    else
      facet->visitid= 0

    if printvridge,
      calls printvridge( fp, vertex, vertexA, centers)
      [see qh_eachvoronoi]

  notes:
    Not used for qhull.exe
    same effect as qh_printvdiagram but ridges not sorted by point id
*/
int qh_eachvoronoi_all(FILE *fp, printvridgeT printvridge, boolT isUpper, qh_RIDGE innerouter, boolT inorder) {
  facetT *facet;
  vertexT *vertex;
  int numcenters= 1;  /* vertex 0 is vertex-at-infinity */
  int totridges= 0;

  qh_clearcenters(qh_ASvoronoi);
  qh_vertexneighbors();
  maximize_(qh visit_id, (unsigned) qh num_facets);
  FORALLfacets {
    facet->visitid= 0;
    facet->seen= False;
    facet->seen2= True;
  }
  FORALLfacets {
    if (facet->upperdelaunay == isUpper)
      facet->visitid= numcenters++;
  }
  FORALLvertices
    vertex->seen= False;
  FORALLvertices {
    if (qh GOODvertex > 0 && qh_pointid(vertex->point)+1 != qh GOODvertex)
      continue;
    totridges += qh_eachvoronoi(fp, printvridge, vertex,
                   !qh_ALL, innerouter, inorder);
  }
  return totridges;
} /* eachvoronoi_all */

/*---------------------------------

  qh_facet2point( facet, point0, point1, mindist )
    return two projected temporary vertices for a 2-d facet
    may be non-simplicial

  returns:
    point0 and point1 oriented and projected to the facet
    returns mindist (maximum distance below plane)
*/
void qh_facet2point(facetT *facet, pointT **point0, pointT **point1, realT *mindist) {
  vertexT *vertex0, *vertex1;
  realT dist;

  if (facet->toporient ^ qh_ORIENTclock) {
    vertex0= SETfirstt_(facet->vertices, vertexT);
    vertex1= SETsecondt_(facet->vertices, vertexT);
  }else {
    vertex1= SETfirstt_(facet->vertices, vertexT);
    vertex0= SETsecondt_(facet->vertices, vertexT);
  }
  zadd_(Zdistio, 2);
  qh_distplane(vertex0->point, facet, &dist);
  *mindist= dist;
  *point0= qh_projectpoint(vertex0->point, facet, dist);
  qh_distplane(vertex1->point, facet, &dist);
  minimize_(*mindist, dist);
  *point1= qh_projectpoint(vertex1->point, facet, dist);
} /* facet2point */


/*---------------------------------

  qh_facetvertices( facetlist, facets, allfacets )
    returns temporary set of vertices in a set and/or list of facets
    if allfacets, ignores qh_skipfacet()

  returns:
    vertices with qh.vertex_visit

  notes:
    optimized for allfacets of facet_list

  design:
    if allfacets of facet_list
      create vertex set from vertex_list
    else
      for each selected facet in facets or facetlist
        append unvisited vertices to vertex set
*/
setT *qh_facetvertices(facetT *facetlist, setT *facets, boolT allfacets) {
  setT *vertices;
  facetT *facet, **facetp;
  vertexT *vertex, **vertexp;

  qh vertex_visit++;
  if (facetlist == qh facet_list && allfacets && !facets) {
    vertices= qh_settemp(qh num_vertices);
    FORALLvertices {
      vertex->visitid= qh vertex_visit;
      qh_setappend(&vertices, vertex);
    }
  }else {
    vertices= qh_settemp(qh TEMPsize);
    FORALLfacet_(facetlist) {
      if (!allfacets && qh_skipfacet(facet))
        continue;
      FOREACHvertex_(facet->vertices) {
        if (vertex->visitid != qh vertex_visit) {
          vertex->visitid= qh vertex_visit;
          qh_setappend(&vertices, vertex);
        }
      }
    }
  }
  FOREACHfacet_(facets) {
    if (!allfacets && qh_skipfacet(facet))
      continue;
    FOREACHvertex_(facet->vertices) {
      if (vertex->visitid != qh vertex_visit) {
        vertex->visitid= qh vertex_visit;
        qh_setappend(&vertices, vertex);
      }
    }
  }
  return vertices;
} /* facetvertices */

/*---------------------------------

  qh_geomplanes( facet, outerplane, innerplane )
    return outer and inner planes for Geomview
    qh.PRINTradius is size of vertices and points (includes qh.JOGGLEmax)

  notes:
    assume precise calculations in io.c with roundoff covered by qh_GEOMepsilon
*/
void qh_geomplanes(facetT *facet, realT *outerplane, realT *innerplane) {
  realT radius;

  if (qh MERGING || qh JOGGLEmax < REALmax/2) {
    qh_outerinner(facet, outerplane, innerplane);
    radius= qh PRINTradius;
    if (qh JOGGLEmax < REALmax/2)
      radius -= qh JOGGLEmax * sqrt((realT)qh hull_dim);  /* already accounted for in qh_outerinner() */
    *outerplane += radius;
    *innerplane -= radius;
    if (qh PRINTcoplanar || qh PRINTspheres) {
      *outerplane += qh MAXabs_coord * qh_GEOMepsilon;
      *innerplane -= qh MAXabs_coord * qh_GEOMepsilon;
    }
  }else
    *innerplane= *outerplane= 0;
} /* geomplanes */


/*---------------------------------

  qh_markkeep( facetlist )
    mark good facets that meet qh.KEEParea, qh.KEEPmerge, and qh.KEEPminArea
    ignores visible facets (!part of convex hull)

  returns:
    may clear facet->good
    recomputes qh.num_good

  design:
    get set of good facets
    if qh.KEEParea
      sort facets by area
      clear facet->good for all but n largest facets
    if qh.KEEPmerge
      sort facets by merge count
      clear facet->good for all but n most merged facets
    if qh.KEEPminarea
      clear facet->good if area too small
    update qh.num_good
*/
void qh_markkeep(facetT *facetlist) {
  facetT *facet, **facetp;
  setT *facets= qh_settemp(qh num_facets);
  int size, count;

  trace2((qh ferr, 2006, "qh_markkeep: only keep %d largest and/or %d most merged facets and/or min area %.2g\n",
          qh KEEParea, qh KEEPmerge, qh KEEPminArea));
  FORALLfacet_(facetlist) {
    if (!facet->visible && facet->good)
      qh_setappend(&facets, facet);
  }
  size= qh_setsize(facets);
  if (qh KEEParea) {
    qsort(SETaddr_(facets, facetT), (size_t)size,
             sizeof(facetT *), qh_compare_facetarea);
    if ((count= size - qh KEEParea) > 0) {
      FOREACHfacet_(facets) {
        facet->good= False;
        if (--count == 0)
          break;
      }
    }
  }
  if (qh KEEPmerge) {
    qsort(SETaddr_(facets, facetT), (size_t)size,
             sizeof(facetT *), qh_compare_facetmerge);
    if ((count= size - qh KEEPmerge) > 0) {
      FOREACHfacet_(facets) {
        facet->good= False;
        if (--count == 0)
          break;
      }
    }
  }
  if (qh KEEPminArea < REALmax/2) {
    FOREACHfacet_(facets) {
      if (!facet->isarea || facet->f.area < qh KEEPminArea)
        facet->good= False;
    }
  }
  qh_settempfree(&facets);
  count= 0;
  FORALLfacet_(facetlist) {
    if (facet->good)
      count++;
  }
  qh num_good= count;
} /* markkeep */


/*---------------------------------

  qh_markvoronoi( facetlist, facets, printall, isLower, numcenters )
    mark voronoi vertices for printing by site pairs

  returns:
    temporary set of vertices indexed by pointid
    isLower set if printing lower hull (i.e., at least one facet is lower hull)
    numcenters= total number of Voronoi vertices
    bumps qh.printoutnum for vertex-at-infinity
    clears all facet->seen and sets facet->seen2

    if selected
      facet->visitid= Voronoi vertex id
    else if upper hull (or 'Qu' and lower hull)
      facet->visitid= 0
    else
      facet->visitid >= qh num_facets

  notes:
    ignores qh.ATinfinity, if defined
*/
setT *qh_markvoronoi(facetT *facetlist, setT *facets, boolT printall, boolT *isLowerp, int *numcentersp) {
  int numcenters=0;
  facetT *facet, **facetp;
  setT *vertices;
  boolT isLower= False;

  qh printoutnum++;
  qh_clearcenters(qh_ASvoronoi);  /* in case, qh_printvdiagram2 called by user */
  qh_vertexneighbors();
  vertices= qh_pointvertex();
  if (qh ATinfinity)
    SETelem_(vertices, qh num_points-1)= NULL;
  qh visit_id++;
  maximize_(qh visit_id, (unsigned) qh num_facets);
  FORALLfacet_(facetlist) {
    if (printall || !qh_skipfacet(facet)) {
      if (!facet->upperdelaunay) {
        isLower= True;
        break;
      }
    }
  }
  FOREACHfacet_(facets) {
    if (printall || !qh_skipfacet(facet)) {
      if (!facet->upperdelaunay) {
        isLower= True;
        break;
      }
    }
  }
  FORALLfacets {
    if (facet->normal && (facet->upperdelaunay == isLower))
      facet->visitid= 0;  /* facetlist or facets may overwrite */
    else
      facet->visitid= qh visit_id;
    facet->seen= False;
    facet->seen2= True;
  }
  numcenters++;  /* qh_INFINITE */
  FORALLfacet_(facetlist) {
    if (printall || !qh_skipfacet(facet))
      facet->visitid= numcenters++;
  }
  FOREACHfacet_(facets) {
    if (printall || !qh_skipfacet(facet))
      facet->visitid= numcenters++;
  }
  *isLowerp= isLower;
  *numcentersp= numcenters;
  trace2((qh ferr, 2007, "qh_markvoronoi: isLower %d numcenters %d\n", isLower, numcenters));
  return vertices;
} /* markvoronoi */

/*---------------------------------

  qh_order_vertexneighbors( vertex )
    order facet neighbors of a 2-d or 3-d vertex by adjacency

  notes:
    does not orient the neighbors

  design:
    initialize a new neighbor set with the first facet in vertex->neighbors
    while vertex->neighbors non-empty
      select next neighbor in the previous facet's neighbor set
    set vertex->neighbors to the new neighbor set
*/
void qh_order_vertexneighbors(vertexT *vertex) {
  setT *newset;
  facetT *facet, *neighbor, **neighborp;

  trace4((qh ferr, 4018, "qh_order_vertexneighbors: order neighbors of v%d for 3-d\n", vertex->id));
  newset= qh_settemp(qh_setsize(vertex->neighbors));
  facet= (facetT*)qh_setdellast(vertex->neighbors);
  qh_setappend(&newset, facet);
  while (qh_setsize(vertex->neighbors)) {
    FOREACHneighbor_(vertex) {
      if (qh_setin(facet->neighbors, neighbor)) {
        qh_setdel(vertex->neighbors, neighbor);
        qh_setappend(&newset, neighbor);
        facet= neighbor;
        break;
      }
    }
    if (!neighbor) {
      qh_fprintf(qh ferr, 6066, "qhull internal error (qh_order_vertexneighbors): no neighbor of v%d for f%d\n",
        vertex->id, facet->id);
      qh_errexit(qh_ERRqhull, facet, NULL);
    }
  }
  qh_setfree(&vertex->neighbors);
  qh_settemppop();
  vertex->neighbors= newset;
} /* order_vertexneighbors */

/*---------------------------------

  qh_prepare_output( )
    prepare for qh_produce_output2() according to
      qh.KEEPminArea, KEEParea, KEEPmerge, GOODvertex, GOODthreshold, GOODpoint, ONLYgood, SPLITthresholds
    does not reset facet->good

  notes
    except for PRINTstatistics, no-op if previously called with same options
*/
void qh_prepare_output(void) {
  if (qh VORONOI) {
    qh_clearcenters (qh_ASvoronoi);
    qh_vertexneighbors();
  }
  if (qh TRIangulate && !qh hasTriangulation) {
    qh_triangulate();
    if (qh VERIFYoutput && !qh CHECKfrequently)
      qh_checkpolygon (qh facet_list);
  }
  qh_findgood_all (qh facet_list);
  if (qh GETarea)
    qh_getarea(qh facet_list);
  if (qh KEEParea || qh KEEPmerge || qh KEEPminArea < REALmax/2)
    qh_markkeep (qh facet_list);
  if (qh PRINTstatistics)
    qh_collectstatistics();
}

/*---------------------------------

  qh_printafacet( fp, format, facet, printall )
    print facet to fp in given output format (see qh.PRINTout)

  returns:
    nop if !printall and qh_skipfacet()
    nop if visible facet and NEWfacets and format != PRINTfacets
    must match qh_countfacets

  notes
    preserves qh.visit_id
    facet->normal may be null if PREmerge/MERGEexact and STOPcone before merge

  see
    qh_printbegin() and qh_printend()

  design:
    test for printing facet
    call appropriate routine for format
    or output results directly
*/
void qh_printafacet(FILE *fp, qh_PRINT format, facetT *facet, boolT printall) {
  realT color[4], offset, dist, outerplane, innerplane;
  boolT zerodiv;
  coordT *point, *normp, *coordp, **pointp, *feasiblep;
  int k;
  vertexT *vertex, **vertexp;
  facetT *neighbor, **neighborp;

  if (!printall && qh_skipfacet(facet))
    return;
  if (facet->visible && qh NEWfacets && format != qh_PRINTfacets)
    return;
  qh printoutnum++;
  switch (format) {
  case qh_PRINTarea:
    if (facet->isarea) {
      qh_fprintf(fp, 9009, qh_REAL_1, facet->f.area);
      qh_fprintf(fp, 9010, "\n");
    }else
      qh_fprintf(fp, 9011, "0\n");
    break;
  case qh_PRINTcoplanars:
    qh_fprintf(fp, 9012, "%d", qh_setsize(facet->coplanarset));
    FOREACHpoint_(facet->coplanarset)
      qh_fprintf(fp, 9013, " %d", qh_pointid(point));
    qh_fprintf(fp, 9014, "\n");
    break;
  case qh_PRINTcentrums:
    qh_printcenter(fp, format, NULL, facet);
    break;
  case qh_PRINTfacets:
    qh_printfacet(fp, facet);
    break;
  case qh_PRINTfacets_xridge:
    qh_printfacetheader(fp, facet);
    break;
  case qh_PRINTgeom:  /* either 2 , 3, or 4-d by qh_printbegin */
    if (!facet->normal)
      break;
    for (k=qh hull_dim; k--; ) {
      color[k]= (facet->normal[k]+1.0)/2.0;
      maximize_(color[k], -1.0);
      minimize_(color[k], +1.0);
    }
    qh_projectdim3 (color, color);
    if (qh PRINTdim != qh hull_dim)
      qh_normalize2 (color, 3, True, NULL, NULL);
    if (qh hull_dim <= 2)
      qh_printfacet2geom(fp, facet, color);
    else if (qh hull_dim == 3) {
      if (facet->simplicial)
        qh_printfacet3geom_simplicial(fp, facet, color);
      else
        qh_printfacet3geom_nonsimplicial(fp, facet, color);
    }else {
      if (facet->simplicial)
        qh_printfacet4geom_simplicial(fp, facet, color);
      else
        qh_printfacet4geom_nonsimplicial(fp, facet, color);
    }
    break;
  case qh_PRINTids:
    qh_fprintf(fp, 9015, "%d\n", facet->id);
    break;
  case qh_PRINTincidences:
  case qh_PRINToff:
  case qh_PRINTtriangles:
    if (qh hull_dim == 3 && format != qh_PRINTtriangles)
      qh_printfacet3vertex(fp, facet, format);
    else if (facet->simplicial || qh hull_dim == 2 || format == qh_PRINToff)
      qh_printfacetNvertex_simplicial(fp, facet, format);
    else
      qh_printfacetNvertex_nonsimplicial(fp, facet, qh printoutvar++, format);
    break;
  case qh_PRINTinner:
    qh_outerinner(facet, NULL, &innerplane);
    offset= facet->offset - innerplane;
    goto LABELprintnorm;
    break; /* prevent warning */
  case qh_PRINTmerges:
    qh_fprintf(fp, 9016, "%d\n", facet->nummerge);
    break;
  case qh_PRINTnormals:
    offset= facet->offset;
    goto LABELprintnorm;
    break; /* prevent warning */
  case qh_PRINTouter:
    qh_outerinner(facet, &outerplane, NULL);
    offset= facet->offset - outerplane;
  LABELprintnorm:
    if (!facet->normal) {
      qh_fprintf(fp, 9017, "no normal for facet f%d\n", facet->id);
      break;
    }
    if (qh CDDoutput) {
      qh_fprintf(fp, 9018, qh_REAL_1, -offset);
      for (k=0; k < qh hull_dim; k++)
        qh_fprintf(fp, 9019, qh_REAL_1, -facet->normal[k]);
    }else {
      for (k=0; k < qh hull_dim; k++)
        qh_fprintf(fp, 9020, qh_REAL_1, facet->normal[k]);
      qh_fprintf(fp, 9021, qh_REAL_1, offset);
    }
    qh_fprintf(fp, 9022, "\n");
    break;
  case qh_PRINTmathematica:  /* either 2 or 3-d by qh_printbegin */
  case qh_PRINTmaple:
    if (qh hull_dim == 2)
      qh_printfacet2math(fp, facet, format, qh printoutvar++);
    else
      qh_printfacet3math(fp, facet, format, qh printoutvar++);
    break;
  case qh_PRINTneighbors:
    qh_fprintf(fp, 9023, "%d", qh_setsize(facet->neighbors));
    FOREACHneighbor_(facet)
      qh_fprintf(fp, 9024, " %d",
               neighbor->visitid ? neighbor->visitid - 1: 0 - neighbor->id);
    qh_fprintf(fp, 9025, "\n");
    break;
  case qh_PRINTpointintersect:
    if (!qh feasible_point) {
      qh_fprintf(qh ferr, 6067, "qhull input error (qh_printafacet): option 'Fp' needs qh feasible_point\n");
      qh_errexit( qh_ERRinput, NULL, NULL);
    }
    if (facet->offset > 0)
      goto LABELprintinfinite;
    point= coordp= (coordT*)qh_memalloc(qh normal_size);
    normp= facet->normal;
    feasiblep= qh feasible_point;
    if (facet->offset < -qh MINdenom) {
      for (k=qh hull_dim; k--; )
        *(coordp++)= (*(normp++) / - facet->offset) + *(feasiblep++);
    }else {
      for (k=qh hull_dim; k--; ) {
        *(coordp++)= qh_divzero(*(normp++), facet->offset, qh MINdenom_1,
                                 &zerodiv) + *(feasiblep++);
        if (zerodiv) {
          qh_memfree(point, qh normal_size);
          goto LABELprintinfinite;
        }
      }
    }
    qh_printpoint(fp, NULL, point);
    qh_memfree(point, qh normal_size);
    break;
  LABELprintinfinite:
    for (k=qh hull_dim; k--; )
      qh_fprintf(fp, 9026, qh_REAL_1, qh_INFINITE);
    qh_fprintf(fp, 9027, "\n");
    break;
  case qh_PRINTpointnearest:
    FOREACHpoint_(facet->coplanarset) {
      int id, id2;
      vertex= qh_nearvertex(facet, point, &dist);
      id= qh_pointid(vertex->point);
      id2= qh_pointid(point);
      qh_fprintf(fp, 9028, "%d %d %d " qh_REAL_1 "\n", id, id2, facet->id, dist);
    }
    break;
  case qh_PRINTpoints:  /* VORONOI only by qh_printbegin */
    if (qh CDDoutput)
      qh_fprintf(fp, 9029, "1 ");
    qh_printcenter(fp, format, NULL, facet);
    break;
  case qh_PRINTvertices:
    qh_fprintf(fp, 9030, "%d", qh_setsize(facet->vertices));
    FOREACHvertex_(facet->vertices)
      qh_fprintf(fp, 9031, " %d", qh_pointid(vertex->point));
    qh_fprintf(fp, 9032, "\n");
    break;
  default:
    break;
  }
} /* printafacet */

/*---------------------------------

  qh_printbegin(  )
    prints header for all output formats

  returns:
    checks for valid format

  notes:
    uses qh.visit_id for 3/4off
    changes qh.interior_point if printing centrums
    qh_countfacets clears facet->visitid for non-good facets

  see
    qh_printend() and qh_printafacet()

  design:
    count facets and related statistics
    print header for format
*/
void qh_printbegin(FILE *fp, qh_PRINT format, facetT *facetlist, setT *facets, boolT printall) {
  int numfacets, numsimplicial, numridges, totneighbors, numcoplanars, numtricoplanars;
  int i, num;
  facetT *facet, **facetp;
  vertexT *vertex, **vertexp;
  setT *vertices;
  pointT *point, **pointp, *pointtemp;

  qh printoutnum= 0;
  qh_countfacets(facetlist, facets, printall, &numfacets, &numsimplicial,
      &totneighbors, &numridges, &numcoplanars, &numtricoplanars);
  switch (format) {
  case qh_PRINTnone:
    break;
  case qh_PRINTarea:
    qh_fprintf(fp, 9033, "%d\n", numfacets);
    break;
  case qh_PRINTcoplanars:
    qh_fprintf(fp, 9034, "%d\n", numfacets);
    break;
  case qh_PRINTcentrums:
    if (qh CENTERtype == qh_ASnone)
      qh_clearcenters(qh_AScentrum);
    qh_fprintf(fp, 9035, "%d\n%d\n", qh hull_dim, numfacets);
    break;
  case qh_PRINTfacets:
  case qh_PRINTfacets_xridge:
    if (facetlist)
      qh_printvertexlist(fp, "Vertices and facets:\n", facetlist, facets, printall);
    break;
  case qh_PRINTgeom:
    if (qh hull_dim > 4)  /* qh_initqhull_globals also checks */
      goto LABELnoformat;
    if (qh VORONOI && qh hull_dim > 3)  /* PRINTdim == DROPdim == hull_dim-1 */
      goto LABELnoformat;
    if (qh hull_dim == 2 && (qh PRINTridges || qh DOintersections))
      qh_fprintf(qh ferr, 7049, "qhull warning: output for ridges and intersections not implemented in 2-d\n");
    if (qh hull_dim == 4 && (qh PRINTinner || qh PRINTouter ||
                             (qh PRINTdim == 4 && qh PRINTcentrums)))
      qh_fprintf(qh ferr, 7050, "qhull warning: output for outer/inner planes and centrums not implemented in 4-d\n");
    if (qh PRINTdim == 4 && (qh PRINTspheres))
      qh_fprintf(qh ferr, 7051, "qhull warning: output for vertices not implemented in 4-d\n");
    if (qh PRINTdim == 4 && qh DOintersections && qh PRINTnoplanes)
      qh_fprintf(qh ferr, 7052, "qhull warning: 'Gnh' generates no output in 4-d\n");
    if (qh PRINTdim == 2) {
      qh_fprintf(fp, 9036, "{appearance {linewidth 3} LIST # %s | %s\n",
              qh rbox_command, qh qhull_command);
    }else if (qh PRINTdim == 3) {
      qh_fprintf(fp, 9037, "{appearance {+edge -evert linewidth 2} LIST # %s | %s\n",
              qh rbox_command, qh qhull_command);
    }else if (qh PRINTdim == 4) {
      qh visit_id++;
      num= 0;
      FORALLfacet_(facetlist)    /* get number of ridges to be printed */
        qh_printend4geom(NULL, facet, &num, printall);
      FOREACHfacet_(facets)
        qh_printend4geom(NULL, facet, &num, printall);
      qh ridgeoutnum= num;
      qh printoutvar= 0;  /* counts number of ridges in output */
      qh_fprintf(fp, 9038, "LIST # %s | %s\n", qh rbox_command, qh qhull_command);
    }

    if (qh PRINTdots) {
      qh printoutnum++;
      num= qh num_points + qh_setsize(qh other_points);
      if (qh DELAUNAY && qh ATinfinity)
        num--;
      if (qh PRINTdim == 4)
        qh_fprintf(fp, 9039, "4VECT %d %d 1\n", num, num);
      else
        qh_fprintf(fp, 9040, "VECT %d %d 1\n", num, num);

      for (i=num; i--; ) {
        if (i % 20 == 0)
          qh_fprintf(fp, 9041, "\n");
        qh_fprintf(fp, 9042, "1 ");
      }
      qh_fprintf(fp, 9043, "# 1 point per line\n1 ");
      for (i=num-1; i--; ) { /* num at least 3 for D2 */
        if (i % 20 == 0)
          qh_fprintf(fp, 9044, "\n");
        qh_fprintf(fp, 9045, "0 ");
      }
      qh_fprintf(fp, 9046, "# 1 color for all\n");
      FORALLpoints {
        if (!qh DELAUNAY || !qh ATinfinity || qh_pointid(point) != qh num_points-1) {
          if (qh PRINTdim == 4)
            qh_printpoint(fp, NULL, point);
            else
              qh_printpoint3 (fp, point);
        }
      }
      FOREACHpoint_(qh other_points) {
        if (qh PRINTdim == 4)
          qh_printpoint(fp, NULL, point);
        else
          qh_printpoint3 (fp, point);
      }
      qh_fprintf(fp, 9047, "0 1 1 1  # color of points\n");
    }

    if (qh PRINTdim == 4  && !qh PRINTnoplanes)
      /* 4dview loads up multiple 4OFF objects slowly */
      qh_fprintf(fp, 9048, "4OFF %d %d 1\n", 3*qh ridgeoutnum, qh ridgeoutnum);
    qh PRINTcradius= 2 * qh DISTround;  /* include test DISTround */
    if (qh PREmerge) {
      maximize_(qh PRINTcradius, qh premerge_centrum + qh DISTround);
    }else if (qh POSTmerge)
      maximize_(qh PRINTcradius, qh postmerge_centrum + qh DISTround);
    qh PRINTradius= qh PRINTcradius;
    if (qh PRINTspheres + qh PRINTcoplanar)
      maximize_(qh PRINTradius, qh MAXabs_coord * qh_MINradius);
    if (qh premerge_cos < REALmax/2) {
      maximize_(qh PRINTradius, (1- qh premerge_cos) * qh MAXabs_coord);
    }else if (!qh PREmerge && qh POSTmerge && qh postmerge_cos < REALmax/2) {
      maximize_(qh PRINTradius, (1- qh postmerge_cos) * qh MAXabs_coord);
    }
    maximize_(qh PRINTradius, qh MINvisible);
    if (qh JOGGLEmax < REALmax/2)
      qh PRINTradius += qh JOGGLEmax * sqrt((realT)qh hull_dim);
    if (qh PRINTdim != 4 &&
        (qh PRINTcoplanar || qh PRINTspheres || qh PRINTcentrums)) {
      vertices= qh_facetvertices(facetlist, facets, printall);
      if (qh PRINTspheres && qh PRINTdim <= 3)
        qh_printspheres(fp, vertices, qh PRINTradius);
      if (qh PRINTcoplanar || qh PRINTcentrums) {
        qh firstcentrum= True;
        if (qh PRINTcoplanar&& !qh PRINTspheres) {
          FOREACHvertex_(vertices)
            qh_printpointvect2 (fp, vertex->point, NULL, qh interior_point, qh PRINTradius);
        }
        FORALLfacet_(facetlist) {
          if (!printall && qh_skipfacet(facet))
            continue;
          if (!facet->normal)
            continue;
          if (qh PRINTcentrums && qh PRINTdim <= 3)
            qh_printcentrum(fp, facet, qh PRINTcradius);
          if (!qh PRINTcoplanar)
            continue;
          FOREACHpoint_(facet->coplanarset)
            qh_printpointvect2 (fp, point, facet->normal, NULL, qh PRINTradius);
          FOREACHpoint_(facet->outsideset)
            qh_printpointvect2 (fp, point, facet->normal, NULL, qh PRINTradius);
        }
        FOREACHfacet_(facets) {
          if (!printall && qh_skipfacet(facet))
            continue;
          if (!facet->normal)
            continue;
          if (qh PRINTcentrums && qh PRINTdim <= 3)
            qh_printcentrum(fp, facet, qh PRINTcradius);
          if (!qh PRINTcoplanar)
            continue;
          FOREACHpoint_(facet->coplanarset)
            qh_printpointvect2 (fp, point, facet->normal, NULL, qh PRINTradius);
          FOREACHpoint_(facet->outsideset)
            qh_printpointvect2 (fp, point, facet->normal, NULL, qh PRINTradius);
        }
      }
      qh_settempfree(&vertices);
    }
    qh visit_id++; /* for printing hyperplane intersections */
    break;
  case qh_PRINTids:
    qh_fprintf(fp, 9049, "%d\n", numfacets);
    break;
  case qh_PRINTincidences:
    if (qh VORONOI && qh PRINTprecision)
      qh_fprintf(qh ferr, 7053, "qhull warning: writing Delaunay.  Use 'p' or 'o' for Voronoi centers\n");
    qh printoutvar= qh vertex_id;  /* centrum id for non-simplicial facets */
    if (qh hull_dim <= 3)
      qh_fprintf(fp, 9050, "%d\n", numfacets);
    else
      qh_fprintf(fp, 9051, "%d\n", numsimplicial+numridges);
    break;
  case qh_PRINTinner:
  case qh_PRINTnormals:
  case qh_PRINTouter:
    if (qh CDDoutput)
      qh_fprintf(fp, 9052, "%s | %s\nbegin\n    %d %d real\n", qh rbox_command,
            qh qhull_command, numfacets, qh hull_dim+1);
    else
      qh_fprintf(fp, 9053, "%d\n%d\n", qh hull_dim+1, numfacets);
    break;
  case qh_PRINTmathematica:
  case qh_PRINTmaple:
    if (qh hull_dim > 3)  /* qh_initbuffers also checks */
      goto LABELnoformat;
    if (qh VORONOI)
      qh_fprintf(qh ferr, 7054, "qhull warning: output is the Delaunay triangulation\n");
    if (format == qh_PRINTmaple) {
      if (qh hull_dim == 2)
        qh_fprintf(fp, 9054, "PLOT(CURVES(\n");
      else
        qh_fprintf(fp, 9055, "PLOT3D(POLYGONS(\n");
    }else
      qh_fprintf(fp, 9056, "{\n");
    qh printoutvar= 0;   /* counts number of facets for notfirst */
    break;
  case qh_PRINTmerges:
    qh_fprintf(fp, 9057, "%d\n", numfacets);
    break;
  case qh_PRINTpointintersect:
    qh_fprintf(fp, 9058, "%d\n%d\n", qh hull_dim, numfacets);
    break;
  case qh_PRINTneighbors:
    qh_fprintf(fp, 9059, "%d\n", numfacets);
    break;
  case qh_PRINToff:
  case qh_PRINTtriangles:
    if (qh VORONOI)
      goto LABELnoformat;
    num = qh hull_dim;
    if (format == qh_PRINToff || qh hull_dim == 2)
      qh_fprintf(fp, 9060, "%d\n%d %d %d\n", num,
        qh num_points+qh_setsize(qh other_points), numfacets, totneighbors/2);
    else { /* qh_PRINTtriangles */
      qh printoutvar= qh num_points+qh_setsize(qh other_points); /* first centrum */
      if (qh DELAUNAY)
        num--;  /* drop last dimension */
      qh_fprintf(fp, 9061, "%d\n%d %d %d\n", num, qh printoutvar
        + numfacets - numsimplicial, numsimplicial + numridges, totneighbors/2);
    }
    FORALLpoints
      qh_printpointid(qh fout, NULL, num, point, -1);
    FOREACHpoint_(qh other_points)
      qh_printpointid(qh fout, NULL, num, point, -1);
    if (format == qh_PRINTtriangles && qh hull_dim > 2) {
      FORALLfacets {
        if (!facet->simplicial && facet->visitid)
          qh_printcenter(qh fout, format, NULL, facet);
      }
    }
    break;
  case qh_PRINTpointnearest:
    qh_fprintf(fp, 9062, "%d\n", numcoplanars);
    break;
  case qh_PRINTpoints:
    if (!qh VORONOI)
      goto LABELnoformat;
    if (qh CDDoutput)
      qh_fprintf(fp, 9063, "%s | %s\nbegin\n%d %d real\n", qh rbox_command,
           qh qhull_command, numfacets, qh hull_dim);
    else
      qh_fprintf(fp, 9064, "%d\n%d\n", qh hull_dim-1, numfacets);
    break;
  case qh_PRINTvertices:
    qh_fprintf(fp, 9065, "%d\n", numfacets);
    break;
  case qh_PRINTsummary:
  default:
  LABELnoformat:
    qh_fprintf(qh ferr, 6068, "qhull internal error (qh_printbegin): can not use this format for dimension %d\n",
         qh hull_dim);
    qh_errexit(qh_ERRqhull, NULL, NULL);
  }
} /* printbegin */

/*---------------------------------

  qh_printcenter( fp, string, facet )
    print facet->center as centrum or Voronoi center
    string may be NULL.  Don't include '%' codes.
    nop if qh CENTERtype neither CENTERvoronoi nor CENTERcentrum
    if upper envelope of Delaunay triangulation and point at-infinity
      prints qh_INFINITE instead;

  notes:
    defines facet->center if needed
    if format=PRINTgeom, adds a 0 if would otherwise be 2-d
    Same as QhullFacet::printCenter
*/
void qh_printcenter(FILE *fp, qh_PRINT format, const char *string, facetT *facet) {
  int k, num;

  if (qh CENTERtype != qh_ASvoronoi && qh CENTERtype != qh_AScentrum)
    return;
  if (string)
    qh_fprintf(fp, 9066, string);
  if (qh CENTERtype == qh_ASvoronoi) {
    num= qh hull_dim-1;
    if (!facet->normal || !facet->upperdelaunay || !qh ATinfinity) {
      if (!facet->center)
        facet->center= qh_facetcenter(facet->vertices);
      for (k=0; k < num; k++)
        qh_fprintf(fp, 9067, qh_REAL_1, facet->center[k]);
    }else {
      for (k=0; k < num; k++)
        qh_fprintf(fp, 9068, qh_REAL_1, qh_INFINITE);
    }
  }else /* qh CENTERtype == qh_AScentrum */ {
    num= qh hull_dim;
    if (format == qh_PRINTtriangles && qh DELAUNAY)
      num--;
    if (!facet->center)
      facet->center= qh_getcentrum(facet);
    for (k=0; k < num; k++)
      qh_fprintf(fp, 9069, qh_REAL_1, facet->center[k]);
  }
  if (format == qh_PRINTgeom && num == 2)
    qh_fprintf(fp, 9070, " 0\n");
  else
    qh_fprintf(fp, 9071, "\n");
} /* printcenter */

/*---------------------------------

  qh_printcentrum( fp, facet, radius )
    print centrum for a facet in OOGL format
    radius defines size of centrum
    2-d or 3-d only

  returns:
    defines facet->center if needed
*/
void qh_printcentrum(FILE *fp, facetT *facet, realT radius) {
  pointT *centrum, *projpt;
  boolT tempcentrum= False;
  realT xaxis[4], yaxis[4], normal[4], dist;
  realT green[3]={0, 1, 0};
  vertexT *apex;
  int k;

  if (qh CENTERtype == qh_AScentrum) {
    if (!facet->center)
      facet->center= qh_getcentrum(facet);
    centrum= facet->center;
  }else {
    centrum= qh_getcentrum(facet);
    tempcentrum= True;
  }
  qh_fprintf(fp, 9072, "{appearance {-normal -edge normscale 0} ");
  if (qh firstcentrum) {
    qh firstcentrum= False;
    qh_fprintf(fp, 9073, "{INST geom { define centrum CQUAD  # f%d\n\
-0.3 -0.3 0.0001     0 0 1 1\n\
 0.3 -0.3 0.0001     0 0 1 1\n\
 0.3  0.3 0.0001     0 0 1 1\n\
-0.3  0.3 0.0001     0 0 1 1 } transform { \n", facet->id);
  }else
    qh_fprintf(fp, 9074, "{INST geom { : centrum } transform { # f%d\n", facet->id);
  apex= SETfirstt_(facet->vertices, vertexT);
  qh_distplane(apex->point, facet, &dist);
  projpt= qh_projectpoint(apex->point, facet, dist);
  for (k=qh hull_dim; k--; ) {
    xaxis[k]= projpt[k] - centrum[k];
    normal[k]= facet->normal[k];
  }
  if (qh hull_dim == 2) {
    xaxis[2]= 0;
    normal[2]= 0;
  }else if (qh hull_dim == 4) {
    qh_projectdim3 (xaxis, xaxis);
    qh_projectdim3 (normal, normal);
    qh_normalize2 (normal, qh PRINTdim, True, NULL, NULL);
  }
  qh_crossproduct(3, xaxis, normal, yaxis);
  qh_fprintf(fp, 9075, "%8.4g %8.4g %8.4g 0\n", xaxis[0], xaxis[1], xaxis[2]);
  qh_fprintf(fp, 9076, "%8.4g %8.4g %8.4g 0\n", yaxis[0], yaxis[1], yaxis[2]);
  qh_fprintf(fp, 9077, "%8.4g %8.4g %8.4g 0\n", normal[0], normal[1], normal[2]);
  qh_printpoint3 (fp, centrum);
  qh_fprintf(fp, 9078, "1 }}}\n");
  qh_memfree(projpt, qh normal_size);
  qh_printpointvect(fp, centrum, facet->normal, NULL, radius, green);
  if (tempcentrum)
    qh_memfree(centrum, qh normal_size);
} /* printcentrum */

/*---------------------------------

  qh_printend( fp, format )
    prints trailer for all output formats

  see:
    qh_printbegin() and qh_printafacet()

*/
void qh_printend(FILE *fp, qh_PRINT format, facetT *facetlist, setT *facets, boolT printall) {
  int num;
  facetT *facet, **facetp;

  if (!qh printoutnum)
    qh_fprintf(qh ferr, 7055, "qhull warning: no facets printed\n");
  switch (format) {
  case qh_PRINTgeom:
    if (qh hull_dim == 4 && qh DROPdim < 0  && !qh PRINTnoplanes) {
      qh visit_id++;
      num= 0;
      FORALLfacet_(facetlist)
        qh_printend4geom(fp, facet,&num, printall);
      FOREACHfacet_(facets)
        qh_printend4geom(fp, facet, &num, printall);
      if (num != qh ridgeoutnum || qh printoutvar != qh ridgeoutnum) {
        qh_fprintf(qh ferr, 6069, "qhull internal error (qh_printend): number of ridges %d != number printed %d and at end %d\n", qh ridgeoutnum, qh printoutvar, num);
        qh_errexit(qh_ERRqhull, NULL, NULL);
      }
    }else
      qh_fprintf(fp, 9079, "}\n");
    break;
  case qh_PRINTinner:
  case qh_PRINTnormals:
  case qh_PRINTouter:
    if (qh CDDoutput)
      qh_fprintf(fp, 9080, "end\n");
    break;
  case qh_PRINTmaple:
    qh_fprintf(fp, 9081, "));\n");
    break;
  case qh_PRINTmathematica:
    qh_fprintf(fp, 9082, "}\n");
    break;
  case qh_PRINTpoints:
    if (qh CDDoutput)
      qh_fprintf(fp, 9083, "end\n");
    break;
  default:
    break;
  }
} /* printend */

/*---------------------------------

  qh_printend4geom( fp, facet, numridges, printall )
    helper function for qh_printbegin/printend

  returns:
    number of printed ridges

  notes:
    just counts printed ridges if fp=NULL
    uses facet->visitid
    must agree with qh_printfacet4geom...

  design:
    computes color for facet from its normal
    prints each ridge of facet
*/
void qh_printend4geom(FILE *fp, facetT *facet, int *nump, boolT printall) {
  realT color[3];
  int i, num= *nump;
  facetT *neighbor, **neighborp;
  ridgeT *ridge, **ridgep;

  if (!printall && qh_skipfacet(facet))
    return;
  if (qh PRINTnoplanes || (facet->visible && qh NEWfacets))
    return;
  if (!facet->normal)
    return;
  if (fp) {
    for (i=0; i < 3; i++) {
      color[i]= (facet->normal[i]+1.0)/2.0;
      maximize_(color[i], -1.0);
      minimize_(color[i], +1.0);
    }
  }
  facet->visitid= qh visit_id;
  if (facet->simplicial) {
    FOREACHneighbor_(facet) {
      if (neighbor->visitid != qh visit_id) {
        if (fp)
          qh_fprintf(fp, 9084, "3 %d %d %d %8.4g %8.4g %8.4g 1 # f%d f%d\n",
                 3*num, 3*num+1, 3*num+2, color[0], color[1], color[2],
                 facet->id, neighbor->id);
        num++;
      }
    }
  }else {
    FOREACHridge_(facet->ridges) {
      neighbor= otherfacet_(ridge, facet);
      if (neighbor->visitid != qh visit_id) {
        if (fp)
          qh_fprintf(fp, 9085, "3 %d %d %d %8.4g %8.4g %8.4g 1 #r%d f%d f%d\n",
                 3*num, 3*num+1, 3*num+2, color[0], color[1], color[2],
                 ridge->id, facet->id, neighbor->id);
        num++;
      }
    }
  }
  *nump= num;
} /* printend4geom */

/*---------------------------------

  qh_printextremes( fp, facetlist, facets, printall )
    print extreme points for convex hulls or halfspace intersections

  notes:
    #points, followed by ids, one per line

    sorted by id
    same order as qh_printpoints_out if no coplanar/interior points
*/
void qh_printextremes(FILE *fp, facetT *facetlist, setT *facets, boolT printall) {
  setT *vertices, *points;
  pointT *point;
  vertexT *vertex, **vertexp;
  int id;
  int numpoints=0, point_i, point_n;
  int allpoints= qh num_points + qh_setsize(qh other_points);

  points= qh_settemp(allpoints);
  qh_setzero(points, 0, allpoints);
  vertices= qh_facetvertices(facetlist, facets, printall);
  FOREACHvertex_(vertices) {
    id= qh_pointid(vertex->point);
    if (id >= 0) {
      SETelem_(points, id)= vertex->point;
      numpoints++;
    }
  }
  qh_settempfree(&vertices);
  qh_fprintf(fp, 9086, "%d\n", numpoints);
  FOREACHpoint_i_(points) {
    if (point)
      qh_fprintf(fp, 9087, "%d\n", point_i);
  }
  qh_settempfree(&points);
} /* printextremes */

/*---------------------------------

  qh_printextremes_2d( fp, facetlist, facets, printall )
    prints point ids for facets in qh_ORIENTclock order

  notes:
    #points, followed by ids, one per line
    if facetlist/facets are disjoint than the output includes skips
    errors if facets form a loop
    does not print coplanar points
*/
void qh_printextremes_2d(FILE *fp, facetT *facetlist, setT *facets, boolT printall) {
  int numfacets, numridges, totneighbors, numcoplanars, numsimplicial, numtricoplanars;
  setT *vertices;
  facetT *facet, *startfacet, *nextfacet;
  vertexT *vertexA, *vertexB;

  qh_countfacets(facetlist, facets, printall, &numfacets, &numsimplicial,
      &totneighbors, &numridges, &numcoplanars, &numtricoplanars); /* marks qh visit_id */
  vertices= qh_facetvertices(facetlist, facets, printall);
  qh_fprintf(fp, 9088, "%d\n", qh_setsize(vertices));
  qh_settempfree(&vertices);
  if (!numfacets)
    return;
  facet= startfacet= facetlist ? facetlist : SETfirstt_(facets, facetT);
  qh vertex_visit++;
  qh visit_id++;
  do {
    if (facet->toporient ^ qh_ORIENTclock) {
      vertexA= SETfirstt_(facet->vertices, vertexT);
      vertexB= SETsecondt_(facet->vertices, vertexT);
      nextfacet= SETfirstt_(facet->neighbors, facetT);
    }else {
      vertexA= SETsecondt_(facet->vertices, vertexT);
      vertexB= SETfirstt_(facet->vertices, vertexT);
      nextfacet= SETsecondt_(facet->neighbors, facetT);
    }
    if (facet->visitid == qh visit_id) {
      qh_fprintf(qh ferr, 6218, "Qhull internal error (qh_printextremes_2d): loop in facet list.  facet %d nextfacet %d\n",
                 facet->id, nextfacet->id);
      qh_errexit2 (qh_ERRqhull, facet, nextfacet);
    }
    if (facet->visitid) {
      if (vertexA->visitid != qh vertex_visit) {
        vertexA->visitid= qh vertex_visit;
        qh_fprintf(fp, 9089, "%d\n", qh_pointid(vertexA->point));
      }
      if (vertexB->visitid != qh vertex_visit) {
        vertexB->visitid= qh vertex_visit;
        qh_fprintf(fp, 9090, "%d\n", qh_pointid(vertexB->point));
      }
    }
    facet->visitid= qh visit_id;
    facet= nextfacet;
  }while (facet && facet != startfacet);
} /* printextremes_2d */

/*---------------------------------

  qh_printextremes_d( fp, facetlist, facets, printall )
    print extreme points of input sites for Delaunay triangulations

  notes:
    #points, followed by ids, one per line

    unordered
*/
void qh_printextremes_d(FILE *fp, facetT *facetlist, setT *facets, boolT printall) {
  setT *vertices;
  vertexT *vertex, **vertexp;
  boolT upperseen, lowerseen;
  facetT *neighbor, **neighborp;
  int numpoints=0;

  vertices= qh_facetvertices(facetlist, facets, printall);
  qh_vertexneighbors();
  FOREACHvertex_(vertices) {
    upperseen= lowerseen= False;
    FOREACHneighbor_(vertex) {
      if (neighbor->upperdelaunay)
        upperseen= True;
      else
        lowerseen= True;
    }
    if (upperseen && lowerseen) {
      vertex->seen= True;
      numpoints++;
    }else
      vertex->seen= False;
  }
  qh_fprintf(fp, 9091, "%d\n", numpoints);
  FOREACHvertex_(vertices) {
    if (vertex->seen)
      qh_fprintf(fp, 9092, "%d\n", qh_pointid(vertex->point));
  }
  qh_settempfree(&vertices);
} /* printextremes_d */

/*---------------------------------

  qh_printfacet( fp, facet )
    prints all fields of a facet to fp

  notes:
    ridges printed in neighbor order
*/
void qh_printfacet(FILE *fp, facetT *facet) {

  qh_printfacetheader(fp, facet);
  if (facet->ridges)
    qh_printfacetridges(fp, facet);
} /* printfacet */


/*---------------------------------

  qh_printfacet2geom( fp, facet, color )
    print facet as part of a 2-d VECT for Geomview

    notes:
      assume precise calculations in io.c with roundoff covered by qh_GEOMepsilon
      mindist is calculated within io.c.  maxoutside is calculated elsewhere
      so a DISTround error may have occured.
*/
void qh_printfacet2geom(FILE *fp, facetT *facet, realT color[3]) {
  pointT *point0, *point1;
  realT mindist, innerplane, outerplane;
  int k;

  qh_facet2point(facet, &point0, &point1, &mindist);
  qh_geomplanes(facet, &outerplane, &innerplane);
  if (qh PRINTouter || (!qh PRINTnoplanes && !qh PRINTinner))
    qh_printfacet2geom_points(fp, point0, point1, facet, outerplane, color);
  if (qh PRINTinner || (!qh PRINTnoplanes && !qh PRINTouter &&
                outerplane - innerplane > 2 * qh MAXabs_coord * qh_GEOMepsilon)) {
    for (k=3; k--; )
      color[k]= 1.0 - color[k];
    qh_printfacet2geom_points(fp, point0, point1, facet, innerplane, color);
  }
  qh_memfree(point1, qh normal_size);
  qh_memfree(point0, qh normal_size);
} /* printfacet2geom */

/*---------------------------------

  qh_printfacet2geom_points( fp, point1, point2, facet, offset, color )
    prints a 2-d facet as a VECT with 2 points at some offset.
    The points are on the facet's plane.
*/
void qh_printfacet2geom_points(FILE *fp, pointT *point1, pointT *point2,
                               facetT *facet, realT offset, realT color[3]) {
  pointT *p1= point1, *p2= point2;

  qh_fprintf(fp, 9093, "VECT 1 2 1 2 1 # f%d\n", facet->id);
  if (offset != 0.0) {
    p1= qh_projectpoint(p1, facet, -offset);
    p2= qh_projectpoint(p2, facet, -offset);
  }
  qh_fprintf(fp, 9094, "%8.4g %8.4g %8.4g\n%8.4g %8.4g %8.4g\n",
           p1[0], p1[1], 0.0, p2[0], p2[1], 0.0);
  if (offset != 0.0) {
    qh_memfree(p1, qh normal_size);
    qh_memfree(p2, qh normal_size);
  }
  qh_fprintf(fp, 9095, "%8.4g %8.4g %8.4g 1.0\n", color[0], color[1], color[2]);
} /* printfacet2geom_points */


/*---------------------------------

  qh_printfacet2math( fp, facet, format, notfirst )
    print 2-d Maple or Mathematica output for a facet
    may be non-simplicial

  notes:
    use %16.8f since Mathematica 2.2 does not handle exponential format
    see qh_printfacet3math
*/
void qh_printfacet2math(FILE *fp, facetT *facet, qh_PRINT format, int notfirst) {
  pointT *point0, *point1;
  realT mindist;
  const char *pointfmt;

  qh_facet2point(facet, &point0, &point1, &mindist);
  if (notfirst)
    qh_fprintf(fp, 9096, ",");
  if (format == qh_PRINTmaple)
    pointfmt= "[[%16.8f, %16.8f], [%16.8f, %16.8f]]\n";
  else
    pointfmt= "Line[{{%16.8f, %16.8f}, {%16.8f, %16.8f}}]\n";
  qh_fprintf(fp, 9097, pointfmt, point0[0], point0[1], point1[0], point1[1]);
  qh_memfree(point1, qh normal_size);
  qh_memfree(point0, qh normal_size);
} /* printfacet2math */


/*---------------------------------

  qh_printfacet3geom_nonsimplicial( fp, facet, color )
    print Geomview OFF for a 3-d nonsimplicial facet.
    if DOintersections, prints ridges to unvisited neighbors(qh visit_id)

  notes
    uses facet->visitid for intersections and ridges
*/
void qh_printfacet3geom_nonsimplicial(FILE *fp, facetT *facet, realT color[3]) {
  ridgeT *ridge, **ridgep;
  setT *projectedpoints, *vertices;
  vertexT *vertex, **vertexp, *vertexA, *vertexB;
  pointT *projpt, *point, **pointp;
  facetT *neighbor;
  realT dist, outerplane, innerplane;
  int cntvertices, k;
  realT black[3]={0, 0, 0}, green[3]={0, 1, 0};

  qh_geomplanes(facet, &outerplane, &innerplane);
  vertices= qh_facet3vertex(facet); /* oriented */
  cntvertices= qh_setsize(vertices);
  projectedpoints= qh_settemp(cntvertices);
  FOREACHvertex_(vertices) {
    zinc_(Zdistio);
    qh_distplane(vertex->point, facet, &dist);
    projpt= qh_projectpoint(vertex->point, facet, dist);
    qh_setappend(&projectedpoints, projpt);
  }
  if (qh PRINTouter || (!qh PRINTnoplanes && !qh PRINTinner))
    qh_printfacet3geom_points(fp, projectedpoints, facet, outerplane, color);
  if (qh PRINTinner || (!qh PRINTnoplanes && !qh PRINTouter &&
                outerplane - innerplane > 2 * qh MAXabs_coord * qh_GEOMepsilon)) {
    for (k=3; k--; )
      color[k]= 1.0 - color[k];
    qh_printfacet3geom_points(fp, projectedpoints, facet, innerplane, color);
  }
  FOREACHpoint_(projectedpoints)
    qh_memfree(point, qh normal_size);
  qh_settempfree(&projectedpoints);
  qh_settempfree(&vertices);
  if ((qh DOintersections || qh PRINTridges)
  && (!facet->visible || !qh NEWfacets)) {
    facet->visitid= qh visit_id;
    FOREACHridge_(facet->ridges) {
      neighbor= otherfacet_(ridge, facet);
      if (neighbor->visitid != qh visit_id) {
        if (qh DOintersections)
          qh_printhyperplaneintersection(fp, facet, neighbor, ridge->vertices, black);
        if (qh PRINTridges) {
          vertexA= SETfirstt_(ridge->vertices, vertexT);
          vertexB= SETsecondt_(ridge->vertices, vertexT);
          qh_printline3geom(fp, vertexA->point, vertexB->point, green);
        }
      }
    }
  }
} /* printfacet3geom_nonsimplicial */

/*---------------------------------

  qh_printfacet3geom_points( fp, points, facet, offset )
    prints a 3-d facet as OFF Geomview object.
    offset is relative to the facet's hyperplane
    Facet is determined as a list of points
*/
void qh_printfacet3geom_points(FILE *fp, setT *points, facetT *facet, realT offset, realT color[3]) {
  int k, n= qh_setsize(points), i;
  pointT *point, **pointp;
  setT *printpoints;

  qh_fprintf(fp, 9098, "{ OFF %d 1 1 # f%d\n", n, facet->id);
  if (offset != 0.0) {
    printpoints= qh_settemp(n);
    FOREACHpoint_(points)
      qh_setappend(&printpoints, qh_projectpoint(point, facet, -offset));
  }else
    printpoints= points;
  FOREACHpoint_(printpoints) {
    for (k=0; k < qh hull_dim; k++) {
      if (k == qh DROPdim)
        qh_fprintf(fp, 9099, "0 ");
      else
        qh_fprintf(fp, 9100, "%8.4g ", point[k]);
    }
    if (printpoints != points)
      qh_memfree(point, qh normal_size);
    qh_fprintf(fp, 9101, "\n");
  }
  if (printpoints != points)
    qh_settempfree(&printpoints);
  qh_fprintf(fp, 9102, "%d ", n);
  for (i=0; i < n; i++)
    qh_fprintf(fp, 9103, "%d ", i);
  qh_fprintf(fp, 9104, "%8.4g %8.4g %8.4g 1.0 }\n", color[0], color[1], color[2]);
} /* printfacet3geom_points */


/*---------------------------------

  qh_printfacet3geom_simplicial(  )
    print Geomview OFF for a 3-d simplicial facet.

  notes:
    may flip color
    uses facet->visitid for intersections and ridges

    assume precise calculations in io.c with roundoff covered by qh_GEOMepsilon
    innerplane may be off by qh DISTround.  Maxoutside is calculated elsewhere
    so a DISTround error may have occured.
*/
void qh_printfacet3geom_simplicial(FILE *fp, facetT *facet, realT color[3]) {
  setT *points, *vertices;
  vertexT *vertex, **vertexp, *vertexA, *vertexB;
  facetT *neighbor, **neighborp;
  realT outerplane, innerplane;
  realT black[3]={0, 0, 0}, green[3]={0, 1, 0};
  int k;

  qh_geomplanes(facet, &outerplane, &innerplane);
  vertices= qh_facet3vertex(facet);
  points= qh_settemp(qh TEMPsize);
  FOREACHvertex_(vertices)
    qh_setappend(&points, vertex->point);
  if (qh PRINTouter || (!qh PRINTnoplanes && !qh PRINTinner))
    qh_printfacet3geom_points(fp, points, facet, outerplane, color);
  if (qh PRINTinner || (!qh PRINTnoplanes && !qh PRINTouter &&
              outerplane - innerplane > 2 * qh MAXabs_coord * qh_GEOMepsilon)) {
    for (k=3; k--; )
      color[k]= 1.0 - color[k];
    qh_printfacet3geom_points(fp, points, facet, innerplane, color);
  }
  qh_settempfree(&points);
  qh_settempfree(&vertices);
  if ((qh DOintersections || qh PRINTridges)
  && (!facet->visible || !qh NEWfacets)) {
    facet->visitid= qh visit_id;
    FOREACHneighbor_(facet) {
      if (neighbor->visitid != qh visit_id) {
        vertices= qh_setnew_delnthsorted(facet->vertices, qh hull_dim,
                          SETindex_(facet->neighbors, neighbor), 0);
        if (qh DOintersections)
           qh_printhyperplaneintersection(fp, facet, neighbor, vertices, black);
        if (qh PRINTridges) {
          vertexA= SETfirstt_(vertices, vertexT);
          vertexB= SETsecondt_(vertices, vertexT);
          qh_printline3geom(fp, vertexA->point, vertexB->point, green);
        }
        qh_setfree(&vertices);
      }
    }
  }
} /* printfacet3geom_simplicial */

/*---------------------------------

  qh_printfacet3math( fp, facet, notfirst )
    print 3-d Maple or Mathematica output for a facet

  notes:
    may be non-simplicial
    use %16.8f since Mathematica 2.2 does not handle exponential format
    see qh_printfacet2math
*/
void qh_printfacet3math(FILE *fp, facetT *facet, qh_PRINT format, int notfirst) {
  vertexT *vertex, **vertexp;
  setT *points, *vertices;
  pointT *point, **pointp;
  boolT firstpoint= True;
  realT dist;
  const char *pointfmt, *endfmt;

  if (notfirst)
    qh_fprintf(fp, 9105, ",\n");
  vertices= qh_facet3vertex(facet);
  points= qh_settemp(qh_setsize(vertices));
  FOREACHvertex_(vertices) {
    zinc_(Zdistio);
    qh_distplane(vertex->point, facet, &dist);
    point= qh_projectpoint(vertex->point, facet, dist);
    qh_setappend(&points, point);
  }
  if (format == qh_PRINTmaple) {
    qh_fprintf(fp, 9106, "[");
    pointfmt= "[%16.8f, %16.8f, %16.8f]";
    endfmt= "]";
  }else {
    qh_fprintf(fp, 9107, "Polygon[{");
    pointfmt= "{%16.8f, %16.8f, %16.8f}";
    endfmt= "}]";
  }
  FOREACHpoint_(points) {
    if (firstpoint)
      firstpoint= False;
    else
      qh_fprintf(fp, 9108, ",\n");
    qh_fprintf(fp, 9109, pointfmt, point[0], point[1], point[2]);
  }
  FOREACHpoint_(points)
    qh_memfree(point, qh normal_size);
  qh_settempfree(&points);
  qh_settempfree(&vertices);
  qh_fprintf(fp, 9110, endfmt);
} /* printfacet3math */


/*---------------------------------

  qh_printfacet3vertex( fp, facet, format )
    print vertices in a 3-d facet as point ids

  notes:
    prints number of vertices first if format == qh_PRINToff
    the facet may be non-simplicial
*/
void qh_printfacet3vertex(FILE *fp, facetT *facet, qh_PRINT format) {
  vertexT *vertex, **vertexp;
  setT *vertices;

  vertices= qh_facet3vertex(facet);
  if (format == qh_PRINToff)
    qh_fprintf(fp, 9111, "%d ", qh_setsize(vertices));
  FOREACHvertex_(vertices)
    qh_fprintf(fp, 9112, "%d ", qh_pointid(vertex->point));
  qh_fprintf(fp, 9113, "\n");
  qh_settempfree(&vertices);
} /* printfacet3vertex */


/*---------------------------------

  qh_printfacet4geom_nonsimplicial(  )
    print Geomview 4OFF file for a 4d nonsimplicial facet
    prints all ridges to unvisited neighbors (qh.visit_id)
    if qh.DROPdim
      prints in OFF format

  notes:
    must agree with printend4geom()
*/
void qh_printfacet4geom_nonsimplicial(FILE *fp, facetT *facet, realT color[3]) {
  facetT *neighbor;
  ridgeT *ridge, **ridgep;
  vertexT *vertex, **vertexp;
  pointT *point;
  int k;
  realT dist;

  facet->visitid= qh visit_id;
  if (qh PRINTnoplanes || (facet->visible && qh NEWfacets))
    return;
  FOREACHridge_(facet->ridges) {
    neighbor= otherfacet_(ridge, facet);
    if (neighbor->visitid == qh visit_id)
      continue;
    if (qh PRINTtransparent && !neighbor->good)
      continue;
    if (qh DOintersections)
      qh_printhyperplaneintersection(fp, facet, neighbor, ridge->vertices, color);
    else {
      if (qh DROPdim >= 0)
        qh_fprintf(fp, 9114, "OFF 3 1 1 # f%d\n", facet->id);
      else {
        qh printoutvar++;
        qh_fprintf(fp, 9115, "# r%d between f%d f%d\n", ridge->id, facet->id, neighbor->id);
      }
      FOREACHvertex_(ridge->vertices) {
        zinc_(Zdistio);
        qh_distplane(vertex->point,facet, &dist);
        point=qh_projectpoint(vertex->point,facet, dist);
        for (k=0; k < qh hull_dim; k++) {
          if (k != qh DROPdim)
            qh_fprintf(fp, 9116, "%8.4g ", point[k]);
        }
        qh_fprintf(fp, 9117, "\n");
        qh_memfree(point, qh normal_size);
      }
      if (qh DROPdim >= 0)
        qh_fprintf(fp, 9118, "3 0 1 2 %8.4g %8.4g %8.4g\n", color[0], color[1], color[2]);
    }
  }
} /* printfacet4geom_nonsimplicial */


/*---------------------------------

  qh_printfacet4geom_simplicial( fp, facet, color )
    print Geomview 4OFF file for a 4d simplicial facet
    prints triangles for unvisited neighbors (qh.visit_id)

  notes:
    must agree with printend4geom()
*/
void qh_printfacet4geom_simplicial(FILE *fp, facetT *facet, realT color[3]) {
  setT *vertices;
  facetT *neighbor, **neighborp;
  vertexT *vertex, **vertexp;
  int k;

  facet->visitid= qh visit_id;
  if (qh PRINTnoplanes || (facet->visible && qh NEWfacets))
    return;
  FOREACHneighbor_(facet) {
    if (neighbor->visitid == qh visit_id)
      continue;
    if (qh PRINTtransparent && !neighbor->good)
      continue;
    vertices= qh_setnew_delnthsorted(facet->vertices, qh hull_dim,
                          SETindex_(facet->neighbors, neighbor), 0);
    if (qh DOintersections)
      qh_printhyperplaneintersection(fp, facet, neighbor, vertices, color);
    else {
      if (qh DROPdim >= 0)
        qh_fprintf(fp, 9119, "OFF 3 1 1 # ridge between f%d f%d\n",
                facet->id, neighbor->id);
      else {
        qh printoutvar++;
        qh_fprintf(fp, 9120, "# ridge between f%d f%d\n", facet->id, neighbor->id);
      }
      FOREACHvertex_(vertices) {
        for (k=0; k < qh hull_dim; k++) {
          if (k != qh DROPdim)
            qh_fprintf(fp, 9121, "%8.4g ", vertex->point[k]);
        }
        qh_fprintf(fp, 9122, "\n");
      }
      if (qh DROPdim >= 0)
        qh_fprintf(fp, 9123, "3 0 1 2 %8.4g %8.4g %8.4g\n", color[0], color[1], color[2]);
    }
    qh_setfree(&vertices);
  }
} /* printfacet4geom_simplicial */


/*---------------------------------

  qh_printfacetNvertex_nonsimplicial( fp, facet, id, format )
    print vertices for an N-d non-simplicial facet
    triangulates each ridge to the id
*/
void qh_printfacetNvertex_nonsimplicial(FILE *fp, facetT *facet, int id, qh_PRINT format) {
  vertexT *vertex, **vertexp;
  ridgeT *ridge, **ridgep;

  if (facet->visible && qh NEWfacets)
    return;
  FOREACHridge_(facet->ridges) {
    if (format == qh_PRINTtriangles)
      qh_fprintf(fp, 9124, "%d ", qh hull_dim);
    qh_fprintf(fp, 9125, "%d ", id);
    if ((ridge->top == facet) ^ qh_ORIENTclock) {
      FOREACHvertex_(ridge->vertices)
        qh_fprintf(fp, 9126, "%d ", qh_pointid(vertex->point));
    }else {
      FOREACHvertexreverse12_(ridge->vertices)
        qh_fprintf(fp, 9127, "%d ", qh_pointid(vertex->point));
    }
    qh_fprintf(fp, 9128, "\n");
  }
} /* printfacetNvertex_nonsimplicial */


/*---------------------------------

  qh_printfacetNvertex_simplicial( fp, facet, format )
    print vertices for an N-d simplicial facet
    prints vertices for non-simplicial facets
      2-d facets (orientation preserved by qh_mergefacet2d)
      PRINToff ('o') for 4-d and higher
*/
void qh_printfacetNvertex_simplicial(FILE *fp, facetT *facet, qh_PRINT format) {
  vertexT *vertex, **vertexp;

  if (format == qh_PRINToff || format == qh_PRINTtriangles)
    qh_fprintf(fp, 9129, "%d ", qh_setsize(facet->vertices));
  if ((facet->toporient ^ qh_ORIENTclock)
  || (qh hull_dim > 2 && !facet->simplicial)) {
    FOREACHvertex_(facet->vertices)
      qh_fprintf(fp, 9130, "%d ", qh_pointid(vertex->point));
  }else {
    FOREACHvertexreverse12_(facet->vertices)
      qh_fprintf(fp, 9131, "%d ", qh_pointid(vertex->point));
  }
  qh_fprintf(fp, 9132, "\n");
} /* printfacetNvertex_simplicial */


/*---------------------------------

  qh_printfacetheader( fp, facet )
    prints header fields of a facet to fp

  notes:
    for 'f' output and debugging
    Same as QhullFacet::printHeader()
*/
void qh_printfacetheader(FILE *fp, facetT *facet) {
  pointT *point, **pointp, *furthest;
  facetT *neighbor, **neighborp;
  realT dist;

  if (facet == qh_MERGEridge) {
    qh_fprintf(fp, 9133, " MERGEridge\n");
    return;
  }else if (facet == qh_DUPLICATEridge) {
    qh_fprintf(fp, 9134, " DUPLICATEridge\n");
    return;
  }else if (!facet) {
    qh_fprintf(fp, 9135, " NULLfacet\n");
    return;
  }
  qh old_randomdist= qh RANDOMdist;
  qh RANDOMdist= False;
  qh_fprintf(fp, 9136, "- f%d\n", facet->id);
  qh_fprintf(fp, 9137, "    - flags:");
  if (facet->toporient)
    qh_fprintf(fp, 9138, " top");
  else
    qh_fprintf(fp, 9139, " bottom");
  if (facet->simplicial)
    qh_fprintf(fp, 9140, " simplicial");
  if (facet->tricoplanar)
    qh_fprintf(fp, 9141, " tricoplanar");
  if (facet->upperdelaunay)
    qh_fprintf(fp, 9142, " upperDelaunay");
  if (facet->visible)
    qh_fprintf(fp, 9143, " visible");
  if (facet->newfacet)
    qh_fprintf(fp, 9144, " new");
  if (facet->tested)
    qh_fprintf(fp, 9145, " tested");
  if (!facet->good)
    qh_fprintf(fp, 9146, " notG");
  if (facet->seen)
    qh_fprintf(fp, 9147, " seen");
  if (facet->coplanar)
    qh_fprintf(fp, 9148, " coplanar");
  if (facet->mergehorizon)
    qh_fprintf(fp, 9149, " mergehorizon");
  if (facet->keepcentrum)
    qh_fprintf(fp, 9150, " keepcentrum");
  if (facet->dupridge)
    qh_fprintf(fp, 9151, " dupridge");
  if (facet->mergeridge && !facet->mergeridge2)
    qh_fprintf(fp, 9152, " mergeridge1");
  if (facet->mergeridge2)
    qh_fprintf(fp, 9153, " mergeridge2");
  if (facet->newmerge)
    qh_fprintf(fp, 9154, " newmerge");
  if (facet->flipped)
    qh_fprintf(fp, 9155, " flipped");
  if (facet->notfurthest)
    qh_fprintf(fp, 9156, " notfurthest");
  if (facet->degenerate)
    qh_fprintf(fp, 9157, " degenerate");
  if (facet->redundant)
    qh_fprintf(fp, 9158, " redundant");
  qh_fprintf(fp, 9159, "\n");
  if (facet->isarea)
    qh_fprintf(fp, 9160, "    - area: %2.2g\n", facet->f.area);
  else if (qh NEWfacets && facet->visible && facet->f.replace)
    qh_fprintf(fp, 9161, "    - replacement: f%d\n", facet->f.replace->id);
  else if (facet->newfacet) {
    if (facet->f.samecycle && facet->f.samecycle != facet)
      qh_fprintf(fp, 9162, "    - shares same visible/horizon as f%d\n", facet->f.samecycle->id);
  }else if (facet->tricoplanar /* !isarea */) {
    if (facet->f.triowner)
      qh_fprintf(fp, 9163, "    - owner of normal & centrum is facet f%d\n", facet->f.triowner->id);
  }else if (facet->f.newcycle)
    qh_fprintf(fp, 9164, "    - was horizon to f%d\n", facet->f.newcycle->id);
  if (facet->nummerge)
    qh_fprintf(fp, 9165, "    - merges: %d\n", facet->nummerge);
  qh_printpointid(fp, "    - normal: ", qh hull_dim, facet->normal, -1);
  qh_fprintf(fp, 9166, "    - offset: %10.7g\n", facet->offset);
  if (qh CENTERtype == qh_ASvoronoi || facet->center)
    qh_printcenter(fp, qh_PRINTfacets, "    - center: ", facet);
#if qh_MAXoutside
  if (facet->maxoutside > qh DISTround)
    qh_fprintf(fp, 9167, "    - maxoutside: %10.7g\n", facet->maxoutside);
#endif
  if (!SETempty_(facet->outsideset)) {
    furthest= (pointT*)qh_setlast(facet->outsideset);
    if (qh_setsize(facet->outsideset) < 6) {
      qh_fprintf(fp, 9168, "    - outside set(furthest p%d):\n", qh_pointid(furthest));
      FOREACHpoint_(facet->outsideset)
        qh_printpoint(fp, "     ", point);
    }else if (qh_setsize(facet->outsideset) < 21) {
      qh_printpoints(fp, "    - outside set:", facet->outsideset);
    }else {
      qh_fprintf(fp, 9169, "    - outside set:  %d points.", qh_setsize(facet->outsideset));
      qh_printpoint(fp, "  Furthest", furthest);
    }
#if !qh_COMPUTEfurthest
    qh_fprintf(fp, 9170, "    - furthest distance= %2.2g\n", facet->furthestdist);
#endif
  }
  if (!SETempty_(facet->coplanarset)) {
    furthest= (pointT*)qh_setlast(facet->coplanarset);
    if (qh_setsize(facet->coplanarset) < 6) {
      qh_fprintf(fp, 9171, "    - coplanar set(furthest p%d):\n", qh_pointid(furthest));
      FOREACHpoint_(facet->coplanarset)
        qh_printpoint(fp, "     ", point);
    }else if (qh_setsize(facet->coplanarset) < 21) {
      qh_printpoints(fp, "    - coplanar set:", facet->coplanarset);
    }else {
      qh_fprintf(fp, 9172, "    - coplanar set:  %d points.", qh_setsize(facet->coplanarset));
      qh_printpoint(fp, "  Furthest", furthest);
    }
    zinc_(Zdistio);
    qh_distplane(furthest, facet, &dist);
    qh_fprintf(fp, 9173, "      furthest distance= %2.2g\n", dist);
  }
  qh_printvertices(fp, "    - vertices:", facet->vertices);
  qh_fprintf(fp, 9174, "    - neighboring facets:");
  FOREACHneighbor_(facet) {
    if (neighbor == qh_MERGEridge)
      qh_fprintf(fp, 9175, " MERGE");
    else if (neighbor == qh_DUPLICATEridge)
      qh_fprintf(fp, 9176, " DUP");
    else
      qh_fprintf(fp, 9177, " f%d", neighbor->id);
  }
  qh_fprintf(fp, 9178, "\n");
  qh RANDOMdist= qh old_randomdist;
} /* printfacetheader */


/*---------------------------------

  qh_printfacetridges( fp, facet )
    prints ridges of a facet to fp

  notes:
    ridges printed in neighbor order
    assumes the ridges exist
    for 'f' output
    same as QhullFacet::printRidges
*/
void qh_printfacetridges(FILE *fp, facetT *facet) {
  facetT *neighbor, **neighborp;
  ridgeT *ridge, **ridgep;
  int numridges= 0;


  if (facet->visible && qh NEWfacets) {
    qh_fprintf(fp, 9179, "    - ridges(ids may be garbage):");
    FOREACHridge_(facet->ridges)
      qh_fprintf(fp, 9180, " r%d", ridge->id);
    qh_fprintf(fp, 9181, "\n");
  }else {
    qh_fprintf(fp, 9182, "    - ridges:\n");
    FOREACHridge_(facet->ridges)
      ridge->seen= False;
    if (qh hull_dim == 3) {
      ridge= SETfirstt_(facet->ridges, ridgeT);
      while (ridge && !ridge->seen) {
        ridge->seen= True;
        qh_printridge(fp, ridge);
        numridges++;
        ridge= qh_nextridge3d(ridge, facet, NULL);
        }
    }else {
      FOREACHneighbor_(facet) {
        FOREACHridge_(facet->ridges) {
          if (otherfacet_(ridge,facet) == neighbor) {
            ridge->seen= True;
            qh_printridge(fp, ridge);
            numridges++;
          }
        }
      }
    }
    if (numridges != qh_setsize(facet->ridges)) {
      qh_fprintf(fp, 9183, "     - all ridges:");
      FOREACHridge_(facet->ridges)
        qh_fprintf(fp, 9184, " r%d", ridge->id);
        qh_fprintf(fp, 9185, "\n");
    }
    FOREACHridge_(facet->ridges) {
      if (!ridge->seen)
        qh_printridge(fp, ridge);
    }
  }
} /* printfacetridges */

/*---------------------------------

  qh_printfacets( fp, format, facetlist, facets, printall )
    prints facetlist and/or facet set in output format

  notes:
    also used for specialized formats ('FO' and summary)
    turns off 'Rn' option since want actual numbers
*/
void qh_printfacets(FILE *fp, qh_PRINT format, facetT *facetlist, setT *facets, boolT printall) {
  int numfacets, numsimplicial, numridges, totneighbors, numcoplanars, numtricoplanars;
  facetT *facet, **facetp;
  setT *vertices;
  coordT *center;
  realT outerplane, innerplane;

  qh old_randomdist= qh RANDOMdist;
  qh RANDOMdist= False;
  if (qh CDDoutput && (format == qh_PRINTcentrums || format == qh_PRINTpointintersect || format == qh_PRINToff))
    qh_fprintf(qh ferr, 7056, "qhull warning: CDD format is not available for centrums, halfspace\nintersections, and OFF file format.\n");
  if (format == qh_PRINTnone)
    ; /* print nothing */
  else if (format == qh_PRINTaverage) {
    vertices= qh_facetvertices(facetlist, facets, printall);
    center= qh_getcenter(vertices);
    qh_fprintf(fp, 9186, "%d 1\n", qh hull_dim);
    qh_printpointid(fp, NULL, qh hull_dim, center, -1);
    qh_memfree(center, qh normal_size);
    qh_settempfree(&vertices);
  }else if (format == qh_PRINTextremes) {
    if (qh DELAUNAY)
      qh_printextremes_d(fp, facetlist, facets, printall);
    else if (qh hull_dim == 2)
      qh_printextremes_2d(fp, facetlist, facets, printall);
    else
      qh_printextremes(fp, facetlist, facets, printall);
  }else if (format == qh_PRINToptions)
    qh_fprintf(fp, 9187, "Options selected for Qhull %s:\n%s\n", qh_version, qh qhull_options);
  else if (format == qh_PRINTpoints && !qh VORONOI)
    qh_printpoints_out(fp, facetlist, facets, printall);
  else if (format == qh_PRINTqhull)
    qh_fprintf(fp, 9188, "%s | %s\n", qh rbox_command, qh qhull_command);
  else if (format == qh_PRINTsize) {
    qh_fprintf(fp, 9189, "0\n2 ");
    qh_fprintf(fp, 9190, qh_REAL_1, qh totarea);
    qh_fprintf(fp, 9191, qh_REAL_1, qh totvol);
    qh_fprintf(fp, 9192, "\n");
  }else if (format == qh_PRINTsummary) {
    qh_countfacets(facetlist, facets, printall, &numfacets, &numsimplicial,
      &totneighbors, &numridges, &numcoplanars, &numtricoplanars);
    vertices= qh_facetvertices(facetlist, facets, printall);
    qh_fprintf(fp, 9193, "10 %d %d %d %d %d %d %d %d %d %d\n2 ", qh hull_dim,
                qh num_points + qh_setsize(qh other_points),
                qh num_vertices, qh num_facets - qh num_visible,
                qh_setsize(vertices), numfacets, numcoplanars,
                numfacets - numsimplicial, zzval_(Zdelvertextot),
                numtricoplanars);
    qh_settempfree(&vertices);
    qh_outerinner(NULL, &outerplane, &innerplane);
    qh_fprintf(fp, 9194, qh_REAL_2n, outerplane, innerplane);
  }else if (format == qh_PRINTvneighbors)
    qh_printvneighbors(fp, facetlist, facets, printall);
  else if (qh VORONOI && format == qh_PRINToff)
    qh_printvoronoi(fp, format, facetlist, facets, printall);
  else if (qh VORONOI && format == qh_PRINTgeom) {
    qh_printbegin(fp, format, facetlist, facets, printall);
    qh_printvoronoi(fp, format, facetlist, facets, printall);
    qh_printend(fp, format, facetlist, facets, printall);
  }else if (qh VORONOI
  && (format == qh_PRINTvertices || format == qh_PRINTinner || format == qh_PRINTouter))
    qh_printvdiagram(fp, format, facetlist, facets, printall);
  else {
    qh_printbegin(fp, format, facetlist, facets, printall);
    FORALLfacet_(facetlist)
      qh_printafacet(fp, format, facet, printall);
    FOREACHfacet_(facets)
      qh_printafacet(fp, format, facet, printall);
    qh_printend(fp, format, facetlist, facets, printall);
  }
  qh RANDOMdist= qh old_randomdist;
} /* printfacets */


/*---------------------------------

  qh_printhyperplaneintersection( fp, facet1, facet2, vertices, color )
    print Geomview OFF or 4OFF for the intersection of two hyperplanes in 3-d or 4-d
*/
void qh_printhyperplaneintersection(FILE *fp, facetT *facet1, facetT *facet2,
                   setT *vertices, realT color[3]) {
  realT costheta, denominator, dist1, dist2, s, t, mindenom, p[4];
  vertexT *vertex, **vertexp;
  int i, k;
  boolT nearzero1, nearzero2;

  costheta= qh_getangle(facet1->normal, facet2->normal);
  denominator= 1 - costheta * costheta;
  i= qh_setsize(vertices);
  if (qh hull_dim == 3)
    qh_fprintf(fp, 9195, "VECT 1 %d 1 %d 1 ", i, i);
  else if (qh hull_dim == 4 && qh DROPdim >= 0)
    qh_fprintf(fp, 9196, "OFF 3 1 1 ");
  else
    qh printoutvar++;
  qh_fprintf(fp, 9197, "# intersect f%d f%d\n", facet1->id, facet2->id);
  mindenom= 1 / (10.0 * qh MAXabs_coord);
  FOREACHvertex_(vertices) {
    zadd_(Zdistio, 2);
    qh_distplane(vertex->point, facet1, &dist1);
    qh_distplane(vertex->point, facet2, &dist2);
    s= qh_divzero(-dist1 + costheta * dist2, denominator,mindenom,&nearzero1);
    t= qh_divzero(-dist2 + costheta * dist1, denominator,mindenom,&nearzero2);
    if (nearzero1 || nearzero2)
      s= t= 0.0;
    for (k=qh hull_dim; k--; )
      p[k]= vertex->point[k] + facet1->normal[k] * s + facet2->normal[k] * t;
    if (qh PRINTdim <= 3) {
      qh_projectdim3 (p, p);
      qh_fprintf(fp, 9198, "%8.4g %8.4g %8.4g # ", p[0], p[1], p[2]);
    }else
      qh_fprintf(fp, 9199, "%8.4g %8.4g %8.4g %8.4g # ", p[0], p[1], p[2], p[3]);
    if (nearzero1+nearzero2)
      qh_fprintf(fp, 9200, "p%d(coplanar facets)\n", qh_pointid(vertex->point));
    else
      qh_fprintf(fp, 9201, "projected p%d\n", qh_pointid(vertex->point));
  }
  if (qh hull_dim == 3)
    qh_fprintf(fp, 9202, "%8.4g %8.4g %8.4g 1.0\n", color[0], color[1], color[2]);
  else if (qh hull_dim == 4 && qh DROPdim >= 0)
    qh_fprintf(fp, 9203, "3 0 1 2 %8.4g %8.4g %8.4g 1.0\n", color[0], color[1], color[2]);
} /* printhyperplaneintersection */

/*---------------------------------

  qh_printline3geom( fp, pointA, pointB, color )
    prints a line as a VECT
    prints 0's for qh.DROPdim

  notes:
    if pointA == pointB,
      it's a 1 point VECT
*/
void qh_printline3geom(FILE *fp, pointT *pointA, pointT *pointB, realT color[3]) {
  int k;
  realT pA[4], pB[4];

  qh_projectdim3(pointA, pA);
  qh_projectdim3(pointB, pB);
  if ((fabs(pA[0] - pB[0]) > 1e-3) ||
      (fabs(pA[1] - pB[1]) > 1e-3) ||
      (fabs(pA[2] - pB[2]) > 1e-3)) {
    qh_fprintf(fp, 9204, "VECT 1 2 1 2 1\n");
    for (k=0; k < 3; k++)
       qh_fprintf(fp, 9205, "%8.4g ", pB[k]);
    qh_fprintf(fp, 9206, " # p%d\n", qh_pointid(pointB));
  }else
    qh_fprintf(fp, 9207, "VECT 1 1 1 1 1\n");
  for (k=0; k < 3; k++)
    qh_fprintf(fp, 9208, "%8.4g ", pA[k]);
  qh_fprintf(fp, 9209, " # p%d\n", qh_pointid(pointA));
  qh_fprintf(fp, 9210, "%8.4g %8.4g %8.4g 1\n", color[0], color[1], color[2]);
}

/*---------------------------------

  qh_printneighborhood( fp, format, facetA, facetB, printall )
    print neighborhood of one or two facets

  notes:
    calls qh_findgood_all()
    bumps qh.visit_id
*/
void qh_printneighborhood(FILE *fp, qh_PRINT format, facetT *facetA, facetT *facetB, boolT printall) {
  facetT *neighbor, **neighborp, *facet;
  setT *facets;

  if (format == qh_PRINTnone)
    return;
  qh_findgood_all(qh facet_list);
  if (facetA == facetB)
    facetB= NULL;
  facets= qh_settemp(2*(qh_setsize(facetA->neighbors)+1));
  qh visit_id++;
  for (facet= facetA; facet; facet= ((facet == facetA) ? facetB : NULL)) {
    if (facet->visitid != qh visit_id) {
      facet->visitid= qh visit_id;
      qh_setappend(&facets, facet);
    }
    FOREACHneighbor_(facet) {
      if (neighbor->visitid == qh visit_id)
        continue;
      neighbor->visitid= qh visit_id;
      if (printall || !qh_skipfacet(neighbor))
        qh_setappend(&facets, neighbor);
    }
  }
  qh_printfacets(fp, format, NULL, facets, printall);
  qh_settempfree(&facets);
} /* printneighborhood */

/*---------------------------------

  qh_printpoint( fp, string, point )
  qh_printpointid( fp, string, dim, point, id )
    prints the coordinates of a point

  returns:
    if string is defined
      prints 'string p%d' (skips p%d if id=-1)

  notes:
    nop if point is NULL
    prints id unless it is undefined (-1)
    Same as QhullPoint's printPoint
*/
void qh_printpoint(FILE *fp, const char *string, pointT *point) {
  int id= qh_pointid( point);

  qh_printpointid( fp, string, qh hull_dim, point, id);
} /* printpoint */

void qh_printpointid(FILE *fp, const char *string, int dim, pointT *point, int id) {
  int k;
  realT r; /*bug fix*/

  if (!point)
    return;
  if (string) {
    qh_fprintf(fp, 9211, "%s", string);
   if (id != -1)
      qh_fprintf(fp, 9212, " p%d: ", id);
  }
  for (k=dim; k--; ) {
    r= *point++;
    if (string)
      qh_fprintf(fp, 9213, " %8.4g", r);
    else
      qh_fprintf(fp, 9214, qh_REAL_1, r);
  }
  qh_fprintf(fp, 9215, "\n");
} /* printpointid */

/*---------------------------------

  qh_printpoint3( fp, point )
    prints 2-d, 3-d, or 4-d point as Geomview 3-d coordinates
*/
void qh_printpoint3 (FILE *fp, pointT *point) {
  int k;
  realT p[4];

  qh_projectdim3 (point, p);
  for (k=0; k < 3; k++)
    qh_fprintf(fp, 9216, "%8.4g ", p[k]);
  qh_fprintf(fp, 9217, " # p%d\n", qh_pointid(point));
} /* printpoint3 */

/*----------------------------------------
-printpoints- print pointids for a set of points starting at index
   see geom.c
*/

/*---------------------------------

  qh_printpoints_out( fp, facetlist, facets, printall )
    prints vertices, coplanar/inside points, for facets by their point coordinates
    allows qh.CDDoutput

  notes:
    same format as qhull input
    if no coplanar/interior points,
      same order as qh_printextremes
*/
void qh_printpoints_out(FILE *fp, facetT *facetlist, setT *facets, boolT printall) {
  int allpoints= qh num_points + qh_setsize(qh other_points);
  int numpoints=0, point_i, point_n;
  setT *vertices, *points;
  facetT *facet, **facetp;
  pointT *point, **pointp;
  vertexT *vertex, **vertexp;
  int id;

  points= qh_settemp(allpoints);
  qh_setzero(points, 0, allpoints);
  vertices= qh_facetvertices(facetlist, facets, printall);
  FOREACHvertex_(vertices) {
    id= qh_pointid(vertex->point);
    if (id >= 0)
      SETelem_(points, id)= vertex->point;
  }
  if (qh KEEPinside || qh KEEPcoplanar || qh KEEPnearinside) {
    FORALLfacet_(facetlist) {
      if (!printall && qh_skipfacet(facet))
        continue;
      FOREACHpoint_(facet->coplanarset) {
        id= qh_pointid(point);
        if (id >= 0)
          SETelem_(points, id)= point;
      }
    }
    FOREACHfacet_(facets) {
      if (!printall && qh_skipfacet(facet))
        continue;
      FOREACHpoint_(facet->coplanarset) {
        id= qh_pointid(point);
        if (id >= 0)
          SETelem_(points, id)= point;
      }
    }
  }
  qh_settempfree(&vertices);
  FOREACHpoint_i_(points) {
    if (point)
      numpoints++;
  }
  if (qh CDDoutput)
    qh_fprintf(fp, 9218, "%s | %s\nbegin\n%d %d real\n", qh rbox_command,
             qh qhull_command, numpoints, qh hull_dim + 1);
  else
    qh_fprintf(fp, 9219, "%d\n%d\n", qh hull_dim, numpoints);
  FOREACHpoint_i_(points) {
    if (point) {
      if (qh CDDoutput)
        qh_fprintf(fp, 9220, "1 ");
      qh_printpoint(fp, NULL, point);
    }
  }
  if (qh CDDoutput)
    qh_fprintf(fp, 9221, "end\n");
  qh_settempfree(&points);
} /* printpoints_out */


/*---------------------------------

  qh_printpointvect( fp, point, normal, center, radius, color )
    prints a 2-d, 3-d, or 4-d point as 3-d VECT's relative to normal or to center point
*/
void qh_printpointvect(FILE *fp, pointT *point, coordT *normal, pointT *center, realT radius, realT color[3]) {
  realT diff[4], pointA[4];
  int k;

  for (k=qh hull_dim; k--; ) {
    if (center)
      diff[k]= point[k]-center[k];
    else if (normal)
      diff[k]= normal[k];
    else
      diff[k]= 0;
  }
  if (center)
    qh_normalize2 (diff, qh hull_dim, True, NULL, NULL);
  for (k=qh hull_dim; k--; )
    pointA[k]= point[k]+diff[k] * radius;
  qh_printline3geom(fp, point, pointA, color);
} /* printpointvect */

/*---------------------------------

  qh_printpointvect2( fp, point, normal, center, radius )
    prints a 2-d, 3-d, or 4-d point as 2 3-d VECT's for an imprecise point
*/
void qh_printpointvect2 (FILE *fp, pointT *point, coordT *normal, pointT *center, realT radius) {
  realT red[3]={1, 0, 0}, yellow[3]={1, 1, 0};

  qh_printpointvect(fp, point, normal, center, radius, red);
  qh_printpointvect(fp, point, normal, center, -radius, yellow);
} /* printpointvect2 */

/*---------------------------------

  qh_printridge( fp, ridge )
    prints the information in a ridge

  notes:
    for qh_printfacetridges()
    same as operator<< [QhullRidge.cpp]
*/
void qh_printridge(FILE *fp, ridgeT *ridge) {

  qh_fprintf(fp, 9222, "     - r%d", ridge->id);
  if (ridge->tested)
    qh_fprintf(fp, 9223, " tested");
  if (ridge->nonconvex)
    qh_fprintf(fp, 9224, " nonconvex");
  qh_fprintf(fp, 9225, "\n");
  qh_printvertices(fp, "           vertices:", ridge->vertices);
  if (ridge->top && ridge->bottom)
    qh_fprintf(fp, 9226, "           between f%d and f%d\n",
            ridge->top->id, ridge->bottom->id);
} /* printridge */

/*---------------------------------

  qh_printspheres( fp, vertices, radius )
    prints 3-d vertices as OFF spheres

  notes:
    inflated octahedron from Stuart Levy earth/mksphere2
*/
void qh_printspheres(FILE *fp, setT *vertices, realT radius) {
  vertexT *vertex, **vertexp;

  qh printoutnum++;
  qh_fprintf(fp, 9227, "{appearance {-edge -normal normscale 0} {\n\
INST geom {define vsphere OFF\n\
18 32 48\n\
\n\
0 0 1\n\
1 0 0\n\
0 1 0\n\
-1 0 0\n\
0 -1 0\n\
0 0 -1\n\
0.707107 0 0.707107\n\
0 -0.707107 0.707107\n\
0.707107 -0.707107 0\n\
-0.707107 0 0.707107\n\
-0.707107 -0.707107 0\n\
0 0.707107 0.707107\n\
-0.707107 0.707107 0\n\
0.707107 0.707107 0\n\
0.707107 0 -0.707107\n\
0 0.707107 -0.707107\n\
-0.707107 0 -0.707107\n\
0 -0.707107 -0.707107\n\
\n\
3 0 6 11\n\
3 0 7 6 \n\
3 0 9 7 \n\
3 0 11 9\n\
3 1 6 8 \n\
3 1 8 14\n\
3 1 13 6\n\
3 1 14 13\n\
3 2 11 13\n\
3 2 12 11\n\
3 2 13 15\n\
3 2 15 12\n\
3 3 9 12\n\
3 3 10 9\n\
3 3 12 16\n\
3 3 16 10\n\
3 4 7 10\n\
3 4 8 7\n\
3 4 10 17\n\
3 4 17 8\n\
3 5 14 17\n\
3 5 15 14\n\
3 5 16 15\n\
3 5 17 16\n\
3 6 13 11\n\
3 7 8 6\n\
3 9 10 7\n\
3 11 12 9\n\
3 14 8 17\n\
3 15 13 14\n\
3 16 12 15\n\
3 17 10 16\n} transforms { TLIST\n");
  FOREACHvertex_(vertices) {
    qh_fprintf(fp, 9228, "%8.4g 0 0 0 # v%d\n 0 %8.4g 0 0\n0 0 %8.4g 0\n",
      radius, vertex->id, radius, radius);
    qh_printpoint3 (fp, vertex->point);
    qh_fprintf(fp, 9229, "1\n");
  }
  qh_fprintf(fp, 9230, "}}}\n");
} /* printspheres */


/*----------------------------------------------
-printsummary-
                see libqhull.c
*/

/*---------------------------------

  qh_printvdiagram( fp, format, facetlist, facets, printall )
    print voronoi diagram
      # of pairs of input sites
      #indices site1 site2 vertex1 ...

    sites indexed by input point id
      point 0 is the first input point
    vertices indexed by 'o' and 'p' order
      vertex 0 is the 'vertex-at-infinity'
      vertex 1 is the first Voronoi vertex

  see:
    qh_printvoronoi()
    qh_eachvoronoi_all()

  notes:
    if all facets are upperdelaunay,
      prints upper hull (furthest-site Voronoi diagram)
*/
void qh_printvdiagram(FILE *fp, qh_PRINT format, facetT *facetlist, setT *facets, boolT printall) {
  setT *vertices;
  int totcount, numcenters;
  boolT isLower;
  qh_RIDGE innerouter= qh_RIDGEall;
  printvridgeT printvridge= NULL;

  if (format == qh_PRINTvertices) {
    innerouter= qh_RIDGEall;
    printvridge= qh_printvridge;
  }else if (format == qh_PRINTinner) {
    innerouter= qh_RIDGEinner;
    printvridge= qh_printvnorm;
  }else if (format == qh_PRINTouter) {
    innerouter= qh_RIDGEouter;
    printvridge= qh_printvnorm;
  }else {
    qh_fprintf(qh ferr, 6219, "Qhull internal error (qh_printvdiagram): unknown print format %d.\n", format);
    qh_errexit(qh_ERRinput, NULL, NULL);
  }
  vertices= qh_markvoronoi(facetlist, facets, printall, &isLower, &numcenters);
  totcount= qh_printvdiagram2 (NULL, NULL, vertices, innerouter, False);
  qh_fprintf(fp, 9231, "%d\n", totcount);
  totcount= qh_printvdiagram2 (fp, printvridge, vertices, innerouter, True /* inorder*/);
  qh_settempfree(&vertices);
#if 0  /* for testing qh_eachvoronoi_all */
  qh_fprintf(fp, 9232, "\n");
  totcount= qh_eachvoronoi_all(fp, printvridge, qh UPPERdelaunay, innerouter, True /* inorder*/);
  qh_fprintf(fp, 9233, "%d\n", totcount);
#endif
} /* printvdiagram */

/*---------------------------------

  qh_printvdiagram2( fp, printvridge, vertices, innerouter, inorder )
    visit all pairs of input sites (vertices) for selected Voronoi vertices
    vertices may include NULLs

  innerouter:
    qh_RIDGEall   print inner ridges(bounded) and outer ridges(unbounded)
    qh_RIDGEinner print only inner ridges
    qh_RIDGEouter print only outer ridges

  inorder:
    print 3-d Voronoi vertices in order

  assumes:
    qh_markvoronoi marked facet->visitid for Voronoi vertices
    all facet->seen= False
    all facet->seen2= True

  returns:
    total number of Voronoi ridges
    if printvridge,
      calls printvridge( fp, vertex, vertexA, centers) for each ridge
      [see qh_eachvoronoi()]

  see:
    qh_eachvoronoi_all()
*/
int qh_printvdiagram2 (FILE *fp, printvridgeT printvridge, setT *vertices, qh_RIDGE innerouter, boolT inorder) {
  int totcount= 0;
  int vertex_i, vertex_n;
  vertexT *vertex;

  FORALLvertices
    vertex->seen= False;
  FOREACHvertex_i_(vertices) {
    if (vertex) {
      if (qh GOODvertex > 0 && qh_pointid(vertex->point)+1 != qh GOODvertex)
        continue;
      totcount += qh_eachvoronoi(fp, printvridge, vertex, !qh_ALL, innerouter, inorder);
    }
  }
  return totcount;
} /* printvdiagram2 */

/*---------------------------------

  qh_printvertex( fp, vertex )
    prints the information in a vertex
    Duplicated as operator<< [QhullVertex.cpp]
*/
void qh_printvertex(FILE *fp, vertexT *vertex) {
  pointT *point;
  int k, count= 0;
  facetT *neighbor, **neighborp;
  realT r; /*bug fix*/

  if (!vertex) {
    qh_fprintf(fp, 9234, "  NULLvertex\n");
    return;
  }
  qh_fprintf(fp, 9235, "- p%d(v%d):", qh_pointid(vertex->point), vertex->id);
  point= vertex->point;
  if (point) {
    for (k=qh hull_dim; k--; ) {
      r= *point++;
      qh_fprintf(fp, 9236, " %5.2g", r);
    }
  }
  if (vertex->deleted)
    qh_fprintf(fp, 9237, " deleted");
  if (vertex->delridge)
    qh_fprintf(fp, 9238, " ridgedeleted");
  qh_fprintf(fp, 9239, "\n");
  if (vertex->neighbors) {
    qh_fprintf(fp, 9240, "  neighbors:");
    FOREACHneighbor_(vertex) {
      if (++count % 100 == 0)
        qh_fprintf(fp, 9241, "\n     ");
      qh_fprintf(fp, 9242, " f%d", neighbor->id);
    }
    qh_fprintf(fp, 9243, "\n");
  }
} /* printvertex */


/*---------------------------------

  qh_printvertexlist( fp, string, facetlist, facets, printall )
    prints vertices used by a facetlist or facet set
    tests qh_skipfacet() if !printall
*/
void qh_printvertexlist(FILE *fp, const char* string, facetT *facetlist,
                         setT *facets, boolT printall) {
  vertexT *vertex, **vertexp;
  setT *vertices;

  vertices= qh_facetvertices(facetlist, facets, printall);
  qh_fprintf(fp, 9244, "%s", string);
  FOREACHvertex_(vertices)
    qh_printvertex(fp, vertex);
  qh_settempfree(&vertices);
} /* printvertexlist */


/*---------------------------------

  qh_printvertices( fp, string, vertices )
    prints vertices in a set
    duplicated as printVertexSet [QhullVertex.cpp]
*/
void qh_printvertices(FILE *fp, const char* string, setT *vertices) {
  vertexT *vertex, **vertexp;

  qh_fprintf(fp, 9245, "%s", string);
  FOREACHvertex_(vertices)
    qh_fprintf(fp, 9246, " p%d(v%d)", qh_pointid(vertex->point), vertex->id);
  qh_fprintf(fp, 9247, "\n");
} /* printvertices */

/*---------------------------------

  qh_printvneighbors( fp, facetlist, facets, printall )
    print vertex neighbors of vertices in facetlist and facets ('FN')

  notes:
    qh_countfacets clears facet->visitid for non-printed facets

  design:
    collect facet count and related statistics
    if necessary, build neighbor sets for each vertex
    collect vertices in facetlist and facets
    build a point array for point->vertex and point->coplanar facet
    for each point
      list vertex neighbors or coplanar facet
*/
void qh_printvneighbors(FILE *fp, facetT* facetlist, setT *facets, boolT printall) {
  int numfacets, numsimplicial, numridges, totneighbors, numneighbors, numcoplanars, numtricoplanars;
  setT *vertices, *vertex_points, *coplanar_points;
  int numpoints= qh num_points + qh_setsize(qh other_points);
  vertexT *vertex, **vertexp;
  int vertex_i, vertex_n;
  facetT *facet, **facetp, *neighbor, **neighborp;
  pointT *point, **pointp;

  qh_countfacets(facetlist, facets, printall, &numfacets, &numsimplicial,
      &totneighbors, &numridges, &numcoplanars, &numtricoplanars);  /* sets facet->visitid */
  qh_fprintf(fp, 9248, "%d\n", numpoints);
  qh_vertexneighbors();
  vertices= qh_facetvertices(facetlist, facets, printall);
  vertex_points= qh_settemp(numpoints);
  coplanar_points= qh_settemp(numpoints);
  qh_setzero(vertex_points, 0, numpoints);
  qh_setzero(coplanar_points, 0, numpoints);
  FOREACHvertex_(vertices)
    qh_point_add(vertex_points, vertex->point, vertex);
  FORALLfacet_(facetlist) {
    FOREACHpoint_(facet->coplanarset)
      qh_point_add(coplanar_points, point, facet);
  }
  FOREACHfacet_(facets) {
    FOREACHpoint_(facet->coplanarset)
      qh_point_add(coplanar_points, point, facet);
  }
  FOREACHvertex_i_(vertex_points) {
    if (vertex) {
      numneighbors= qh_setsize(vertex->neighbors);
      qh_fprintf(fp, 9249, "%d", numneighbors);
      if (qh hull_dim == 3)
        qh_order_vertexneighbors(vertex);
      else if (qh hull_dim >= 4)
        qsort(SETaddr_(vertex->neighbors, facetT), (size_t)numneighbors,
             sizeof(facetT *), qh_compare_facetvisit);
      FOREACHneighbor_(vertex)
        qh_fprintf(fp, 9250, " %d",
                 neighbor->visitid ? neighbor->visitid - 1 : 0 - neighbor->id);
      qh_fprintf(fp, 9251, "\n");
    }else if ((facet= SETelemt_(coplanar_points, vertex_i, facetT)))
      qh_fprintf(fp, 9252, "1 %d\n",
                  facet->visitid ? facet->visitid - 1 : 0 - facet->id);
    else
      qh_fprintf(fp, 9253, "0\n");
  }
  qh_settempfree(&coplanar_points);
  qh_settempfree(&vertex_points);
  qh_settempfree(&vertices);
} /* printvneighbors */

/*---------------------------------

  qh_printvoronoi( fp, format, facetlist, facets, printall )
    print voronoi diagram in 'o' or 'G' format
    for 'o' format
      prints voronoi centers for each facet and for infinity
      for each vertex, lists ids of printed facets or infinity
      assumes facetlist and facets are disjoint
    for 'G' format
      prints an OFF object
      adds a 0 coordinate to center
      prints infinity but does not list in vertices

  see:
    qh_printvdiagram()

  notes:
    if 'o',
      prints a line for each point except "at-infinity"
    if all facets are upperdelaunay,
      reverses lower and upper hull
*/
void qh_printvoronoi(FILE *fp, qh_PRINT format, facetT *facetlist, setT *facets, boolT printall) {
  int k, numcenters, numvertices= 0, numneighbors, numinf, vid=1, vertex_i, vertex_n;
  facetT *facet, **facetp, *neighbor, **neighborp;
  setT *vertices;
  vertexT *vertex;
  boolT isLower;
  unsigned int numfacets= (unsigned int) qh num_facets;

  vertices= qh_markvoronoi(facetlist, facets, printall, &isLower, &numcenters);
  FOREACHvertex_i_(vertices) {
    if (vertex) {
      numvertices++;
      numneighbors = numinf = 0;
      FOREACHneighbor_(vertex) {
        if (neighbor->visitid == 0)
          numinf= 1;
        else if (neighbor->visitid < numfacets)
          numneighbors++;
      }
      if (numinf && !numneighbors) {
        SETelem_(vertices, vertex_i)= NULL;
        numvertices--;
      }
    }
  }
  if (format == qh_PRINTgeom)
    qh_fprintf(fp, 9254, "{appearance {+edge -face} OFF %d %d 1 # Voronoi centers and cells\n",
                numcenters, numvertices);
  else
    qh_fprintf(fp, 9255, "%d\n%d %d 1\n", qh hull_dim-1, numcenters, qh_setsize(vertices));
  if (format == qh_PRINTgeom) {
    for (k=qh hull_dim-1; k--; )
      qh_fprintf(fp, 9256, qh_REAL_1, 0.0);
    qh_fprintf(fp, 9257, " 0 # infinity not used\n");
  }else {
    for (k=qh hull_dim-1; k--; )
      qh_fprintf(fp, 9258, qh_REAL_1, qh_INFINITE);
    qh_fprintf(fp, 9259, "\n");
  }
  FORALLfacet_(facetlist) {
    if (facet->visitid && facet->visitid < numfacets) {
      if (format == qh_PRINTgeom)
        qh_fprintf(fp, 9260, "# %d f%d\n", vid++, facet->id);
      qh_printcenter(fp, format, NULL, facet);
    }
  }
  FOREACHfacet_(facets) {
    if (facet->visitid && facet->visitid < numfacets) {
      if (format == qh_PRINTgeom)
        qh_fprintf(fp, 9261, "# %d f%d\n", vid++, facet->id);
      qh_printcenter(fp, format, NULL, facet);
    }
  }
  FOREACHvertex_i_(vertices) {
    numneighbors= 0;
    numinf=0;
    if (vertex) {
      if (qh hull_dim == 3)
        qh_order_vertexneighbors(vertex);
      else if (qh hull_dim >= 4)
        qsort(SETaddr_(vertex->neighbors, facetT),
             (size_t)qh_setsize(vertex->neighbors),
             sizeof(facetT *), qh_compare_facetvisit);
      FOREACHneighbor_(vertex) {
        if (neighbor->visitid == 0)
          numinf= 1;
        else if (neighbor->visitid < numfacets)
          numneighbors++;
      }
    }
    if (format == qh_PRINTgeom) {
      if (vertex) {
        qh_fprintf(fp, 9262, "%d", numneighbors);
        FOREACHneighbor_(vertex) {
          if (neighbor->visitid && neighbor->visitid < numfacets)
            qh_fprintf(fp, 9263, " %d", neighbor->visitid);
        }
        qh_fprintf(fp, 9264, " # p%d(v%d)\n", vertex_i, vertex->id);
      }else
        qh_fprintf(fp, 9265, " # p%d is coplanar or isolated\n", vertex_i);
    }else {
      if (numinf)
        numneighbors++;
      qh_fprintf(fp, 9266, "%d", numneighbors);
      if (vertex) {
        FOREACHneighbor_(vertex) {
          if (neighbor->visitid == 0) {
            if (numinf) {
              numinf= 0;
              qh_fprintf(fp, 9267, " %d", neighbor->visitid);
            }
          }else if (neighbor->visitid < numfacets)
            qh_fprintf(fp, 9268, " %d", neighbor->visitid);
        }
      }
      qh_fprintf(fp, 9269, "\n");
    }
  }
  if (format == qh_PRINTgeom)
    qh_fprintf(fp, 9270, "}\n");
  qh_settempfree(&vertices);
} /* printvoronoi */

/*---------------------------------

  qh_printvnorm( fp, vertex, vertexA, centers, unbounded )
    print one separating plane of the Voronoi diagram for a pair of input sites
    unbounded==True if centers includes vertex-at-infinity

  assumes:
    qh_ASvoronoi and qh_vertexneighbors() already set

  note:
    parameter unbounded is UNUSED by this callback

  see:
    qh_printvdiagram()
    qh_eachvoronoi()
*/
void qh_printvnorm(FILE *fp, vertexT *vertex, vertexT *vertexA, setT *centers, boolT unbounded) {
  pointT *normal;
  realT offset;
  int k;
  QHULL_UNUSED(unbounded);

  normal= qh_detvnorm(vertex, vertexA, centers, &offset);
  qh_fprintf(fp, 9271, "%d %d %d ",
      2+qh hull_dim, qh_pointid(vertex->point), qh_pointid(vertexA->point));
  for (k=0; k< qh hull_dim-1; k++)
    qh_fprintf(fp, 9272, qh_REAL_1, normal[k]);
  qh_fprintf(fp, 9273, qh_REAL_1, offset);
  qh_fprintf(fp, 9274, "\n");
} /* printvnorm */

/*---------------------------------

  qh_printvridge( fp, vertex, vertexA, centers, unbounded )
    print one ridge of the Voronoi diagram for a pair of input sites
    unbounded==True if centers includes vertex-at-infinity

  see:
    qh_printvdiagram()

  notes:
    the user may use a different function
    parameter unbounded is UNUSED
*/
void qh_printvridge(FILE *fp, vertexT *vertex, vertexT *vertexA, setT *centers, boolT unbounded) {
  facetT *facet, **facetp;
  QHULL_UNUSED(unbounded);

  qh_fprintf(fp, 9275, "%d %d %d", qh_setsize(centers)+2,
       qh_pointid(vertex->point), qh_pointid(vertexA->point));
  FOREACHfacet_(centers)
    qh_fprintf(fp, 9276, " %d", facet->visitid);
  qh_fprintf(fp, 9277, "\n");
} /* printvridge */

/*---------------------------------

  qh_projectdim3( source, destination )
    project 2-d 3-d or 4-d point to a 3-d point
    uses qh.DROPdim and qh.hull_dim
    source and destination may be the same

  notes:
    allocate 4 elements to destination just in case
*/
void qh_projectdim3 (pointT *source, pointT *destination) {
  int i,k;

  for (k=0, i=0; k < qh hull_dim; k++) {
    if (qh hull_dim == 4) {
      if (k != qh DROPdim)
        destination[i++]= source[k];
    }else if (k == qh DROPdim)
      destination[i++]= 0;
    else
      destination[i++]= source[k];
  }
  while (i < 3)
    destination[i++]= 0.0;
} /* projectdim3 */

/*---------------------------------

  qh_readfeasible( dim, curline )
    read feasible point from current line and qh.fin

  returns:
    number of lines read from qh.fin
    sets qh.FEASIBLEpoint with malloc'd coordinates

  notes:
    checks for qh.HALFspace
    assumes dim > 1

  see:
    qh_setfeasible
*/
int qh_readfeasible(int dim, const char *curline) {
  boolT isfirst= True;
  int linecount= 0, tokcount= 0;
  const char *s;
  char *t, firstline[qh_MAXfirst+1];
  coordT *coords, value;

  if (!qh HALFspace) {
    qh_fprintf(qh ferr, 6070, "qhull input error: feasible point(dim 1 coords) is only valid for halfspace intersection\n");
    qh_errexit(qh_ERRinput, NULL, NULL);
  }
  if (qh feasible_string)
    qh_fprintf(qh ferr, 7057, "qhull input warning: feasible point(dim 1 coords) overrides 'Hn,n,n' feasible point for halfspace intersection\n");
  if (!(qh feasible_point= (coordT*)qh_malloc(dim* sizeof(coordT)))) {
    qh_fprintf(qh ferr, 6071, "qhull error: insufficient memory for feasible point\n");
    qh_errexit(qh_ERRmem, NULL, NULL);
  }
  coords= qh feasible_point;
  while ((s= (isfirst ?  curline : fgets(firstline, qh_MAXfirst, qh fin)))) {
    if (isfirst)
      isfirst= False;
    else
      linecount++;
    while (*s) {
      while (isspace(*s))
        s++;
      value= qh_strtod(s, &t);
      if (s == t)
        break;
      s= t;
      *(coords++)= value;
      if (++tokcount == dim) {
        while (isspace(*s))
          s++;
        qh_strtod(s, &t);
        if (s != t) {
          qh_fprintf(qh ferr, 6072, "qhull input error: coordinates for feasible point do not finish out the line: %s\n",
               s);
          qh_errexit(qh_ERRinput, NULL, NULL);
        }
        return linecount;
      }
    }
  }
  qh_fprintf(qh ferr, 6073, "qhull input error: only %d coordinates.  Could not read %d-d feasible point.\n",
           tokcount, dim);
  qh_errexit(qh_ERRinput, NULL, NULL);
  return 0;
} /* readfeasible */

/*---------------------------------

  qh_readpoints( numpoints, dimension, ismalloc )
    read points from qh.fin into qh.first_point, qh.num_points
    qh.fin is lines of coordinates, one per vertex, first line number of points
    if 'rbox D4',
      gives message
    if qh.ATinfinity,
      adds point-at-infinity for Delaunay triangulations

  returns:
    number of points, array of point coordinates, dimension, ismalloc True
    if qh.DELAUNAY & !qh.PROJECTinput, projects points to paraboloid
        and clears qh.PROJECTdelaunay
    if qh.HALFspace, reads optional feasible point, reads halfspaces,
        converts to dual.

  for feasible point in "cdd format" in 3-d:
    3 1
    coordinates
    comments
    begin
    n 4 real/integer
    ...
    end

  notes:
    dimension will change in qh_initqhull_globals if qh.PROJECTinput
    uses malloc() since qh_mem not initialized
    FIXUP QH11012: qh_readpoints needs rewriting, too long
*/
coordT *qh_readpoints(int *numpoints, int *dimension, boolT *ismalloc) {
  coordT *points, *coords, *infinity= NULL;
  realT paraboloid, maxboloid= -REALmax, value;
  realT *coordp= NULL, *offsetp= NULL, *normalp= NULL;
  char *s= 0, *t, firstline[qh_MAXfirst+1];
  int diminput=0, numinput=0, dimfeasible= 0, newnum, k, tempi;
  int firsttext=0, firstshort=0, firstlong=0, firstpoint=0;
  int tokcount= 0, linecount=0, maxcount, coordcount=0;
  boolT islong, isfirst= True, wasbegin= False;
  boolT isdelaunay= qh DELAUNAY && !qh PROJECTinput;

  if (qh CDDinput) {
    while ((s= fgets(firstline, qh_MAXfirst, qh fin))) {
      linecount++;
      if (qh HALFspace && linecount == 1 && isdigit(*s)) {
        dimfeasible= qh_strtol(s, &s);
        while (isspace(*s))
          s++;
        if (qh_strtol(s, &s) == 1)
          linecount += qh_readfeasible(dimfeasible, s);
        else
          dimfeasible= 0;
      }else if (!memcmp(firstline, "begin", (size_t)5) || !memcmp(firstline, "BEGIN", (size_t)5))
        break;
      else if (!*qh rbox_command)
        strncat(qh rbox_command, s, sizeof(qh rbox_command)-1);
    }
    if (!s) {
      qh_fprintf(qh ferr, 6074, "qhull input error: missing \"begin\" for cdd-formated input\n");
      qh_errexit(qh_ERRinput, NULL, NULL);
    }
  }
  while (!numinput && (s= fgets(firstline, qh_MAXfirst, qh fin))) {
    linecount++;
    if (!memcmp(s, "begin", (size_t)5) || !memcmp(s, "BEGIN", (size_t)5))
      wasbegin= True;
    while (*s) {
      while (isspace(*s))
        s++;
      if (!*s)
        break;
      if (!isdigit(*s)) {
        if (!*qh rbox_command) {
          strncat(qh rbox_command, s, sizeof(qh rbox_command)-1);
          firsttext= linecount;
        }
        break;
      }
      if (!diminput)
        diminput= qh_strtol(s, &s);
      else {
        numinput= qh_strtol(s, &s);
        if (numinput == 1 && diminput >= 2 && qh HALFspace && !qh CDDinput) {
          linecount += qh_readfeasible(diminput, s); /* checks if ok */
          dimfeasible= diminput;
          diminput= numinput= 0;
        }else
          break;
      }
    }
  }
  if (!s) {
    qh_fprintf(qh ferr, 6075, "qhull input error: short input file.  Did not find dimension and number of points\n");
    qh_errexit(qh_ERRinput, NULL, NULL);
  }
  if (diminput > numinput) {
    tempi= diminput;    /* exchange dim and n, e.g., for cdd input format */
    diminput= numinput;
    numinput= tempi;
  }
  if (diminput < 2) {
    qh_fprintf(qh ferr, 6220,"qhull input error: dimension %d(first number) should be at least 2\n",
            diminput);
    qh_errexit(qh_ERRinput, NULL, NULL);
  }
  if (isdelaunay) {
    qh PROJECTdelaunay= False;
    if (qh CDDinput)
      *dimension= diminput;
    else
      *dimension= diminput+1;
    *numpoints= numinput;
    if (qh ATinfinity)
      (*numpoints)++;
  }else if (qh HALFspace) {
    *dimension= diminput - 1;
    *numpoints= numinput;
    if (diminput < 3) {
      qh_fprintf(qh ferr, 6221,"qhull input error: dimension %d(first number, includes offset) should be at least 3 for halfspaces\n",
            diminput);
      qh_errexit(qh_ERRinput, NULL, NULL);
    }
    if (dimfeasible) {
      if (dimfeasible != *dimension) {
        qh_fprintf(qh ferr, 6222,"qhull input error: dimension %d of feasible point is not one less than dimension %d for halfspaces\n",
          dimfeasible, diminput);
        qh_errexit(qh_ERRinput, NULL, NULL);
      }
    }else
      qh_setfeasible(*dimension);
  }else {
    if (qh CDDinput)
      *dimension= diminput-1;
    else
      *dimension= diminput;
    *numpoints= numinput;
  }
  qh normal_size= *dimension * sizeof(coordT); /* for tracing with qh_printpoint */
  if (qh HALFspace) {
    qh half_space= coordp= (coordT*)qh_malloc(qh normal_size + sizeof(coordT));
    if (qh CDDinput) {
      offsetp= qh half_space;
      normalp= offsetp + 1;
    }else {
      normalp= qh half_space;
      offsetp= normalp + *dimension;
    }
  }
  qh maxline= diminput * (qh_REALdigits + 5);
  maximize_(qh maxline, 500);
  qh line= (char*)qh_malloc((qh maxline+1) * sizeof(char));
  *ismalloc= True;  /* use malloc since memory not setup */
  coords= points= qh temp_malloc=
        (coordT*)qh_malloc((*numpoints)*(*dimension)*sizeof(coordT));
  if (!coords || !qh line || (qh HALFspace && !qh half_space)) {
    qh_fprintf(qh ferr, 6076, "qhull error: insufficient memory to read %d points\n",
            numinput);
    qh_errexit(qh_ERRmem, NULL, NULL);
  }
  if (isdelaunay && qh ATinfinity) {
    infinity= points + numinput * (*dimension);
    for (k= (*dimension) - 1; k--; )
      infinity[k]= 0.0;
  }
  maxcount= numinput * diminput;
  paraboloid= 0.0;
  while ((s= (isfirst ?  s : fgets(qh line, qh maxline, qh fin)))) {
    if (!isfirst) {
      linecount++;
      if (*s == 'e' || *s == 'E') {
        if (!memcmp(s, "end", (size_t)3) || !memcmp(s, "END", (size_t)3)) {
          if (qh CDDinput )
            break;
          else if (wasbegin)
            qh_fprintf(qh ferr, 7058, "qhull input warning: the input appears to be in cdd format.  If so, use 'Fd'\n");
        }
      }
    }
    islong= False;
    while (*s) {
      while (isspace(*s))
        s++;
      value= qh_strtod(s, &t);
      if (s == t) {
        if (!*qh rbox_command)
         strncat(qh rbox_command, s, sizeof(qh rbox_command)-1);
        if (*s && !firsttext)
          firsttext= linecount;
        if (!islong && !firstshort && coordcount)
          firstshort= linecount;
        break;
      }
      if (!firstpoint)
        firstpoint= linecount;
      s= t;
      if (++tokcount > maxcount)
        continue;
      if (qh HALFspace) {
        if (qh CDDinput)
          *(coordp++)= -value; /* both coefficients and offset */
        else
          *(coordp++)= value;
      }else {
        *(coords++)= value;
        if (qh CDDinput && !coordcount) {
          if (value != 1.0) {
            qh_fprintf(qh ferr, 6077, "qhull input error: for cdd format, point at line %d does not start with '1'\n",
                   linecount);
            qh_errexit(qh_ERRinput, NULL, NULL);
          }
          coords--;
        }else if (isdelaunay) {
          paraboloid += value * value;
          if (qh ATinfinity) {
            if (qh CDDinput)
              infinity[coordcount-1] += value;
            else
              infinity[coordcount] += value;
          }
        }
      }
      if (++coordcount == diminput) {
        coordcount= 0;
        if (isdelaunay) {
          *(coords++)= paraboloid;
          maximize_(maxboloid, paraboloid);
          paraboloid= 0.0;
        }else if (qh HALFspace) {
          if (!qh_sethalfspace(*dimension, coords, &coords, normalp, offsetp, qh feasible_point)) {
            qh_fprintf(qh ferr, 8048, "The halfspace was on line %d\n", linecount);
            if (wasbegin)
              qh_fprintf(qh ferr, 8049, "The input appears to be in cdd format.  If so, you should use option 'Fd'\n");
            qh_errexit(qh_ERRinput, NULL, NULL);
          }
          coordp= qh half_space;
        }
        while (isspace(*s))
          s++;
        if (*s) {
          islong= True;
          if (!firstlong)
            firstlong= linecount;
        }
      }
    }
    if (!islong && !firstshort && coordcount)
      firstshort= linecount;
    if (!isfirst && s - qh line >= qh maxline) {
      qh_fprintf(qh ferr, 6078, "qhull input error: line %d contained more than %d characters\n",
              linecount, (int) (s - qh line));   /* WARN64 */
      qh_errexit(qh_ERRinput, NULL, NULL);
    }
    isfirst= False;
  }
  if (tokcount != maxcount) {
    newnum= fmin_(numinput, tokcount/diminput);
    qh_fprintf(qh ferr, 7073,"\
qhull warning: instead of %d %d-dimensional points, input contains\n\
%d points and %d extra coordinates.  Line %d is the first\npoint",
       numinput, diminput, tokcount/diminput, tokcount % diminput, firstpoint);
    if (firsttext)
      qh_fprintf(qh ferr, 8051, ", line %d is the first comment", firsttext);
    if (firstshort)
      qh_fprintf(qh ferr, 8052, ", line %d is the first short\nline", firstshort);
    if (firstlong)
      qh_fprintf(qh ferr, 8053, ", line %d is the first long line", firstlong);
    qh_fprintf(qh ferr, 8054, ".  Continue with %d points.\n", newnum);
    numinput= newnum;
    if (isdelaunay && qh ATinfinity) {
      for (k= tokcount % diminput; k--; )
        infinity[k] -= *(--coords);
      *numpoints= newnum+1;
    }else {
      coords -= tokcount % diminput;
      *numpoints= newnum;
    }
  }
  if (isdelaunay && qh ATinfinity) {
    for (k= (*dimension) -1; k--; )
      infinity[k] /= numinput;
    if (coords == infinity)
      coords += (*dimension) -1;
    else {
      for (k=0; k < (*dimension) -1; k++)
        *(coords++)= infinity[k];
    }
    *(coords++)= maxboloid * 1.1;
  }
  if (qh rbox_command[0]) {
    qh rbox_command[strlen(qh rbox_command)-1]= '\0';
    if (!strcmp(qh rbox_command, "./rbox D4"))
      qh_fprintf(qh ferr, 8055, "\n\
This is the qhull test case.  If any errors or core dumps occur,\n\
recompile qhull with 'make new'.  If errors still occur, there is\n\
an incompatibility.  You should try a different compiler.  You can also\n\
change the choices in user.h.  If you discover the source of the problem,\n\
please send mail to qhull_bug@qhull.org.\n\
\n\
Type 'qhull' for a short list of options.\n");
  }
  qh_free(qh line);
  qh line= NULL;
  if (qh half_space) {
    qh_free(qh half_space);
    qh half_space= NULL;
  }
  qh temp_malloc= NULL;
  trace1((qh ferr, 1008,"qh_readpoints: read in %d %d-dimensional points\n",
          numinput, diminput));
  return(points);
} /* readpoints */


/*---------------------------------

  qh_setfeasible( dim )
    set qh.FEASIBLEpoint from qh.feasible_string in "n,n,n" or "n n n" format

  notes:
    "n,n,n" already checked by qh_initflags()
    see qh_readfeasible()
*/
void qh_setfeasible(int dim) {
  int tokcount= 0;
  char *s;
  coordT *coords, value;

  if (!(s= qh feasible_string)) {
    qh_fprintf(qh ferr, 6223, "\
qhull input error: halfspace intersection needs a feasible point.\n\
Either prepend the input with 1 point or use 'Hn,n,n'.  See manual.\n");
    qh_errexit(qh_ERRinput, NULL, NULL);
  }
  if (!(qh feasible_point= (pointT*)qh_malloc(dim * sizeof(coordT)))) {
    qh_fprintf(qh ferr, 6079, "qhull error: insufficient memory for 'Hn,n,n'\n");
    qh_errexit(qh_ERRmem, NULL, NULL);
  }
  coords= qh feasible_point;
  while (*s) {
    value= qh_strtod(s, &s);
    if (++tokcount > dim) {
      qh_fprintf(qh ferr, 7059, "qhull input warning: more coordinates for 'H%s' than dimension %d\n",
          qh feasible_string, dim);
      break;
    }
    *(coords++)= value;
    if (*s)
      s++;
  }
  while (++tokcount <= dim)
    *(coords++)= 0.0;
} /* setfeasible */

/*---------------------------------

  qh_skipfacet( facet )
    returns 'True' if this facet is not to be printed

  notes:
    based on the user provided slice thresholds and 'good' specifications
*/
boolT qh_skipfacet(facetT *facet) {
  facetT *neighbor, **neighborp;

  if (qh PRINTneighbors) {
    if (facet->good)
      return !qh PRINTgood;
    FOREACHneighbor_(facet) {
      if (neighbor->good)
        return False;
    }
    return True;
  }else if (qh PRINTgood)
    return !facet->good;
  else if (!facet->normal)
    return True;
  return(!qh_inthresholds(facet->normal, NULL));
} /* skipfacet */

/*---------------------------------

  qh_skipfilename( string )
    returns pointer to character after filename

  notes:
    skips leading spaces
    ends with spacing or eol
    if starts with ' or " ends with the same, skipping \' or \"
    For qhull, qh_argv_to_command() only uses double quotes
*/
char *qh_skipfilename(char *filename) {
  char *s= filename;  /* non-const due to return */
  char c;

  while (*s && isspace(*s))
    s++;
  c= *s++;
  if (c == '\0') {
    qh_fprintf(qh ferr, 6204, "qhull input error: filename expected, none found.\n");
    qh_errexit(qh_ERRinput, NULL, NULL);
  }
  if (c == '\'' || c == '"') {
    while (*s !=c || s[-1] == '\\') {
      if (!*s) {
        qh_fprintf(qh ferr, 6203, "qhull input error: missing quote after filename -- %s\n", filename);
        qh_errexit(qh_ERRinput, NULL, NULL);
      }
      s++;
    }
    s++;
  }
  else while (*s && !isspace(*s))
      s++;
  return s;
} /* skipfilename */

qhull-2012.1/src/libqhull/io.h0000644000076400010400000001736611710144466017310 0ustar  bbarberAdministrators/*
  ---------------------------------

   io.h
   declarations of Input/Output functions

   see README, libqhull.h and io.c

   Copyright (c) 1993-2012 The Geometry Center.
   $Id: //main/2011/qhull/src/libqhull/io.h#3 $$Change: 1464 $
   $DateTime: 2012/01/25 22:58:41 $$Author: bbarber $
*/

#ifndef qhDEFio
#define qhDEFio 1

#include "libqhull.h"

/*============ constants and flags ==================*/

/*----------------------------------

  qh_MAXfirst
    maximum length of first two lines of stdin
*/
#define qh_MAXfirst  200

/*----------------------------------

  qh_MINradius
    min radius for Gp and Gv, fraction of maxcoord
*/
#define qh_MINradius 0.02

/*----------------------------------

  qh_GEOMepsilon
    adjust outer planes for 'lines closer' and geomview roundoff.
    This prevents bleed through.
*/
#define qh_GEOMepsilon 2e-3

/*----------------------------------

  qh_WHITESPACE
    possible values of white space
*/
#define qh_WHITESPACE " \n\t\v\r\f"


/*----------------------------------

  qh_RIDGE
    to select which ridges to print in qh_eachvoronoi
*/
typedef enum
{
    qh_RIDGEall = 0, qh_RIDGEinner, qh_RIDGEouter
}
qh_RIDGE;

/*----------------------------------

  printvridgeT
    prints results of qh_printvdiagram

  see:
    qh_printvridge for an example
*/
typedef void (*printvridgeT)(FILE *fp, vertexT *vertex, vertexT *vertexA, setT *centers, boolT unbounded);

/*============== -prototypes in alphabetical order =========*/

void    dfacet(unsigned id);
void    dvertex(unsigned id);
int     qh_compare_facetarea(const void *p1, const void *p2);
int     qh_compare_facetmerge(const void *p1, const void *p2);
int     qh_compare_facetvisit(const void *p1, const void *p2);
int     qh_compare_vertexpoint(const void *p1, const void *p2); /* not used */
void    qh_copyfilename(char *filename, int size, const char* source, int length);
void    qh_countfacets(facetT *facetlist, setT *facets, boolT printall,
              int *numfacetsp, int *numsimplicialp, int *totneighborsp,
              int *numridgesp, int *numcoplanarsp, int *numnumtricoplanarsp);
pointT *qh_detvnorm(vertexT *vertex, vertexT *vertexA, setT *centers, realT *offsetp);
setT   *qh_detvridge(vertexT *vertex);
setT   *qh_detvridge3 (vertexT *atvertex, vertexT *vertex);
int     qh_eachvoronoi(FILE *fp, printvridgeT printvridge, vertexT *atvertex, boolT visitall, qh_RIDGE innerouter, boolT inorder);
int     qh_eachvoronoi_all(FILE *fp, printvridgeT printvridge, boolT isUpper, qh_RIDGE innerouter, boolT inorder);
void    qh_facet2point(facetT *facet, pointT **point0, pointT **point1, realT *mindist);
setT   *qh_facetvertices(facetT *facetlist, setT *facets, boolT allfacets);
void    qh_geomplanes(facetT *facet, realT *outerplane, realT *innerplane);
void    qh_markkeep(facetT *facetlist);
setT   *qh_markvoronoi(facetT *facetlist, setT *facets, boolT printall, boolT *isLowerp, int *numcentersp);
void    qh_order_vertexneighbors(vertexT *vertex);
void    qh_prepare_output(void);
void    qh_printafacet(FILE *fp, qh_PRINT format, facetT *facet, boolT printall);
void    qh_printbegin(FILE *fp, qh_PRINT format, facetT *facetlist, setT *facets, boolT printall);
void    qh_printcenter(FILE *fp, qh_PRINT format, const char *string, facetT *facet);
void    qh_printcentrum(FILE *fp, facetT *facet, realT radius);
void    qh_printend(FILE *fp, qh_PRINT format, facetT *facetlist, setT *facets, boolT printall);
void    qh_printend4geom(FILE *fp, facetT *facet, int *num, boolT printall);
void    qh_printextremes(FILE *fp, facetT *facetlist, setT *facets, boolT printall);
void    qh_printextremes_2d(FILE *fp, facetT *facetlist, setT *facets, boolT printall);
void    qh_printextremes_d(FILE *fp, facetT *facetlist, setT *facets, boolT printall);
void    qh_printfacet(FILE *fp, facetT *facet);
void    qh_printfacet2math(FILE *fp, facetT *facet, qh_PRINT format, int notfirst);
void    qh_printfacet2geom(FILE *fp, facetT *facet, realT color[3]);
void    qh_printfacet2geom_points(FILE *fp, pointT *point1, pointT *point2,
                               facetT *facet, realT offset, realT color[3]);
void    qh_printfacet3math(FILE *fp, facetT *facet, qh_PRINT format, int notfirst);
void    qh_printfacet3geom_nonsimplicial(FILE *fp, facetT *facet, realT color[3]);
void    qh_printfacet3geom_points(FILE *fp, setT *points, facetT *facet, realT offset, realT color[3]);
void    qh_printfacet3geom_simplicial(FILE *fp, facetT *facet, realT color[3]);
void    qh_printfacet3vertex(FILE *fp, facetT *facet, qh_PRINT format);
void    qh_printfacet4geom_nonsimplicial(FILE *fp, facetT *facet, realT color[3]);
void    qh_printfacet4geom_simplicial(FILE *fp, facetT *facet, realT color[3]);
void    qh_printfacetNvertex_nonsimplicial(FILE *fp, facetT *facet, int id, qh_PRINT format);
void    qh_printfacetNvertex_simplicial(FILE *fp, facetT *facet, qh_PRINT format);
void    qh_printfacetheader(FILE *fp, facetT *facet);
void    qh_printfacetridges(FILE *fp, facetT *facet);
void    qh_printfacets(FILE *fp, qh_PRINT format, facetT *facetlist, setT *facets, boolT printall);
void    qh_printhyperplaneintersection(FILE *fp, facetT *facet1, facetT *facet2,
                   setT *vertices, realT color[3]);
void    qh_printneighborhood(FILE *fp, qh_PRINT format, facetT *facetA, facetT *facetB, boolT printall);
void    qh_printline3geom(FILE *fp, pointT *pointA, pointT *pointB, realT color[3]);
void    qh_printpoint(FILE *fp, const char *string, pointT *point);
void    qh_printpointid(FILE *fp, const char *string, int dim, pointT *point, int id);
void    qh_printpoint3 (FILE *fp, pointT *point);
void    qh_printpoints_out(FILE *fp, facetT *facetlist, setT *facets, boolT printall);
void    qh_printpointvect(FILE *fp, pointT *point, coordT *normal, pointT *center, realT radius, realT color[3]);
void    qh_printpointvect2 (FILE *fp, pointT *point, coordT *normal, pointT *center, realT radius);
void    qh_printridge(FILE *fp, ridgeT *ridge);
void    qh_printspheres(FILE *fp, setT *vertices, realT radius);
void    qh_printvdiagram(FILE *fp, qh_PRINT format, facetT *facetlist, setT *facets, boolT printall);
int     qh_printvdiagram2 (FILE *fp, printvridgeT printvridge, setT *vertices, qh_RIDGE innerouter, boolT inorder);
void    qh_printvertex(FILE *fp, vertexT *vertex);
void    qh_printvertexlist(FILE *fp, const char* string, facetT *facetlist,
                         setT *facets, boolT printall);
void    qh_printvertices(FILE *fp, const char* string, setT *vertices);
void    qh_printvneighbors(FILE *fp, facetT* facetlist, setT *facets, boolT printall);
void    qh_printvoronoi(FILE *fp, qh_PRINT format, facetT *facetlist, setT *facets, boolT printall);
void    qh_printvnorm(FILE *fp, vertexT *vertex, vertexT *vertexA, setT *centers, boolT unbounded);
void    qh_printvridge(FILE *fp, vertexT *vertex, vertexT *vertexA, setT *centers, boolT unbounded);
void    qh_produce_output(void);
void    qh_produce_output2(void);
void    qh_projectdim3 (pointT *source, pointT *destination);
int     qh_readfeasible(int dim, const char *curline);
coordT *qh_readpoints(int *numpoints, int *dimension, boolT *ismalloc);
void    qh_setfeasible(int dim);
boolT   qh_skipfacet(facetT *facet);
char   *qh_skipfilename(char *filename);

#endif /* qhDEFio */
qhull-2012.1/src/libqhull/libqhull.c0000644000076400010400000014515111710144466020502 0ustar  bbarberAdministrators/*
  ---------------------------------

   libqhull.c
   Quickhull algorithm for convex hulls

   qhull() and top-level routines

   see qh-qhull.htm, libqhull.h, unix.c

   see qhull_a.h for internal functions

   Copyright (c) 1993-2012 The Geometry Center.
   $Id: //main/2011/qhull/src/libqhull/libqhull.c#4 $$Change: 1464 $
   $DateTime: 2012/01/25 22:58:41 $$Author: bbarber $
*/

#include "qhull_a.h"

/*============= functions in alphabetic order after qhull() =======*/

/*---------------------------------

  qh_qhull()
    compute DIM3 convex hull of qh.num_points starting at qh.first_point
    qh contains all global options and variables

  returns:
    returns polyhedron
      qh.facet_list, qh.num_facets, qh.vertex_list, qh.num_vertices,

    returns global variables
      qh.hulltime, qh.max_outside, qh.interior_point, qh.max_vertex, qh.min_vertex

    returns precision constants
      qh.ANGLEround, centrum_radius, cos_max, DISTround, MAXabs_coord, ONEmerge

  notes:
    unless needed for output
      qh.max_vertex and qh.min_vertex are max/min due to merges

  see:
    to add individual points to either qh.num_points
      use qh_addpoint()

    if qh.GETarea
      qh_produceoutput() returns qh.totarea and qh.totvol via qh_getarea()

  design:
    record starting time
    initialize hull and partition points
    build convex hull
    unless early termination
      update facet->maxoutside for vertices, coplanar, and near-inside points
    error if temporary sets exist
    record end time
*/

void qh_qhull(void) {
  int numoutside;

  qh hulltime= qh_CPUclock;
  if (qh RERUN || qh JOGGLEmax < REALmax/2)
    qh_build_withrestart();
  else {
    qh_initbuild();
    qh_buildhull();
  }
  if (!qh STOPpoint && !qh STOPcone) {
    if (qh ZEROall_ok && !qh TESTvneighbors && qh MERGEexact)
      qh_checkzero( qh_ALL);
    if (qh ZEROall_ok && !qh TESTvneighbors && !qh WAScoplanar) {
      trace2((qh ferr, 2055, "qh_qhull: all facets are clearly convex and no coplanar points.  Post-merging and check of maxout not needed.\n"));
      qh DOcheckmax= False;
    }else {
      if (qh MERGEexact || (qh hull_dim > qh_DIMreduceBuild && qh PREmerge))
        qh_postmerge("First post-merge", qh premerge_centrum, qh premerge_cos,
             (qh POSTmerge ? False : qh TESTvneighbors));
      else if (!qh POSTmerge && qh TESTvneighbors)
        qh_postmerge("For testing vertex neighbors", qh premerge_centrum,
             qh premerge_cos, True);
      if (qh POSTmerge)
        qh_postmerge("For post-merging", qh postmerge_centrum,
             qh postmerge_cos, qh TESTvneighbors);
      if (qh visible_list == qh facet_list) { /* i.e., merging done */
        qh findbestnew= True;
        qh_partitionvisible(/*visible_list, newfacet_list*/ !qh_ALL, &numoutside);
        qh findbestnew= False;
        qh_deletevisible(/*qh visible_list*/);
        qh_resetlists(False, qh_RESETvisible /*qh visible_list newvertex_list newfacet_list */);
      }
    }
    if (qh DOcheckmax){
      if (qh REPORTfreq) {
        qh_buildtracing(NULL, NULL);
        qh_fprintf(qh ferr, 8115, "\nTesting all coplanar points.\n");
      }
      qh_check_maxout();
    }
    if (qh KEEPnearinside && !qh maxoutdone)
      qh_nearcoplanar();
  }
  if (qh_setsize(qhmem.tempstack) != 0) {
    qh_fprintf(qh ferr, 6164, "qhull internal error (qh_qhull): temporary sets not empty(%d)\n",
             qh_setsize(qhmem.tempstack));
    qh_errexit(qh_ERRqhull, NULL, NULL);
  }
  qh hulltime= qh_CPUclock - qh hulltime;
  qh QHULLfinished= True;
  trace1((qh ferr, 1036, "Qhull: algorithm completed\n"));
} /* qhull */

/*---------------------------------

  qh_addpoint( furthest, facet, checkdist )
    add point (usually furthest point) above facet to hull
    if checkdist,
      check that point is above facet.
      if point is not outside of the hull, uses qh_partitioncoplanar()
      assumes that facet is defined by qh_findbestfacet()
    else if facet specified,
      assumes that point is above facet (major damage if below)
    for Delaunay triangulations,
      Use qh_setdelaunay() to lift point to paraboloid and scale by 'Qbb' if needed
      Do not use options 'Qbk', 'QBk', or 'QbB' since they scale the coordinates.

  returns:
    returns False if user requested an early termination
     qh.visible_list, newfacet_list, delvertex_list, NEWfacets may be defined
    updates qh.facet_list, qh.num_facets, qh.vertex_list, qh.num_vertices
    clear qh.maxoutdone (will need to call qh_check_maxout() for facet->maxoutside)
    if unknown point, adds a pointer to qh.other_points
      do not deallocate the point's coordinates

  notes:
    assumes point is near its best facet and not at a local minimum of a lens
      distributions.  Use qh_findbestfacet to avoid this case.
    uses qh.visible_list, qh.newfacet_list, qh.delvertex_list, qh.NEWfacets

  see also:
    qh_triangulate() -- triangulate non-simplicial facets

  design:
    add point to other_points if needed
    if checkdist
      if point not above facet
        partition coplanar point
        exit
    exit if pre STOPpoint requested
    find horizon and visible facets for point
    make new facets for point to horizon
    make hyperplanes for point
    compute balance statistics
    match neighboring new facets
    update vertex neighbors and delete interior vertices
    exit if STOPcone requested
    merge non-convex new facets
    if merge found, many merges, or 'Qf'
       use qh_findbestnew() instead of qh_findbest()
    partition outside points from visible facets
    delete visible facets
    check polyhedron if requested
    exit if post STOPpoint requested
    reset working lists of facets and vertices
*/
boolT qh_addpoint(pointT *furthest, facetT *facet, boolT checkdist) {
  int goodvisible, goodhorizon;
  vertexT *vertex;
  facetT *newfacet;
  realT dist, newbalance, pbalance;
  boolT isoutside= False;
  int numpart, numpoints, numnew, firstnew;

  qh maxoutdone= False;
  if (qh_pointid(furthest) == -1)
    qh_setappend(&qh other_points, furthest);
  if (!facet) {
    qh_fprintf(qh ferr, 6213, "qhull internal error (qh_addpoint): NULL facet.  Need to call qh_findbestfacet first\n");
    qh_errexit(qh_ERRqhull, NULL, NULL);
  }
  if (checkdist) {
    facet= qh_findbest(furthest, facet, !qh_ALL, !qh_ISnewfacets, !qh_NOupper,
                        &dist, &isoutside, &numpart);
    zzadd_(Zpartition, numpart);
    if (!isoutside) {
      zinc_(Znotmax);  /* last point of outsideset is no longer furthest. */
      facet->notfurthest= True;
      qh_partitioncoplanar(furthest, facet, &dist);
      return True;
    }
  }
  qh_buildtracing(furthest, facet);
  if (qh STOPpoint < 0 && qh furthest_id == -qh STOPpoint-1) {
    facet->notfurthest= True;
    return False;
  }
  qh_findhorizon(furthest, facet, &goodvisible, &goodhorizon);
  if (qh ONLYgood && !(goodvisible+goodhorizon) && !qh GOODclosest) {
    zinc_(Znotgood);
    facet->notfurthest= True;
    /* last point of outsideset is no longer furthest.  This is ok
       since all points of the outside are likely to be bad */
    qh_resetlists(False, qh_RESETvisible /*qh visible_list newvertex_list newfacet_list */);
    return True;
  }
  zzinc_(Zprocessed);
  firstnew= qh facet_id;
  vertex= qh_makenewfacets(furthest /*visible_list, attaches if !ONLYgood */);
  qh_makenewplanes(/* newfacet_list */);
  numnew= qh facet_id - firstnew;
  newbalance= numnew - (realT) (qh num_facets-qh num_visible)
                         * qh hull_dim/qh num_vertices;
  wadd_(Wnewbalance, newbalance);
  wadd_(Wnewbalance2, newbalance * newbalance);
  if (qh ONLYgood
  && !qh_findgood(qh newfacet_list, goodhorizon) && !qh GOODclosest) {
    FORALLnew_facets
      qh_delfacet(newfacet);
    qh_delvertex(vertex);
    qh_resetlists(True, qh_RESETvisible /*qh visible_list newvertex_list newfacet_list */);
    zinc_(Znotgoodnew);
    facet->notfurthest= True;
    return True;
  }
  if (qh ONLYgood)
    qh_attachnewfacets(/*visible_list*/);
  qh_matchnewfacets();
  qh_updatevertices();
  if (qh STOPcone && qh furthest_id == qh STOPcone-1) {
    facet->notfurthest= True;
    return False;  /* visible_list etc. still defined */
  }
  qh findbestnew= False;
  if (qh PREmerge || qh MERGEexact) {
    qh_premerge(vertex, qh premerge_centrum, qh premerge_cos);
    if (qh_USEfindbestnew)
      qh findbestnew= True;
    else {
      FORALLnew_facets {
        if (!newfacet->simplicial) {
          qh findbestnew= True;  /* use qh_findbestnew instead of qh_findbest*/
          break;
        }
      }
    }
  }else if (qh BESToutside)
    qh findbestnew= True;
  qh_partitionvisible(/*visible_list, newfacet_list*/ !qh_ALL, &numpoints);
  qh findbestnew= False;
  qh findbest_notsharp= False;
  zinc_(Zpbalance);
  pbalance= numpoints - (realT) qh hull_dim /* assumes all points extreme */
                * (qh num_points - qh num_vertices)/qh num_vertices;
  wadd_(Wpbalance, pbalance);
  wadd_(Wpbalance2, pbalance * pbalance);
  qh_deletevisible(/*qh visible_list*/);
  zmax_(Zmaxvertex, qh num_vertices);
  qh NEWfacets= False;
  if (qh IStracing >= 4) {
    if (qh num_facets < 2000)
      qh_printlists();
    qh_printfacetlist(qh newfacet_list, NULL, True);
    qh_checkpolygon(qh facet_list);
  }else if (qh CHECKfrequently) {
    if (qh num_facets < 50)
      qh_checkpolygon(qh facet_list);
    else
      qh_checkpolygon(qh newfacet_list);
  }
  if (qh STOPpoint > 0 && qh furthest_id == qh STOPpoint-1)
    return False;
  qh_resetlists(True, qh_RESETvisible /*qh visible_list newvertex_list newfacet_list */);
  /* qh_triangulate(); to test qh.TRInormals */
  trace2((qh ferr, 2056, "qh_addpoint: added p%d new facets %d new balance %2.2g point balance %2.2g\n",
    qh_pointid(furthest), numnew, newbalance, pbalance));
  return True;
} /* addpoint */

/*---------------------------------

  qh_build_withrestart()
    allow restarts due to qh.JOGGLEmax while calling qh_buildhull()
    qh.FIRSTpoint/qh.NUMpoints is point array
        it may be moved by qh_joggleinput()
*/
void qh_build_withrestart(void) {
  int restart;

  qh ALLOWrestart= True;
  while (True) {
    restart= setjmp(qh restartexit); /* simple statement for CRAY J916 */
    if (restart) {       /* only from qh_precision() */
      zzinc_(Zretry);
      wmax_(Wretrymax, qh JOGGLEmax);
      /* QH7078 warns about using 'TCn' with 'QJn' */
      qh STOPcone= -1; /* if break from joggle, prevents normal output */
    }
    if (!qh RERUN && qh JOGGLEmax < REALmax/2) {
      if (qh build_cnt > qh_JOGGLEmaxretry) {
        qh_fprintf(qh ferr, 6229, "qhull precision error: %d attempts to construct a convex hull\n\
        with joggled input.  Increase joggle above 'QJ%2.2g'\n\
        or modify qh_JOGGLE... parameters in user.h\n",
           qh build_cnt, qh JOGGLEmax);
        qh_errexit(qh_ERRqhull, NULL, NULL);
      }
      if (qh build_cnt && !restart)
        break;
    }else if (qh build_cnt && qh build_cnt >= qh RERUN)
      break;
    qh STOPcone= 0;
    qh_freebuild(True);  /* first call is a nop */
    qh build_cnt++;
    if (!qh qhull_optionsiz)
      qh qhull_optionsiz= (int)strlen(qh qhull_options);   /* WARN64 */
    else {
      qh qhull_options [qh qhull_optionsiz]= '\0';
      qh qhull_optionlen= qh_OPTIONline;  /* starts a new line */
    }
    qh_option("_run", &qh build_cnt, NULL);
    if (qh build_cnt == qh RERUN) {
      qh IStracing= qh TRACElastrun;  /* duplicated from qh_initqhull_globals */
      if (qh TRACEpoint != -1 || qh TRACEdist < REALmax/2 || qh TRACEmerge) {
        qh TRACElevel= (qh IStracing? qh IStracing : 3);
        qh IStracing= 0;
      }
      qhmem.IStracing= qh IStracing;
    }
    if (qh JOGGLEmax < REALmax/2)
      qh_joggleinput();
    qh_initbuild();
    qh_buildhull();
    if (qh JOGGLEmax < REALmax/2 && !qh MERGING)
      qh_checkconvex(qh facet_list, qh_ALGORITHMfault);
  }
  qh ALLOWrestart= False;
} /* qh_build_withrestart */

/*---------------------------------

  qh_buildhull()
    construct a convex hull by adding outside points one at a time

  returns:

  notes:
    may be called multiple times
    checks facet and vertex lists for incorrect flags
    to recover from STOPcone, call qh_deletevisible and qh_resetlists

  design:
    check visible facet and newfacet flags
    check newlist vertex flags and qh.STOPcone/STOPpoint
    for each facet with a furthest outside point
      add point to facet
      exit if qh.STOPcone or qh.STOPpoint requested
    if qh.NARROWhull for initial simplex
      partition remaining outside points to coplanar sets
*/
void qh_buildhull(void) {
  facetT *facet;
  pointT *furthest;
  vertexT *vertex;
  int id;

  trace1((qh ferr, 1037, "qh_buildhull: start build hull\n"));
  FORALLfacets {
    if (facet->visible || facet->newfacet) {
      qh_fprintf(qh ferr, 6165, "qhull internal error (qh_buildhull): visible or new facet f%d in facet list\n",
                   facet->id);
      qh_errexit(qh_ERRqhull, facet, NULL);
    }
  }
  FORALLvertices {
    if (vertex->newlist) {
      qh_fprintf(qh ferr, 6166, "qhull internal error (qh_buildhull): new vertex f%d in vertex list\n",
                   vertex->id);
      qh_errprint("ERRONEOUS", NULL, NULL, NULL, vertex);
      qh_errexit(qh_ERRqhull, NULL, NULL);
    }
    id= qh_pointid(vertex->point);
    if ((qh STOPpoint>0 && id == qh STOPpoint-1) ||
        (qh STOPpoint<0 && id == -qh STOPpoint-1) ||
        (qh STOPcone>0 && id == qh STOPcone-1)) {
      trace1((qh ferr, 1038,"qh_buildhull: stop point or cone P%d in initial hull\n", id));
      return;
    }
  }
  qh facet_next= qh facet_list;      /* advance facet when processed */
  while ((furthest= qh_nextfurthest(&facet))) {
    qh num_outside--;  /* if ONLYmax, furthest may not be outside */
    if (!qh_addpoint(furthest, facet, qh ONLYmax))
      break;
  }
  if (qh NARROWhull) /* move points from outsideset to coplanarset */
    qh_outcoplanar( /* facet_list */ );
  if (qh num_outside && !furthest) {
    qh_fprintf(qh ferr, 6167, "qhull internal error (qh_buildhull): %d outside points were never processed.\n", qh num_outside);
    qh_errexit(qh_ERRqhull, NULL, NULL);
  }
  trace1((qh ferr, 1039, "qh_buildhull: completed the hull construction\n"));
} /* buildhull */


/*---------------------------------

  qh_buildtracing( furthest, facet )
    trace an iteration of qh_buildhull() for furthest point and facet
    if !furthest, prints progress message

  returns:
    tracks progress with qh.lastreport
    updates qh.furthest_id (-3 if furthest is NULL)
    also resets visit_id, vertext_visit on wrap around

  see:
    qh_tracemerging()

  design:
    if !furthest
      print progress message
      exit
    if 'TFn' iteration
      print progress message
    else if tracing
      trace furthest point and facet
    reset qh.visit_id and qh.vertex_visit if overflow may occur
    set qh.furthest_id for tracing
*/
void qh_buildtracing(pointT *furthest, facetT *facet) {
  realT dist= 0;
  float cpu;
  int total, furthestid;
  time_t timedata;
  struct tm *tp;
  vertexT *vertex;

  qh old_randomdist= qh RANDOMdist;
  qh RANDOMdist= False;
  if (!furthest) {
    time(&timedata);
    tp= localtime(&timedata);
    cpu= (float)qh_CPUclock - (float)qh hulltime;
    cpu /= (float)qh_SECticks;
    total= zzval_(Ztotmerge) - zzval_(Zcyclehorizon) + zzval_(Zcyclefacettot);
    qh_fprintf(qh ferr, 8118, "\n\
At %02d:%02d:%02d & %2.5g CPU secs, qhull has created %d facets and merged %d.\n\
 The current hull contains %d facets and %d vertices.  Last point was p%d\n",
      tp->tm_hour, tp->tm_min, tp->tm_sec, cpu, qh facet_id -1,
      total, qh num_facets, qh num_vertices, qh furthest_id);
    return;
  }
  furthestid= qh_pointid(furthest);
  if (qh TRACEpoint == furthestid) {
    qh IStracing= qh TRACElevel;
    qhmem.IStracing= qh TRACElevel;
  }else if (qh TRACEpoint != -1 && qh TRACEdist < REALmax/2) {
    qh IStracing= 0;
    qhmem.IStracing= 0;
  }
  if (qh REPORTfreq && (qh facet_id-1 > qh lastreport+qh REPORTfreq)) {
    qh lastreport= qh facet_id-1;
    time(&timedata);
    tp= localtime(&timedata);
    cpu= (float)qh_CPUclock - (float)qh hulltime;
    cpu /= (float)qh_SECticks;
    total= zzval_(Ztotmerge) - zzval_(Zcyclehorizon) + zzval_(Zcyclefacettot);
    zinc_(Zdistio);
    qh_distplane(furthest, facet, &dist);
    qh_fprintf(qh ferr, 8119, "\n\
At %02d:%02d:%02d & %2.5g CPU secs, qhull has created %d facets and merged %d.\n\
 The current hull contains %d facets and %d vertices.  There are %d\n\
 outside points.  Next is point p%d(v%d), %2.2g above f%d.\n",
      tp->tm_hour, tp->tm_min, tp->tm_sec, cpu, qh facet_id -1,
      total, qh num_facets, qh num_vertices, qh num_outside+1,
      furthestid, qh vertex_id, dist, getid_(facet));
  }else if (qh IStracing >=1) {
    cpu= (float)qh_CPUclock - (float)qh hulltime;
    cpu /= (float)qh_SECticks;
    qh_distplane(furthest, facet, &dist);
    qh_fprintf(qh ferr, 8120, "qh_addpoint: add p%d(v%d) to hull of %d facets(%2.2g above f%d) and %d outside at %4.4g CPU secs.  Previous was p%d.\n",
      furthestid, qh vertex_id, qh num_facets, dist,
      getid_(facet), qh num_outside+1, cpu, qh furthest_id);
  }
  zmax_(Zvisit2max, (int)qh visit_id/2);
  if (qh visit_id > (unsigned) INT_MAX) {
    zinc_(Zvisit);
    qh visit_id= 0;
    FORALLfacets
      facet->visitid= 0;
  }
  zmax_(Zvvisit2max, (int)qh vertex_visit/2);
  if (qh vertex_visit > (unsigned) INT_MAX/2) { /* 31 bits */
    zinc_(Zvvisit);
    qh vertex_visit= 0;
    FORALLvertices
      vertex->visitid= 0;
  }
  qh furthest_id= furthestid;
  qh RANDOMdist= qh old_randomdist;
} /* buildtracing */

/*---------------------------------

  qh_errexit2( exitcode, facet, otherfacet )
    return exitcode to system after an error
    report two facets

  returns:
    assumes exitcode non-zero

  see:
    normally use qh_errexit() in user.c(reports a facet and a ridge)
*/
void qh_errexit2(int exitcode, facetT *facet, facetT *otherfacet) {

  qh_errprint("ERRONEOUS", facet, otherfacet, NULL, NULL);
  qh_errexit(exitcode, NULL, NULL);
} /* errexit2 */


/*---------------------------------

  qh_findhorizon( point, facet, goodvisible, goodhorizon )
    given a visible facet, find the point's horizon and visible facets
    for all facets, !facet-visible

  returns:
    returns qh.visible_list/num_visible with all visible facets
      marks visible facets with ->visible
    updates count of good visible and good horizon facets
    updates qh.max_outside, qh.max_vertex, facet->maxoutside

  see:
    similar to qh_delpoint()

  design:
    move facet to qh.visible_list at end of qh.facet_list
    for all visible facets
     for each unvisited neighbor of a visible facet
       compute distance of point to neighbor
       if point above neighbor
         move neighbor to end of qh.visible_list
       else if point is coplanar with neighbor
         update qh.max_outside, qh.max_vertex, neighbor->maxoutside
         mark neighbor coplanar (will create a samecycle later)
         update horizon statistics
*/
void qh_findhorizon(pointT *point, facetT *facet, int *goodvisible, int *goodhorizon) {
  facetT *neighbor, **neighborp, *visible;
  int numhorizon= 0, coplanar= 0;
  realT dist;

  trace1((qh ferr, 1040,"qh_findhorizon: find horizon for point p%d facet f%d\n",qh_pointid(point),facet->id));
  *goodvisible= *goodhorizon= 0;
  zinc_(Ztotvisible);
  qh_removefacet(facet);  /* visible_list at end of qh facet_list */
  qh_appendfacet(facet);
  qh num_visible= 1;
  if (facet->good)
    (*goodvisible)++;
  qh visible_list= facet;
  facet->visible= True;
  facet->f.replace= NULL;
  if (qh IStracing >=4)
    qh_errprint("visible", facet, NULL, NULL, NULL);
  qh visit_id++;
  FORALLvisible_facets {
    if (visible->tricoplanar && !qh TRInormals) {
      qh_fprintf(qh ferr, 6230, "Qhull internal error (qh_findhorizon): does not work for tricoplanar facets.  Use option 'Q11'\n");
      qh_errexit(qh_ERRqhull, visible, NULL);
    }
    visible->visitid= qh visit_id;
    FOREACHneighbor_(visible) {
      if (neighbor->visitid == qh visit_id)
        continue;
      neighbor->visitid= qh visit_id;
      zzinc_(Znumvisibility);
      qh_distplane(point, neighbor, &dist);
      if (dist > qh MINvisible) {
        zinc_(Ztotvisible);
        qh_removefacet(neighbor);  /* append to end of qh visible_list */
        qh_appendfacet(neighbor);
        neighbor->visible= True;
        neighbor->f.replace= NULL;
        qh num_visible++;
        if (neighbor->good)
          (*goodvisible)++;
        if (qh IStracing >=4)
          qh_errprint("visible", neighbor, NULL, NULL, NULL);
      }else {
        if (dist > - qh MAXcoplanar) {
          neighbor->coplanar= True;
          zzinc_(Zcoplanarhorizon);
          qh_precision("coplanar horizon");
          coplanar++;
          if (qh MERGING) {
            if (dist > 0) {
              maximize_(qh max_outside, dist);
              maximize_(qh max_vertex, dist);
#if qh_MAXoutside
              maximize_(neighbor->maxoutside, dist);
#endif
            }else
              minimize_(qh min_vertex, dist);  /* due to merge later */
          }
          trace2((qh ferr, 2057, "qh_findhorizon: point p%d is coplanar to horizon f%d, dist=%2.7g < qh MINvisible(%2.7g)\n",
              qh_pointid(point), neighbor->id, dist, qh MINvisible));
        }else
          neighbor->coplanar= False;
        zinc_(Ztothorizon);
        numhorizon++;
        if (neighbor->good)
          (*goodhorizon)++;
        if (qh IStracing >=4)
          qh_errprint("horizon", neighbor, NULL, NULL, NULL);
      }
    }
  }
  if (!numhorizon) {
    qh_precision("empty horizon");
    qh_fprintf(qh ferr, 6168, "qhull precision error (qh_findhorizon): empty horizon\n\
QhullPoint p%d was above all facets.\n", qh_pointid(point));
    qh_printfacetlist(qh facet_list, NULL, True);
    qh_errexit(qh_ERRprec, NULL, NULL);
  }
  trace1((qh ferr, 1041, "qh_findhorizon: %d horizon facets(good %d), %d visible(good %d), %d coplanar\n",
       numhorizon, *goodhorizon, qh num_visible, *goodvisible, coplanar));
  if (qh IStracing >= 4 && qh num_facets < 50)
    qh_printlists();
} /* findhorizon */

/*---------------------------------

  qh_nextfurthest( visible )
    returns next furthest point and visible facet for qh_addpoint()
    starts search at qh.facet_next

  returns:
    removes furthest point from outside set
    NULL if none available
    advances qh.facet_next over facets with empty outside sets

  design:
    for each facet from qh.facet_next
      if empty outside set
        advance qh.facet_next
      else if qh.NARROWhull
        determine furthest outside point
        if furthest point is not outside
          advance qh.facet_next(point will be coplanar)
    remove furthest point from outside set
*/
pointT *qh_nextfurthest(facetT **visible) {
  facetT *facet;
  int size, idx;
  realT randr, dist;
  pointT *furthest;

  while ((facet= qh facet_next) != qh facet_tail) {
    if (!facet->outsideset) {
      qh facet_next= facet->next;
      continue;
    }
    SETreturnsize_(facet->outsideset, size);
    if (!size) {
      qh_setfree(&facet->outsideset);
      qh facet_next= facet->next;
      continue;
    }
    if (qh NARROWhull) {
      if (facet->notfurthest)
        qh_furthestout(facet);
      furthest= (pointT*)qh_setlast(facet->outsideset);
#if qh_COMPUTEfurthest
      qh_distplane(furthest, facet, &dist);
      zinc_(Zcomputefurthest);
#else
      dist= facet->furthestdist;
#endif
      if (dist < qh MINoutside) { /* remainder of outside set is coplanar for qh_outcoplanar */
        qh facet_next= facet->next;
        continue;
      }
    }
    if (!qh RANDOMoutside && !qh VIRTUALmemory) {
      if (qh PICKfurthest) {
        qh_furthestnext(/* qh facet_list */);
        facet= qh facet_next;
      }
      *visible= facet;
      return((pointT*)qh_setdellast(facet->outsideset));
    }
    if (qh RANDOMoutside) {
      int outcoplanar = 0;
      if (qh NARROWhull) {
        FORALLfacets {
          if (facet == qh facet_next)
            break;
          if (facet->outsideset)
            outcoplanar += qh_setsize( facet->outsideset);
        }
      }
      randr= qh_RANDOMint;
      randr= randr/(qh_RANDOMmax+1);
      idx= (int)floor((qh num_outside - outcoplanar) * randr);
      FORALLfacet_(qh facet_next) {
        if (facet->outsideset) {
          SETreturnsize_(facet->outsideset, size);
          if (!size)
            qh_setfree(&facet->outsideset);
          else if (size > idx) {
            *visible= facet;
            return((pointT*)qh_setdelnth(facet->outsideset, idx));
          }else
            idx -= size;
        }
      }
      qh_fprintf(qh ferr, 6169, "qhull internal error (qh_nextfurthest): num_outside %d is too low\nby at least %d, or a random real %g >= 1.0\n",
              qh num_outside, idx+1, randr);
      qh_errexit(qh_ERRqhull, NULL, NULL);
    }else { /* VIRTUALmemory */
      facet= qh facet_tail->previous;
      if (!(furthest= (pointT*)qh_setdellast(facet->outsideset))) {
        if (facet->outsideset)
          qh_setfree(&facet->outsideset);
        qh_removefacet(facet);
        qh_prependfacet(facet, &qh facet_list);
        continue;
      }
      *visible= facet;
      return furthest;
    }
  }
  return NULL;
} /* nextfurthest */

/*---------------------------------

  qh_partitionall( vertices, points, numpoints )
    partitions all points in points/numpoints to the outsidesets of facets
    vertices= vertices in qh.facet_list(!partitioned)

  returns:
    builds facet->outsideset
    does not partition qh.GOODpoint
    if qh.ONLYgood && !qh.MERGING,
      does not partition qh.GOODvertex

  notes:
    faster if qh.facet_list sorted by anticipated size of outside set

  design:
    initialize pointset with all points
    remove vertices from pointset
    remove qh.GOODpointp from pointset (unless it's qh.STOPcone or qh.STOPpoint)
    for all facets
      for all remaining points in pointset
        compute distance from point to facet
        if point is outside facet
          remove point from pointset (by not reappending)
          update bestpoint
          append point or old bestpoint to facet's outside set
      append bestpoint to facet's outside set (furthest)
    for all points remaining in pointset
      partition point into facets' outside sets and coplanar sets
*/
void qh_partitionall(setT *vertices, pointT *points, int numpoints){
  setT *pointset;
  vertexT *vertex, **vertexp;
  pointT *point, **pointp, *bestpoint;
  int size, point_i, point_n, point_end, remaining, i, id;
  facetT *facet;
  realT bestdist= -REALmax, dist, distoutside;

  trace1((qh ferr, 1042, "qh_partitionall: partition all points into outside sets\n"));
  pointset= qh_settemp(numpoints);
  qh num_outside= 0;
  pointp= SETaddr_(pointset, pointT);
  for (i=numpoints, point= points; i--; point += qh hull_dim)
    *(pointp++)= point;
  qh_settruncate(pointset, numpoints);
  FOREACHvertex_(vertices) {
    if ((id= qh_pointid(vertex->point)) >= 0)
      SETelem_(pointset, id)= NULL;
  }
  id= qh_pointid(qh GOODpointp);
  if (id >=0 && qh STOPcone-1 != id && -qh STOPpoint-1 != id)
    SETelem_(pointset, id)= NULL;
  if (qh GOODvertexp && qh ONLYgood && !qh MERGING) { /* matches qhull()*/
    if ((id= qh_pointid(qh GOODvertexp)) >= 0)
      SETelem_(pointset, id)= NULL;
  }
  if (!qh BESToutside) {  /* matches conditional for qh_partitionpoint below */
    distoutside= qh_DISToutside; /* multiple of qh.MINoutside & qh.max_outside, see user.h */
    zval_(Ztotpartition)= qh num_points - qh hull_dim - 1; /*misses GOOD... */
    remaining= qh num_facets;
    point_end= numpoints;
    FORALLfacets {
      size= point_end/(remaining--) + 100;
      facet->outsideset= qh_setnew(size);
      bestpoint= NULL;
      point_end= 0;
      FOREACHpoint_i_(pointset) {
        if (point) {
          zzinc_(Zpartitionall);
          qh_distplane(point, facet, &dist);
          if (dist < distoutside)
            SETelem_(pointset, point_end++)= point;
          else {
            qh num_outside++;
            if (!bestpoint) {
              bestpoint= point;
              bestdist= dist;
            }else if (dist > bestdist) {
              qh_setappend(&facet->outsideset, bestpoint);
              bestpoint= point;
              bestdist= dist;
            }else
              qh_setappend(&facet->outsideset, point);
          }
        }
      }
      if (bestpoint) {
        qh_setappend(&facet->outsideset, bestpoint);
#if !qh_COMPUTEfurthest
        facet->furthestdist= bestdist;
#endif
      }else
        qh_setfree(&facet->outsideset);
      qh_settruncate(pointset, point_end);
    }
  }
  /* if !qh BESToutside, pointset contains points not assigned to outsideset */
  if (qh BESToutside || qh MERGING || qh KEEPcoplanar || qh KEEPinside) {
    qh findbestnew= True;
    FOREACHpoint_i_(pointset) {
      if (point)
        qh_partitionpoint(point, qh facet_list);
    }
    qh findbestnew= False;
  }
  zzadd_(Zpartitionall, zzval_(Zpartition));
  zzval_(Zpartition)= 0;
  qh_settempfree(&pointset);
  if (qh IStracing >= 4)
    qh_printfacetlist(qh facet_list, NULL, True);
} /* partitionall */


/*---------------------------------

  qh_partitioncoplanar( point, facet, dist )
    partition coplanar point to a facet
    dist is distance from point to facet
    if dist NULL,
      searches for bestfacet and does nothing if inside
    if qh.findbestnew set,
      searches new facets instead of using qh_findbest()

  returns:
    qh.max_ouside updated
    if qh.KEEPcoplanar or qh.KEEPinside
      point assigned to best coplanarset

  notes:
    facet->maxoutside is updated at end by qh_check_maxout

  design:
    if dist undefined
      find best facet for point
      if point sufficiently below facet (depends on qh.NEARinside and qh.KEEPinside)
        exit
    if keeping coplanar/nearinside/inside points
      if point is above furthest coplanar point
        append point to coplanar set (it is the new furthest)
        update qh.max_outside
      else
        append point one before end of coplanar set
    else if point is clearly outside of qh.max_outside and bestfacet->coplanarset
    and bestfacet is more than perpendicular to facet
      repartition the point using qh_findbest() -- it may be put on an outsideset
    else
      update qh.max_outside
*/
void qh_partitioncoplanar(pointT *point, facetT *facet, realT *dist) {
  facetT *bestfacet;
  pointT *oldfurthest;
  realT bestdist, dist2= 0, angle;
  int numpart= 0, oldfindbest;
  boolT isoutside;

  qh WAScoplanar= True;
  if (!dist) {
    if (qh findbestnew)
      bestfacet= qh_findbestnew(point, facet, &bestdist, qh_ALL, &isoutside, &numpart);
    else
      bestfacet= qh_findbest(point, facet, qh_ALL, !qh_ISnewfacets, qh DELAUNAY,
                          &bestdist, &isoutside, &numpart);
    zinc_(Ztotpartcoplanar);
    zzadd_(Zpartcoplanar, numpart);
    if (!qh DELAUNAY && !qh KEEPinside) { /*  for 'd', bestdist skips upperDelaunay facets */
      if (qh KEEPnearinside) {
        if (bestdist < -qh NEARinside) {
          zinc_(Zcoplanarinside);
          trace4((qh ferr, 4062, "qh_partitioncoplanar: point p%d is more than near-inside facet f%d dist %2.2g findbestnew %d\n",
                  qh_pointid(point), bestfacet->id, bestdist, qh findbestnew));
          return;
        }
      }else if (bestdist < -qh MAXcoplanar) {
          trace4((qh ferr, 4063, "qh_partitioncoplanar: point p%d is inside facet f%d dist %2.2g findbestnew %d\n",
                  qh_pointid(point), bestfacet->id, bestdist, qh findbestnew));
        zinc_(Zcoplanarinside);
        return;
      }
    }
  }else {
    bestfacet= facet;
    bestdist= *dist;
  }
  if (bestdist > qh max_outside) {
    if (!dist && facet != bestfacet) {
      zinc_(Zpartangle);
      angle= qh_getangle(facet->normal, bestfacet->normal);
      if (angle < 0) {
        /* typically due to deleted vertex and coplanar facets, e.g.,
             RBOX 1000 s Z1 G1e-13 t1001185205 | QHULL Tv */
        zinc_(Zpartflip);
        trace2((qh ferr, 2058, "qh_partitioncoplanar: repartition point p%d from f%d.  It is above flipped facet f%d dist %2.2g\n",
                qh_pointid(point), facet->id, bestfacet->id, bestdist));
        oldfindbest= qh findbestnew;
        qh findbestnew= False;
        qh_partitionpoint(point, bestfacet);
        qh findbestnew= oldfindbest;
        return;
      }
    }
    qh max_outside= bestdist;
    if (bestdist > qh TRACEdist) {
      qh_fprintf(qh ferr, 8122, "qh_partitioncoplanar: ====== p%d from f%d increases max_outside to %2.2g of f%d last p%d\n",
                     qh_pointid(point), facet->id, bestdist, bestfacet->id, qh furthest_id);
      qh_errprint("DISTANT", facet, bestfacet, NULL, NULL);
    }
  }
  if (qh KEEPcoplanar + qh KEEPinside + qh KEEPnearinside) {
    oldfurthest= (pointT*)qh_setlast(bestfacet->coplanarset);
    if (oldfurthest) {
      zinc_(Zcomputefurthest);
      qh_distplane(oldfurthest, bestfacet, &dist2);
    }
    if (!oldfurthest || dist2 < bestdist)
      qh_setappend(&bestfacet->coplanarset, point);
    else
      qh_setappend2ndlast(&bestfacet->coplanarset, point);
  }
  trace4((qh ferr, 4064, "qh_partitioncoplanar: point p%d is coplanar with facet f%d(or inside) dist %2.2g\n",
          qh_pointid(point), bestfacet->id, bestdist));
} /* partitioncoplanar */

/*---------------------------------

  qh_partitionpoint( point, facet )
    assigns point to an outside set, coplanar set, or inside set (i.e., dropt)
    if qh.findbestnew
      uses qh_findbestnew() to search all new facets
    else
      uses qh_findbest()

  notes:
    after qh_distplane(), this and qh_findbest() are most expensive in 3-d

  design:
    find best facet for point
      (either exhaustive search of new facets or directed search from facet)
    if qh.NARROWhull
      retain coplanar and nearinside points as outside points
    if point is outside bestfacet
      if point above furthest point for bestfacet
        append point to outside set (it becomes the new furthest)
        if outside set was empty
          move bestfacet to end of qh.facet_list (i.e., after qh.facet_next)
        update bestfacet->furthestdist
      else
        append point one before end of outside set
    else if point is coplanar to bestfacet
      if keeping coplanar points or need to update qh.max_outside
        partition coplanar point into bestfacet
    else if near-inside point
      partition as coplanar point into bestfacet
    else is an inside point
      if keeping inside points
        partition as coplanar point into bestfacet
*/
void qh_partitionpoint(pointT *point, facetT *facet) {
  realT bestdist;
  boolT isoutside;
  facetT *bestfacet;
  int numpart;
#if qh_COMPUTEfurthest
  realT dist;
#endif

  if (qh findbestnew)
    bestfacet= qh_findbestnew(point, facet, &bestdist, qh BESToutside, &isoutside, &numpart);
  else
    bestfacet= qh_findbest(point, facet, qh BESToutside, qh_ISnewfacets, !qh_NOupper,
                          &bestdist, &isoutside, &numpart);
  zinc_(Ztotpartition);
  zzadd_(Zpartition, numpart);
  if (qh NARROWhull) {
    if (qh DELAUNAY && !isoutside && bestdist >= -qh MAXcoplanar)
      qh_precision("nearly incident point(narrow hull)");
    if (qh KEEPnearinside) {
      if (bestdist >= -qh NEARinside)
        isoutside= True;
    }else if (bestdist >= -qh MAXcoplanar)
      isoutside= True;
  }

  if (isoutside) {
    if (!bestfacet->outsideset
    || !qh_setlast(bestfacet->outsideset)) {
      qh_setappend(&(bestfacet->outsideset), point);
      if (!bestfacet->newfacet) {
        qh_removefacet(bestfacet);  /* make sure it's after qh facet_next */
        qh_appendfacet(bestfacet);
      }
#if !qh_COMPUTEfurthest
      bestfacet->furthestdist= bestdist;
#endif
    }else {
#if qh_COMPUTEfurthest
      zinc_(Zcomputefurthest);
      qh_distplane(oldfurthest, bestfacet, &dist);
      if (dist < bestdist)
        qh_setappend(&(bestfacet->outsideset), point);
      else
        qh_setappend2ndlast(&(bestfacet->outsideset), point);
#else
      if (bestfacet->furthestdist < bestdist) {
        qh_setappend(&(bestfacet->outsideset), point);
        bestfacet->furthestdist= bestdist;
      }else
        qh_setappend2ndlast(&(bestfacet->outsideset), point);
#endif
    }
    qh num_outside++;
    trace4((qh ferr, 4065, "qh_partitionpoint: point p%d is outside facet f%d new? %d (or narrowhull)\n",
          qh_pointid(point), bestfacet->id, bestfacet->newfacet));
  }else if (qh DELAUNAY || bestdist >= -qh MAXcoplanar) { /* for 'd', bestdist skips upperDelaunay facets */
    zzinc_(Zcoplanarpart);
    if (qh DELAUNAY)
      qh_precision("nearly incident point");
    if ((qh KEEPcoplanar + qh KEEPnearinside) || bestdist > qh max_outside)
      qh_partitioncoplanar(point, bestfacet, &bestdist);
    else {
      trace4((qh ferr, 4066, "qh_partitionpoint: point p%d is coplanar to facet f%d (dropped)\n",
          qh_pointid(point), bestfacet->id));
    }
  }else if (qh KEEPnearinside && bestdist > -qh NEARinside) {
    zinc_(Zpartnear);
    qh_partitioncoplanar(point, bestfacet, &bestdist);
  }else {
    zinc_(Zpartinside);
    trace4((qh ferr, 4067, "qh_partitionpoint: point p%d is inside all facets, closest to f%d dist %2.2g\n",
          qh_pointid(point), bestfacet->id, bestdist));
    if (qh KEEPinside)
      qh_partitioncoplanar(point, bestfacet, &bestdist);
  }
} /* partitionpoint */

/*---------------------------------

  qh_partitionvisible( allpoints, numoutside )
    partitions points in visible facets to qh.newfacet_list
    qh.visible_list= visible facets
    for visible facets
      1st neighbor (if any) points to a horizon facet or a new facet
    if allpoints(!used),
      repartitions coplanar points

  returns:
    updates outside sets and coplanar sets of qh.newfacet_list
    updates qh.num_outside (count of outside points)

  notes:
    qh.findbest_notsharp should be clear (extra work if set)

  design:
    for all visible facets with outside set or coplanar set
      select a newfacet for visible facet
      if outside set
        partition outside set into new facets
      if coplanar set and keeping coplanar/near-inside/inside points
        if allpoints
          partition coplanar set into new facets, may be assigned outside
        else
          partition coplanar set into coplanar sets of new facets
    for each deleted vertex
      if allpoints
        partition vertex into new facets, may be assigned outside
      else
        partition vertex into coplanar sets of new facets
*/
void qh_partitionvisible(/*visible_list*/ boolT allpoints, int *numoutside) {
  facetT *visible, *newfacet;
  pointT *point, **pointp;
  int coplanar=0, size;
  unsigned count;
  vertexT *vertex, **vertexp;

  if (qh ONLYmax)
    maximize_(qh MINoutside, qh max_vertex);
  *numoutside= 0;
  FORALLvisible_facets {
    if (!visible->outsideset && !visible->coplanarset)
      continue;
    newfacet= visible->f.replace;
    count= 0;
    while (newfacet && newfacet->visible) {
      newfacet= newfacet->f.replace;
      if (count++ > qh facet_id)
        qh_infiniteloop(visible);
    }
    if (!newfacet)
      newfacet= qh newfacet_list;
    if (newfacet == qh facet_tail) {
      qh_fprintf(qh ferr, 6170, "qhull precision error (qh_partitionvisible): all new facets deleted as\n        degenerate facets. Can not continue.\n");
      qh_errexit(qh_ERRprec, NULL, NULL);
    }
    if (visible->outsideset) {
      size= qh_setsize(visible->outsideset);
      *numoutside += size;
      qh num_outside -= size;
      FOREACHpoint_(visible->outsideset)
        qh_partitionpoint(point, newfacet);
    }
    if (visible->coplanarset && (qh KEEPcoplanar + qh KEEPinside + qh KEEPnearinside)) {
      size= qh_setsize(visible->coplanarset);
      coplanar += size;
      FOREACHpoint_(visible->coplanarset) {
        if (allpoints) /* not used */
          qh_partitionpoint(point, newfacet);
        else
          qh_partitioncoplanar(point, newfacet, NULL);
      }
    }
  }
  FOREACHvertex_(qh del_vertices) {
    if (vertex->point) {
      if (allpoints) /* not used */
        qh_partitionpoint(vertex->point, qh newfacet_list);
      else
        qh_partitioncoplanar(vertex->point, qh newfacet_list, NULL);
    }
  }
  trace1((qh ferr, 1043,"qh_partitionvisible: partitioned %d points from outsidesets and %d points from coplanarsets\n", *numoutside, coplanar));
} /* partitionvisible */



/*---------------------------------

  qh_precision( reason )
    restart on precision errors if not merging and if 'QJn'
*/
void qh_precision(const char *reason) {

  if (qh ALLOWrestart && !qh PREmerge && !qh MERGEexact) {
    if (qh JOGGLEmax < REALmax/2) {
      trace0((qh ferr, 26, "qh_precision: qhull restart because of %s\n", reason));
      longjmp(qh restartexit, qh_ERRprec);
    }
  }
} /* qh_precision */

/*---------------------------------

  qh_printsummary( fp )
    prints summary to fp

  notes:
    not in io.c so that user_eg.c can prevent io.c from loading
    qh_printsummary and qh_countfacets must match counts

  design:
    determine number of points, vertices, and coplanar points
    print summary
*/
void qh_printsummary(FILE *fp) {
  realT ratio, outerplane, innerplane;
  float cpu;
  int size, id, nummerged, numvertices, numcoplanars= 0, nonsimplicial=0;
  int goodused;
  facetT *facet;
  const char *s;
  int numdel= zzval_(Zdelvertextot);
  int numtricoplanars= 0;

  size= qh num_points + qh_setsize(qh other_points);
  numvertices= qh num_vertices - qh_setsize(qh del_vertices);
  id= qh_pointid(qh GOODpointp);
  FORALLfacets {
    if (facet->coplanarset)
      numcoplanars += qh_setsize( facet->coplanarset);
    if (facet->good) {
      if (facet->simplicial) {
        if (facet->keepcentrum && facet->tricoplanar)
          numtricoplanars++;
      }else if (qh_setsize(facet->vertices) != qh hull_dim)
        nonsimplicial++;
    }
  }
  if (id >=0 && qh STOPcone-1 != id && -qh STOPpoint-1 != id)
    size--;
  if (qh STOPcone || qh STOPpoint)
      qh_fprintf(fp, 9288, "\nAt a premature exit due to 'TVn', 'TCn', 'TRn', or precision error with 'QJn'.");
  if (qh UPPERdelaunay)
    goodused= qh GOODvertex + qh GOODpoint + qh SPLITthresholds;
  else if (qh DELAUNAY)
    goodused= qh GOODvertex + qh GOODpoint + qh GOODthreshold;
  else
    goodused= qh num_good;
  nummerged= zzval_(Ztotmerge) - zzval_(Zcyclehorizon) + zzval_(Zcyclefacettot);
  if (qh VORONOI) {
    if (qh UPPERdelaunay)
      qh_fprintf(fp, 9289, "\n\
Furthest-site Voronoi vertices by the convex hull of %d points in %d-d:\n\n", size, qh hull_dim);
    else
      qh_fprintf(fp, 9290, "\n\
Voronoi diagram by the convex hull of %d points in %d-d:\n\n", size, qh hull_dim);
    qh_fprintf(fp, 9291, "  Number of Voronoi regions%s: %d\n",
              qh ATinfinity ? " and at-infinity" : "", numvertices);
    if (numdel)
      qh_fprintf(fp, 9292, "  Total number of deleted points due to merging: %d\n", numdel);
    if (numcoplanars - numdel > 0)
      qh_fprintf(fp, 9293, "  Number of nearly incident points: %d\n", numcoplanars - numdel);
    else if (size - numvertices - numdel > 0)
      qh_fprintf(fp, 9294, "  Total number of nearly incident points: %d\n", size - numvertices - numdel);
    qh_fprintf(fp, 9295, "  Number of%s Voronoi vertices: %d\n",
              goodused ? " 'good'" : "", qh num_good);
    if (nonsimplicial)
      qh_fprintf(fp, 9296, "  Number of%s non-simplicial Voronoi vertices: %d\n",
              goodused ? " 'good'" : "", nonsimplicial);
  }else if (qh DELAUNAY) {
    if (qh UPPERdelaunay)
      qh_fprintf(fp, 9297, "\n\
Furthest-site Delaunay triangulation by the convex hull of %d points in %d-d:\n\n", size, qh hull_dim);
    else
      qh_fprintf(fp, 9298, "\n\
Delaunay triangulation by the convex hull of %d points in %d-d:\n\n", size, qh hull_dim);
    qh_fprintf(fp, 9299, "  Number of input sites%s: %d\n",
              qh ATinfinity ? " and at-infinity" : "", numvertices);
    if (numdel)
      qh_fprintf(fp, 9300, "  Total number of deleted points due to merging: %d\n", numdel);
    if (numcoplanars - numdel > 0)
      qh_fprintf(fp, 9301, "  Number of nearly incident points: %d\n", numcoplanars - numdel);
    else if (size - numvertices - numdel > 0)
      qh_fprintf(fp, 9302, "  Total number of nearly incident points: %d\n", size - numvertices - numdel);
    qh_fprintf(fp, 9303, "  Number of%s Delaunay regions: %d\n",
              goodused ? " 'good'" : "", qh num_good);
    if (nonsimplicial)
      qh_fprintf(fp, 9304, "  Number of%s non-simplicial Delaunay regions: %d\n",
              goodused ? " 'good'" : "", nonsimplicial);
  }else if (qh HALFspace) {
    qh_fprintf(fp, 9305, "\n\
Halfspace intersection by the convex hull of %d points in %d-d:\n\n", size, qh hull_dim);
    qh_fprintf(fp, 9306, "  Number of halfspaces: %d\n", size);
    qh_fprintf(fp, 9307, "  Number of non-redundant halfspaces: %d\n", numvertices);
    if (numcoplanars) {
      if (qh KEEPinside && qh KEEPcoplanar)
        s= "similar and redundant";
      else if (qh KEEPinside)
        s= "redundant";
      else
        s= "similar";
      qh_fprintf(fp, 9308, "  Number of %s halfspaces: %d\n", s, numcoplanars);
    }
    qh_fprintf(fp, 9309, "  Number of intersection points: %d\n", qh num_facets - qh num_visible);
    if (goodused)
      qh_fprintf(fp, 9310, "  Number of 'good' intersection points: %d\n", qh num_good);
    if (nonsimplicial)
      qh_fprintf(fp, 9311, "  Number of%s non-simplicial intersection points: %d\n",
              goodused ? " 'good'" : "", nonsimplicial);
  }else {
    qh_fprintf(fp, 9312, "\n\
Convex hull of %d points in %d-d:\n\n", size, qh hull_dim);
    qh_fprintf(fp, 9313, "  Number of vertices: %d\n", numvertices);
    if (numcoplanars) {
      if (qh KEEPinside && qh KEEPcoplanar)
        s= "coplanar and interior";
      else if (qh KEEPinside)
        s= "interior";
      else
        s= "coplanar";
      qh_fprintf(fp, 9314, "  Number of %s points: %d\n", s, numcoplanars);
    }
    qh_fprintf(fp, 9315, "  Number of facets: %d\n", qh num_facets - qh num_visible);
    if (goodused)
      qh_fprintf(fp, 9316, "  Number of 'good' facets: %d\n", qh num_good);
    if (nonsimplicial)
      qh_fprintf(fp, 9317, "  Number of%s non-simplicial facets: %d\n",
              goodused ? " 'good'" : "", nonsimplicial);
  }
  if (numtricoplanars)
      qh_fprintf(fp, 9318, "  Number of triangulated facets: %d\n", numtricoplanars);
  qh_fprintf(fp, 9319, "\nStatistics for: %s | %s",
                      qh rbox_command, qh qhull_command);
  if (qh ROTATErandom != INT_MIN)
    qh_fprintf(fp, 9320, " QR%d\n\n", qh ROTATErandom);
  else
    qh_fprintf(fp, 9321, "\n\n");
  qh_fprintf(fp, 9322, "  Number of points processed: %d\n", zzval_(Zprocessed));
  qh_fprintf(fp, 9323, "  Number of hyperplanes created: %d\n", zzval_(Zsetplane));
  if (qh DELAUNAY)
    qh_fprintf(fp, 9324, "  Number of facets in hull: %d\n", qh num_facets - qh num_visible);
  qh_fprintf(fp, 9325, "  Number of distance tests for qhull: %d\n", zzval_(Zpartition)+
      zzval_(Zpartitionall)+zzval_(Znumvisibility)+zzval_(Zpartcoplanar));
#if 0  /* NOTE: must print before printstatistics() */
  {realT stddev, ave;
  qh_fprintf(fp, 9326, "  average new facet balance: %2.2g\n",
          wval_(Wnewbalance)/zval_(Zprocessed));
  stddev= qh_stddev(zval_(Zprocessed), wval_(Wnewbalance),
                                 wval_(Wnewbalance2), &ave);
  qh_fprintf(fp, 9327, "  new facet standard deviation: %2.2g\n", stddev);
  qh_fprintf(fp, 9328, "  average partition balance: %2.2g\n",
          wval_(Wpbalance)/zval_(Zpbalance));
  stddev= qh_stddev(zval_(Zpbalance), wval_(Wpbalance),
                                 wval_(Wpbalance2), &ave);
  qh_fprintf(fp, 9329, "  partition standard deviation: %2.2g\n", stddev);
  }
#endif
  if (nummerged) {
    qh_fprintf(fp, 9330,"  Number of distance tests for merging: %d\n",zzval_(Zbestdist)+
          zzval_(Zcentrumtests)+zzval_(Zdistconvex)+zzval_(Zdistcheck)+
          zzval_(Zdistzero));
    qh_fprintf(fp, 9331,"  Number of distance tests for checking: %d\n",zzval_(Zcheckpart));
    qh_fprintf(fp, 9332,"  Number of merged facets: %d\n", nummerged);
  }
  if (!qh RANDOMoutside && qh QHULLfinished) {
    cpu= (float)qh hulltime;
    cpu /= (float)qh_SECticks;
    wval_(Wcpu)= cpu;
    qh_fprintf(fp, 9333, "  CPU seconds to compute hull (after input): %2.4g\n", cpu);
  }
  if (qh RERUN) {
    if (!qh PREmerge && !qh MERGEexact)
      qh_fprintf(fp, 9334, "  Percentage of runs with precision errors: %4.1f\n",
           zzval_(Zretry)*100.0/qh build_cnt);  /* careful of order */
  }else if (qh JOGGLEmax < REALmax/2) {
    if (zzval_(Zretry))
      qh_fprintf(fp, 9335, "  After %d retries, input joggled by: %2.2g\n",
         zzval_(Zretry), qh JOGGLEmax);
    else
      qh_fprintf(fp, 9336, "  Input joggled by: %2.2g\n", qh JOGGLEmax);
  }
  if (qh totarea != 0.0)
    qh_fprintf(fp, 9337, "  %s facet area:   %2.8g\n",
            zzval_(Ztotmerge) ? "Approximate" : "Total", qh totarea);
  if (qh totvol != 0.0)
    qh_fprintf(fp, 9338, "  %s volume:       %2.8g\n",
            zzval_(Ztotmerge) ? "Approximate" : "Total", qh totvol);
  if (qh MERGING) {
    qh_outerinner(NULL, &outerplane, &innerplane);
    if (outerplane > 2 * qh DISTround) {
      qh_fprintf(fp, 9339, "  Maximum distance of %spoint above facet: %2.2g",
            (qh QHULLfinished ? "" : "merged "), outerplane);
      ratio= outerplane/(qh ONEmerge + qh DISTround);
      /* don't report ratio if MINoutside is large */
      if (ratio > 0.05 && 2* qh ONEmerge > qh MINoutside && qh JOGGLEmax > REALmax/2)
        qh_fprintf(fp, 9340, " (%.1fx)\n", ratio);
      else
        qh_fprintf(fp, 9341, "\n");
    }
    if (innerplane < -2 * qh DISTround) {
      qh_fprintf(fp, 9342, "  Maximum distance of %svertex below facet: %2.2g",
            (qh QHULLfinished ? "" : "merged "), innerplane);
      ratio= -innerplane/(qh ONEmerge+qh DISTround);
      if (ratio > 0.05 && qh JOGGLEmax > REALmax/2)
        qh_fprintf(fp, 9343, " (%.1fx)\n", ratio);
      else
        qh_fprintf(fp, 9344, "\n");
    }
  }
  qh_fprintf(fp, 9345, "\n");
} /* printsummary */


qhull-2012.1/src/libqhull/libqhull.h0000644000076400010400000014174211710144466020511 0ustar  bbarberAdministrators/*
  ---------------------------------

   libqhull.h
   user-level header file for using qhull.a library

   see qh-qhull.htm, qhull_a.h

   Copyright (c) 1993-2012 The Geometry Center.
   $Id: //main/2011/qhull/src/libqhull/libqhull.h#7 $$Change: 1464 $
   $DateTime: 2012/01/25 22:58:41 $$Author: bbarber $

   NOTE: access to qh_qh is via the 'qh' macro.  This allows
   qh_qh to be either a pointer or a structure.  An example
   of using qh is "qh DROPdim" which accesses the DROPdim
   field of qh_qh.  Similarly, access to qh_qhstat is via
   the 'qhstat' macro.

   includes function prototypes for libqhull.c, geom.c, global.c, io.c, user.c

   use mem.h for mem.c
   use qset.h for qset.c

   see unix.c for an example of using libqhull.h

   recompile qhull if you change this file
*/

#ifndef qhDEFlibqhull
#define qhDEFlibqhull 1

/*=========================== -included files ==============*/

#include "user.h"      /* user definable constants (e.g., qh_QHpointer) */

#include 
#include 
#include 
#include 

#if __MWERKS__ && __POWERPC__
#include  
#include  
#include        
#endif

#ifndef __STDC__
#ifndef __cplusplus
#if     !_MSC_VER
#error  Neither __STDC__ nor __cplusplus is defined.  Please use strict ANSI C or C++ to compile
#error  Qhull.  You may need to turn off compiler extensions in your project configuration.  If
#error  your compiler is a standard C compiler, you can delete this warning from libqhull.h
#endif
#endif
#endif

/*============ constants and basic types ====================*/

extern const char *qh_version; /* defined in global.c */

/*----------------------------------

  coordT
    coordinates and coefficients are stored as realT (i.e., double)

  notes:
    Qhull works well if realT is 'float'.  If so joggle (QJ) is not effective.

    Could use 'float' for data and 'double' for calculations (realT vs. coordT)
      This requires many type casts, and adjusted error bounds.
      Also C compilers may do expressions in double anyway.
*/
#define coordT realT

/*----------------------------------

  pointT
    a point is an array of coordinates, usually qh.hull_dim
*/
#define pointT coordT

/*----------------------------------

  flagT
    Boolean flag as a bit
*/
#define flagT unsigned int

/*----------------------------------

  boolT
    boolean value, either True or False

  notes:
    needed for portability
    Use qh_False/qh_True as synonyms
*/
#define boolT unsigned int
#ifdef False
#undef False
#endif
#ifdef True
#undef True
#endif
#define False 0
#define True 1
#define qh_False 0
#define qh_True 1

/*----------------------------------

  qh_CENTER
    to distinguish facet->center
*/
typedef enum
{
    qh_ASnone = 0, qh_ASvoronoi, qh_AScentrum
}
qh_CENTER;

/*----------------------------------

  qh_PRINT
    output formats for printing (qh.PRINTout).
    'Fa' 'FV' 'Fc' 'FC'


   notes:
   some of these names are similar to qh names.  The similar names are only
   used in switch statements in qh_printbegin() etc.
*/
typedef enum {qh_PRINTnone= 0,
  qh_PRINTarea, qh_PRINTaverage,           /* 'Fa' 'FV' 'Fc' 'FC' */
  qh_PRINTcoplanars, qh_PRINTcentrums,
  qh_PRINTfacets, qh_PRINTfacets_xridge,   /* 'f' 'FF' 'G' 'FI' 'Fi' 'Fn' */
  qh_PRINTgeom, qh_PRINTids, qh_PRINTinner, qh_PRINTneighbors,
  qh_PRINTnormals, qh_PRINTouter, qh_PRINTmaple, /* 'n' 'Fo' 'i' 'm' 'Fm' 'FM', 'o' */
  qh_PRINTincidences, qh_PRINTmathematica, qh_PRINTmerges, qh_PRINToff,
  qh_PRINToptions, qh_PRINTpointintersect, /* 'FO' 'Fp' 'FP' 'p' 'FQ' 'FS' */
  qh_PRINTpointnearest, qh_PRINTpoints, qh_PRINTqhull, qh_PRINTsize,
  qh_PRINTsummary, qh_PRINTtriangles,      /* 'Fs' 'Ft' 'Fv' 'FN' 'Fx' */
  qh_PRINTvertices, qh_PRINTvneighbors, qh_PRINTextremes,
  qh_PRINTEND} qh_PRINT;

/*----------------------------------

  qh_ALL
    argument flag for selecting everything
*/
#define qh_ALL      True
#define qh_NOupper  True     /* argument for qh_findbest */
#define qh_IScheckmax  True     /* argument for qh_findbesthorizon */
#define qh_ISnewfacets  True     /* argument for qh_findbest */
#define qh_RESETvisible  True     /* argument for qh_resetlists */

/*----------------------------------

  qh_ERR
    Qhull exit codes, for indicating errors
    See: MSG_ERROR and MSG_WARNING [user.h]
*/
#define qh_ERRnone  0    /* no error occurred during qhull */
#define qh_ERRinput 1    /* input inconsistency */
#define qh_ERRsingular 2 /* singular input data */
#define qh_ERRprec  3    /* precision error */
#define qh_ERRmem   4    /* insufficient memory, matches mem.h */
#define qh_ERRqhull 5    /* internal error detected, matches mem.h */

/*----------------------------------

qh_FILEstderr
Fake stderr to distinguish error output from normal output
For C++ interface.  Must redefine qh_fprintf_qhull
*/
#define qh_FILEstderr (FILE*)1

/* ============ -structures- ====================
   each of the following structures is defined by a typedef
   all realT and coordT fields occur at the beginning of a structure
        (otherwise space may be wasted due to alignment)
   define all flags together and pack into 32-bit number
*/

typedef struct vertexT vertexT;
typedef struct ridgeT ridgeT;
typedef struct facetT facetT;
#ifndef DEFsetT
#define DEFsetT 1
typedef struct setT setT;          /* defined in qset.h */
#endif

#ifndef DEFqhstatT
#define DEFqhstatT 1
typedef struct qhstatT qhstatT;    /* defined in stat.h */
#endif

/*----------------------------------

  facetT
    defines a facet

  notes:
   qhull() generates the hull as a list of facets.

  topological information:
    f.previous,next     doubly-linked list of facets
    f.vertices          set of vertices
    f.ridges            set of ridges
    f.neighbors         set of neighbors
    f.toporient         True if facet has top-orientation (else bottom)

  geometric information:
    f.offset,normal     hyperplane equation
    f.maxoutside        offset to outer plane -- all points inside
    f.center            centrum for testing convexity
    f.simplicial        True if facet is simplicial
    f.flipped           True if facet does not include qh.interior_point

  for constructing hull:
    f.visible           True if facet on list of visible facets (will be deleted)
    f.newfacet          True if facet on list of newly created facets
    f.coplanarset       set of points coplanar with this facet
                        (includes near-inside points for later testing)
    f.outsideset        set of points outside of this facet
    f.furthestdist      distance to furthest point of outside set
    f.visitid           marks visited facets during a loop
    f.replace           replacement facet for to-be-deleted, visible facets
    f.samecycle,newcycle cycle of facets for merging into horizon facet

  see below for other flags and fields
*/
struct facetT {
#if !qh_COMPUTEfurthest
  coordT   furthestdist;/* distance to furthest point of outsideset */
#endif
#if qh_MAXoutside
  coordT   maxoutside;  /* max computed distance of point to facet
                        Before QHULLfinished this is an approximation
                        since maxdist not always set for mergefacet
                        Actual outer plane is +DISTround and
                        computed outer plane is +2*DISTround */
#endif
  coordT   offset;      /* exact offset of hyperplane from origin */
  coordT  *normal;      /* normal of hyperplane, hull_dim coefficients */
                        /*   if tricoplanar, shared with a neighbor */
  union {               /* in order of testing */
   realT   area;        /* area of facet, only in io.c if  ->isarea */
   facetT *replace;     /*  replacement facet if ->visible and NEWfacets
                             is NULL only if qh_mergedegen_redundant or interior */
   facetT *samecycle;   /*  cycle of facets from the same visible/horizon intersection,
                             if ->newfacet */
   facetT *newcycle;    /*  in horizon facet, current samecycle of new facets */
   facetT *trivisible;  /* visible facet for ->tricoplanar facets during qh_triangulate() */
   facetT *triowner;    /* owner facet for ->tricoplanar, !isarea facets w/ ->keepcentrum */
  }f;
  coordT  *center;      /*  centrum for convexity, qh CENTERtype == qh_AScentrum */
                        /*  Voronoi center, qh CENTERtype == qh_ASvoronoi */
                        /*   if tricoplanar, shared with a neighbor */
  facetT  *previous;    /* previous facet in the facet_list */
  facetT  *next;        /* next facet in the facet_list */
  setT    *vertices;    /* vertices for this facet, inverse sorted by ID
                           if simplicial, 1st vertex was apex/furthest */
  setT    *ridges;      /* explicit ridges for nonsimplicial facets.
                           for simplicial facets, neighbors define the ridges */
  setT    *neighbors;   /* neighbors of the facet.  If simplicial, the kth
                           neighbor is opposite the kth vertex, and the first
                           neighbor is the horizon facet for the first vertex*/
  setT    *outsideset;  /* set of points outside this facet
                           if non-empty, last point is furthest
                           if NARROWhull, includes coplanars for partitioning*/
  setT    *coplanarset; /* set of points coplanar with this facet
                           > qh.min_vertex and <= facet->max_outside
                           a point is assigned to the furthest facet
                           if non-empty, last point is furthest away */
  unsigned visitid;     /* visit_id, for visiting all neighbors,
                           all uses are independent */
  unsigned id;          /* unique identifier from qh facet_id */
  unsigned nummerge:9;  /* number of merges */
#define qh_MAXnummerge 511 /*     2^9-1, 32 flags total, see "flags:" in io.c */
  flagT    tricoplanar:1; /* True if TRIangulate and simplicial and coplanar with a neighbor */
                          /*   all tricoplanars share the same ->center, ->normal, ->offset, ->maxoutside */
                          /*   all tricoplanars share the same apex */
                          /*   if ->degenerate, does not span facet (one logical ridge) */
                          /*   one tricoplanar has ->keepcentrum and ->coplanarset */
                          /*   during qh_triangulate, f.trivisible points to original facet */
  flagT    newfacet:1;  /* True if facet on qh newfacet_list (new or merged) */
  flagT    visible:1;   /* True if visible facet (will be deleted) */
  flagT    toporient:1; /* True if created with top orientation
                           after merging, use ridge orientation */
  flagT    simplicial:1;/* True if simplicial facet, ->ridges may be implicit */
  flagT    seen:1;      /* used to perform operations only once, like visitid */
  flagT    seen2:1;     /* used to perform operations only once, like visitid */
  flagT    flipped:1;   /* True if facet is flipped */
  flagT    upperdelaunay:1; /* True if facet is upper envelope of Delaunay triangulation */
  flagT    notfurthest:1; /* True if last point of outsideset is not furthest*/

/*-------- flags primarily for output ---------*/
  flagT    good:1;      /* True if a facet marked good for output */
  flagT    isarea:1;    /* True if facet->f.area is defined */

/*-------- flags for merging ------------------*/
  flagT    dupridge:1;  /* True if duplicate ridge in facet */
  flagT    mergeridge:1; /* True if facet or neighbor contains a qh_MERGEridge
                            ->normal defined (also defined for mergeridge2) */
  flagT    mergeridge2:1; /* True if neighbor contains a qh_MERGEridge (mark_dupridges */
  flagT    coplanar:1;  /* True if horizon facet is coplanar at last use */
  flagT     mergehorizon:1; /* True if will merge into horizon (->coplanar) */
  flagT     cycledone:1;/* True if mergecycle_all already done */
  flagT    tested:1;    /* True if facet convexity has been tested (false after merge */
  flagT    keepcentrum:1; /* True if keep old centrum after a merge, or marks owner for ->tricoplanar */
  flagT    newmerge:1;  /* True if facet is newly merged for reducevertices */
  flagT    degenerate:1; /* True if facet is degenerate (degen_mergeset or ->tricoplanar) */
  flagT    redundant:1;  /* True if facet is redundant (degen_mergeset) */
};


/*----------------------------------

  ridgeT
    defines a ridge

  notes:
  a ridge is hull_dim-1 simplex between two neighboring facets.  If the
  facets are non-simplicial, there may be more than one ridge between
  two facets.  E.G. a 4-d hypercube has two triangles between each pair
  of neighboring facets.

  topological information:
    vertices            a set of vertices
    top,bottom          neighboring facets with orientation

  geometric information:
    tested              True if ridge is clearly convex
    nonconvex           True if ridge is non-convex
*/
struct ridgeT {
  setT    *vertices;    /* vertices belonging to this ridge, inverse sorted by ID
                           NULL if a degen ridge (matchsame) */
  facetT  *top;         /* top facet this ridge is part of */
  facetT  *bottom;      /* bottom facet this ridge is part of */
  unsigned id:24;       /* unique identifier, =>room for 8 flags, bit field matches qh.ridge_id */
  flagT    seen:1;      /* used to perform operations only once */
  flagT    tested:1;    /* True when ridge is tested for convexity */
  flagT    nonconvex:1; /* True if getmergeset detected a non-convex neighbor
                           only one ridge between neighbors may have nonconvex */
};

/*----------------------------------

  vertexT
     defines a vertex

  topological information:
    next,previous       doubly-linked list of all vertices
    neighbors           set of adjacent facets (only if qh.VERTEXneighbors)

  geometric information:
    point               array of DIM3 coordinates
*/
struct vertexT {
  vertexT *next;        /* next vertex in vertex_list */
  vertexT *previous;    /* previous vertex in vertex_list */
  pointT  *point;       /* hull_dim coordinates (coordT) */
  setT    *neighbors;   /* neighboring facets of vertex, qh_vertexneighbors()
                           inits in io.c or after first merge */
  unsigned visitid:31;  /* for use with qh vertex_visit, size must match */
  flagT    seen2:1;     /* another seen flag */
  unsigned id:24;       /* unique identifier, bit field matches qh.vertex_id */
  unsigned dim:4;       /* dimension of point if non-zero, used by cpp */
                        /* =>room for 4 flags */
  flagT    seen:1;      /* used to perform operations only once */
  flagT    delridge:1;  /* vertex was part of a deleted ridge */
  flagT    deleted:1;   /* true if vertex on qh del_vertices */
  flagT    newlist:1;   /* true if vertex on qh newvertex_list */
};

#define MAX_vdim 15  /* Maximum size of vertex->dim */

/*======= -global variables -qh ============================*/

/*----------------------------------

  qh
   all global variables for qhull are in qh, qhmem, and qhstat

  notes:
   qhmem is defined in mem.h, qhstat is defined in stat.h, qhrbox is defined in rboxpoints.h
   Access to qh_qh is via the "qh" macro.  See qh_QHpointer in user.h

   All global variables for qhull are in qh, qhmem, and qhstat
   qh must be unique for each instance of qhull
   qhstat may be shared between qhull instances.
   qhmem may be shared across multiple instances of Qhull.
   Rbox uses global variables rbox_inuse and rbox, but does not persist data across calls.

   Qhull is not multithreaded.  Global state could be stored in thread-local storage.
*/

extern int qhull_inuse;

typedef struct qhT qhT;
#if qh_QHpointer_dllimport
#define qh qh_qh->
__declspec(dllimport) extern qhT *qh_qh;     /* allocated in global.c */
#elif qh_QHpointer
#define qh qh_qh->
extern qhT *qh_qh;     /* allocated in global.c */
#elif qh_dllimport
#define qh qh_qh.
__declspec(dllimport) extern qhT qh_qh;      /* allocated in global.c */
#else
#define qh qh_qh.
extern qhT qh_qh;
#endif

struct qhT {

/*----------------------------------

  qh constants
    configuration flags and constants for Qhull

  notes:
    The user configures Qhull by defining flags.  They are
    copied into qh by qh_setflags().  qh-quick.htm#options defines the flags.
*/
  boolT ALLpoints;        /* true 'Qs' if search all points for initial simplex */
  boolT ANGLEmerge;       /* true 'Qa' if sort potential merges by angle */
  boolT APPROXhull;       /* true 'Wn' if MINoutside set */
  realT   MINoutside;     /*   'Wn' min. distance for an outside point */
  boolT ANNOTATEoutput;   /* true 'Ta' if annotate output with message codes */
  boolT ATinfinity;       /* true 'Qz' if point num_points-1 is "at-infinity"
                             for improving precision in Delaunay triangulations */
  boolT AVOIDold;         /* true 'Q4' if avoid old->new merges */
  boolT BESToutside;      /* true 'Qf' if partition points into best outsideset */
  boolT CDDinput;         /* true 'Pc' if input uses CDD format (1.0/offset first) */
  boolT CDDoutput;        /* true 'PC' if print normals in CDD format (offset first) */
  boolT CHECKfrequently;  /* true 'Tc' if checking frequently */
  realT premerge_cos;     /*   'A-n'   cos_max when pre merging */
  realT postmerge_cos;    /*   'An'    cos_max when post merging */
  boolT DELAUNAY;         /* true 'd' if computing DELAUNAY triangulation */
  boolT DOintersections;  /* true 'Gh' if print hyperplane intersections */
  int   DROPdim;          /* drops dim 'GDn' for 4-d -> 3-d output */
  boolT FORCEoutput;      /* true 'Po' if forcing output despite degeneracies */
  int   GOODpoint;        /* 1+n for 'QGn', good facet if visible/not(-) from point n*/
  pointT *GOODpointp;     /*   the actual point */
  boolT GOODthreshold;    /* true if qh lower_threshold/upper_threshold defined
                             false if qh SPLITthreshold */
  int   GOODvertex;       /* 1+n, good facet if vertex for point n */
  pointT *GOODvertexp;     /*   the actual point */
  boolT HALFspace;        /* true 'Hn,n,n' if halfspace intersection */
  int   IStracing;        /* trace execution, 0=none, 1=least, 4=most, -1=events */
  int   KEEParea;         /* 'PAn' number of largest facets to keep */
  boolT KEEPcoplanar;     /* true 'Qc' if keeping nearest facet for coplanar points */
  boolT KEEPinside;       /* true 'Qi' if keeping nearest facet for inside points
                              set automatically if 'd Qc' */
  int   KEEPmerge;        /* 'PMn' number of facets to keep with most merges */
  realT KEEPminArea;      /* 'PFn' minimum facet area to keep */
  realT MAXcoplanar;      /* 'Un' max distance below a facet to be coplanar*/
  boolT MERGEexact;       /* true 'Qx' if exact merges (coplanar, degen, dupridge, flipped) */
  boolT MERGEindependent; /* true 'Q2' if merging independent sets */
  boolT MERGING;          /* true if exact-, pre- or post-merging, with angle and centrum tests */
  realT   premerge_centrum;  /*   'C-n' centrum_radius when pre merging.  Default is round-off */
  realT   postmerge_centrum; /*   'Cn' centrum_radius when post merging.  Default is round-off */
  boolT MERGEvertices;    /* true 'Q3' if merging redundant vertices */
  realT MINvisible;       /* 'Vn' min. distance for a facet to be visible */
  boolT NOnarrow;         /* true 'Q10' if no special processing for narrow distributions */
  boolT NOnearinside;     /* true 'Q8' if ignore near-inside points when partitioning */
  boolT NOpremerge;       /* true 'Q0' if no defaults for C-0 or Qx */
  boolT ONLYgood;         /* true 'Qg' if process points with good visible or horizon facets */
  boolT ONLYmax;          /* true 'Qm' if only process points that increase max_outside */
  boolT PICKfurthest;     /* true 'Q9' if process furthest of furthest points*/
  boolT POSTmerge;        /* true if merging after buildhull (Cn or An) */
  boolT PREmerge;         /* true if merging during buildhull (C-n or A-n) */
                        /* NOTE: some of these names are similar to qh_PRINT names */
  boolT PRINTcentrums;    /* true 'Gc' if printing centrums */
  boolT PRINTcoplanar;    /* true 'Gp' if printing coplanar points */
  int   PRINTdim;         /* print dimension for Geomview output */
  boolT PRINTdots;        /* true 'Ga' if printing all points as dots */
  boolT PRINTgood;        /* true 'Pg' if printing good facets */
  boolT PRINTinner;       /* true 'Gi' if printing inner planes */
  boolT PRINTneighbors;   /* true 'PG' if printing neighbors of good facets */
  boolT PRINTnoplanes;    /* true 'Gn' if printing no planes */
  boolT PRINToptions1st;  /* true 'FO' if printing options to stderr */
  boolT PRINTouter;       /* true 'Go' if printing outer planes */
  boolT PRINTprecision;   /* false 'Pp' if not reporting precision problems */
  qh_PRINT PRINTout[qh_PRINTEND]; /* list of output formats to print */
  boolT PRINTridges;      /* true 'Gr' if print ridges */
  boolT PRINTspheres;     /* true 'Gv' if print vertices as spheres */
  boolT PRINTstatistics;  /* true 'Ts' if printing statistics to stderr */
  boolT PRINTsummary;     /* true 's' if printing summary to stderr */
  boolT PRINTtransparent; /* true 'Gt' if print transparent outer ridges */
  boolT PROJECTdelaunay;  /* true if DELAUNAY, no readpoints() and
                             need projectinput() for Delaunay in qh_init_B */
  int   PROJECTinput;     /* number of projected dimensions 'bn:0Bn:0' */
  boolT QUICKhelp;        /* true if quick help message for degen input */
  boolT RANDOMdist;       /* true if randomly change distplane and setfacetplane */
  realT RANDOMfactor;     /*    maximum random perturbation */
  realT RANDOMa;          /*    qh_randomfactor is randr * RANDOMa + RANDOMb */
  realT RANDOMb;
  boolT RANDOMoutside;    /* true if select a random outside point */
  int   REPORTfreq;       /* buildtracing reports every n facets */
  int   REPORTfreq2;      /* tracemerging reports every REPORTfreq/2 facets */
  int   RERUN;            /* 'TRn' rerun qhull n times (qh.build_cnt) */
  int   ROTATErandom;     /* 'QRn' seed, 0 time, >= rotate input */
  boolT SCALEinput;       /* true 'Qbk' if scaling input */
  boolT SCALElast;        /* true 'Qbb' if scale last coord to max prev coord */
  boolT SETroundoff;      /* true 'E' if qh DISTround is predefined */
  boolT SKIPcheckmax;     /* true 'Q5' if skip qh_check_maxout */
  boolT SKIPconvex;       /* true 'Q6' if skip convexity testing during pre-merge */
  boolT SPLITthresholds;  /* true if upper_/lower_threshold defines a region
                               used only for printing (!for qh ONLYgood) */
  int   STOPcone;         /* 'TCn' 1+n for stopping after cone for point n */
                          /*       also used by qh_build_withresart for err exit*/
  int   STOPpoint;        /* 'TVn' 'TV-n' 1+n for stopping after/before(-)
                                        adding point n */
  int   TESTpoints;       /* 'QTn' num of test points after qh.num_points.  Test points always coplanar. */
  boolT TESTvneighbors;   /*  true 'Qv' if test vertex neighbors at end */
  int   TRACElevel;       /* 'Tn' conditional IStracing level */
  int   TRACElastrun;     /*  qh.TRACElevel applies to last qh.RERUN */
  int   TRACEpoint;       /* 'TPn' start tracing when point n is a vertex */
  realT TRACEdist;        /* 'TWn' start tracing when merge distance too big */
  int   TRACEmerge;       /* 'TMn' start tracing before this merge */
  boolT TRIangulate;      /* true 'Qt' if triangulate non-simplicial facets */
  boolT TRInormals;       /* true 'Q11' if triangulate duplicates normals (sets Qt) */
  boolT UPPERdelaunay;    /* true 'Qu' if computing furthest-site Delaunay */
  boolT USEstdout;        /* true 'Tz' if using stdout instead of stderr */
  boolT VERIFYoutput;     /* true 'Tv' if verify output at end of qhull */
  boolT VIRTUALmemory;    /* true 'Q7' if depth-first processing in buildhull */
  boolT VORONOI;          /* true 'v' if computing Voronoi diagram */

  /*--------input constants ---------*/
  realT AREAfactor;       /* 1/(hull_dim-1)! for converting det's to area */
  boolT DOcheckmax;       /* true if calling qh_check_maxout (qh_initqhull_globals) */
  char  *feasible_string;  /* feasible point 'Hn,n,n' for halfspace intersection */
  coordT *feasible_point;  /*    as coordinates, both malloc'd */
  boolT GETarea;          /* true 'Fa', 'FA', 'FS', 'PAn', 'PFn' if compute facet area/Voronoi volume in io.c */
  boolT KEEPnearinside;   /* true if near-inside points in coplanarset */
  int   hull_dim;         /* dimension of hull, set by initbuffers */
  int   input_dim;        /* dimension of input, set by initbuffers */
  int   num_points;       /* number of input points */
  pointT *first_point;    /* array of input points, see POINTSmalloc */
  boolT POINTSmalloc;     /*   true if qh first_point/num_points allocated */
  pointT *input_points;   /* copy of original qh.first_point for input points for qh_joggleinput */
  boolT input_malloc;     /* true if qh input_points malloc'd */
  char  qhull_command[256];/* command line that invoked this program */
  int   qhull_commandsiz2; /*    size of qhull_command at qh_clear_outputflags */
  char  rbox_command[256]; /* command line that produced the input points */
  char  qhull_options[512];/* descriptive list of options */
  int   qhull_optionlen;  /*    length of last line */
  int   qhull_optionsiz;  /*    size of qhull_options at qh_build_withrestart */
  int   qhull_optionsiz2; /*    size of qhull_options at qh_clear_outputflags */
  int   run_id;           /* non-zero, random identifier for this instance of qhull */
  boolT VERTEXneighbors;  /* true if maintaining vertex neighbors */
  boolT ZEROcentrum;      /* true if 'C-0' or 'C-0 Qx'.  sets ZEROall_ok */
  realT *upper_threshold; /* don't print if facet->normal[k]>=upper_threshold[k]
                             must set either GOODthreshold or SPLITthreshold
                             if Delaunay, default is 0.0 for upper envelope */
  realT *lower_threshold; /* don't print if facet->normal[k] <=lower_threshold[k] */
  realT *upper_bound;     /* scale point[k] to new upper bound */
  realT *lower_bound;     /* scale point[k] to new lower bound
                             project if both upper_ and lower_bound == 0 */

/*----------------------------------

  qh precision constants
    precision constants for Qhull

  notes:
    qh_detroundoff() computes the maximum roundoff error for distance
    and other computations.  It also sets default values for the
    qh constants above.
*/
  realT ANGLEround;       /* max round off error for angles */
  realT centrum_radius;   /* max centrum radius for convexity (roundoff added) */
  realT cos_max;          /* max cosine for convexity (roundoff added) */
  realT DISTround;        /* max round off error for distances, 'E' overrides */
  realT MAXabs_coord;     /* max absolute coordinate */
  realT MAXlastcoord;     /* max last coordinate for qh_scalelast */
  realT MAXsumcoord;      /* max sum of coordinates */
  realT MAXwidth;         /* max rectilinear width of point coordinates */
  realT MINdenom_1;       /* min. abs. value for 1/x */
  realT MINdenom;         /*    use divzero if denominator < MINdenom */
  realT MINdenom_1_2;     /* min. abs. val for 1/x that allows normalization */
  realT MINdenom_2;       /*    use divzero if denominator < MINdenom_2 */
  realT MINlastcoord;     /* min. last coordinate for qh_scalelast */
  boolT NARROWhull;       /* set in qh_initialhull if angle < qh_MAXnarrow */
  realT *NEARzero;        /* hull_dim array for near zero in gausselim */
  realT NEARinside;       /* keep points for qh_check_maxout if close to facet */
  realT ONEmerge;         /* max distance for merging simplicial facets */
  realT outside_err;      /* application's epsilon for coplanar points
                             qh_check_bestdist() qh_check_points() reports error if point outside */
  realT WIDEfacet;        /* size of wide facet for skipping ridge in
                             area computation and locking centrum */

/*----------------------------------

  qh internal constants
    internal constants for Qhull
*/
  char qhull[sizeof("qhull")]; /* "qhull" for checking ownership while debugging */
  jmp_buf errexit;        /* exit label for qh_errexit, defined by setjmp() */
  char jmpXtra[40];       /* extra bytes in case jmp_buf is defined wrong by compiler */
  jmp_buf restartexit;    /* restart label for qh_errexit, defined by setjmp() */
  char jmpXtra2[40];      /* extra bytes in case jmp_buf is defined wrong by compiler*/
  FILE *fin;              /* pointer to input file, init by qh_meminit */
  FILE *fout;             /* pointer to output file */
  FILE *ferr;             /* pointer to error file */
  pointT *interior_point; /* center point of the initial simplex*/
  int normal_size;     /* size in bytes for facet normals and point coords*/
  int center_size;     /* size in bytes for Voronoi centers */
  int   TEMPsize;         /* size for small, temporary sets (in quick mem) */

/*----------------------------------

  qh facet and vertex lists
    defines lists of facets, new facets, visible facets, vertices, and
    new vertices.  Includes counts, next ids, and trace ids.
  see:
    qh_resetlists()
*/
  facetT *facet_list;     /* first facet */
  facetT  *facet_tail;     /* end of facet_list (dummy facet) */
  facetT *facet_next;     /* next facet for buildhull()
                             previous facets do not have outside sets
                             NARROWhull: previous facets may have coplanar outside sets for qh_outcoplanar */
  facetT *newfacet_list;  /* list of new facets to end of facet_list */
  facetT *visible_list;   /* list of visible facets preceeding newfacet_list,
                             facet->visible set */
  int       num_visible;  /* current number of visible facets */
  unsigned tracefacet_id;  /* set at init, then can print whenever */
  facetT *tracefacet;     /*   set in newfacet/mergefacet, undone in delfacet*/
  unsigned tracevertex_id;  /* set at buildtracing, can print whenever */
  vertexT *tracevertex;     /*   set in newvertex, undone in delvertex*/
  vertexT *vertex_list;     /* list of all vertices, to vertex_tail */
  vertexT  *vertex_tail;    /*      end of vertex_list (dummy vertex) */
  vertexT *newvertex_list; /* list of vertices in newfacet_list, to vertex_tail
                             all vertices have 'newlist' set */
  int   num_facets;       /* number of facets in facet_list
                             includes visble faces (num_visible) */
  int   num_vertices;     /* number of vertices in facet_list */
  int   num_outside;      /* number of points in outsidesets (for tracing and RANDOMoutside)
                               includes coplanar outsideset points for NARROWhull/qh_outcoplanar() */
  int   num_good;         /* number of good facets (after findgood_all) */
  unsigned facet_id;      /* ID of next, new facet from newfacet() */
  unsigned ridge_id:24;   /* ID of next, new ridge from newridge() */
  unsigned vertex_id:24;  /* ID of next, new vertex from newvertex() */

/*----------------------------------

  qh global variables
    defines minimum and maximum distances, next visit ids, several flags,
    and other global variables.
    initialize in qh_initbuild or qh_maxmin if used in qh_buildhull
*/
  unsigned long hulltime; /* ignore time to set up input and randomize */
                          /*   use unsigned to avoid wrap-around errors */
  boolT ALLOWrestart;     /* true if qh_precision can use qh.restartexit */
  int   build_cnt;        /* number of calls to qh_initbuild */
  qh_CENTER CENTERtype;   /* current type of facet->center, qh_CENTER */
  int   furthest_id;      /* pointid of furthest point, for tracing */
  facetT *GOODclosest;    /* closest facet to GOODthreshold in qh_findgood */
  boolT hasAreaVolume;    /* true if totarea, totvol was defined by qh_getarea */
  boolT hasTriangulation; /* true if triangulation created by qh_triangulate */
  realT JOGGLEmax;        /* set 'QJn' if randomly joggle input */
  boolT maxoutdone;       /* set qh_check_maxout(), cleared by qh_addpoint() */
  realT max_outside;      /* maximum distance from a point to a facet,
                               before roundoff, not simplicial vertices
                               actual outer plane is +DISTround and
                               computed outer plane is +2*DISTround */
  realT max_vertex;       /* maximum distance (>0) from vertex to a facet,
                               before roundoff, due to a merge */
  realT min_vertex;       /* minimum distance (<0) from vertex to a facet,
                               before roundoff, due to a merge
                               if qh.JOGGLEmax, qh_makenewplanes sets it
                               recomputed if qh.DOcheckmax, default -qh.DISTround */
  boolT NEWfacets;        /* true while visible facets invalid due to new or merge
                              from makecone/attachnewfacets to deletevisible */
  boolT findbestnew;      /* true if partitioning calls qh_findbestnew */
  boolT findbest_notsharp; /* true if new facets are at least 90 degrees */
  boolT NOerrexit;        /* true if qh.errexit is not available */
  realT PRINTcradius;     /* radius for printing centrums */
  realT PRINTradius;      /* radius for printing vertex spheres and points */
  boolT POSTmerging;      /* true when post merging */
  int   printoutvar;      /* temporary variable for qh_printbegin, etc. */
  int   printoutnum;      /* number of facets printed */
  boolT QHULLfinished;    /* True after qhull() is finished */
  realT totarea;          /* 'FA': total facet area computed by qh_getarea, hasAreaVolume */
  realT totvol;           /* 'FA': total volume computed by qh_getarea, hasAreaVolume */
  unsigned int visit_id;  /* unique ID for searching neighborhoods, */
  unsigned int vertex_visit:31; /* unique ID for searching vertices, reset with qh_buildtracing */
  boolT ZEROall_ok;       /* True if qh_checkzero always succeeds */
  boolT WAScoplanar;      /* True if qh_partitioncoplanar (qh_check_maxout) */

/*----------------------------------

  qh global sets
    defines sets for merging, initial simplex, hashing, extra input points,
    and deleted vertices
*/
  setT *facet_mergeset;   /* temporary set of merges to be done */
  setT *degen_mergeset;   /* temporary set of degenerate and redundant merges */
  setT *hash_table;       /* hash table for matching ridges in qh_matchfacets
                             size is setsize() */
  setT *other_points;     /* additional points */
  setT *del_vertices;     /* vertices to partition and delete with visible
                             facets.  Have deleted set for checkfacet */

/*----------------------------------

  qh global buffers
    defines buffers for maxtrix operations, input, and error messages
*/
  coordT *gm_matrix;      /* (dim+1)Xdim matrix for geom.c */
  coordT **gm_row;        /* array of gm_matrix rows */
  char* line;             /* malloc'd input line of maxline+1 chars */
  int maxline;
  coordT *half_space;     /* malloc'd input array for halfspace (qh normal_size+coordT) */
  coordT *temp_malloc;    /* malloc'd input array for points */

/*----------------------------------

  qh static variables
    defines static variables for individual functions

  notes:
    do not use 'static' within a function.  Multiple instances of qhull
    may exist.

    do not assume zero initialization, 'QPn' may cause a restart
*/
  boolT ERREXITcalled;    /* true during qh_errexit (prevents duplicate calls */
  boolT firstcentrum;     /* for qh_printcentrum */
  boolT old_randomdist;   /* save RANDOMdist flag during io, tracing, or statistics */
  setT *coplanarfacetset;  /* set of coplanar facets for searching qh_findbesthorizon() */
  realT last_low;         /* qh_scalelast parameters for qh_setdelaunay */
  realT last_high;
  realT last_newhigh;
  unsigned lastreport;    /* for qh_buildtracing */
  int mergereport;        /* for qh_tracemerging */
  qhstatT *old_qhstat;    /* for saving qh_qhstat in save_qhull() and UsingLibQhull.  Free with qh_free() */
  setT *old_tempstack;    /* for saving qhmem.tempstack in save_qhull */
  int   ridgeoutnum;      /* number of ridges for 4OFF output (qh_printbegin,etc) */
};

/*=========== -macros- =========================*/

/*----------------------------------

  otherfacet_(ridge, facet)
    return neighboring facet for a ridge in facet
*/
#define otherfacet_(ridge, facet) \
                        (((ridge)->top == (facet)) ? (ridge)->bottom : (ridge)->top)

/*----------------------------------

  getid_(p)
    return int ID for facet, ridge, or vertex
    return -1 if NULL
*/
#define getid_(p)       ((p) ? (int)((p)->id) : -1)

/*============== FORALL macros ===================*/

/*----------------------------------

  FORALLfacets { ... }
    assign 'facet' to each facet in qh.facet_list

  notes:
    uses 'facetT *facet;'
    assumes last facet is a sentinel

  see:
    FORALLfacet_( facetlist )
*/
#define FORALLfacets for (facet=qh facet_list;facet && facet->next;facet=facet->next)

/*----------------------------------

  FORALLpoints { ... }
    assign 'point' to each point in qh.first_point, qh.num_points

  declare:
    coordT *point, *pointtemp;
*/
#define FORALLpoints FORALLpoint_(qh first_point, qh num_points)

/*----------------------------------

  FORALLpoint_( points, num) { ... }
    assign 'point' to each point in points array of num points

  declare:
    coordT *point, *pointtemp;
*/
#define FORALLpoint_(points, num) for (point= (points), \
      pointtemp= (points)+qh hull_dim*(num); point < pointtemp; point += qh hull_dim)

/*----------------------------------

  FORALLvertices { ... }
    assign 'vertex' to each vertex in qh.vertex_list

  declare:
    vertexT *vertex;

  notes:
    assumes qh.vertex_list terminated with a sentinel
*/
#define FORALLvertices for (vertex=qh vertex_list;vertex && vertex->next;vertex= vertex->next)

/*----------------------------------

  FOREACHfacet_( facets ) { ... }
    assign 'facet' to each facet in facets

  declare:
    facetT *facet, **facetp;

  see:
    FOREACHsetelement_
*/
#define FOREACHfacet_(facets)    FOREACHsetelement_(facetT, facets, facet)

/*----------------------------------

  FOREACHneighbor_( facet ) { ... }
    assign 'neighbor' to each neighbor in facet->neighbors

  FOREACHneighbor_( vertex ) { ... }
    assign 'neighbor' to each neighbor in vertex->neighbors

  declare:
    facetT *neighbor, **neighborp;

  see:
    FOREACHsetelement_
*/
#define FOREACHneighbor_(facet)  FOREACHsetelement_(facetT, facet->neighbors, neighbor)

/*----------------------------------

  FOREACHpoint_( points ) { ... }
    assign 'point' to each point in points set

  declare:
    pointT *point, **pointp;

  see:
    FOREACHsetelement_
*/
#define FOREACHpoint_(points)    FOREACHsetelement_(pointT, points, point)

/*----------------------------------

  FOREACHridge_( ridges ) { ... }
    assign 'ridge' to each ridge in ridges set

  declare:
    ridgeT *ridge, **ridgep;

  see:
    FOREACHsetelement_
*/
#define FOREACHridge_(ridges)    FOREACHsetelement_(ridgeT, ridges, ridge)

/*----------------------------------

  FOREACHvertex_( vertices ) { ... }
    assign 'vertex' to each vertex in vertices set

  declare:
    vertexT *vertex, **vertexp;

  see:
    FOREACHsetelement_
*/
#define FOREACHvertex_(vertices) FOREACHsetelement_(vertexT, vertices,vertex)

/*----------------------------------

  FOREACHfacet_i_( facets ) { ... }
    assign 'facet' and 'facet_i' for each facet in facets set

  declare:
    facetT *facet;
    int     facet_n, facet_i;

  see:
    FOREACHsetelement_i_
*/
#define FOREACHfacet_i_(facets)    FOREACHsetelement_i_(facetT, facets, facet)

/*----------------------------------

  FOREACHneighbor_i_( facet ) { ... }
    assign 'neighbor' and 'neighbor_i' for each neighbor in facet->neighbors

  FOREACHneighbor_i_( vertex ) { ... }
    assign 'neighbor' and 'neighbor_i' for each neighbor in vertex->neighbors

  declare:
    facetT *neighbor;
    int     neighbor_n, neighbor_i;

  see:
    FOREACHsetelement_i_
*/
#define FOREACHneighbor_i_(facet)  FOREACHsetelement_i_(facetT, facet->neighbors, neighbor)

/*----------------------------------

  FOREACHpoint_i_( points ) { ... }
    assign 'point' and 'point_i' for each point in points set

  declare:
    pointT *point;
    int     point_n, point_i;

  see:
    FOREACHsetelement_i_
*/
#define FOREACHpoint_i_(points)    FOREACHsetelement_i_(pointT, points, point)

/*----------------------------------

  FOREACHridge_i_( ridges ) { ... }
    assign 'ridge' and 'ridge_i' for each ridge in ridges set

  declare:
    ridgeT *ridge;
    int     ridge_n, ridge_i;

  see:
    FOREACHsetelement_i_
*/
#define FOREACHridge_i_(ridges)    FOREACHsetelement_i_(ridgeT, ridges, ridge)

/*----------------------------------

  FOREACHvertex_i_( vertices ) { ... }
    assign 'vertex' and 'vertex_i' for each vertex in vertices set

  declare:
    vertexT *vertex;
    int     vertex_n, vertex_i;

  see:
    FOREACHsetelement_i_
*/
#define FOREACHvertex_i_(vertices) FOREACHsetelement_i_(vertexT, vertices,vertex)

/********* -libqhull.c prototypes (duplicated from qhull_a.h) **********************/

void    qh_qhull(void);
boolT   qh_addpoint(pointT *furthest, facetT *facet, boolT checkdist);
void    qh_printsummary(FILE *fp);

/********* -user.c prototypes (alphabetical) **********************/

void    qh_errexit(int exitcode, facetT *facet, ridgeT *ridge);
void    qh_errprint(const char* string, facetT *atfacet, facetT *otherfacet, ridgeT *atridge, vertexT *atvertex);
int     qh_new_qhull(int dim, int numpoints, coordT *points, boolT ismalloc,
                char *qhull_cmd, FILE *outfile, FILE *errfile);
void    qh_printfacetlist(facetT *facetlist, setT *facets, boolT printall);
void    qh_printhelp_degenerate(FILE *fp);
void    qh_printhelp_narrowhull(FILE *fp, realT minangle);
void    qh_printhelp_singular(FILE *fp);
void    qh_user_memsizes(void);

/********* -usermem.c prototypes (alphabetical) **********************/
void    qh_exit(int exitcode);
void    qh_free(void *mem);
void   *qh_malloc(size_t size);

/********* -userprintf.c and userprintf_rbox.c prototypes **********************/
void    qh_fprintf(FILE *fp, int msgcode, const char *fmt, ... );
void    qh_fprintf_rbox(FILE *fp, int msgcode, const char *fmt, ... );

/***** -geom.c/geom2.c/random.c prototypes (duplicated from geom.h, random.h) ****************/

facetT *qh_findbest(pointT *point, facetT *startfacet,
                     boolT bestoutside, boolT newfacets, boolT noupper,
                     realT *dist, boolT *isoutside, int *numpart);
facetT *qh_findbestnew(pointT *point, facetT *startfacet,
                     realT *dist, boolT bestoutside, boolT *isoutside, int *numpart);
boolT   qh_gram_schmidt(int dim, realT **rows);
void    qh_outerinner(facetT *facet, realT *outerplane, realT *innerplane);
void    qh_printsummary(FILE *fp);
void    qh_projectinput(void);
void    qh_randommatrix(realT *buffer, int dim, realT **row);
void    qh_rotateinput(realT **rows);
void    qh_scaleinput(void);
void    qh_setdelaunay(int dim, int count, pointT *points);
coordT  *qh_sethalfspace_all(int dim, int count, coordT *halfspaces, pointT *feasible);

/***** -global.c prototypes (alphabetical) ***********************/

unsigned long qh_clock(void);
void    qh_checkflags(char *command, char *hiddenflags);
void    qh_clear_outputflags(void);
void    qh_freebuffers(void);
void    qh_freeqhull(boolT allmem);
void    qh_freeqhull2(boolT allmem);
void    qh_init_A(FILE *infile, FILE *outfile, FILE *errfile, int argc, char *argv[]);
void    qh_init_B(coordT *points, int numpoints, int dim, boolT ismalloc);
void    qh_init_qhull_command(int argc, char *argv[]);
void    qh_initbuffers(coordT *points, int numpoints, int dim, boolT ismalloc);
void    qh_initflags(char *command);
void    qh_initqhull_buffers(void);
void    qh_initqhull_globals(coordT *points, int numpoints, int dim, boolT ismalloc);
void    qh_initqhull_mem(void);
void    qh_initqhull_outputflags(void);
void    qh_initqhull_start(FILE *infile, FILE *outfile, FILE *errfile);
void    qh_initqhull_start2(FILE *infile, FILE *outfile, FILE *errfile);
void    qh_initthresholds(char *command);
void    qh_option(const char *option, int *i, realT *r);
#if qh_QHpointer
void    qh_restore_qhull(qhT **oldqh);
qhT    *qh_save_qhull(void);
#endif

/***** -io.c prototypes (duplicated from io.h) ***********************/

void    dfacet( unsigned id);
void    dvertex( unsigned id);
void    qh_printneighborhood(FILE *fp, qh_PRINT format, facetT *facetA, facetT *facetB, boolT printall);
void    qh_produce_output(void);
coordT *qh_readpoints(int *numpoints, int *dimension, boolT *ismalloc);


/********* -mem.c prototypes (duplicated from mem.h) **********************/

void qh_meminit(FILE *ferr);
void qh_memfreeshort(int *curlong, int *totlong);

/********* -poly.c/poly2.c prototypes (duplicated from poly.h) **********************/

void    qh_check_output(void);
void    qh_check_points(void);
setT   *qh_facetvertices(facetT *facetlist, setT *facets, boolT allfacets);
facetT *qh_findbestfacet(pointT *point, boolT bestoutside,
           realT *bestdist, boolT *isoutside);
vertexT *qh_nearvertex(facetT *facet, pointT *point, realT *bestdistp);
pointT *qh_point(int id);
setT   *qh_pointfacet(void /*qh.facet_list*/);
int     qh_pointid(pointT *point);
setT   *qh_pointvertex(void /*qh.facet_list*/);
void    qh_setvoronoi_all(void);
void    qh_triangulate(void /*qh facet_list*/);

/********* -rboxpoints.c prototypes **********************/
int     qh_rboxpoints(FILE* fout, FILE* ferr, char* rbox_command);
void    qh_errexit_rbox(int exitcode);

/********* -stat.c prototypes (duplicated from stat.h) **********************/

void    qh_collectstatistics(void);
void    qh_printallstatistics(FILE *fp, const char *string);

#endif /* qhDEFlibqhull */
qhull-2012.1/src/libqhull/libqhull.pro0000644000076400010400000000275311710424343021053 0ustar  bbarberAdministrators# -------------------------------------------------
# libqhull.pro -- Qt project for Qhull shared library
#   Built with qh_QHpointer=1
# -------------------------------------------------

include(../qhull-warn.pri)

DESTDIR = ../../lib
DLLDESTDIR = ../../bin
TEMPLATE = lib
CONFIG += shared warn_on
CONFIG -= qt

build_pass:CONFIG(debug, debug|release):{
    TARGET = qhull_d
    OBJECTS_DIR = Debug
}else:build_pass:CONFIG(release, debug|release):{
    TARGET = qhull
    OBJECTS_DIR = Release
}
win32-msvc* : QMAKE_LFLAGS += /INCREMENTAL:NO

win32-msvc* : DEF_FILE += ../../src/libqhull/qhull-exports.def

# Order object files by frequency of execution.  Small files at end.
SOURCES += rboxlib.c
SOURCES += user.c
SOURCES += global.c
SOURCES += stat.c
SOURCES += io.c
SOURCES += geom2.c
SOURCES += poly2.c
SOURCES += merge.c
SOURCES += libqhull.c
SOURCES += geom.c
SOURCES += poly.c
SOURCES += qset.c
SOURCES += mem.c
SOURCES += usermem.c
SOURCES += userprintf.c
SOURCES += userprintf_rbox.c
SOURCES += random.c

HEADERS += geom.h
HEADERS += io.h
HEADERS += libqhull.h
HEADERS += mem.h
HEADERS += merge.h
HEADERS += poly.h
HEADERS += random.h
HEADERS += qhull_a.h
HEADERS += qset.h
HEADERS += stat.h
HEADERS += user.h

OTHER_FILES += Mborland
OTHER_FILES += qh-geom.htm
OTHER_FILES += qh-globa.htm
OTHER_FILES += qh-io.htm
OTHER_FILES += qh-mem.htm
OTHER_FILES += qh-merge.htm
OTHER_FILES += qh-poly.htm
OTHER_FILES += qh-qhull.htm
OTHER_FILES += qh-set.htm
OTHER_FILES += qh-stat.htm
OTHER_FILES += qh-user.htm
qhull-2012.1/src/libqhull/Makefile0000644000076400010400000001505511716353753020170 0ustar  bbarberAdministrators# Simple gcc Makefile for qhull and rbox (default gcc/g++)
#
#       see README.txt  
#       
# Results
#	qhull 	  Computes convex hulls and related structures
#       qconvex, qdelaunay, qhalf, qvoronoi
#                 Specializations of qhull for each geometric structure
#	user_eg	  An example of using shared library qhull6_p (with qh_QHpointer)
#       user_eg2  An example of using shared library qhull (without qh_QHpointer)
#       testqset  Standalone test of qset.c with mem.c
#       libqhullstatic.a Static library for qhull
#
# Make targets
#       make             Produce all of the results
#       make qhull_all   Produce qconvex, etc.
#                        Links program sources into src/libqhull
#       make qtest       Quick test of qset, rbox, and qhull
#       make doc         Print documentation
#       make install     Copy qhull, rbox, qhull.1, rbox.1 to BINDIR, MANDIR
#       make new         Rebuild qhull and rbox from source
#
#       make printall    Print all files
#       make clean       Remove object files
#       make cleanall    Remove generated files
#
#       BINDIR           directory where to copy executables
#       DESTDIR          destination directory
#       DOCDIR           directory where to copy html documentation
#       INCDIR           directory where to copy headers
#       LIBDIR           directory where to copy libraries
#       MANDIR           directory where to copy manual pages
#       PRINTMAN         command for printing manual pages
#       PRINTC           command for printing C files
#       CC               ANSI C or C++ compiler
#       CC_OPTS1         options used to compile .c files
#       CC_OPTS2         options used to link .o files
#       CC_OPTS3         options to build shared libraries
#
#       LIBQHULL_OBJS    .o files for linking
#       LIBQHULL_HDRS    .h files for printing
#       CFILES           .c files for printing
#       DOCFILES         documentation files
#       FILES            miscellaneous files for printing
#       TFILES           .txt versions of html files
#       FILES            all other files
#       LIBQHULL_OBJS    specifies the object files of libqhullstatic.a
#
# Do not replace tabs with spaces.  Needed by 'make' for build rules

# You may build the qhull programs without using a library
# make qhullx

DESTDIR = /usr/local
BINDIR	= $(DESTDIR)/bin
INCDIR	= $(DESTDIR)/include
LIBDIR	= $(DESTDIR)/lib
DOCDIR	= $(DESTDIR)/share/doc/qhull
MANDIR	= $(DESTDIR)/share/man/man1

# if you do not have enscript, try a2ps or just use lpr.  The files are text.
PRINTMAN = enscript -2rl
PRINTC = enscript -2r
# PRINTMAN = lpr
# PRINTC = lpr

#for Gnu's gcc compiler, -O2 for optimization, -g for debugging
CC        = gcc
CC_OPTS1  = -O2 -fPIC -ansi $(CC_WARNINGS)

# for Sun's cc compiler, -fast or O2 for optimization, -g for debugging, -Xc for ANSI
#CC       = cc
#CC_OPTS1 = -Xc -v -fast

# for Silicon Graphics cc compiler, -O2 for optimization, -g for debugging
#CC       = cc
#CC_OPTS1 = -ansi -O2

# for Next cc compiler with fat executable
#CC       = cc
#CC_OPTS1 = -ansi -O2 -arch m68k -arch i386 -arch hppa

# For loader, ld, 
CC_OPTS2 = $(CC_OPTS1)
CXX_OPTS2 = $(CXX_OPTS1)

# Default targets for make
     
all: qhull_links qhull_all qtest

clean:
	rm -f *.o 
	# Delete linked files from other directories [qhull_links]
	rm -f qconvex.c unix.c qdelaun.c qhalf.c qvoronoi.c rbox.c
	rm -f user_eg.c user_eg2.c testqset.c 
	
cleanall: clean
	rm -f qconvex qdelaunay qhalf qvoronoi qhull *.exe
	rm -f core user_eg user_eg2 testqset libqhullstatic.a

doc: 
	$(PRINTMAN) $(TXTFILES) $(DOCFILES)

install:
	mkdir -p $(BINDIR)
	mkdir -p $(DOCDIR)
	mkdir -p $(INCDIR)/libqhull
	mkdir -p $(MANDIR)
	cp -p qconvex qdelaunay qhalf qhull qvoronoi rbox $(BINDIR)
	cp -p libqhullstatic.a $(LIBDIR)
	cp -p ../../html/qhull.man $(MANDIR)/qhull.1
	cp -p ../../html/rbox.man $(MANDIR)/rbox.1
	cp -p ../../html/* $(DOCDIR)
	cp *.h $(INCDIR)/libqhull

new:	cleanall all

printall: doc printh printc printf

printh:
	$(PRINTC) $(LIBQHULL_HDRS)

printc:
	$(PRINTC) $(CFILES)

# LIBQHULL_OBJS_1 ordered by frequency of execution with small files at end.  Better locality.
# Same definitions as ../../Makefile

LIBQHULLS_OBJS_1= global.o stat.o geom2.o poly2.o merge.o \
        libqhull.o geom.o poly.o qset.o mem.o random.o 

LIBQHULLS_OBJS_2= $(LIBQHULLS_OBJS_1) usermem.o userprintf.o io.o user.o

LIBQHULLS_OBJS= $(LIBQHULLS_OBJS_2)  rboxlib.o userprintf_rbox.o

LIBQHULL_HDRS= user.h libqhull.h qhull_a.h geom.h \
        io.h mem.h merge.h poly.h random.h \
        qset.h stat.h

# CFILES ordered alphabetically after libqhull.c 
CFILES= ../qhull/unix.c libqhull.c geom.c geom2.c global.c io.c \
	mem.c merge.c poly.c poly2.c random.c rboxlib.c \
	qset.c stat.c user.c usermem.c userprintf.c \
	../qconvex/qconvex.c ../qdelaunay/qdelaun.c ../qhalf/qhalf.c ../qvoronoi/qvoronoi.c

TXTFILES= ../../Announce.txt ../../REGISTER.txt ../../COPYING.txt ../../README.txt ../Changes.txt
DOCFILES= ../../html/rbox.txt ../../html/qhull.txt

.c.o:
	$(CC) -c $(CC_OPTS1) -o $@ $<

# Work around problems with ../ in Red Hat Linux
qhull_links:
	[ -f qconvex.c ]  || ln -s ../qconvex/qconvex.c
	[ -f qdelaun.c ]  || ln -s ../qdelaunay/qdelaun.c
	[ -f qhalf.c ]    || ln -s ../qhalf/qhalf.c
	[ -f qvoronoi.c ] || ln -s ../qvoronoi/qvoronoi.c
	[ -f qhull.c ]    || ln -s ../qhull/unix.c
	[ -f rbox.c ]     || ln -s ../rbox/rbox.c
	[ -f user_eg.c ]     || ln -s ../user_eg/user_eg.c
	[ -f user_eg2.c ]     || ln -s ../user_eg2/user_eg2.c
	[ -f testqset.c ]     || ln -s ../testqset/testqset.c

# compile qhull without using bin/libqhullstatic.a
qhull_all: qconvex.o qdelaun.o qhalf.o qvoronoi.o unix.o user_eg.o user_eg2.o rbox.o testqset.o $(LIBQHULLS_OBJS)
	$(CC) -o qconvex $(CC_OPTS2) -lm $(LIBQHULLS_OBJS_2) qconvex.o 
	$(CC) -o qdelaunay $(CC_OPTS2) -lm $(LIBQHULLS_OBJS_2) qdelaun.o
	$(CC) -o qhalf $(CC_OPTS2) -lm $(LIBQHULLS_OBJS_2) qhalf.o 
	$(CC) -o qvoronoi $(CC_OPTS2) -lm $(LIBQHULLS_OBJS_2) qvoronoi.o 
	$(CC) -o qhull $(CC_OPTS2) -lm $(LIBQHULLS_OBJS_2) unix.o 
	$(CC) -o rbox $(CC_OPTS2) -lm rbox.o rboxlib.o random.o usermem.o userprintf_rbox.o
	$(CC) -o user_eg $(CC_OPTS2) -lm $(LIBQHULLS_OBJS_2) user_eg.o 
	$(CC) -o user_eg2 $(CC_OPTS2) -lm $(LIBQHULLS_OBJS_1) user_eg2.o  usermem.o userprintf.o io.o
	$(CC) -o testqset $(CC_OPTS2) -lm mem.o qset.o testqset.o
	-ar -rs libqhullstatic.a $(LIBQHULLS_OBJS)
	#libqhullstatic.a is not needed for qhull
	#If 'ar -rs' fails try using 'ar -s' with 'ranlib'
	#ranlib libqhullstatic.a

qtest:
	@echo Testing qset.c and mem.c with testqset
	./testqset 10000
	@echo Run the qhull smoketest
	./rbox D4 | ./qhull
	
# end of Makefile
qhull-2012.1/src/libqhull/Mborland0000644000076400010400000001366711710424412020201 0ustar  bbarberAdministrators#########################################################################
#  Borland C++ 4.02 for Win32 and DOS Power Pack			#
#  Makefile for qhull and rbox					        #
#								        #
#       make -fMborland all       to produce qconvex, qhull, and rbox   #
#       make -fMborland user_eg   to produce user_eg		        #
#       make -fMborland user_eg2  to produce user_eg2		        #
#       make -fMborland new       to rebuild qhull and rbox from source #
#       make -fMborland clean     to remove object files		#
#       make -fMborland cleanall  to remove all generated files	        #
#       make -fMborland test      to test rbox and qhull		#
#								        #
#  Author: D. Zwick of Germany, C.B. Barber			        #
#########################################################################

CC      = bcc32    # 32 bit compiler for DOS
		   # bcc32i - Intel's compiler
LINKER  = $(CC)    # bcc calls tlink32 with needed options
CFLAGS  = -w- -A -O2   
		    # -w- no warnings, bcc doesn't handle assigns in conditions
			# -A Ansi standard
			# -X no auto-dependency outputs
			# -v debugging, use CCOPTS for both 
			# -O2 optimization   
!if $d(_DPMI)
LFLAGS  = -WX -w-   # -WX loads DPMI library
!else
LFLAGS  = -lap -lx -lc
					# -lap 32-bit console application
					# -lx no map file
					# -lc case is significant 
!endif

EXERB = rbox
EXEQH = qhull
EXEQC = qconvex
EXEQD = qdelaunay
EXEQV = qvoronoi
EXEQF = qhalf
EXEEG = user_eg
EXEEG2 = user_eg2

TMPFILE = BCC32tmp.cfg

OBJS1 =   global.obj stat.obj geom2.obj poly2.obj merge.obj
OBJS2 =   libqhull.obj geom.obj poly.obj qset.obj mem.obj 
OBJS3 =   random.obj usermem.obj userprintf.obj io.obj user.obj
OBJS4 =   rboxlib.obj random.obj usermem.obj userprintf_rbox.obj

HFILES1 = libqhull.h stat.h qhull_a.h user.h


# General rules

.c.obj:
	$(CC) -c $(CFLAGS) $<

# Default

all:	  $(EXERB) $(EXEQH) $(EXEQC) $(EXEQD) $(EXEQV) $(EXEQF) test

help:
	@echo  USAGE:
	@echo  "make all       to produce qhull, rbox, qconvex, qdelaun, qvoronoi, qhalf"
	@echo  "make user_eg   to produce user_eg"
	@echo  "make user_eg2  to produce user_eg2"
	@echo  "make new       to rebuild qhull and rbox from source"
	@echo  "make clean     to remove object files"
	@echo  "make cleanall  to remove all generated file"
	@echo  "make test      to test rbox and qhull"
	@echo  OPTIONS (default is 32-bit console app):
	@echo  "-D_DPMI	for C++ 4.01 and DOS Power Pack"

# Executables

$(EXEQH):     ..\..\bin\$(EXEQH).exe
	@echo Made ..\..\bin\$(EXEQH).exe

unix.obj: ..\qhull\unix.c 
..\..\bin\$(EXEQH).exe: unix.obj $(OBJS1) $(OBJS2) $(OBJS3)
	@echo unix.obj > $(TMPFILE)
	@echo $(OBJS1) >> $(TMPFILE)
	@echo $(OBJS2) >> $(TMPFILE)
	@echo $(OBJS3) >> $(TMPFILE)
	$(LINKER) -e$@ $(CFLAGS) $(LFLAGS) @$(TMPFILE)

$(EXEQC):     ..\..\bin\$(EXEQC).exe
	@echo Made ..\..\bin\$(EXEQC).exe

qconvex.obj: ..\qconvex\qconvex.c
..\..\bin\$(EXEQC).exe: qconvex.obj $(OBJS1) $(OBJS2) $(OBJS3)
	@echo qconvex.obj > $(TMPFILE)
	@echo $(OBJS1) >> $(TMPFILE)
	@echo $(OBJS2) >> $(TMPFILE)
	@echo $(OBJS3) >> $(TMPFILE)
	$(LINKER) -e$@ $(CFLAGS) $(LFLAGS) @$(TMPFILE)

$(EXEQD):     ..\..\bin\$(EXEQD).exe
	@echo Made ..\..\bin\$(EXEQD).exe

qdelaun.obj: ..\qdelaunay\qdelaun.c
..\..\bin\$(EXEQD).exe: qdelaun.obj $(OBJS1) $(OBJS2) $(OBJS3)
	@echo qdelaun.obj > $(TMPFILE)
	@echo $(OBJS1) >> $(TMPFILE)
	@echo $(OBJS2) >> $(TMPFILE)
	@echo $(OBJS3) >> $(TMPFILE)
	$(LINKER) -e$@ $(CFLAGS) $(LFLAGS) @$(TMPFILE)

$(EXEQV):     ..\..\bin\$(EXEQV).exe
	@echo Made ..\..\bin\$(EXEQV).exe

qvoronoi.obj: ..\qvoronoi\qvoronoi.c
..\..\bin\$(EXEQV).exe: qvoronoi.obj $(OBJS1) $(OBJS2) $(OBJS3)
	@echo qvoronoi.obj > $(TMPFILE)
	@echo $(OBJS1) >> $(TMPFILE)
	@echo $(OBJS2) >> $(TMPFILE)
	@echo $(OBJS3) >> $(TMPFILE)
	$(LINKER) -e$@ $(CFLAGS) $(LFLAGS) @$(TMPFILE)

$(EXEQF):     ..\..\bin\$(EXEQF).exe
	@echo Made ..\..\bin\$(EXEQF).exe

qhalf.obj: ..\qhalf\qhalf.c
..\..\bin\$(EXEQF).exe:  qhalf.obj $(OBJS1) $(OBJS2) $(OBJS3)
	@echo qhalf.obj > $(TMPFILE)
	@echo $(OBJS1) >> $(TMPFILE)
	@echo $(OBJS2) >> $(TMPFILE)
	@echo $(OBJS3) >> $(TMPFILE)
	$(LINKER) -e$@ $(CFLAGS) $(LFLAGS) @$(TMPFILE)

$(EXEEG):     ..\..\bin\$(EXEEG).exe
	@echo Made ..\..\bin\$(EXEEG).exe

user_eg.obj: ..\user_eg\user_eg.c
..\..\bin\$(EXEEG).exe: user_eg.obj $(OBJS1) $(OBJS2) $(OBJS3)
	@echo user_eg.obj > $(TMPFILE)
	@echo $(OBJS1) >> $(TMPFILE)
	@echo $(OBJS2) >> $(TMPFILE)
	@echo $(OBJS3) >> $(TMPFILE)
	$(LINKER) -e$@ $(CFLAGS) $(LFLAGS) @$(TMPFILE)

$(EXEEG2):     ..\..\bin\$(EXEEG2).exe
	@echo Made ..\..\bin\$(EXEEG2).exe

user_eg2.obj: ..\user_eg2\user_eg2.c
..\..\bin\$(EXEEG2).exe: user_eg2.obj $(OBJS1) $(OBJS2) $(OBJS3)
	@echo user_eg2.obj > $(TMPFILE)
	@echo $(OBJS1) >> $(TMPFILE)
	@echo $(OBJS2) >> $(TMPFILE)
	@echo $(OBJS3) >> $(TMPFILE)
	$(LINKER) -e$@ $(CFLAGS) $(LFLAGS) @$(TMPFILE)

$(EXERB):     ..\..\bin\$(EXERB).exe
	@echo Made ..\..\bin\$(EXERB).exe

rbox.obj: ..\rbox\rbox.c 
..\..\bin\$(EXERB).exe: rbox.obj $(OBJS4)
	@echo rbox.obj > $(TMPFILE)
	@echo $(OBJS4) >> $(TMPFILE)
	$(LINKER) -e$@ $(CFLAGS) $(LFLAGS) @$(TMPFILE)

# Test rbox and qhull

test:   
	@..\..\bin\rbox D4 > test.x
	@..\..\bin\qhull 
  ---------------------------------

  mem.c
    memory management routines for qhull

  This is a standalone program.

  To initialize memory:

    qh_meminit(stderr);
    qh_meminitbuffers(qh IStracing, qh_MEMalign, 7, qh_MEMbufsize,qh_MEMinitbuf);
    qh_memsize((int)sizeof(facetT));
    qh_memsize((int)sizeof(facetT));
    ...
    qh_memsetup();

  To free up all memory buffers:
    qh_memfreeshort(&curlong, &totlong);

  if qh_NOmem,
    malloc/free is used instead of mem.c

  notes:
    uses Quickfit algorithm (freelists for commonly allocated sizes)
    assumes small sizes for freelists (it discards the tail of memory buffers)

  see:
    qh-mem.htm and mem.h
    global.c (qh_initbuffers) for an example of using mem.c

  Copyright (c) 1993-2012 The Geometry Center.
  $Id: //main/2011/qhull/src/libqhull/mem.c#4 $$Change: 1464 $
  $DateTime: 2012/01/25 22:58:41 $$Author: bbarber $
*/

#include "mem.h"
#include 
#include 
#include 

#ifndef qhDEFlibqhull
typedef struct ridgeT ridgeT;
typedef struct facetT facetT;
#ifdef _MSC_VER  /* Microsoft Visual C++ -- warning level 4 */
#pragma warning( disable : 4127)  /* conditional expression is constant */
#pragma warning( disable : 4706)  /* assignment within conditional function */
#endif
void    qh_errexit(int exitcode, facetT *, ridgeT *);
void    qh_exit(int exitcode);
void    qh_fprintf(FILE *fp, int msgcode, const char *fmt, ... );
void    qh_free(void *mem);
void   *qh_malloc(size_t size);
#endif

/*============ -global data structure ==============
    see mem.h for definition
*/

qhmemT qhmem= {0,0,0,0,0,0,0,0,0,0,0,
               0,0,0,0,0,0,0,0,0,0,0,
               0,0,0,0,0,0,0};     /* remove "= {0}" if this causes a compiler error */

#ifndef qh_NOmem

/*============= internal functions ==============*/

static int qh_intcompare(const void *i, const void *j);

/*========== functions in alphabetical order ======== */

/*---------------------------------

  qh_intcompare( i, j )
    used by qsort and bsearch to compare two integers
*/
static int qh_intcompare(const void *i, const void *j) {
  return(*((const int *)i) - *((const int *)j));
} /* intcompare */


/*----------------------------------

  qh_memalloc( insize )
    returns object of insize bytes
    qhmem is the global memory structure

  returns:
    pointer to allocated memory
    errors if insufficient memory

  notes:
    use explicit type conversion to avoid type warnings on some compilers
    actual object may be larger than insize
    use qh_memalloc_() for inline code for quick allocations
    logs allocations if 'T5'

  design:
    if size < qhmem.LASTsize
      if qhmem.freelists[size] non-empty
        return first object on freelist
      else
        round up request to size of qhmem.freelists[size]
        allocate new allocation buffer if necessary
        allocate object from allocation buffer
    else
      allocate object with qh_malloc() in user.c
*/
void *qh_memalloc(int insize) {
  void **freelistp, *newbuffer;
  int idx, size, n;
  int outsize, bufsize;
  void *object;

  if (insize<0) {
      qh_fprintf(qhmem.ferr, 6235, "qhull error (qh_memalloc): negative request size (%d).  Did int overflow due to high-D?\n", insize); /* WARN64 */
      qh_errexit(qhmem_ERRmem, NULL, NULL);
  }
  if (insize>=0 && insize <= qhmem.LASTsize) {
    idx= qhmem.indextable[insize];
    outsize= qhmem.sizetable[idx];
    qhmem.totshort += outsize;
    freelistp= qhmem.freelists+idx;
    if ((object= *freelistp)) {
      qhmem.cntquick++;
      qhmem.totfree -= outsize;
      *freelistp= *((void **)*freelistp);  /* replace freelist with next object */
#ifdef qh_TRACEshort
      n= qhmem.cntshort+qhmem.cntquick+qhmem.freeshort;
      if (qhmem.IStracing >= 5)
          qh_fprintf(qhmem.ferr, 8141, "qh_mem %p n %8d alloc quick: %d bytes (tot %d cnt %d)\n", object, n, outsize, qhmem.totshort, qhmem.cntshort+qhmem.cntquick-qhmem.freeshort);
#endif
      return(object);
    }else {
      qhmem.cntshort++;
      if (outsize > qhmem .freesize) {
        qhmem .totdropped += qhmem .freesize;
        if (!qhmem.curbuffer)
          bufsize= qhmem.BUFinit;
        else
          bufsize= qhmem.BUFsize;
        if (!(newbuffer= qh_malloc((size_t)bufsize))) {
          qh_fprintf(qhmem.ferr, 6080, "qhull error (qh_memalloc): insufficient memory to allocate short memory buffer (%d bytes)\n", bufsize);
          qh_errexit(qhmem_ERRmem, NULL, NULL);
        }
        *((void **)newbuffer)= qhmem.curbuffer;  /* prepend newbuffer to curbuffer
                                                    list */
        qhmem.curbuffer= newbuffer;
        size= (sizeof(void **) + qhmem.ALIGNmask) & ~qhmem.ALIGNmask;
        qhmem.freemem= (void *)((char *)newbuffer+size);
        qhmem.freesize= bufsize - size;
        qhmem.totbuffer += bufsize - size; /* easier to check */
        /* Periodically test totbuffer.  It matches at beginning and exit of every call */
        n = qhmem.totshort + qhmem.totfree + qhmem.totdropped + qhmem.freesize - outsize;
        if (qhmem.totbuffer != n) {
            qh_fprintf(qhmem.ferr, 6212, "qh_memalloc internal error: short totbuffer %d != totshort+totfree... %d\n", qhmem.totbuffer, n);
            qh_errexit(qhmem_ERRmem, NULL, NULL);
        }
      }
      object= qhmem.freemem;
      qhmem.freemem= (void *)((char *)qhmem.freemem + outsize);
      qhmem.freesize -= outsize;
      qhmem.totunused += outsize - insize;
#ifdef qh_TRACEshort
      n= qhmem.cntshort+qhmem.cntquick+qhmem.freeshort;
      if (qhmem.IStracing >= 5)
          qh_fprintf(qhmem.ferr, 8140, "qh_mem %p n %8d alloc short: %d bytes (tot %d cnt %d)\n", object, n, outsize, qhmem.totshort, qhmem.cntshort+qhmem.cntquick-qhmem.freeshort);
#endif
      return object;
    }
  }else {                     /* long allocation */
    if (!qhmem.indextable) {
      qh_fprintf(qhmem.ferr, 6081, "qhull internal error (qh_memalloc): qhmem has not been initialized.\n");
      qh_errexit(qhmem_ERRqhull, NULL, NULL);
    }
    outsize= insize;
    qhmem .cntlong++;
    qhmem .totlong += outsize;
    if (qhmem.maxlong < qhmem.totlong)
      qhmem.maxlong= qhmem.totlong;
    if (!(object= qh_malloc((size_t)outsize))) {
      qh_fprintf(qhmem.ferr, 6082, "qhull error (qh_memalloc): insufficient memory to allocate %d bytes\n", outsize);
      qh_errexit(qhmem_ERRmem, NULL, NULL);
    }
    if (qhmem.IStracing >= 5)
      qh_fprintf(qhmem.ferr, 8057, "qh_mem %p n %8d alloc long: %d bytes (tot %d cnt %d)\n", object, qhmem.cntlong+qhmem.freelong, outsize, qhmem.totlong, qhmem.cntlong-qhmem.freelong);
  }
  return(object);
} /* memalloc */


/*----------------------------------

  qh_memfree( object, insize )
    free up an object of size bytes
    size is insize from qh_memalloc

  notes:
    object may be NULL
    type checking warns if using (void **)object
    use qh_memfree_() for quick free's of small objects

  design:
    if size <= qhmem.LASTsize
      append object to corresponding freelist
    else
      call qh_free(object)
*/
void qh_memfree(void *object, int insize) {
  void **freelistp;
  int idx, outsize;

  if (!object)
    return;
  if (insize <= qhmem.LASTsize) {
    qhmem .freeshort++;
    idx= qhmem.indextable[insize];
    outsize= qhmem.sizetable[idx];
    qhmem .totfree += outsize;
    qhmem .totshort -= outsize;
    freelistp= qhmem.freelists + idx;
    *((void **)object)= *freelistp;
    *freelistp= object;
#ifdef qh_TRACEshort
    idx= qhmem.cntshort+qhmem.cntquick+qhmem.freeshort;
    if (qhmem.IStracing >= 5)
        qh_fprintf(qhmem.ferr, 8142, "qh_mem %p n %8d free short: %d bytes (tot %d cnt %d)\n", object, idx, outsize, qhmem.totshort, qhmem.cntshort+qhmem.cntquick-qhmem.freeshort);
#endif
  }else {
    qhmem .freelong++;
    qhmem .totlong -= insize;
    qh_free(object);
    if (qhmem.IStracing >= 5)
      qh_fprintf(qhmem.ferr, 8058, "qh_mem %p n %8d free long: %d bytes (tot %d cnt %d)\n", object, qhmem.cntlong+qhmem.freelong, insize, qhmem.totlong, qhmem.cntlong-qhmem.freelong);
  }
} /* memfree */


/*---------------------------------

  qh_memfreeshort( curlong, totlong )
    frees up all short and qhmem memory allocations

  returns:
    number and size of current long allocations

  see:
    qh_freeqhull(allMem)
    qh_memtotal(curlong, totlong, curshort, totshort, maxlong, totbuffer);
*/
void qh_memfreeshort(int *curlong, int *totlong) {
  void *buffer, *nextbuffer;
  FILE *ferr;

  *curlong= qhmem .cntlong - qhmem .freelong;
  *totlong= qhmem .totlong;
  for (buffer= qhmem.curbuffer; buffer; buffer= nextbuffer) {
    nextbuffer= *((void **) buffer);
    qh_free(buffer);
  }
  qhmem.curbuffer= NULL;
  if (qhmem .LASTsize) {
    qh_free(qhmem .indextable);
    qh_free(qhmem .freelists);
    qh_free(qhmem .sizetable);
  }
  ferr= qhmem.ferr;
  memset((char *)&qhmem, 0, sizeof(qhmem));  /* every field is 0, FALSE, NULL */
  qhmem.ferr= ferr;
} /* memfreeshort */


/*----------------------------------

  qh_meminit( ferr )
    initialize qhmem and test sizeof( void*)
*/
void qh_meminit(FILE *ferr) {

  memset((char *)&qhmem, 0, sizeof(qhmem));  /* every field is 0, FALSE, NULL */
  qhmem.ferr= ferr;
  if (sizeof(void*) < sizeof(int)) {
    qh_fprintf(ferr, 6083, "qhull internal error (qh_meminit): sizeof(void*) %d < sizeof(int) %d.  qset.c will not work\n", (int)sizeof(void*), (int)sizeof(int));
    qh_exit(qhmem_ERRqhull);  /* can not use qh_errexit() */
  }
  if (sizeof(void*) > sizeof(ptr_intT)) {
      qh_fprintf(ferr, 6084, "qhull internal error (qh_meminit): sizeof(void*) %d > sizeof(ptr_intT) %d. Change ptr_intT in mem.h to 'long long'\n", (int)sizeof(void*), (int)sizeof(ptr_intT));
      qh_exit(qhmem_ERRqhull);  /* can not use qh_errexit() */
  }
} /* meminit */

/*---------------------------------

  qh_meminitbuffers( tracelevel, alignment, numsizes, bufsize, bufinit )
    initialize qhmem
    if tracelevel >= 5, trace memory allocations
    alignment= desired address alignment for memory allocations
    numsizes= number of freelists
    bufsize=  size of additional memory buffers for short allocations
    bufinit=  size of initial memory buffer for short allocations
*/
void qh_meminitbuffers(int tracelevel, int alignment, int numsizes, int bufsize, int bufinit) {

  qhmem.IStracing= tracelevel;
  qhmem.NUMsizes= numsizes;
  qhmem.BUFsize= bufsize;
  qhmem.BUFinit= bufinit;
  qhmem.ALIGNmask= alignment-1;
  if (qhmem.ALIGNmask & ~qhmem.ALIGNmask) {
    qh_fprintf(qhmem.ferr, 6085, "qhull internal error (qh_meminit): memory alignment %d is not a power of 2\n", alignment);
    qh_errexit(qhmem_ERRqhull, NULL, NULL);
  }
  qhmem.sizetable= (int *) calloc((size_t)numsizes, sizeof(int));
  qhmem.freelists= (void **) calloc((size_t)numsizes, sizeof(void *));
  if (!qhmem.sizetable || !qhmem.freelists) {
    qh_fprintf(qhmem.ferr, 6086, "qhull error (qh_meminit): insufficient memory\n");
    qh_errexit(qhmem_ERRmem, NULL, NULL);
  }
  if (qhmem.IStracing >= 1)
    qh_fprintf(qhmem.ferr, 8059, "qh_meminitbuffers: memory initialized with alignment %d\n", alignment);
} /* meminitbuffers */

/*---------------------------------

  qh_memsetup()
    set up memory after running memsize()
*/
void qh_memsetup(void) {
  int k,i;

  qsort(qhmem.sizetable, (size_t)qhmem.TABLEsize, sizeof(int), qh_intcompare);
  qhmem.LASTsize= qhmem.sizetable[qhmem.TABLEsize-1];
  if (qhmem .LASTsize >= qhmem .BUFsize || qhmem.LASTsize >= qhmem .BUFinit) {
    qh_fprintf(qhmem.ferr, 6087, "qhull error (qh_memsetup): largest mem size %d is >= buffer size %d or initial buffer size %d\n",
            qhmem .LASTsize, qhmem .BUFsize, qhmem .BUFinit);
    qh_errexit(qhmem_ERRmem, NULL, NULL);
  }
  if (!(qhmem.indextable= (int *)qh_malloc((qhmem.LASTsize+1) * sizeof(int)))) {
    qh_fprintf(qhmem.ferr, 6088, "qhull error (qh_memsetup): insufficient memory\n");
    qh_errexit(qhmem_ERRmem, NULL, NULL);
  }
  for (k=qhmem.LASTsize+1; k--; )
    qhmem.indextable[k]= k;
  i= 0;
  for (k=0; k <= qhmem.LASTsize; k++) {
    if (qhmem.indextable[k] <= qhmem.sizetable[i])
      qhmem.indextable[k]= i;
    else
      qhmem.indextable[k]= ++i;
  }
} /* memsetup */

/*---------------------------------

  qh_memsize( size )
    define a free list for this size
*/
void qh_memsize(int size) {
  int k;

  if (qhmem .LASTsize) {
    qh_fprintf(qhmem.ferr, 6089, "qhull error (qh_memsize): called after qhmem_setup\n");
    qh_errexit(qhmem_ERRqhull, NULL, NULL);
  }
  size= (size + qhmem.ALIGNmask) & ~qhmem.ALIGNmask;
  for (k=qhmem.TABLEsize; k--; ) {
    if (qhmem.sizetable[k] == size)
      return;
  }
  if (qhmem.TABLEsize < qhmem.NUMsizes)
    qhmem.sizetable[qhmem.TABLEsize++]= size;
  else
    qh_fprintf(qhmem.ferr, 7060, "qhull warning (memsize): free list table has room for only %d sizes\n", qhmem.NUMsizes);
} /* memsize */


/*---------------------------------

  qh_memstatistics( fp )
    print out memory statistics

    Verifies that qhmem.totfree == sum of freelists
*/
void qh_memstatistics(FILE *fp) {
  int i, count, totfree= 0;
  void *object;

  for (i=0; i < qhmem.TABLEsize; i++) {
    count=0;
    for (object= qhmem .freelists[i]; object; object= *((void **)object))
      count++;
    totfree += qhmem.sizetable[i] * count;
  }
  if (totfree != qhmem .totfree) {
      qh_fprintf(qhmem.ferr, 6211, "qh_memstatistics internal error: totfree %d not equal to freelist total %d\n", qhmem.totfree, totfree);
      qh_errexit(qhmem_ERRqhull, NULL, NULL);
  }
  qh_fprintf(fp, 9278, "\nmemory statistics:\n\
%7d quick allocations\n\
%7d short allocations\n\
%7d long allocations\n\
%7d short frees\n\
%7d long frees\n\
%7d bytes of short memory in use\n\
%7d bytes of short memory in freelists\n\
%7d bytes of dropped short memory\n\
%7d bytes of unused short memory (estimated)\n\
%7d bytes of long memory allocated (max, except for input)\n\
%7d bytes of long memory in use (in %d pieces)\n\
%7d bytes of short memory buffers (minus links)\n\
%7d bytes per short memory buffer (initially %d bytes)\n",
           qhmem .cntquick, qhmem .cntshort, qhmem .cntlong,
           qhmem .freeshort, qhmem .freelong,
           qhmem .totshort, qhmem .totfree,
           qhmem .totdropped + qhmem .freesize, qhmem .totunused,
           qhmem .maxlong, qhmem .totlong, qhmem .cntlong - qhmem .freelong,
           qhmem .totbuffer, qhmem .BUFsize, qhmem .BUFinit);
  if (qhmem.cntlarger) {
    qh_fprintf(fp, 9279, "%7d calls to qh_setlarger\n%7.2g     average copy size\n",
           qhmem.cntlarger, ((float)qhmem.totlarger)/(float)qhmem.cntlarger);
    qh_fprintf(fp, 9280, "  freelists(bytes->count):");
  }
  for (i=0; i < qhmem.TABLEsize; i++) {
    count=0;
    for (object= qhmem .freelists[i]; object; object= *((void **)object))
      count++;
    qh_fprintf(fp, 9281, " %d->%d", qhmem.sizetable[i], count);
  }
  qh_fprintf(fp, 9282, "\n\n");
} /* memstatistics */


/*---------------------------------

  qh_NOmem
    turn off quick-fit memory allocation

  notes:
    uses qh_malloc() and qh_free() instead
*/
#else /* qh_NOmem */

void *qh_memalloc(int insize) {
  void *object;

  if (!(object= qh_malloc((size_t)insize))) {
    qh_fprintf(qhmem.ferr, 6090, "qhull error (qh_memalloc): insufficient memory\n");
    qh_errexit(qhmem_ERRmem, NULL, NULL);
  }
  qhmem .cntlong++;
  qhmem .totlong += insize;
  if (qhmem.maxlong < qhmem.totlong)
      qhmem.maxlong= qhmem.totlong;
  if (qhmem.IStracing >= 5)
    qh_fprintf(qhmem.ferr, 8060, "qh_mem %p n %8d alloc long: %d bytes (tot %d cnt %d)\n", object, qhmem.cntlong+qhmem.freelong, insize, qhmem.totlong, qhmem.cntlong-qhmem.freelong);
  return object;
}

void qh_memfree(void *object, int insize) {

  if (!object)
    return;
  qh_free(object);
  qhmem .freelong++;
  qhmem .totlong -= insize;
  if (qhmem.IStracing >= 5)
    qh_fprintf(qhmem.ferr, 8061, "qh_mem %p n %8d free long: %d bytes (tot %d cnt %d)\n", object, qhmem.cntlong+qhmem.freelong, insize, qhmem.totlong, qhmem.cntlong-qhmem.freelong);
}

void qh_memfreeshort(int *curlong, int *totlong) {
  *totlong= qhmem .totlong;
  *curlong= qhmem .cntlong - qhmem .freelong;
  memset((char *)&qhmem, 0, sizeof(qhmem));  /* every field is 0, FALSE, NULL */
}

void qh_meminit(FILE *ferr) {

  memset((char *)&qhmem, 0, sizeof(qhmem));  /* every field is 0, FALSE, NULL */
  qhmem.ferr= ferr;
  if (sizeof(void*) < sizeof(int)) {
    qh_fprintf(ferr, 6091, "qhull internal error (qh_meminit): sizeof(void*) %d < sizeof(int) %d.  qset.c will not work\n", (int)sizeof(void*), (int)sizeof(int));
    qh_errexit(qhmem_ERRqhull, NULL, NULL);
  }
}

void qh_meminitbuffers(int tracelevel, int alignment, int numsizes, int bufsize, int bufinit) {

  qhmem.IStracing= tracelevel;
}

void qh_memsetup(void) {

}

void qh_memsize(int size) {

}

void qh_memstatistics(FILE *fp) {

  qh_fprintf(fp, 9409, "\nmemory statistics:\n\
%7d long allocations\n\
%7d long frees\n\
%7d bytes of long memory allocated (max, except for input)\n\
%7d bytes of long memory in use (in %d pieces)\n",
           qhmem .cntlong,
           qhmem .freelong,
           qhmem .maxlong, qhmem .totlong, qhmem .cntlong - qhmem .freelong);
}

#endif /* qh_NOmem */

/*---------------------------------

  qh_memtotal( totlong, curlong, totshort, curshort, maxlong, totbuffer )
    Return the total, allocated long and short memory

  returns:
    Returns the total current bytes of long and short allocations
    Returns the current count of long and short allocations
    Returns the maximum long memory and total short buffer (minus one link per buffer)
    Does not error (UsingLibQhull.cpp)
*/
void qh_memtotal(int *totlong, int *curlong, int *totshort, int *curshort, int *maxlong, int *totbuffer) {
    *totlong= qhmem .totlong;
    *curlong= qhmem .cntlong - qhmem .freelong;
    *totshort= qhmem .totshort;
    *curshort= qhmem .cntshort + qhmem .cntquick - qhmem .freeshort;
    *maxlong= qhmem .maxlong;
    *totbuffer= qhmem .totbuffer;
} /* memtotlong */

qhull-2012.1/src/libqhull/mem.h0000644000076400010400000002053111710144466017443 0ustar  bbarberAdministrators/*
  ---------------------------------

   mem.h
     prototypes for memory management functions

   see qh-mem.htm, mem.c and qset.h

   for error handling, writes message and calls
     qh_errexit(qhmem_ERRmem, NULL, NULL) if insufficient memory
       and
     qh_errexit(qhmem_ERRqhull, NULL, NULL) otherwise

   Copyright (c) 1993-2012 The Geometry Center.
   $Id: //main/2011/qhull/src/libqhull/mem.h#4 $$Change: 1464 $
   $DateTime: 2012/01/25 22:58:41 $$Author: bbarber $
*/

#ifndef qhDEFmem
#define qhDEFmem 1

#include 

/*---------------------------------

  qh_NOmem
    turn off quick-fit memory allocation

  notes:
    mem.c implements Quickfit memory allocation for about 20% time
    savings.  If it fails on your machine, try to locate the
    problem, and send the answer to qhull@qhull.org.  If this can
    not be done, define qh_NOmem to use malloc/free instead.

   #define qh_NOmem
*/

/*---------------------------------

qh_TRACEshort
Trace short and quick memory allocations at T5

*/
#define qh_TRACEshort

/*-------------------------------------------
    to avoid bus errors, memory allocation must consider alignment requirements.
    malloc() automatically takes care of alignment.   Since mem.c manages
    its own memory, we need to explicitly specify alignment in
    qh_meminitbuffers().

    A safe choice is sizeof(double).  sizeof(float) may be used if doubles
    do not occur in data structures and pointers are the same size.  Be careful
    of machines (e.g., DEC Alpha) with large pointers.  If gcc is available,
    use __alignof__(double) or fmax_(__alignof__(float), __alignof__(void *)).

   see qh_MEMalign in user.h for qhull's alignment
*/

#define qhmem_ERRmem 4    /* matches qh_ERRmem in libqhull.h */
#define qhmem_ERRqhull 5  /* matches qh_ERRqhull in libqhull.h */

/*----------------------------------

  ptr_intT
    for casting a void * to an integer-type that holds a pointer
    Used for integer expressions (e.g., computing qh_gethash() in poly.c)

  notes:
    WARN64 -- these notes indicate 64-bit issues
    On 64-bit machines, a pointer may be larger than an 'int'.
    qh_meminit()/mem.c checks that 'ptr_intT' holds a 'void*'
    ptr_intT is typically a signed value, but not necessarily so
    size_t is typically unsigned, but should match the parameter type
    Qhull uses int instead of size_t except for system calls such as malloc, qsort, qh_malloc, etc.
    This matches Qt convention and is easier to work with.  
*/
#if _MSC_VER && defined(_WIN64)
typedef long long ptr_intT;
#else
typedef long ptr_intT;
#endif

/*----------------------------------

  qhmemT
    global memory structure for mem.c

 notes:
   users should ignore qhmem except for writing extensions
   qhmem is allocated in mem.c

   qhmem could be swapable like qh and qhstat, but then
   multiple qh's and qhmem's would need to keep in synch.
   A swapable qhmem would also waste memory buffers.  As long
   as memory operations are atomic, there is no problem with
   multiple qh structures being active at the same time.
   If you need separate address spaces, you can swap the
   contents of qhmem.
*/
typedef struct qhmemT qhmemT;
extern qhmemT qhmem;

#ifndef DEFsetT
#define DEFsetT 1
typedef struct setT setT;          /* defined in qset.h */
#endif

/* Update qhmem in mem.c if add or remove fields */
struct qhmemT {               /* global memory management variables */
  int      BUFsize;           /* size of memory allocation buffer */
  int      BUFinit;           /* initial size of memory allocation buffer */
  int      TABLEsize;         /* actual number of sizes in free list table */
  int      NUMsizes;          /* maximum number of sizes in free list table */
  int      LASTsize;          /* last size in free list table */
  int      ALIGNmask;         /* worst-case alignment, must be 2^n-1 */
  void   **freelists;          /* free list table, linked by offset 0 */
  int     *sizetable;         /* size of each freelist */
  int     *indextable;        /* size->index table */
  void    *curbuffer;         /* current buffer, linked by offset 0 */
  void    *freemem;           /*   free memory in curbuffer */
  int      freesize;          /*   size of freemem in bytes */
  setT    *tempstack;         /* stack of temporary memory, managed by users */
  FILE    *ferr;              /* file for reporting errors, only user is qh_fprintf() */
  int      IStracing;         /* =5 if tracing memory allocations */
  int      cntquick;          /* count of quick allocations */
                              /* Note: removing statistics doesn't effect speed */
  int      cntshort;          /* count of short allocations */
  int      cntlong;           /* count of long allocations */
  int      freeshort;         /* count of short memfrees */
  int      freelong;          /* count of long memfrees */
  int      totbuffer;         /* total short memory buffers minus buffer links */
  int      totdropped;        /* total dropped memory at end of short memory buffers (e.g., freesize) */
  int      totfree;           /* total size of free, short memory on freelists */
  int      totlong;           /* total size of long memory in use */
  int      maxlong;           /*   maximum totlong */
  int      totshort;          /* total size of short memory in use */
  int      totunused;         /* total unused short memory (estimated, short size - request size of first allocations) */
  int      cntlarger;         /* count of setlarger's */
  int      totlarger;         /* total copied by setlarger */
};


/*==================== -macros ====================*/

/*----------------------------------

  qh_memalloc_(insize, object, type)
    returns object of size bytes
        assumes size<=qhmem.LASTsize and void **freelistp is a temp
*/

#if defined qh_NOmem
#define qh_memalloc_(insize, freelistp, object, type) {\
  object= (type*)qh_memalloc(insize); }
#elif defined qh_TRACEshort
#define qh_memalloc_(insize, freelistp, object, type) {\
    freelistp= NULL; /* Avoid warnings */ \
    object= (type*)qh_memalloc(insize); }
#else /* !qh_NOmem */

#define qh_memalloc_(insize, freelistp, object, type) {\
  freelistp= qhmem.freelists + qhmem.indextable[insize];\
  if ((object= (type*)*freelistp)) {\
    qhmem.totshort += qhmem.sizetable[qhmem.indextable[insize]]; \
    qhmem.totfree -= qhmem.sizetable[qhmem.indextable[insize]]; \
    qhmem.cntquick++;  \
    *freelistp= *((void **)*freelistp);\
  }else object= (type*)qh_memalloc(insize);}
#endif

/*----------------------------------

  qh_memfree_(object, insize)
    free up an object

  notes:
    object may be NULL
    assumes size<=qhmem.LASTsize and void **freelistp is a temp
*/
#if defined qh_NOmem
#define qh_memfree_(object, insize, freelistp) {\
  qh_memfree(object, insize); }
#elif defined qh_TRACEshort
#define qh_memfree_(object, insize, freelistp) {\
    freelistp= NULL; /* Avoid warnings */ \
    qh_memfree(object, insize); }
#else /* !qh_NOmem */

#define qh_memfree_(object, insize, freelistp) {\
  if (object) { \
    qhmem .freeshort++;\
    freelistp= qhmem.freelists + qhmem.indextable[insize];\
    qhmem.totshort -= qhmem.sizetable[qhmem.indextable[insize]]; \
    qhmem.totfree += qhmem.sizetable[qhmem.indextable[insize]]; \
    *((void **)object)= *freelistp;\
    *freelistp= object;}}
#endif

/*=============== prototypes in alphabetical order ============*/

void *qh_memalloc(int insize);
void qh_memfree(void *object, int insize);
void qh_memfreeshort(int *curlong, int *totlong);
void qh_meminit(FILE *ferr);
void qh_meminitbuffers(int tracelevel, int alignment, int numsizes,
                        int bufsize, int bufinit);
void qh_memsetup(void);
void qh_memsize(int size);
void qh_memstatistics(FILE *fp);
void qh_memtotal(int *totlong, int *curlong, int *totshort, int *curshort, int *maxlong, int *totbuffer);

#endif /* qhDEFmem */
qhull-2012.1/src/libqhull/merge.c0000644000076400010400000035553211720036003017757 0ustar  bbarberAdministrators/*
  ---------------------------------

   merge.c
   merges non-convex facets

   see qh-merge.htm and merge.h

   other modules call qh_premerge() and qh_postmerge()

   the user may call qh_postmerge() to perform additional merges.

   To remove deleted facets and vertices (qhull() in libqhull.c):
     qh_partitionvisible(!qh_ALL, &numoutside);  // visible_list, newfacet_list
     qh_deletevisible();         // qh.visible_list
     qh_resetlists(False, qh_RESETvisible);       // qh.visible_list newvertex_list newfacet_list

   assumes qh.CENTERtype= centrum

   merges occur in qh_mergefacet and in qh_mergecycle
   vertex->neighbors not set until the first merge occurs

   Copyright (c) 1993-2012 C.B. Barber.
   $Id: //main/2011/qhull/src/libqhull/merge.c#4 $$Change: 1490 $
   $DateTime: 2012/02/19 20:27:01 $$Author: bbarber $
*/

#include "qhull_a.h"

#ifndef qh_NOmerge

/*===== functions(alphabetical after premerge and postmerge) ======*/

/*---------------------------------

  qh_premerge( apex, maxcentrum )
    pre-merge nonconvex facets in qh.newfacet_list for apex
    maxcentrum defines coplanar and concave (qh_test_appendmerge)

  returns:
    deleted facets added to qh.visible_list with facet->visible set

  notes:
    uses globals, qh.MERGEexact, qh.PREmerge

  design:
    mark duplicate ridges in qh.newfacet_list
    merge facet cycles in qh.newfacet_list
    merge duplicate ridges and concave facets in qh.newfacet_list
    check merged facet cycles for degenerate and redundant facets
    merge degenerate and redundant facets
    collect coplanar and concave facets
    merge concave, coplanar, degenerate, and redundant facets
*/
void qh_premerge(vertexT *apex, realT maxcentrum, realT maxangle) {
  boolT othermerge= False;
  facetT *newfacet;

  if (qh ZEROcentrum && qh_checkzero(!qh_ALL))
    return;
  trace2((qh ferr, 2008, "qh_premerge: premerge centrum %2.2g angle %2.2g for apex v%d facetlist f%d\n",
            maxcentrum, maxangle, apex->id, getid_(qh newfacet_list)));
  if (qh IStracing >= 4 && qh num_facets < 50)
    qh_printlists();
  qh centrum_radius= maxcentrum;
  qh cos_max= maxangle;
  qh degen_mergeset= qh_settemp(qh TEMPsize);
  qh facet_mergeset= qh_settemp(qh TEMPsize);
  if (qh hull_dim >=3) {
    qh_mark_dupridges(qh newfacet_list); /* facet_mergeset */
    qh_mergecycle_all(qh newfacet_list, &othermerge);
    qh_forcedmerges(&othermerge /* qh facet_mergeset */);
    FORALLnew_facets {  /* test samecycle merges */
      if (!newfacet->simplicial && !newfacet->mergeridge)
        qh_degen_redundant_neighbors(newfacet, NULL);
    }
    if (qh_merge_degenredundant())
      othermerge= True;
  }else /* qh hull_dim == 2 */
    qh_mergecycle_all(qh newfacet_list, &othermerge);
  qh_flippedmerges(qh newfacet_list, &othermerge);
  if (!qh MERGEexact || zzval_(Ztotmerge)) {
    zinc_(Zpremergetot);
    qh POSTmerging= False;
    qh_getmergeset_initial(qh newfacet_list);
    qh_all_merges(othermerge, False);
  }
  qh_settempfree(&qh facet_mergeset);
  qh_settempfree(&qh degen_mergeset);
} /* premerge */

/*---------------------------------

  qh_postmerge( reason, maxcentrum, maxangle, vneighbors )
    post-merge nonconvex facets as defined by maxcentrum and maxangle
    'reason' is for reporting progress
    if vneighbors,
      calls qh_test_vneighbors at end of qh_all_merge
    if firstmerge,
      calls qh_reducevertices before qh_getmergeset

  returns:
    if first call (qh.visible_list != qh.facet_list),
      builds qh.facet_newlist, qh.newvertex_list
    deleted facets added to qh.visible_list with facet->visible
    qh.visible_list == qh.facet_list

  notes:


  design:
    if first call
      set qh.visible_list and qh.newfacet_list to qh.facet_list
      add all facets to qh.newfacet_list
      mark non-simplicial facets, facet->newmerge
      set qh.newvertext_list to qh.vertex_list
      add all vertices to qh.newvertex_list
      if a pre-merge occured
        set vertex->delridge {will retest the ridge}
        if qh.MERGEexact
          call qh_reducevertices()
      if no pre-merging
        merge flipped facets
    determine non-convex facets
    merge all non-convex facets
*/
void qh_postmerge(const char *reason, realT maxcentrum, realT maxangle,
                      boolT vneighbors) {
  facetT *newfacet;
  boolT othermerges= False;
  vertexT *vertex;

  if (qh REPORTfreq || qh IStracing) {
    qh_buildtracing(NULL, NULL);
    qh_printsummary(qh ferr);
    if (qh PRINTstatistics)
      qh_printallstatistics(qh ferr, "reason");
    qh_fprintf(qh ferr, 8062, "\n%s with 'C%.2g' and 'A%.2g'\n",
        reason, maxcentrum, maxangle);
  }
  trace2((qh ferr, 2009, "qh_postmerge: postmerge.  test vneighbors? %d\n",
            vneighbors));
  qh centrum_radius= maxcentrum;
  qh cos_max= maxangle;
  qh POSTmerging= True;
  qh degen_mergeset= qh_settemp(qh TEMPsize);
  qh facet_mergeset= qh_settemp(qh TEMPsize);
  if (qh visible_list != qh facet_list) {  /* first call */
    qh NEWfacets= True;
    qh visible_list= qh newfacet_list= qh facet_list;
    FORALLnew_facets {
      newfacet->newfacet= True;
       if (!newfacet->simplicial)
        newfacet->newmerge= True;
     zinc_(Zpostfacets);
    }
    qh newvertex_list= qh vertex_list;
    FORALLvertices
      vertex->newlist= True;
    if (qh VERTEXneighbors) { /* a merge has occurred */
      FORALLvertices
        vertex->delridge= True; /* test for redundant, needed? */
      if (qh MERGEexact) {
        if (qh hull_dim <= qh_DIMreduceBuild)
          qh_reducevertices(); /* was skipped during pre-merging */
      }
    }
    if (!qh PREmerge && !qh MERGEexact)
      qh_flippedmerges(qh newfacet_list, &othermerges);
  }
  qh_getmergeset_initial(qh newfacet_list);
  qh_all_merges(False, vneighbors);
  qh_settempfree(&qh facet_mergeset);
  qh_settempfree(&qh degen_mergeset);
} /* post_merge */

/*---------------------------------

  qh_all_merges( othermerge, vneighbors )
    merge all non-convex facets

    set othermerge if already merged facets (for qh_reducevertices)
    if vneighbors
      tests vertex neighbors for convexity at end
    qh.facet_mergeset lists the non-convex ridges in qh_newfacet_list
    qh.degen_mergeset is defined
    if qh.MERGEexact && !qh.POSTmerging,
      does not merge coplanar facets

  returns:
    deleted facets added to qh.visible_list with facet->visible
    deleted vertices added qh.delvertex_list with vertex->delvertex

  notes:
    unless !qh.MERGEindependent,
      merges facets in independent sets
    uses qh.newfacet_list as argument since merges call qh_removefacet()

  design:
    while merges occur
      for each merge in qh.facet_mergeset
        unless one of the facets was already merged in this pass
          merge the facets
        test merged facets for additional merges
        add merges to qh.facet_mergeset
      if vertices record neighboring facets
        rename redundant vertices
          update qh.facet_mergeset
    if vneighbors ??
      tests vertex neighbors for convexity at end
*/
void qh_all_merges(boolT othermerge, boolT vneighbors) {
  facetT *facet1, *facet2;
  mergeT *merge;
  boolT wasmerge= True, isreduce;
  void **freelistp;  /* used !qh_NOmem */
  vertexT *vertex;
  mergeType mergetype;
  int numcoplanar=0, numconcave=0, numdegenredun= 0, numnewmerges= 0;

  trace2((qh ferr, 2010, "qh_all_merges: starting to merge facets beginning from f%d\n",
            getid_(qh newfacet_list)));
  while (True) {
    wasmerge= False;
    while (qh_setsize(qh facet_mergeset)) {
      while ((merge= (mergeT*)qh_setdellast(qh facet_mergeset))) {
        facet1= merge->facet1;
        facet2= merge->facet2;
        mergetype= merge->type;
        qh_memfree_(merge, (int)sizeof(mergeT), freelistp);
        if (facet1->visible || facet2->visible) /*deleted facet*/
          continue;
        if ((facet1->newfacet && !facet1->tested)
                || (facet2->newfacet && !facet2->tested)) {
          if (qh MERGEindependent && mergetype <= MRGanglecoplanar)
            continue;      /* perform independent sets of merges */
        }
        qh_merge_nonconvex(facet1, facet2, mergetype);
        numdegenredun += qh_merge_degenredundant();
        numnewmerges++;
        wasmerge= True;
        if (mergetype == MRGconcave)
          numconcave++;
        else /* MRGcoplanar or MRGanglecoplanar */
          numcoplanar++;
      } /* while setdellast */
      if (qh POSTmerging && qh hull_dim <= qh_DIMreduceBuild
      && numnewmerges > qh_MAXnewmerges) {
        numnewmerges= 0;
        qh_reducevertices();  /* otherwise large post merges too slow */
      }
      qh_getmergeset(qh newfacet_list); /* facet_mergeset */
    } /* while mergeset */
    if (qh VERTEXneighbors) {
      isreduce= False;
      if (qh hull_dim >=4 && qh POSTmerging) {
        FORALLvertices
          vertex->delridge= True;
        isreduce= True;
      }
      if ((wasmerge || othermerge) && (!qh MERGEexact || qh POSTmerging)
          && qh hull_dim <= qh_DIMreduceBuild) {
        othermerge= False;
        isreduce= True;
      }
      if (isreduce) {
        if (qh_reducevertices()) {
          qh_getmergeset(qh newfacet_list); /* facet_mergeset */
          continue;
        }
      }
    }
    if (vneighbors && qh_test_vneighbors(/* qh newfacet_list */))
      continue;
    break;
  } /* while (True) */
  if (qh CHECKfrequently && !qh MERGEexact) {
    qh old_randomdist= qh RANDOMdist;
    qh RANDOMdist= False;
    qh_checkconvex(qh newfacet_list, qh_ALGORITHMfault);
    /* qh_checkconnect(); [this is slow and it changes the facet order] */
    qh RANDOMdist= qh old_randomdist;
  }
  trace1((qh ferr, 1009, "qh_all_merges: merged %d coplanar facets %d concave facets and %d degen or redundant facets.\n",
    numcoplanar, numconcave, numdegenredun));
  if (qh IStracing >= 4 && qh num_facets < 50)
    qh_printlists();
} /* all_merges */


/*---------------------------------

  qh_appendmergeset( facet, neighbor, mergetype, angle )
    appends an entry to qh.facet_mergeset or qh.degen_mergeset

    angle ignored if NULL or !qh.ANGLEmerge

  returns:
    merge appended to facet_mergeset or degen_mergeset
      sets ->degenerate or ->redundant if degen_mergeset

  see:
    qh_test_appendmerge()

  design:
    allocate merge entry
    if regular merge
      append to qh.facet_mergeset
    else if degenerate merge and qh.facet_mergeset is all degenerate
      append to qh.degen_mergeset
    else if degenerate merge
      prepend to qh.degen_mergeset
    else if redundant merge
      append to qh.degen_mergeset
*/
void qh_appendmergeset(facetT *facet, facetT *neighbor, mergeType mergetype, realT *angle) {
  mergeT *merge, *lastmerge;
  void **freelistp; /* used !qh_NOmem */

  if (facet->redundant)
    return;
  if (facet->degenerate && mergetype == MRGdegen)
    return;
  qh_memalloc_((int)sizeof(mergeT), freelistp, merge, mergeT);
  merge->facet1= facet;
  merge->facet2= neighbor;
  merge->type= mergetype;
  if (angle && qh ANGLEmerge)
    merge->angle= *angle;
  if (mergetype < MRGdegen)
    qh_setappend(&(qh facet_mergeset), merge);
  else if (mergetype == MRGdegen) {
    facet->degenerate= True;
    if (!(lastmerge= (mergeT*)qh_setlast(qh degen_mergeset))
    || lastmerge->type == MRGdegen)
      qh_setappend(&(qh degen_mergeset), merge);
    else
      qh_setaddnth(&(qh degen_mergeset), 0, merge);
  }else if (mergetype == MRGredundant) {
    facet->redundant= True;
    qh_setappend(&(qh degen_mergeset), merge);
  }else /* mergetype == MRGmirror */ {
    if (facet->redundant || neighbor->redundant) {
      qh_fprintf(qh ferr, 6092, "qhull error (qh_appendmergeset): facet f%d or f%d is already a mirrored facet\n",
           facet->id, neighbor->id);
      qh_errexit2 (qh_ERRqhull, facet, neighbor);
    }
    if (!qh_setequal(facet->vertices, neighbor->vertices)) {
      qh_fprintf(qh ferr, 6093, "qhull error (qh_appendmergeset): mirrored facets f%d and f%d do not have the same vertices\n",
           facet->id, neighbor->id);
      qh_errexit2 (qh_ERRqhull, facet, neighbor);
    }
    facet->redundant= True;
    neighbor->redundant= True;
    qh_setappend(&(qh degen_mergeset), merge);
  }
} /* appendmergeset */


/*---------------------------------

  qh_basevertices( samecycle )
    return temporary set of base vertices for samecycle
    samecycle is first facet in the cycle
    assumes apex is SETfirst_( samecycle->vertices )

  returns:
    vertices(settemp)
    all ->seen are cleared

  notes:
    uses qh_vertex_visit;

  design:
    for each facet in samecycle
      for each unseen vertex in facet->vertices
        append to result
*/
setT *qh_basevertices(facetT *samecycle) {
  facetT *same;
  vertexT *apex, *vertex, **vertexp;
  setT *vertices= qh_settemp(qh TEMPsize);

  apex= SETfirstt_(samecycle->vertices, vertexT);
  apex->visitid= ++qh vertex_visit;
  FORALLsame_cycle_(samecycle) {
    if (same->mergeridge)
      continue;
    FOREACHvertex_(same->vertices) {
      if (vertex->visitid != qh vertex_visit) {
        qh_setappend(&vertices, vertex);
        vertex->visitid= qh vertex_visit;
        vertex->seen= False;
      }
    }
  }
  trace4((qh ferr, 4019, "qh_basevertices: found %d vertices\n",
         qh_setsize(vertices)));
  return vertices;
} /* basevertices */

/*---------------------------------

  qh_checkconnect()
    check that new facets are connected
    new facets are on qh.newfacet_list

  notes:
    this is slow and it changes the order of the facets
    uses qh.visit_id

  design:
    move first new facet to end of qh.facet_list
    for all newly appended facets
      append unvisited neighbors to end of qh.facet_list
    for all new facets
      report error if unvisited
*/
void qh_checkconnect(void /* qh newfacet_list */) {
  facetT *facet, *newfacet, *errfacet= NULL, *neighbor, **neighborp;

  facet= qh newfacet_list;
  qh_removefacet(facet);
  qh_appendfacet(facet);
  facet->visitid= ++qh visit_id;
  FORALLfacet_(facet) {
    FOREACHneighbor_(facet) {
      if (neighbor->visitid != qh visit_id) {
        qh_removefacet(neighbor);
        qh_appendfacet(neighbor);
        neighbor->visitid= qh visit_id;
      }
    }
  }
  FORALLnew_facets {
    if (newfacet->visitid == qh visit_id)
      break;
    qh_fprintf(qh ferr, 6094, "qhull error: f%d is not attached to the new facets\n",
         newfacet->id);
    errfacet= newfacet;
  }
  if (errfacet)
    qh_errexit(qh_ERRqhull, errfacet, NULL);
} /* checkconnect */

/*---------------------------------

  qh_checkzero( testall )
    check that facets are clearly convex for qh.DISTround with qh.MERGEexact

    if testall,
      test all facets for qh.MERGEexact post-merging
    else
      test qh.newfacet_list

    if qh.MERGEexact,
      allows coplanar ridges
      skips convexity test while qh.ZEROall_ok

  returns:
    True if all facets !flipped, !dupridge, normal
         if all horizon facets are simplicial
         if all vertices are clearly below neighbor
         if all opposite vertices of horizon are below
    clears qh.ZEROall_ok if any problems or coplanar facets

  notes:
    uses qh.vertex_visit
    horizon facets may define multiple new facets

  design:
    for all facets in qh.newfacet_list or qh.facet_list
      check for flagged faults (flipped, etc.)
    for all facets in qh.newfacet_list or qh.facet_list
      for each neighbor of facet
        skip horizon facets for qh.newfacet_list
        test the opposite vertex
      if qh.newfacet_list
        test the other vertices in the facet's horizon facet
*/
boolT qh_checkzero(boolT testall) {
  facetT *facet, *neighbor, **neighborp;
  facetT *horizon, *facetlist;
  int neighbor_i;
  vertexT *vertex, **vertexp;
  realT dist;

  if (testall)
    facetlist= qh facet_list;
  else {
    facetlist= qh newfacet_list;
    FORALLfacet_(facetlist) {
      horizon= SETfirstt_(facet->neighbors, facetT);
      if (!horizon->simplicial)
        goto LABELproblem;
      if (facet->flipped || facet->dupridge || !facet->normal)
        goto LABELproblem;
    }
    if (qh MERGEexact && qh ZEROall_ok) {
      trace2((qh ferr, 2011, "qh_checkzero: skip convexity check until first pre-merge\n"));
      return True;
    }
  }
  FORALLfacet_(facetlist) {
    qh vertex_visit++;
    neighbor_i= 0;
    horizon= NULL;
    FOREACHneighbor_(facet) {
      if (!neighbor_i && !testall) {
        horizon= neighbor;
        neighbor_i++;
        continue; /* horizon facet tested in qh_findhorizon */
      }
      vertex= SETelemt_(facet->vertices, neighbor_i++, vertexT);
      vertex->visitid= qh vertex_visit;
      zzinc_(Zdistzero);
      qh_distplane(vertex->point, neighbor, &dist);
      if (dist >= -qh DISTround) {
        qh ZEROall_ok= False;
        if (!qh MERGEexact || testall || dist > qh DISTround)
          goto LABELnonconvex;
      }
    }
    if (!testall) {
      FOREACHvertex_(horizon->vertices) {
        if (vertex->visitid != qh vertex_visit) {
          zzinc_(Zdistzero);
          qh_distplane(vertex->point, facet, &dist);
          if (dist >= -qh DISTround) {
            qh ZEROall_ok= False;
            if (!qh MERGEexact || dist > qh DISTround)
              goto LABELnonconvex;
          }
          break;
        }
      }
    }
  }
  trace2((qh ferr, 2012, "qh_checkzero: testall %d, facets are %s\n", testall,
        (qh MERGEexact && !testall) ?
           "not concave, flipped, or duplicate ridged" : "clearly convex"));
  return True;

 LABELproblem:
  qh ZEROall_ok= False;
  trace2((qh ferr, 2013, "qh_checkzero: facet f%d needs pre-merging\n",
       facet->id));
  return False;

 LABELnonconvex:
  trace2((qh ferr, 2014, "qh_checkzero: facet f%d and f%d are not clearly convex.  v%d dist %.2g\n",
         facet->id, neighbor->id, vertex->id, dist));
  return False;
} /* checkzero */

/*---------------------------------

  qh_compareangle( angle1, angle2 )
    used by qsort() to order merges by angle
*/
int qh_compareangle(const void *p1, const void *p2) {
  const mergeT *a= *((mergeT *const*)p1), *b= *((mergeT *const*)p2);

  return((a->angle > b->angle) ? 1 : -1);
} /* compareangle */

/*---------------------------------

  qh_comparemerge( merge1, merge2 )
    used by qsort() to order merges
*/
int qh_comparemerge(const void *p1, const void *p2) {
  const mergeT *a= *((mergeT *const*)p1), *b= *((mergeT *const*)p2);

  return(a->type - b->type);
} /* comparemerge */

/*---------------------------------

  qh_comparevisit( vertex1, vertex2 )
    used by qsort() to order vertices by their visitid
*/
int qh_comparevisit(const void *p1, const void *p2) {
  const vertexT *a= *((vertexT *const*)p1), *b= *((vertexT *const*)p2);

  return(a->visitid - b->visitid);
} /* comparevisit */

/*---------------------------------

  qh_copynonconvex( atridge )
    set non-convex flag on other ridges (if any) between same neighbors

  notes:
    may be faster if use smaller ridge set

  design:
    for each ridge of atridge's top facet
      if ridge shares the same neighbor
        set nonconvex flag
*/
void qh_copynonconvex(ridgeT *atridge) {
  facetT *facet, *otherfacet;
  ridgeT *ridge, **ridgep;

  facet= atridge->top;
  otherfacet= atridge->bottom;
  FOREACHridge_(facet->ridges) {
    if (otherfacet == otherfacet_(ridge, facet) && ridge != atridge) {
      ridge->nonconvex= True;
      trace4((qh ferr, 4020, "qh_copynonconvex: moved nonconvex flag from r%d to r%d\n",
              atridge->id, ridge->id));
      break;
    }
  }
} /* copynonconvex */

/*---------------------------------

  qh_degen_redundant_facet( facet )
    check facet for degen. or redundancy

  notes:
    bumps vertex_visit
    called if a facet was redundant but no longer is (qh_merge_degenredundant)
    qh_appendmergeset() only appends first reference to facet (i.e., redundant)

  see:
    qh_degen_redundant_neighbors()

  design:
    test for redundant neighbor
    test for degenerate facet
*/
void qh_degen_redundant_facet(facetT *facet) {
  vertexT *vertex, **vertexp;
  facetT *neighbor, **neighborp;

  trace4((qh ferr, 4021, "qh_degen_redundant_facet: test facet f%d for degen/redundant\n",
          facet->id));
  FOREACHneighbor_(facet) {
    qh vertex_visit++;
    FOREACHvertex_(neighbor->vertices)
      vertex->visitid= qh vertex_visit;
    FOREACHvertex_(facet->vertices) {
      if (vertex->visitid != qh vertex_visit)
        break;
    }
    if (!vertex) {
      qh_appendmergeset(facet, neighbor, MRGredundant, NULL);
      trace2((qh ferr, 2015, "qh_degen_redundant_facet: f%d is contained in f%d.  merge\n", facet->id, neighbor->id));
      return;
    }
  }
  if (qh_setsize(facet->neighbors) < qh hull_dim) {
    qh_appendmergeset(facet, facet, MRGdegen, NULL);
    trace2((qh ferr, 2016, "qh_degen_redundant_neighbors: f%d is degenerate.\n", facet->id));
  }
} /* degen_redundant_facet */


/*---------------------------------

  qh_degen_redundant_neighbors( facet, delfacet,  )
    append degenerate and redundant neighbors to facet_mergeset
    if delfacet,
      only checks neighbors of both delfacet and facet
    also checks current facet for degeneracy

  notes:
    bumps vertex_visit
    called for each qh_mergefacet() and qh_mergecycle()
    merge and statistics occur in merge_nonconvex
    qh_appendmergeset() only appends first reference to facet (i.e., redundant)
      it appends redundant facets after degenerate ones

    a degenerate facet has fewer than hull_dim neighbors
    a redundant facet's vertices is a subset of its neighbor's vertices
    tests for redundant merges first (appendmergeset is nop for others)
    in a merge, only needs to test neighbors of merged facet

  see:
    qh_merge_degenredundant() and qh_degen_redundant_facet()

  design:
    test for degenerate facet
    test for redundant neighbor
    test for degenerate neighbor
*/
void qh_degen_redundant_neighbors(facetT *facet, facetT *delfacet) {
  vertexT *vertex, **vertexp;
  facetT *neighbor, **neighborp;
  int size;

  trace4((qh ferr, 4022, "qh_degen_redundant_neighbors: test neighbors of f%d with delfacet f%d\n",
          facet->id, getid_(delfacet)));
  if ((size= qh_setsize(facet->neighbors)) < qh hull_dim) {
    qh_appendmergeset(facet, facet, MRGdegen, NULL);
    trace2((qh ferr, 2017, "qh_degen_redundant_neighbors: f%d is degenerate with %d neighbors.\n", facet->id, size));
  }
  if (!delfacet)
    delfacet= facet;
  qh vertex_visit++;
  FOREACHvertex_(facet->vertices)
    vertex->visitid= qh vertex_visit;
  FOREACHneighbor_(delfacet) {
    /* uses early out instead of checking vertex count */
    if (neighbor == facet)
      continue;
    FOREACHvertex_(neighbor->vertices) {
      if (vertex->visitid != qh vertex_visit)
        break;
    }
    if (!vertex) {
      qh_appendmergeset(neighbor, facet, MRGredundant, NULL);
      trace2((qh ferr, 2018, "qh_degen_redundant_neighbors: f%d is contained in f%d.  merge\n", neighbor->id, facet->id));
    }
  }
  FOREACHneighbor_(delfacet) {   /* redundant merges occur first */
    if (neighbor == facet)
      continue;
    if ((size= qh_setsize(neighbor->neighbors)) < qh hull_dim) {
      qh_appendmergeset(neighbor, neighbor, MRGdegen, NULL);
      trace2((qh ferr, 2019, "qh_degen_redundant_neighbors: f%d is degenerate with %d neighbors.  Neighbor of f%d.\n", neighbor->id, size, facet->id));
    }
  }
} /* degen_redundant_neighbors */


/*---------------------------------

  qh_find_newvertex( oldvertex, vertices, ridges )
    locate new vertex for renaming old vertex
    vertices is a set of possible new vertices
      vertices sorted by number of deleted ridges

  returns:
    newvertex or NULL
      each ridge includes both vertex and oldvertex
    vertices sorted by number of deleted ridges

  notes:
    modifies vertex->visitid
    new vertex is in one of the ridges
    renaming will not cause a duplicate ridge
    renaming will minimize the number of deleted ridges
    newvertex may not be adjacent in the dual (though unlikely)

  design:
    for each vertex in vertices
      set vertex->visitid to number of references in ridges
    remove unvisited vertices
    set qh.vertex_visit above all possible values
    sort vertices by number of references in ridges
    add each ridge to qh.hash_table
    for each vertex in vertices
      look for a vertex that would not cause a duplicate ridge after a rename
*/
vertexT *qh_find_newvertex(vertexT *oldvertex, setT *vertices, setT *ridges) {
  vertexT *vertex, **vertexp;
  setT *newridges;
  ridgeT *ridge, **ridgep;
  int size, hashsize;
  int hash;

#ifndef qh_NOtrace
  if (qh IStracing >= 4) {
    qh_fprintf(qh ferr, 8063, "qh_find_newvertex: find new vertex for v%d from ",
             oldvertex->id);
    FOREACHvertex_(vertices)
      qh_fprintf(qh ferr, 8064, "v%d ", vertex->id);
    FOREACHridge_(ridges)
      qh_fprintf(qh ferr, 8065, "r%d ", ridge->id);
    qh_fprintf(qh ferr, 8066, "\n");
  }
#endif
  FOREACHvertex_(vertices)
    vertex->visitid= 0;
  FOREACHridge_(ridges) {
    FOREACHvertex_(ridge->vertices)
      vertex->visitid++;
  }
  FOREACHvertex_(vertices) {
    if (!vertex->visitid) {
      qh_setdelnth(vertices, SETindex_(vertices,vertex));
      vertexp--; /* repeat since deleted this vertex */
    }
  }
  qh vertex_visit += (unsigned int)qh_setsize(ridges);
  if (!qh_setsize(vertices)) {
    trace4((qh ferr, 4023, "qh_find_newvertex: vertices not in ridges for v%d\n",
            oldvertex->id));
    return NULL;
  }
  qsort(SETaddr_(vertices, vertexT), (size_t)qh_setsize(vertices),
                sizeof(vertexT *), qh_comparevisit);
  /* can now use qh vertex_visit */
  if (qh PRINTstatistics) {
    size= qh_setsize(vertices);
    zinc_(Zintersect);
    zadd_(Zintersecttot, size);
    zmax_(Zintersectmax, size);
  }
  hashsize= qh_newhashtable(qh_setsize(ridges));
  FOREACHridge_(ridges)
    qh_hashridge(qh hash_table, hashsize, ridge, oldvertex);
  FOREACHvertex_(vertices) {
    newridges= qh_vertexridges(vertex);
    FOREACHridge_(newridges) {
      if (qh_hashridge_find(qh hash_table, hashsize, ridge, vertex, oldvertex, &hash)) {
        zinc_(Zdupridge);
        break;
      }
    }
    qh_settempfree(&newridges);
    if (!ridge)
      break;  /* found a rename */
  }
  if (vertex) {
    /* counted in qh_renamevertex */
    trace2((qh ferr, 2020, "qh_find_newvertex: found v%d for old v%d from %d vertices and %d ridges.\n",
      vertex->id, oldvertex->id, qh_setsize(vertices), qh_setsize(ridges)));
  }else {
    zinc_(Zfindfail);
    trace0((qh ferr, 14, "qh_find_newvertex: no vertex for renaming v%d(all duplicated ridges) during p%d\n",
      oldvertex->id, qh furthest_id));
  }
  qh_setfree(&qh hash_table);
  return vertex;
} /* find_newvertex */

/*---------------------------------

  qh_findbest_test( testcentrum, facet, neighbor, bestfacet, dist, mindist, maxdist )
    test neighbor of facet for qh_findbestneighbor()
    if testcentrum,
      tests centrum (assumes it is defined)
    else
      tests vertices

  returns:
    if a better facet (i.e., vertices/centrum of facet closer to neighbor)
      updates bestfacet, dist, mindist, and maxdist
*/
void qh_findbest_test(boolT testcentrum, facetT *facet, facetT *neighbor,
      facetT **bestfacet, realT *distp, realT *mindistp, realT *maxdistp) {
  realT dist, mindist, maxdist;

  if (testcentrum) {
    zzinc_(Zbestdist);
    qh_distplane(facet->center, neighbor, &dist);
    dist *= qh hull_dim; /* estimate furthest vertex */
    if (dist < 0) {
      maxdist= 0;
      mindist= dist;
      dist= -dist;
    }else {
      mindist= 0;
      maxdist= dist;
    }
  }else
    dist= qh_getdistance(facet, neighbor, &mindist, &maxdist);
  if (dist < *distp) {
    *bestfacet= neighbor;
    *mindistp= mindist;
    *maxdistp= maxdist;
    *distp= dist;
  }
} /* findbest_test */

/*---------------------------------

  qh_findbestneighbor( facet, dist, mindist, maxdist )
    finds best neighbor (least dist) of a facet for merging

  returns:
    returns min and max distances and their max absolute value

  notes:
    avoids merging old into new
    assumes ridge->nonconvex only set on one ridge between a pair of facets
    could use an early out predicate but not worth it

  design:
    if a large facet
      will test centrum
    else
      will test vertices
    if a large facet
      test nonconvex neighbors for best merge
    else
      test all neighbors for the best merge
    if testing centrum
      get distance information
*/
facetT *qh_findbestneighbor(facetT *facet, realT *distp, realT *mindistp, realT *maxdistp) {
  facetT *neighbor, **neighborp, *bestfacet= NULL;
  ridgeT *ridge, **ridgep;
  boolT nonconvex= True, testcentrum= False;
  int size= qh_setsize(facet->vertices);

  *distp= REALmax;
  if (size > qh_BESTcentrum2 * qh hull_dim + qh_BESTcentrum) {
    testcentrum= True;
    zinc_(Zbestcentrum);
    if (!facet->center)
       facet->center= qh_getcentrum(facet);
  }
  if (size > qh hull_dim + qh_BESTnonconvex) {
    FOREACHridge_(facet->ridges) {
      if (ridge->nonconvex) {
        neighbor= otherfacet_(ridge, facet);
        qh_findbest_test(testcentrum, facet, neighbor,
                          &bestfacet, distp, mindistp, maxdistp);
      }
    }
  }
  if (!bestfacet) {
    nonconvex= False;
    FOREACHneighbor_(facet)
      qh_findbest_test(testcentrum, facet, neighbor,
                        &bestfacet, distp, mindistp, maxdistp);
  }
  if (!bestfacet) {
    qh_fprintf(qh ferr, 6095, "qhull internal error (qh_findbestneighbor): no neighbors for f%d\n", facet->id);

    qh_errexit(qh_ERRqhull, facet, NULL);
  }
  if (testcentrum)
    qh_getdistance(facet, bestfacet, mindistp, maxdistp);
  trace3((qh ferr, 3002, "qh_findbestneighbor: f%d is best neighbor for f%d testcentrum? %d nonconvex? %d dist %2.2g min %2.2g max %2.2g\n",
     bestfacet->id, facet->id, testcentrum, nonconvex, *distp, *mindistp, *maxdistp));
  return(bestfacet);
} /* findbestneighbor */


/*---------------------------------

  qh_flippedmerges( facetlist, wasmerge )
    merge flipped facets into best neighbor
    assumes qh.facet_mergeset at top of temporary stack

  returns:
    no flipped facets on facetlist
    sets wasmerge if merge occurred
    degen/redundant merges passed through

  notes:
    othermerges not needed since qh.facet_mergeset is empty before & after
      keep it in case of change

  design:
    append flipped facets to qh.facetmergeset
    for each flipped merge
      find best neighbor
      merge facet into neighbor
      merge degenerate and redundant facets
    remove flipped merges from qh.facet_mergeset
*/
void qh_flippedmerges(facetT *facetlist, boolT *wasmerge) {
  facetT *facet, *neighbor, *facet1;
  realT dist, mindist, maxdist;
  mergeT *merge, **mergep;
  setT *othermerges;
  int nummerge=0;

  trace4((qh ferr, 4024, "qh_flippedmerges: begin\n"));
  FORALLfacet_(facetlist) {
    if (facet->flipped && !facet->visible)
      qh_appendmergeset(facet, facet, MRGflip, NULL);
  }
  othermerges= qh_settemppop(); /* was facet_mergeset */
  qh facet_mergeset= qh_settemp(qh TEMPsize);
  qh_settemppush(othermerges);
  FOREACHmerge_(othermerges) {
    facet1= merge->facet1;
    if (merge->type != MRGflip || facet1->visible)
      continue;
    if (qh TRACEmerge-1 == zzval_(Ztotmerge))
      qhmem.IStracing= qh IStracing= qh TRACElevel;
    neighbor= qh_findbestneighbor(facet1, &dist, &mindist, &maxdist);
    trace0((qh ferr, 15, "qh_flippedmerges: merge flipped f%d into f%d dist %2.2g during p%d\n",
      facet1->id, neighbor->id, dist, qh furthest_id));
    qh_mergefacet(facet1, neighbor, &mindist, &maxdist, !qh_MERGEapex);
    nummerge++;
    if (qh PRINTstatistics) {
      zinc_(Zflipped);
      wadd_(Wflippedtot, dist);
      wmax_(Wflippedmax, dist);
    }
    qh_merge_degenredundant();
  }
  FOREACHmerge_(othermerges) {
    if (merge->facet1->visible || merge->facet2->visible)
      qh_memfree(merge, (int)sizeof(mergeT));
    else
      qh_setappend(&qh facet_mergeset, merge);
  }
  qh_settempfree(&othermerges);
  if (nummerge)
    *wasmerge= True;
  trace1((qh ferr, 1010, "qh_flippedmerges: merged %d flipped facets into a good neighbor\n", nummerge));
} /* flippedmerges */


/*---------------------------------

  qh_forcedmerges( wasmerge )
    merge duplicated ridges

  returns:
    removes all duplicate ridges on facet_mergeset
    wasmerge set if merge
    qh.facet_mergeset may include non-forced merges(none for now)
    qh.degen_mergeset includes degen/redun merges

  notes:
    duplicate ridges occur when the horizon is pinched,
        i.e. a subridge occurs in more than two horizon ridges.
     could rename vertices that pinch the horizon
    assumes qh_merge_degenredundant() has not be called
    othermerges isn't needed since facet_mergeset is empty afterwards
      keep it in case of change

  design:
    for each duplicate ridge
      find current facets by chasing f.replace links
      determine best direction for facet
      merge one facet into the other
      remove duplicate ridges from qh.facet_mergeset
*/
void qh_forcedmerges(boolT *wasmerge) {
  facetT *facet1, *facet2;
  mergeT *merge, **mergep;
  realT dist1, dist2, mindist1, mindist2, maxdist1, maxdist2;
  setT *othermerges;
  int nummerge=0, numflip=0;

  if (qh TRACEmerge-1 == zzval_(Ztotmerge))
    qhmem.IStracing= qh IStracing= qh TRACElevel;
  trace4((qh ferr, 4025, "qh_forcedmerges: begin\n"));
  othermerges= qh_settemppop(); /* was facet_mergeset */
  qh facet_mergeset= qh_settemp(qh TEMPsize);
  qh_settemppush(othermerges);
  FOREACHmerge_(othermerges) {
    if (merge->type != MRGridge)
        continue;
    facet1= merge->facet1;
    facet2= merge->facet2;
    while (facet1->visible)      /* must exist, no qh_merge_degenredunant */
      facet1= facet1->f.replace; /* previously merged facet */
    while (facet2->visible)
      facet2= facet2->f.replace; /* previously merged facet */
    if (facet1 == facet2)
      continue;
    if (!qh_setin(facet2->neighbors, facet1)) {
      qh_fprintf(qh ferr, 6096, "qhull internal error (qh_forcedmerges): f%d and f%d had a duplicate ridge but as f%d and f%d they are no longer neighbors\n",
               merge->facet1->id, merge->facet2->id, facet1->id, facet2->id);
      qh_errexit2 (qh_ERRqhull, facet1, facet2);
    }
    if (qh TRACEmerge-1 == zzval_(Ztotmerge))
      qhmem.IStracing= qh IStracing= qh TRACElevel;
    dist1= qh_getdistance(facet1, facet2, &mindist1, &maxdist1);
    dist2= qh_getdistance(facet2, facet1, &mindist2, &maxdist2);
    trace0((qh ferr, 16, "qh_forcedmerges: duplicate ridge between f%d and f%d, dist %2.2g and reverse dist %2.2g during p%d\n",
            facet1->id, facet2->id, dist1, dist2, qh furthest_id));
    if (dist1 < dist2)
      qh_mergefacet(facet1, facet2, &mindist1, &maxdist1, !qh_MERGEapex);
    else {
      qh_mergefacet(facet2, facet1, &mindist2, &maxdist2, !qh_MERGEapex);
      dist1= dist2;
      facet1= facet2;
    }
    if (facet1->flipped) {
      zinc_(Zmergeflipdup);
      numflip++;
    }else
      nummerge++;
    if (qh PRINTstatistics) {
      zinc_(Zduplicate);
      wadd_(Wduplicatetot, dist1);
      wmax_(Wduplicatemax, dist1);
    }
  }
  FOREACHmerge_(othermerges) {
    if (merge->type == MRGridge)
      qh_memfree(merge, (int)sizeof(mergeT));
    else
      qh_setappend(&qh facet_mergeset, merge);
  }
  qh_settempfree(&othermerges);
  if (nummerge)
    *wasmerge= True;
  trace1((qh ferr, 1011, "qh_forcedmerges: merged %d facets and %d flipped facets across duplicated ridges\n",
                nummerge, numflip));
} /* forcedmerges */


/*---------------------------------

  qh_getmergeset( facetlist )
    determines nonconvex facets on facetlist
    tests !tested ridges and nonconvex ridges of !tested facets

  returns:
    returns sorted qh.facet_mergeset of facet-neighbor pairs to be merged
    all ridges tested

  notes:
    assumes no nonconvex ridges with both facets tested
    uses facet->tested/ridge->tested to prevent duplicate tests
    can not limit tests to modified ridges since the centrum changed
    uses qh.visit_id

  see:
    qh_getmergeset_initial()

  design:
    for each facet on facetlist
      for each ridge of facet
        if untested ridge
          test ridge for convexity
          if non-convex
            append ridge to qh.facet_mergeset
    sort qh.facet_mergeset by angle
*/
void qh_getmergeset(facetT *facetlist) {
  facetT *facet, *neighbor, **neighborp;
  ridgeT *ridge, **ridgep;
  int nummerges;

  nummerges= qh_setsize(qh facet_mergeset);
  trace4((qh ferr, 4026, "qh_getmergeset: started.\n"));
  qh visit_id++;
  FORALLfacet_(facetlist) {
    if (facet->tested)
      continue;
    facet->visitid= qh visit_id;
    facet->tested= True;  /* must be non-simplicial due to merge */
    FOREACHneighbor_(facet)
      neighbor->seen= False;
    FOREACHridge_(facet->ridges) {
      if (ridge->tested && !ridge->nonconvex)
        continue;
      /* if tested & nonconvex, need to append merge */
      neighbor= otherfacet_(ridge, facet);
      if (neighbor->seen) {
        ridge->tested= True;
        ridge->nonconvex= False;
      }else if (neighbor->visitid != qh visit_id) {
        ridge->tested= True;
        ridge->nonconvex= False;
        neighbor->seen= True;      /* only one ridge is marked nonconvex */
        if (qh_test_appendmerge(facet, neighbor))
          ridge->nonconvex= True;
      }
    }
  }
  nummerges= qh_setsize(qh facet_mergeset);
  if (qh ANGLEmerge)
    qsort(SETaddr_(qh facet_mergeset, mergeT), (size_t)nummerges, sizeof(mergeT *), qh_compareangle);
  else
    qsort(SETaddr_(qh facet_mergeset, mergeT), (size_t)nummerges, sizeof(mergeT *), qh_comparemerge);
  if (qh POSTmerging) {
    zadd_(Zmergesettot2, nummerges);
  }else {
    zadd_(Zmergesettot, nummerges);
    zmax_(Zmergesetmax, nummerges);
  }
  trace2((qh ferr, 2021, "qh_getmergeset: %d merges found\n", nummerges));
} /* getmergeset */


/*---------------------------------

  qh_getmergeset_initial( facetlist )
    determine initial qh.facet_mergeset for facets
    tests all facet/neighbor pairs on facetlist

  returns:
    sorted qh.facet_mergeset with nonconvex ridges
    sets facet->tested, ridge->tested, and ridge->nonconvex

  notes:
    uses visit_id, assumes ridge->nonconvex is False

  see:
    qh_getmergeset()

  design:
    for each facet on facetlist
      for each untested neighbor of facet
        test facet and neighbor for convexity
        if non-convex
          append merge to qh.facet_mergeset
          mark one of the ridges as nonconvex
    sort qh.facet_mergeset by angle
*/
void qh_getmergeset_initial(facetT *facetlist) {
  facetT *facet, *neighbor, **neighborp;
  ridgeT *ridge, **ridgep;
  int nummerges;

  qh visit_id++;
  FORALLfacet_(facetlist) {
    facet->visitid= qh visit_id;
    facet->tested= True;
    FOREACHneighbor_(facet) {
      if (neighbor->visitid != qh visit_id) {
        if (qh_test_appendmerge(facet, neighbor)) {
          FOREACHridge_(neighbor->ridges) {
            if (facet == otherfacet_(ridge, neighbor)) {
              ridge->nonconvex= True;
              break;    /* only one ridge is marked nonconvex */
            }
          }
        }
      }
    }
    FOREACHridge_(facet->ridges)
      ridge->tested= True;
  }
  nummerges= qh_setsize(qh facet_mergeset);
  if (qh ANGLEmerge)
    qsort(SETaddr_(qh facet_mergeset, mergeT), (size_t)nummerges, sizeof(mergeT *), qh_compareangle);
  else
    qsort(SETaddr_(qh facet_mergeset, mergeT), (size_t)nummerges, sizeof(mergeT *), qh_comparemerge);
  if (qh POSTmerging) {
    zadd_(Zmergeinittot2, nummerges);
  }else {
    zadd_(Zmergeinittot, nummerges);
    zmax_(Zmergeinitmax, nummerges);
  }
  trace2((qh ferr, 2022, "qh_getmergeset_initial: %d merges found\n", nummerges));
} /* getmergeset_initial */


/*---------------------------------

  qh_hashridge( hashtable, hashsize, ridge, oldvertex )
    add ridge to hashtable without oldvertex

  notes:
    assumes hashtable is large enough

  design:
    determine hash value for ridge without oldvertex
    find next empty slot for ridge
*/
void qh_hashridge(setT *hashtable, int hashsize, ridgeT *ridge, vertexT *oldvertex) {
  int hash;
  ridgeT *ridgeA;

  hash= qh_gethash(hashsize, ridge->vertices, qh hull_dim-1, 0, oldvertex);
  while (True) {
    if (!(ridgeA= SETelemt_(hashtable, hash, ridgeT))) {
      SETelem_(hashtable, hash)= ridge;
      break;
    }else if (ridgeA == ridge)
      break;
    if (++hash == hashsize)
      hash= 0;
  }
} /* hashridge */


/*---------------------------------

  qh_hashridge_find( hashtable, hashsize, ridge, vertex, oldvertex, hashslot )
    returns matching ridge without oldvertex in hashtable
      for ridge without vertex
    if oldvertex is NULL
      matches with any one skip

  returns:
    matching ridge or NULL
    if no match,
      if ridge already in   table
        hashslot= -1
      else
        hashslot= next NULL index

  notes:
    assumes hashtable is large enough
    can't match ridge to itself

  design:
    get hash value for ridge without vertex
    for each hashslot
      return match if ridge matches ridgeA without oldvertex
*/
ridgeT *qh_hashridge_find(setT *hashtable, int hashsize, ridgeT *ridge,
              vertexT *vertex, vertexT *oldvertex, int *hashslot) {
  int hash;
  ridgeT *ridgeA;

  *hashslot= 0;
  zinc_(Zhashridge);
  hash= qh_gethash(hashsize, ridge->vertices, qh hull_dim-1, 0, vertex);
  while ((ridgeA= SETelemt_(hashtable, hash, ridgeT))) {
    if (ridgeA == ridge)
      *hashslot= -1;
    else {
      zinc_(Zhashridgetest);
      if (qh_setequal_except(ridge->vertices, vertex, ridgeA->vertices, oldvertex))
        return ridgeA;
    }
    if (++hash == hashsize)
      hash= 0;
  }
  if (!*hashslot)
    *hashslot= hash;
  return NULL;
} /* hashridge_find */


/*---------------------------------

  qh_makeridges( facet )
    creates explicit ridges between simplicial facets

  returns:
    facet with ridges and without qh_MERGEridge
    ->simplicial is False

  notes:
    allows qh_MERGEridge flag
    uses existing ridges
    duplicate neighbors ok if ridges already exist (qh_mergecycle_ridges)

  see:
    qh_mergecycle_ridges()

  design:
    look for qh_MERGEridge neighbors
    mark neighbors that already have ridges
    for each unprocessed neighbor of facet
      create a ridge for neighbor and facet
    if any qh_MERGEridge neighbors
      delete qh_MERGEridge flags (already handled by qh_mark_dupridges)
*/
void qh_makeridges(facetT *facet) {
  facetT *neighbor, **neighborp;
  ridgeT *ridge, **ridgep;
  int neighbor_i, neighbor_n;
  boolT toporient, mergeridge= False;

  if (!facet->simplicial)
    return;
  trace4((qh ferr, 4027, "qh_makeridges: make ridges for f%d\n", facet->id));
  facet->simplicial= False;
  FOREACHneighbor_(facet) {
    if (neighbor == qh_MERGEridge)
      mergeridge= True;
    else
      neighbor->seen= False;
  }
  FOREACHridge_(facet->ridges)
    otherfacet_(ridge, facet)->seen= True;
  FOREACHneighbor_i_(facet) {
    if (neighbor == qh_MERGEridge)
      continue;  /* fixed by qh_mark_dupridges */
    else if (!neighbor->seen) {  /* no current ridges */
      ridge= qh_newridge();
      ridge->vertices= qh_setnew_delnthsorted(facet->vertices, qh hull_dim,
                                                          neighbor_i, 0);
      toporient= facet->toporient ^ (neighbor_i & 0x1);
      if (toporient) {
        ridge->top= facet;
        ridge->bottom= neighbor;
      }else {
        ridge->top= neighbor;
        ridge->bottom= facet;
      }
#if 0 /* this also works */
      flip= (facet->toporient ^ neighbor->toporient)^(skip1 & 0x1) ^ (skip2 & 0x1);
      if (facet->toporient ^ (skip1 & 0x1) ^ flip) {
        ridge->top= neighbor;
        ridge->bottom= facet;
      }else {
        ridge->top= facet;
        ridge->bottom= neighbor;
      }
#endif
      qh_setappend(&(facet->ridges), ridge);
      qh_setappend(&(neighbor->ridges), ridge);
    }
  }
  if (mergeridge) {
    while (qh_setdel(facet->neighbors, qh_MERGEridge))
      ; /* delete each one */
  }
} /* makeridges */


/*---------------------------------

  qh_mark_dupridges( facetlist )
    add duplicated ridges to qh.facet_mergeset
    facet->dupridge is true

  returns:
    duplicate ridges on qh.facet_mergeset
    ->mergeridge/->mergeridge2 set
    duplicate ridges marked by qh_MERGEridge and both sides facet->dupridge
    no MERGEridges in neighbor sets

  notes:
    duplicate ridges occur when the horizon is pinched,
        i.e. a subridge occurs in more than two horizon ridges.
    could rename vertices that pinch the horizon
    uses qh.visit_id

  design:
    for all facets on facetlist
      if facet contains a duplicate ridge
        for each neighbor of facet
          if neighbor marked qh_MERGEridge (one side of the merge)
            set facet->mergeridge
          else
            if neighbor contains a duplicate ridge
            and the back link is qh_MERGEridge
              append duplicate ridge to qh.facet_mergeset
   for each duplicate ridge
     make ridge sets in preparation for merging
     remove qh_MERGEridge from neighbor set
   for each duplicate ridge
     restore the missing neighbor from the neighbor set that was qh_MERGEridge
     add the missing ridge for this neighbor
*/
void qh_mark_dupridges(facetT *facetlist) {
  facetT *facet, *neighbor, **neighborp;
  int nummerge=0;
  mergeT *merge, **mergep;


  trace4((qh ferr, 4028, "qh_mark_dupridges: identify duplicate ridges\n"));
  FORALLfacet_(facetlist) {
    if (facet->dupridge) {
      FOREACHneighbor_(facet) {
        if (neighbor == qh_MERGEridge) {
          facet->mergeridge= True;
          continue;
        }
        if (neighbor->dupridge
        && !qh_setin(neighbor->neighbors, facet)) { /* qh_MERGEridge */
          qh_appendmergeset(facet, neighbor, MRGridge, NULL);
          facet->mergeridge2= True;
          facet->mergeridge= True;
          nummerge++;
        }
      }
    }
  }
  if (!nummerge)
    return;
  FORALLfacet_(facetlist) {            /* gets rid of qh_MERGEridge */
    if (facet->mergeridge && !facet->mergeridge2)
      qh_makeridges(facet);
  }
  FOREACHmerge_(qh facet_mergeset) {   /* restore the missing neighbors */
    if (merge->type == MRGridge) {
      qh_setappend(&merge->facet2->neighbors, merge->facet1);
      qh_makeridges(merge->facet1);   /* and the missing ridges */
    }
  }
  trace1((qh ferr, 1012, "qh_mark_dupridges: found %d duplicated ridges\n",
                nummerge));
} /* mark_dupridges */

/*---------------------------------

  qh_maydropneighbor( facet )
    drop neighbor relationship if no ridge between facet and neighbor

  returns:
    neighbor sets updated
    appends degenerate facets to qh.facet_mergeset

  notes:
    won't cause redundant facets since vertex inclusion is the same
    may drop vertex and neighbor if no ridge
    uses qh.visit_id

  design:
    visit all neighbors with ridges
    for each unvisited neighbor of facet
      delete neighbor and facet from the neighbor sets
      if neighbor becomes degenerate
        append neighbor to qh.degen_mergeset
    if facet is degenerate
      append facet to qh.degen_mergeset
*/
void qh_maydropneighbor(facetT *facet) {
  ridgeT *ridge, **ridgep;
  realT angledegen= qh_ANGLEdegen;
  facetT *neighbor, **neighborp;

  qh visit_id++;
  trace4((qh ferr, 4029, "qh_maydropneighbor: test f%d for no ridges to a neighbor\n",
          facet->id));
  FOREACHridge_(facet->ridges) {
    ridge->top->visitid= qh visit_id;
    ridge->bottom->visitid= qh visit_id;
  }
  FOREACHneighbor_(facet) {
    if (neighbor->visitid != qh visit_id) {
      trace0((qh ferr, 17, "qh_maydropneighbor: facets f%d and f%d are no longer neighbors during p%d\n",
            facet->id, neighbor->id, qh furthest_id));
      zinc_(Zdropneighbor);
      qh_setdel(facet->neighbors, neighbor);
      neighborp--;  /* repeat, deleted a neighbor */
      qh_setdel(neighbor->neighbors, facet);
      if (qh_setsize(neighbor->neighbors) < qh hull_dim) {
        zinc_(Zdropdegen);
        qh_appendmergeset(neighbor, neighbor, MRGdegen, &angledegen);
        trace2((qh ferr, 2023, "qh_maydropneighbors: f%d is degenerate.\n", neighbor->id));
      }
    }
  }
  if (qh_setsize(facet->neighbors) < qh hull_dim) {
    zinc_(Zdropdegen);
    qh_appendmergeset(facet, facet, MRGdegen, &angledegen);
    trace2((qh ferr, 2024, "qh_maydropneighbors: f%d is degenerate.\n", facet->id));
  }
} /* maydropneighbor */


/*---------------------------------

  qh_merge_degenredundant()
    merge all degenerate and redundant facets
    qh.degen_mergeset contains merges from qh_degen_redundant_neighbors()

  returns:
    number of merges performed
    resets facet->degenerate/redundant
    if deleted (visible) facet has no neighbors
      sets ->f.replace to NULL

  notes:
    redundant merges happen before degenerate ones
    merging and renaming vertices can result in degen/redundant facets

  design:
    for each merge on qh.degen_mergeset
      if redundant merge
        if non-redundant facet merged into redundant facet
          recheck facet for redundancy
        else
          merge redundant facet into other facet
*/
int qh_merge_degenredundant(void) {
  int size;
  mergeT *merge;
  facetT *bestneighbor, *facet1, *facet2;
  realT dist, mindist, maxdist;
  vertexT *vertex, **vertexp;
  int nummerges= 0;
  mergeType mergetype;

  while ((merge= (mergeT*)qh_setdellast(qh degen_mergeset))) {
    facet1= merge->facet1;
    facet2= merge->facet2;
    mergetype= merge->type;
    qh_memfree(merge, (int)sizeof(mergeT));
    if (facet1->visible)
      continue;
    facet1->degenerate= False;
    facet1->redundant= False;
    if (qh TRACEmerge-1 == zzval_(Ztotmerge))
      qhmem.IStracing= qh IStracing= qh TRACElevel;
    if (mergetype == MRGredundant) {
      zinc_(Zneighbor);
      while (facet2->visible) {
        if (!facet2->f.replace) {
          qh_fprintf(qh ferr, 6097, "qhull internal error (qh_merge_degenredunant): f%d redundant but f%d has no replacement\n",
               facet1->id, facet2->id);
          qh_errexit2 (qh_ERRqhull, facet1, facet2);
        }
        facet2= facet2->f.replace;
      }
      if (facet1 == facet2) {
        qh_degen_redundant_facet(facet1); /* in case of others */
        continue;
      }
      trace2((qh ferr, 2025, "qh_merge_degenredundant: facet f%d is contained in f%d, will merge\n",
            facet1->id, facet2->id));
      qh_mergefacet(facet1, facet2, NULL, NULL, !qh_MERGEapex);
      /* merge distance is already accounted for */
      nummerges++;
    }else {  /* mergetype == MRGdegen, other merges may have fixed */
      if (!(size= qh_setsize(facet1->neighbors))) {
        zinc_(Zdelfacetdup);
        trace2((qh ferr, 2026, "qh_merge_degenredundant: facet f%d has no neighbors.  Deleted\n", facet1->id));
        qh_willdelete(facet1, NULL);
        FOREACHvertex_(facet1->vertices) {
          qh_setdel(vertex->neighbors, facet1);
          if (!SETfirst_(vertex->neighbors)) {
            zinc_(Zdegenvertex);
            trace2((qh ferr, 2027, "qh_merge_degenredundant: deleted v%d because f%d has no neighbors\n",
                 vertex->id, facet1->id));
            vertex->deleted= True;
            qh_setappend(&qh del_vertices, vertex);
          }
        }
        nummerges++;
      }else if (size < qh hull_dim) {
        bestneighbor= qh_findbestneighbor(facet1, &dist, &mindist, &maxdist);
        trace2((qh ferr, 2028, "qh_merge_degenredundant: facet f%d has %d neighbors, merge into f%d dist %2.2g\n",
              facet1->id, size, bestneighbor->id, dist));
        qh_mergefacet(facet1, bestneighbor, &mindist, &maxdist, !qh_MERGEapex);
        nummerges++;
        if (qh PRINTstatistics) {
          zinc_(Zdegen);
          wadd_(Wdegentot, dist);
          wmax_(Wdegenmax, dist);
        }
      } /* else, another merge fixed the degeneracy and redundancy tested */
    }
  }
  return nummerges;
} /* merge_degenredundant */

/*---------------------------------

  qh_merge_nonconvex( facet1, facet2, mergetype )
    remove non-convex ridge between facet1 into facet2
    mergetype gives why the facet's are non-convex

  returns:
    merges one of the facets into the best neighbor

  design:
    if one of the facets is a new facet
      prefer merging new facet into old facet
    find best neighbors for both facets
    merge the nearest facet into its best neighbor
    update the statistics
*/
void qh_merge_nonconvex(facetT *facet1, facetT *facet2, mergeType mergetype) {
  facetT *bestfacet, *bestneighbor, *neighbor;
  realT dist, dist2, mindist, mindist2, maxdist, maxdist2;

  if (qh TRACEmerge-1 == zzval_(Ztotmerge))
    qhmem.IStracing= qh IStracing= qh TRACElevel;
  trace3((qh ferr, 3003, "qh_merge_nonconvex: merge #%d for f%d and f%d type %d\n",
      zzval_(Ztotmerge) + 1, facet1->id, facet2->id, mergetype));
  /* concave or coplanar */
  if (!facet1->newfacet) {
    bestfacet= facet2;   /* avoid merging old facet if new is ok */
    facet2= facet1;
    facet1= bestfacet;
  }else
    bestfacet= facet1;
  bestneighbor= qh_findbestneighbor(bestfacet, &dist, &mindist, &maxdist);
  neighbor= qh_findbestneighbor(facet2, &dist2, &mindist2, &maxdist2);
  if (dist < dist2) {
    qh_mergefacet(bestfacet, bestneighbor, &mindist, &maxdist, !qh_MERGEapex);
  }else if (qh AVOIDold && !facet2->newfacet
  && ((mindist >= -qh MAXcoplanar && maxdist <= qh max_outside)
       || dist * 1.5 < dist2)) {
    zinc_(Zavoidold);
    wadd_(Wavoidoldtot, dist);
    wmax_(Wavoidoldmax, dist);
    trace2((qh ferr, 2029, "qh_merge_nonconvex: avoid merging old facet f%d dist %2.2g.  Use f%d dist %2.2g instead\n",
           facet2->id, dist2, facet1->id, dist2));
    qh_mergefacet(bestfacet, bestneighbor, &mindist, &maxdist, !qh_MERGEapex);
  }else {
    qh_mergefacet(facet2, neighbor, &mindist2, &maxdist2, !qh_MERGEapex);
    dist= dist2;
  }
  if (qh PRINTstatistics) {
    if (mergetype == MRGanglecoplanar) {
      zinc_(Zacoplanar);
      wadd_(Wacoplanartot, dist);
      wmax_(Wacoplanarmax, dist);
    }else if (mergetype == MRGconcave) {
      zinc_(Zconcave);
      wadd_(Wconcavetot, dist);
      wmax_(Wconcavemax, dist);
    }else { /* MRGcoplanar */
      zinc_(Zcoplanar);
      wadd_(Wcoplanartot, dist);
      wmax_(Wcoplanarmax, dist);
    }
  }
} /* merge_nonconvex */

/*---------------------------------

  qh_mergecycle( samecycle, newfacet )
    merge a cycle of facets starting at samecycle into a newfacet
    newfacet is a horizon facet with ->normal
    samecycle facets are simplicial from an apex

  returns:
    initializes vertex neighbors on first merge
    samecycle deleted (placed on qh.visible_list)
    newfacet at end of qh.facet_list
    deleted vertices on qh.del_vertices

  see:
    qh_mergefacet()
    called by qh_mergecycle_all() for multiple, same cycle facets

  design:
    make vertex neighbors if necessary
    make ridges for newfacet
    merge neighbor sets of samecycle into newfacet
    merge ridges of samecycle into newfacet
    merge vertex neighbors of samecycle into newfacet
    make apex of samecycle the apex of newfacet
    if newfacet wasn't a new facet
      add its vertices to qh.newvertex_list
    delete samecycle facets a make newfacet a newfacet
*/
void qh_mergecycle(facetT *samecycle, facetT *newfacet) {
  int traceonce= False, tracerestore= 0;
  vertexT *apex;
#ifndef qh_NOtrace
  facetT *same;
#endif

  if (newfacet->tricoplanar) {
    if (!qh TRInormals) {
      qh_fprintf(qh ferr, 6224, "Qhull internal error (qh_mergecycle): does not work for tricoplanar facets.  Use option 'Q11'\n");
      qh_errexit(qh_ERRqhull, newfacet, NULL);
    }
    newfacet->tricoplanar= False;
    newfacet->keepcentrum= False;
  }
  if (!qh VERTEXneighbors)
    qh_vertexneighbors();
  zzinc_(Ztotmerge);
  if (qh REPORTfreq2 && qh POSTmerging) {
    if (zzval_(Ztotmerge) > qh mergereport + qh REPORTfreq2)
      qh_tracemerging();
  }
#ifndef qh_NOtrace
  if (qh TRACEmerge == zzval_(Ztotmerge))
    qhmem.IStracing= qh IStracing= qh TRACElevel;
  trace2((qh ferr, 2030, "qh_mergecycle: merge #%d for facets from cycle f%d into coplanar horizon f%d\n",
        zzval_(Ztotmerge), samecycle->id, newfacet->id));
  if (newfacet == qh tracefacet) {
    tracerestore= qh IStracing;
    qh IStracing= 4;
    qh_fprintf(qh ferr, 8068, "qh_mergecycle: ========= trace merge %d of samecycle %d into trace f%d, furthest is p%d\n",
               zzval_(Ztotmerge), samecycle->id, newfacet->id,  qh furthest_id);
    traceonce= True;
  }
  if (qh IStracing >=4) {
    qh_fprintf(qh ferr, 8069, "  same cycle:");
    FORALLsame_cycle_(samecycle)
      qh_fprintf(qh ferr, 8070, " f%d", same->id);
    qh_fprintf(qh ferr, 8071, "\n");
  }
  if (qh IStracing >=4)
    qh_errprint("MERGING CYCLE", samecycle, newfacet, NULL, NULL);
#endif /* !qh_NOtrace */
  apex= SETfirstt_(samecycle->vertices, vertexT);
  qh_makeridges(newfacet);
  qh_mergecycle_neighbors(samecycle, newfacet);
  qh_mergecycle_ridges(samecycle, newfacet);
  qh_mergecycle_vneighbors(samecycle, newfacet);
  if (SETfirstt_(newfacet->vertices, vertexT) != apex)
    qh_setaddnth(&newfacet->vertices, 0, apex);  /* apex has last id */
  if (!newfacet->newfacet)
    qh_newvertices(newfacet->vertices);
  qh_mergecycle_facets(samecycle, newfacet);
  qh_tracemerge(samecycle, newfacet);
  /* check for degen_redundant_neighbors after qh_forcedmerges() */
  if (traceonce) {
    qh_fprintf(qh ferr, 8072, "qh_mergecycle: end of trace facet\n");
    qh IStracing= tracerestore;
  }
} /* mergecycle */

/*---------------------------------

  qh_mergecycle_all( facetlist, wasmerge )
    merge all samecycles of coplanar facets into horizon
    don't merge facets with ->mergeridge (these already have ->normal)
    all facets are simplicial from apex
    all facet->cycledone == False

  returns:
    all newfacets merged into coplanar horizon facets
    deleted vertices on  qh.del_vertices
    sets wasmerge if any merge

  see:
    calls qh_mergecycle for multiple, same cycle facets

  design:
    for each facet on facetlist
      skip facets with duplicate ridges and normals
      check that facet is in a samecycle (->mergehorizon)
      if facet only member of samecycle
        sets vertex->delridge for all vertices except apex
        merge facet into horizon
      else
        mark all facets in samecycle
        remove facets with duplicate ridges from samecycle
        merge samecycle into horizon (deletes facets from facetlist)
*/
void qh_mergecycle_all(facetT *facetlist, boolT *wasmerge) {
  facetT *facet, *same, *prev, *horizon;
  facetT *samecycle= NULL, *nextfacet, *nextsame;
  vertexT *apex, *vertex, **vertexp;
  int cycles=0, total=0, facets, nummerge;

  trace2((qh ferr, 2031, "qh_mergecycle_all: begin\n"));
  for (facet= facetlist; facet && (nextfacet= facet->next); facet= nextfacet) {
    if (facet->normal)
      continue;
    if (!facet->mergehorizon) {
      qh_fprintf(qh ferr, 6225, "Qhull internal error (qh_mergecycle_all): f%d without normal\n", facet->id);
      qh_errexit(qh_ERRqhull, facet, NULL);
    }
    horizon= SETfirstt_(facet->neighbors, facetT);
    if (facet->f.samecycle == facet) {
      zinc_(Zonehorizon);
      /* merge distance done in qh_findhorizon */
      apex= SETfirstt_(facet->vertices, vertexT);
      FOREACHvertex_(facet->vertices) {
        if (vertex != apex)
          vertex->delridge= True;
      }
      horizon->f.newcycle= NULL;
      qh_mergefacet(facet, horizon, NULL, NULL, qh_MERGEapex);
    }else {
      samecycle= facet;
      facets= 0;
      prev= facet;
      for (same= facet->f.samecycle; same;  /* FORALLsame_cycle_(facet) */
           same= (same == facet ? NULL :nextsame)) { /* ends at facet */
        nextsame= same->f.samecycle;
        if (same->cycledone || same->visible)
          qh_infiniteloop(same);
        same->cycledone= True;
        if (same->normal) {
          prev->f.samecycle= same->f.samecycle; /* unlink ->mergeridge */
          same->f.samecycle= NULL;
        }else {
          prev= same;
          facets++;
        }
      }
      while (nextfacet && nextfacet->cycledone)  /* will delete samecycle */
        nextfacet= nextfacet->next;
      horizon->f.newcycle= NULL;
      qh_mergecycle(samecycle, horizon);
      nummerge= horizon->nummerge + facets;
      if (nummerge > qh_MAXnummerge)
        horizon->nummerge= qh_MAXnummerge;
      else
        horizon->nummerge= (short unsigned int)nummerge;
      zzinc_(Zcyclehorizon);
      total += facets;
      zzadd_(Zcyclefacettot, facets);
      zmax_(Zcyclefacetmax, facets);
    }
    cycles++;
  }
  if (cycles)
    *wasmerge= True;
  trace1((qh ferr, 1013, "qh_mergecycle_all: merged %d same cycles or facets into coplanar horizons\n", cycles));
} /* mergecycle_all */

/*---------------------------------

  qh_mergecycle_facets( samecycle, newfacet )
    finish merge of samecycle into newfacet

  returns:
    samecycle prepended to visible_list for later deletion and partitioning
      each facet->f.replace == newfacet

    newfacet moved to end of qh.facet_list
      makes newfacet a newfacet (get's facet1->id if it was old)
      sets newfacet->newmerge
      clears newfacet->center (unless merging into a large facet)
      clears newfacet->tested and ridge->tested for facet1

    adds neighboring facets to facet_mergeset if redundant or degenerate

  design:
    make newfacet a new facet and set its flags
    move samecycle facets to qh.visible_list for later deletion
    unless newfacet is large
      remove its centrum
*/
void qh_mergecycle_facets(facetT *samecycle, facetT *newfacet) {
  facetT *same, *next;

  trace4((qh ferr, 4030, "qh_mergecycle_facets: make newfacet new and samecycle deleted\n"));
  qh_removefacet(newfacet);  /* append as a newfacet to end of qh facet_list */
  qh_appendfacet(newfacet);
  newfacet->newfacet= True;
  newfacet->simplicial= False;
  newfacet->newmerge= True;

  for (same= samecycle->f.samecycle; same; same= (same == samecycle ?  NULL : next)) {
    next= same->f.samecycle;  /* reused by willdelete */
    qh_willdelete(same, newfacet);
  }
  if (newfacet->center
      && qh_setsize(newfacet->vertices) <= qh hull_dim + qh_MAXnewcentrum) {
    qh_memfree(newfacet->center, qh normal_size);
    newfacet->center= NULL;
  }
  trace3((qh ferr, 3004, "qh_mergecycle_facets: merged facets from cycle f%d into f%d\n",
             samecycle->id, newfacet->id));
} /* mergecycle_facets */

/*---------------------------------

  qh_mergecycle_neighbors( samecycle, newfacet )
    add neighbors for samecycle facets to newfacet

  returns:
    newfacet with updated neighbors and vice-versa
    newfacet has ridges
    all neighbors of newfacet marked with qh.visit_id
    samecycle facets marked with qh.visit_id-1
    ridges updated for simplicial neighbors of samecycle with a ridge

  notes:
    assumes newfacet not in samecycle
    usually, samecycle facets are new, simplicial facets without internal ridges
      not so if horizon facet is coplanar to two different samecycles

  see:
    qh_mergeneighbors()

  design:
    check samecycle
    delete neighbors from newfacet that are also in samecycle
    for each neighbor of a facet in samecycle
      if neighbor is simplicial
        if first visit
          move the neighbor relation to newfacet
          update facet links for its ridges
        else
          make ridges for neighbor
          remove samecycle reference
      else
        update neighbor sets
*/
void qh_mergecycle_neighbors(facetT *samecycle, facetT *newfacet) {
  facetT *same, *neighbor, **neighborp;
  int delneighbors= 0, newneighbors= 0;
  unsigned int samevisitid;
  ridgeT *ridge, **ridgep;

  samevisitid= ++qh visit_id;
  FORALLsame_cycle_(samecycle) {
    if (same->visitid == samevisitid || same->visible)
      qh_infiniteloop(samecycle);
    same->visitid= samevisitid;
  }
  newfacet->visitid= ++qh visit_id;
  trace4((qh ferr, 4031, "qh_mergecycle_neighbors: delete shared neighbors from newfacet\n"));
  FOREACHneighbor_(newfacet) {
    if (neighbor->visitid == samevisitid) {
      SETref_(neighbor)= NULL;  /* samecycle neighbors deleted */
      delneighbors++;
    }else
      neighbor->visitid= qh visit_id;
  }
  qh_setcompact(newfacet->neighbors);

  trace4((qh ferr, 4032, "qh_mergecycle_neighbors: update neighbors\n"));
  FORALLsame_cycle_(samecycle) {
    FOREACHneighbor_(same) {
      if (neighbor->visitid == samevisitid)
        continue;
      if (neighbor->simplicial) {
        if (neighbor->visitid != qh visit_id) {
          qh_setappend(&newfacet->neighbors, neighbor);
          qh_setreplace(neighbor->neighbors, same, newfacet);
          newneighbors++;
          neighbor->visitid= qh visit_id;
          FOREACHridge_(neighbor->ridges) { /* update ridge in case of qh_makeridges */
            if (ridge->top == same) {
              ridge->top= newfacet;
              break;
            }else if (ridge->bottom == same) {
              ridge->bottom= newfacet;
              break;
            }
          }
        }else {
          qh_makeridges(neighbor);
          qh_setdel(neighbor->neighbors, same);
          /* same can't be horizon facet for neighbor */
        }
      }else { /* non-simplicial neighbor */
        qh_setdel(neighbor->neighbors, same);
        if (neighbor->visitid != qh visit_id) {
          qh_setappend(&neighbor->neighbors, newfacet);
          qh_setappend(&newfacet->neighbors, neighbor);
          neighbor->visitid= qh visit_id;
          newneighbors++;
        }
      }
    }
  }
  trace2((qh ferr, 2032, "qh_mergecycle_neighbors: deleted %d neighbors and added %d\n",
             delneighbors, newneighbors));
} /* mergecycle_neighbors */

/*---------------------------------

  qh_mergecycle_ridges( samecycle, newfacet )
    add ridges/neighbors for facets in samecycle to newfacet
    all new/old neighbors of newfacet marked with qh.visit_id
    facets in samecycle marked with qh.visit_id-1
    newfacet marked with qh.visit_id

  returns:
    newfacet has merged ridges

  notes:
    ridge already updated for simplicial neighbors of samecycle with a ridge

  see:
    qh_mergeridges()
    qh_makeridges()

  design:
    remove ridges between newfacet and samecycle
    for each facet in samecycle
      for each ridge in facet
        update facet pointers in ridge
        skip ridges processed in qh_mergecycle_neighors
        free ridges between newfacet and samecycle
        free ridges between facets of samecycle (on 2nd visit)
        append remaining ridges to newfacet
      if simpilicial facet
        for each neighbor of facet
          if simplicial facet
          and not samecycle facet or newfacet
            make ridge between neighbor and newfacet
*/
void qh_mergecycle_ridges(facetT *samecycle, facetT *newfacet) {
  facetT *same, *neighbor= NULL;
  int numold=0, numnew=0;
  int neighbor_i, neighbor_n;
  unsigned int samevisitid;
  ridgeT *ridge, **ridgep;
  boolT toporient;
  void **freelistp; /* used !qh_NOmem */

  trace4((qh ferr, 4033, "qh_mergecycle_ridges: delete shared ridges from newfacet\n"));
  samevisitid= qh visit_id -1;
  FOREACHridge_(newfacet->ridges) {
    neighbor= otherfacet_(ridge, newfacet);
    if (neighbor->visitid == samevisitid)
      SETref_(ridge)= NULL; /* ridge free'd below */
  }
  qh_setcompact(newfacet->ridges);

  trace4((qh ferr, 4034, "qh_mergecycle_ridges: add ridges to newfacet\n"));
  FORALLsame_cycle_(samecycle) {
    FOREACHridge_(same->ridges) {
      if (ridge->top == same) {
        ridge->top= newfacet;
        neighbor= ridge->bottom;
      }else if (ridge->bottom == same) {
        ridge->bottom= newfacet;
        neighbor= ridge->top;
      }else if (ridge->top == newfacet || ridge->bottom == newfacet) {
        qh_setappend(&newfacet->ridges, ridge);
        numold++;  /* already set by qh_mergecycle_neighbors */
        continue;
      }else {
        qh_fprintf(qh ferr, 6098, "qhull internal error (qh_mergecycle_ridges): bad ridge r%d\n", ridge->id);
        qh_errexit(qh_ERRqhull, NULL, ridge);
      }
      if (neighbor == newfacet) {
        qh_setfree(&(ridge->vertices));
        qh_memfree_(ridge, (int)sizeof(ridgeT), freelistp);
        numold++;
      }else if (neighbor->visitid == samevisitid) {
        qh_setdel(neighbor->ridges, ridge);
        qh_setfree(&(ridge->vertices));
        qh_memfree_(ridge, (int)sizeof(ridgeT), freelistp);
        numold++;
      }else {
        qh_setappend(&newfacet->ridges, ridge);
        numold++;
      }
    }
    if (same->ridges)
      qh_settruncate(same->ridges, 0);
    if (!same->simplicial)
      continue;
    FOREACHneighbor_i_(same) {       /* note: !newfact->simplicial */
      if (neighbor->visitid != samevisitid && neighbor->simplicial) {
        ridge= qh_newridge();
        ridge->vertices= qh_setnew_delnthsorted(same->vertices, qh hull_dim,
                                                          neighbor_i, 0);
        toporient= same->toporient ^ (neighbor_i & 0x1);
        if (toporient) {
          ridge->top= newfacet;
          ridge->bottom= neighbor;
        }else {
          ridge->top= neighbor;
          ridge->bottom= newfacet;
        }
        qh_setappend(&(newfacet->ridges), ridge);
        qh_setappend(&(neighbor->ridges), ridge);
        numnew++;
      }
    }
  }

  trace2((qh ferr, 2033, "qh_mergecycle_ridges: found %d old ridges and %d new ones\n",
             numold, numnew));
} /* mergecycle_ridges */

/*---------------------------------

  qh_mergecycle_vneighbors( samecycle, newfacet )
    create vertex neighbors for newfacet from vertices of facets in samecycle
    samecycle marked with visitid == qh.visit_id - 1

  returns:
    newfacet vertices with updated neighbors
    marks newfacet with qh.visit_id-1
    deletes vertices that are merged away
    sets delridge on all vertices (faster here than in mergecycle_ridges)

  see:
    qh_mergevertex_neighbors()

  design:
    for each vertex of samecycle facet
      set vertex->delridge
      delete samecycle facets from vertex neighbors
      append newfacet to vertex neighbors
      if vertex only in newfacet
        delete it from newfacet
        add it to qh.del_vertices for later deletion
*/
void qh_mergecycle_vneighbors(facetT *samecycle, facetT *newfacet) {
  facetT *neighbor, **neighborp;
  unsigned int mergeid;
  vertexT *vertex, **vertexp, *apex;
  setT *vertices;

  trace4((qh ferr, 4035, "qh_mergecycle_vneighbors: update vertex neighbors for newfacet\n"));
  mergeid= qh visit_id - 1;
  newfacet->visitid= mergeid;
  vertices= qh_basevertices(samecycle); /* temp */
  apex= SETfirstt_(samecycle->vertices, vertexT);
  qh_setappend(&vertices, apex);
  FOREACHvertex_(vertices) {
    vertex->delridge= True;
    FOREACHneighbor_(vertex) {
      if (neighbor->visitid == mergeid)
        SETref_(neighbor)= NULL;
    }
    qh_setcompact(vertex->neighbors);
    qh_setappend(&vertex->neighbors, newfacet);
    if (!SETsecond_(vertex->neighbors)) {
      zinc_(Zcyclevertex);
      trace2((qh ferr, 2034, "qh_mergecycle_vneighbors: deleted v%d when merging cycle f%d into f%d\n",
        vertex->id, samecycle->id, newfacet->id));
      qh_setdelsorted(newfacet->vertices, vertex);
      vertex->deleted= True;
      qh_setappend(&qh del_vertices, vertex);
    }
  }
  qh_settempfree(&vertices);
  trace3((qh ferr, 3005, "qh_mergecycle_vneighbors: merged vertices from cycle f%d into f%d\n",
             samecycle->id, newfacet->id));
} /* mergecycle_vneighbors */

/*---------------------------------

  qh_mergefacet( facet1, facet2, mindist, maxdist, mergeapex )
    merges facet1 into facet2
    mergeapex==qh_MERGEapex if merging new facet into coplanar horizon

  returns:
    qh.max_outside and qh.min_vertex updated
    initializes vertex neighbors on first merge

  returns:
    facet2 contains facet1's vertices, neighbors, and ridges
      facet2 moved to end of qh.facet_list
      makes facet2 a newfacet
      sets facet2->newmerge set
      clears facet2->center (unless merging into a large facet)
      clears facet2->tested and ridge->tested for facet1

    facet1 prepended to visible_list for later deletion and partitioning
      facet1->f.replace == facet2

    adds neighboring facets to facet_mergeset if redundant or degenerate

  notes:
    mindist/maxdist may be NULL (only if both NULL)
    traces merge if fmax_(maxdist,-mindist) > TRACEdist

  see:
    qh_mergecycle()

  design:
    trace merge and check for degenerate simplex
    make ridges for both facets
    update qh.max_outside, qh.max_vertex, qh.min_vertex
    update facet2->maxoutside and keepcentrum
    update facet2->nummerge
    update tested flags for facet2
    if facet1 is simplicial
      merge facet1 into facet2
    else
      merge facet1's neighbors into facet2
      merge facet1's ridges into facet2
      merge facet1's vertices into facet2
      merge facet1's vertex neighbors into facet2
      add facet2's vertices to qh.new_vertexlist
      unless qh_MERGEapex
        test facet2 for degenerate or redundant neighbors
      move facet1 to qh.visible_list for later deletion
      move facet2 to end of qh.newfacet_list
*/
void qh_mergefacet(facetT *facet1, facetT *facet2, realT *mindist, realT *maxdist, boolT mergeapex) {
  boolT traceonce= False;
  vertexT *vertex, **vertexp;
  int tracerestore=0, nummerge;

  if (facet1->tricoplanar || facet2->tricoplanar) {
    if (!qh TRInormals) {
      qh_fprintf(qh ferr, 6226, "Qhull internal error (qh_mergefacet): does not work for tricoplanar facets.  Use option 'Q11'\n");
      qh_errexit2 (qh_ERRqhull, facet1, facet2);
    }
    if (facet2->tricoplanar) {
      facet2->tricoplanar= False;
      facet2->keepcentrum= False;
    }
  }
  zzinc_(Ztotmerge);
  if (qh REPORTfreq2 && qh POSTmerging) {
    if (zzval_(Ztotmerge) > qh mergereport + qh REPORTfreq2)
      qh_tracemerging();
  }
#ifndef qh_NOtrace
  if (qh build_cnt >= qh RERUN) {
    if (mindist && (-*mindist > qh TRACEdist || *maxdist > qh TRACEdist)) {
      tracerestore= 0;
      qh IStracing= qh TRACElevel;
      traceonce= True;
      qh_fprintf(qh ferr, 8075, "qh_mergefacet: ========= trace wide merge #%d(%2.2g) for f%d into f%d, last point was p%d\n", zzval_(Ztotmerge),
             fmax_(-*mindist, *maxdist), facet1->id, facet2->id, qh furthest_id);
    }else if (facet1 == qh tracefacet || facet2 == qh tracefacet) {
      tracerestore= qh IStracing;
      qh IStracing= 4;
      traceonce= True;
      qh_fprintf(qh ferr, 8076, "qh_mergefacet: ========= trace merge #%d involving f%d, furthest is p%d\n",
                 zzval_(Ztotmerge), qh tracefacet_id,  qh furthest_id);
    }
  }
  if (qh IStracing >= 2) {
    realT mergemin= -2;
    realT mergemax= -2;

    if (mindist) {
      mergemin= *mindist;
      mergemax= *maxdist;
    }
    qh_fprintf(qh ferr, 8077, "qh_mergefacet: #%d merge f%d into f%d, mindist= %2.2g, maxdist= %2.2g\n",
    zzval_(Ztotmerge), facet1->id, facet2->id, mergemin, mergemax);
  }
#endif /* !qh_NOtrace */
  if (facet1 == facet2 || facet1->visible || facet2->visible) {
    qh_fprintf(qh ferr, 6099, "qhull internal error (qh_mergefacet): either f%d and f%d are the same or one is a visible facet\n",
             facet1->id, facet2->id);
    qh_errexit2 (qh_ERRqhull, facet1, facet2);
  }
  if (qh num_facets - qh num_visible <= qh hull_dim + 1) {
    qh_fprintf(qh ferr, 6227, "\n\
qhull precision error: Only %d facets remain.  Can not merge another\n\
pair.  The input is too degenerate or the convexity constraints are\n\
too strong.\n", qh hull_dim+1);
    if (qh hull_dim >= 5 && !qh MERGEexact)
      qh_fprintf(qh ferr, 8079, "Option 'Qx' may avoid this problem.\n");
    qh_errexit(qh_ERRprec, NULL, NULL);
  }
  if (!qh VERTEXneighbors)
    qh_vertexneighbors();
  qh_makeridges(facet1);
  qh_makeridges(facet2);
  if (qh IStracing >=4)
    qh_errprint("MERGING", facet1, facet2, NULL, NULL);
  if (mindist) {
    maximize_(qh max_outside, *maxdist);
    maximize_(qh max_vertex, *maxdist);
#if qh_MAXoutside
    maximize_(facet2->maxoutside, *maxdist);
#endif
    minimize_(qh min_vertex, *mindist);
    if (!facet2->keepcentrum
    && (*maxdist > qh WIDEfacet || *mindist < -qh WIDEfacet)) {
      facet2->keepcentrum= True;
      zinc_(Zwidefacet);
    }
  }
  nummerge= facet1->nummerge + facet2->nummerge + 1;
  if (nummerge >= qh_MAXnummerge)
    facet2->nummerge= qh_MAXnummerge;
  else
    facet2->nummerge= (short unsigned int)nummerge;
  facet2->newmerge= True;
  facet2->dupridge= False;
  qh_updatetested  (facet1, facet2);
  if (qh hull_dim > 2 && qh_setsize(facet1->vertices) == qh hull_dim)
    qh_mergesimplex(facet1, facet2, mergeapex);
  else {
    qh vertex_visit++;
    FOREACHvertex_(facet2->vertices)
      vertex->visitid= qh vertex_visit;
    if (qh hull_dim == 2)
      qh_mergefacet2d(facet1, facet2);
    else {
      qh_mergeneighbors(facet1, facet2);
      qh_mergevertices(facet1->vertices, &facet2->vertices);
    }
    qh_mergeridges(facet1, facet2);
    qh_mergevertex_neighbors(facet1, facet2);
    if (!facet2->newfacet)
      qh_newvertices(facet2->vertices);
  }
  if (!mergeapex)
    qh_degen_redundant_neighbors(facet2, facet1);
  if (facet2->coplanar || !facet2->newfacet) {
    zinc_(Zmergeintohorizon);
  }else if (!facet1->newfacet && facet2->newfacet) {
    zinc_(Zmergehorizon);
  }else {
    zinc_(Zmergenew);
  }
  qh_willdelete(facet1, facet2);
  qh_removefacet(facet2);  /* append as a newfacet to end of qh facet_list */
  qh_appendfacet(facet2);
  facet2->newfacet= True;
  facet2->tested= False;
  qh_tracemerge(facet1, facet2);
  if (traceonce) {
    qh_fprintf(qh ferr, 8080, "qh_mergefacet: end of wide tracing\n");
    qh IStracing= tracerestore;
  }
} /* mergefacet */


/*---------------------------------

  qh_mergefacet2d( facet1, facet2 )
    in 2d, merges neighbors and vertices of facet1 into facet2

  returns:
    build ridges for neighbors if necessary
    facet2 looks like a simplicial facet except for centrum, ridges
      neighbors are opposite the corresponding vertex
      maintains orientation of facet2

  notes:
    qh_mergefacet() retains non-simplicial structures
      they are not needed in 2d, but later routines may use them
    preserves qh.vertex_visit for qh_mergevertex_neighbors()

  design:
    get vertices and neighbors
    determine new vertices and neighbors
    set new vertices and neighbors and adjust orientation
    make ridges for new neighbor if needed
*/
void qh_mergefacet2d(facetT *facet1, facetT *facet2) {
  vertexT *vertex1A, *vertex1B, *vertex2A, *vertex2B, *vertexA, *vertexB;
  facetT *neighbor1A, *neighbor1B, *neighbor2A, *neighbor2B, *neighborA, *neighborB;

  vertex1A= SETfirstt_(facet1->vertices, vertexT);
  vertex1B= SETsecondt_(facet1->vertices, vertexT);
  vertex2A= SETfirstt_(facet2->vertices, vertexT);
  vertex2B= SETsecondt_(facet2->vertices, vertexT);
  neighbor1A= SETfirstt_(facet1->neighbors, facetT);
  neighbor1B= SETsecondt_(facet1->neighbors, facetT);
  neighbor2A= SETfirstt_(facet2->neighbors, facetT);
  neighbor2B= SETsecondt_(facet2->neighbors, facetT);
  if (vertex1A == vertex2A) {
    vertexA= vertex1B;
    vertexB= vertex2B;
    neighborA= neighbor2A;
    neighborB= neighbor1A;
  }else if (vertex1A == vertex2B) {
    vertexA= vertex1B;
    vertexB= vertex2A;
    neighborA= neighbor2B;
    neighborB= neighbor1A;
  }else if (vertex1B == vertex2A) {
    vertexA= vertex1A;
    vertexB= vertex2B;
    neighborA= neighbor2A;
    neighborB= neighbor1B;
  }else { /* 1B == 2B */
    vertexA= vertex1A;
    vertexB= vertex2A;
    neighborA= neighbor2B;
    neighborB= neighbor1B;
  }
  /* vertexB always from facet2, neighborB always from facet1 */
  if (vertexA->id > vertexB->id) {
    SETfirst_(facet2->vertices)= vertexA;
    SETsecond_(facet2->vertices)= vertexB;
    if (vertexB == vertex2A)
      facet2->toporient= !facet2->toporient;
    SETfirst_(facet2->neighbors)= neighborA;
    SETsecond_(facet2->neighbors)= neighborB;
  }else {
    SETfirst_(facet2->vertices)= vertexB;
    SETsecond_(facet2->vertices)= vertexA;
    if (vertexB == vertex2B)
      facet2->toporient= !facet2->toporient;
    SETfirst_(facet2->neighbors)= neighborB;
    SETsecond_(facet2->neighbors)= neighborA;
  }
  qh_makeridges(neighborB);
  qh_setreplace(neighborB->neighbors, facet1, facet2);
  trace4((qh ferr, 4036, "qh_mergefacet2d: merged v%d and neighbor f%d of f%d into f%d\n",
       vertexA->id, neighborB->id, facet1->id, facet2->id));
} /* mergefacet2d */


/*---------------------------------

  qh_mergeneighbors( facet1, facet2 )
    merges the neighbors of facet1 into facet2

  see:
    qh_mergecycle_neighbors()

  design:
    for each neighbor of facet1
      if neighbor is also a neighbor of facet2
        if neighbor is simpilicial
          make ridges for later deletion as a degenerate facet
        update its neighbor set
      else
        move the neighbor relation to facet2
    remove the neighbor relation for facet1 and facet2
*/
void qh_mergeneighbors(facetT *facet1, facetT *facet2) {
  facetT *neighbor, **neighborp;

  trace4((qh ferr, 4037, "qh_mergeneighbors: merge neighbors of f%d and f%d\n",
          facet1->id, facet2->id));
  qh visit_id++;
  FOREACHneighbor_(facet2) {
    neighbor->visitid= qh visit_id;
  }
  FOREACHneighbor_(facet1) {
    if (neighbor->visitid == qh visit_id) {
      if (neighbor->simplicial)    /* is degen, needs ridges */
        qh_makeridges(neighbor);
      if (SETfirstt_(neighbor->neighbors, facetT) != facet1) /*keep newfacet->horizon*/
        qh_setdel(neighbor->neighbors, facet1);
      else {
        qh_setdel(neighbor->neighbors, facet2);
        qh_setreplace(neighbor->neighbors, facet1, facet2);
      }
    }else if (neighbor != facet2) {
      qh_setappend(&(facet2->neighbors), neighbor);
      qh_setreplace(neighbor->neighbors, facet1, facet2);
    }
  }
  qh_setdel(facet1->neighbors, facet2);  /* here for makeridges */
  qh_setdel(facet2->neighbors, facet1);
} /* mergeneighbors */


/*---------------------------------

  qh_mergeridges( facet1, facet2 )
    merges the ridge set of facet1 into facet2

  returns:
    may delete all ridges for a vertex
    sets vertex->delridge on deleted ridges

  see:
    qh_mergecycle_ridges()

  design:
    delete ridges between facet1 and facet2
      mark (delridge) vertices on these ridges for later testing
    for each remaining ridge
      rename facet1 to facet2
*/
void qh_mergeridges(facetT *facet1, facetT *facet2) {
  ridgeT *ridge, **ridgep;
  vertexT *vertex, **vertexp;

  trace4((qh ferr, 4038, "qh_mergeridges: merge ridges of f%d and f%d\n",
          facet1->id, facet2->id));
  FOREACHridge_(facet2->ridges) {
    if ((ridge->top == facet1) || (ridge->bottom == facet1)) {
      FOREACHvertex_(ridge->vertices)
        vertex->delridge= True;
      qh_delridge(ridge);  /* expensive in high-d, could rebuild */
      ridgep--; /*repeat*/
    }
  }
  FOREACHridge_(facet1->ridges) {
    if (ridge->top == facet1)
      ridge->top= facet2;
    else
      ridge->bottom= facet2;
    qh_setappend(&(facet2->ridges), ridge);
  }
} /* mergeridges */


/*---------------------------------

  qh_mergesimplex( facet1, facet2, mergeapex )
    merge simplicial facet1 into facet2
    mergeapex==qh_MERGEapex if merging samecycle into horizon facet
      vertex id is latest (most recently created)
    facet1 may be contained in facet2
    ridges exist for both facets

  returns:
    facet2 with updated vertices, ridges, neighbors
    updated neighbors for facet1's vertices
    facet1 not deleted
    sets vertex->delridge on deleted ridges

  notes:
    special case code since this is the most common merge
    called from qh_mergefacet()

  design:
    if qh_MERGEapex
      add vertices of facet2 to qh.new_vertexlist if necessary
      add apex to facet2
    else
      for each ridge between facet1 and facet2
        set vertex->delridge
      determine the apex for facet1 (i.e., vertex to be merged)
      unless apex already in facet2
        insert apex into vertices for facet2
      add vertices of facet2 to qh.new_vertexlist if necessary
      add apex to qh.new_vertexlist if necessary
      for each vertex of facet1
        if apex
          rename facet1 to facet2 in its vertex neighbors
        else
          delete facet1 from vertex neighors
          if only in facet2
            add vertex to qh.del_vertices for later deletion
      for each ridge of facet1
        delete ridges between facet1 and facet2
        append other ridges to facet2 after renaming facet to facet2
*/
void qh_mergesimplex(facetT *facet1, facetT *facet2, boolT mergeapex) {
  vertexT *vertex, **vertexp, *apex;
  ridgeT *ridge, **ridgep;
  boolT issubset= False;
  int vertex_i= -1, vertex_n;
  facetT *neighbor, **neighborp, *otherfacet;

  if (mergeapex) {
    if (!facet2->newfacet)
      qh_newvertices(facet2->vertices);  /* apex is new */
    apex= SETfirstt_(facet1->vertices, vertexT);
    if (SETfirstt_(facet2->vertices, vertexT) != apex)
      qh_setaddnth(&facet2->vertices, 0, apex);  /* apex has last id */
    else
      issubset= True;
  }else {
    zinc_(Zmergesimplex);
    FOREACHvertex_(facet1->vertices)
      vertex->seen= False;
    FOREACHridge_(facet1->ridges) {
      if (otherfacet_(ridge, facet1) == facet2) {
        FOREACHvertex_(ridge->vertices) {
          vertex->seen= True;
          vertex->delridge= True;
        }
        break;
      }
    }
    FOREACHvertex_(facet1->vertices) {
      if (!vertex->seen)
        break;  /* must occur */
    }
    apex= vertex;
    trace4((qh ferr, 4039, "qh_mergesimplex: merge apex v%d of f%d into facet f%d\n",
          apex->id, facet1->id, facet2->id));
    FOREACHvertex_i_(facet2->vertices) {
      if (vertex->id < apex->id) {
        break;
      }else if (vertex->id == apex->id) {
        issubset= True;
        break;
      }
    }
    if (!issubset)
      qh_setaddnth(&facet2->vertices, vertex_i, apex);
    if (!facet2->newfacet)
      qh_newvertices(facet2->vertices);
    else if (!apex->newlist) {
      qh_removevertex(apex);
      qh_appendvertex(apex);
    }
  }
  trace4((qh ferr, 4040, "qh_mergesimplex: update vertex neighbors of f%d\n",
          facet1->id));
  FOREACHvertex_(facet1->vertices) {
    if (vertex == apex && !issubset)
      qh_setreplace(vertex->neighbors, facet1, facet2);
    else {
      qh_setdel(vertex->neighbors, facet1);
      if (!SETsecond_(vertex->neighbors))
        qh_mergevertex_del(vertex, facet1, facet2);
    }
  }
  trace4((qh ferr, 4041, "qh_mergesimplex: merge ridges and neighbors of f%d into f%d\n",
          facet1->id, facet2->id));
  qh visit_id++;
  FOREACHneighbor_(facet2)
    neighbor->visitid= qh visit_id;
  FOREACHridge_(facet1->ridges) {
    otherfacet= otherfacet_(ridge, facet1);
    if (otherfacet == facet2) {
      qh_setdel(facet2->ridges, ridge);
      qh_setfree(&(ridge->vertices));
      qh_memfree(ridge, (int)sizeof(ridgeT));
      qh_setdel(facet2->neighbors, facet1);
    }else {
      qh_setappend(&facet2->ridges, ridge);
      if (otherfacet->visitid != qh visit_id) {
        qh_setappend(&facet2->neighbors, otherfacet);
        qh_setreplace(otherfacet->neighbors, facet1, facet2);
        otherfacet->visitid= qh visit_id;
      }else {
        if (otherfacet->simplicial)    /* is degen, needs ridges */
          qh_makeridges(otherfacet);
        if (SETfirstt_(otherfacet->neighbors, facetT) != facet1)
          qh_setdel(otherfacet->neighbors, facet1);
        else {   /*keep newfacet->neighbors->horizon*/
          qh_setdel(otherfacet->neighbors, facet2);
          qh_setreplace(otherfacet->neighbors, facet1, facet2);
        }
      }
      if (ridge->top == facet1) /* wait until after qh_makeridges */
        ridge->top= facet2;
      else
        ridge->bottom= facet2;
    }
  }
  SETfirst_(facet1->ridges)= NULL; /* it will be deleted */
  trace3((qh ferr, 3006, "qh_mergesimplex: merged simplex f%d apex v%d into facet f%d\n",
          facet1->id, getid_(apex), facet2->id));
} /* mergesimplex */

/*---------------------------------

  qh_mergevertex_del( vertex, facet1, facet2 )
    delete a vertex because of merging facet1 into facet2

  returns:
    deletes vertex from facet2
    adds vertex to qh.del_vertices for later deletion
*/
void qh_mergevertex_del(vertexT *vertex, facetT *facet1, facetT *facet2) {

  zinc_(Zmergevertex);
  trace2((qh ferr, 2035, "qh_mergevertex_del: deleted v%d when merging f%d into f%d\n",
          vertex->id, facet1->id, facet2->id));
  qh_setdelsorted(facet2->vertices, vertex);
  vertex->deleted= True;
  qh_setappend(&qh del_vertices, vertex);
} /* mergevertex_del */

/*---------------------------------

  qh_mergevertex_neighbors( facet1, facet2 )
    merge the vertex neighbors of facet1 to facet2

  returns:
    if vertex is current qh.vertex_visit
      deletes facet1 from vertex->neighbors
    else
      renames facet1 to facet2 in vertex->neighbors
    deletes vertices if only one neighbor

  notes:
    assumes vertex neighbor sets are good
*/
void qh_mergevertex_neighbors(facetT *facet1, facetT *facet2) {
  vertexT *vertex, **vertexp;

  trace4((qh ferr, 4042, "qh_mergevertex_neighbors: merge vertex neighbors of f%d and f%d\n",
          facet1->id, facet2->id));
  if (qh tracevertex) {
    qh_fprintf(qh ferr, 8081, "qh_mergevertex_neighbors: of f%d and f%d at furthest p%d f0= %p\n",
             facet1->id, facet2->id, qh furthest_id, qh tracevertex->neighbors->e[0].p);
    qh_errprint("TRACE", NULL, NULL, NULL, qh tracevertex);
  }
  FOREACHvertex_(facet1->vertices) {
    if (vertex->visitid != qh vertex_visit)
      qh_setreplace(vertex->neighbors, facet1, facet2);
    else {
      qh_setdel(vertex->neighbors, facet1);
      if (!SETsecond_(vertex->neighbors))
        qh_mergevertex_del(vertex, facet1, facet2);
    }
  }
  if (qh tracevertex)
    qh_errprint("TRACE", NULL, NULL, NULL, qh tracevertex);
} /* mergevertex_neighbors */


/*---------------------------------

  qh_mergevertices( vertices1, vertices2 )
    merges the vertex set of facet1 into facet2

  returns:
    replaces vertices2 with merged set
    preserves vertex_visit for qh_mergevertex_neighbors
    updates qh.newvertex_list

  design:
    create a merged set of both vertices (in inverse id order)
*/
void qh_mergevertices(setT *vertices1, setT **vertices2) {
  int newsize= qh_setsize(vertices1)+qh_setsize(*vertices2) - qh hull_dim + 1;
  setT *mergedvertices;
  vertexT *vertex, **vertexp, **vertex2= SETaddr_(*vertices2, vertexT);

  mergedvertices= qh_settemp(newsize);
  FOREACHvertex_(vertices1) {
    if (!*vertex2 || vertex->id > (*vertex2)->id)
      qh_setappend(&mergedvertices, vertex);
    else {
      while (*vertex2 && (*vertex2)->id > vertex->id)
        qh_setappend(&mergedvertices, *vertex2++);
      if (!*vertex2 || (*vertex2)->id < vertex->id)
        qh_setappend(&mergedvertices, vertex);
      else
        qh_setappend(&mergedvertices, *vertex2++);
    }
  }
  while (*vertex2)
    qh_setappend(&mergedvertices, *vertex2++);
  if (newsize < qh_setsize(mergedvertices)) {
    qh_fprintf(qh ferr, 6100, "qhull internal error (qh_mergevertices): facets did not share a ridge\n");
    qh_errexit(qh_ERRqhull, NULL, NULL);
  }
  qh_setfree(vertices2);
  *vertices2= mergedvertices;
  qh_settemppop();
} /* mergevertices */


/*---------------------------------

  qh_neighbor_intersections( vertex )
    return intersection of all vertices in vertex->neighbors except for vertex

  returns:
    returns temporary set of vertices
    does not include vertex
    NULL if a neighbor is simplicial
    NULL if empty set

  notes:
    used for renaming vertices

  design:
    initialize the intersection set with vertices of the first two neighbors
    delete vertex from the intersection
    for each remaining neighbor
      intersect its vertex set with the intersection set
      return NULL if empty
    return the intersection set
*/
setT *qh_neighbor_intersections(vertexT *vertex) {
  facetT *neighbor, **neighborp, *neighborA, *neighborB;
  setT *intersect;
  int neighbor_i, neighbor_n;

  FOREACHneighbor_(vertex) {
    if (neighbor->simplicial)
      return NULL;
  }
  neighborA= SETfirstt_(vertex->neighbors, facetT);
  neighborB= SETsecondt_(vertex->neighbors, facetT);
  zinc_(Zintersectnum);
  if (!neighborA)
    return NULL;
  if (!neighborB)
    intersect= qh_setcopy(neighborA->vertices, 0);
  else
    intersect= qh_vertexintersect_new(neighborA->vertices, neighborB->vertices);
  qh_settemppush(intersect);
  qh_setdelsorted(intersect, vertex);
  FOREACHneighbor_i_(vertex) {
    if (neighbor_i >= 2) {
      zinc_(Zintersectnum);
      qh_vertexintersect(&intersect, neighbor->vertices);
      if (!SETfirst_(intersect)) {
        zinc_(Zintersectfail);
        qh_settempfree(&intersect);
        return NULL;
      }
    }
  }
  trace3((qh ferr, 3007, "qh_neighbor_intersections: %d vertices in neighbor intersection of v%d\n",
          qh_setsize(intersect), vertex->id));
  return intersect;
} /* neighbor_intersections */

/*---------------------------------

  qh_newvertices( vertices )
    add vertices to end of qh.vertex_list (marks as new vertices)

  returns:
    vertices on qh.newvertex_list
    vertex->newlist set
*/
void qh_newvertices(setT *vertices) {
  vertexT *vertex, **vertexp;

  FOREACHvertex_(vertices) {
    if (!vertex->newlist) {
      qh_removevertex(vertex);
      qh_appendvertex(vertex);
    }
  }
} /* newvertices */

/*---------------------------------

  qh_reducevertices()
    reduce extra vertices, shared vertices, and redundant vertices
    facet->newmerge is set if merged since last call
    if !qh.MERGEvertices, only removes extra vertices

  returns:
    True if also merged degen_redundant facets
    vertices are renamed if possible
    clears facet->newmerge and vertex->delridge

  notes:
    ignored if 2-d

  design:
    merge any degenerate or redundant facets
    for each newly merged facet
      remove extra vertices
    if qh.MERGEvertices
      for each newly merged facet
        for each vertex
          if vertex was on a deleted ridge
            rename vertex if it is shared
      remove delridge flag from new vertices
*/
boolT qh_reducevertices(void) {
  int numshare=0, numrename= 0;
  boolT degenredun= False;
  facetT *newfacet;
  vertexT *vertex, **vertexp;

  if (qh hull_dim == 2)
    return False;
  if (qh_merge_degenredundant())
    degenredun= True;
 LABELrestart:
  FORALLnew_facets {
    if (newfacet->newmerge) {
      if (!qh MERGEvertices)
        newfacet->newmerge= False;
      qh_remove_extravertices(newfacet);
    }
  }
  if (!qh MERGEvertices)
    return False;
  FORALLnew_facets {
    if (newfacet->newmerge) {
      newfacet->newmerge= False;
      FOREACHvertex_(newfacet->vertices) {
        if (vertex->delridge) {
          if (qh_rename_sharedvertex(vertex, newfacet)) {
            numshare++;
            vertexp--; /* repeat since deleted vertex */
          }
        }
      }
    }
  }
  FORALLvertex_(qh newvertex_list) {
    if (vertex->delridge && !vertex->deleted) {
      vertex->delridge= False;
      if (qh hull_dim >= 4 && qh_redundant_vertex(vertex)) {
        numrename++;
        if (qh_merge_degenredundant()) {
          degenredun= True;
          goto LABELrestart;
        }
      }
    }
  }
  trace1((qh ferr, 1014, "qh_reducevertices: renamed %d shared vertices and %d redundant vertices. Degen? %d\n",
          numshare, numrename, degenredun));
  return degenredun;
} /* reducevertices */

/*---------------------------------

  qh_redundant_vertex( vertex )
    detect and rename a redundant vertex
    vertices have full vertex->neighbors

  returns:
    returns true if find a redundant vertex
      deletes vertex(vertex->deleted)

  notes:
    only needed if vertex->delridge and hull_dim >= 4
    may add degenerate facets to qh.facet_mergeset
    doesn't change vertex->neighbors or create redundant facets

  design:
    intersect vertices of all facet neighbors of vertex
    determine ridges for these vertices
    if find a new vertex for vertex amoung these ridges and vertices
      rename vertex to the new vertex
*/
vertexT *qh_redundant_vertex(vertexT *vertex) {
  vertexT *newvertex= NULL;
  setT *vertices, *ridges;

  trace3((qh ferr, 3008, "qh_redundant_vertex: check if v%d can be renamed\n", vertex->id));
  if ((vertices= qh_neighbor_intersections(vertex))) {
    ridges= qh_vertexridges(vertex);
    if ((newvertex= qh_find_newvertex(vertex, vertices, ridges)))
      qh_renamevertex(vertex, newvertex, ridges, NULL, NULL);
    qh_settempfree(&ridges);
    qh_settempfree(&vertices);
  }
  return newvertex;
} /* redundant_vertex */

/*---------------------------------

  qh_remove_extravertices( facet )
    remove extra vertices from non-simplicial facets

  returns:
    returns True if it finds them

  design:
    for each vertex in facet
      if vertex not in a ridge (i.e., no longer used)
        delete vertex from facet
        delete facet from vertice's neighbors
        unless vertex in another facet
          add vertex to qh.del_vertices for later deletion
*/
boolT qh_remove_extravertices(facetT *facet) {
  ridgeT *ridge, **ridgep;
  vertexT *vertex, **vertexp;
  boolT foundrem= False;

  trace4((qh ferr, 4043, "qh_remove_extravertices: test f%d for extra vertices\n",
          facet->id));
  FOREACHvertex_(facet->vertices)
    vertex->seen= False;
  FOREACHridge_(facet->ridges) {
    FOREACHvertex_(ridge->vertices)
      vertex->seen= True;
  }
  FOREACHvertex_(facet->vertices) {
    if (!vertex->seen) {
      foundrem= True;
      zinc_(Zremvertex);
      qh_setdelsorted(facet->vertices, vertex);
      qh_setdel(vertex->neighbors, facet);
      if (!qh_setsize(vertex->neighbors)) {
        vertex->deleted= True;
        qh_setappend(&qh del_vertices, vertex);
        zinc_(Zremvertexdel);
        trace2((qh ferr, 2036, "qh_remove_extravertices: v%d deleted because it's lost all ridges\n", vertex->id));
      }else
        trace3((qh ferr, 3009, "qh_remove_extravertices: v%d removed from f%d because it's lost all ridges\n", vertex->id, facet->id));
      vertexp--; /*repeat*/
    }
  }
  return foundrem;
} /* remove_extravertices */

/*---------------------------------

  qh_rename_sharedvertex( vertex, facet )
    detect and rename if shared vertex in facet
    vertices have full ->neighbors

  returns:
    newvertex or NULL
    the vertex may still exist in other facets (i.e., a neighbor was pinched)
    does not change facet->neighbors
    updates vertex->neighbors

  notes:
    a shared vertex for a facet is only in ridges to one neighbor
    this may undo a pinched facet

    it does not catch pinches involving multiple facets.  These appear
      to be difficult to detect, since an exhaustive search is too expensive.

  design:
    if vertex only has two neighbors
      determine the ridges that contain the vertex
      determine the vertices shared by both neighbors
      if can find a new vertex in this set
        rename the vertex to the new vertex
*/
vertexT *qh_rename_sharedvertex(vertexT *vertex, facetT *facet) {
  facetT *neighbor, **neighborp, *neighborA= NULL;
  setT *vertices, *ridges;
  vertexT *newvertex;

  if (qh_setsize(vertex->neighbors) == 2) {
    neighborA= SETfirstt_(vertex->neighbors, facetT);
    if (neighborA == facet)
      neighborA= SETsecondt_(vertex->neighbors, facetT);
  }else if (qh hull_dim == 3)
    return NULL;
  else {
    qh visit_id++;
    FOREACHneighbor_(facet)
      neighbor->visitid= qh visit_id;
    FOREACHneighbor_(vertex) {
      if (neighbor->visitid == qh visit_id) {
        if (neighborA)
          return NULL;
        neighborA= neighbor;
      }
    }
    if (!neighborA) {
      qh_fprintf(qh ferr, 6101, "qhull internal error (qh_rename_sharedvertex): v%d's neighbors not in f%d\n",
        vertex->id, facet->id);
      qh_errprint("ERRONEOUS", facet, NULL, NULL, vertex);
      qh_errexit(qh_ERRqhull, NULL, NULL);
    }
  }
  /* the vertex is shared by facet and neighborA */
  ridges= qh_settemp(qh TEMPsize);
  neighborA->visitid= ++qh visit_id;
  qh_vertexridges_facet(vertex, facet, &ridges);
  trace2((qh ferr, 2037, "qh_rename_sharedvertex: p%d(v%d) is shared by f%d(%d ridges) and f%d\n",
    qh_pointid(vertex->point), vertex->id, facet->id, qh_setsize(ridges), neighborA->id));
  zinc_(Zintersectnum);
  vertices= qh_vertexintersect_new(facet->vertices, neighborA->vertices);
  qh_setdel(vertices, vertex);
  qh_settemppush(vertices);
  if ((newvertex= qh_find_newvertex(vertex, vertices, ridges)))
    qh_renamevertex(vertex, newvertex, ridges, facet, neighborA);
  qh_settempfree(&vertices);
  qh_settempfree(&ridges);
  return newvertex;
} /* rename_sharedvertex */

/*---------------------------------

  qh_renameridgevertex( ridge, oldvertex, newvertex )
    renames oldvertex as newvertex in ridge

  returns:

  design:
    delete oldvertex from ridge
    if newvertex already in ridge
      copy ridge->noconvex to another ridge if possible
      delete the ridge
    else
      insert newvertex into the ridge
      adjust the ridge's orientation
*/
void qh_renameridgevertex(ridgeT *ridge, vertexT *oldvertex, vertexT *newvertex) {
  int nth= 0, oldnth;
  facetT *temp;
  vertexT *vertex, **vertexp;

  oldnth= qh_setindex(ridge->vertices, oldvertex);
  qh_setdelnthsorted(ridge->vertices, oldnth);
  FOREACHvertex_(ridge->vertices) {
    if (vertex == newvertex) {
      zinc_(Zdelridge);
      if (ridge->nonconvex) /* only one ridge has nonconvex set */
        qh_copynonconvex(ridge);
      qh_delridge(ridge);
      trace2((qh ferr, 2038, "qh_renameridgevertex: ridge r%d deleted.  It contained both v%d and v%d\n",
        ridge->id, oldvertex->id, newvertex->id));
      return;
    }
    if (vertex->id < newvertex->id)
      break;
    nth++;
  }
  qh_setaddnth(&ridge->vertices, nth, newvertex);
  if (abs(oldnth - nth)%2) {
    trace3((qh ferr, 3010, "qh_renameridgevertex: swapped the top and bottom of ridge r%d\n",
            ridge->id));
    temp= ridge->top;
    ridge->top= ridge->bottom;
    ridge->bottom= temp;
  }
} /* renameridgevertex */


/*---------------------------------

  qh_renamevertex( oldvertex, newvertex, ridges, oldfacet, neighborA )
    renames oldvertex as newvertex in ridges
    gives oldfacet/neighborA if oldvertex is shared between two facets

  returns:
    oldvertex may still exist afterwards


  notes:
    can not change neighbors of newvertex (since it's a subset)

  design:
    for each ridge in ridges
      rename oldvertex to newvertex and delete degenerate ridges
    if oldfacet not defined
      for each neighbor of oldvertex
        delete oldvertex from neighbor's vertices
        remove extra vertices from neighbor
      add oldvertex to qh.del_vertices
    else if oldvertex only between oldfacet and neighborA
      delete oldvertex from oldfacet and neighborA
      add oldvertex to qh.del_vertices
    else oldvertex is in oldfacet and neighborA and other facets (i.e., pinched)
      delete oldvertex from oldfacet
      delete oldfacet from oldvertice's neighbors
      remove extra vertices (e.g., oldvertex) from neighborA
*/
void qh_renamevertex(vertexT *oldvertex, vertexT *newvertex, setT *ridges, facetT *oldfacet, facetT *neighborA) {
  facetT *neighbor, **neighborp;
  ridgeT *ridge, **ridgep;
  boolT istrace= False;

  if (qh IStracing >= 2 || oldvertex->id == qh tracevertex_id ||
        newvertex->id == qh tracevertex_id)
    istrace= True;
  FOREACHridge_(ridges)
    qh_renameridgevertex(ridge, oldvertex, newvertex);
  if (!oldfacet) {
    zinc_(Zrenameall);
    if (istrace)
      qh_fprintf(qh ferr, 8082, "qh_renamevertex: renamed v%d to v%d in several facets\n",
               oldvertex->id, newvertex->id);
    FOREACHneighbor_(oldvertex) {
      qh_maydropneighbor(neighbor);
      qh_setdelsorted(neighbor->vertices, oldvertex);
      if (qh_remove_extravertices(neighbor))
        neighborp--; /* neighbor may be deleted */
    }
    if (!oldvertex->deleted) {
      oldvertex->deleted= True;
      qh_setappend(&qh del_vertices, oldvertex);
    }
  }else if (qh_setsize(oldvertex->neighbors) == 2) {
    zinc_(Zrenameshare);
    if (istrace)
      qh_fprintf(qh ferr, 8083, "qh_renamevertex: renamed v%d to v%d in oldfacet f%d\n",
               oldvertex->id, newvertex->id, oldfacet->id);
    FOREACHneighbor_(oldvertex)
      qh_setdelsorted(neighbor->vertices, oldvertex);
    oldvertex->deleted= True;
    qh_setappend(&qh del_vertices, oldvertex);
  }else {
    zinc_(Zrenamepinch);
    if (istrace || qh IStracing)
      qh_fprintf(qh ferr, 8084, "qh_renamevertex: renamed pinched v%d to v%d between f%d and f%d\n",
               oldvertex->id, newvertex->id, oldfacet->id, neighborA->id);
    qh_setdelsorted(oldfacet->vertices, oldvertex);
    qh_setdel(oldvertex->neighbors, oldfacet);
    qh_remove_extravertices(neighborA);
  }
} /* renamevertex */


/*---------------------------------

  qh_test_appendmerge( facet, neighbor )
    tests facet/neighbor for convexity
    appends to mergeset if non-convex
    if pre-merging,
      nop if qh.SKIPconvex, or qh.MERGEexact and coplanar

  returns:
    true if appends facet/neighbor to mergeset
    sets facet->center as needed
    does not change facet->seen

  design:
    if qh.cos_max is defined
      if the angle between facet normals is too shallow
        append an angle-coplanar merge to qh.mergeset
        return True
    make facet's centrum if needed
    if facet's centrum is above the neighbor
      set isconcave
    else
      if facet's centrum is not below the neighbor
        set iscoplanar
      make neighbor's centrum if needed
      if neighbor's centrum is above the facet
        set isconcave
      else if neighbor's centrum is not below the facet
        set iscoplanar
   if isconcave or iscoplanar
     get angle if needed
     append concave or coplanar merge to qh.mergeset
*/
boolT qh_test_appendmerge(facetT *facet, facetT *neighbor) {
  realT dist, dist2= -REALmax, angle= -REALmax;
  boolT isconcave= False, iscoplanar= False, okangle= False;

  if (qh SKIPconvex && !qh POSTmerging)
    return False;
  if ((!qh MERGEexact || qh POSTmerging) && qh cos_max < REALmax/2) {
    angle= qh_getangle(facet->normal, neighbor->normal);
    zinc_(Zangletests);
    if (angle > qh cos_max) {
      zinc_(Zcoplanarangle);
      qh_appendmergeset(facet, neighbor, MRGanglecoplanar, &angle);
      trace2((qh ferr, 2039, "qh_test_appendmerge: coplanar angle %4.4g between f%d and f%d\n",
         angle, facet->id, neighbor->id));
      return True;
    }else
      okangle= True;
  }
  if (!facet->center)
    facet->center= qh_getcentrum(facet);
  zzinc_(Zcentrumtests);
  qh_distplane(facet->center, neighbor, &dist);
  if (dist > qh centrum_radius)
    isconcave= True;
  else {
    if (dist > -qh centrum_radius)
      iscoplanar= True;
    if (!neighbor->center)
      neighbor->center= qh_getcentrum(neighbor);
    zzinc_(Zcentrumtests);
    qh_distplane(neighbor->center, facet, &dist2);
    if (dist2 > qh centrum_radius)
      isconcave= True;
    else if (!iscoplanar && dist2 > -qh centrum_radius)
      iscoplanar= True;
  }
  if (!isconcave && (!iscoplanar || (qh MERGEexact && !qh POSTmerging)))
    return False;
  if (!okangle && qh ANGLEmerge) {
    angle= qh_getangle(facet->normal, neighbor->normal);
    zinc_(Zangletests);
  }
  if (isconcave) {
    zinc_(Zconcaveridge);
    if (qh ANGLEmerge)
      angle += qh_ANGLEconcave + 0.5;
    qh_appendmergeset(facet, neighbor, MRGconcave, &angle);
    trace0((qh ferr, 18, "qh_test_appendmerge: concave f%d to f%d dist %4.4g and reverse dist %4.4g angle %4.4g during p%d\n",
           facet->id, neighbor->id, dist, dist2, angle, qh furthest_id));
  }else /* iscoplanar */ {
    zinc_(Zcoplanarcentrum);
    qh_appendmergeset(facet, neighbor, MRGcoplanar, &angle);
    trace2((qh ferr, 2040, "qh_test_appendmerge: coplanar f%d to f%d dist %4.4g, reverse dist %4.4g angle %4.4g\n",
              facet->id, neighbor->id, dist, dist2, angle));
  }
  return True;
} /* test_appendmerge */

/*---------------------------------

  qh_test_vneighbors()
    test vertex neighbors for convexity
    tests all facets on qh.newfacet_list

  returns:
    true if non-convex vneighbors appended to qh.facet_mergeset
    initializes vertex neighbors if needed

  notes:
    assumes all facet neighbors have been tested
    this can be expensive
    this does not guarantee that a centrum is below all facets
      but it is unlikely
    uses qh.visit_id

  design:
    build vertex neighbors if necessary
    for all new facets
      for all vertices
        for each unvisited facet neighbor of the vertex
          test new facet and neighbor for convexity
*/
boolT qh_test_vneighbors(void /* qh newfacet_list */) {
  facetT *newfacet, *neighbor, **neighborp;
  vertexT *vertex, **vertexp;
  int nummerges= 0;

  trace1((qh ferr, 1015, "qh_test_vneighbors: testing vertex neighbors for convexity\n"));
  if (!qh VERTEXneighbors)
    qh_vertexneighbors();
  FORALLnew_facets
    newfacet->seen= False;
  FORALLnew_facets {
    newfacet->seen= True;
    newfacet->visitid= qh visit_id++;
    FOREACHneighbor_(newfacet)
      newfacet->visitid= qh visit_id;
    FOREACHvertex_(newfacet->vertices) {
      FOREACHneighbor_(vertex) {
        if (neighbor->seen || neighbor->visitid == qh visit_id)
          continue;
        if (qh_test_appendmerge(newfacet, neighbor))
          nummerges++;
      }
    }
  }
  zadd_(Ztestvneighbor, nummerges);
  trace1((qh ferr, 1016, "qh_test_vneighbors: found %d non-convex, vertex neighbors\n",
           nummerges));
  return (nummerges > 0);
} /* test_vneighbors */

/*---------------------------------

  qh_tracemerge( facet1, facet2 )
    print trace message after merge
*/
void qh_tracemerge(facetT *facet1, facetT *facet2) {
  boolT waserror= False;

#ifndef qh_NOtrace
  if (qh IStracing >= 4)
    qh_errprint("MERGED", facet2, NULL, NULL, NULL);
  if (facet2 == qh tracefacet || (qh tracevertex && qh tracevertex->newlist)) {
    qh_fprintf(qh ferr, 8085, "qh_tracemerge: trace facet and vertex after merge of f%d and f%d, furthest p%d\n", facet1->id, facet2->id, qh furthest_id);
    if (facet2 != qh tracefacet)
      qh_errprint("TRACE", qh tracefacet,
        (qh tracevertex && qh tracevertex->neighbors) ?
           SETfirstt_(qh tracevertex->neighbors, facetT) : NULL,
        NULL, qh tracevertex);
  }
  if (qh tracevertex) {
    if (qh tracevertex->deleted)
      qh_fprintf(qh ferr, 8086, "qh_tracemerge: trace vertex deleted at furthest p%d\n",
            qh furthest_id);
    else
      qh_checkvertex(qh tracevertex);
  }
  if (qh tracefacet) {
    qh_checkfacet(qh tracefacet, True, &waserror);
    if (waserror)
      qh_errexit(qh_ERRqhull, qh tracefacet, NULL);
  }
#endif /* !qh_NOtrace */
  if (qh CHECKfrequently || qh IStracing >= 4) { /* can't check polygon here */
    qh_checkfacet(facet2, True, &waserror);
    if (waserror)
      qh_errexit(qh_ERRqhull, NULL, NULL);
  }
} /* tracemerge */

/*---------------------------------

  qh_tracemerging()
    print trace message during POSTmerging

  returns:
    updates qh.mergereport

  notes:
    called from qh_mergecycle() and qh_mergefacet()

  see:
    qh_buildtracing()
*/
void qh_tracemerging(void) {
  realT cpu;
  int total;
  time_t timedata;
  struct tm *tp;

  qh mergereport= zzval_(Ztotmerge);
  time(&timedata);
  tp= localtime(&timedata);
  cpu= qh_CPUclock;
  cpu /= qh_SECticks;
  total= zzval_(Ztotmerge) - zzval_(Zcyclehorizon) + zzval_(Zcyclefacettot);
  qh_fprintf(qh ferr, 8087, "\n\
At %d:%d:%d & %2.5g CPU secs, qhull has merged %d facets.  The hull\n\
  contains %d facets and %d vertices.\n",
      tp->tm_hour, tp->tm_min, tp->tm_sec, cpu,
      total, qh num_facets - qh num_visible,
      qh num_vertices-qh_setsize(qh del_vertices));
} /* tracemerging */

/*---------------------------------

  qh_updatetested( facet1, facet2 )
    clear facet2->tested and facet1->ridge->tested for merge

  returns:
    deletes facet2->center unless it's already large
      if so, clears facet2->ridge->tested

  design:
    clear facet2->tested
    clear ridge->tested for facet1's ridges
    if facet2 has a centrum
      if facet2 is large
        set facet2->keepcentrum
      else if facet2 has 3 vertices due to many merges, or not large and post merging
        clear facet2->keepcentrum
      unless facet2->keepcentrum
        clear facet2->center to recompute centrum later
        clear ridge->tested for facet2's ridges
*/
void qh_updatetested(facetT *facet1, facetT *facet2) {
  ridgeT *ridge, **ridgep;
  int size;

  facet2->tested= False;
  FOREACHridge_(facet1->ridges)
    ridge->tested= False;
  if (!facet2->center)
    return;
  size= qh_setsize(facet2->vertices);
  if (!facet2->keepcentrum) {
    if (size > qh hull_dim + qh_MAXnewcentrum) {
      facet2->keepcentrum= True;
      zinc_(Zwidevertices);
    }
  }else if (size <= qh hull_dim + qh_MAXnewcentrum) {
    /* center and keepcentrum was set */
    if (size == qh hull_dim || qh POSTmerging)
      facet2->keepcentrum= False; /* if many merges need to recompute centrum */
  }
  if (!facet2->keepcentrum) {
    qh_memfree(facet2->center, qh normal_size);
    facet2->center= NULL;
    FOREACHridge_(facet2->ridges)
      ridge->tested= False;
  }
} /* updatetested */

/*---------------------------------

  qh_vertexridges( vertex )
    return temporary set of ridges adjacent to a vertex
    vertex->neighbors defined

  ntoes:
    uses qh.visit_id
    does not include implicit ridges for simplicial facets

  design:
    for each neighbor of vertex
      add ridges that include the vertex to ridges
*/
setT *qh_vertexridges(vertexT *vertex) {
  facetT *neighbor, **neighborp;
  setT *ridges= qh_settemp(qh TEMPsize);
  int size;

  qh visit_id++;
  FOREACHneighbor_(vertex)
    neighbor->visitid= qh visit_id;
  FOREACHneighbor_(vertex) {
    if (*neighborp)   /* no new ridges in last neighbor */
      qh_vertexridges_facet(vertex, neighbor, &ridges);
  }
  if (qh PRINTstatistics || qh IStracing) {
    size= qh_setsize(ridges);
    zinc_(Zvertexridge);
    zadd_(Zvertexridgetot, size);
    zmax_(Zvertexridgemax, size);
    trace3((qh ferr, 3011, "qh_vertexridges: found %d ridges for v%d\n",
             size, vertex->id));
  }
  return ridges;
} /* vertexridges */

/*---------------------------------

  qh_vertexridges_facet( vertex, facet, ridges )
    add adjacent ridges for vertex in facet
    neighbor->visitid==qh.visit_id if it hasn't been visited

  returns:
    ridges updated
    sets facet->visitid to qh.visit_id-1

  design:
    for each ridge of facet
      if ridge of visited neighbor (i.e., unprocessed)
        if vertex in ridge
          append ridge to vertex
    mark facet processed
*/
void qh_vertexridges_facet(vertexT *vertex, facetT *facet, setT **ridges) {
  ridgeT *ridge, **ridgep;
  facetT *neighbor;

  FOREACHridge_(facet->ridges) {
    neighbor= otherfacet_(ridge, facet);
    if (neighbor->visitid == qh visit_id
    && qh_setin(ridge->vertices, vertex))
      qh_setappend(ridges, ridge);
  }
  facet->visitid= qh visit_id-1;
} /* vertexridges_facet */

/*---------------------------------

  qh_willdelete( facet, replace )
    moves facet to visible list
    sets facet->f.replace to replace (may be NULL)

  returns:
    bumps qh.num_visible
*/
void qh_willdelete(facetT *facet, facetT *replace) {

  qh_removefacet(facet);
  qh_prependfacet(facet, &qh visible_list);
  qh num_visible++;
  facet->visible= True;
  facet->f.replace= replace;
} /* willdelete */

#else /* qh_NOmerge */
void qh_premerge(vertexT *apex, realT maxcentrum, realT maxangle) {
}
void qh_postmerge(const char *reason, realT maxcentrum, realT maxangle,
                      boolT vneighbors) {
}
boolT qh_checkzero(boolT testall) {
   }
#endif /* qh_NOmerge */

qhull-2012.1/src/libqhull/merge.h0000644000076400010400000001620511710144466017767 0ustar  bbarberAdministrators/*
  ---------------------------------

   merge.h
   header file for merge.c

   see qh-merge.htm and merge.c

   Copyright (c) 1993-2012 C.B. Barber.
   $Id: //main/2011/qhull/src/libqhull/merge.h#3 $$Change: 1464 $
   $DateTime: 2012/01/25 22:58:41 $$Author: bbarber $
*/

#ifndef qhDEFmerge
#define qhDEFmerge 1

#include "libqhull.h"


/*============ -constants- ==============*/

/*----------------------------------

  qh_ANGLEredundant
    indicates redundant merge in mergeT->angle
*/
#define qh_ANGLEredundant 6.0

/*----------------------------------

  qh_ANGLEdegen
    indicates degenerate facet in mergeT->angle
*/
#define qh_ANGLEdegen     5.0

/*----------------------------------

  qh_ANGLEconcave
    offset to indicate concave facets in mergeT->angle

  notes:
    concave facets are assigned the range of [2,4] in mergeT->angle
    roundoff error may make the angle less than 2
*/
#define qh_ANGLEconcave  1.5

/*----------------------------------

  MRG... (mergeType)
    indicates the type of a merge (mergeT->type)
*/
typedef enum {  /* in sort order for facet_mergeset */
  MRGnone= 0,
  MRGcoplanar,          /* centrum coplanar */
  MRGanglecoplanar,     /* angle coplanar */
                        /* could detect half concave ridges */
  MRGconcave,           /* concave ridge */
  MRGflip,              /* flipped facet. facet1 == facet2 */
  MRGridge,             /* duplicate ridge (qh_MERGEridge) */
                        /* degen and redundant go onto degen_mergeset */
  MRGdegen,             /* degenerate facet (!enough neighbors) facet1 == facet2 */
  MRGredundant,         /* redundant facet (vertex subset) */
                        /* merge_degenredundant assumes degen < redundant */
  MRGmirror,            /* mirror facet from qh_triangulate */
  ENDmrg
} mergeType;

/*----------------------------------

  qh_MERGEapex
    flag for qh_mergefacet() to indicate an apex merge
*/
#define qh_MERGEapex     True

/*============ -structures- ====================*/

/*----------------------------------

  mergeT
    structure used to merge facets
*/

typedef struct mergeT mergeT;
struct mergeT {         /* initialize in qh_appendmergeset */
  realT   angle;        /* angle between normals of facet1 and facet2 */
  facetT *facet1;       /* will merge facet1 into facet2 */
  facetT *facet2;
  mergeType type;
};


/*=========== -macros- =========================*/

/*----------------------------------

  FOREACHmerge_( merges ) {...}
    assign 'merge' to each merge in merges

  notes:
    uses 'mergeT *merge, **mergep;'
    if qh_mergefacet(),
      restart since qh.facet_mergeset may change
    see FOREACHsetelement_
*/
#define FOREACHmerge_( merges ) FOREACHsetelement_(mergeT, merges, merge)

/*============ prototypes in alphabetical order after pre/postmerge =======*/

void    qh_premerge(vertexT *apex, realT maxcentrum, realT maxangle);
void    qh_postmerge(const char *reason, realT maxcentrum, realT maxangle,
             boolT vneighbors);
void    qh_all_merges(boolT othermerge, boolT vneighbors);
void    qh_appendmergeset(facetT *facet, facetT *neighbor, mergeType mergetype, realT *angle);
setT   *qh_basevertices( facetT *samecycle);
void    qh_checkconnect(void /* qh new_facets */);
boolT   qh_checkzero(boolT testall);
int     qh_compareangle(const void *p1, const void *p2);
int     qh_comparemerge(const void *p1, const void *p2);
int     qh_comparevisit(const void *p1, const void *p2);
void    qh_copynonconvex(ridgeT *atridge);
void    qh_degen_redundant_facet(facetT *facet);
void    qh_degen_redundant_neighbors(facetT *facet, facetT *delfacet);
vertexT *qh_find_newvertex(vertexT *oldvertex, setT *vertices, setT *ridges);
void    qh_findbest_test(boolT testcentrum, facetT *facet, facetT *neighbor,
           facetT **bestfacet, realT *distp, realT *mindistp, realT *maxdistp);
facetT *qh_findbestneighbor(facetT *facet, realT *distp, realT *mindistp, realT *maxdistp);
void    qh_flippedmerges(facetT *facetlist, boolT *wasmerge);
void    qh_forcedmerges( boolT *wasmerge);
void    qh_getmergeset(facetT *facetlist);
void    qh_getmergeset_initial(facetT *facetlist);
void    qh_hashridge(setT *hashtable, int hashsize, ridgeT *ridge, vertexT *oldvertex);
ridgeT *qh_hashridge_find(setT *hashtable, int hashsize, ridgeT *ridge,
              vertexT *vertex, vertexT *oldvertex, int *hashslot);
void    qh_makeridges(facetT *facet);
void    qh_mark_dupridges(facetT *facetlist);
void    qh_maydropneighbor(facetT *facet);
int     qh_merge_degenredundant(void);
void    qh_merge_nonconvex( facetT *facet1, facetT *facet2, mergeType mergetype);
void    qh_mergecycle(facetT *samecycle, facetT *newfacet);
void    qh_mergecycle_all(facetT *facetlist, boolT *wasmerge);
void    qh_mergecycle_facets( facetT *samecycle, facetT *newfacet);
void    qh_mergecycle_neighbors(facetT *samecycle, facetT *newfacet);
void    qh_mergecycle_ridges(facetT *samecycle, facetT *newfacet);
void    qh_mergecycle_vneighbors( facetT *samecycle, facetT *newfacet);
void    qh_mergefacet(facetT *facet1, facetT *facet2, realT *mindist, realT *maxdist, boolT mergeapex);
void    qh_mergefacet2d(facetT *facet1, facetT *facet2);
void    qh_mergeneighbors(facetT *facet1, facetT *facet2);
void    qh_mergeridges(facetT *facet1, facetT *facet2);
void    qh_mergesimplex(facetT *facet1, facetT *facet2, boolT mergeapex);
void    qh_mergevertex_del(vertexT *vertex, facetT *facet1, facetT *facet2);
void    qh_mergevertex_neighbors(facetT *facet1, facetT *facet2);
void    qh_mergevertices(setT *vertices1, setT **vertices);
setT   *qh_neighbor_intersections(vertexT *vertex);
void    qh_newvertices(setT *vertices);
boolT   qh_reducevertices(void);
vertexT *qh_redundant_vertex(vertexT *vertex);
boolT   qh_remove_extravertices(facetT *facet);
vertexT *qh_rename_sharedvertex(vertexT *vertex, facetT *facet);
void    qh_renameridgevertex(ridgeT *ridge, vertexT *oldvertex, vertexT *newvertex);
void    qh_renamevertex(vertexT *oldvertex, vertexT *newvertex, setT *ridges,
                        facetT *oldfacet, facetT *neighborA);
boolT   qh_test_appendmerge(facetT *facet, facetT *neighbor);
boolT   qh_test_vneighbors(void /* qh newfacet_list */);
void    qh_tracemerge(facetT *facet1, facetT *facet2);
void    qh_tracemerging(void);
void    qh_updatetested( facetT *facet1, facetT *facet2);
setT   *qh_vertexridges(vertexT *vertex);
void    qh_vertexridges_facet(vertexT *vertex, facetT *facet, setT **ridges);
void    qh_willdelete(facetT *facet, facetT *replace);

#endif /* qhDEFmerge */
qhull-2012.1/src/libqhull/poly.c0000644000076400010400000011562411710144466017653 0ustar  bbarberAdministrators/*
  ---------------------------------

   poly.c
   implements polygons and simplices

   see qh-poly.htm, poly.h and libqhull.h

   infrequent code is in poly2.c
   (all but top 50 and their callers 12/3/95)

   Copyright (c) 1993-2012 The Geometry Center.
   $Id: //main/2011/qhull/src/libqhull/poly.c#5 $$Change: 1464 $
   $DateTime: 2012/01/25 22:58:41 $$Author: bbarber $
*/

#include "qhull_a.h"

/*======== functions in alphabetical order ==========*/

/*---------------------------------

  qh_appendfacet( facet )
    appends facet to end of qh.facet_list,

  returns:
    updates qh.newfacet_list, facet_next, facet_list
    increments qh.numfacets

  notes:
    assumes qh.facet_list/facet_tail is defined (createsimplex)

  see:
    qh_removefacet()

*/
void qh_appendfacet(facetT *facet) {
  facetT *tail= qh facet_tail;

  if (tail == qh newfacet_list)
    qh newfacet_list= facet;
  if (tail == qh facet_next)
    qh facet_next= facet;
  facet->previous= tail->previous;
  facet->next= tail;
  if (tail->previous)
    tail->previous->next= facet;
  else
    qh facet_list= facet;
  tail->previous= facet;
  qh num_facets++;
  trace4((qh ferr, 4044, "qh_appendfacet: append f%d to facet_list\n", facet->id));
} /* appendfacet */


/*---------------------------------

  qh_appendvertex( vertex )
    appends vertex to end of qh.vertex_list,

  returns:
    sets vertex->newlist
    updates qh.vertex_list, newvertex_list
    increments qh.num_vertices

  notes:
    assumes qh.vertex_list/vertex_tail is defined (createsimplex)

*/
void qh_appendvertex(vertexT *vertex) {
  vertexT *tail= qh vertex_tail;

  if (tail == qh newvertex_list)
    qh newvertex_list= vertex;
  vertex->newlist= True;
  vertex->previous= tail->previous;
  vertex->next= tail;
  if (tail->previous)
    tail->previous->next= vertex;
  else
    qh vertex_list= vertex;
  tail->previous= vertex;
  qh num_vertices++;
  trace4((qh ferr, 4045, "qh_appendvertex: append v%d to vertex_list\n", vertex->id));
} /* appendvertex */


/*---------------------------------

  qh_attachnewfacets( )
    attach horizon facets to new facets in qh.newfacet_list
    newfacets have neighbor and ridge links to horizon but not vice versa
    only needed for qh.ONLYgood

  returns:
    set qh.NEWfacets
    horizon facets linked to new facets
      ridges changed from visible facets to new facets
      simplicial ridges deleted
    qh.visible_list, no ridges valid
    facet->f.replace is a newfacet (if any)

  design:
    delete interior ridges and neighbor sets by
      for each visible, non-simplicial facet
        for each ridge
          if last visit or if neighbor is simplicial
            if horizon neighbor
              delete ridge for horizon's ridge set
            delete ridge
        erase neighbor set
    attach horizon facets and new facets by
      for all new facets
        if corresponding horizon facet is simplicial
          locate corresponding visible facet {may be more than one}
          link visible facet to new facet
          replace visible facet with new facet in horizon
        else it's non-simplicial
          for all visible neighbors of the horizon facet
            link visible neighbor to new facet
            delete visible neighbor from horizon facet
          append new facet to horizon's neighbors
          the first ridge of the new facet is the horizon ridge
          link the new facet into the horizon ridge
*/
void qh_attachnewfacets(void ) {
  facetT *newfacet= NULL, *neighbor, **neighborp, *horizon, *visible;
  ridgeT *ridge, **ridgep;

  qh NEWfacets= True;
  trace3((qh ferr, 3012, "qh_attachnewfacets: delete interior ridges\n"));
  qh visit_id++;
  FORALLvisible_facets {
    visible->visitid= qh visit_id;
    if (visible->ridges) {
      FOREACHridge_(visible->ridges) {
        neighbor= otherfacet_(ridge, visible);
        if (neighbor->visitid == qh visit_id
            || (!neighbor->visible && neighbor->simplicial)) {
          if (!neighbor->visible)  /* delete ridge for simplicial horizon */
            qh_setdel(neighbor->ridges, ridge);
          qh_setfree(&(ridge->vertices)); /* delete on 2nd visit */
          qh_memfree(ridge, (int)sizeof(ridgeT));
        }
      }
      SETfirst_(visible->ridges)= NULL;
    }
    SETfirst_(visible->neighbors)= NULL;
  }
  trace1((qh ferr, 1017, "qh_attachnewfacets: attach horizon facets to new facets\n"));
  FORALLnew_facets {
    horizon= SETfirstt_(newfacet->neighbors, facetT);
    if (horizon->simplicial) {
      visible= NULL;
      FOREACHneighbor_(horizon) {   /* may have more than one horizon ridge */
        if (neighbor->visible) {
          if (visible) {
            if (qh_setequal_skip(newfacet->vertices, 0, horizon->vertices,
                                  SETindex_(horizon->neighbors, neighbor))) {
              visible= neighbor;
              break;
            }
          }else
            visible= neighbor;
        }
      }
      if (visible) {
        visible->f.replace= newfacet;
        qh_setreplace(horizon->neighbors, visible, newfacet);
      }else {
        qh_fprintf(qh ferr, 6102, "qhull internal error (qh_attachnewfacets): couldn't find visible facet for horizon f%d of newfacet f%d\n",
                 horizon->id, newfacet->id);
        qh_errexit2 (qh_ERRqhull, horizon, newfacet);
      }
    }else { /* non-simplicial, with a ridge for newfacet */
      FOREACHneighbor_(horizon) {    /* may hold for many new facets */
        if (neighbor->visible) {
          neighbor->f.replace= newfacet;
          qh_setdelnth(horizon->neighbors,
                        SETindex_(horizon->neighbors, neighbor));
          neighborp--; /* repeat */
        }
      }
      qh_setappend(&horizon->neighbors, newfacet);
      ridge= SETfirstt_(newfacet->ridges, ridgeT);
      if (ridge->top == horizon)
        ridge->bottom= newfacet;
      else
        ridge->top= newfacet;
      }
  } /* newfacets */
  if (qh PRINTstatistics) {
    FORALLvisible_facets {
      if (!visible->f.replace)
        zinc_(Zinsidevisible);
    }
  }
} /* attachnewfacets */

/*---------------------------------

  qh_checkflipped( facet, dist, allerror )
    checks facet orientation to interior point

    if allerror set,
      tests against qh.DISTround
    else
      tests against 0 since tested against DISTround before

  returns:
    False if it flipped orientation (sets facet->flipped)
    distance if non-NULL
*/
boolT qh_checkflipped(facetT *facet, realT *distp, boolT allerror) {
  realT dist;

  if (facet->flipped && !distp)
    return False;
  zzinc_(Zdistcheck);
  qh_distplane(qh interior_point, facet, &dist);
  if (distp)
    *distp= dist;
  if ((allerror && dist > -qh DISTround)|| (!allerror && dist >= 0.0)) {
    facet->flipped= True;
    zzinc_(Zflippedfacets);
    trace0((qh ferr, 19, "qh_checkflipped: facet f%d is flipped, distance= %6.12g during p%d\n",
              facet->id, dist, qh furthest_id));
    qh_precision("flipped facet");
    return False;
  }
  return True;
} /* checkflipped */

/*---------------------------------

  qh_delfacet( facet )
    removes facet from facet_list and frees up its memory

  notes:
    assumes vertices and ridges already freed
*/
void qh_delfacet(facetT *facet) {
  void **freelistp; /* used !qh_NOmem */

  trace4((qh ferr, 4046, "qh_delfacet: delete f%d\n", facet->id));
  if (facet == qh tracefacet)
    qh tracefacet= NULL;
  if (facet == qh GOODclosest)
    qh GOODclosest= NULL;
  qh_removefacet(facet);
  if (!facet->tricoplanar || facet->keepcentrum) {
    qh_memfree_(facet->normal, qh normal_size, freelistp);
    if (qh CENTERtype == qh_ASvoronoi) {   /* uses macro calls */
      qh_memfree_(facet->center, qh center_size, freelistp);
    }else /* AScentrum */ {
      qh_memfree_(facet->center, qh normal_size, freelistp);
    }
  }
  qh_setfree(&(facet->neighbors));
  if (facet->ridges)
    qh_setfree(&(facet->ridges));
  qh_setfree(&(facet->vertices));
  if (facet->outsideset)
    qh_setfree(&(facet->outsideset));
  if (facet->coplanarset)
    qh_setfree(&(facet->coplanarset));
  qh_memfree_(facet, (int)sizeof(facetT), freelistp);
} /* delfacet */


/*---------------------------------

  qh_deletevisible()
    delete visible facets and vertices

  returns:
    deletes each facet and removes from facetlist
    at exit, qh.visible_list empty (== qh.newfacet_list)

  notes:
    ridges already deleted
    horizon facets do not reference facets on qh.visible_list
    new facets in qh.newfacet_list
    uses   qh.visit_id;
*/
void qh_deletevisible(void /*qh visible_list*/) {
  facetT *visible, *nextfacet;
  vertexT *vertex, **vertexp;
  int numvisible= 0, numdel= qh_setsize(qh del_vertices);

  trace1((qh ferr, 1018, "qh_deletevisible: delete %d visible facets and %d vertices\n",
         qh num_visible, numdel));
  for (visible= qh visible_list; visible && visible->visible;
                visible= nextfacet) { /* deleting current */
    nextfacet= visible->next;
    numvisible++;
    qh_delfacet(visible);
  }
  if (numvisible != qh num_visible) {
    qh_fprintf(qh ferr, 6103, "qhull internal error (qh_deletevisible): qh num_visible %d is not number of visible facets %d\n",
             qh num_visible, numvisible);
    qh_errexit(qh_ERRqhull, NULL, NULL);
  }
  qh num_visible= 0;
  zadd_(Zvisfacettot, numvisible);
  zmax_(Zvisfacetmax, numvisible);
  zzadd_(Zdelvertextot, numdel);
  zmax_(Zdelvertexmax, numdel);
  FOREACHvertex_(qh del_vertices)
    qh_delvertex(vertex);
  qh_settruncate(qh del_vertices, 0);
} /* deletevisible */

/*---------------------------------

  qh_facetintersect( facetA, facetB, skipa, skipB, prepend )
    return vertices for intersection of two simplicial facets
    may include 1 prepended entry (if more, need to settemppush)

  returns:
    returns set of qh.hull_dim-1 + prepend vertices
    returns skipped index for each test and checks for exactly one

  notes:
    does not need settemp since set in quick memory

  see also:
    qh_vertexintersect and qh_vertexintersect_new
    use qh_setnew_delnthsorted to get nth ridge (no skip information)

  design:
    locate skipped vertex by scanning facet A's neighbors
    locate skipped vertex by scanning facet B's neighbors
    intersect the vertex sets
*/
setT *qh_facetintersect(facetT *facetA, facetT *facetB,
                         int *skipA,int *skipB, int prepend) {
  setT *intersect;
  int dim= qh hull_dim, i, j;
  facetT **neighborsA, **neighborsB;

  neighborsA= SETaddr_(facetA->neighbors, facetT);
  neighborsB= SETaddr_(facetB->neighbors, facetT);
  i= j= 0;
  if (facetB == *neighborsA++)
    *skipA= 0;
  else if (facetB == *neighborsA++)
    *skipA= 1;
  else if (facetB == *neighborsA++)
    *skipA= 2;
  else {
    for (i=3; i < dim; i++) {
      if (facetB == *neighborsA++) {
        *skipA= i;
        break;
      }
    }
  }
  if (facetA == *neighborsB++)
    *skipB= 0;
  else if (facetA == *neighborsB++)
    *skipB= 1;
  else if (facetA == *neighborsB++)
    *skipB= 2;
  else {
    for (j=3; j < dim; j++) {
      if (facetA == *neighborsB++) {
        *skipB= j;
        break;
      }
    }
  }
  if (i >= dim || j >= dim) {
    qh_fprintf(qh ferr, 6104, "qhull internal error (qh_facetintersect): f%d or f%d not in others neighbors\n",
            facetA->id, facetB->id);
    qh_errexit2 (qh_ERRqhull, facetA, facetB);
  }
  intersect= qh_setnew_delnthsorted(facetA->vertices, qh hull_dim, *skipA, prepend);
  trace4((qh ferr, 4047, "qh_facetintersect: f%d skip %d matches f%d skip %d\n",
          facetA->id, *skipA, facetB->id, *skipB));
  return(intersect);
} /* facetintersect */

/*---------------------------------

  qh_gethash( hashsize, set, size, firstindex, skipelem )
    return hashvalue for a set with firstindex and skipelem

  notes:
    returned hash is in [0,hashsize)
    assumes at least firstindex+1 elements
    assumes skipelem is NULL, in set, or part of hash

    hashes memory addresses which may change over different runs of the same data
    using sum for hash does badly in high d
*/
int qh_gethash(int hashsize, setT *set, int size, int firstindex, void *skipelem) {
  void **elemp= SETelemaddr_(set, firstindex, void);
  ptr_intT hash = 0, elem;
  unsigned result;
  int i;
#ifdef _MSC_VER                   /* Microsoft Visual C++ -- warn about 64-bit issues */
#pragma warning( push)            /* WARN64 -- ptr_intT holds a 64-bit pointer */
#pragma warning( disable : 4311)  /* 'type cast': pointer truncation from 'void*' to 'ptr_intT' */
#endif

  switch (size-firstindex) {
  case 1:
    hash= (ptr_intT)(*elemp) - (ptr_intT) skipelem;
    break;
  case 2:
    hash= (ptr_intT)(*elemp) + (ptr_intT)elemp[1] - (ptr_intT) skipelem;
    break;
  case 3:
    hash= (ptr_intT)(*elemp) + (ptr_intT)elemp[1] + (ptr_intT)elemp[2]
      - (ptr_intT) skipelem;
    break;
  case 4:
    hash= (ptr_intT)(*elemp) + (ptr_intT)elemp[1] + (ptr_intT)elemp[2]
      + (ptr_intT)elemp[3] - (ptr_intT) skipelem;
    break;
  case 5:
    hash= (ptr_intT)(*elemp) + (ptr_intT)elemp[1] + (ptr_intT)elemp[2]
      + (ptr_intT)elemp[3] + (ptr_intT)elemp[4] - (ptr_intT) skipelem;
    break;
  case 6:
    hash= (ptr_intT)(*elemp) + (ptr_intT)elemp[1] + (ptr_intT)elemp[2]
      + (ptr_intT)elemp[3] + (ptr_intT)elemp[4]+ (ptr_intT)elemp[5]
      - (ptr_intT) skipelem;
    break;
  default:
    hash= 0;
    i= 3;
    do {     /* this is about 10% in 10-d */
      if ((elem= (ptr_intT)*elemp++) != (ptr_intT)skipelem) {
        hash ^= (elem << i) + (elem >> (32-i));
        i += 3;
        if (i >= 32)
          i -= 32;
      }
    }while (*elemp);
    break;
  }
  if (hashsize<0) {
    qh_fprintf(qh ferr, 6202, "qhull internal error: negative hashsize %d passed to qh_gethash [poly.c]\n", hashsize);
    qh_errexit2 (qh_ERRqhull, NULL, NULL);
  }
  result= (unsigned)hash;
  result %= (unsigned)hashsize;
  /* result= 0; for debugging */
  return result;
#ifdef _MSC_VER
#pragma warning( pop)
#endif
} /* gethash */

/*---------------------------------

  qh_makenewfacet( vertices, toporient, horizon )
    creates a toporient? facet from vertices

  returns:
    returns newfacet
      adds newfacet to qh.facet_list
      newfacet->vertices= vertices
      if horizon
        newfacet->neighbor= horizon, but not vice versa
    newvertex_list updated with vertices
*/
facetT *qh_makenewfacet(setT *vertices, boolT toporient,facetT *horizon) {
  facetT *newfacet;
  vertexT *vertex, **vertexp;

  FOREACHvertex_(vertices) {
    if (!vertex->newlist) {
      qh_removevertex(vertex);
      qh_appendvertex(vertex);
    }
  }
  newfacet= qh_newfacet();
  newfacet->vertices= vertices;
  newfacet->toporient= (unsigned char)toporient;
  if (horizon)
    qh_setappend(&(newfacet->neighbors), horizon);
  qh_appendfacet(newfacet);
  return(newfacet);
} /* makenewfacet */


/*---------------------------------

  qh_makenewplanes()
    make new hyperplanes for facets on qh.newfacet_list

  returns:
    all facets have hyperplanes or are marked for   merging
    doesn't create hyperplane if horizon is coplanar (will merge)
    updates qh.min_vertex if qh.JOGGLEmax

  notes:
    facet->f.samecycle is defined for facet->mergehorizon facets
*/
void qh_makenewplanes(void /* newfacet_list */) {
  facetT *newfacet;

  FORALLnew_facets {
    if (!newfacet->mergehorizon)
      qh_setfacetplane(newfacet);
  }
  if (qh JOGGLEmax < REALmax/2)
    minimize_(qh min_vertex, -wwval_(Wnewvertexmax));
} /* makenewplanes */

/*---------------------------------

  qh_makenew_nonsimplicial( visible, apex, numnew )
    make new facets for ridges of a visible facet

  returns:
    first newfacet, bumps numnew as needed
    attaches new facets if !qh.ONLYgood
    marks ridge neighbors for simplicial visible
    if (qh.ONLYgood)
      ridges on newfacet, horizon, and visible
    else
      ridge and neighbors between newfacet and   horizon
      visible facet's ridges are deleted

  notes:
    qh.visit_id if visible has already been processed
    sets neighbor->seen for building f.samecycle
      assumes all 'seen' flags initially false

  design:
    for each ridge of visible facet
      get neighbor of visible facet
      if neighbor was already processed
        delete the ridge (will delete all visible facets later)
      if neighbor is a horizon facet
        create a new facet
        if neighbor coplanar
          adds newfacet to f.samecycle for later merging
        else
          updates neighbor's neighbor set
          (checks for non-simplicial facet with multiple ridges to visible facet)
        updates neighbor's ridge set
        (checks for simplicial neighbor to non-simplicial visible facet)
        (deletes ridge if neighbor is simplicial)

*/
#ifndef qh_NOmerge
facetT *qh_makenew_nonsimplicial(facetT *visible, vertexT *apex, int *numnew) {
  void **freelistp; /* used !qh_NOmem */
  ridgeT *ridge, **ridgep;
  facetT *neighbor, *newfacet= NULL, *samecycle;
  setT *vertices;
  boolT toporient;
  int ridgeid;

  FOREACHridge_(visible->ridges) {
    ridgeid= ridge->id;
    neighbor= otherfacet_(ridge, visible);
    if (neighbor->visible) {
      if (!qh ONLYgood) {
        if (neighbor->visitid == qh visit_id) {
          qh_setfree(&(ridge->vertices));  /* delete on 2nd visit */
          qh_memfree_(ridge, (int)sizeof(ridgeT), freelistp);
        }
      }
    }else {  /* neighbor is an horizon facet */
      toporient= (ridge->top == visible);
      vertices= qh_setnew(qh hull_dim); /* makes sure this is quick */
      qh_setappend(&vertices, apex);
      qh_setappend_set(&vertices, ridge->vertices);
      newfacet= qh_makenewfacet(vertices, toporient, neighbor);
      (*numnew)++;
      if (neighbor->coplanar) {
        newfacet->mergehorizon= True;
        if (!neighbor->seen) {
          newfacet->f.samecycle= newfacet;
          neighbor->f.newcycle= newfacet;
        }else {
          samecycle= neighbor->f.newcycle;
          newfacet->f.samecycle= samecycle->f.samecycle;
          samecycle->f.samecycle= newfacet;
        }
      }
      if (qh ONLYgood) {
        if (!neighbor->simplicial)
          qh_setappend(&(newfacet->ridges), ridge);
      }else {  /* qh_attachnewfacets */
        if (neighbor->seen) {
          if (neighbor->simplicial) {
            qh_fprintf(qh ferr, 6105, "qhull internal error (qh_makenew_nonsimplicial): simplicial f%d sharing two ridges with f%d\n",
                   neighbor->id, visible->id);
            qh_errexit2 (qh_ERRqhull, neighbor, visible);
          }
          qh_setappend(&(neighbor->neighbors), newfacet);
        }else
          qh_setreplace(neighbor->neighbors, visible, newfacet);
        if (neighbor->simplicial) {
          qh_setdel(neighbor->ridges, ridge);
          qh_setfree(&(ridge->vertices));
          qh_memfree(ridge, (int)sizeof(ridgeT));
        }else {
          qh_setappend(&(newfacet->ridges), ridge);
          if (toporient)
            ridge->top= newfacet;
          else
            ridge->bottom= newfacet;
        }
      trace4((qh ferr, 4048, "qh_makenew_nonsimplicial: created facet f%d from v%d and r%d of horizon f%d\n",
            newfacet->id, apex->id, ridgeid, neighbor->id));
      }
    }
    neighbor->seen= True;
  } /* for each ridge */
  if (!qh ONLYgood)
    SETfirst_(visible->ridges)= NULL;
  return newfacet;
} /* makenew_nonsimplicial */
#else /* qh_NOmerge */
facetT *qh_makenew_nonsimplicial(facetT *visible, vertexT *apex, int *numnew) {
  return NULL;
}
#endif /* qh_NOmerge */

/*---------------------------------

  qh_makenew_simplicial( visible, apex, numnew )
    make new facets for simplicial visible facet and apex

  returns:
    attaches new facets if (!qh.ONLYgood)
      neighbors between newfacet and horizon

  notes:
    nop if neighbor->seen or neighbor->visible(see qh_makenew_nonsimplicial)

  design:
    locate neighboring horizon facet for visible facet
    determine vertices and orientation
    create new facet
    if coplanar,
      add new facet to f.samecycle
    update horizon facet's neighbor list
*/
facetT *qh_makenew_simplicial(facetT *visible, vertexT *apex, int *numnew) {
  facetT *neighbor, **neighborp, *newfacet= NULL;
  setT *vertices;
  boolT flip, toporient;
  int horizonskip, visibleskip;

  FOREACHneighbor_(visible) {
    if (!neighbor->seen && !neighbor->visible) {
      vertices= qh_facetintersect(neighbor,visible, &horizonskip, &visibleskip, 1);
      SETfirst_(vertices)= apex;
      flip= ((horizonskip & 0x1) ^ (visibleskip & 0x1));
      if (neighbor->toporient)
        toporient= horizonskip & 0x1;
      else
        toporient= (horizonskip & 0x1) ^ 0x1;
      newfacet= qh_makenewfacet(vertices, toporient, neighbor);
      (*numnew)++;
      if (neighbor->coplanar && (qh PREmerge || qh MERGEexact)) {
#ifndef qh_NOmerge
        newfacet->f.samecycle= newfacet;
        newfacet->mergehorizon= True;
#endif
      }
      if (!qh ONLYgood)
        SETelem_(neighbor->neighbors, horizonskip)= newfacet;
      trace4((qh ferr, 4049, "qh_makenew_simplicial: create facet f%d top %d from v%d and horizon f%d skip %d top %d and visible f%d skip %d, flip? %d\n",
            newfacet->id, toporient, apex->id, neighbor->id, horizonskip,
              neighbor->toporient, visible->id, visibleskip, flip));
    }
  }
  return newfacet;
} /* makenew_simplicial */

/*---------------------------------

  qh_matchneighbor( newfacet, newskip, hashsize, hashcount )
    either match subridge of newfacet with neighbor or add to hash_table

  returns:
    duplicate ridges are unmatched and marked by qh_DUPLICATEridge

  notes:
    ridge is newfacet->vertices w/o newskip vertex
    do not allocate memory (need to free hash_table cleanly)
    uses linear hash chains

  see also:
    qh_matchduplicates

  design:
    for each possible matching facet in qh.hash_table
      if vertices match
        set ismatch, if facets have opposite orientation
        if ismatch and matching facet doesn't have a match
          match the facets by updating their neighbor sets
        else
          indicate a duplicate ridge
          set facet hyperplane for later testing
          add facet to hashtable
          unless the other facet was already a duplicate ridge
            mark both facets with a duplicate ridge
            add other facet (if defined) to hash table
*/
void qh_matchneighbor(facetT *newfacet, int newskip, int hashsize, int *hashcount) {
  boolT newfound= False;   /* True, if new facet is already in hash chain */
  boolT same, ismatch;
  int hash, scan;
  facetT *facet, *matchfacet;
  int skip, matchskip;

  hash= qh_gethash(hashsize, newfacet->vertices, qh hull_dim, 1,
                     SETelem_(newfacet->vertices, newskip));
  trace4((qh ferr, 4050, "qh_matchneighbor: newfacet f%d skip %d hash %d hashcount %d\n",
          newfacet->id, newskip, hash, *hashcount));
  zinc_(Zhashlookup);
  for (scan= hash; (facet= SETelemt_(qh hash_table, scan, facetT));
       scan= (++scan >= hashsize ? 0 : scan)) {
    if (facet == newfacet) {
      newfound= True;
      continue;
    }
    zinc_(Zhashtests);
    if (qh_matchvertices(1, newfacet->vertices, newskip, facet->vertices, &skip, &same)) {
      if (SETelem_(newfacet->vertices, newskip) ==
          SETelem_(facet->vertices, skip)) {
        qh_precision("two facets with the same vertices");
        qh_fprintf(qh ferr, 6106, "qhull precision error: Vertex sets are the same for f%d and f%d.  Can not force output.\n",
          facet->id, newfacet->id);
        qh_errexit2 (qh_ERRprec, facet, newfacet);
      }
      ismatch= (same == (boolT)((newfacet->toporient ^ facet->toporient)));
      matchfacet= SETelemt_(facet->neighbors, skip, facetT);
      if (ismatch && !matchfacet) {
        SETelem_(facet->neighbors, skip)= newfacet;
        SETelem_(newfacet->neighbors, newskip)= facet;
        (*hashcount)--;
        trace4((qh ferr, 4051, "qh_matchneighbor: f%d skip %d matched with new f%d skip %d\n",
           facet->id, skip, newfacet->id, newskip));
        return;
      }
      if (!qh PREmerge && !qh MERGEexact) {
        qh_precision("a ridge with more than two neighbors");
        qh_fprintf(qh ferr, 6107, "qhull precision error: facets f%d, f%d and f%d meet at a ridge with more than 2 neighbors.  Can not continue.\n",
                 facet->id, newfacet->id, getid_(matchfacet));
        qh_errexit2 (qh_ERRprec, facet, newfacet);
      }
      SETelem_(newfacet->neighbors, newskip)= qh_DUPLICATEridge;
      newfacet->dupridge= True;
      if (!newfacet->normal)
        qh_setfacetplane(newfacet);
      qh_addhash(newfacet, qh hash_table, hashsize, hash);
      (*hashcount)++;
      if (!facet->normal)
        qh_setfacetplane(facet);
      if (matchfacet != qh_DUPLICATEridge) {
        SETelem_(facet->neighbors, skip)= qh_DUPLICATEridge;
        facet->dupridge= True;
        if (!facet->normal)
          qh_setfacetplane(facet);
        if (matchfacet) {
          matchskip= qh_setindex(matchfacet->neighbors, facet);
          SETelem_(matchfacet->neighbors, matchskip)= qh_DUPLICATEridge;
          matchfacet->dupridge= True;
          if (!matchfacet->normal)
            qh_setfacetplane(matchfacet);
          qh_addhash(matchfacet, qh hash_table, hashsize, hash);
          *hashcount += 2;
        }
      }
      trace4((qh ferr, 4052, "qh_matchneighbor: new f%d skip %d duplicates ridge for f%d skip %d matching f%d ismatch %d at hash %d\n",
           newfacet->id, newskip, facet->id, skip,
           (matchfacet == qh_DUPLICATEridge ? -2 : getid_(matchfacet)),
           ismatch, hash));
      return; /* end of duplicate ridge */
    }
  }
  if (!newfound)
    SETelem_(qh hash_table, scan)= newfacet;  /* same as qh_addhash */
  (*hashcount)++;
  trace4((qh ferr, 4053, "qh_matchneighbor: no match for f%d skip %d at hash %d\n",
           newfacet->id, newskip, hash));
} /* matchneighbor */


/*---------------------------------

  qh_matchnewfacets()
    match newfacets in qh.newfacet_list to their newfacet neighbors

  returns:
    qh.newfacet_list with full neighbor sets
      get vertices with nth neighbor by deleting nth vertex
    if qh.PREmerge/MERGEexact or qh.FORCEoutput
      sets facet->flippped if flipped normal (also prevents point partitioning)
    if duplicate ridges and qh.PREmerge/MERGEexact
      sets facet->dupridge
      missing neighbor links identifies extra ridges to be merging (qh_MERGEridge)

  notes:
    newfacets already have neighbor[0] (horizon facet)
    assumes qh.hash_table is NULL
    vertex->neighbors has not been updated yet
    do not allocate memory after qh.hash_table (need to free it cleanly)

  design:
    delete neighbor sets for all new facets
    initialize a hash table
    for all new facets
      match facet with neighbors
    if unmatched facets (due to duplicate ridges)
      for each new facet with a duplicate ridge
        match it with a facet
    check for flipped facets
*/
void qh_matchnewfacets(void /* qh newfacet_list */) {
  int numnew=0, hashcount=0, newskip;
  facetT *newfacet, *neighbor;
  int dim= qh hull_dim, hashsize, neighbor_i, neighbor_n;
  setT *neighbors;
#ifndef qh_NOtrace
  int facet_i, facet_n, numfree= 0;
  facetT *facet;
#endif

  trace1((qh ferr, 1019, "qh_matchnewfacets: match neighbors for new facets.\n"));
  FORALLnew_facets {
    numnew++;
    {  /* inline qh_setzero(newfacet->neighbors, 1, qh hull_dim); */
      neighbors= newfacet->neighbors;
      neighbors->e[neighbors->maxsize].i= dim+1; /*may be overwritten*/
      memset((char *)SETelemaddr_(neighbors, 1, void), 0, dim * SETelemsize);
    }
  }

  qh_newhashtable(numnew*(qh hull_dim-1)); /* twice what is normally needed,
                                     but every ridge could be DUPLICATEridge */
  hashsize= qh_setsize(qh hash_table);
  FORALLnew_facets {
    for (newskip=1; newskipneighbors, k, facetT);
          if (!neighbor || neighbor == qh_DUPLICATEridge)
            count++;
        }
        if (facet == newfacet)
          break;
      }
      if (count != hashcount) {
        qh_fprintf(qh ferr, 8088, "qh_matchnewfacets: after adding facet %d, hashcount %d != count %d\n",
                 newfacet->id, hashcount, count);
        qh_errexit(qh_ERRqhull, newfacet, NULL);
      }
    }
#endif  /* end of trap code */
  }
  if (hashcount) {
    FORALLnew_facets {
      if (newfacet->dupridge) {
        FOREACHneighbor_i_(newfacet) {
          if (neighbor == qh_DUPLICATEridge) {
            qh_matchduplicates(newfacet, neighbor_i, hashsize, &hashcount);
                    /* this may report MERGEfacet */
          }
        }
      }
    }
  }
  if (hashcount) {
    qh_fprintf(qh ferr, 6108, "qhull internal error (qh_matchnewfacets): %d neighbors did not match up\n",
        hashcount);
    qh_printhashtable(qh ferr);
    qh_errexit(qh_ERRqhull, NULL, NULL);
  }
#ifndef qh_NOtrace
  if (qh IStracing >= 2) {
    FOREACHfacet_i_(qh hash_table) {
      if (!facet)
        numfree++;
    }
    qh_fprintf(qh ferr, 8089, "qh_matchnewfacets: %d new facets, %d unused hash entries .  hashsize %d\n",
             numnew, numfree, qh_setsize(qh hash_table));
  }
#endif /* !qh_NOtrace */
  qh_setfree(&qh hash_table);
  if (qh PREmerge || qh MERGEexact) {
    if (qh IStracing >= 4)
      qh_printfacetlist(qh newfacet_list, NULL, qh_ALL);
    FORALLnew_facets {
      if (newfacet->normal)
        qh_checkflipped(newfacet, NULL, qh_ALL);
    }
  }else if (qh FORCEoutput)
    qh_checkflipped_all(qh newfacet_list);  /* prints warnings for flipped */
} /* matchnewfacets */


/*---------------------------------

  qh_matchvertices( firstindex, verticesA, skipA, verticesB, skipB, same )
    tests whether vertices match with a single skip
    starts match at firstindex since all new facets have a common vertex

  returns:
    true if matched vertices
    skip index for each set
    sets same iff vertices have the same orientation

  notes:
    assumes skipA is in A and both sets are the same size

  design:
    set up pointers
    scan both sets checking for a match
    test orientation
*/
boolT qh_matchvertices(int firstindex, setT *verticesA, int skipA,
       setT *verticesB, int *skipB, boolT *same) {
  vertexT **elemAp, **elemBp, **skipBp=NULL, **skipAp;

  elemAp= SETelemaddr_(verticesA, firstindex, vertexT);
  elemBp= SETelemaddr_(verticesB, firstindex, vertexT);
  skipAp= SETelemaddr_(verticesA, skipA, vertexT);
  do if (elemAp != skipAp) {
    while (*elemAp != *elemBp++) {
      if (skipBp)
        return False;
      skipBp= elemBp;  /* one extra like FOREACH */
    }
  }while (*(++elemAp));
  if (!skipBp)
    skipBp= ++elemBp;
  *skipB= SETindex_(verticesB, skipB); /* i.e., skipBp - verticesB */
  *same= !((skipA & 0x1) ^ (*skipB & 0x1)); /* result is 0 or 1 */
  trace4((qh ferr, 4054, "qh_matchvertices: matched by skip %d(v%d) and skip %d(v%d) same? %d\n",
          skipA, (*skipAp)->id, *skipB, (*(skipBp-1))->id, *same));
  return(True);
} /* matchvertices */

/*---------------------------------

  qh_newfacet()
    return a new facet

  returns:
    all fields initialized or cleared   (NULL)
    preallocates neighbors set
*/
facetT *qh_newfacet(void) {
  facetT *facet;
  void **freelistp; /* used !qh_NOmem */

  qh_memalloc_((int)sizeof(facetT), freelistp, facet, facetT);
  memset((char *)facet, (size_t)0, sizeof(facetT));
  if (qh facet_id == qh tracefacet_id)
    qh tracefacet= facet;
  facet->id= qh facet_id++;
  facet->neighbors= qh_setnew(qh hull_dim);
#if !qh_COMPUTEfurthest
  facet->furthestdist= 0.0;
#endif
#if qh_MAXoutside
  if (qh FORCEoutput && qh APPROXhull)
    facet->maxoutside= qh MINoutside;
  else
    facet->maxoutside= qh DISTround;
#endif
  facet->simplicial= True;
  facet->good= True;
  facet->newfacet= True;
  trace4((qh ferr, 4055, "qh_newfacet: created facet f%d\n", facet->id));
  return(facet);
} /* newfacet */


/*---------------------------------

  qh_newridge()
    return a new ridge
*/
ridgeT *qh_newridge(void) {
  ridgeT *ridge;
  void **freelistp;   /* used !qh_NOmem */

  qh_memalloc_((int)sizeof(ridgeT), freelistp, ridge, ridgeT);
  memset((char *)ridge, (size_t)0, sizeof(ridgeT));
  zinc_(Ztotridges);
  if (qh ridge_id == 0xFFFFFF) {
    qh_fprintf(qh ferr, 7074, "\
qhull warning: more than %d ridges.  ID field overflows and two ridges\n\
may have the same identifier.  Otherwise output ok.\n", 0xFFFFFF);
  }
  ridge->id= qh ridge_id++;
  trace4((qh ferr, 4056, "qh_newridge: created ridge r%d\n", ridge->id));
  return(ridge);
} /* newridge */


/*---------------------------------

  qh_pointid(  )
    return id for a point,
    returns -3 if null, -2 if interior, or -1 if not known

  alternative code:
    unsigned long id;
    id= ((unsigned long)point - (unsigned long)qh.first_point)/qh.normal_size;

  notes:
    WARN64 -- id truncated to 32-bits, at most 2G points
    NOerrors returned (QhullPoint::id)
    if point not in point array
      the code does a comparison of unrelated pointers.
*/
int qh_pointid(pointT *point) {
  ptr_intT offset, id;

  if (!point)
    return -3;
  else if (point == qh interior_point)
    return -2;
  else if (point >= qh first_point
  && point < qh first_point + qh num_points * qh hull_dim) {
    offset= (ptr_intT)(point - qh first_point);
    id= offset / qh hull_dim;
  }else if ((id= qh_setindex(qh other_points, point)) != -1)
    id += qh num_points;
  else
    return -1;
  return (int)id;
} /* pointid */

/*---------------------------------

  qh_removefacet( facet )
    unlinks facet from qh.facet_list,

  returns:
    updates qh.facet_list .newfacet_list .facet_next visible_list
    decrements qh.num_facets

  see:
    qh_appendfacet
*/
void qh_removefacet(facetT *facet) {
  facetT *next= facet->next, *previous= facet->previous;

  if (facet == qh newfacet_list)
    qh newfacet_list= next;
  if (facet == qh facet_next)
    qh facet_next= next;
  if (facet == qh visible_list)
    qh visible_list= next;
  if (previous) {
    previous->next= next;
    next->previous= previous;
  }else {  /* 1st facet in qh facet_list */
    qh facet_list= next;
    qh facet_list->previous= NULL;
  }
  qh num_facets--;
  trace4((qh ferr, 4057, "qh_removefacet: remove f%d from facet_list\n", facet->id));
} /* removefacet */


/*---------------------------------

  qh_removevertex( vertex )
    unlinks vertex from qh.vertex_list,

  returns:
    updates qh.vertex_list .newvertex_list
    decrements qh.num_vertices
*/
void qh_removevertex(vertexT *vertex) {
  vertexT *next= vertex->next, *previous= vertex->previous;

  if (vertex == qh newvertex_list)
    qh newvertex_list= next;
  if (previous) {
    previous->next= next;
    next->previous= previous;
  }else {  /* 1st vertex in qh vertex_list */
    qh vertex_list= vertex->next;
    qh vertex_list->previous= NULL;
  }
  qh num_vertices--;
  trace4((qh ferr, 4058, "qh_removevertex: remove v%d from vertex_list\n", vertex->id));
} /* removevertex */


/*---------------------------------

  qh_updatevertices()
    update vertex neighbors and delete interior vertices

  returns:
    if qh.VERTEXneighbors, updates neighbors for each vertex
      if qh.newvertex_list,
         removes visible neighbors  from vertex neighbors
      if qh.newfacet_list
         adds new facets to vertex neighbors
    if qh.visible_list
       interior vertices added to qh.del_vertices for later partitioning

  design:
    if qh.VERTEXneighbors
      deletes references to visible facets from vertex neighbors
      appends new facets to the neighbor list for each vertex
      checks all vertices of visible facets
        removes visible facets from neighbor lists
        marks unused vertices for deletion
*/
void qh_updatevertices(void /*qh newvertex_list, newfacet_list, visible_list*/) {
  facetT *newfacet= NULL, *neighbor, **neighborp, *visible;
  vertexT *vertex, **vertexp;

  trace3((qh ferr, 3013, "qh_updatevertices: delete interior vertices and update vertex->neighbors\n"));
  if (qh VERTEXneighbors) {
    FORALLvertex_(qh newvertex_list) {
      FOREACHneighbor_(vertex) {
        if (neighbor->visible)
          SETref_(neighbor)= NULL;
      }
      qh_setcompact(vertex->neighbors);
    }
    FORALLnew_facets {
      FOREACHvertex_(newfacet->vertices)
        qh_setappend(&vertex->neighbors, newfacet);
    }
    FORALLvisible_facets {
      FOREACHvertex_(visible->vertices) {
        if (!vertex->newlist && !vertex->deleted) {
          FOREACHneighbor_(vertex) { /* this can happen under merging */
            if (!neighbor->visible)
              break;
          }
          if (neighbor)
            qh_setdel(vertex->neighbors, visible);
          else {
            vertex->deleted= True;
            qh_setappend(&qh del_vertices, vertex);
            trace2((qh ferr, 2041, "qh_updatevertices: delete vertex p%d(v%d) in f%d\n",
                  qh_pointid(vertex->point), vertex->id, visible->id));
          }
        }
      }
    }
  }else {  /* !VERTEXneighbors */
    FORALLvisible_facets {
      FOREACHvertex_(visible->vertices) {
        if (!vertex->newlist && !vertex->deleted) {
          vertex->deleted= True;
          qh_setappend(&qh del_vertices, vertex);
          trace2((qh ferr, 2042, "qh_updatevertices: delete vertex p%d(v%d) in f%d\n",
                  qh_pointid(vertex->point), vertex->id, visible->id));
        }
      }
    }
  }
} /* updatevertices */



qhull-2012.1/src/libqhull/poly.h0000644000076400010400000002526711710144466017663 0ustar  bbarberAdministrators/*
  ---------------------------------

   poly.h
   header file for poly.c and poly2.c

   see qh-poly.htm, libqhull.h and poly.c

   Copyright (c) 1993-2012 The Geometry Center.
   $Id: //main/2011/qhull/src/libqhull/poly.h#3 $$Change: 1464 $
   $DateTime: 2012/01/25 22:58:41 $$Author: bbarber $
*/

#ifndef qhDEFpoly
#define qhDEFpoly 1

#include "libqhull.h"

/*===============   constants ========================== */

/*----------------------------------

  ALGORITHMfault
    use as argument to checkconvex() to report errors during buildhull
*/
#define qh_ALGORITHMfault 0

/*----------------------------------

  DATAfault
    use as argument to checkconvex() to report errors during initialhull
*/
#define qh_DATAfault 1

/*----------------------------------

  DUPLICATEridge
    special value for facet->neighbor to indicate a duplicate ridge

  notes:
    set by matchneighbor, used by matchmatch and mark_dupridge
*/
#define qh_DUPLICATEridge (facetT *)1L

/*----------------------------------

  MERGEridge       flag in facet
    special value for facet->neighbor to indicate a merged ridge

  notes:
    set by matchneighbor, used by matchmatch and mark_dupridge
*/
#define qh_MERGEridge (facetT *)2L


/*============ -structures- ====================*/

/*=========== -macros- =========================*/

/*----------------------------------

  FORALLfacet_( facetlist ) { ... }
    assign 'facet' to each facet in facetlist

  notes:
    uses 'facetT *facet;'
    assumes last facet is a sentinel

  see:
    FORALLfacets
*/
#define FORALLfacet_( facetlist ) if (facetlist ) for ( facet=( facetlist ); facet && facet->next; facet= facet->next )

/*----------------------------------

  FORALLnew_facets { ... }
    assign 'newfacet' to each facet in qh.newfacet_list

  notes:
    uses 'facetT *newfacet;'
    at exit, newfacet==NULL
*/
#define FORALLnew_facets for ( newfacet=qh newfacet_list;newfacet && newfacet->next;newfacet=newfacet->next )

/*----------------------------------

  FORALLvertex_( vertexlist ) { ... }
    assign 'vertex' to each vertex in vertexlist

  notes:
    uses 'vertexT *vertex;'
    at exit, vertex==NULL
*/
#define FORALLvertex_( vertexlist ) for (vertex=( vertexlist );vertex && vertex->next;vertex= vertex->next )

/*----------------------------------

  FORALLvisible_facets { ... }
    assign 'visible' to each visible facet in qh.visible_list

  notes:
    uses 'vacetT *visible;'
    at exit, visible==NULL
*/
#define FORALLvisible_facets for (visible=qh visible_list; visible && visible->visible; visible= visible->next)

/*----------------------------------

  FORALLsame_( newfacet ) { ... }
    assign 'same' to each facet in newfacet->f.samecycle

  notes:
    uses 'facetT *same;'
    stops when it returns to newfacet
*/
#define FORALLsame_(newfacet) for (same= newfacet->f.samecycle; same != newfacet; same= same->f.samecycle)

/*----------------------------------

  FORALLsame_cycle_( newfacet ) { ... }
    assign 'same' to each facet in newfacet->f.samecycle

  notes:
    uses 'facetT *same;'
    at exit, same == NULL
*/
#define FORALLsame_cycle_(newfacet) \
     for (same= newfacet->f.samecycle; \
         same; same= (same == newfacet ?  NULL : same->f.samecycle))

/*----------------------------------

  FOREACHneighborA_( facet ) { ... }
    assign 'neighborA' to each neighbor in facet->neighbors

  FOREACHneighborA_( vertex ) { ... }
    assign 'neighborA' to each neighbor in vertex->neighbors

  declare:
    facetT *neighborA, **neighborAp;

  see:
    FOREACHsetelement_
*/
#define FOREACHneighborA_(facet)  FOREACHsetelement_(facetT, facet->neighbors, neighborA)

/*----------------------------------

  FOREACHvisible_( facets ) { ... }
    assign 'visible' to each facet in facets

  notes:
    uses 'facetT *facet, *facetp;'
    see FOREACHsetelement_
*/
#define FOREACHvisible_(facets) FOREACHsetelement_(facetT, facets, visible)

/*----------------------------------

  FOREACHnewfacet_( facets ) { ... }
    assign 'newfacet' to each facet in facets

  notes:
    uses 'facetT *newfacet, *newfacetp;'
    see FOREACHsetelement_
*/
#define FOREACHnewfacet_(facets) FOREACHsetelement_(facetT, facets, newfacet)

/*----------------------------------

  FOREACHvertexA_( vertices ) { ... }
    assign 'vertexA' to each vertex in vertices

  notes:
    uses 'vertexT *vertexA, *vertexAp;'
    see FOREACHsetelement_
*/
#define FOREACHvertexA_(vertices) FOREACHsetelement_(vertexT, vertices, vertexA)

/*----------------------------------

  FOREACHvertexreverse12_( vertices ) { ... }
    assign 'vertex' to each vertex in vertices
    reverse order of first two vertices

  notes:
    uses 'vertexT *vertex, *vertexp;'
    see FOREACHsetelement_
*/
#define FOREACHvertexreverse12_(vertices) FOREACHsetelementreverse12_(vertexT, vertices, vertex)


/*=============== prototypes poly.c in alphabetical order ================*/

void    qh_appendfacet(facetT *facet);
void    qh_appendvertex(vertexT *vertex);
void    qh_attachnewfacets(void);
boolT   qh_checkflipped(facetT *facet, realT *dist, boolT allerror);
void    qh_delfacet(facetT *facet);
void    qh_deletevisible(void /*qh visible_list, qh horizon_list*/);
setT   *qh_facetintersect(facetT *facetA, facetT *facetB, int *skipAp,int *skipBp, int extra);
int     qh_gethash(int hashsize, setT *set, int size, int firstindex, void *skipelem);
facetT *qh_makenewfacet(setT *vertices, boolT toporient, facetT *facet);
void    qh_makenewplanes(void /* newfacet_list */);
facetT *qh_makenew_nonsimplicial(facetT *visible, vertexT *apex, int *numnew);
facetT *qh_makenew_simplicial(facetT *visible, vertexT *apex, int *numnew);
void    qh_matchneighbor(facetT *newfacet, int newskip, int hashsize,
                          int *hashcount);
void    qh_matchnewfacets(void);
boolT   qh_matchvertices(int firstindex, setT *verticesA, int skipA,
                          setT *verticesB, int *skipB, boolT *same);
facetT *qh_newfacet(void);
ridgeT *qh_newridge(void);
int     qh_pointid(pointT *point);
void    qh_removefacet(facetT *facet);
void    qh_removevertex(vertexT *vertex);
void    qh_updatevertices(void);


/*========== -prototypes poly2.c in alphabetical order ===========*/

void    qh_addhash(void* newelem, setT *hashtable, int hashsize, int hash);
void    qh_check_bestdist(void);
void    qh_check_maxout(void);
void    qh_check_output(void);
void    qh_check_point(pointT *point, facetT *facet, realT *maxoutside, realT *maxdist, facetT **errfacet1, facetT **errfacet2);
void    qh_check_points(void);
void    qh_checkconvex(facetT *facetlist, int fault);
void    qh_checkfacet(facetT *facet, boolT newmerge, boolT *waserrorp);
void    qh_checkflipped_all(facetT *facetlist);
void    qh_checkpolygon(facetT *facetlist);
void    qh_checkvertex(vertexT *vertex);
void    qh_clearcenters(qh_CENTER type);
void    qh_createsimplex(setT *vertices);
void    qh_delridge(ridgeT *ridge);
void    qh_delvertex(vertexT *vertex);
setT   *qh_facet3vertex(facetT *facet);
facetT *qh_findbestfacet(pointT *point, boolT bestoutside,
           realT *bestdist, boolT *isoutside);
facetT *qh_findbestlower(facetT *upperfacet, pointT *point, realT *bestdistp, int *numpart);
facetT *qh_findfacet_all(pointT *point, realT *bestdist, boolT *isoutside,
                          int *numpart);
int     qh_findgood(facetT *facetlist, int goodhorizon);
void    qh_findgood_all(facetT *facetlist);
void    qh_furthestnext(void /* qh facet_list */);
void    qh_furthestout(facetT *facet);
void    qh_infiniteloop(facetT *facet);
void    qh_initbuild(void);
void    qh_initialhull(setT *vertices);
setT   *qh_initialvertices(int dim, setT *maxpoints, pointT *points, int numpoints);
vertexT *qh_isvertex(pointT *point, setT *vertices);
vertexT *qh_makenewfacets(pointT *point /*horizon_list, visible_list*/);
void    qh_matchduplicates(facetT *atfacet, int atskip, int hashsize, int *hashcount);
void    qh_nearcoplanar(void /* qh.facet_list */);
vertexT *qh_nearvertex(facetT *facet, pointT *point, realT *bestdistp);
int     qh_newhashtable(int newsize);
vertexT *qh_newvertex(pointT *point);
ridgeT *qh_nextridge3d(ridgeT *atridge, facetT *facet, vertexT **vertexp);
void    qh_outcoplanar(void /* facet_list */);
pointT *qh_point(int id);
void    qh_point_add(setT *set, pointT *point, void *elem);
setT   *qh_pointfacet(void /*qh facet_list*/);
setT   *qh_pointvertex(void /*qh facet_list*/);
void    qh_prependfacet(facetT *facet, facetT **facetlist);
void    qh_printhashtable(FILE *fp);
void    qh_printlists(void);
void    qh_resetlists(boolT stats, boolT resetVisible /*qh newvertex_list newfacet_list visible_list*/);
void    qh_setvoronoi_all(void);
void    qh_triangulate(void /*qh facet_list*/);
void    qh_triangulate_facet(facetT *facetA, vertexT **first_vertex);
void    qh_triangulate_link(facetT *oldfacetA, facetT *facetA, facetT *oldfacetB, facetT *facetB);
void    qh_triangulate_mirror(facetT *facetA, facetT *facetB);
void    qh_triangulate_null(facetT *facetA);
void    qh_vertexintersect(setT **vertexsetA,setT *vertexsetB);
setT   *qh_vertexintersect_new(setT *vertexsetA,setT *vertexsetB);
void    qh_vertexneighbors(void /*qh facet_list*/);
boolT   qh_vertexsubset(setT *vertexsetA, setT *vertexsetB);


#endif /* qhDEFpoly */
qhull-2012.1/src/libqhull/poly2.c0000644000076400010400000032726511720317611017736 0ustar  bbarberAdministrators/*
  ---------------------------------

   poly2.c
   implements polygons and simplices

   see qh-poly.htm, poly.h and libqhull.h

   frequently used code is in poly.c

   Copyright (c) 1993-2012 The Geometry Center.
   $Id: //main/2011/qhull/src/libqhull/poly2.c#5 $$Change: 1490 $
   $DateTime: 2012/02/19 20:27:01 $$Author: bbarber $
*/

#include "qhull_a.h"

/*======== functions in alphabetical order ==========*/

/*---------------------------------

  qh_addhash( newelem, hashtable, hashsize, hash )
    add newelem to linear hash table at hash if not already there
*/
void qh_addhash(void* newelem, setT *hashtable, int hashsize, int hash) {
  int scan;
  void *elem;

  for (scan= (int)hash; (elem= SETelem_(hashtable, scan));
       scan= (++scan >= hashsize ? 0 : scan)) {
    if (elem == newelem)
      break;
  }
  /* loop terminates because qh_HASHfactor >= 1.1 by qh_initbuffers */
  if (!elem)
    SETelem_(hashtable, scan)= newelem;
} /* addhash */

/*---------------------------------

  qh_check_bestdist()
    check that all points are within max_outside of the nearest facet
    if qh.ONLYgood,
      ignores !good facets

  see:
    qh_check_maxout(), qh_outerinner()

  notes:
    only called from qh_check_points()
      seldom used since qh.MERGING is almost always set
    if notverified>0 at end of routine
      some points were well inside the hull.  If the hull contains
      a lens-shaped component, these points were not verified.  Use
      options 'Qi Tv' to verify all points.  (Exhaustive check also verifies)

  design:
    determine facet for each point (if any)
    for each point
      start with the assigned facet or with the first facet
      find the best facet for the point and check all coplanar facets
      error if point is outside of facet
*/
void qh_check_bestdist(void) {
  boolT waserror= False, unassigned;
  facetT *facet, *bestfacet, *errfacet1= NULL, *errfacet2= NULL;
  facetT *facetlist;
  realT dist, maxoutside, maxdist= -REALmax;
  pointT *point;
  int numpart= 0, facet_i, facet_n, notgood= 0, notverified= 0;
  setT *facets;

  trace1((qh ferr, 1020, "qh_check_bestdist: check points below nearest facet.  Facet_list f%d\n",
      qh facet_list->id));
  maxoutside= qh_maxouter();
  maxoutside += qh DISTround;
  /* one more qh.DISTround for check computation */
  trace1((qh ferr, 1021, "qh_check_bestdist: check that all points are within %2.2g of best facet\n", maxoutside));
  facets= qh_pointfacet(/*qh facet_list*/);
  if (!qh_QUICKhelp && qh PRINTprecision)
    qh_fprintf(qh ferr, 8091, "\n\
qhull output completed.  Verifying that %d points are\n\
below %2.2g of the nearest %sfacet.\n",
             qh_setsize(facets), maxoutside, (qh ONLYgood ?  "good " : ""));
  FOREACHfacet_i_(facets) {  /* for each point with facet assignment */
    if (facet)
      unassigned= False;
    else {
      unassigned= True;
      facet= qh facet_list;
    }
    point= qh_point(facet_i);
    if (point == qh GOODpointp)
      continue;
    qh_distplane(point, facet, &dist);
    numpart++;
    bestfacet= qh_findbesthorizon(!qh_IScheckmax, point, facet, qh_NOupper, &dist, &numpart);
    /* occurs after statistics reported */
    maximize_(maxdist, dist);
    if (dist > maxoutside) {
      if (qh ONLYgood && !bestfacet->good
          && !((bestfacet= qh_findgooddist(point, bestfacet, &dist, &facetlist))
               && dist > maxoutside))
        notgood++;
      else {
        waserror= True;
        qh_fprintf(qh ferr, 6109, "qhull precision error: point p%d is outside facet f%d, distance= %6.8g maxoutside= %6.8g\n",
                facet_i, bestfacet->id, dist, maxoutside);
        if (errfacet1 != bestfacet) {
          errfacet2= errfacet1;
          errfacet1= bestfacet;
        }
      }
    }else if (unassigned && dist < -qh MAXcoplanar)
      notverified++;
  }
  qh_settempfree(&facets);
  if (notverified && !qh DELAUNAY && !qh_QUICKhelp && qh PRINTprecision)
    qh_fprintf(qh ferr, 8092, "\n%d points were well inside the hull.  If the hull contains\n\
a lens-shaped component, these points were not verified.  Use\n\
options 'Qci Tv' to verify all points.\n", notverified);
  if (maxdist > qh outside_err) {
    qh_fprintf(qh ferr, 6110, "qhull precision error (qh_check_bestdist): a coplanar point is %6.2g from convex hull.  The maximum value(qh.outside_err) is %6.2g\n",
              maxdist, qh outside_err);
    qh_errexit2 (qh_ERRprec, errfacet1, errfacet2);
  }else if (waserror && qh outside_err > REALmax/2)
    qh_errexit2 (qh_ERRprec, errfacet1, errfacet2);
  /* else if waserror, the error was logged to qh.ferr but does not effect the output */
  trace0((qh ferr, 20, "qh_check_bestdist: max distance outside %2.2g\n", maxdist));
} /* check_bestdist */

/*---------------------------------

  qh_check_maxout()
    updates qh.max_outside by checking all points against bestfacet
    if qh.ONLYgood, ignores !good facets

  returns:
    updates facet->maxoutside via qh_findbesthorizon()
    sets qh.maxoutdone
    if printing qh.min_vertex (qh_outerinner),
      it is updated to the current vertices
    removes inside/coplanar points from coplanarset as needed

  notes:
    defines coplanar as min_vertex instead of MAXcoplanar
    may not need to check near-inside points because of qh.MAXcoplanar
      and qh.KEEPnearinside (before it was -DISTround)

  see also:
    qh_check_bestdist()

  design:
    if qh.min_vertex is needed
      for all neighbors of all vertices
        test distance from vertex to neighbor
    determine facet for each point (if any)
    for each point with an assigned facet
      find the best facet for the point and check all coplanar facets
        (updates outer planes)
    remove near-inside points from coplanar sets
*/
#ifndef qh_NOmerge
void qh_check_maxout(void) {
  facetT *facet, *bestfacet, *neighbor, **neighborp, *facetlist;
  realT dist, maxoutside, minvertex, old_maxoutside;
  pointT *point;
  int numpart= 0, facet_i, facet_n, notgood= 0;
  setT *facets, *vertices;
  vertexT *vertex;

  trace1((qh ferr, 1022, "qh_check_maxout: check and update maxoutside for each facet.\n"));
  maxoutside= minvertex= 0;
  if (qh VERTEXneighbors
  && (qh PRINTsummary || qh KEEPinside || qh KEEPcoplanar
        || qh TRACElevel || qh PRINTstatistics
        || qh PRINTout[0] == qh_PRINTsummary || qh PRINTout[0] == qh_PRINTnone)) {
    trace1((qh ferr, 1023, "qh_check_maxout: determine actual maxoutside and minvertex\n"));
    vertices= qh_pointvertex(/*qh facet_list*/);
    FORALLvertices {
      FOREACHneighbor_(vertex) {
        zinc_(Zdistvertex);  /* distance also computed by main loop below */
        qh_distplane(vertex->point, neighbor, &dist);
        minimize_(minvertex, dist);
        if (-dist > qh TRACEdist || dist > qh TRACEdist
        || neighbor == qh tracefacet || vertex == qh tracevertex)
          qh_fprintf(qh ferr, 8093, "qh_check_maxout: p%d(v%d) is %.2g from f%d\n",
                    qh_pointid(vertex->point), vertex->id, dist, neighbor->id);
      }
    }
    if (qh MERGING) {
      wmin_(Wminvertex, qh min_vertex);
    }
    qh min_vertex= minvertex;
    qh_settempfree(&vertices);
  }
  facets= qh_pointfacet(/*qh facet_list*/);
  do {
    old_maxoutside= fmax_(qh max_outside, maxoutside);
    FOREACHfacet_i_(facets) {     /* for each point with facet assignment */
      if (facet) {
        point= qh_point(facet_i);
        if (point == qh GOODpointp)
          continue;
        zzinc_(Ztotcheck);
        qh_distplane(point, facet, &dist);
        numpart++;
        bestfacet= qh_findbesthorizon(qh_IScheckmax, point, facet, !qh_NOupper, &dist, &numpart);
        if (bestfacet && dist > maxoutside) {
          if (qh ONLYgood && !bestfacet->good
          && !((bestfacet= qh_findgooddist(point, bestfacet, &dist, &facetlist))
               && dist > maxoutside))
            notgood++;
          else
            maxoutside= dist;
        }
        if (dist > qh TRACEdist || (bestfacet && bestfacet == qh tracefacet))
          qh_fprintf(qh ferr, 8094, "qh_check_maxout: p%d is %.2g above f%d\n",
                     qh_pointid(point), dist, bestfacet->id);
      }
    }
  }while
    (maxoutside > 2*old_maxoutside);
    /* if qh.maxoutside increases substantially, qh_SEARCHdist is not valid
          e.g., RBOX 5000 s Z1 G1e-13 t1001200614 | qhull */
  zzadd_(Zcheckpart, numpart);
  qh_settempfree(&facets);
  wval_(Wmaxout)= maxoutside - qh max_outside;
  wmax_(Wmaxoutside, qh max_outside);
  qh max_outside= maxoutside;
  qh_nearcoplanar(/*qh.facet_list*/);
  qh maxoutdone= True;
  trace1((qh ferr, 1024, "qh_check_maxout: maxoutside %2.2g, min_vertex %2.2g, outside of not good %d\n",
       maxoutside, qh min_vertex, notgood));
} /* check_maxout */
#else /* qh_NOmerge */
void qh_check_maxout(void) {
}
#endif

/*---------------------------------

  qh_check_output()
    performs the checks at the end of qhull algorithm
    Maybe called after voronoi output.  Will recompute otherwise centrums are Voronoi centers instead
*/
void qh_check_output(void) {
  int i;

  if (qh STOPcone)
    return;
  if (qh VERIFYoutput | qh IStracing | qh CHECKfrequently) {
    qh_checkpolygon(qh facet_list);
    qh_checkflipped_all(qh facet_list);
    qh_checkconvex(qh facet_list, qh_ALGORITHMfault);
  }else if (!qh MERGING && qh_newstats(qhstat precision, &i)) {
    qh_checkflipped_all(qh facet_list);
    qh_checkconvex(qh facet_list, qh_ALGORITHMfault);
  }
} /* check_output */



/*---------------------------------

  qh_check_point( point, facet, maxoutside, maxdist, errfacet1, errfacet2 )
    check that point is less than maxoutside from facet
*/
void qh_check_point(pointT *point, facetT *facet, realT *maxoutside, realT *maxdist, facetT **errfacet1, facetT **errfacet2) {
  realT dist;

  /* occurs after statistics reported */
  qh_distplane(point, facet, &dist);
  if (dist > *maxoutside) {
    if (*errfacet1 != facet) {
      *errfacet2= *errfacet1;
      *errfacet1= facet;
    }
    qh_fprintf(qh ferr, 6111, "qhull precision error: point p%d is outside facet f%d, distance= %6.8g maxoutside= %6.8g\n",
              qh_pointid(point), facet->id, dist, *maxoutside);
  }
  maximize_(*maxdist, dist);
} /* qh_check_point */


/*---------------------------------

  qh_check_points()
    checks that all points are inside all facets

  notes:
    if many points and qh_check_maxout not called (i.e., !qh.MERGING),
       calls qh_findbesthorizon (seldom done).
    ignores flipped facets
    maxoutside includes 2 qh.DISTrounds
      one qh.DISTround for the computed distances in qh_check_points
    qh_printafacet and qh_printsummary needs only one qh.DISTround
    the computation for qh.VERIFYdirect does not account for qh.other_points

  design:
    if many points
      use qh_check_bestdist()
    else
      for all facets
        for all points
          check that point is inside facet
*/
void qh_check_points(void) {
  facetT *facet, *errfacet1= NULL, *errfacet2= NULL;
  realT total, maxoutside, maxdist= -REALmax;
  pointT *point, **pointp, *pointtemp;
  boolT testouter;

  maxoutside= qh_maxouter();
  maxoutside += qh DISTround;
  /* one more qh.DISTround for check computation */
  trace1((qh ferr, 1025, "qh_check_points: check all points below %2.2g of all facet planes\n",
          maxoutside));
  if (qh num_good)   /* miss counts other_points and !good facets */
     total= (float)qh num_good * (float)qh num_points;
  else
     total= (float)qh num_facets * (float)qh num_points;
  if (total >= qh_VERIFYdirect && !qh maxoutdone) {
    if (!qh_QUICKhelp && qh SKIPcheckmax && qh MERGING)
      qh_fprintf(qh ferr, 7075, "qhull input warning: merging without checking outer planes('Q5' or 'Po').\n\
Verify may report that a point is outside of a facet.\n");
    qh_check_bestdist();
  }else {
    if (qh_MAXoutside && qh maxoutdone)
      testouter= True;
    else
      testouter= False;
    if (!qh_QUICKhelp) {
      if (qh MERGEexact)
        qh_fprintf(qh ferr, 7076, "qhull input warning: exact merge ('Qx').  Verify may report that a point\n\
is outside of a facet.  See qh-optq.htm#Qx\n");
      else if (qh SKIPcheckmax || qh NOnearinside)
        qh_fprintf(qh ferr, 7077, "qhull input warning: no outer plane check ('Q5') or no processing of\n\
near-inside points ('Q8').  Verify may report that a point is outside\n\
of a facet.\n");
    }
    if (qh PRINTprecision) {
      if (testouter)
        qh_fprintf(qh ferr, 8098, "\n\
Output completed.  Verifying that all points are below outer planes of\n\
all %sfacets.  Will make %2.0f distance computations.\n",
              (qh ONLYgood ?  "good " : ""), total);
      else
        qh_fprintf(qh ferr, 8099, "\n\
Output completed.  Verifying that all points are below %2.2g of\n\
all %sfacets.  Will make %2.0f distance computations.\n",
              maxoutside, (qh ONLYgood ?  "good " : ""), total);
    }
    FORALLfacets {
      if (!facet->good && qh ONLYgood)
        continue;
      if (facet->flipped)
        continue;
      if (!facet->normal) {
        qh_fprintf(qh ferr, 7061, "qhull warning (qh_check_points): missing normal for facet f%d\n", facet->id);
        continue;
      }
      if (testouter) {
#if qh_MAXoutside
        maxoutside= facet->maxoutside + 2* qh DISTround;
        /* one DISTround to actual point and another to computed point */
#endif
      }
      FORALLpoints {
        if (point != qh GOODpointp)
          qh_check_point(point, facet, &maxoutside, &maxdist, &errfacet1, &errfacet2);
      }
      FOREACHpoint_(qh other_points) {
        if (point != qh GOODpointp)
          qh_check_point(point, facet, &maxoutside, &maxdist, &errfacet1, &errfacet2);
      }
    }
    if (maxdist > qh outside_err) {
      qh_fprintf(qh ferr, 6112, "qhull precision error (qh_check_points): a coplanar point is %6.2g from convex hull.  The maximum value(qh.outside_err) is %6.2g\n",
                maxdist, qh outside_err );
      qh_errexit2( qh_ERRprec, errfacet1, errfacet2 );
    }else if (errfacet1 && qh outside_err > REALmax/2)
        qh_errexit2( qh_ERRprec, errfacet1, errfacet2 );
    /* else if errfacet1, the error was logged to qh.ferr but does not effect the output */
    trace0((qh ferr, 21, "qh_check_points: max distance outside %2.2g\n", maxdist));
  }
} /* check_points */


/*---------------------------------

  qh_checkconvex( facetlist, fault )
    check that each ridge in facetlist is convex
    fault = qh_DATAfault if reporting errors
          = qh_ALGORITHMfault otherwise

  returns:
    counts Zconcaveridges and Zcoplanarridges
    errors if concaveridge or if merging an coplanar ridge

  note:
    if not merging,
      tests vertices for neighboring simplicial facets
    else if ZEROcentrum,
      tests vertices for neighboring simplicial   facets
    else
      tests centrums of neighboring facets

  design:
    for all facets
      report flipped facets
      if ZEROcentrum and simplicial neighbors
        test vertices for neighboring simplicial facets
      else
        test centrum against all neighbors
*/
void qh_checkconvex(facetT *facetlist, int fault) {
  facetT *facet, *neighbor, **neighborp, *errfacet1=NULL, *errfacet2=NULL;
  vertexT *vertex;
  realT dist;
  pointT *centrum;
  boolT waserror= False, centrum_warning= False, tempcentrum= False, allsimplicial;
  int neighbor_i;

  trace1((qh ferr, 1026, "qh_checkconvex: check all ridges are convex\n"));
  if (!qh RERUN) {
    zzval_(Zconcaveridges)= 0;
    zzval_(Zcoplanarridges)= 0;
  }
  FORALLfacet_(facetlist) {
    if (facet->flipped) {
      qh_precision("flipped facet");
      qh_fprintf(qh ferr, 6113, "qhull precision error: f%d is flipped(interior point is outside)\n",
               facet->id);
      errfacet1= facet;
      waserror= True;
      continue;
    }
    if (qh MERGING && (!qh ZEROcentrum || !facet->simplicial || facet->tricoplanar))
      allsimplicial= False;
    else {
      allsimplicial= True;
      neighbor_i= 0;
      FOREACHneighbor_(facet) {
        vertex= SETelemt_(facet->vertices, neighbor_i++, vertexT);
        if (!neighbor->simplicial || neighbor->tricoplanar) {
          allsimplicial= False;
          continue;
        }
        qh_distplane(vertex->point, neighbor, &dist);
        if (dist > -qh DISTround) {
          if (fault == qh_DATAfault) {
            qh_precision("coplanar or concave ridge");
            qh_fprintf(qh ferr, 6114, "qhull precision error: initial simplex is not convex. Distance=%.2g\n", dist);
            qh_errexit(qh_ERRsingular, NULL, NULL);
          }
          if (dist > qh DISTround) {
            zzinc_(Zconcaveridges);
            qh_precision("concave ridge");
            qh_fprintf(qh ferr, 6115, "qhull precision error: f%d is concave to f%d, since p%d(v%d) is %6.4g above\n",
              facet->id, neighbor->id, qh_pointid(vertex->point), vertex->id, dist);
            errfacet1= facet;
            errfacet2= neighbor;
            waserror= True;
          }else if (qh ZEROcentrum) {
            if (dist > 0) {     /* qh_checkzero checks that dist < - qh DISTround */
              zzinc_(Zcoplanarridges);
              qh_precision("coplanar ridge");
              qh_fprintf(qh ferr, 6116, "qhull precision error: f%d is clearly not convex to f%d, since p%d(v%d) is %6.4g above\n",
                facet->id, neighbor->id, qh_pointid(vertex->point), vertex->id, dist);
              errfacet1= facet;
              errfacet2= neighbor;
              waserror= True;
            }
          }else {
            zzinc_(Zcoplanarridges);
            qh_precision("coplanar ridge");
            trace0((qh ferr, 22, "qhull precision error: f%d may be coplanar to f%d, since p%d(v%d) is within %6.4g during p%d\n",
              facet->id, neighbor->id, qh_pointid(vertex->point), vertex->id, dist, qh furthest_id));
          }
        }
      }
    }
    if (!allsimplicial) {
      if (qh CENTERtype == qh_AScentrum) {
        if (!facet->center)
          facet->center= qh_getcentrum(facet);
        centrum= facet->center;
      }else {
        if (!centrum_warning && (!facet->simplicial || facet->tricoplanar)) {
           centrum_warning= True;
           qh_fprintf(qh ferr, 7062, "qhull warning: recomputing centrums for convexity test.  This may lead to false, precision errors.\n");
        }
        centrum= qh_getcentrum(facet);
        tempcentrum= True;
      }
      FOREACHneighbor_(facet) {
        if (qh ZEROcentrum && facet->simplicial && neighbor->simplicial)
          continue;
        if (facet->tricoplanar || neighbor->tricoplanar)
          continue;
        zzinc_(Zdistconvex);
        qh_distplane(centrum, neighbor, &dist);
        if (dist > qh DISTround) {
          zzinc_(Zconcaveridges);
          qh_precision("concave ridge");
          qh_fprintf(qh ferr, 6117, "qhull precision error: f%d is concave to f%d.  Centrum of f%d is %6.4g above f%d\n",
            facet->id, neighbor->id, facet->id, dist, neighbor->id);
          errfacet1= facet;
          errfacet2= neighbor;
          waserror= True;
        }else if (dist >= 0.0) {   /* if arithmetic always rounds the same,
                                     can test against centrum radius instead */
          zzinc_(Zcoplanarridges);
          qh_precision("coplanar ridge");
          qh_fprintf(qh ferr, 6118, "qhull precision error: f%d is coplanar or concave to f%d.  Centrum of f%d is %6.4g above f%d\n",
            facet->id, neighbor->id, facet->id, dist, neighbor->id);
          errfacet1= facet;
          errfacet2= neighbor;
          waserror= True;
        }
      }
      if (tempcentrum)
        qh_memfree(centrum, qh normal_size);
    }
  }
  if (waserror && !qh FORCEoutput)
    qh_errexit2 (qh_ERRprec, errfacet1, errfacet2);
} /* checkconvex */


/*---------------------------------

  qh_checkfacet( facet, newmerge, waserror )
    checks for consistency errors in facet
    newmerge set if from merge.c

  returns:
    sets waserror if any error occurs

  checks:
    vertex ids are inverse sorted
    unless newmerge, at least hull_dim neighbors and vertices (exactly if simplicial)
    if non-simplicial, at least as many ridges as neighbors
    neighbors are not duplicated
    ridges are not duplicated
    in 3-d, ridges=verticies
    (qh.hull_dim-1) ridge vertices
    neighbors are reciprocated
    ridge neighbors are facet neighbors and a ridge for every neighbor
    simplicial neighbors match facetintersect
    vertex intersection matches vertices of common ridges
    vertex neighbors and facet vertices agree
    all ridges have distinct vertex sets

  notes:
    uses neighbor->seen

  design:
    check sets
    check vertices
    check sizes of neighbors and vertices
    check for qh_MERGEridge and qh_DUPLICATEridge flags
    check neighbor set
    check ridge set
    check ridges, neighbors, and vertices
*/
void qh_checkfacet(facetT *facet, boolT newmerge, boolT *waserrorp) {
  facetT *neighbor, **neighborp, *errother=NULL;
  ridgeT *ridge, **ridgep, *errridge= NULL, *ridge2;
  vertexT *vertex, **vertexp;
  unsigned previousid= INT_MAX;
  int numneighbors, numvertices, numridges=0, numRvertices=0;
  boolT waserror= False;
  int skipA, skipB, ridge_i, ridge_n, i;
  setT *intersection;

  if (facet->visible) {
    qh_fprintf(qh ferr, 6119, "qhull internal error (qh_checkfacet): facet f%d is on the visible_list\n",
      facet->id);
    qh_errexit(qh_ERRqhull, facet, NULL);
  }
  if (!facet->normal) {
    qh_fprintf(qh ferr, 6120, "qhull internal error (qh_checkfacet): facet f%d does not have  a normal\n",
      facet->id);
    waserror= True;
  }
  qh_setcheck(facet->vertices, "vertices for f", facet->id);
  qh_setcheck(facet->ridges, "ridges for f", facet->id);
  qh_setcheck(facet->outsideset, "outsideset for f", facet->id);
  qh_setcheck(facet->coplanarset, "coplanarset for f", facet->id);
  qh_setcheck(facet->neighbors, "neighbors for f", facet->id);
  FOREACHvertex_(facet->vertices) {
    if (vertex->deleted) {
      qh_fprintf(qh ferr, 6121, "qhull internal error (qh_checkfacet): deleted vertex v%d in f%d\n", vertex->id, facet->id);
      qh_errprint("ERRONEOUS", NULL, NULL, NULL, vertex);
      waserror= True;
    }
    if (vertex->id >= previousid) {
      qh_fprintf(qh ferr, 6122, "qhull internal error (qh_checkfacet): vertices of f%d are not in descending id order at v%d\n", facet->id, vertex->id);
      waserror= True;
      break;
    }
    previousid= vertex->id;
  }
  numneighbors= qh_setsize(facet->neighbors);
  numvertices= qh_setsize(facet->vertices);
  numridges= qh_setsize(facet->ridges);
  if (facet->simplicial) {
    if (numvertices+numneighbors != 2*qh hull_dim
    && !facet->degenerate && !facet->redundant) {
      qh_fprintf(qh ferr, 6123, "qhull internal error (qh_checkfacet): for simplicial facet f%d, #vertices %d + #neighbors %d != 2*qh hull_dim\n",
                facet->id, numvertices, numneighbors);
      qh_setprint(qh ferr, "", facet->neighbors);
      waserror= True;
    }
  }else { /* non-simplicial */
    if (!newmerge
    &&(numvertices < qh hull_dim || numneighbors < qh hull_dim)
    && !facet->degenerate && !facet->redundant) {
      qh_fprintf(qh ferr, 6124, "qhull internal error (qh_checkfacet): for facet f%d, #vertices %d or #neighbors %d < qh hull_dim\n",
         facet->id, numvertices, numneighbors);
       waserror= True;
    }
    /* in 3-d, can get a vertex twice in an edge list, e.g., RBOX 1000 s W1e-13 t995849315 D2 | QHULL d Tc Tv TP624 TW1e-13 T4 */
    if (numridges < numneighbors
    ||(qh hull_dim == 3 && numvertices > numridges && !qh NEWfacets)
    ||(qh hull_dim == 2 && numridges + numvertices + numneighbors != 6)) {
      if (!facet->degenerate && !facet->redundant) {
        qh_fprintf(qh ferr, 6125, "qhull internal error (qh_checkfacet): for facet f%d, #ridges %d < #neighbors %d or(3-d) > #vertices %d or(2-d) not all 2\n",
            facet->id, numridges, numneighbors, numvertices);
        waserror= True;
      }
    }
  }
  FOREACHneighbor_(facet) {
    if (neighbor == qh_MERGEridge || neighbor == qh_DUPLICATEridge) {
      qh_fprintf(qh ferr, 6126, "qhull internal error (qh_checkfacet): facet f%d still has a MERGE or DUP neighbor\n", facet->id);
      qh_errexit(qh_ERRqhull, facet, NULL);
    }
    neighbor->seen= True;
  }
  FOREACHneighbor_(facet) {
    if (!qh_setin(neighbor->neighbors, facet)) {
      qh_fprintf(qh ferr, 6127, "qhull internal error (qh_checkfacet): facet f%d has neighbor f%d, but f%d does not have neighbor f%d\n",
              facet->id, neighbor->id, neighbor->id, facet->id);
      errother= neighbor;
      waserror= True;
    }
    if (!neighbor->seen) {
      qh_fprintf(qh ferr, 6128, "qhull internal error (qh_checkfacet): facet f%d has a duplicate neighbor f%d\n",
              facet->id, neighbor->id);
      errother= neighbor;
      waserror= True;
    }
    neighbor->seen= False;
  }
  FOREACHridge_(facet->ridges) {
    qh_setcheck(ridge->vertices, "vertices for r", ridge->id);
    ridge->seen= False;
  }
  FOREACHridge_(facet->ridges) {
    if (ridge->seen) {
      qh_fprintf(qh ferr, 6129, "qhull internal error (qh_checkfacet): facet f%d has a duplicate ridge r%d\n",
              facet->id, ridge->id);
      errridge= ridge;
      waserror= True;
    }
    ridge->seen= True;
    numRvertices= qh_setsize(ridge->vertices);
    if (numRvertices != qh hull_dim - 1) {
      qh_fprintf(qh ferr, 6130, "qhull internal error (qh_checkfacet): ridge between f%d and f%d has %d vertices\n",
                ridge->top->id, ridge->bottom->id, numRvertices);
      errridge= ridge;
      waserror= True;
    }
    neighbor= otherfacet_(ridge, facet);
    neighbor->seen= True;
    if (!qh_setin(facet->neighbors, neighbor)) {
      qh_fprintf(qh ferr, 6131, "qhull internal error (qh_checkfacet): for facet f%d, neighbor f%d of ridge r%d not in facet\n",
           facet->id, neighbor->id, ridge->id);
      errridge= ridge;
      waserror= True;
    }
  }
  if (!facet->simplicial) {
    FOREACHneighbor_(facet) {
      if (!neighbor->seen) {
        qh_fprintf(qh ferr, 6132, "qhull internal error (qh_checkfacet): facet f%d does not have a ridge for neighbor f%d\n",
              facet->id, neighbor->id);
        errother= neighbor;
        waserror= True;
      }
      intersection= qh_vertexintersect_new(facet->vertices, neighbor->vertices);
      qh_settemppush(intersection);
      FOREACHvertex_(facet->vertices) {
        vertex->seen= False;
        vertex->seen2= False;
      }
      FOREACHvertex_(intersection)
        vertex->seen= True;
      FOREACHridge_(facet->ridges) {
        if (neighbor != otherfacet_(ridge, facet))
            continue;
        FOREACHvertex_(ridge->vertices) {
          if (!vertex->seen) {
            qh_fprintf(qh ferr, 6133, "qhull internal error (qh_checkfacet): vertex v%d in r%d not in f%d intersect f%d\n",
                  vertex->id, ridge->id, facet->id, neighbor->id);
            qh_errexit(qh_ERRqhull, facet, ridge);
          }
          vertex->seen2= True;
        }
      }
      if (!newmerge) {
        FOREACHvertex_(intersection) {
          if (!vertex->seen2) {
            if (qh IStracing >=3 || !qh MERGING) {
              qh_fprintf(qh ferr, 6134, "qhull precision error (qh_checkfacet): vertex v%d in f%d intersect f%d but\n\
 not in a ridge.  This is ok under merging.  Last point was p%d\n",
                     vertex->id, facet->id, neighbor->id, qh furthest_id);
              if (!qh FORCEoutput && !qh MERGING) {
                qh_errprint("ERRONEOUS", facet, neighbor, NULL, vertex);
                if (!qh MERGING)
                  qh_errexit(qh_ERRqhull, NULL, NULL);
              }
            }
          }
        }
      }
      qh_settempfree(&intersection);
    }
  }else { /* simplicial */
    FOREACHneighbor_(facet) {
      if (neighbor->simplicial) {
        skipA= SETindex_(facet->neighbors, neighbor);
        skipB= qh_setindex(neighbor->neighbors, facet);
        if (!qh_setequal_skip(facet->vertices, skipA, neighbor->vertices, skipB)) {
          qh_fprintf(qh ferr, 6135, "qhull internal error (qh_checkfacet): facet f%d skip %d and neighbor f%d skip %d do not match \n",
                   facet->id, skipA, neighbor->id, skipB);
          errother= neighbor;
          waserror= True;
        }
      }
    }
  }
  if (qh hull_dim < 5 && (qh IStracing > 2 || qh CHECKfrequently)) {
    FOREACHridge_i_(facet->ridges) {           /* expensive */
      for (i=ridge_i+1; i < ridge_n; i++) {
        ridge2= SETelemt_(facet->ridges, i, ridgeT);
        if (qh_setequal(ridge->vertices, ridge2->vertices)) {
          qh_fprintf(qh ferr, 6227, "Qhull internal error (qh_checkfacet): ridges r%d and r%d have the same vertices\n",
                  ridge->id, ridge2->id);
          errridge= ridge;
          waserror= True;
        }
      }
    }
  }
  if (waserror) {
    qh_errprint("ERRONEOUS", facet, errother, errridge, NULL);
    *waserrorp= True;
  }
} /* checkfacet */


/*---------------------------------

  qh_checkflipped_all( facetlist )
    checks orientation of facets in list against interior point
*/
void qh_checkflipped_all(facetT *facetlist) {
  facetT *facet;
  boolT waserror= False;
  realT dist;

  if (facetlist == qh facet_list)
    zzval_(Zflippedfacets)= 0;
  FORALLfacet_(facetlist) {
    if (facet->normal && !qh_checkflipped(facet, &dist, !qh_ALL)) {
      qh_fprintf(qh ferr, 6136, "qhull precision error: facet f%d is flipped, distance= %6.12g\n",
              facet->id, dist);
      if (!qh FORCEoutput) {
        qh_errprint("ERRONEOUS", facet, NULL, NULL, NULL);
        waserror= True;
      }
    }
  }
  if (waserror) {
    qh_fprintf(qh ferr, 8101, "\n\
A flipped facet occurs when its distance to the interior point is\n\
greater than %2.2g, the maximum roundoff error.\n", -qh DISTround);
    qh_errexit(qh_ERRprec, NULL, NULL);
  }
} /* checkflipped_all */

/*---------------------------------

  qh_checkpolygon( facetlist )
    checks the correctness of the structure

  notes:
    call with either qh.facet_list or qh.newfacet_list
    checks num_facets and num_vertices if qh.facet_list

  design:
    for each facet
      checks facet and outside set
    initializes vertexlist
    for each facet
      checks vertex set
    if checking all facets(qh.facetlist)
      check facet count
      if qh.VERTEXneighbors
        check vertex neighbors and count
      check vertex count
*/
void qh_checkpolygon(facetT *facetlist) {
  facetT *facet;
  vertexT *vertex, **vertexp, *vertexlist;
  int numfacets= 0, numvertices= 0, numridges= 0;
  int totvneighbors= 0, totvertices= 0;
  boolT waserror= False, nextseen= False, visibleseen= False;

  trace1((qh ferr, 1027, "qh_checkpolygon: check all facets from f%d\n", facetlist->id));
  if (facetlist != qh facet_list || qh ONLYgood)
    nextseen= True;
  FORALLfacet_(facetlist) {
    if (facet == qh visible_list)
      visibleseen= True;
    if (!facet->visible) {
      if (!nextseen) {
        if (facet == qh facet_next)
          nextseen= True;
        else if (qh_setsize(facet->outsideset)) {
          if (!qh NARROWhull
#if !qh_COMPUTEfurthest
               || facet->furthestdist >= qh MINoutside
#endif
                        ) {
            qh_fprintf(qh ferr, 6137, "qhull internal error (qh_checkpolygon): f%d has outside points before qh facet_next\n",
                     facet->id);
            qh_errexit(qh_ERRqhull, facet, NULL);
          }
        }
      }
      numfacets++;
      qh_checkfacet(facet, False, &waserror);
    }
  }
  if (qh visible_list && !visibleseen && facetlist == qh facet_list) {
    qh_fprintf(qh ferr, 6138, "qhull internal error (qh_checkpolygon): visible list f%d no longer on facet list\n", qh visible_list->id);
    qh_printlists();
    qh_errexit(qh_ERRqhull, qh visible_list, NULL);
  }
  if (facetlist == qh facet_list)
    vertexlist= qh vertex_list;
  else if (facetlist == qh newfacet_list)
    vertexlist= qh newvertex_list;
  else
    vertexlist= NULL;
  FORALLvertex_(vertexlist) {
    vertex->seen= False;
    vertex->visitid= 0;
  }
  FORALLfacet_(facetlist) {
    if (facet->visible)
      continue;
    if (facet->simplicial)
      numridges += qh hull_dim;
    else
      numridges += qh_setsize(facet->ridges);
    FOREACHvertex_(facet->vertices) {
      vertex->visitid++;
      if (!vertex->seen) {
        vertex->seen= True;
        numvertices++;
        if (qh_pointid(vertex->point) == -1) {
          qh_fprintf(qh ferr, 6139, "qhull internal error (qh_checkpolygon): unknown point %p for vertex v%d first_point %p\n",
                   vertex->point, vertex->id, qh first_point);
          waserror= True;
        }
      }
    }
  }
  qh vertex_visit += (unsigned int)numfacets;
  if (facetlist == qh facet_list) {
    if (numfacets != qh num_facets - qh num_visible) {
      qh_fprintf(qh ferr, 6140, "qhull internal error (qh_checkpolygon): actual number of facets is %d, cumulative facet count is %d - %d visible facets\n",
              numfacets, qh num_facets, qh num_visible);
      waserror= True;
    }
    qh vertex_visit++;
    if (qh VERTEXneighbors) {
      FORALLvertices {
        qh_setcheck(vertex->neighbors, "neighbors for v", vertex->id);
        if (vertex->deleted)
          continue;
        totvneighbors += qh_setsize(vertex->neighbors);
      }
      FORALLfacet_(facetlist)
        totvertices += qh_setsize(facet->vertices);
      if (totvneighbors != totvertices) {
        qh_fprintf(qh ferr, 6141, "qhull internal error (qh_checkpolygon): vertex neighbors inconsistent.  Totvneighbors %d, totvertices %d\n",
                totvneighbors, totvertices);
        waserror= True;
      }
    }
    if (numvertices != qh num_vertices - qh_setsize(qh del_vertices)) {
      qh_fprintf(qh ferr, 6142, "qhull internal error (qh_checkpolygon): actual number of vertices is %d, cumulative vertex count is %d\n",
              numvertices, qh num_vertices - qh_setsize(qh del_vertices));
      waserror= True;
    }
    if (qh hull_dim == 2 && numvertices != numfacets) {
      qh_fprintf(qh ferr, 6143, "qhull internal error (qh_checkpolygon): #vertices %d != #facets %d\n",
        numvertices, numfacets);
      waserror= True;
    }
    if (qh hull_dim == 3 && numvertices + numfacets - numridges/2 != 2) {
      qh_fprintf(qh ferr, 7063, "qhull warning: #vertices %d + #facets %d - #edges %d != 2\n\
        A vertex appears twice in a edge list.  May occur during merging.",
        numvertices, numfacets, numridges/2);
      /* occurs if lots of merging and a vertex ends up twice in an edge list.  e.g., RBOX 1000 s W1e-13 t995849315 D2 | QHULL d Tc Tv */
    }
  }
  if (waserror)
    qh_errexit(qh_ERRqhull, NULL, NULL);
} /* checkpolygon */


/*---------------------------------

  qh_checkvertex( vertex )
    check vertex for consistency
    checks vertex->neighbors

  notes:
    neighbors checked efficiently in checkpolygon
*/
void qh_checkvertex(vertexT *vertex) {
  boolT waserror= False;
  facetT *neighbor, **neighborp, *errfacet=NULL;

  if (qh_pointid(vertex->point) == -1) {
    qh_fprintf(qh ferr, 6144, "qhull internal error (qh_checkvertex): unknown point id %p\n", vertex->point);
    waserror= True;
  }
  if (vertex->id >= qh vertex_id) {
    qh_fprintf(qh ferr, 6145, "qhull internal error (qh_checkvertex): unknown vertex id %d\n", vertex->id);
    waserror= True;
  }
  if (!waserror && !vertex->deleted) {
    if (qh_setsize(vertex->neighbors)) {
      FOREACHneighbor_(vertex) {
        if (!qh_setin(neighbor->vertices, vertex)) {
          qh_fprintf(qh ferr, 6146, "qhull internal error (qh_checkvertex): neighbor f%d does not contain v%d\n", neighbor->id, vertex->id);
          errfacet= neighbor;
          waserror= True;
        }
      }
    }
  }
  if (waserror) {
    qh_errprint("ERRONEOUS", NULL, NULL, NULL, vertex);
    qh_errexit(qh_ERRqhull, errfacet, NULL);
  }
} /* checkvertex */

/*---------------------------------

  qh_clearcenters( type )
    clear old data from facet->center

  notes:
    sets new centertype
    nop if CENTERtype is the same
*/
void qh_clearcenters(qh_CENTER type) {
  facetT *facet;

  if (qh CENTERtype != type) {
    FORALLfacets {
      if (facet->tricoplanar && !facet->keepcentrum)
          facet->center= NULL;
      else if (qh CENTERtype == qh_ASvoronoi){
        if (facet->center) {
          qh_memfree(facet->center, qh center_size);
          facet->center= NULL;
        }
      }else /* qh CENTERtype == qh_AScentrum */ {
        if (facet->center) {
          qh_memfree(facet->center, qh normal_size);
          facet->center= NULL;
        }
      }
    }
    qh CENTERtype= type;
  }
  trace2((qh ferr, 2043, "qh_clearcenters: switched to center type %d\n", type));
} /* clearcenters */

/*---------------------------------

  qh_createsimplex( vertices )
    creates a simplex from a set of vertices

  returns:
    initializes qh.facet_list to the simplex
    initializes qh.newfacet_list, .facet_tail
    initializes qh.vertex_list, .newvertex_list, .vertex_tail

  design:
    initializes lists
    for each vertex
      create a new facet
    for each new facet
      create its neighbor set
*/
void qh_createsimplex(setT *vertices) {
  facetT *facet= NULL, *newfacet;
  boolT toporient= True;
  int vertex_i, vertex_n, nth;
  setT *newfacets= qh_settemp(qh hull_dim+1);
  vertexT *vertex;

  qh facet_list= qh newfacet_list= qh facet_tail= qh_newfacet();
  qh num_facets= qh num_vertices= qh num_visible= 0;
  qh vertex_list= qh newvertex_list= qh vertex_tail= qh_newvertex(NULL);
  FOREACHvertex_i_(vertices) {
    newfacet= qh_newfacet();
    newfacet->vertices= qh_setnew_delnthsorted(vertices, vertex_n,
                                                vertex_i, 0);
    newfacet->toporient= (unsigned char)toporient;
    qh_appendfacet(newfacet);
    newfacet->newfacet= True;
    qh_appendvertex(vertex);
    qh_setappend(&newfacets, newfacet);
    toporient ^= True;
  }
  FORALLnew_facets {
    nth= 0;
    FORALLfacet_(qh newfacet_list) {
      if (facet != newfacet)
        SETelem_(newfacet->neighbors, nth++)= facet;
    }
    qh_settruncate(newfacet->neighbors, qh hull_dim);
  }
  qh_settempfree(&newfacets);
  trace1((qh ferr, 1028, "qh_createsimplex: created simplex\n"));
} /* createsimplex */

/*---------------------------------

  qh_delridge( ridge )
    deletes ridge from data structures it belongs to
    frees up its memory

  notes:
    in merge.c, caller sets vertex->delridge for each vertex
    ridges also freed in qh_freeqhull
*/
void qh_delridge(ridgeT *ridge) {
  void **freelistp; /* used !qh_NOmem */

  qh_setdel(ridge->top->ridges, ridge);
  qh_setdel(ridge->bottom->ridges, ridge);
  qh_setfree(&(ridge->vertices));
  qh_memfree_(ridge, (int)sizeof(ridgeT), freelistp);
} /* delridge */


/*---------------------------------

  qh_delvertex( vertex )
    deletes a vertex and frees its memory

  notes:
    assumes vertex->adjacencies have been updated if needed
    unlinks from vertex_list
*/
void qh_delvertex(vertexT *vertex) {

  if (vertex == qh tracevertex)
    qh tracevertex= NULL;
  qh_removevertex(vertex);
  qh_setfree(&vertex->neighbors);
  qh_memfree(vertex, (int)sizeof(vertexT));
} /* delvertex */


/*---------------------------------

  qh_facet3vertex(  )
    return temporary set of 3-d vertices in qh_ORIENTclock order

  design:
    if simplicial facet
      build set from facet->vertices with facet->toporient
    else
      for each ridge in order
        build set from ridge's vertices
*/
setT *qh_facet3vertex(facetT *facet) {
  ridgeT *ridge, *firstridge;
  vertexT *vertex;
  int cntvertices, cntprojected=0;
  setT *vertices;

  cntvertices= qh_setsize(facet->vertices);
  vertices= qh_settemp(cntvertices);
  if (facet->simplicial) {
    if (cntvertices != 3) {
      qh_fprintf(qh ferr, 6147, "qhull internal error (qh_facet3vertex): only %d vertices for simplicial facet f%d\n",
                  cntvertices, facet->id);
      qh_errexit(qh_ERRqhull, facet, NULL);
    }
    qh_setappend(&vertices, SETfirst_(facet->vertices));
    if (facet->toporient ^ qh_ORIENTclock)
      qh_setappend(&vertices, SETsecond_(facet->vertices));
    else
      qh_setaddnth(&vertices, 0, SETsecond_(facet->vertices));
    qh_setappend(&vertices, SETelem_(facet->vertices, 2));
  }else {
    ridge= firstridge= SETfirstt_(facet->ridges, ridgeT);   /* no infinite */
    while ((ridge= qh_nextridge3d(ridge, facet, &vertex))) {
      qh_setappend(&vertices, vertex);
      if (++cntprojected > cntvertices || ridge == firstridge)
        break;
    }
    if (!ridge || cntprojected != cntvertices) {
      qh_fprintf(qh ferr, 6148, "qhull internal error (qh_facet3vertex): ridges for facet %d don't match up.  got at least %d\n",
                  facet->id, cntprojected);
      qh_errexit(qh_ERRqhull, facet, ridge);
    }
  }
  return vertices;
} /* facet3vertex */

/*---------------------------------

  qh_findbestfacet( point, bestoutside, bestdist, isoutside )
    find facet that is furthest below a point

    for Delaunay triangulations,
      Use qh_setdelaunay() to lift point to paraboloid and scale by 'Qbb' if needed
      Do not use options 'Qbk', 'QBk', or 'QbB' since they scale the coordinates.

  returns:
    if bestoutside is set (e.g., qh_ALL)
      returns best facet that is not upperdelaunay
      if Delaunay and inside, point is outside circumsphere of bestfacet
    else
      returns first facet below point
      if point is inside, returns nearest, !upperdelaunay facet
    distance to facet
    isoutside set if outside of facet

  notes:
    For tricoplanar facets, this finds one of the tricoplanar facets closest
    to the point.  For Delaunay triangulations, the point may be inside a
    different tricoplanar facet. See locate a facet with qh_findbestfacet()

    If inside, qh_findbestfacet performs an exhaustive search
       this may be too conservative.  Sometimes it is clearly required.

    qh_findbestfacet is not used by qhull.
    uses qh.visit_id and qh.coplanarset

  see:
    qh_findbest
*/
facetT *qh_findbestfacet(pointT *point, boolT bestoutside,
           realT *bestdist, boolT *isoutside) {
  facetT *bestfacet= NULL;
  int numpart, totpart= 0;

  bestfacet= qh_findbest(point, qh facet_list,
                            bestoutside, !qh_ISnewfacets, bestoutside /* qh_NOupper */,
                            bestdist, isoutside, &totpart);
  if (*bestdist < -qh DISTround) {
    bestfacet= qh_findfacet_all(point, bestdist, isoutside, &numpart);
    totpart += numpart;
    if ((isoutside && bestoutside)
    || (!isoutside && bestfacet->upperdelaunay)) {
      bestfacet= qh_findbest(point, bestfacet,
                            bestoutside, False, bestoutside,
                            bestdist, isoutside, &totpart);
      totpart += numpart;
    }
  }
  trace3((qh ferr, 3014, "qh_findbestfacet: f%d dist %2.2g isoutside %d totpart %d\n",
          bestfacet->id, *bestdist, *isoutside, totpart));
  return bestfacet;
} /* findbestfacet */

/*---------------------------------

  qh_findbestlower( facet, point, bestdist, numpart )
    returns best non-upper, non-flipped neighbor of facet for point
    if needed, searches vertex neighbors

  returns:
    returns bestdist and updates numpart

  notes:
    if Delaunay and inside, point is outside of circumsphere of bestfacet
    called by qh_findbest() for points above an upperdelaunay facet

*/
facetT *qh_findbestlower(facetT *upperfacet, pointT *point, realT *bestdistp, int *numpart) {
  facetT *neighbor, **neighborp, *bestfacet= NULL;
  realT bestdist= -REALmax/2 /* avoid underflow */;
  realT dist;
  vertexT *vertex;

  zinc_(Zbestlower);
  FOREACHneighbor_(upperfacet) {
    if (neighbor->upperdelaunay || neighbor->flipped)
      continue;
    (*numpart)++;
    qh_distplane(point, neighbor, &dist);
    if (dist > bestdist) {
      bestfacet= neighbor;
      bestdist= dist;
    }
  }
  if (!bestfacet) {
    zinc_(Zbestlowerv);
    /* rarely called, numpart does not count nearvertex computations */
    vertex= qh_nearvertex(upperfacet, point, &dist);
    qh_vertexneighbors();
    FOREACHneighbor_(vertex) {
      if (neighbor->upperdelaunay || neighbor->flipped)
        continue;
      (*numpart)++;
      qh_distplane(point, neighbor, &dist);
      if (dist > bestdist) {
        bestfacet= neighbor;
        bestdist= dist;
      }
    }
  }
  if (!bestfacet) {
    qh_fprintf(qh ferr, 6228, "\n\
Qhull internal error (qh_findbestlower): all neighbors of facet %d are flipped or upper Delaunay.\n\
Please report this error to qhull_bug@qhull.org with the input and all of the output.\n",
       upperfacet->id);
    qh_errexit(qh_ERRqhull, upperfacet, NULL);
  }
  *bestdistp= bestdist;
  trace3((qh ferr, 3015, "qh_findbestlower: f%d dist %2.2g for f%d p%d\n",
          bestfacet->id, bestdist, upperfacet->id, qh_pointid(point)));
  return bestfacet;
} /* findbestlower */

/*---------------------------------

  qh_findfacet_all( point, bestdist, isoutside, numpart )
    exhaustive search for facet below a point

    for Delaunay triangulations,
      Use qh_setdelaunay() to lift point to paraboloid and scale by 'Qbb' if needed
      Do not use options 'Qbk', 'QBk', or 'QbB' since they scale the coordinates.

  returns:
    returns first facet below point
    if point is inside,
      returns nearest facet
    distance to facet
    isoutside if point is outside of the hull
    number of distance tests

  notes:
    for library users, not used by Qhull
*/
facetT *qh_findfacet_all(pointT *point, realT *bestdist, boolT *isoutside,
                          int *numpart) {
  facetT *bestfacet= NULL, *facet;
  realT dist;
  int totpart= 0;

  *bestdist= -REALmax;
  *isoutside= False;
  FORALLfacets {
    if (facet->flipped || !facet->normal)
      continue;
    totpart++;
    qh_distplane(point, facet, &dist);
    if (dist > *bestdist) {
      *bestdist= dist;
      bestfacet= facet;
      if (dist > qh MINoutside) {
        *isoutside= True;
        break;
      }
    }
  }
  *numpart= totpart;
  trace3((qh ferr, 3016, "qh_findfacet_all: f%d dist %2.2g isoutside %d totpart %d\n",
          getid_(bestfacet), *bestdist, *isoutside, totpart));
  return bestfacet;
} /* findfacet_all */

/*---------------------------------

  qh_findgood( facetlist, goodhorizon )
    identify good facets for qh.PRINTgood
    if qh.GOODvertex>0
      facet includes point as vertex
      if !match, returns goodhorizon
      inactive if qh.MERGING
    if qh.GOODpoint
      facet is visible or coplanar (>0) or not visible (<0)
    if qh.GOODthreshold
      facet->normal matches threshold
    if !goodhorizon and !match,
      selects facet with closest angle
      sets GOODclosest

  returns:
    number of new, good facets found
    determines facet->good
    may update qh.GOODclosest

  notes:
    qh_findgood_all further reduces the good region

  design:
    count good facets
    mark good facets for qh.GOODpoint
    mark good facets for qh.GOODthreshold
    if necessary
      update qh.GOODclosest
*/
int qh_findgood(facetT *facetlist, int goodhorizon) {
  facetT *facet, *bestfacet= NULL;
  realT angle, bestangle= REALmax, dist;
  int  numgood=0;

  FORALLfacet_(facetlist) {
    if (facet->good)
      numgood++;
  }
  if (qh GOODvertex>0 && !qh MERGING) {
    FORALLfacet_(facetlist) {
      if (!qh_isvertex(qh GOODvertexp, facet->vertices)) {
        facet->good= False;
        numgood--;
      }
    }
  }
  if (qh GOODpoint && numgood) {
    FORALLfacet_(facetlist) {
      if (facet->good && facet->normal) {
        zinc_(Zdistgood);
        qh_distplane(qh GOODpointp, facet, &dist);
        if ((qh GOODpoint > 0) ^ (dist > 0.0)) {
          facet->good= False;
          numgood--;
        }
      }
    }
  }
  if (qh GOODthreshold && (numgood || goodhorizon || qh GOODclosest)) {
    FORALLfacet_(facetlist) {
      if (facet->good && facet->normal) {
        if (!qh_inthresholds(facet->normal, &angle)) {
          facet->good= False;
          numgood--;
          if (angle < bestangle) {
            bestangle= angle;
            bestfacet= facet;
          }
        }
      }
    }
    if (!numgood && (!goodhorizon || qh GOODclosest)) {
      if (qh GOODclosest) {
        if (qh GOODclosest->visible)
          qh GOODclosest= NULL;
        else {
          qh_inthresholds(qh GOODclosest->normal, &angle);
          if (angle < bestangle)
            bestfacet= qh GOODclosest;
        }
      }
      if (bestfacet && bestfacet != qh GOODclosest) {
        if (qh GOODclosest)
          qh GOODclosest->good= False;
        qh GOODclosest= bestfacet;
        bestfacet->good= True;
        numgood++;
        trace2((qh ferr, 2044, "qh_findgood: f%d is closest(%2.2g) to thresholds\n",
           bestfacet->id, bestangle));
        return numgood;
      }
    }else if (qh GOODclosest) { /* numgood > 0 */
      qh GOODclosest->good= False;
      qh GOODclosest= NULL;
    }
  }
  zadd_(Zgoodfacet, numgood);
  trace2((qh ferr, 2045, "qh_findgood: found %d good facets with %d good horizon\n",
               numgood, goodhorizon));
  if (!numgood && qh GOODvertex>0 && !qh MERGING)
    return goodhorizon;
  return numgood;
} /* findgood */

/*---------------------------------

  qh_findgood_all( facetlist )
    apply other constraints for good facets (used by qh.PRINTgood)
    if qh.GOODvertex
      facet includes (>0) or doesn't include (<0) point as vertex
      if last good facet and ONLYgood, prints warning and continues
    if qh.SPLITthresholds
      facet->normal matches threshold, or if none, the closest one
    calls qh_findgood
    nop if good not used

  returns:
    clears facet->good if not good
    sets qh.num_good

  notes:
    this is like qh_findgood but more restrictive

  design:
    uses qh_findgood to mark good facets
    marks facets for qh.GOODvertex
    marks facets for qh.SPLITthreholds
*/
void qh_findgood_all(facetT *facetlist) {
  facetT *facet, *bestfacet=NULL;
  realT angle, bestangle= REALmax;
  int  numgood=0, startgood;

  if (!qh GOODvertex && !qh GOODthreshold && !qh GOODpoint
  && !qh SPLITthresholds)
    return;
  if (!qh ONLYgood)
    qh_findgood(qh facet_list, 0);
  FORALLfacet_(facetlist) {
    if (facet->good)
      numgood++;
  }
  if (qh GOODvertex <0 || (qh GOODvertex > 0 && qh MERGING)) {
    FORALLfacet_(facetlist) {
      if (facet->good && ((qh GOODvertex > 0) ^ !!qh_isvertex(qh GOODvertexp, facet->vertices))) {
        if (!--numgood) {
          if (qh ONLYgood) {
            qh_fprintf(qh ferr, 7064, "qhull warning: good vertex p%d does not match last good facet f%d.  Ignored.\n",
               qh_pointid(qh GOODvertexp), facet->id);
            return;
          }else if (qh GOODvertex > 0)
            qh_fprintf(qh ferr, 7065, "qhull warning: point p%d is not a vertex('QV%d').\n",
                qh GOODvertex-1, qh GOODvertex-1);
          else
            qh_fprintf(qh ferr, 7066, "qhull warning: point p%d is a vertex for every facet('QV-%d').\n",
                -qh GOODvertex - 1, -qh GOODvertex - 1);
        }
        facet->good= False;
      }
    }
  }
  startgood= numgood;
  if (qh SPLITthresholds) {
    FORALLfacet_(facetlist) {
      if (facet->good) {
        if (!qh_inthresholds(facet->normal, &angle)) {
          facet->good= False;
          numgood--;
          if (angle < bestangle) {
            bestangle= angle;
            bestfacet= facet;
          }
        }
      }
    }
    if (!numgood && bestfacet) {
      bestfacet->good= True;
      numgood++;
      trace0((qh ferr, 23, "qh_findgood_all: f%d is closest(%2.2g) to thresholds\n",
           bestfacet->id, bestangle));
      return;
    }
  }
  qh num_good= numgood;
  trace0((qh ferr, 24, "qh_findgood_all: %d good facets remain out of %d facets\n",
        numgood, startgood));
} /* findgood_all */

/*---------------------------------

  qh_furthestnext()
    set qh.facet_next to facet with furthest of all furthest points
    searches all facets on qh.facet_list

  notes:
    this may help avoid precision problems
*/
void qh_furthestnext(void /* qh facet_list */) {
  facetT *facet, *bestfacet= NULL;
  realT dist, bestdist= -REALmax;

  FORALLfacets {
    if (facet->outsideset) {
#if qh_COMPUTEfurthest
      pointT *furthest;
      furthest= (pointT*)qh_setlast(facet->outsideset);
      zinc_(Zcomputefurthest);
      qh_distplane(furthest, facet, &dist);
#else
      dist= facet->furthestdist;
#endif
      if (dist > bestdist) {
        bestfacet= facet;
        bestdist= dist;
      }
    }
  }
  if (bestfacet) {
    qh_removefacet(bestfacet);
    qh_prependfacet(bestfacet, &qh facet_next);
    trace1((qh ferr, 1029, "qh_furthestnext: made f%d next facet(dist %.2g)\n",
            bestfacet->id, bestdist));
  }
} /* furthestnext */

/*---------------------------------

  qh_furthestout( facet )
    make furthest outside point the last point of outsideset

  returns:
    updates facet->outsideset
    clears facet->notfurthest
    sets facet->furthestdist

  design:
    determine best point of outsideset
    make it the last point of outsideset
*/
void qh_furthestout(facetT *facet) {
  pointT *point, **pointp, *bestpoint= NULL;
  realT dist, bestdist= -REALmax;

  FOREACHpoint_(facet->outsideset) {
    qh_distplane(point, facet, &dist);
    zinc_(Zcomputefurthest);
    if (dist > bestdist) {
      bestpoint= point;
      bestdist= dist;
    }
  }
  if (bestpoint) {
    qh_setdel(facet->outsideset, point);
    qh_setappend(&facet->outsideset, point);
#if !qh_COMPUTEfurthest
    facet->furthestdist= bestdist;
#endif
  }
  facet->notfurthest= False;
  trace3((qh ferr, 3017, "qh_furthestout: p%d is furthest outside point of f%d\n",
          qh_pointid(point), facet->id));
} /* furthestout */


/*---------------------------------

  qh_infiniteloop( facet )
    report infinite loop error due to facet
*/
void qh_infiniteloop(facetT *facet) {

  qh_fprintf(qh ferr, 6149, "qhull internal error (qh_infiniteloop): potential infinite loop detected\n");
  qh_errexit(qh_ERRqhull, facet, NULL);
} /* qh_infiniteloop */

/*---------------------------------

  qh_initbuild()
    initialize hull and outside sets with point array
    qh.FIRSTpoint/qh.NUMpoints is point array
    if qh.GOODpoint
      adds qh.GOODpoint to initial hull

  returns:
    qh_facetlist with initial hull
    points partioned into outside sets, coplanar sets, or inside
    initializes qh.GOODpointp, qh.GOODvertexp,

  design:
    initialize global variables used during qh_buildhull
    determine precision constants and points with max/min coordinate values
      if qh.SCALElast, scale last coordinate(for 'd')
    build initial simplex
    partition input points into facets of initial simplex
    set up lists
    if qh.ONLYgood
      check consistency
      add qh.GOODvertex if defined
*/
void qh_initbuild( void) {
  setT *maxpoints, *vertices;
  facetT *facet;
  int i, numpart;
  realT dist;
  boolT isoutside;

  qh furthest_id= -1;
  qh lastreport= 0;
  qh facet_id= qh vertex_id= qh ridge_id= 0;
  qh visit_id= qh vertex_visit= 0;
  qh maxoutdone= False;

  if (qh GOODpoint > 0)
    qh GOODpointp= qh_point(qh GOODpoint-1);
  else if (qh GOODpoint < 0)
    qh GOODpointp= qh_point(-qh GOODpoint-1);
  if (qh GOODvertex > 0)
    qh GOODvertexp= qh_point(qh GOODvertex-1);
  else if (qh GOODvertex < 0)
    qh GOODvertexp= qh_point(-qh GOODvertex-1);
  if ((qh GOODpoint
       && (qh GOODpointp < qh first_point  /* also catches !GOODpointp */
           || qh GOODpointp > qh_point(qh num_points-1)))
    || (qh GOODvertex
        && (qh GOODvertexp < qh first_point  /* also catches !GOODvertexp */
            || qh GOODvertexp > qh_point(qh num_points-1)))) {
    qh_fprintf(qh ferr, 6150, "qhull input error: either QGn or QVn point is > p%d\n",
             qh num_points-1);
    qh_errexit(qh_ERRinput, NULL, NULL);
  }
  maxpoints= qh_maxmin(qh first_point, qh num_points, qh hull_dim);
  if (qh SCALElast)
    qh_scalelast(qh first_point, qh num_points, qh hull_dim,
               qh MINlastcoord, qh MAXlastcoord, qh MAXwidth);
  qh_detroundoff();
  if (qh DELAUNAY && qh upper_threshold[qh hull_dim-1] > REALmax/2
                  && qh lower_threshold[qh hull_dim-1] < -REALmax/2) {
    for (i=qh_PRINTEND; i--; ) {
      if (qh PRINTout[i] == qh_PRINTgeom && qh DROPdim < 0
          && !qh GOODthreshold && !qh SPLITthresholds)
        break;  /* in this case, don't set upper_threshold */
    }
    if (i < 0) {
      if (qh UPPERdelaunay) { /* matches qh.upperdelaunay in qh_setfacetplane */
        qh lower_threshold[qh hull_dim-1]= qh ANGLEround * qh_ZEROdelaunay;
        qh GOODthreshold= True;
      }else {
        qh upper_threshold[qh hull_dim-1]= -qh ANGLEround * qh_ZEROdelaunay;
        if (!qh GOODthreshold)
          qh SPLITthresholds= True; /* build upper-convex hull even if Qg */
          /* qh_initqhull_globals errors if Qg without Pdk/etc. */
      }
    }
  }
  vertices= qh_initialvertices(qh hull_dim, maxpoints, qh first_point, qh num_points);
  qh_initialhull(vertices);  /* initial qh facet_list */
  qh_partitionall(vertices, qh first_point, qh num_points);
  if (qh PRINToptions1st || qh TRACElevel || qh IStracing) {
    if (qh TRACElevel || qh IStracing)
      qh_fprintf(qh ferr, 8103, "\nTrace level %d for %s | %s\n",
         qh IStracing ? qh IStracing : qh TRACElevel, qh rbox_command, qh qhull_command);
    qh_fprintf(qh ferr, 8104, "Options selected for Qhull %s:\n%s\n", qh_version, qh qhull_options);
  }
  qh_resetlists(False, qh_RESETvisible /*qh visible_list newvertex_list newfacet_list */);
  qh facet_next= qh facet_list;
  qh_furthestnext(/* qh facet_list */);
  if (qh PREmerge) {
    qh cos_max= qh premerge_cos;
    qh centrum_radius= qh premerge_centrum;
  }
  if (qh ONLYgood) {
    if (qh GOODvertex > 0 && qh MERGING) {
      qh_fprintf(qh ferr, 6151, "qhull input error: 'Qg QVn' (only good vertex) does not work with merging.\nUse 'QJ' to joggle the input or 'Q0' to turn off merging.\n");
      qh_errexit(qh_ERRinput, NULL, NULL);
    }
    if (!(qh GOODthreshold || qh GOODpoint
         || (!qh MERGEexact && !qh PREmerge && qh GOODvertexp))) {
      qh_fprintf(qh ferr, 6152, "qhull input error: 'Qg' (ONLYgood) needs a good threshold('Pd0D0'), a\n\
good point(QGn or QG-n), or a good vertex with 'QJ' or 'Q0' (QVn).\n");
      qh_errexit(qh_ERRinput, NULL, NULL);
    }
    if (qh GOODvertex > 0  && !qh MERGING  /* matches qh_partitionall */
        && !qh_isvertex(qh GOODvertexp, vertices)) {
      facet= qh_findbestnew(qh GOODvertexp, qh facet_list,
                          &dist, !qh_ALL, &isoutside, &numpart);
      zadd_(Zdistgood, numpart);
      if (!isoutside) {
        qh_fprintf(qh ferr, 6153, "qhull input error: point for QV%d is inside initial simplex.  It can not be made a vertex.\n",
               qh_pointid(qh GOODvertexp));
        qh_errexit(qh_ERRinput, NULL, NULL);
      }
      if (!qh_addpoint(qh GOODvertexp, facet, False)) {
        qh_settempfree(&vertices);
        qh_settempfree(&maxpoints);
        return;
      }
    }
    qh_findgood(qh facet_list, 0);
  }
  qh_settempfree(&vertices);
  qh_settempfree(&maxpoints);
  trace1((qh ferr, 1030, "qh_initbuild: initial hull created and points partitioned\n"));
} /* initbuild */

/*---------------------------------

  qh_initialhull( vertices )
    constructs the initial hull as a DIM3 simplex of vertices

  design:
    creates a simplex (initializes lists)
    determines orientation of simplex
    sets hyperplanes for facets
    doubles checks orientation (in case of axis-parallel facets with Gaussian elimination)
    checks for flipped facets and qh.NARROWhull
    checks the result
*/
void qh_initialhull(setT *vertices) {
  facetT *facet, *firstfacet, *neighbor, **neighborp;
  realT dist, angle, minangle= REALmax;
#ifndef qh_NOtrace
  int k;
#endif

  qh_createsimplex(vertices);  /* qh facet_list */
  qh_resetlists(False, qh_RESETvisible);
  qh facet_next= qh facet_list;      /* advance facet when processed */
  qh interior_point= qh_getcenter(vertices);
  firstfacet= qh facet_list;
  qh_setfacetplane(firstfacet);
  zinc_(Znumvisibility); /* needs to be in printsummary */
  qh_distplane(qh interior_point, firstfacet, &dist);
  if (dist > 0) {
    FORALLfacets
      facet->toporient ^= (unsigned char)True;
  }
  FORALLfacets
    qh_setfacetplane(facet);
  FORALLfacets {
    if (!qh_checkflipped(facet, NULL, qh_ALL)) {/* due to axis-parallel facet */
      trace1((qh ferr, 1031, "qh_initialhull: initial orientation incorrect.  Correct all facets\n"));
      facet->flipped= False;
      FORALLfacets {
        facet->toporient ^= (unsigned char)True;
        qh_orientoutside(facet);
      }
      break;
    }
  }
  FORALLfacets {
    if (!qh_checkflipped(facet, NULL, !qh_ALL)) {  /* can happen with 'R0.1' */
      if (qh DELAUNAY && ! qh ATinfinity) {
        if (qh UPPERdelaunay)
          qh_fprintf(qh ferr, 6240, "Qhull input error: Can not compute the upper Delaunay triangulation or upper Voronoi diagram of cocircular/cospherical points.\n");
        else
          qh_fprintf(qh ferr, 6239, "Qhull input error: Use option 'Qz' for the Delaunay triangulation or Voronoi diagram of cocircular/cospherical points.  Option 'Qz' adds a point \"at infinity\" (above the corresponding paraboloid).\n");
        qh_errexit(qh_ERRinput, NULL, NULL);
      }
      qh_precision("initial facet is coplanar with interior point");
      qh_fprintf(qh ferr, 6154, "qhull precision error: initial facet %d is coplanar with the interior point\n",
                   facet->id);
      qh_errexit(qh_ERRsingular, facet, NULL);
    }
    FOREACHneighbor_(facet) {
      angle= qh_getangle(facet->normal, neighbor->normal);
      minimize_( minangle, angle);
    }
  }
  if (minangle < qh_MAXnarrow && !qh NOnarrow) {
    realT diff= 1.0 + minangle;

    qh NARROWhull= True;
    qh_option("_narrow-hull", NULL, &diff);
    if (minangle < qh_WARNnarrow && !qh RERUN && qh PRINTprecision)
      qh_printhelp_narrowhull(qh ferr, minangle);
  }
  zzval_(Zprocessed)= qh hull_dim+1;
  qh_checkpolygon(qh facet_list);
  qh_checkconvex(qh facet_list,   qh_DATAfault);
#ifndef qh_NOtrace
  if (qh IStracing >= 1) {
    qh_fprintf(qh ferr, 8105, "qh_initialhull: simplex constructed, interior point:");
    for (k=0; k < qh hull_dim; k++)
      qh_fprintf(qh ferr, 8106, " %6.4g", qh interior_point[k]);
    qh_fprintf(qh ferr, 8107, "\n");
  }
#endif
} /* initialhull */

/*---------------------------------

  qh_initialvertices( dim, maxpoints, points, numpoints )
    determines a non-singular set of initial vertices
    maxpoints may include duplicate points

  returns:
    temporary set of dim+1 vertices in descending order by vertex id
    if qh.RANDOMoutside && !qh.ALLpoints
      picks random points
    if dim >= qh_INITIALmax,
      uses min/max x and max points with non-zero determinants

  notes:
    unless qh.ALLpoints,
      uses maxpoints as long as determinate is non-zero
*/
setT *qh_initialvertices(int dim, setT *maxpoints, pointT *points, int numpoints) {
  pointT *point, **pointp;
  setT *vertices, *simplex, *tested;
  realT randr;
  int idx, point_i, point_n, k;
  boolT nearzero= False;

  vertices= qh_settemp(dim + 1);
  simplex= qh_settemp(dim+1);
  if (qh ALLpoints)
    qh_maxsimplex(dim, NULL, points, numpoints, &simplex);
  else if (qh RANDOMoutside) {
    while (qh_setsize(simplex) != dim+1) {
      randr= qh_RANDOMint;
      randr= randr/(qh_RANDOMmax+1);
      idx= (int)floor(qh num_points * randr);
      while (qh_setin(simplex, qh_point(idx))) {
            idx++; /* in case qh_RANDOMint always returns the same value */
        idx= idx < qh num_points ? idx : 0;
      }
      qh_setappend(&simplex, qh_point(idx));
    }
  }else if (qh hull_dim >= qh_INITIALmax) {
    tested= qh_settemp(dim+1);
    qh_setappend(&simplex, SETfirst_(maxpoints));   /* max and min X coord */
    qh_setappend(&simplex, SETsecond_(maxpoints));
    qh_maxsimplex(fmin_(qh_INITIALsearch, dim), maxpoints, points, numpoints, &simplex);
    k= qh_setsize(simplex);
    FOREACHpoint_i_(maxpoints) {
      if (point_i & 0x1) {     /* first pick up max. coord. points */
        if (!qh_setin(simplex, point) && !qh_setin(tested, point)){
          qh_detsimplex(point, simplex, k, &nearzero);
          if (nearzero)
            qh_setappend(&tested, point);
          else {
            qh_setappend(&simplex, point);
            if (++k == dim)  /* use search for last point */
              break;
          }
        }
      }
    }
    while (k != dim && (point= (pointT*)qh_setdellast(maxpoints))) {
      if (!qh_setin(simplex, point) && !qh_setin(tested, point)){
        qh_detsimplex(point, simplex, k, &nearzero);
        if (nearzero)
          qh_setappend(&tested, point);
        else {
          qh_setappend(&simplex, point);
          k++;
        }
      }
    }
    idx= 0;
    while (k != dim && (point= qh_point(idx++))) {
      if (!qh_setin(simplex, point) && !qh_setin(tested, point)){
        qh_detsimplex(point, simplex, k, &nearzero);
        if (!nearzero){
          qh_setappend(&simplex, point);
          k++;
        }
      }
    }
    qh_settempfree(&tested);
    qh_maxsimplex(dim, maxpoints, points, numpoints, &simplex);
  }else
    qh_maxsimplex(dim, maxpoints, points, numpoints, &simplex);
  FOREACHpoint_(simplex)
    qh_setaddnth(&vertices, 0, qh_newvertex(point)); /* descending order */
  qh_settempfree(&simplex);
  return vertices;
} /* initialvertices */


/*---------------------------------

  qh_isvertex(  )
    returns vertex if point is in vertex set, else returns NULL

  notes:
    for qh.GOODvertex
*/
vertexT *qh_isvertex(pointT *point, setT *vertices) {
  vertexT *vertex, **vertexp;

  FOREACHvertex_(vertices) {
    if (vertex->point == point)
      return vertex;
  }
  return NULL;
} /* isvertex */

/*---------------------------------

  qh_makenewfacets( point )
    make new facets from point and qh.visible_list

  returns:
    qh.newfacet_list= list of new facets with hyperplanes and ->newfacet
    qh.newvertex_list= list of vertices in new facets with ->newlist set

    if (qh.ONLYgood)
      newfacets reference horizon facets, but not vice versa
      ridges reference non-simplicial horizon ridges, but not vice versa
      does not change existing facets
    else
      sets qh.NEWfacets
      new facets attached to horizon facets and ridges
      for visible facets,
        visible->r.replace is corresponding new facet

  see also:
    qh_makenewplanes() -- make hyperplanes for facets
    qh_attachnewfacets() -- attachnewfacets if not done here(qh ONLYgood)
    qh_matchnewfacets() -- match up neighbors
    qh_updatevertices() -- update vertex neighbors and delvertices
    qh_deletevisible() -- delete visible facets
    qh_checkpolygon() --check the result
    qh_triangulate() -- triangulate a non-simplicial facet

  design:
    for each visible facet
      make new facets to its horizon facets
      update its f.replace
      clear its neighbor set
*/
vertexT *qh_makenewfacets(pointT *point /*visible_list*/) {
  facetT *visible, *newfacet= NULL, *newfacet2= NULL, *neighbor, **neighborp;
  vertexT *apex;
  int numnew=0;

  qh newfacet_list= qh facet_tail;
  qh newvertex_list= qh vertex_tail;
  apex= qh_newvertex(point);
  qh_appendvertex(apex);
  qh visit_id++;
  if (!qh ONLYgood)
    qh NEWfacets= True;
  FORALLvisible_facets {
    FOREACHneighbor_(visible)
      neighbor->seen= False;
    if (visible->ridges) {
      visible->visitid= qh visit_id;
      newfacet2= qh_makenew_nonsimplicial(visible, apex, &numnew);
    }
    if (visible->simplicial)
      newfacet= qh_makenew_simplicial(visible, apex, &numnew);
    if (!qh ONLYgood) {
      if (newfacet2)  /* newfacet is null if all ridges defined */
        newfacet= newfacet2;
      if (newfacet)
        visible->f.replace= newfacet;
      else
        zinc_(Zinsidevisible);
      SETfirst_(visible->neighbors)= NULL;
    }
  }
  trace1((qh ferr, 1032, "qh_makenewfacets: created %d new facets from point p%d to horizon\n",
          numnew, qh_pointid(point)));
  if (qh IStracing >= 4)
    qh_printfacetlist(qh newfacet_list, NULL, qh_ALL);
  return apex;
} /* makenewfacets */

/*---------------------------------

  qh_matchduplicates( atfacet, atskip, hashsize, hashcount )
    match duplicate ridges in qh.hash_table for atfacet/atskip
    duplicates marked with ->dupridge and qh_DUPLICATEridge

  returns:
    picks match with worst merge (min distance apart)
    updates hashcount

  see also:
    qh_matchneighbor

  notes:

  design:
    compute hash value for atfacet and atskip
    repeat twice -- once to make best matches, once to match the rest
      for each possible facet in qh.hash_table
        if it is a matching facet and pass 2
          make match
          unless tricoplanar, mark match for merging (qh_MERGEridge)
          [e.g., tricoplanar RBOX s 1000 t993602376 | QHULL C-1e-3 d Qbb FA Qt]
        if it is a matching facet and pass 1
          test if this is a better match
      if pass 1,
        make best match (it will not be merged)
*/
#ifndef qh_NOmerge
void qh_matchduplicates(facetT *atfacet, int atskip, int hashsize, int *hashcount) {
  boolT same, ismatch;
  int hash, scan;
  facetT *facet, *newfacet, *maxmatch= NULL, *maxmatch2= NULL, *nextfacet;
  int skip, newskip, nextskip= 0, maxskip= 0, maxskip2= 0, makematch;
  realT maxdist= -REALmax, mindist, dist2, low, high;

  hash= qh_gethash(hashsize, atfacet->vertices, qh hull_dim, 1,
                     SETelem_(atfacet->vertices, atskip));
  trace2((qh ferr, 2046, "qh_matchduplicates: find duplicate matches for f%d skip %d hash %d hashcount %d\n",
          atfacet->id, atskip, hash, *hashcount));
  for (makematch= 0; makematch < 2; makematch++) {
    qh visit_id++;
    for (newfacet= atfacet, newskip= atskip; newfacet; newfacet= nextfacet, newskip= nextskip) {
      zinc_(Zhashlookup);
      nextfacet= NULL;
      newfacet->visitid= qh visit_id;
      for (scan= hash; (facet= SETelemt_(qh hash_table, scan, facetT));
           scan= (++scan >= hashsize ? 0 : scan)) {
        if (!facet->dupridge || facet->visitid == qh visit_id)
          continue;
        zinc_(Zhashtests);
        if (qh_matchvertices(1, newfacet->vertices, newskip, facet->vertices, &skip, &same)) {
          ismatch= (same == (boolT)(newfacet->toporient ^ facet->toporient));
          if (SETelemt_(facet->neighbors, skip, facetT) != qh_DUPLICATEridge) {
            if (!makematch) {
              qh_fprintf(qh ferr, 6155, "qhull internal error (qh_matchduplicates): missing dupridge at f%d skip %d for new f%d skip %d hash %d\n",
                     facet->id, skip, newfacet->id, newskip, hash);
              qh_errexit2 (qh_ERRqhull, facet, newfacet);
            }
          }else if (ismatch && makematch) {
            if (SETelemt_(newfacet->neighbors, newskip, facetT) == qh_DUPLICATEridge) {
              SETelem_(facet->neighbors, skip)= newfacet;
              if (newfacet->tricoplanar)
                SETelem_(newfacet->neighbors, newskip)= facet;
              else
                SETelem_(newfacet->neighbors, newskip)= qh_MERGEridge;
              *hashcount -= 2; /* removed two unmatched facets */
              trace4((qh ferr, 4059, "qh_matchduplicates: duplicate f%d skip %d matched with new f%d skip %d merge\n",
                    facet->id, skip, newfacet->id, newskip));
            }
          }else if (ismatch) {
            mindist= qh_getdistance(facet, newfacet, &low, &high);
            dist2= qh_getdistance(newfacet, facet, &low, &high);
            minimize_(mindist, dist2);
            if (mindist > maxdist) {
              maxdist= mindist;
              maxmatch= facet;
              maxskip= skip;
              maxmatch2= newfacet;
              maxskip2= newskip;
            }
            trace3((qh ferr, 3018, "qh_matchduplicates: duplicate f%d skip %d new f%d skip %d at dist %2.2g, max is now f%d f%d\n",
                    facet->id, skip, newfacet->id, newskip, mindist,
                    maxmatch->id, maxmatch2->id));
          }else { /* !ismatch */
            nextfacet= facet;
            nextskip= skip;
          }
        }
        if (makematch && !facet
        && SETelemt_(facet->neighbors, skip, facetT) == qh_DUPLICATEridge) {
          qh_fprintf(qh ferr, 6156, "qhull internal error (qh_matchduplicates): no MERGEridge match for duplicate f%d skip %d at hash %d\n",
                     newfacet->id, newskip, hash);
          qh_errexit(qh_ERRqhull, newfacet, NULL);
        }
      }
    } /* end of for each new facet at hash */
    if (!makematch) {
      if (!maxmatch) {
        qh_fprintf(qh ferr, 6157, "qhull internal error (qh_matchduplicates): no maximum match at duplicate f%d skip %d at hash %d\n",
                     atfacet->id, atskip, hash);
        qh_errexit(qh_ERRqhull, atfacet, NULL);
      }
      SETelem_(maxmatch->neighbors, maxskip)= maxmatch2;
      SETelem_(maxmatch2->neighbors, maxskip2)= maxmatch;
      *hashcount -= 2; /* removed two unmatched facets */
      zzinc_(Zmultiridge);
      trace0((qh ferr, 25, "qh_matchduplicates: duplicate f%d skip %d matched with new f%d skip %d keep\n",
              maxmatch->id, maxskip, maxmatch2->id, maxskip2));
      qh_precision("ridge with multiple neighbors");
      if (qh IStracing >= 4)
        qh_errprint("DUPLICATED/MATCH", maxmatch, maxmatch2, NULL, NULL);
    }
  }
} /* matchduplicates */

/*---------------------------------

  qh_nearcoplanar()
    for all facets, remove near-inside points from facet->coplanarset
    coplanar points defined by innerplane from qh_outerinner()

  returns:
    if qh KEEPcoplanar && !qh KEEPinside
      facet->coplanarset only contains coplanar points
    if qh.JOGGLEmax
      drops inner plane by another qh.JOGGLEmax diagonal since a
        vertex could shift out while a coplanar point shifts in

  notes:
    used for qh.PREmerge and qh.JOGGLEmax
    must agree with computation of qh.NEARcoplanar in qh_detroundoff()
  design:
    if not keeping coplanar or inside points
      free all coplanar sets
    else if not keeping both coplanar and inside points
      remove !coplanar or !inside points from coplanar sets
*/
void qh_nearcoplanar(void /* qh.facet_list */) {
  facetT *facet;
  pointT *point, **pointp;
  int numpart;
  realT dist, innerplane;

  if (!qh KEEPcoplanar && !qh KEEPinside) {
    FORALLfacets {
      if (facet->coplanarset)
        qh_setfree( &facet->coplanarset);
    }
  }else if (!qh KEEPcoplanar || !qh KEEPinside) {
    qh_outerinner(NULL, NULL, &innerplane);
    if (qh JOGGLEmax < REALmax/2)
      innerplane -= qh JOGGLEmax * sqrt((realT)qh hull_dim);
    numpart= 0;
    FORALLfacets {
      if (facet->coplanarset) {
        FOREACHpoint_(facet->coplanarset) {
          numpart++;
          qh_distplane(point, facet, &dist);
          if (dist < innerplane) {
            if (!qh KEEPinside)
              SETref_(point)= NULL;
          }else if (!qh KEEPcoplanar)
            SETref_(point)= NULL;
        }
        qh_setcompact(facet->coplanarset);
      }
    }
    zzadd_(Zcheckpart, numpart);
  }
} /* nearcoplanar */

/*---------------------------------

  qh_nearvertex( facet, point, bestdist )
    return nearest vertex in facet to point

  returns:
    vertex and its distance

  notes:
    if qh.DELAUNAY
      distance is measured in the input set
    searches neighboring tricoplanar facets (requires vertexneighbors)
      Slow implementation.  Recomputes vertex set for each point.
    The vertex set could be stored in the qh.keepcentrum facet.
*/
vertexT *qh_nearvertex(facetT *facet, pointT *point, realT *bestdistp) {
  realT bestdist= REALmax, dist;
  vertexT *bestvertex= NULL, *vertex, **vertexp, *apex;
  coordT *center;
  facetT *neighbor, **neighborp;
  setT *vertices;
  int dim= qh hull_dim;

  if (qh DELAUNAY)
    dim--;
  if (facet->tricoplanar) {
    if (!qh VERTEXneighbors || !facet->center) {
      qh_fprintf(qh ferr, 6158, "qhull internal error (qh_nearvertex): qh.VERTEXneighbors and facet->center required for tricoplanar facets\n");
      qh_errexit(qh_ERRqhull, facet, NULL);
    }
    vertices= qh_settemp(qh TEMPsize);
    apex= SETfirstt_(facet->vertices, vertexT);
    center= facet->center;
    FOREACHneighbor_(apex) {
      if (neighbor->center == center) {
        FOREACHvertex_(neighbor->vertices)
          qh_setappend(&vertices, vertex);
      }
    }
  }else
    vertices= facet->vertices;
  FOREACHvertex_(vertices) {
    dist= qh_pointdist(vertex->point, point, -dim);
    if (dist < bestdist) {
      bestdist= dist;
      bestvertex= vertex;
    }
  }
  if (facet->tricoplanar)
    qh_settempfree(&vertices);
  *bestdistp= sqrt(bestdist);
  trace3((qh ferr, 3019, "qh_nearvertex: v%d dist %2.2g for f%d p%d\n",
        bestvertex->id, *bestdistp, facet->id, qh_pointid(point)));
  return bestvertex;
} /* nearvertex */

/*---------------------------------

  qh_newhashtable( newsize )
    returns size of qh.hash_table of at least newsize slots

  notes:
    assumes qh.hash_table is NULL
    qh_HASHfactor determines the number of extra slots
    size is not divisible by 2, 3, or 5
*/
int qh_newhashtable(int newsize) {
  int size;

  size= ((newsize+1)*qh_HASHfactor) | 0x1;  /* odd number */
  while (True) {
    if (newsize<0 || size<0) {
        qh_fprintf(qhmem.ferr, 6236, "qhull error (qh_newhashtable): negative request (%d) or size (%d).  Did int overflow due to high-D?\n", newsize, size); /* WARN64 */
        qh_errexit(qhmem_ERRmem, NULL, NULL);
    }
    if ((size%3) && (size%5))
      break;
    size += 2;
    /* loop terminates because there is an infinite number of primes */
  }
  qh hash_table= qh_setnew(size);
  qh_setzero(qh hash_table, 0, size);
  return size;
} /* newhashtable */

/*---------------------------------

  qh_newvertex( point )
    returns a new vertex for point
*/
vertexT *qh_newvertex(pointT *point) {
  vertexT *vertex;

  zinc_(Ztotvertices);
  vertex= (vertexT *)qh_memalloc((int)sizeof(vertexT));
  memset((char *) vertex, (size_t)0, sizeof(vertexT));
  if (qh vertex_id == 0xFFFFFF) {
    qh_fprintf(qh ferr, 6159, "qhull error: more than %d vertices.  ID field overflows and two vertices\n\
may have the same identifier.  Vertices will not be sorted correctly.\n", 0xFFFFFF);
    qh_errexit(qh_ERRqhull, NULL, NULL);
  }
  if (qh vertex_id == qh tracevertex_id)
    qh tracevertex= vertex;
  vertex->id= qh vertex_id++;
  vertex->point= point;
  vertex->dim= (unsigned char)(qh hull_dim <= MAX_vdim ? qh hull_dim : 0);
  trace4((qh ferr, 4060, "qh_newvertex: vertex p%d(v%d) created\n", qh_pointid(vertex->point),
          vertex->id));
  return(vertex);
} /* newvertex */

/*---------------------------------

  qh_nextridge3d( atridge, facet, vertex )
    return next ridge and vertex for a 3d facet
    returns NULL on error
    [for QhullFacet::nextRidge3d] Does not call qh_errexit nor access qh_qh.

  notes:
    in qh_ORIENTclock order
    this is a O(n^2) implementation to trace all ridges
    be sure to stop on any 2nd visit
    same as QhullRidge::nextRidge3d
    does not use qh_qh or qh_errexit [QhullFacet.cpp]

  design:
    for each ridge
      exit if it is the ridge after atridge
*/
ridgeT *qh_nextridge3d(ridgeT *atridge, facetT *facet, vertexT **vertexp) {
  vertexT *atvertex, *vertex, *othervertex;
  ridgeT *ridge, **ridgep;

  if ((atridge->top == facet) ^ qh_ORIENTclock)
    atvertex= SETsecondt_(atridge->vertices, vertexT);
  else
    atvertex= SETfirstt_(atridge->vertices, vertexT);
  FOREACHridge_(facet->ridges) {
    if (ridge == atridge)
      continue;
    if ((ridge->top == facet) ^ qh_ORIENTclock) {
      othervertex= SETsecondt_(ridge->vertices, vertexT);
      vertex= SETfirstt_(ridge->vertices, vertexT);
    }else {
      vertex= SETsecondt_(ridge->vertices, vertexT);
      othervertex= SETfirstt_(ridge->vertices, vertexT);
    }
    if (vertex == atvertex) {
      if (vertexp)
        *vertexp= othervertex;
      return ridge;
    }
  }
  return NULL;
} /* nextridge3d */
#else /* qh_NOmerge */
void qh_matchduplicates(facetT *atfacet, int atskip, int hashsize, int *hashcount) {
}
ridgeT *qh_nextridge3d(ridgeT *atridge, facetT *facet, vertexT **vertexp) {

  return NULL;
}
#endif /* qh_NOmerge */

/*---------------------------------

  qh_outcoplanar()
    move points from all facets' outsidesets to their coplanarsets

  notes:
    for post-processing under qh.NARROWhull

  design:
    for each facet
      for each outside point for facet
        partition point into coplanar set
*/
void qh_outcoplanar(void /* facet_list */) {
  pointT *point, **pointp;
  facetT *facet;
  realT dist;

  trace1((qh ferr, 1033, "qh_outcoplanar: move outsideset to coplanarset for qh NARROWhull\n"));
  FORALLfacets {
    FOREACHpoint_(facet->outsideset) {
      qh num_outside--;
      if (qh KEEPcoplanar || qh KEEPnearinside) {
        qh_distplane(point, facet, &dist);
        zinc_(Zpartition);
        qh_partitioncoplanar(point, facet, &dist);
      }
    }
    qh_setfree(&facet->outsideset);
  }
} /* outcoplanar */

/*---------------------------------

  qh_point( id )
    return point for a point id, or NULL if unknown

  alternative code:
    return((pointT *)((unsigned   long)qh.first_point
           + (unsigned long)((id)*qh.normal_size)));
*/
pointT *qh_point(int id) {

  if (id < 0)
    return NULL;
  if (id < qh num_points)
    return qh first_point + id * qh hull_dim;
  id -= qh num_points;
  if (id < qh_setsize(qh other_points))
    return SETelemt_(qh other_points, id, pointT);
  return NULL;
} /* point */

/*---------------------------------

  qh_point_add( set, point, elem )
    stores elem at set[point.id]

  returns:
    access function for qh_pointfacet and qh_pointvertex

  notes:
    checks point.id
*/
void qh_point_add(setT *set, pointT *point, void *elem) {
  int id, size;

  SETreturnsize_(set, size);
  if ((id= qh_pointid(point)) < 0)
    qh_fprintf(qh ferr, 7067, "qhull internal warning (point_add): unknown point %p id %d\n",
      point, id);
  else if (id >= size) {
    qh_fprintf(qh ferr, 6160, "qhull internal errror(point_add): point p%d is out of bounds(%d)\n",
             id, size);
    qh_errexit(qh_ERRqhull, NULL, NULL);
  }else
    SETelem_(set, id)= elem;
} /* point_add */


/*---------------------------------

  qh_pointfacet()
    return temporary set of facet for each point
    the set is indexed by point id

  notes:
    vertices assigned to one of the facets
    coplanarset assigned to the facet
    outside set assigned to the facet
    NULL if no facet for point (inside)
      includes qh.GOODpointp

  access:
    FOREACHfacet_i_(facets) { ... }
    SETelem_(facets, i)

  design:
    for each facet
      add each vertex
      add each coplanar point
      add each outside point
*/
setT *qh_pointfacet(void /*qh facet_list*/) {
  int numpoints= qh num_points + qh_setsize(qh other_points);
  setT *facets;
  facetT *facet;
  vertexT *vertex, **vertexp;
  pointT *point, **pointp;

  facets= qh_settemp(numpoints);
  qh_setzero(facets, 0, numpoints);
  qh vertex_visit++;
  FORALLfacets {
    FOREACHvertex_(facet->vertices) {
      if (vertex->visitid != qh vertex_visit) {
        vertex->visitid= qh vertex_visit;
        qh_point_add(facets, vertex->point, facet);
      }
    }
    FOREACHpoint_(facet->coplanarset)
      qh_point_add(facets, point, facet);
    FOREACHpoint_(facet->outsideset)
      qh_point_add(facets, point, facet);
  }
  return facets;
} /* pointfacet */

/*---------------------------------

  qh_pointvertex(  )
    return temporary set of vertices indexed by point id
    entry is NULL if no vertex for a point
      this will include qh.GOODpointp

  access:
    FOREACHvertex_i_(vertices) { ... }
    SETelem_(vertices, i)
*/
setT *qh_pointvertex(void /*qh facet_list*/) {
  int numpoints= qh num_points + qh_setsize(qh other_points);
  setT *vertices;
  vertexT *vertex;

  vertices= qh_settemp(numpoints);
  qh_setzero(vertices, 0, numpoints);
  FORALLvertices
    qh_point_add(vertices, vertex->point, vertex);
  return vertices;
} /* pointvertex */


/*---------------------------------

  qh_prependfacet( facet, facetlist )
    prepend facet to the start of a facetlist

  returns:
    increments qh.numfacets
    updates facetlist, qh.facet_list, facet_next

  notes:
    be careful of prepending since it can lose a pointer.
      e.g., can lose _next by deleting and then prepending before _next
*/
void qh_prependfacet(facetT *facet, facetT **facetlist) {
  facetT *prevfacet, *list;


  trace4((qh ferr, 4061, "qh_prependfacet: prepend f%d before f%d\n",
          facet->id, getid_(*facetlist)));
  if (!*facetlist)
    (*facetlist)= qh facet_tail;
  list= *facetlist;
  prevfacet= list->previous;
  facet->previous= prevfacet;
  if (prevfacet)
    prevfacet->next= facet;
  list->previous= facet;
  facet->next= *facetlist;
  if (qh facet_list == list)  /* this may change *facetlist */
    qh facet_list= facet;
  if (qh facet_next == list)
    qh facet_next= facet;
  *facetlist= facet;
  qh num_facets++;
} /* prependfacet */


/*---------------------------------

  qh_printhashtable( fp )
    print hash table to fp

  notes:
    not in I/O to avoid bringing io.c in

  design:
    for each hash entry
      if defined
        if unmatched or will merge (NULL, qh_MERGEridge, qh_DUPLICATEridge)
          print entry and neighbors
*/
void qh_printhashtable(FILE *fp) {
  facetT *facet, *neighbor;
  int id, facet_i, facet_n, neighbor_i= 0, neighbor_n= 0;
  vertexT *vertex, **vertexp;

  FOREACHfacet_i_(qh hash_table) {
    if (facet) {
      FOREACHneighbor_i_(facet) {
        if (!neighbor || neighbor == qh_MERGEridge || neighbor == qh_DUPLICATEridge)
          break;
      }
      if (neighbor_i == neighbor_n)
        continue;
      qh_fprintf(fp, 9283, "hash %d f%d ", facet_i, facet->id);
      FOREACHvertex_(facet->vertices)
        qh_fprintf(fp, 9284, "v%d ", vertex->id);
      qh_fprintf(fp, 9285, "\n neighbors:");
      FOREACHneighbor_i_(facet) {
        if (neighbor == qh_MERGEridge)
          id= -3;
        else if (neighbor == qh_DUPLICATEridge)
          id= -2;
        else
          id= getid_(neighbor);
        qh_fprintf(fp, 9286, " %d", id);
      }
      qh_fprintf(fp, 9287, "\n");
    }
  }
} /* printhashtable */


/*---------------------------------

  qh_printlists( fp )
    print out facet and vertex list for debugging (without 'f/v' tags)
*/
void qh_printlists(void) {
  facetT *facet;
  vertexT *vertex;
  int count= 0;

  qh_fprintf(qh ferr, 8108, "qh_printlists: facets:");
  FORALLfacets {
    if (++count % 100 == 0)
      qh_fprintf(qh ferr, 8109, "\n     ");
    qh_fprintf(qh ferr, 8110, " %d", facet->id);
  }
  qh_fprintf(qh ferr, 8111, "\n  new facets %d visible facets %d next facet for qh_addpoint %d\n  vertices(new %d):",
     getid_(qh newfacet_list), getid_(qh visible_list), getid_(qh facet_next),
     getid_(qh newvertex_list));
  count = 0;
  FORALLvertices {
    if (++count % 100 == 0)
      qh_fprintf(qh ferr, 8112, "\n     ");
    qh_fprintf(qh ferr, 8113, " %d", vertex->id);
  }
  qh_fprintf(qh ferr, 8114, "\n");
} /* printlists */

/*---------------------------------

  qh_resetlists( stats, qh_RESETvisible )
    reset newvertex_list, newfacet_list, visible_list
    if stats,
      maintains statistics

  returns:
    visible_list is empty if qh_deletevisible was called
*/
void qh_resetlists(boolT stats, boolT resetVisible /*qh newvertex_list newfacet_list visible_list*/) {
  vertexT *vertex;
  facetT *newfacet, *visible;
  int totnew=0, totver=0;

  if (stats) {
    FORALLvertex_(qh newvertex_list)
      totver++;
    FORALLnew_facets
      totnew++;
    zadd_(Zvisvertextot, totver);
    zmax_(Zvisvertexmax, totver);
    zadd_(Znewfacettot, totnew);
    zmax_(Znewfacetmax, totnew);
  }
  FORALLvertex_(qh newvertex_list)
    vertex->newlist= False;
  qh newvertex_list= NULL;
  FORALLnew_facets
    newfacet->newfacet= False;
  qh newfacet_list= NULL;
  if (resetVisible) {
    FORALLvisible_facets {
      visible->f.replace= NULL;
      visible->visible= False;
    }
    qh num_visible= 0;
  }
  qh visible_list= NULL; /* may still have visible facets via qh_triangulate */
  qh NEWfacets= False;
} /* resetlists */

/*---------------------------------

  qh_setvoronoi_all()
    compute Voronoi centers for all facets
    includes upperDelaunay facets if qh.UPPERdelaunay ('Qu')

  returns:
    facet->center is the Voronoi center

  notes:
    this is unused/untested code
      please email bradb@shore.net if this works ok for you

  use:
    FORALLvertices {...} to locate the vertex for a point.
    FOREACHneighbor_(vertex) {...} to visit the Voronoi centers for a Voronoi cell.
*/
void qh_setvoronoi_all(void) {
  facetT *facet;

  qh_clearcenters(qh_ASvoronoi);
  qh_vertexneighbors();

  FORALLfacets {
    if (!facet->normal || !facet->upperdelaunay || qh UPPERdelaunay) {
      if (!facet->center)
        facet->center= qh_facetcenter(facet->vertices);
    }
  }
} /* setvoronoi_all */

#ifndef qh_NOmerge

/*---------------------------------

  qh_triangulate()
    triangulate non-simplicial facets on qh.facet_list,
    if qh VORONOI, sets Voronoi centers of non-simplicial facets
    nop if hasTriangulation

  returns:
    all facets simplicial
    each tricoplanar facet has ->f.triowner == owner of ->center,normal,etc.

  notes:
    call after qh_check_output since may switch to Voronoi centers
    Output may overwrite ->f.triowner with ->f.area
*/
void qh_triangulate(void /*qh facet_list*/) {
  facetT *facet, *nextfacet, *owner;
  int onlygood= qh ONLYgood;
  facetT *neighbor, *visible= NULL, *facet1, *facet2, *new_facet_list= NULL;
  facetT *orig_neighbor= NULL, *otherfacet;
  vertexT *new_vertex_list= NULL;
  mergeT *merge;
  mergeType mergetype;
  int neighbor_i, neighbor_n;

  if (qh hasTriangulation)
      return;
  trace1((qh ferr, 1034, "qh_triangulate: triangulate non-simplicial facets\n"));
  if (qh hull_dim == 2)
    return;
  if (qh VORONOI) {  /* otherwise lose Voronoi centers [could rebuild vertex set from tricoplanar] */
    qh_clearcenters(qh_ASvoronoi);
    qh_vertexneighbors();
  }
  qh ONLYgood= False; /* for makenew_nonsimplicial */
  qh visit_id++;
  qh NEWfacets= True;
  qh degen_mergeset= qh_settemp(qh TEMPsize);
  qh newvertex_list= qh vertex_tail;
  for (facet= qh facet_list; facet && facet->next; facet= nextfacet) { /* non-simplicial facets moved to end */
    nextfacet= facet->next;
    if (facet->visible || facet->simplicial)
      continue;
    /* triangulate all non-simplicial facets, otherwise merging does not work, e.g., RBOX c P-0.1 P+0.1 P+0.1 D3 | QHULL d Qt Tv */
    if (!new_facet_list)
      new_facet_list= facet;  /* will be moved to end */
    qh_triangulate_facet(facet, &new_vertex_list);
  }
  trace2((qh ferr, 2047, "qh_triangulate: delete null facets from f%d -- apex same as second vertex\n", getid_(new_facet_list)));
  for (facet= new_facet_list; facet && facet->next; facet= nextfacet) { /* null facets moved to end */
    nextfacet= facet->next;
    if (facet->visible)
      continue;
    if (facet->ridges) {
      if (qh_setsize(facet->ridges) > 0) {
        qh_fprintf(qh ferr, 6161, "qhull error (qh_triangulate): ridges still defined for f%d\n", facet->id);
        qh_errexit(qh_ERRqhull, facet, NULL);
      }
      qh_setfree(&facet->ridges);
    }
    if (SETfirst_(facet->vertices) == SETsecond_(facet->vertices)) {
      zinc_(Ztrinull);
      qh_triangulate_null(facet);
    }
  }
  trace2((qh ferr, 2048, "qh_triangulate: delete %d or more mirror facets -- same vertices and neighbors\n", qh_setsize(qh degen_mergeset)));
  qh visible_list= qh facet_tail;
  while ((merge= (mergeT*)qh_setdellast(qh degen_mergeset))) {
    facet1= merge->facet1;
    facet2= merge->facet2;
    mergetype= merge->type;
    qh_memfree(merge, (int)sizeof(mergeT));
    if (mergetype == MRGmirror) {
      zinc_(Ztrimirror);
      qh_triangulate_mirror(facet1, facet2);
    }
  }
  qh_settempfree(&qh degen_mergeset);
  trace2((qh ferr, 2049, "qh_triangulate: update neighbor lists for vertices from v%d\n", getid_(new_vertex_list)));
  qh newvertex_list= new_vertex_list;  /* all vertices of new facets */
  qh visible_list= NULL;
  qh_updatevertices(/*qh newvertex_list, empty newfacet_list and visible_list*/);
  qh_resetlists(False, !qh_RESETvisible /*qh newvertex_list, empty newfacet_list and visible_list*/);

  trace2((qh ferr, 2050, "qh_triangulate: identify degenerate tricoplanar facets from f%d\n", getid_(new_facet_list)));
  trace2((qh ferr, 2051, "qh_triangulate: and replace facet->f.triowner with tricoplanar facets that own center, normal, etc.\n"));
  FORALLfacet_(new_facet_list) {
    if (facet->tricoplanar && !facet->visible) {
      FOREACHneighbor_i_(facet) {
        if (neighbor_i == 0) {  /* first iteration */
          if (neighbor->tricoplanar)
            orig_neighbor= neighbor->f.triowner;
          else
            orig_neighbor= neighbor;
        }else {
          if (neighbor->tricoplanar)
            otherfacet= neighbor->f.triowner;
          else
            otherfacet= neighbor;
          if (orig_neighbor == otherfacet) {
            zinc_(Ztridegen);
            facet->degenerate= True;
            break;
          }
        }
      }
    }
  }

  trace2((qh ferr, 2052, "qh_triangulate: delete visible facets -- non-simplicial, null, and mirrored facets\n"));
  owner= NULL;
  visible= NULL;
  for (facet= new_facet_list; facet && facet->next; facet= nextfacet) { /* may delete facet */
    nextfacet= facet->next;
    if (facet->visible) {
      if (facet->tricoplanar) { /* a null or mirrored facet */
        qh_delfacet(facet);
        qh num_visible--;
      }else {  /* a non-simplicial facet followed by its tricoplanars */
        if (visible && !owner) {
          /*  RBOX 200 s D5 t1001471447 | QHULL Qt C-0.01 Qx Qc Tv Qt -- f4483 had 6 vertices/neighbors and 8 ridges */
          trace2((qh ferr, 2053, "qh_triangulate: all tricoplanar facets degenerate for non-simplicial facet f%d\n",
                       visible->id));
          qh_delfacet(visible);
          qh num_visible--;
        }
        visible= facet;
        owner= NULL;
      }
    }else if (facet->tricoplanar) {
      if (facet->f.triowner != visible) {
        qh_fprintf(qh ferr, 6162, "qhull error (qh_triangulate): tricoplanar facet f%d not owned by its visible, non-simplicial facet f%d\n", facet->id, getid_(visible));
        qh_errexit2 (qh_ERRqhull, facet, visible);
      }
      if (owner)
        facet->f.triowner= owner;
      else if (!facet->degenerate) {
        owner= facet;
        nextfacet= visible->next; /* rescan tricoplanar facets with owner */
        facet->keepcentrum= True;  /* one facet owns ->normal, etc. */
        facet->coplanarset= visible->coplanarset;
        facet->outsideset= visible->outsideset;
        visible->coplanarset= NULL;
        visible->outsideset= NULL;
        if (!qh TRInormals) { /* center and normal copied to tricoplanar facets */
          visible->center= NULL;
          visible->normal= NULL;
        }
        qh_delfacet(visible);
        qh num_visible--;
      }
    }
  }
  if (visible && !owner) {
    trace2((qh ferr, 2054, "qh_triangulate: all tricoplanar facets degenerate for last non-simplicial facet f%d\n",
                 visible->id));
    qh_delfacet(visible);
    qh num_visible--;
  }
  qh NEWfacets= False;
  qh ONLYgood= onlygood; /* restore value */
  if (qh CHECKfrequently)
    qh_checkpolygon(qh facet_list);
  qh hasTriangulation= True;
} /* triangulate */


/*---------------------------------

  qh_triangulate_facet(facetA)
    triangulate a non-simplicial facet
      if qh.CENTERtype=qh_ASvoronoi, sets its Voronoi center
  returns:
    qh.newfacet_list == simplicial facets
      facet->tricoplanar set and ->keepcentrum false
      facet->degenerate set if duplicated apex
      facet->f.trivisible set to facetA
      facet->center copied from facetA (created if qh_ASvoronoi)
        qh_eachvoronoi, qh_detvridge, qh_detvridge3 assume centers copied
      facet->normal,offset,maxoutside copied from facetA

  notes:
      qh_makenew_nonsimplicial uses neighbor->seen for the same

  see also:
      qh_addpoint() -- add a point
      qh_makenewfacets() -- construct a cone of facets for a new vertex

  design:
      if qh_ASvoronoi,
         compute Voronoi center (facet->center)
      select first vertex (highest ID to preserve ID ordering of ->vertices)
      triangulate from vertex to ridges
      copy facet->center, normal, offset
      update vertex neighbors
*/
void qh_triangulate_facet(facetT *facetA, vertexT **first_vertex) {
  facetT *newfacet;
  facetT *neighbor, **neighborp;
  vertexT *apex;
  int numnew=0;

  trace3((qh ferr, 3020, "qh_triangulate_facet: triangulate facet f%d\n", facetA->id));

  if (qh IStracing >= 4)
    qh_printfacet(qh ferr, facetA);
  FOREACHneighbor_(facetA) {
    neighbor->seen= False;
    neighbor->coplanar= False;
  }
  if (qh CENTERtype == qh_ASvoronoi && !facetA->center  /* matches upperdelaunay in qh_setfacetplane() */
        && fabs_(facetA->normal[qh hull_dim -1]) >= qh ANGLEround * qh_ZEROdelaunay) {
    facetA->center= qh_facetcenter(facetA->vertices);
  }
  qh_willdelete(facetA, NULL);
  qh newfacet_list= qh facet_tail;
  facetA->visitid= qh visit_id;
  apex= SETfirstt_(facetA->vertices, vertexT);
  qh_makenew_nonsimplicial(facetA, apex, &numnew);
  SETfirst_(facetA->neighbors)= NULL;
  FORALLnew_facets {
    newfacet->tricoplanar= True;
    newfacet->f.trivisible= facetA;
    newfacet->degenerate= False;
    newfacet->upperdelaunay= facetA->upperdelaunay;
    newfacet->good= facetA->good;
    if (qh TRInormals) {
      newfacet->keepcentrum= True;
      newfacet->normal= qh_copypoints(facetA->normal, 1, qh hull_dim);
      if (qh CENTERtype == qh_AScentrum)
        newfacet->center= qh_getcentrum(newfacet);
      else
        newfacet->center= qh_copypoints(facetA->center, 1, qh hull_dim);
    }else {
      newfacet->keepcentrum= False;
      newfacet->normal= facetA->normal;
      newfacet->center= facetA->center;
    }
    newfacet->offset= facetA->offset;
#if qh_MAXoutside
    newfacet->maxoutside= facetA->maxoutside;
#endif
  }
  qh_matchnewfacets(/*qh newfacet_list*/);
  zinc_(Ztricoplanar);
  zadd_(Ztricoplanartot, numnew);
  zmax_(Ztricoplanarmax, numnew);
  qh visible_list= NULL;
  if (!(*first_vertex))
    (*first_vertex)= qh newvertex_list;
  qh newvertex_list= NULL;
  qh_updatevertices(/*qh newfacet_list, empty visible_list and newvertex_list*/);
  qh_resetlists(False, !qh_RESETvisible /*qh newfacet_list, empty visible_list and newvertex_list*/);
} /* triangulate_facet */

/*---------------------------------

  qh_triangulate_link(oldfacetA, facetA, oldfacetB, facetB)
    relink facetA to facetB via oldfacets
  returns:
    adds mirror facets to qh degen_mergeset (4-d and up only)
  design:
    if they are already neighbors, the opposing neighbors become MRGmirror facets
*/
void qh_triangulate_link(facetT *oldfacetA, facetT *facetA, facetT *oldfacetB, facetT *facetB) {
  int errmirror= False;

  trace3((qh ferr, 3021, "qh_triangulate_link: relink old facets f%d and f%d between neighbors f%d and f%d\n",
         oldfacetA->id, oldfacetB->id, facetA->id, facetB->id));
  if (qh_setin(facetA->neighbors, facetB)) {
    if (!qh_setin(facetB->neighbors, facetA))
      errmirror= True;
    else
      qh_appendmergeset(facetA, facetB, MRGmirror, NULL);
  }else if (qh_setin(facetB->neighbors, facetA))
    errmirror= True;
  if (errmirror) {
    qh_fprintf(qh ferr, 6163, "qhull error (qh_triangulate_link): mirror facets f%d and f%d do not match for old facets f%d and f%d\n",
       facetA->id, facetB->id, oldfacetA->id, oldfacetB->id);
    qh_errexit2 (qh_ERRqhull, facetA, facetB);
  }
  qh_setreplace(facetB->neighbors, oldfacetB, facetA);
  qh_setreplace(facetA->neighbors, oldfacetA, facetB);
} /* triangulate_link */

/*---------------------------------

  qh_triangulate_mirror(facetA, facetB)
    delete mirrored facets from qh_triangulate_null() and qh_triangulate_mirror
      a mirrored facet shares the same vertices of a logical ridge
  design:
    since a null facet duplicates the first two vertices, the opposing neighbors absorb the null facet
    if they are already neighbors, the opposing neighbors become MRGmirror facets
*/
void qh_triangulate_mirror(facetT *facetA, facetT *facetB) {
  facetT *neighbor, *neighborB;
  int neighbor_i, neighbor_n;

  trace3((qh ferr, 3022, "qh_triangulate_mirror: delete mirrored facets f%d and f%d\n",
         facetA->id, facetB->id));
  FOREACHneighbor_i_(facetA) {
    neighborB= SETelemt_(facetB->neighbors, neighbor_i, facetT);
    if (neighbor == neighborB)
      continue; /* occurs twice */
    qh_triangulate_link(facetA, neighbor, facetB, neighborB);
  }
  qh_willdelete(facetA, NULL);
  qh_willdelete(facetB, NULL);
} /* triangulate_mirror */

/*---------------------------------

  qh_triangulate_null(facetA)
    remove null facetA from qh_triangulate_facet()
      a null facet has vertex #1 (apex) == vertex #2
  returns:
    adds facetA to ->visible for deletion after qh_updatevertices
    qh degen_mergeset contains mirror facets (4-d and up only)
  design:
    since a null facet duplicates the first two vertices, the opposing neighbors absorb the null facet
    if they are already neighbors, the opposing neighbors become MRGmirror facets
*/
void qh_triangulate_null(facetT *facetA) {
  facetT *neighbor, *otherfacet;

  trace3((qh ferr, 3023, "qh_triangulate_null: delete null facet f%d\n", facetA->id));
  neighbor= SETfirstt_(facetA->neighbors, facetT);
  otherfacet= SETsecondt_(facetA->neighbors, facetT);
  qh_triangulate_link(facetA, neighbor, facetA, otherfacet);
  qh_willdelete(facetA, NULL);
} /* triangulate_null */

#else /* qh_NOmerge */
void qh_triangulate(void) {
}
#endif /* qh_NOmerge */

   /*---------------------------------

  qh_vertexintersect( vertexsetA, vertexsetB )
    intersects two vertex sets (inverse id ordered)
    vertexsetA is a temporary set at the top of qhmem.tempstack

  returns:
    replaces vertexsetA with the intersection

  notes:
    could overwrite vertexsetA if currently too slow
*/
void qh_vertexintersect(setT **vertexsetA,setT *vertexsetB) {
  setT *intersection;

  intersection= qh_vertexintersect_new(*vertexsetA, vertexsetB);
  qh_settempfree(vertexsetA);
  *vertexsetA= intersection;
  qh_settemppush(intersection);
} /* vertexintersect */

/*---------------------------------

  qh_vertexintersect_new(  )
    intersects two vertex sets (inverse id ordered)

  returns:
    a new set
*/
setT *qh_vertexintersect_new(setT *vertexsetA,setT *vertexsetB) {
  setT *intersection= qh_setnew(qh hull_dim - 1);
  vertexT **vertexA= SETaddr_(vertexsetA, vertexT);
  vertexT **vertexB= SETaddr_(vertexsetB, vertexT);

  while (*vertexA && *vertexB) {
    if (*vertexA  == *vertexB) {
      qh_setappend(&intersection, *vertexA);
      vertexA++; vertexB++;
    }else {
      if ((*vertexA)->id > (*vertexB)->id)
        vertexA++;
      else
        vertexB++;
    }
  }
  return intersection;
} /* vertexintersect_new */

/*---------------------------------

  qh_vertexneighbors()
    for each vertex in qh.facet_list,
      determine its neighboring facets

  returns:
    sets qh.VERTEXneighbors
      nop if qh.VERTEXneighbors already set
      qh_addpoint() will maintain them

  notes:
    assumes all vertex->neighbors are NULL

  design:
    for each facet
      for each vertex
        append facet to vertex->neighbors
*/
void qh_vertexneighbors(void /*qh facet_list*/) {
  facetT *facet;
  vertexT *vertex, **vertexp;

  if (qh VERTEXneighbors)
    return;
  trace1((qh ferr, 1035, "qh_vertexneighbors: determing neighboring facets for each vertex\n"));
  qh vertex_visit++;
  FORALLfacets {
    if (facet->visible)
      continue;
    FOREACHvertex_(facet->vertices) {
      if (vertex->visitid != qh vertex_visit) {
        vertex->visitid= qh vertex_visit;
        vertex->neighbors= qh_setnew(qh hull_dim);
      }
      qh_setappend(&vertex->neighbors, facet);
    }
  }
  qh VERTEXneighbors= True;
} /* vertexneighbors */

/*---------------------------------

  qh_vertexsubset( vertexsetA, vertexsetB )
    returns True if vertexsetA is a subset of vertexsetB
    assumes vertexsets are sorted

  note:
    empty set is a subset of any other set
*/
boolT qh_vertexsubset(setT *vertexsetA, setT *vertexsetB) {
  vertexT **vertexA= (vertexT **) SETaddr_(vertexsetA, vertexT);
  vertexT **vertexB= (vertexT **) SETaddr_(vertexsetB, vertexT);

  while (True) {
    if (!*vertexA)
      return True;
    if (!*vertexB)
      return False;
    if ((*vertexA)->id > (*vertexB)->id)
      return False;
    if (*vertexA  == *vertexB)
      vertexA++;
    vertexB++;
  }
  return False; /* avoid warnings */
} /* vertexsubset */
qhull-2012.1/src/libqhull/qh-geom.htm0000644000076400010400000003141211710144470020556 0ustar  bbarberAdministrators



geom.c, geom2.c -- geometric and floating point routines





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geom.c, geom2.c, random.c -- geometric and floating point routines




Geometrically, a vertex is a point with d coordinates
and a facet is a halfspace. A halfspace is defined by an
oriented hyperplane through the facet's vertices. A hyperplane
is defined by d normalized coefficients and an offset. A
point is above a facet if its distance to the facet is
positive.



Qhull uses floating point coordinates for input points,
vertices, halfspace equations, centrums, and an interior point.



Qhull may be configured for single precision or double
precision floating point arithmetic (see realT
). 



Each floating point operation may incur round-off error (see
Merge). The maximum error for distance
computations is determined at initialization. The roundoff error
in halfspace computation is accounted for by computing the
distance from vertices to the halfspace. 




Copyright © 1995-2012 C.B. Barber




» Geom
• Global •
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Merge • Poly •
Qhull • Set •
Stat • User 



Index to geom.c,
geom2.c, geom.h,
random.c, random.h






»geometric data types
and constants



    

  • coordT coordinates and
coefficients are stored as realT
    • 

  • pointT a point is an array
of DIM3 coordinates 
    • 




»mathematical macros



    

  • fabs_ returns the absolute
value of a 
    • 

  • fmax_ returns the maximum
value of a and b 
    • 

  • fmin_ returns the minimum
value of a and b 
    • 

  • maximize_ maximize a value

    • 

  • minimize_ minimize a value

    • 

  • det2_ compute a 2-d
determinate 
    • 

  • det3_ compute a 3-d
determinate 
    • 

  • dX, dY, dZ compute the difference
between two coordinates 
    • 




»mathematical functions





»computational geometry functions





»point array functions




»geometric facet functions




»geometric roundoff functions


    

  • qh_detjoggle determine
default joggle for points and distance roundoff error
    • 

  • qh_detroundoff
determine maximum roundoff error and other precision constants
    • 

  • qh_distround compute
maximum roundoff error due to a distance computation to a
normalized hyperplane
    • 

  • qh_divzero divide by a
number that is nearly zero 
    • 

  • qh_maxouter return maximum outer
plane
    • 

  • qh_outerinner return actual
outer and inner planes




 




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global.c -- global variables and their functions





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global.c -- global variables and their functions




Qhull uses a global data structure, qh, to store
globally defined constants, lists, sets, and variables. This
allows multiple instances of Qhull to execute at the same time.
The structure may be statically allocated or
dynamically allocated with malloc().  See
QHpointer.





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Index to global.c and
libqhull.h





»Qhull's global
variables





»Global variable and
initialization routines





 




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io.c -- input and output operations





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io.c -- input and output operations





Qhull provides a wide range of input
and output options. To organize the code, most output formats use
the same driver: 



    qh_printbegin( fp, format, facetlist, facets, printall );

    FORALLfacet_( facetlist )
      qh_printafacet( fp, format, facet, printall );

    FOREACHfacet_( facets )
      qh_printafacet( fp, format, facet, printall );

    qh_printend( fp, format );




Note the 'printall' flag. It selects whether or not
qh_skipfacet() is tested. 





Copyright © 1995-2012 C.B. Barber




» Geom •
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Index to io.c and io.h





»io.h constants and types





»User level functions





»Print functions for all
output formats





»Text output functions




»Text utility functions




»Geomview output functions



»Geomview utility functions





 




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mem.c -- memory operations





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mem.c -- memory operations




Qhull uses quick-fit memory allocation. It maintains a
set of free lists for a variety of small allocations. A
small request returns a block from the best fitting free
list. If the free list is empty, Qhull allocates a block
from a reserved buffer. 


Use 'T5' to trace memory allocations.





Copyright © 1995-2012 C.B. Barber




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Index to mem.c and
mem.h



»mem.h data types and constants


    

  • ptr_intT for casting
a void* to an integer-type 
    • 

  • qhmemT global memory
structure for mem.c 
    • 

  • qh_NOmem disable memory allocation
    • 



»mem.h macros



»User level
functions




»Initialization and
termination functions




 




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qhull-2012.1/src/libqhull/qh-merge.htm0000644000076400010400000003545011710144470020734 0ustar  bbarberAdministrators



merge.c -- facet merge operations





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merge.c -- facet merge operations




Qhull handles precision problems by merged facets or joggled input.
Except for redundant vertices, it corrects a problem by
merging two facets. When done, all facets are clearly
convex. See Imprecision in Qhull
for further information. 


Users may joggle the input ('QJn')
instead of merging facets. 


Qhull detects and corrects the following problems: 


    

  • More than two facets meeting at a ridge. When
Qhull creates facets, it creates an even number
of facets for each ridge. A convex hull always
has two facets for each ridge. More than two
facets may be created if non-adjacent facets
share a vertex. This is called a duplicate
ridge. In 2-d, a duplicate ridge would
create a loop of facets. 
    • 



    

  • A facet contained in another facet. Facet
merging may leave all vertices of one facet as a
subset of the vertices of another facet. This is
called a redundant facet. 
    • 



    

  • A facet with fewer than three neighbors. Facet
merging may leave a facet with one or two
neighbors. This is called a degenerate facet.

    • 



    

  • A facet with flipped orientation. A
facet's hyperplane may define a halfspace that
does not include the interior point.This is
called a flipped facet. 
    • 



    

  • A coplanar horizon facet. A
newly processed point may be coplanar with an
horizon facet. Qhull creates a new facet without
a hyperplane. It links new facets for the same
horizon facet together. This is called a samecycle.
The new facet or samecycle is merged into the
horizon facet. 
    • 



    

  • Concave facets. A facet's centrum may be
above a neighboring facet. If so, the facets meet
at a concave angle. 
    • 



    

  • Coplanar facets. A facet's centrum may be
coplanar with a neighboring facet (i.e., it is
neither clearly below nor clearly above the
facet's hyperplane). Qhull removes coplanar
facets in independent sets sorted by angle.
    • 



    

  • Redundant vertex. A vertex may have fewer
than three neighboring facets. If so, it is
redundant and may be renamed to an adjacent
vertex without changing the topological
structure.This is called a redundant vertex.

    • 





Copyright © 1995-2012 C.B. Barber




» Geom
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Index to merge.c and
merge.h




»merge.h data
types, macros, and global sets


    

  • mergeT structure to
identify a merge of two facets
    • 

  • FOREACHmerge_
assign 'merge' to each merge in merges 
    • 

  • qh global sets
qh.facet_mergeset contains non-convex merges
while qh.degen_mergeset contains degenerate and
redundant facets
    • 



»merge.h
constants



»top-level merge
functions




»functions for
identifying merges




»functions for
determining the best merge




»functions for
merging facets




»functions for
merging a cycle of facets


If a point is coplanar with an horizon facet, the
corresponding new facets are linked together (a samecycle)
for merging.



»functions
for renaming a vertex




»functions
for identifying vertices for renaming




»functions for check and
trace




 




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poly.c, poly2.c -- polyhedron operations





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poly.c, poly2.c -- polyhedron operations





Qhull uses dimension-free terminology. Qhull builds a
polyhedron in dimension d. A polyhedron is a
simplicial complex of faces with geometric information for the
top and bottom-level faces. A (d-1)-face is a facet,
a (d-2)-face is a ridge, and a 0-face
is a vertex. For example in 3-d, a facet is a polygon
and a ridge is an edge. A facet is built from a ridge (the base)
and a vertex (the apex). See
Qhull's data structures.



Qhull's primary data structure is a polyhedron. A
polyhedron is a list of facets. Each facet has a set of
neighboring facets and a set of vertices. Each facet has a
hyperplane. For example, a tetrahedron has four facets.
If its vertices are a, b, c, d, and its facets
are 1, 2, 3, 4, the tetrahedron is 




    

  • facet 1 
      
    
    • vertices: b c d 
      • 
    
    • neighbors: 2 3 4 
      • 

    

    • 

  • facet 2 
      
    
    • vertices: a c d 
      • 
    
    • neighbors: 1 3 4 
      • 

    

    • 

  • facet 3 
      
    
    • vertices: a b d 
      • 
    
    • neighbors: 1 2 4 
      • 

    

    • 

  • facet 4 
      
    
    • vertices: a b c 
      • 
    
    • neighbors: 1 2 3 
      • 

    

    • 





A facet may be simplicial or non-simplicial. In 3-d, a
simplicial facet has three vertices and three
neighbors. A nonsimplicial facet has more than
three vertices and more than three neighbors. A
nonsimplicial facet has a set of ridges and a centrum. 



A simplicial facet has an orientation. An orientation
is either top or bottom.
The flag, facet->toporient,
defines the orientation of the facet's vertices.  For example in 3-d,
'top' is left-handed orientation (i.e., the vertex order follows the direction
of the left-hand fingers when the thumb is pointing away from the center).
Except for axis-parallel facets in 5-d and higher, topological orientation
determines the geometric orientation of the facet's hyperplane.


A nonsimplicial facet is due to merging two or more
facets. The facet's ridge set determine a simplicial
decomposition of the facet. Each ridge is a 1-face (i.e.,
it has two vertices and two neighboring facets). The
orientation of a ridge is determined by the order of the
neighboring facets. The flag, facet->toporient,is
ignored. 


A nonsimplicial facet has a centrum for testing
convexity. A centrum is a point on the facet's
hyperplane that is near the center of the facet. Except
for large facets, it is the arithmetic average of the
facet's vertices. 


A nonsimplicial facet is an approximation that is
defined by offsets from the facet's hyperplane. When
Qhull finishes, the outer plane is above all
points while the inner plane is below the facet's
vertices. This guarantees that any exact convex hull
passes between the inner and outer planes. The outer
plane is defined by facet->maxoutside while
the inner plane is computed from the facet's vertices.



Qhull 3.1 includes triangulation of non-simplicial facets
('Qt').
These facets,
called tricoplanar, share the same normal. centrum, and Voronoi center.
One facet (keepcentrum) owns these data structures.
While tricoplanar facets are more accurate than the simplicial facets from
joggled input, they
may have zero area or flipped orientation.




Copyright © 1995-2012 C.B. Barber




» Geom
• Global
• Io • Mem
• Merge • Poly
• Qhull • Set
• Stat • User



Index to poly.c,
poly2.c, poly.h,
and libqhull.h



»Data
types and global lists for polyhedrons



»poly.h constants


    

  • ALGORITHMfault
flag to not report errors in qh_checkconvex() 
    • 

  • DATAfault flag to
report errors in qh_checkconvex() 
    • 

  • DUPLICATEridge
special value for facet->neighbor to indicate
a duplicate ridge 
    • 

  • MERGEridge
special value for facet->neighbor to indicate
a merged ridge 
    • 



»Global FORALL
macros



»FORALL macros



»FOREACH macros



»Indexed
FOREACH macros


    

  • FOREACHfacet_i_
assign 'facet' and 'facet_i' to each facet in
facet set 
    • 

  • FOREACHneighbor_i_
assign 'neighbor' and 'neighbor_i' to each facet
in facet->neighbors or vertex->neighbors
    • 

  • FOREACHpoint_i_
assign 'point' and 'point_i' to each point in
points set 
    • 

  • FOREACHridge_i_
assign 'ridge' and 'ridge_i' to each ridge in
ridges set 
    • 

  • FOREACHvertex_i_
assign 'vertex' and 'vertex_i' to each vertex in
vertices set 
    • 

  • FOREACHvertexreverse12_
assign 'vertex' to each vertex in vertex set;
reverse the order of first two vertices 
    • 



»Other macros for polyhedrons


    

  • getid_ return ID for
a facet, ridge, or vertex 
    • 

  • otherfacet_
return neighboring facet for a ridge in a facet 
    • 



»Facetlist
functions



»Facet
functions



»Vertex,
ridge, and point functions



»Hashtable functions



»Allocation and
deallocation functions



»Check
functions





 




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qhull-2012.1/src/libqhull/qh-qhull.htm0000644000076400010400000003062711710144470020763 0ustar  bbarberAdministrators



libqhull.c -- top-level functions and basic data types





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libqhull.c -- top-level functions and basic data types




Qhull implements the Quickhull algorithm for computing
the convex hull. The Quickhull algorithm combines two
well-known algorithms: the 2-d quickhull algorithm and
the n-d beneath-beyond algorithm. See
Description of Qhull. 


This section provides an index to the top-level
functions and base data types.  The top-level header file, libqhull.h,
contains prototypes for these functions.




Copyright © 1995-2012 C.B. Barber




» Geom
• Global
• Io • Mem
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• Qhull • Set
• Stat • User



Index to libqhull.c,
libqhull.h, and
unix.c




»libqhull.h and unix.c
data types and constants


    

  • flagT Boolean flag as
a bit 
    • 

  • boolT boolean value,
either True or False 
    • 

  • CENTERtype to
distinguish facet->center 
    • 

  • qh_PRINT output
formats for printing (qh.PRINTout) 
    • 

  • qh_ALL argument flag
for selecting everything 
    • 

  • qh_ERR Qhull exit
codes for indicating errors 
    • 

  • qh_FILEstderr Fake stderr
to distinguish error output from normal output [C++ only]
    • 

  • qh_prompt version and long prompt for Qhull
    • 

  • qh_prompt2 synopsis for Qhull
    • 

  • qh_prompt3 concise prompt for Qhull
    • 

  • qh_version version stamp
    • 




»libqhull.h other
macros


    

  • traceN print trace
message if qh.IStracing >= N. 
    • 

  • QHULL_UNUSED declare an
 unused variable to avoid warnings. 
    • 




»Quickhull
routines in call order




»Top-level routines for initializing and terminating Qhull (in other modules)




»Top-level routines for reading and modifying the input (in other modules)




»Top-level routines for calling Qhull (in other modules)




»Top-level routines for returning results (in other modules)




»Top-level routines for testing and debugging (in other modules)




 




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qhull-2012.1/src/libqhull/qh-set.htm0000644000076400010400000003144411710144470020427 0ustar  bbarberAdministrators



qset.c -- set data type and operations





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qset.c -- set data type and operations




Qhull's data structures are constructed from sets. The
functions and macros in qset.c construct, iterate, and
modify these sets. They are the most frequently called
functions in Qhull. For this reason, efficiency is the
primary concern. 


In Qhull, a set is represented by an unordered
array of pointers with a maximum size and a NULL
terminator (setT).
Most sets correspond to mathematical sets
(i.e., the pointers are unique). Some sets are sorted to
enforce uniqueness. Some sets are ordered. For example,
the order of vertices in a ridge determine the ridge's
orientation. If you reverse the order of adjacent
vertices, the orientation reverses. Some sets are not
mathematical sets. They may be indexed as an array and
they may include NULL pointers. 


The most common operation on a set is to iterate its
members. This is done with a 'FOREACH...' macro. Each set
has a custom macro. For example, 'FOREACHvertex_'
iterates over a set of vertices. Each vertex is assigned
to the variable 'vertex' from the pointer 'vertexp'. 


Most sets are constructed by appending elements to the
set. The last element of a set is either NULL or the
index of the terminating NULL for a partially full set.
If a set is full, appending an element copies the set to
a larger array. 





Copyright © 1995-2012 C.B. Barber




» Geom
• Global •
Io • Mem •
Merge • Poly
• Qhull • Set
• Stat • User



Index to qset.c and
qset.h



»Data types and
constants


    

  • SETelemsize size
of a set element in bytes 
    • 

  • setT a set with a
maximum size and a current size
    • 

  • qh global sets
global sets for temporary sets, etc. 
    • 



»FOREACH macros



»Access and
size macros



»Internal macros


    

  • SETsizeaddr_
return pointer to end element of a set (indicates
current size) 
    • 




»address macros


    

  • SETaddr_ return
address of a set's elements 
    • 

  • SETelemaddr_
return address of the n'th element of a set 
    • 

  • SETref_ l.h.s. for
modifying the current element in a FOREACH
iteration 
    • 




»Allocation and
deallocation functions




»Access and
predicate functions 




»Add functions




»Check and print functions




»Copy, compact, and zero functions




»Delete functions




»Temporary set functions




 




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qhull-2012.1/src/libqhull/qh-stat.htm0000644000076400010400000001564611710144470020615 0ustar  bbarberAdministrators



stat.c -- statistical operations





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stat.c -- statistical operations




Qhull records many statistics. These functions and
macros make it inexpensive to add a statistic.

As with Qhull's global variables, the statistics data structure is
accessed by a macro, 'qhstat'.  If qh_QHpointer is defined, the macro
is 'qh_qhstat->', otherwise the macro is 'qh_qhstat.'.
Statistics
may be turned off in user.h. If so, all but the 'zz'
statistics are ignored.




Copyright © 1995-2012 C.B. Barber




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Index to stat.c and
stat.h




»stat.h types


    

  • intrealT union of
integer and real
    • 

  • qhstat global data
structure for statistics 
    • 



»stat.h
constants


    

  • qh_KEEPstatistics 0 turns off most statistics
    • 

  • Z..., W... integer (Z) and real (W) statistics

    • 

  • ZZstat Z.../W... statistics that
remain defined if qh_KEEPstatistics=0

    • 

  • ztype zdoc, zinc, etc.
for definining statistics 
    • 



»stat.h macros


    

  • MAYdebugx called
frequently for error trapping 
    • 

  • zadd_/wadd_ add value
to an integer or real statistic 
    • 

  • zdef_ define a
statistic 
    • 

  • zinc_ increment an
integer statistic 
    • 

  • zmax_/wmax_ update
integer or real maximum statistic 
    • 

  • zmin_/wmin_ update
integer or real minimum statistic 
    • 

  • zval_/wval_ set or
return value of a statistic 
    • 




»stat.c
functions




 




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qhull-2012.1/src/libqhull/qh-user.htm0000644000076400010400000002612711710144470020614 0ustar  bbarberAdministrators



user.c -- user-definable operations





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user.c -- user-definable operations




This section contains functions and constants that the
user may want to change. 





Copyright © 1995-2012 C.B. Barber




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Index to user.c, usermem.c, userprintf.c, userprintf_rbox.c and
user.h




»Qhull library constants





»user.h data
types and configuration macros




»definition constants


    

  • qh_DEFAULTbox
define default box size for rbox, 'Qbb', and 'QbB' (Geomview expects 0.5) 
    • 

  • qh_INFINITE on
output, indicates Voronoi center at infinity 
    • 

  • qh_ORIENTclock
define convention for orienting facets
    • 

  • qh_ZEROdelaunay
define facets that are ignored in Delaunay triangulations
    • 




»joggle constants




»performance
related constants




»memory constants




»conditional compilation




»merge
constants




»user.c
functions




»usermem.c
functions


    

  • qh_exit exit program, same as exit().
    • 

  • qh_free free memory, same as free().
    • 

  • qh_malloc allocate memory, same as malloc()
    • 




»userprintf.c
 and userprintf_rbox,c functions


    

  • qh_fprintf print
information from Qhull, sames as fprintf(). 
    • 

  • qh_fprintf_rbox print
information from Rbox, sames as fprintf(). 
    • 




 




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qhull-2012.1/src/libqhull/qhull-exports.def0000644000076400010400000001656711710424255022036 0ustar  bbarberAdministrators; qhull-exports.def -- msvc module-definition file
;
;   Generated from depends.exe by cut-and-paste of exported symbols by mingw gcc
;   [mar'11] 399 symbols 
;   Annotate as DATA qh_qh qh_qhstat qhmem qhull_inuse rbox_inuse
;   Same as ../libqhullp/qhull_p-exports.def without qh_save_qhull and qh_restore_qhull
;
; $Id: //main/2011/qhull/src/libqhull/qhull-exports.def#4 $$Change: 1468 $
; $DateTime: 2012/01/26 23:42:31 $$Author: bbarber $
; 
; Define qhull_VERSION in CMakeLists.txt, Makefile, qhull-exports.def, qhull_p-exports.def, and qhull-warn.pri
VERSION 6.3
EXPORTS
dfacet
dvertex
out1
out2n
out3n
qh_addhash
qh_addpoint
qh_all_merges
qh_allstatA
qh_allstatB
qh_allstatC
qh_allstatD
qh_allstatE
qh_allstatE2
qh_allstatF
qh_allstatG
qh_allstatH
qh_allstatI
qh_allstatistics
qh_appendfacet
qh_appendmergeset
qh_appendprint
qh_appendvertex
qh_argv_to_command
qh_argv_to_command_size
qh_attachnewfacets
qh_backnormal
qh_basevertices
qh_build_withrestart
qh_buildhull
qh_buildtracing
qh_check_bestdist
qh_check_maxout
qh_check_output
qh_check_point
qh_check_points
qh_checkconnect
qh_checkconvex
qh_checkfacet
qh_checkflags
qh_checkflipped
qh_checkflipped_all
qh_checkpolygon
qh_checkvertex
qh_checkzero
qh_clear_outputflags
qh_clearcenters
qh_clock
qh_collectstatistics
qh_compare_facetarea
qh_compare_facetmerge
qh_compare_facetvisit
qh_compare_vertexpoint
qh_compareangle
qh_comparemerge
qh_comparevisit
qh_copyfilename
qh_copynonconvex
qh_copypoints
qh_countfacets
qh_createsimplex
qh_crossproduct
qh_degen_redundant_facet
qh_degen_redundant_neighbors
qh_deletevisible
qh_delfacet
qh_delridge
qh_delvertex
qh_determinant
qh_detjoggle
qh_detroundoff
qh_detsimplex
qh_detvnorm
qh_detvridge
qh_detvridge3
qh_distnorm
qh_distplane
qh_distround
qh_divzero
qh_eachvoronoi
qh_eachvoronoi_all
qh_errexit
qh_errexit2
qh_errexit_rbox
qh_errprint
qh_exit
qh_facet2point
qh_facet3vertex
qh_facetarea
qh_facetarea_simplex
qh_facetcenter
qh_facetintersect
qh_facetvertices
qh_find_newvertex
qh_findbest
qh_findbest_test
qh_findbestfacet
qh_findbesthorizon
qh_findbestlower
qh_findbestneighbor
qh_findbestnew
qh_findfacet_all
qh_findgood
qh_findgood_all
qh_findgooddist
qh_findhorizon
qh_flippedmerges
qh_forcedmerges
qh_fprintf
qh_fprintf_rbox
qh_free
qh_freebuffers
qh_freebuild
qh_freeqhull
qh_freeqhull2
qh_freestatistics
qh_furthestnext
qh_furthestout
qh_gausselim
qh_geomplanes
qh_getangle
qh_getarea
qh_getcenter
qh_getcentrum
qh_getdistance
qh_gethash
qh_getmergeset
qh_getmergeset_initial
qh_gram_schmidt
qh_hashridge
qh_hashridge_find
qh_infiniteloop
qh_init_A
qh_init_B
qh_init_qhull_command
qh_initbuild
qh_initflags
qh_initialhull
qh_initialvertices
qh_initqhull_buffers
qh_initqhull_globals
qh_initqhull_mem
qh_initqhull_outputflags
qh_initqhull_start
qh_initqhull_start2
qh_initstatistics
qh_initthresholds
qh_inthresholds
qh_isvertex
qh_joggleinput
qh_makenew_nonsimplicial
qh_makenew_simplicial
qh_makenewfacet
qh_makenewfacets
qh_makenewplanes
qh_makeridges
qh_malloc
qh_mark_dupridges
qh_markkeep
qh_markvoronoi
qh_matchduplicates
qh_matchneighbor
qh_matchnewfacets
qh_matchvertices
qh_maxabsval
qh_maxmin
qh_maxouter
qh_maxsimplex
qh_maydropneighbor
qh_memalloc
qh_memfree
qh_memfreeshort
qh_meminit
qh_meminitbuffers
qh_memsetup
qh_memsize
qh_memstatistics
qh_memtotal
qh_merge_degenredundant
qh_merge_nonconvex
qh_mergecycle
qh_mergecycle_all
qh_mergecycle_facets
qh_mergecycle_neighbors
qh_mergecycle_ridges
qh_mergecycle_vneighbors
qh_mergefacet
qh_mergefacet2d
qh_mergeneighbors
qh_mergeridges
qh_mergesimplex
qh_mergevertex_del
qh_mergevertex_neighbors
qh_mergevertices
qh_minabsval
qh_mindiff
qh_nearcoplanar
qh_nearvertex
qh_neighbor_intersections
qh_new_qhull
qh_newfacet
qh_newhashtable
qh_newridge
qh_newstats
qh_newvertex
qh_newvertices
qh_nextfurthest
qh_nextridge3d
qh_normalize
qh_normalize2
qh_nostatistic
qh_option
qh_order_vertexneighbors
qh_orientoutside
qh_outcoplanar
qh_outerinner
qh_partitionall
qh_partitioncoplanar
qh_partitionpoint
qh_partitionvisible
qh_point
qh_point_add
qh_pointdist
qh_pointfacet
qh_pointid
qh_pointvertex
qh_postmerge
qh_precision
qh_premerge
qh_prepare_output
qh_prependfacet
qh_printafacet
qh_printallstatistics
qh_printbegin
qh_printcenter
qh_printcentrum
qh_printend
qh_printend4geom
qh_printextremes
qh_printextremes_2d
qh_printextremes_d
qh_printfacet
qh_printfacet2geom
qh_printfacet2geom_points
qh_printfacet2math
qh_printfacet3geom_nonsimplicial
qh_printfacet3geom_points
qh_printfacet3geom_simplicial
qh_printfacet3math
qh_printfacet3vertex
qh_printfacet4geom_nonsimplicial
qh_printfacet4geom_simplicial
qh_printfacetNvertex_nonsimplicial
qh_printfacetNvertex_simplicial
qh_printfacetheader
qh_printfacetlist
qh_printfacetridges
qh_printfacets
qh_printhashtable
qh_printhelp_degenerate
qh_printhelp_narrowhull
qh_printhelp_singular
qh_printhyperplaneintersection
qh_printline3geom
qh_printlists
qh_printmatrix
qh_printneighborhood
qh_printpoint
qh_printpoint3
qh_printpointid
qh_printpoints
qh_printpoints_out
qh_printpointvect
qh_printpointvect2
qh_printridge
qh_printspheres
qh_printstatistics
qh_printstatlevel
qh_printstats
qh_printsummary
qh_printvdiagram
qh_printvdiagram2
qh_printvertex
qh_printvertexlist
qh_printvertices
qh_printvneighbors
qh_printvnorm
qh_printvoronoi
qh_printvridge
qh_produce_output
qh_produce_output2
qh_projectdim3
qh_projectinput
qh_projectpoint
qh_projectpoints
; Mark as DATA, otherwise links a separate qh_qh.  Requires __dcelspec
qh_qh               DATA
qh_qhstat           DATA
qh_qhull
qh_rand
qh_rand_seed
qh_randomfactor
qh_randommatrix
qh_rboxpoints
qh_readfeasible
qh_readpoints
qh_reducevertices
qh_redundant_vertex
qh_remove_extravertices
qh_removefacet
qh_removevertex
qh_rename_sharedvertex
qh_renameridgevertex
qh_renamevertex
qh_resetlists
qh_rotateinput
qh_rotatepoints
qh_scaleinput
qh_scalelast
qh_scalepoints
qh_setaddnth
qh_setaddsorted
qh_setappend
qh_setappend2ndlast
qh_setappend_set
qh_setcheck
qh_setcompact
qh_setcopy
qh_setdel
qh_setdelaunay
qh_setdellast
qh_setdelnth
qh_setdelnthsorted
qh_setdelsorted
qh_setduplicate
qh_setequal
qh_setequal_except
qh_setequal_skip
qh_setfacetplane
qh_setfeasible
qh_setfree
qh_setfree2
qh_setfreelong
qh_sethalfspace
qh_sethalfspace_all
qh_sethyperplane_det
qh_sethyperplane_gauss
qh_setin
qh_setindex
qh_setlarger
qh_setlast
qh_setnew
qh_setnew_delnthsorted
qh_setprint
qh_setreplace
qh_setsize
qh_settemp
qh_settempfree
qh_settempfree_all
qh_settemppop
qh_settemppush
qh_settruncate
qh_setunique
qh_setvoronoi_all
qh_setzero
qh_sharpnewfacets
qh_skipfacet
qh_skipfilename
qh_srand
qh_stddev
qh_strtod
qh_strtol
qh_test_appendmerge
qh_test_vneighbors
qh_tracemerge
qh_tracemerging
qh_triangulate
qh_triangulate_facet
qh_triangulate_link
qh_triangulate_mirror
qh_triangulate_null
qh_updatetested
qh_updatevertices
qh_user_memsizes
qh_version
qh_vertexintersect
qh_vertexintersect_new
qh_vertexneighbors
qh_vertexridges
qh_vertexridges_facet
qh_vertexsubset
qh_voronoi_center
qh_willdelete
; Mark as DATA, otherwise links a separate qhmem.  Requires __dcelspec
qhmem                   DATA
qhull_inuse             DATA
rbox
rbox_inuse              DATA
roundi
qhull-2012.1/src/libqhull/qhull_a.h0000644000076400010400000001147611710144467020323 0ustar  bbarberAdministrators/*
  ---------------------------------

   qhull_a.h
   all header files for compiling qhull

   see qh-qhull.htm

   see libqhull.h for user-level definitions

   see user.h for user-defineable constants

   defines internal functions for libqhull.c global.c

   Copyright (c) 1993-2012 The Geometry Center.
   $Id: //main/2011/qhull/src/libqhull/qhull_a.h#3 $$Change: 1464 $
   $DateTime: 2012/01/25 22:58:41 $$Author: bbarber $

   Notes:  grep for ((" and (" to catch fprintf("lkasdjf");
           full parens around (x?y:z)
           use '#include qhull/qhull_a.h' to avoid name clashes
*/

#ifndef qhDEFqhulla
#define qhDEFqhulla 1

#include "libqhull.h"  /* Defines data types */

#include "stat.h"
#include "random.h"
#include "mem.h"
#include "qset.h"
#include "geom.h"
#include "merge.h"
#include "poly.h"
#include "io.h"

#include 
#include 
#include 
#include     /* some compilers will not need float.h */
#include 
#include 
#include 
#include 
#include 
/*** uncomment here and qset.c
     if string.h does not define memcpy()
#include 
*/

#if qh_CLOCKtype == 2  /* defined in user.h from libqhull.h */
#include 
#include 
#include 
#endif

#ifdef _MSC_VER  /* Microsoft Visual C++ -- warning level 4 */
#pragma warning( disable : 4100)  /* unreferenced formal parameter */
#pragma warning( disable : 4127)  /* conditional expression is constant */
#pragma warning( disable : 4706)  /* assignment within conditional function */
#pragma warning( disable : 4996)  /* function was declared deprecated(strcpy, localtime, etc.) */
#endif

/* ======= -macros- =========== */

/*----------------------------------

  traceN((qh ferr, 0Nnnn, "format\n", vars));
    calls qh_fprintf if qh.IStracing >= N

    Add debugging traps to the end of qh_fprintf

  notes:
    removing tracing reduces code size but doesn't change execution speed
*/
#ifndef qh_NOtrace
#define trace0(args) {if (qh IStracing) qh_fprintf args;}
#define trace1(args) {if (qh IStracing >= 1) qh_fprintf args;}
#define trace2(args) {if (qh IStracing >= 2) qh_fprintf args;}
#define trace3(args) {if (qh IStracing >= 3) qh_fprintf args;}
#define trace4(args) {if (qh IStracing >= 4) qh_fprintf args;}
#define trace5(args) {if (qh IStracing >= 5) qh_fprintf args;}
#else /* qh_NOtrace */
#define trace0(args) {}
#define trace1(args) {}
#define trace2(args) {}
#define trace3(args) {}
#define trace4(args) {}
#define trace5(args) {}
#endif /* qh_NOtrace */

/*----------------------------------

*/

/* See Qt's qglobal.h */
#if !defined(SAG_COM) && (defined(WIN64) || defined(_WIN64) || defined(__WIN64__) || defined(WIN32) || defined(_WIN32) || defined(__WIN32__) || defined(__NT__))
#   define QHULL_OS_WIN
#elif defined(__MWERKS__) && defined(__INTEL__)
#   define QHULL_OS_WIN
#endif
#if defined(__INTEL_COMPILER) && !defined(QHULL_OS_WIN)
template 
inline void qhullUnused(T &x) { (void)x; }
#  define QHULL_UNUSED(x) qhullUnused(x);
#else
#  define QHULL_UNUSED(x) (void)x;
#endif

/***** -libqhull.c prototypes (alphabetical after qhull) ********************/

void    qh_qhull(void);
boolT   qh_addpoint(pointT *furthest, facetT *facet, boolT checkdist);
void    qh_buildhull(void);
void    qh_buildtracing(pointT *furthest, facetT *facet);
void    qh_build_withrestart(void);
void    qh_errexit2(int exitcode, facetT *facet, facetT *otherfacet);
void    qh_findhorizon(pointT *point, facetT *facet, int *goodvisible,int *goodhorizon);
pointT *qh_nextfurthest(facetT **visible);
void    qh_partitionall(setT *vertices, pointT *points,int npoints);
void    qh_partitioncoplanar(pointT *point, facetT *facet, realT *dist);
void    qh_partitionpoint(pointT *point, facetT *facet);
void    qh_partitionvisible(boolT allpoints, int *numpoints);
void    qh_precision(const char *reason);
void    qh_printsummary(FILE *fp);

/***** -global.c internal prototypes (alphabetical) ***********************/

void    qh_appendprint(qh_PRINT format);
void    qh_freebuild(boolT allmem);
void    qh_freebuffers(void);
void    qh_initbuffers(coordT *points, int numpoints, int dim, boolT ismalloc);

/***** -stat.c internal prototypes (alphabetical) ***********************/

void    qh_allstatA(void);
void    qh_allstatB(void);
void    qh_allstatC(void);
void    qh_allstatD(void);
void    qh_allstatE(void);
void    qh_allstatE2 (void);
void    qh_allstatF(void);
void    qh_allstatG(void);
void    qh_allstatH(void);
void    qh_freebuffers(void);
void    qh_initbuffers(coordT *points, int numpoints, int dim, boolT ismalloc);

#endif /* qhDEFqhulla */
qhull-2012.1/src/libqhull/qset.c0000644000076400010400000010146611710661342017640 0ustar  bbarberAdministrators/*
  ---------------------------------

   qset.c
   implements set manipulations needed for quickhull

   see qh-set.htm and qset.h

   Be careful of strict aliasing (two pointers of different types
   that reference the same location).  The last slot of a set is
   either the actual size of the set plus 1, or the NULL terminator
   of the set (i.e., setelemT).

   Copyright (c) 1993-2012 The Geometry Center.
   $Id: //main/2011/qhull/src/libqhull/qset.c#6 $$Change: 1475 $
   $DateTime: 2012/01/27 22:32:16 $$Author: bbarber $
*/

#include "qset.h"
#include "mem.h"
#include 
#include 
/*** uncomment here and qhull_a.h
     if string.h does not define memcpy()
#include 
*/

#ifndef qhDEFlibqhull
typedef struct ridgeT ridgeT;
typedef struct facetT facetT;
void    qh_errexit(int exitcode, facetT *, ridgeT *);
void    qh_fprintf(FILE *fp, int msgcode, const char *fmt, ... );
#  ifdef _MSC_VER  /* Microsoft Visual C++ -- warning level 4 */
#  pragma warning( disable : 4127)  /* conditional expression is constant */
#  pragma warning( disable : 4706)  /* assignment within conditional function */
#  endif
#endif

/*=============== internal macros ===========================*/

/*============ functions in alphabetical order ===================*/

/*----------------------------------

  qh_setaddnth( setp, nth, newelem)
    adds newelem as n'th element of sorted or unsorted *setp

  notes:
    *setp and newelem must be defined
    *setp may be a temp set
    nth=0 is first element
    errors if nth is out of bounds

  design:
    expand *setp if empty or full
    move tail of *setp up one
    insert newelem
*/
void qh_setaddnth(setT **setp, int nth, void *newelem) {
  int oldsize, i;
  setelemT *sizep;          /* avoid strict aliasing */
  setelemT *oldp, *newp;

  if (!*setp || (sizep= SETsizeaddr_(*setp))->i==0) {
    qh_setlarger(setp);
    sizep= SETsizeaddr_(*setp);
  }
  oldsize= sizep->i - 1;
  if (nth < 0 || nth > oldsize) {
    qh_fprintf(qhmem.ferr, 6171, "qhull internal error (qh_setaddnth): nth %d is out-of-bounds for set:\n", nth);
    qh_setprint(qhmem.ferr, "", *setp);
    qh_errexit(qhmem_ERRqhull, NULL, NULL);
  }
  sizep->i++;
  oldp= (setelemT *)SETelemaddr_(*setp, oldsize, void);   /* NULL */
  newp= oldp+1;
  for (i=oldsize-nth+1; i--; )  /* move at least NULL  */
    (newp--)->p= (oldp--)->p;       /* may overwrite *sizep */
  newp->p= newelem;
} /* setaddnth */


/*----------------------------------

  setaddsorted( setp, newelem )
    adds an newelem into sorted *setp

  notes:
    *setp and newelem must be defined
    *setp may be a temp set
    nop if newelem already in set

  design:
    find newelem's position in *setp
    insert newelem
*/
void qh_setaddsorted(setT **setp, void *newelem) {
  int newindex=0;
  void *elem, **elemp;

  FOREACHelem_(*setp) {          /* could use binary search instead */
    if (elem < newelem)
      newindex++;
    else if (elem == newelem)
      return;
    else
      break;
  }
  qh_setaddnth(setp, newindex, newelem);
} /* setaddsorted */


/*---------------------------------

  qh_setappend( setp, newelem)
    append newelem to *setp

  notes:
    *setp may be a temp set
    *setp and newelem may be NULL

  design:
    expand *setp if empty or full
    append newelem to *setp

*/
void qh_setappend(setT **setp, void *newelem) {
  setelemT *sizep;  /* Avoid strict aliasing.  Writing to *endp may overwrite *sizep */
  setelemT *endp;
  int count;

  if (!newelem)
    return;
  if (!*setp || (sizep= SETsizeaddr_(*setp))->i==0) {
    qh_setlarger(setp);
    sizep= SETsizeaddr_(*setp);
  }
  count= (sizep->i)++ - 1;
  endp= (setelemT *)SETelemaddr_(*setp, count, void);
  (endp++)->p= newelem;
  endp->p= NULL;
} /* setappend */

/*---------------------------------

  qh_setappend_set( setp, setA)
    appends setA to *setp

  notes:
    *setp can not be a temp set
    *setp and setA may be NULL

  design:
    setup for copy
    expand *setp if it is too small
    append all elements of setA to *setp
*/
void qh_setappend_set(setT **setp, setT *setA) {
  int sizeA, size;
  setT *oldset;
  setelemT *sizep;

  if (!setA)
    return;
  SETreturnsize_(setA, sizeA);
  if (!*setp)
    *setp= qh_setnew(sizeA);
  sizep= SETsizeaddr_(*setp);
  if (!(size= sizep->i))
    size= (*setp)->maxsize;
  else
    size--;
  if (size + sizeA > (*setp)->maxsize) {
    oldset= *setp;
    *setp= qh_setcopy(oldset, sizeA);
    qh_setfree(&oldset);
    sizep= SETsizeaddr_(*setp);
  }
  if (sizeA > 0) {
    sizep->i= size+sizeA+1;   /* memcpy may overwrite */
    memcpy((char *)&((*setp)->e[size].p), (char *)&(setA->e[0].p), (size_t)(sizeA+1) * SETelemsize);
  }
} /* setappend_set */


/*---------------------------------

  qh_setappend2ndlast( setp, newelem )
    makes newelem the next to the last element in *setp

  notes:
    *setp must have at least one element
    newelem must be defined
    *setp may be a temp set

  design:
    expand *setp if empty or full
    move last element of *setp up one
    insert newelem
*/
void qh_setappend2ndlast(setT **setp, void *newelem) {
    setelemT *sizep;  /* Avoid strict aliasing.  Writing to *endp may overwrite *sizep */
    setelemT *endp, *lastp;
    int count;

    if (!*setp || (sizep= SETsizeaddr_(*setp))->i==0) {
        qh_setlarger(setp);
        sizep= SETsizeaddr_(*setp);
    }
    count= (sizep->i)++ - 1;
    endp= (setelemT *)SETelemaddr_(*setp, count, void); /* NULL */
    lastp= endp-1;
    *(endp++)= *lastp;
    endp->p= NULL;    /* may overwrite *sizep */
    lastp->p= newelem;
} /* setappend2ndlast */

/*---------------------------------

  qh_setcheck( set, typename, id )
    check set for validity
    report errors with typename and id

  design:
    checks that maxsize, actual size, and NULL terminator agree
*/
void qh_setcheck(setT *set, const char *tname, unsigned id) {
  int maxsize, size;
  int waserr= 0;

  if (!set)
    return;
  SETreturnsize_(set, size);
  maxsize= set->maxsize;
  if (size > maxsize || !maxsize) {
    qh_fprintf(qhmem.ferr, 6172, "qhull internal error (qh_setcheck): actual size %d of %s%d is greater than max size %d\n",
             size, tname, id, maxsize);
    waserr= 1;
  }else if (set->e[size].p) {
    qh_fprintf(qhmem.ferr, 6173, "qhull internal error (qh_setcheck): %s%d(size %d max %d) is not null terminated.\n",
             tname, id, size-1, maxsize);
    waserr= 1;
  }
  if (waserr) {
    qh_setprint(qhmem.ferr, "ERRONEOUS", set);
    qh_errexit(qhmem_ERRqhull, NULL, NULL);
  }
} /* setcheck */


/*---------------------------------

  qh_setcompact( set )
    remove internal NULLs from an unsorted set

  returns:
    updated set

  notes:
    set may be NULL
    it would be faster to swap tail of set into holes, like qh_setdel

  design:
    setup pointers into set
    skip NULLs while copying elements to start of set
    update the actual size
*/
void qh_setcompact(setT *set) {
  int size;
  void **destp, **elemp, **endp, **firstp;

  if (!set)
    return;
  SETreturnsize_(set, size);
  destp= elemp= firstp= SETaddr_(set, void);
  endp= destp + size;
  while (1) {
    if (!(*destp++ = *elemp++)) {
      destp--;
      if (elemp > endp)
        break;
    }
  }
  qh_settruncate(set, (int)(destp-firstp));   /* WARN64 */
} /* setcompact */


/*---------------------------------

  qh_setcopy( set, extra )
    make a copy of a sorted or unsorted set with extra slots

  returns:
    new set

  design:
    create a newset with extra slots
    copy the elements to the newset

*/
setT *qh_setcopy(setT *set, int extra) {
  setT *newset;
  int size;

  if (extra < 0)
    extra= 0;
  SETreturnsize_(set, size);
  newset= qh_setnew(size+extra);
  SETsizeaddr_(newset)->i= size+1;    /* memcpy may overwrite */
  memcpy((char *)&(newset->e[0].p), (char *)&(set->e[0].p), (size_t)(size+1) * SETelemsize);
  return(newset);
} /* setcopy */


/*---------------------------------

  qh_setdel( set, oldelem )
    delete oldelem from an unsorted set

  returns:
    returns oldelem if found
    returns NULL otherwise

  notes:
    set may be NULL
    oldelem must not be NULL;
    only deletes one copy of oldelem in set

  design:
    locate oldelem
    update actual size if it was full
    move the last element to the oldelem's location
*/
void *qh_setdel(setT *set, void *oldelem) {
  setelemT *sizep;
  setelemT *elemp;
  setelemT *lastp;

  if (!set)
    return NULL;
  elemp= (setelemT *)SETaddr_(set, void);
  while (elemp->p != oldelem && elemp->p)
    elemp++;
  if (elemp->p) {
    sizep= SETsizeaddr_(set);
    if (!(sizep->i)--)         /*  if was a full set */
      sizep->i= set->maxsize;  /*     *sizep= (maxsize-1)+ 1 */
    lastp= (setelemT *)SETelemaddr_(set, sizep->i-1, void);
    elemp->p= lastp->p;      /* may overwrite itself */
    lastp->p= NULL;
    return oldelem;
  }
  return NULL;
} /* setdel */


/*---------------------------------

  qh_setdellast( set)
    return last element of set or NULL

  notes:
    deletes element from set
    set may be NULL

  design:
    return NULL if empty
    if full set
      delete last element and set actual size
    else
      delete last element and update actual size
*/
void *qh_setdellast(setT *set) {
  int setsize;  /* actually, actual_size + 1 */
  int maxsize;
  setelemT *sizep;
  void *returnvalue;

  if (!set || !(set->e[0].p))
    return NULL;
  sizep= SETsizeaddr_(set);
  if ((setsize= sizep->i)) {
    returnvalue= set->e[setsize - 2].p;
    set->e[setsize - 2].p= NULL;
    sizep->i--;
  }else {
    maxsize= set->maxsize;
    returnvalue= set->e[maxsize - 1].p;
    set->e[maxsize - 1].p= NULL;
    sizep->i= maxsize;
  }
  return returnvalue;
} /* setdellast */


/*---------------------------------

  qh_setdelnth( set, nth )
    deletes nth element from unsorted set
    0 is first element

  returns:
    returns the element (needs type conversion)

  notes:
    errors if nth invalid

  design:
    setup points and check nth
    delete nth element and overwrite with last element
*/
void *qh_setdelnth(setT *set, int nth) {
  void *elem;
  setelemT *sizep;
  setelemT *elemp, *lastp;

  elemp= (setelemT *)SETelemaddr_(set, nth, void);
  sizep= SETsizeaddr_(set);
  if ((sizep->i--)==0)         /*  if was a full set */
    sizep->i= set->maxsize;  /*     *sizep= (maxsize-1)+ 1 */
  if (nth < 0 || nth >= sizep->i) {
    qh_fprintf(qhmem.ferr, 6174, "qhull internal error (qh_setdelnth): nth %d is out-of-bounds for set:\n", nth);
    qh_setprint(qhmem.ferr, "", set);
    qh_errexit(qhmem_ERRqhull, NULL, NULL);
  }
  lastp= (setelemT *)SETelemaddr_(set, sizep->i-1, void);
  elem= elemp->p;
  elemp->p= lastp->p;      /* may overwrite itself */
  lastp->p= NULL;
  return elem;
} /* setdelnth */

/*---------------------------------

  qh_setdelnthsorted( set, nth )
    deletes nth element from sorted set

  returns:
    returns the element (use type conversion)

  notes:
    errors if nth invalid

  see also:
    setnew_delnthsorted

  design:
    setup points and check nth
    copy remaining elements down one
    update actual size
*/
void *qh_setdelnthsorted(setT *set, int nth) {
  void *elem;
  setelemT *sizep;
  setelemT *newp, *oldp;

  sizep= SETsizeaddr_(set);
  if (nth < 0 || (sizep->i && nth >= sizep->i-1) || nth >= set->maxsize) {
    qh_fprintf(qhmem.ferr, 6175, "qhull internal error (qh_setdelnthsorted): nth %d is out-of-bounds for set:\n", nth);
    qh_setprint(qhmem.ferr, "", set);
    qh_errexit(qhmem_ERRqhull, NULL, NULL);
  }
  newp= (setelemT *)SETelemaddr_(set, nth, void);
  elem= newp->p;
  oldp= newp+1;
  while (((newp++)->p= (oldp++)->p))
    ; /* copy remaining elements and NULL */
  if ((sizep->i--)==0)         /*  if was a full set */
    sizep->i= set->maxsize;  /*     *sizep= (max size-1)+ 1 */
  return elem;
} /* setdelnthsorted */


/*---------------------------------

  qh_setdelsorted( set, oldelem )
    deletes oldelem from sorted set

  returns:
    returns oldelem if it was deleted

  notes:
    set may be NULL

  design:
    locate oldelem in set
    copy remaining elements down one
    update actual size
*/
void *qh_setdelsorted(setT *set, void *oldelem) {
  setelemT *sizep;
  setelemT *newp, *oldp;

  if (!set)
    return NULL;
  newp= (setelemT *)SETaddr_(set, void);
  while(newp->p != oldelem && newp->p)
    newp++;
  if (newp->p) {
    oldp= newp+1;
    while (((newp++)->p= (oldp++)->p))
      ; /* copy remaining elements */
    sizep= SETsizeaddr_(set);
    if ((sizep->i--)==0)    /*  if was a full set */
      sizep->i= set->maxsize;  /*     *sizep= (max size-1)+ 1 */
    return oldelem;
  }
  return NULL;
} /* setdelsorted */


/*---------------------------------

  qh_setduplicate( set, elemsize )
    duplicate a set of elemsize elements

  notes:
    use setcopy if retaining old elements

  design:
    create a new set
    for each elem of the old set
      create a newelem
      append newelem to newset
*/
setT *qh_setduplicate(setT *set, int elemsize) {
  void          *elem, **elemp, *newElem;
  setT          *newSet;
  int           size;

  if (!(size= qh_setsize(set)))
    return NULL;
  newSet= qh_setnew(size);
  FOREACHelem_(set) {
    newElem= qh_memalloc(elemsize);
    memcpy(newElem, elem, (size_t)elemsize);
    qh_setappend(&newSet, newElem);
  }
  return newSet;
} /* setduplicate */


/*---------------------------------

  qh_setendpointer( set )
    Returns pointer to NULL terminator of a set's elements
    set can not be NULL

*/
void **qh_setendpointer(setT *set) {

  setelemT *sizep= SETsizeaddr_(set);
  int n= sizep->i;
  return (n ? &set->e[n-1].p : &sizep->p);
} /* qh_setendpointer */

/*---------------------------------

  qh_setequal(  )
    returns 1 if two sorted sets are equal, otherwise returns 0

  notes:
    either set may be NULL

  design:
    check size of each set
    setup pointers
    compare elements of each set
*/
int qh_setequal(setT *setA, setT *setB) {
  void **elemAp, **elemBp;
  int sizeA= 0, sizeB= 0;

  if (setA) {
    SETreturnsize_(setA, sizeA);
  }
  if (setB) {
    SETreturnsize_(setB, sizeB);
  }
  if (sizeA != sizeB)
    return 0;
  if (!sizeA)
    return 1;
  elemAp= SETaddr_(setA, void);
  elemBp= SETaddr_(setB, void);
  if (!memcmp((char *)elemAp, (char *)elemBp, sizeA*SETelemsize))
    return 1;
  return 0;
} /* setequal */


/*---------------------------------

  qh_setequal_except( setA, skipelemA, setB, skipelemB )
    returns 1 if sorted setA and setB are equal except for skipelemA & B

  returns:
    false if either skipelemA or skipelemB are missing

  notes:
    neither set may be NULL

    if skipelemB is NULL,
      can skip any one element of setB

  design:
    setup pointers
    search for skipelemA, skipelemB, and mismatches
    check results
*/
int qh_setequal_except(setT *setA, void *skipelemA, setT *setB, void *skipelemB) {
  void **elemA, **elemB;
  int skip=0;

  elemA= SETaddr_(setA, void);
  elemB= SETaddr_(setB, void);
  while (1) {
    if (*elemA == skipelemA) {
      skip++;
      elemA++;
    }
    if (skipelemB) {
      if (*elemB == skipelemB) {
        skip++;
        elemB++;
      }
    }else if (*elemA != *elemB) {
      skip++;
      if (!(skipelemB= *elemB++))
        return 0;
    }
    if (!*elemA)
      break;
    if (*elemA++ != *elemB++)
      return 0;
  }
  if (skip != 2 || *elemB)
    return 0;
  return 1;
} /* setequal_except */


/*---------------------------------

  qh_setequal_skip( setA, skipA, setB, skipB )
    returns 1 if sorted setA and setB are equal except for elements skipA & B

  returns:
    false if different size

  notes:
    neither set may be NULL

  design:
    setup pointers
    search for mismatches while skipping skipA and skipB
*/
int qh_setequal_skip(setT *setA, int skipA, setT *setB, int skipB) {
  void **elemA, **elemB, **skipAp, **skipBp;

  elemA= SETaddr_(setA, void);
  elemB= SETaddr_(setB, void);
  skipAp= SETelemaddr_(setA, skipA, void);
  skipBp= SETelemaddr_(setB, skipB, void);
  while (1) {
    if (elemA == skipAp)
      elemA++;
    if (elemB == skipBp)
      elemB++;
    if (!*elemA)
      break;
    if (*elemA++ != *elemB++)
      return 0;
  }
  if (*elemB)
    return 0;
  return 1;
} /* setequal_skip */


/*---------------------------------

  qh_setfree( setp )
    frees the space occupied by a sorted or unsorted set

  returns:
    sets setp to NULL

  notes:
    set may be NULL

  design:
    free array
    free set
*/
void qh_setfree(setT **setp) {
  int size;
  void **freelistp;  /* used !qh_NOmem */

  if (*setp) {
    size= sizeof(setT) + ((*setp)->maxsize)*SETelemsize;
    if (size <= qhmem.LASTsize) {
      qh_memfree_(*setp, size, freelistp);
    }else
      qh_memfree(*setp, size);
    *setp= NULL;
  }
} /* setfree */


/*---------------------------------

  qh_setfree2( setp, elemsize )
    frees the space occupied by a set and its elements

  notes:
    set may be NULL

  design:
    free each element
    free set
*/
void qh_setfree2 (setT **setp, int elemsize) {
  void          *elem, **elemp;

  FOREACHelem_(*setp)
    qh_memfree(elem, elemsize);
  qh_setfree(setp);
} /* setfree2 */



/*---------------------------------

  qh_setfreelong( setp )
    frees a set only if it's in long memory

  returns:
    sets setp to NULL if it is freed

  notes:
    set may be NULL

  design:
    if set is large
      free it
*/
void qh_setfreelong(setT **setp) {
  int size;

  if (*setp) {
    size= sizeof(setT) + ((*setp)->maxsize)*SETelemsize;
    if (size > qhmem.LASTsize) {
      qh_memfree(*setp, size);
      *setp= NULL;
    }
  }
} /* setfreelong */


/*---------------------------------

  qh_setin( set, setelem )
    returns 1 if setelem is in a set, 0 otherwise

  notes:
    set may be NULL or unsorted

  design:
    scans set for setelem
*/
int qh_setin(setT *set, void *setelem) {
  void *elem, **elemp;

  FOREACHelem_(set) {
    if (elem == setelem)
      return 1;
  }
  return 0;
} /* setin */


/*---------------------------------

  qh_setindex( set, atelem )
    returns the index of atelem in set.
    returns -1, if not in set or maxsize wrong

  notes:
    set may be NULL and may contain nulls.
    NOerrors returned (qh_pointid, QhullPoint::id)

  design:
    checks maxsize
    scans set for atelem
*/
int qh_setindex(setT *set, void *atelem) {
  void **elem;
  int size, i;

  if (!set)
    return -1;
  SETreturnsize_(set, size);
  if (size > set->maxsize)
    return -1;
  elem= SETaddr_(set, void);
  for (i=0; i < size; i++) {
    if (*elem++ == atelem)
      return i;
  }
  return -1;
} /* setindex */


/*---------------------------------

  qh_setlarger( oldsetp )
    returns a larger set that contains all elements of *oldsetp

  notes:
    the set is at least twice as large
    if temp set, updates qhmem.tempstack

  design:
    creates a new set
    copies the old set to the new set
    updates pointers in tempstack
    deletes the old set
*/
void qh_setlarger(setT **oldsetp) {
  int size= 1;
  setT *newset, *set, **setp, *oldset;
  setelemT *sizep;
  setelemT *newp, *oldp;

  if (*oldsetp) {
    oldset= *oldsetp;
    SETreturnsize_(oldset, size);
    qhmem.cntlarger++;
    qhmem.totlarger += size+1;
    newset= qh_setnew(2 * size);
    oldp= (setelemT *)SETaddr_(oldset, void);
    newp= (setelemT *)SETaddr_(newset, void);
    memcpy((char *)newp, (char *)oldp, (size_t)(size+1) * SETelemsize);
    sizep= SETsizeaddr_(newset);
    sizep->i= size+1;
    FOREACHset_((setT *)qhmem.tempstack) {
      if (set == oldset)
        *(setp-1)= newset;
    }
    qh_setfree(oldsetp);
  }else
    newset= qh_setnew(3);
  *oldsetp= newset;
} /* setlarger */


/*---------------------------------

  qh_setlast(  )
    return last element of set or NULL (use type conversion)

  notes:
    set may be NULL

  design:
    return last element
*/
void *qh_setlast(setT *set) {
  int size;

  if (set) {
    size= SETsizeaddr_(set)->i;
    if (!size)
      return SETelem_(set, set->maxsize - 1);
    else if (size > 1)
      return SETelem_(set, size - 2);
  }
  return NULL;
} /* setlast */


/*---------------------------------

  qh_setnew( setsize )
    creates and allocates space for a set

  notes:
    setsize means the number of elements (!including the NULL terminator)
    use qh_settemp/qh_setfreetemp if set is temporary

  design:
    allocate memory for set
    roundup memory if small set
    initialize as empty set
*/
setT *qh_setnew(int setsize) {
  setT *set;
  int sizereceived; /* used !qh_NOmem */
  int size;
  void **freelistp; /* used !qh_NOmem */

  if (!setsize)
    setsize++;
  size= sizeof(setT) + setsize * SETelemsize;
  if (size>0 && size <= qhmem.LASTsize) {
    qh_memalloc_(size, freelistp, set, setT);
#ifndef qh_NOmem
    sizereceived= qhmem.sizetable[ qhmem.indextable[size]];
    if (sizereceived > size)
      setsize += (sizereceived - size)/SETelemsize;
#endif
  }else
    set= (setT*)qh_memalloc(size);
  set->maxsize= setsize;
  set->e[setsize].i= 1;
  set->e[0].p= NULL;
  return(set);
} /* setnew */


/*---------------------------------

  qh_setnew_delnthsorted( set, size, nth, prepend )
    creates a sorted set not containing nth element
    if prepend, the first prepend elements are undefined

  notes:
    set must be defined
    checks nth
    see also: setdelnthsorted

  design:
    create new set
    setup pointers and allocate room for prepend'ed entries
    append head of old set to new set
    append tail of old set to new set
*/
setT *qh_setnew_delnthsorted(setT *set, int size, int nth, int prepend) {
  setT *newset;
  void **oldp, **newp;
  int tailsize= size - nth -1, newsize;

  if (tailsize < 0) {
    qh_fprintf(qhmem.ferr, 6176, "qhull internal error (qh_setnew_delnthsorted): nth %d is out-of-bounds for set:\n", nth);
    qh_setprint(qhmem.ferr, "", set);
    qh_errexit(qhmem_ERRqhull, NULL, NULL);
  }
  newsize= size-1 + prepend;
  newset= qh_setnew(newsize);
  newset->e[newset->maxsize].i= newsize+1;  /* may be overwritten */
  oldp= SETaddr_(set, void);
  newp= SETaddr_(newset, void) + prepend;
  switch (nth) {
  case 0:
    break;
  case 1:
    *(newp++)= *oldp++;
    break;
  case 2:
    *(newp++)= *oldp++;
    *(newp++)= *oldp++;
    break;
  case 3:
    *(newp++)= *oldp++;
    *(newp++)= *oldp++;
    *(newp++)= *oldp++;
    break;
  case 4:
    *(newp++)= *oldp++;
    *(newp++)= *oldp++;
    *(newp++)= *oldp++;
    *(newp++)= *oldp++;
    break;
  default:
    memcpy((char *)newp, (char *)oldp, (size_t)nth * SETelemsize);
    newp += nth;
    oldp += nth;
    break;
  }
  oldp++;
  switch (tailsize) {
  case 0:
    break;
  case 1:
    *(newp++)= *oldp++;
    break;
  case 2:
    *(newp++)= *oldp++;
    *(newp++)= *oldp++;
    break;
  case 3:
    *(newp++)= *oldp++;
    *(newp++)= *oldp++;
    *(newp++)= *oldp++;
    break;
  case 4:
    *(newp++)= *oldp++;
    *(newp++)= *oldp++;
    *(newp++)= *oldp++;
    *(newp++)= *oldp++;
    break;
  default:
    memcpy((char *)newp, (char *)oldp, (size_t)tailsize * SETelemsize);
    newp += tailsize;
  }
  *newp= NULL;
  return(newset);
} /* setnew_delnthsorted */


/*---------------------------------

  qh_setprint( fp, string, set )
    print set elements to fp with identifying string

  notes:
    never errors
*/
void qh_setprint(FILE *fp, const char* string, setT *set) {
  int size, k;

  if (!set)
    qh_fprintf(fp, 9346, "%s set is null\n", string);
  else {
    SETreturnsize_(set, size);
    qh_fprintf(fp, 9347, "%s set=%p maxsize=%d size=%d elems=",
             string, set, set->maxsize, size);
    if (size > set->maxsize)
      size= set->maxsize+1;
    for (k=0; k < size; k++)
      qh_fprintf(fp, 9348, " %p", set->e[k].p);
    qh_fprintf(fp, 9349, "\n");
  }
} /* setprint */

/*---------------------------------

  qh_setreplace( set, oldelem, newelem )
    replaces oldelem in set with newelem

  notes:
    errors if oldelem not in the set
    newelem may be NULL, but it turns the set into an indexed set (no FOREACH)

  design:
    find oldelem
    replace with newelem
*/
void qh_setreplace(setT *set, void *oldelem, void *newelem) {
  void **elemp;

  elemp= SETaddr_(set, void);
  while (*elemp != oldelem && *elemp)
    elemp++;
  if (*elemp)
    *elemp= newelem;
  else {
    qh_fprintf(qhmem.ferr, 6177, "qhull internal error (qh_setreplace): elem %p not found in set\n",
       oldelem);
    qh_setprint(qhmem.ferr, "", set);
    qh_errexit(qhmem_ERRqhull, NULL, NULL);
  }
} /* setreplace */


/*---------------------------------

  qh_setsize( set )
    returns the size of a set

  notes:
    errors if set's maxsize is incorrect
    same as SETreturnsize_(set)
    same code for qh_setsize [qset.c] and QhullSetBase::count

  design:
    determine actual size of set from maxsize
*/
int qh_setsize(setT *set) {
  int size;
  setelemT *sizep;

  if (!set)
    return(0);
  sizep= SETsizeaddr_(set);
  if ((size= sizep->i)) {
    size--;
    if (size > set->maxsize) {
      qh_fprintf(qhmem.ferr, 6178, "qhull internal error (qh_setsize): current set size %d is greater than maximum size %d\n",
               size, set->maxsize);
      qh_setprint(qhmem.ferr, "set: ", set);
      qh_errexit(qhmem_ERRqhull, NULL, NULL);
    }
  }else
    size= set->maxsize;
  return size;
} /* setsize */

/*---------------------------------

  qh_settemp( setsize )
    return a stacked, temporary set of upto setsize elements

  notes:
    use settempfree or settempfree_all to release from qhmem.tempstack
    see also qh_setnew

  design:
    allocate set
    append to qhmem.tempstack

*/
setT *qh_settemp(int setsize) {
  setT *newset;

  newset= qh_setnew(setsize);
  qh_setappend(&qhmem.tempstack, newset);
  if (qhmem.IStracing >= 5)
    qh_fprintf(qhmem.ferr, 8123, "qh_settemp: temp set %p of %d elements, depth %d\n",
       newset, newset->maxsize, qh_setsize(qhmem.tempstack));
  return newset;
} /* settemp */

/*---------------------------------

  qh_settempfree( set )
    free temporary set at top of qhmem.tempstack

  notes:
    nop if set is NULL
    errors if set not from previous   qh_settemp

  to locate errors:
    use 'T2' to find source and then find mis-matching qh_settemp

  design:
    check top of qhmem.tempstack
    free it
*/
void qh_settempfree(setT **set) {
  setT *stackedset;

  if (!*set)
    return;
  stackedset= qh_settemppop();
  if (stackedset != *set) {
    qh_settemppush(stackedset);
    qh_fprintf(qhmem.ferr, 6179, "qhull internal error (qh_settempfree): set %p(size %d) was not last temporary allocated(depth %d, set %p, size %d)\n",
             *set, qh_setsize(*set), qh_setsize(qhmem.tempstack)+1,
             stackedset, qh_setsize(stackedset));
    qh_errexit(qhmem_ERRqhull, NULL, NULL);
  }
  qh_setfree(set);
} /* settempfree */

/*---------------------------------

  qh_settempfree_all(  )
    free all temporary sets in qhmem.tempstack

  design:
    for each set in tempstack
      free set
    free qhmem.tempstack
*/
void qh_settempfree_all(void) {
  setT *set, **setp;

  FOREACHset_(qhmem.tempstack)
    qh_setfree(&set);
  qh_setfree(&qhmem.tempstack);
} /* settempfree_all */

/*---------------------------------

  qh_settemppop(  )
    pop and return temporary set from qhmem.tempstack

  notes:
    the returned set is permanent

  design:
    pop and check top of qhmem.tempstack
*/
setT *qh_settemppop(void) {
  setT *stackedset;

  stackedset= (setT*)qh_setdellast(qhmem.tempstack);
  if (!stackedset) {
    qh_fprintf(qhmem.ferr, 6180, "qhull internal error (qh_settemppop): pop from empty temporary stack\n");
    qh_errexit(qhmem_ERRqhull, NULL, NULL);
  }
  if (qhmem.IStracing >= 5)
    qh_fprintf(qhmem.ferr, 8124, "qh_settemppop: depth %d temp set %p of %d elements\n",
       qh_setsize(qhmem.tempstack)+1, stackedset, qh_setsize(stackedset));
  return stackedset;
} /* settemppop */

/*---------------------------------

  qh_settemppush( set )
    push temporary set unto qhmem.tempstack (makes it temporary)

  notes:
    duplicates settemp() for tracing

  design:
    append set to tempstack
*/
void qh_settemppush(setT *set) {
    if (!set) {
        fprintf (qhmem.ferr, "qhull error (qh_settemppush): can not push a NULL temp\n");
        qh_errexit (qhmem_ERRqhull, NULL, NULL);
    }
  qh_setappend(&qhmem.tempstack, set);
  if (qhmem.IStracing >= 5)
    qh_fprintf(qhmem.ferr, 8125, "qh_settemppush: depth %d temp set %p of %d elements\n",
      qh_setsize(qhmem.tempstack), set, qh_setsize(set));
} /* settemppush */


/*---------------------------------

  qh_settruncate( set, size )
    truncate set to size elements

  notes:
    set must be defined

  see:
    SETtruncate_

  design:
    check size
    update actual size of set
*/
void qh_settruncate(setT *set, int size) {

  if (size < 0 || size > set->maxsize) {
    qh_fprintf(qhmem.ferr, 6181, "qhull internal error (qh_settruncate): size %d out of bounds for set:\n", size);
    qh_setprint(qhmem.ferr, "", set);
    qh_errexit(qhmem_ERRqhull, NULL, NULL);
  }
  set->e[set->maxsize].i= size+1;   /* maybe overwritten */
  set->e[size].p= NULL;
} /* settruncate */

/*---------------------------------

  qh_setunique( set, elem )
    add elem to unsorted set unless it is already in set

  notes:
    returns 1 if it is appended

  design:
    if elem not in set
      append elem to set
*/
int qh_setunique(setT **set, void *elem) {

  if (!qh_setin(*set, elem)) {
    qh_setappend(set, elem);
    return 1;
  }
  return 0;
} /* setunique */

/*---------------------------------

  qh_setzero( set, index, size )
    zero elements from index on
    set actual size of set to size

  notes:
    set must be defined
    the set becomes an indexed set (can not use FOREACH...)

  see also:
    qh_settruncate

  design:
    check index and size
    update actual size
    zero elements starting at e[index]
*/
void qh_setzero(setT *set, int idx, int size) {
  int count;

  if (idx < 0 || idx >= size || size > set->maxsize) {
    qh_fprintf(qhmem.ferr, 6182, "qhull internal error (qh_setzero): index %d or size %d out of bounds for set:\n", idx, size);
    qh_setprint(qhmem.ferr, "", set);
    qh_errexit(qhmem_ERRqhull, NULL, NULL);
  }
  set->e[set->maxsize].i=  size+1;  /* may be overwritten */
  count= size - idx + 1;   /* +1 for NULL terminator */
  memset((char *)SETelemaddr_(set, idx, void), 0, (size_t)count * SETelemsize);
} /* setzero */


qhull-2012.1/src/libqhull/qset.h0000644000076400010400000003475611710144467017660 0ustar  bbarberAdministrators/*
  ---------------------------------

   qset.h
     header file for qset.c that implements set

   see qh-set.htm and qset.c

   only uses mem.c, malloc/free

   for error handling, writes message and calls
      qh_errexit(qhmem_ERRqhull, NULL, NULL);

   set operations satisfy the following properties:
    - sets have a max size, the actual size (if different) is stored at the end
    - every set is NULL terminated
    - sets may be sorted or unsorted, the caller must distinguish this

   Copyright (c) 1993-2012 The Geometry Center.
   $Id: //main/2011/qhull/src/libqhull/qset.h#4 $$Change: 1464 $
   $DateTime: 2012/01/25 22:58:41 $$Author: bbarber $
*/

#ifndef qhDEFset
#define qhDEFset 1

#include 

/*================= -structures- ===============*/

#ifndef DEFsetT
#define DEFsetT 1
typedef struct setT setT;   /* a set is a sorted or unsorted array of pointers */
#endif

/*------------------------------------------

setT
  a set or list of pointers with maximum size and actual size.

variations:
  unsorted, unique   -- a list of unique pointers with NULL terminator
                           user guarantees uniqueness
  sorted             -- a sorted list of unique pointers with NULL terminator
                           qset.c guarantees uniqueness
  unsorted           -- a list of pointers terminated with NULL
  indexed            -- an array of pointers with NULL elements

structure for set of n elements:

        --------------
        |  maxsize
        --------------
        |  e[0] - a pointer, may be NULL for indexed sets
        --------------
        |  e[1]

        --------------
        |  ...
        --------------
        |  e[n-1]
        --------------
        |  e[n] = NULL
        --------------
        |  ...
        --------------
        |  e[maxsize] - n+1 or NULL (determines actual size of set)
        --------------

*/

/*-- setelemT -- internal type to allow both pointers and indices
*/
typedef union setelemT setelemT;
union setelemT {
  void    *p;
  int      i;         /* integer used for e[maxSize] */
};

struct setT {
  int maxsize;          /* maximum number of elements (except NULL) */
  setelemT e[1];        /* array of pointers, tail is NULL */
                        /* last slot (unless NULL) is actual size+1
                           e[maxsize]==NULL or e[e[maxsize]-1]==NULL */
                        /* this may generate a warning since e[] contains
                           maxsize elements */
};

/*=========== -constants- =========================*/

/*-------------------------------------

  SETelemsize
    size of a set element in bytes
*/
#define SETelemsize ((int)sizeof(setelemT))


/*=========== -macros- =========================*/

/*-------------------------------------

   FOREACHsetelement_(type, set, variable)
     define FOREACH iterator

   declare:
     assumes *variable and **variablep are declared
     no space in "variable)" [DEC Alpha cc compiler]

   each iteration:
     variable is set element
     variablep is one beyond variable.

   to repeat an element:
     variablep--; / *repeat* /

   at exit:
     variable is NULL at end of loop

   example:
     #define FOREACHfacet_( facets ) FOREACHsetelement_( facetT, facets, facet )

   notes:
     use FOREACHsetelement_i_() if need index or include NULLs

   WARNING:
     nested loops can't use the same variable (define another FOREACH)

     needs braces if nested inside another FOREACH
     this includes intervening blocks, e.g. FOREACH...{ if () FOREACH...} )
*/
#define FOREACHsetelement_(type, set, variable) \
        if (((variable= NULL), set)) for (\
          variable##p= (type **)&((set)->e[0].p); \
          (variable= *variable##p++);)

/*------------------------------------------

   FOREACHsetelement_i_(type, set, variable)
     define indexed FOREACH iterator

   declare:
     type *variable, variable_n, variable_i;

   each iteration:
     variable is set element, may be NULL
     variable_i is index, variable_n is qh_setsize()

   to repeat an element:
     variable_i--; variable_n-- repeats for deleted element

   at exit:
     variable==NULL and variable_i==variable_n

   example:
     #define FOREACHfacet_i_( facets ) FOREACHsetelement_i_( facetT, facets, facet )

   WARNING:
     nested loops can't use the same variable (define another FOREACH)

     needs braces if nested inside another FOREACH
     this includes intervening blocks, e.g. FOREACH...{ if () FOREACH...} )
*/
#define FOREACHsetelement_i_(type, set, variable) \
        if (((variable= NULL), set)) for (\
          variable##_i= 0, variable= (type *)((set)->e[0].p), \
                   variable##_n= qh_setsize(set);\
          variable##_i < variable##_n;\
          variable= (type *)((set)->e[++variable##_i].p) )

/*----------------------------------------

   FOREACHsetelementreverse_(type, set, variable)-
     define FOREACH iterator in reverse order

   declare:
     assumes *variable and **variablep are declared
     also declare 'int variabletemp'

   each iteration:
     variable is set element

   to repeat an element:
     variabletemp++; / *repeat* /

   at exit:
     variable is NULL

   example:
     #define FOREACHvertexreverse_( vertices ) FOREACHsetelementreverse_( vertexT, vertices, vertex )

   notes:
     use FOREACHsetelementreverse12_() to reverse first two elements
     WARNING: needs braces if nested inside another FOREACH
*/
#define FOREACHsetelementreverse_(type, set, variable) \
        if (((variable= NULL), set)) for (\
           variable##temp= qh_setsize(set)-1, variable= qh_setlast(set);\
           variable; variable= \
           ((--variable##temp >= 0) ? SETelemt_(set, variable##temp, type) : NULL))

/*-------------------------------------

   FOREACHsetelementreverse12_(type, set, variable)-
     define FOREACH iterator with e[1] and e[0] reversed

   declare:
     assumes *variable and **variablep are declared

   each iteration:
     variable is set element
     variablep is one after variable.

   to repeat an element:
     variablep--; / *repeat* /

   at exit:
     variable is NULL at end of loop

   example
     #define FOREACHvertexreverse12_( vertices ) FOREACHsetelementreverse12_( vertexT, vertices, vertex )

   notes:
     WARNING: needs braces if nested inside another FOREACH
*/
#define FOREACHsetelementreverse12_(type, set, variable) \
        if (((variable= NULL), set)) for (\
          variable##p= (type **)&((set)->e[1].p); \
          (variable= *variable##p); \
          variable##p == ((type **)&((set)->e[0].p))?variable##p += 2: \
              (variable##p == ((type **)&((set)->e[1].p))?variable##p--:variable##p++))

/*-------------------------------------

   FOREACHelem_( set )-
     iterate elements in a set

   declare:
     void *elem, *elemp;

   each iteration:
     elem is set element
     elemp is one beyond

   to repeat an element:
     elemp--; / *repeat* /

   at exit:
     elem == NULL at end of loop

   example:
     FOREACHelem_(set) {

   notes:
     WARNING: needs braces if nested inside another FOREACH
*/
#define FOREACHelem_(set) FOREACHsetelement_(void, set, elem)

/*-------------------------------------

   FOREACHset_( set )-
     iterate a set of sets

   declare:
     setT *set, **setp;

   each iteration:
     set is set element
     setp is one beyond

   to repeat an element:
     setp--; / *repeat* /

   at exit:
     set == NULL at end of loop

   example
     FOREACHset_(sets) {

   notes:
     WARNING: needs braces if nested inside another FOREACH
*/
#define FOREACHset_(sets) FOREACHsetelement_(setT, sets, set)

/*-------------------------------------------

   SETindex_( set, elem )
     return index of elem in set

   notes:
     for use with FOREACH iteration
     WARN64 -- Maximum set size is 2G

   example:
     i= SETindex_(ridges, ridge)
*/
#define SETindex_(set, elem) ((int)((void **)elem##p - (void **)&(set)->e[1].p))

/*-----------------------------------------

   SETref_( elem )
     l.h.s. for modifying the current element in a FOREACH iteration

   example:
     SETref_(ridge)= anotherridge;
*/
#define SETref_(elem) (elem##p[-1])

/*-----------------------------------------

   SETelem_(set, n)
     return the n'th element of set

   notes:
      assumes that n is valid [0..size] and that set is defined
      use SETelemt_() for type cast
*/
#define SETelem_(set, n)           ((set)->e[n].p)

/*-----------------------------------------

   SETelemt_(set, n, type)
     return the n'th element of set as a type

   notes:
      assumes that n is valid [0..size] and that set is defined
*/
#define SETelemt_(set, n, type)    ((type*)((set)->e[n].p))

/*-----------------------------------------

   SETelemaddr_(set, n, type)
     return address of the n'th element of a set

   notes:
      assumes that n is valid [0..size] and set is defined
*/
#define SETelemaddr_(set, n, type) ((type **)(&((set)->e[n].p)))

/*-----------------------------------------

   SETfirst_(set)
     return first element of set

*/
#define SETfirst_(set)             ((set)->e[0].p)

/*-----------------------------------------

   SETfirstt_(set, type)
     return first element of set as a type

*/
#define SETfirstt_(set, type)      ((type*)((set)->e[0].p))

/*-----------------------------------------

   SETsecond_(set)
     return second element of set

*/
#define SETsecond_(set)            ((set)->e[1].p)

/*-----------------------------------------

   SETsecondt_(set, type)
     return second element of set as a type
*/
#define SETsecondt_(set, type)     ((type*)((set)->e[1].p))

/*-----------------------------------------

   SETaddr_(set, type)
       return address of set's elements
*/
#define SETaddr_(set,type)         ((type **)(&((set)->e[0].p)))

/*-----------------------------------------

   SETreturnsize_(set, size)
     return size of a set

   notes:
      set must be defined
      use qh_setsize(set) unless speed is critical
*/
#define SETreturnsize_(set, size) (((size)= ((set)->e[(set)->maxsize].i))?(--(size)):((size)= (set)->maxsize))

/*-----------------------------------------

   SETempty_(set)
     return true(1) if set is empty

   notes:
      set may be NULL
*/
#define SETempty_(set)            (!set || (SETfirst_(set) ? 0 : 1))

/*---------------------------------

  SETsizeaddr_(set)
    return pointer to 'actual size+1' of set (set CANNOT be NULL!!)
    Its type is setelemT* for strict aliasing
    All SETelemaddr_ must be cast to setelemT


  notes:
    *SETsizeaddr==NULL or e[*SETsizeaddr-1].p==NULL
*/
#define SETsizeaddr_(set) (&((set)->e[(set)->maxsize]))

/*-----------------------------------------

   SETtruncate_(set, size)
     truncate set to size

   see:
     qh_settruncate()

*/
#define SETtruncate_(set, size) {set->e[set->maxsize].i= size+1; /* maybe overwritten */ \
      set->e[size].p= NULL;}

/*======= prototypes in alphabetical order ============*/

void  qh_setaddsorted(setT **setp, void *elem);
void  qh_setaddnth(setT **setp, int nth, void *newelem);
void  qh_setappend(setT **setp, void *elem);
void  qh_setappend_set(setT **setp, setT *setA);
void  qh_setappend2ndlast(setT **setp, void *elem);
void  qh_setcheck(setT *set, const char *tname, unsigned id);
void  qh_setcompact(setT *set);
setT *qh_setcopy(setT *set, int extra);
void *qh_setdel(setT *set, void *elem);
void *qh_setdellast(setT *set);
void *qh_setdelnth(setT *set, int nth);
void *qh_setdelnthsorted(setT *set, int nth);
void *qh_setdelsorted(setT *set, void *newelem);
setT *qh_setduplicate( setT *set, int elemsize);
int   qh_setequal(setT *setA, setT *setB);
int   qh_setequal_except(setT *setA, void *skipelemA, setT *setB, void *skipelemB);
int   qh_setequal_skip(setT *setA, int skipA, setT *setB, int skipB);
void **qh_setendpointer(setT *set);
void  qh_setfree(setT **set);
void  qh_setfree2( setT **setp, int elemsize);
void  qh_setfreelong(setT **set);
int   qh_setin(setT *set, void *setelem);
int   qh_setindex(setT *set, void *setelem);
void  qh_setlarger(setT **setp);
void *qh_setlast(setT *set);
setT *qh_setnew(int size);
setT *qh_setnew_delnthsorted(setT *set, int size, int nth, int prepend);
void  qh_setprint(FILE *fp, const char* string, setT *set);
void  qh_setreplace(setT *set, void *oldelem, void *newelem);
int   qh_setsize(setT *set);
setT *qh_settemp(int setsize);
void  qh_settempfree(setT **set);
void  qh_settempfree_all(void);
setT *qh_settemppop(void);
void  qh_settemppush(setT *set);
void  qh_settruncate(setT *set, int size);
int   qh_setunique(setT **set, void *elem);
void  qh_setzero(setT *set, int idx, int size);


#endif /* qhDEFset */
qhull-2012.1/src/libqhull/random.c0000644000076400010400000001432511663315545020151 0ustar  bbarberAdministrators/*
  ---------------------------------

   random.c -- utilities
     Park & Miller's minimimal standard random number generator
     argc/argv conversion

     Used by rbox.  Do not use 'qh' 
*/

#include "libqhull.h"
#include 
#include 
#include 

#ifdef _MSC_VER  /* Microsoft Visual C++ -- warning level 4 */
#pragma warning( disable : 4706)  /* assignment within conditional function */
#pragma warning( disable : 4996)  /* function was declared deprecated(strcpy, localtime, etc.) */
#endif

/*---------------------------------

 qh_argv_to_command( argc, argv, command, max_size )

    build command from argc/argv
    max_size is at least

 returns:
    a space-delimited string of options (just as typed)
    returns false if max_size is too short

 notes:
    silently removes
    makes option string easy to input and output
    matches qh_argv_to_command_size()

    argc may be 0
*/
int qh_argv_to_command(int argc, char *argv[], char* command, int max_size) {
  int i, remaining;
  char *s;
  *command= '\0';  /* max_size > 0 */

  if (argc) {
    if ((s= strrchr( argv[0], '\\')) /* get filename w/o .exe extension */
    || (s= strrchr( argv[0], '/')))
        s++;
    else
        s= argv[0];
    if ((int)strlen(s) < max_size)   /* WARN64 */
        strcpy(command, s);
    else
        goto error_argv;
    if ((s= strstr(command, ".EXE"))
    ||  (s= strstr(command, ".exe")))
        *s= '\0';
  }
  for (i=1; i < argc; i++) {
    s= argv[i];
    remaining= max_size - (int)strlen(command) - (int)strlen(s) - 2;   /* WARN64 */
    if (!*s || strchr(s, ' ')) {
      char *t= command + strlen(command);
      remaining -= 2;
      if (remaining < 0) {
        goto error_argv;
      }
      *t++= ' ';
      *t++= '"';
      while (*s) {
        if (*s == '"') {
          if (--remaining < 0)
            goto error_argv;
          *t++= '\\';
        }
        *t++= *s++;
      }
      *t++= '"';
      *t= '\0';
    }else if (remaining < 0) {
      goto error_argv;
    }else
      strcat(command, " ");
      strcat(command, s);
  }
  return 1;

error_argv:
  return 0;
} /* argv_to_command */

/*---------------------------------

qh_argv_to_command_size( argc, argv )

    return size to allocate for qh_argv_to_command()

notes:
    argc may be 0
    actual size is usually shorter
*/
int qh_argv_to_command_size(int argc, char *argv[]) {
    unsigned int count= 1; /* null-terminator if argc==0 */
    int i;
    char *s;

    for (i=0; i0 && strchr(argv[i], ' ')) {
        count += 2;  /* quote delimiters */
        for (s=argv[i]; *s; s++) {
          if (*s == '"') {
            count++;
          }
        }
      }
    }
    return count;
} /* argv_to_command_size */

/*---------------------------------

  qh_rand()
  qh_srand( seed )
    generate pseudo-random number between 1 and 2^31 -2

  notes:
    For qhull and rbox, called from qh_RANDOMint(),etc. [user.h]

    From Park & Miller's minimal standard random number generator
      Communications of the ACM, 31:1192-1201, 1988.
    Does not use 0 or 2^31 -1
      this is silently enforced by qh_srand()
    Can make 'Rn' much faster by moving qh_rand to qh_distplane
*/

/* Global variables and constants */

int qh_rand_seed= 1;  /* define as global variable instead of using qh */

#define qh_rand_a 16807
#define qh_rand_m 2147483647
#define qh_rand_q 127773  /* m div a */
#define qh_rand_r 2836    /* m mod a */

int qh_rand( void) {
    int lo, hi, test;
    int seed = qh_rand_seed;

    hi = seed / qh_rand_q;  /* seed div q */
    lo = seed % qh_rand_q;  /* seed mod q */
    test = qh_rand_a * lo - qh_rand_r * hi;
    if (test > 0)
        seed= test;
    else
        seed= test + qh_rand_m;
    qh_rand_seed= seed;
    /* seed = seed < qh_RANDOMmax/2 ? 0 : qh_RANDOMmax;  for testing */
    /* seed = qh_RANDOMmax;  for testing */
    return seed;
} /* rand */

void qh_srand( int seed) {
    if (seed < 1)
        qh_rand_seed= 1;
    else if (seed >= qh_rand_m)
        qh_rand_seed= qh_rand_m - 1;
    else
        qh_rand_seed= seed;
} /* qh_srand */

/*---------------------------------

qh_randomfactor( scale, offset )
return a random factor r * scale + offset

notes:
qh.RANDOMa/b are defined in global.c
*/
realT qh_randomfactor(realT scale, realT offset) {
    realT randr;

    randr= qh_RANDOMint;
    return randr * scale + offset;
} /* randomfactor */

/*---------------------------------

qh_randommatrix( buffer, dim, rows )
generate a random dim X dim matrix in range [-1,1]
assumes buffer is [dim+1, dim]

returns:
sets buffer to random numbers
sets rows to rows of buffer
sets row[dim] as scratch row
*/
void qh_randommatrix(realT *buffer, int dim, realT **rows) {
    int i, k;
    realT **rowi, *coord, realr;

    coord= buffer;
    rowi= rows;
    for (i=0; i < dim; i++) {
        *(rowi++)= coord;
        for (k=0; k < dim; k++) {
            realr= qh_RANDOMint;
            *(coord++)= 2.0 * realr/(qh_RANDOMmax+1) - 1.0;
        }
    }
    *rowi= coord;
} /* randommatrix */

/*---------------------------------

  qh_strtol( s, endp) qh_strtod( s, endp)
    internal versions of strtol() and strtod()
    does not skip trailing spaces
  notes:
    some implementations of strtol()/strtod() skip trailing spaces
*/
double qh_strtod(const char *s, char **endp) {
  double result;

  result= strtod(s, endp);
  if (s < (*endp) && (*endp)[-1] == ' ')
    (*endp)--;
  return result;
} /* strtod */

int qh_strtol(const char *s, char **endp) {
  int result;

  result= (int) strtol(s, endp, 10);     /* WARN64 */
  if (s< (*endp) && (*endp)[-1] == ' ')
    (*endp)--;
  return result;
} /* strtol */
qhull-2012.1/src/libqhull/random.h0000644000076400010400000000164711710144467020155 0ustar  bbarberAdministrators/*
  ---------------------------------

  random.h
    header file for random routines

   see qh-geom.htm and random.c

   Copyright (c) 1993-2012 The Geometry Center.
   $Id: //main/2011/qhull/src/libqhull/random.h#3 $$Change: 1464 $
   $DateTime: 2012/01/25 22:58:41 $$Author: bbarber $
*/

#ifndef qhDEFrandom
#define qhDEFrandom 1

#include "libqhull.h"

/*============= prototypes in alphabetical order ======= */


int     qh_argv_to_command(int argc, char *argv[], char* command, int max_size);
int     qh_argv_to_command_size(int argc, char *argv[]);
int     qh_rand( void);
void    qh_srand( int seed);
realT   qh_randomfactor(realT scale, realT offset);
void    qh_randommatrix(realT *buffer, int dim, realT **row);
int     qh_strtol(const char *s, char **endp);
double  qh_strtod(const char *s, char **endp);

#endif /* qhDEFrandom */



qhull-2012.1/src/libqhull/rboxlib.c0000644000076400010400000005333711552177772020345 0ustar  bbarberAdministrators/*
  ---------------------------------

   rboxlib.c
     Generate input points

   notes:
     For documentation, see prompt[] of rbox.c
     50 points generated for 'rbox D4'

   WARNING:
     incorrect range if qh_RANDOMmax is defined wrong (user.h)
*/

#include "random.h"
#include "libqhull.h"

#include 
#include 
#include 
#include 
#include 
#include 
#include 
#include 

#ifdef _MSC_VER  /* Microsoft Visual C++ */
#pragma warning( disable : 4706)  /* assignment within conditional expression. */
#pragma warning( disable : 4996)  /* this function (strncat,sprintf,strcpy) or variable may be unsafe. */
#endif

#define MAXdim 200
#define PI 3.1415926535897932384

/* ------------------------------ prototypes ----------------*/
int roundi( double a);
void out1( double a);
void out2n( double a, double b);
void out3n( double a, double b, double c);

void    qh_fprintf_rbox(FILE *fp, int msgcode, const char *fmt, ... );
void    qh_free(void *mem);
void   *qh_malloc(size_t size);
int     qh_rand( void);
void    qh_srand( int seed);


/* ------------------------------ globals -------------------*/

/* No state is carried between rbox requests */
typedef struct rboxT rboxT;
struct rboxT {
  FILE *fout;
  FILE *ferr;
  int isinteger;
  double out_offset;
  jmp_buf errexit;        /* exit label for rboxpoints, defined by setjmp(), called by qh_errexit_rbox() */
};


int rbox_inuse= 0;
rboxT rbox;

/*---------------------------------

  qh_rboxpoints( fout, ferr, rbox_command )
    Generate points to fout according to rbox options
    Report errors on ferr

  returns:
    0 (qh_ERRnone) on success
    1 (qh_ERRinput) on input error
    4 (qh_ERRmem) on memory error
    5 (qh_ERRqhull) on internal error

  notes:
    To avoid stdio, redefine qh_malloc, qh_free, and qh_fprintf_rbox (user.c)
    Rbox is not multithreaded.

  design:
    Straight line code (consider defining a struct and functions):

    Parse arguments into variables
    Determine the number of points
    Generate the points
*/
int qh_rboxpoints(FILE* fout, FILE* ferr, char* rbox_command) {
  int i,j,k;
  int gendim;
  int cubesize, diamondsize, seed=0, count, apex;
  int dim=3 , numpoints= 0, totpoints, addpoints=0;
  int issphere=0, isaxis=0,  iscdd= 0, islens= 0, isregular=0, iswidth=0, addcube=0;
  int isgap=0, isspiral=0, NOcommand= 0, adddiamond=0;
  int israndom=0, istime=0;
  int isbox=0, issimplex=0, issimplex2=0, ismesh=0;
  double width=0.0, gap=0.0, radius= 0.0;
  double coord[MAXdim], offset, meshm=3.0, meshn=4.0, meshr=5.0;
  double *simplex= NULL, *simplexp;
  int nthroot, mult[MAXdim];
  double norm, factor, randr, rangap, lensangle= 0, lensbase= 1;
  double anglediff, angle, x, y, cube= 0.0, diamond= 0.0;
  double box= qh_DEFAULTbox; /* scale all numbers before output */
  double randmax= qh_RANDOMmax;
  char command[200], seedbuf[200];
  char *s= command, *t, *first_point= NULL;
  time_t timedata;
  int exitcode;

  if (rbox_inuse) {
    qh_fprintf_rbox(rbox.ferr, 6188, "rbox error: rbox in use by another process.  Please lock calls to rbox.\n");
    return qh_ERRqhull;
  }
  rbox_inuse= True;
  rbox.ferr= ferr;
  rbox.fout= fout;

  exitcode= setjmp(rbox.errexit);
  if (exitcode) {
    /* same code for error exit and normal return */
    if (simplex)
        qh_free(simplex);
    rbox_inuse= False;
    return exitcode;
  }

  *command= '\0';
  strncat(command, rbox_command, sizeof(command)-strlen(command)-1);

  while (*s && !isspace(*s))  /* skip program name */
    s++;
  while (*s) {
    while (*s && isspace(*s))
      s++;
    if (*s == '-')
      s++;
    if (!*s)
      break;
    if (isdigit(*s)) {
      numpoints= qh_strtol(s, &s);
      continue;
    }
    /* ============= read flags =============== */
    switch (*s++) {
    case 'c':
      addcube= 1;
      t= s;
      while (isspace(*t))
        t++;
      if (*t == 'G')
        cube= qh_strtod(++t, &s);
      break;
    case 'd':
      adddiamond= 1;
      t= s;
      while (isspace(*t))
        t++;
      if (*t == 'G')
        diamond= qh_strtod(++t, &s);
      break;
    case 'h':
      iscdd= 1;
      break;
    case 'l':
      isspiral= 1;
      break;
    case 'n':
      NOcommand= 1;
      break;
    case 'r':
      isregular= 1;
      break;
    case 's':
      issphere= 1;
      break;
    case 't':
      istime= 1;
      if (isdigit(*s)) {
        seed= qh_strtol(s, &s);
        israndom= 0;
      }else
        israndom= 1;
      break;
    case 'x':
      issimplex= 1;
      break;
    case 'y':
      issimplex2= 1;
      break;
    case 'z':
      rbox.isinteger= 1;
      break;
    case 'B':
      box= qh_strtod(s, &s);
      isbox= 1;
      break;
    case 'D':
      dim= qh_strtol(s, &s);
      if (dim < 1
      || dim > MAXdim) {
        qh_fprintf_rbox(rbox.ferr, 6189, "rbox error: dimension, D%d, out of bounds (>=%d or <=0)", dim, MAXdim);
        qh_errexit_rbox(qh_ERRinput);
      }
      break;
    case 'G':
      if (isdigit(*s))
        gap= qh_strtod(s, &s);
      else
        gap= 0.5;
      isgap= 1;
      break;
    case 'L':
      if (isdigit(*s))
        radius= qh_strtod(s, &s);
      else
        radius= 10;
      islens= 1;
      break;
    case 'M':
      ismesh= 1;
      if (*s)
        meshn= qh_strtod(s, &s);
      if (*s == ',') {
        ++s;
        meshm= qh_strtod(s, &s);
      }else
        meshm= 0.0;
      if (*s == ',') {
        ++s;
        meshr= qh_strtod(s, &s);
      }else
        meshr= sqrt(meshn*meshn + meshm*meshm);
      if (*s && !isspace(*s)) {
        qh_fprintf_rbox(rbox.ferr, 7069, "rbox warning: assuming 'M3,4,5' since mesh args are not integers or reals\n");
        meshn= 3.0, meshm=4.0, meshr=5.0;
      }
      break;
    case 'O':
      rbox.out_offset= qh_strtod(s, &s);
      break;
    case 'P':
      if (!first_point)
        first_point= s-1;
      addpoints++;
      while (*s && !isspace(*s))   /* read points later */
        s++;
      break;
    case 'W':
      width= qh_strtod(s, &s);
      iswidth= 1;
      break;
    case 'Z':
      if (isdigit(*s))
        radius= qh_strtod(s, &s);
      else
        radius= 1.0;
      isaxis= 1;
      break;
    default:
      qh_fprintf_rbox(rbox.ferr, 7070, "rbox error: unknown flag at %s.\nExecute 'rbox' without arguments for documentation.\n", s);
      qh_errexit_rbox(qh_ERRinput);
    }
    if (*s && !isspace(*s)) {
      qh_fprintf_rbox(rbox.ferr, 7071, "rbox error: missing space between flags at %s.\n", s);
      qh_errexit_rbox(qh_ERRinput);
    }
  }

  /* ============= defaults, constants, and sizes =============== */
  if (rbox.isinteger && !isbox)
    box= qh_DEFAULTzbox;
  if (addcube) {
    cubesize= (int)floor(ldexp(1.0,dim)+0.5);
    if (cube == 0.0)
      cube= box;
  }else
    cubesize= 0;
  if (adddiamond) {
    diamondsize= 2*dim;
    if (diamond == 0.0)
      diamond= box;
  }else
    diamondsize= 0;
  if (islens) {
    if (isaxis) {
        qh_fprintf_rbox(rbox.ferr, 6190, "rbox error: can not combine 'Ln' with 'Zn'\n");
        qh_errexit_rbox(qh_ERRinput);
    }
    if (radius <= 1.0) {
        qh_fprintf_rbox(rbox.ferr, 6191, "rbox error: lens radius %.2g should be greater than 1.0\n",
               radius);
        qh_errexit_rbox(qh_ERRinput);
    }
    lensangle= asin(1.0/radius);
    lensbase= radius * cos(lensangle);
  }

  if (!numpoints) {
    if (issimplex2)
        ; /* ok */
    else if (isregular + issimplex + islens + issphere + isaxis + isspiral + iswidth + ismesh) {
        qh_fprintf_rbox(rbox.ferr, 6192, "rbox error: missing count\n");
        qh_errexit_rbox(qh_ERRinput);
    }else if (adddiamond + addcube + addpoints)
        ; /* ok */
    else {
        numpoints= 50;  /* ./rbox D4 is the test case */
        issphere= 1;
    }
  }
  if ((issimplex + islens + isspiral + ismesh > 1)
  || (issimplex + issphere + isspiral + ismesh > 1)) {
    qh_fprintf_rbox(rbox.ferr, 6193, "rbox error: can only specify one of 'l', 's', 'x', 'Ln', or 'Mn,m,r' ('Ln s' is ok).\n");
    qh_errexit_rbox(qh_ERRinput);
  }

  /* ============= print header with total points =============== */
  if (issimplex || ismesh)
    totpoints= numpoints;
  else if (issimplex2)
    totpoints= numpoints+dim+1;
  else if (isregular) {
    totpoints= numpoints;
    if (dim == 2) {
        if (islens)
          totpoints += numpoints - 2;
    }else if (dim == 3) {
        if (islens)
          totpoints += 2 * numpoints;
      else if (isgap)
        totpoints += 1 + numpoints;
      else
        totpoints += 2;
    }
  }else
    totpoints= numpoints + isaxis;
  totpoints += cubesize + diamondsize + addpoints;

  /* ============= seed randoms =============== */
  if (istime == 0) {
    for (s=command; *s; s++) {
      if (issimplex2 && *s == 'y') /* make 'y' same seed as 'x' */
        i= 'x';
      else
        i= *s;
      seed= 11*seed + i;
    }
  }else if (israndom) {
    seed= (int)time(&timedata);
    sprintf(seedbuf, " t%d", seed);  /* appends an extra t, not worth removing */
    strncat(command, seedbuf, sizeof(command)-strlen(command)-1);
    t= strstr(command, " t ");
    if (t)
      strcpy(t+1, t+3); /* remove " t " */
  } /* else, seed explicitly set to n */
  qh_RANDOMseed_(seed);

  /* ============= print header =============== */

  if (iscdd)
      qh_fprintf_rbox(rbox.fout, 9391, "%s\nbegin\n        %d %d %s\n",
      NOcommand ? "" : command,
      totpoints, dim+1,
      rbox.isinteger ? "integer" : "real");
  else if (NOcommand)
      qh_fprintf_rbox(rbox.fout, 9392, "%d\n%d\n", dim, totpoints);
  else
      qh_fprintf_rbox(rbox.fout, 9393, "%d %s\n%d\n", dim, command, totpoints);

  /* ============= explicit points =============== */
  if ((s= first_point)) {
    while (s && *s) { /* 'P' */
      count= 0;
      if (iscdd)
        out1( 1.0);
      while (*++s) {
        out1( qh_strtod(s, &s));
        count++;
        if (isspace(*s) || !*s)
          break;
        if (*s != ',') {
          qh_fprintf_rbox(rbox.ferr, 6194, "rbox error: missing comma after coordinate in %s\n\n", s);
          qh_errexit_rbox(qh_ERRinput);
        }
      }
      if (count < dim) {
        for (k=dim-count; k--; )
          out1( 0.0);
      }else if (count > dim) {
        qh_fprintf_rbox(rbox.ferr, 6195, "rbox error: %d coordinates instead of %d coordinates in %s\n\n",
                  count, dim, s);
        qh_errexit_rbox(qh_ERRinput);
      }
      qh_fprintf_rbox(rbox.fout, 9394, "\n");
      while ((s= strchr(s, 'P'))) {
        if (isspace(s[-1]))
          break;
      }
    }
  }

  /* ============= simplex distribution =============== */
  if (issimplex+issimplex2) {
    if (!(simplex= (double*)qh_malloc( dim * (dim+1) * sizeof(double)))) {
      qh_fprintf_rbox(rbox.ferr, 6196, "rbox error: insufficient memory for simplex\n");
      qh_errexit_rbox(qh_ERRmem); /* qh_ERRmem */
    }
    simplexp= simplex;
    if (isregular) {
      for (i=0; i randmax/2)
          coord[dim-1]= -coord[dim-1];
      /* ============= project 'Wn' point toward boundary =============== */
      }else if (iswidth && !issphere) {
        j= qh_RANDOMint % gendim;
        if (coord[j] < 0)
          coord[j]= -1.0 - coord[j] * width;
        else
          coord[j]= 1.0 - coord[j] * width;
      }
      /* ============= write point =============== */
      if (iscdd)
        out1( 1.0);
      for (k=0; k < dim; k++)
        out1( coord[k] * box);
      qh_fprintf_rbox(rbox.fout, 9399, "\n");
    }
  }

  /* ============= write cube vertices =============== */
  if (addcube) {
    for (j=0; j=0; k--) {
        if (j & ( 1 << k))
          out1( cube);
        else
          out1( -cube);
      }
      qh_fprintf_rbox(rbox.fout, 9400, "\n");
    }
  }

  /* ============= write diamond vertices =============== */
  if (adddiamond) {
    for (j=0; j=0; k--) {
        if (j/2 != k)
          out1( 0.0);
        else if (j & 0x1)
          out1( diamond);
        else
          out1( -diamond);
      }
      qh_fprintf_rbox(rbox.fout, 9401, "\n");
    }
  }

  if (iscdd)
    qh_fprintf_rbox(rbox.fout, 9402, "end\nhull\n");

  /* same code for error exit and normal return */
  if (simplex)
    qh_free(simplex);
  rbox_inuse= False;
  return qh_ERRnone;
} /* rboxpoints */

/*------------------------------------------------
outxxx - output functions
*/
int roundi( double a) {
  if (a < 0.0) {
    if (a - 0.5 < INT_MIN) {
      qh_fprintf_rbox(rbox.ferr, 6200, "rbox input error: negative coordinate %2.2g is too large.  Reduce 'Bn'\n", a);
      qh_errexit_rbox(qh_ERRinput);
    }
    return (int)(a - 0.5);
  }else {
    if (a + 0.5 > INT_MAX) {
      qh_fprintf_rbox(rbox.ferr, 6201, "rbox input error: coordinate %2.2g is too large.  Reduce 'Bn'\n", a);
      qh_errexit_rbox(qh_ERRinput);
    }
    return (int)(a + 0.5);
  }
} /* roundi */

void out1(double a) {

  if (rbox.isinteger)
    qh_fprintf_rbox(rbox.fout, 9403, "%d ", roundi( a+rbox.out_offset));
  else
    qh_fprintf_rbox(rbox.fout, 9404, qh_REAL_1, a+rbox.out_offset);
} /* out1 */

void out2n( double a, double b) {

  if (rbox.isinteger)
    qh_fprintf_rbox(rbox.fout, 9405, "%d %d\n", roundi(a+rbox.out_offset), roundi(b+rbox.out_offset));
  else
    qh_fprintf_rbox(rbox.fout, 9406, qh_REAL_2n, a+rbox.out_offset, b+rbox.out_offset);
} /* out2n */

void out3n( double a, double b, double c) {

  if (rbox.isinteger)
    qh_fprintf_rbox(rbox.fout, 9407, "%d %d %d\n", roundi(a+rbox.out_offset), roundi(b+rbox.out_offset), roundi(c+rbox.out_offset));
  else
    qh_fprintf_rbox(rbox.fout, 9408, qh_REAL_3n, a+rbox.out_offset, b+rbox.out_offset, c+rbox.out_offset);
} /* out3n */

void qh_errexit_rbox(int exitcode)
{
    longjmp(rbox.errexit, exitcode);
} /* rbox_errexit */

qhull-2012.1/src/libqhull/stat.c0000644000076400010400000007344611710144467017651 0ustar  bbarberAdministrators/*
  ---------------------------------

   stat.c
   contains all statistics that are collected for qhull

   see qh-stat.htm and stat.h

   Copyright (c) 1993-2012 The Geometry Center.
   $Id: //main/2011/qhull/src/libqhull/stat.c#3 $$Change: 1464 $
   $DateTime: 2012/01/25 22:58:41 $$Author: bbarber $
*/

#include "qhull_a.h"

/*============ global data structure ==========*/

#if qh_QHpointer
qhstatT *qh_qhstat=NULL;  /* global data structure */
#else
qhstatT qh_qhstat;   /* add "={0}" if this causes a compiler error */
#endif

/*========== functions in alphabetic order ================*/

/*---------------------------------

  qh_allstatA()
    define statistics in groups of 20

  notes:
    (otherwise, 'gcc -O2' uses too much memory)
    uses qhstat.next
*/
void qh_allstatA(void) {

   /* zdef_(type,name,doc,average) */
  zzdef_(zdoc, Zdoc2, "precision statistics", -1);
  zdef_(zinc, Znewvertex, NULL, -1);
  zdef_(wadd, Wnewvertex, "ave. distance of a new vertex to a facet(!0s)", Znewvertex);
  zzdef_(wmax, Wnewvertexmax, "max. distance of a new vertex to a facet", -1);
  zdef_(wmax, Wvertexmax, "max. distance of an output vertex to a facet", -1);
  zdef_(wmin, Wvertexmin, "min. distance of an output vertex to a facet", -1);
  zdef_(wmin, Wmindenom, "min. denominator in hyperplane computation", -1);

  qhstat precision= qhstat next;  /* call qh_precision for each of these */
  zzdef_(zdoc, Zdoc3, "precision problems (corrected unless 'Q0' or an error)", -1);
  zzdef_(zinc, Zcoplanarridges, "coplanar half ridges in output", -1);
  zzdef_(zinc, Zconcaveridges, "concave half ridges in output", -1);
  zzdef_(zinc, Zflippedfacets, "flipped facets", -1);
  zzdef_(zinc, Zcoplanarhorizon, "coplanar horizon facets for new vertices", -1);
  zzdef_(zinc, Zcoplanarpart, "coplanar points during partitioning", -1);
  zzdef_(zinc, Zminnorm, "degenerate hyperplanes recomputed with gaussian elimination", -1);
  zzdef_(zinc, Znearlysingular, "nearly singular or axis-parallel hyperplanes", -1);
  zzdef_(zinc, Zback0, "zero divisors during back substitute", -1);
  zzdef_(zinc, Zgauss0, "zero divisors during gaussian elimination", -1);
  zzdef_(zinc, Zmultiridge, "ridges with multiple neighbors", -1);
}
void qh_allstatB(void) {
  zzdef_(zdoc, Zdoc1, "summary information", -1);
  zdef_(zinc, Zvertices, "number of vertices in output", -1);
  zdef_(zinc, Znumfacets, "number of facets in output", -1);
  zdef_(zinc, Znonsimplicial, "number of non-simplicial facets in output", -1);
  zdef_(zinc, Znowsimplicial, "number of simplicial facets that were merged", -1);
  zdef_(zinc, Znumridges, "number of ridges in output", -1);
  zdef_(zadd, Znumridges, "average number of ridges per facet", Znumfacets);
  zdef_(zmax, Zmaxridges, "maximum number of ridges", -1);
  zdef_(zadd, Znumneighbors, "average number of neighbors per facet", Znumfacets);
  zdef_(zmax, Zmaxneighbors, "maximum number of neighbors", -1);
  zdef_(zadd, Znumvertices, "average number of vertices per facet", Znumfacets);
  zdef_(zmax, Zmaxvertices, "maximum number of vertices", -1);
  zdef_(zadd, Znumvneighbors, "average number of neighbors per vertex", Zvertices);
  zdef_(zmax, Zmaxvneighbors, "maximum number of neighbors", -1);
  zdef_(wadd, Wcpu, "cpu seconds for qhull after input", -1);
  zdef_(zinc, Ztotvertices, "vertices created altogether", -1);
  zzdef_(zinc, Zsetplane, "facets created altogether", -1);
  zdef_(zinc, Ztotridges, "ridges created altogether", -1);
  zdef_(zinc, Zpostfacets, "facets before post merge", -1);
  zdef_(zadd, Znummergetot, "average merges per facet(at most 511)", Znumfacets);
  zdef_(zmax, Znummergemax, "  maximum merges for a facet(at most 511)", -1);
  zdef_(zinc, Zangle, NULL, -1);
  zdef_(wadd, Wangle, "average angle(cosine) of facet normals for all ridges", Zangle);
  zdef_(wmax, Wanglemax, "  maximum angle(cosine) of facet normals across a ridge", -1);
  zdef_(wmin, Wanglemin, "  minimum angle(cosine) of facet normals across a ridge", -1);
  zdef_(wadd, Wareatot, "total area of facets", -1);
  zdef_(wmax, Wareamax, "  maximum facet area", -1);
  zdef_(wmin, Wareamin, "  minimum facet area", -1);
}
void qh_allstatC(void) {
  zdef_(zdoc, Zdoc9, "build hull statistics", -1);
  zzdef_(zinc, Zprocessed, "points processed", -1);
  zzdef_(zinc, Zretry, "retries due to precision problems", -1);
  zdef_(wmax, Wretrymax, "  max. random joggle", -1);
  zdef_(zmax, Zmaxvertex, "max. vertices at any one time", -1);
  zdef_(zinc, Ztotvisible, "ave. visible facets per iteration", Zprocessed);
  zdef_(zinc, Zinsidevisible, "  ave. visible facets without an horizon neighbor", Zprocessed);
  zdef_(zadd, Zvisfacettot,  "  ave. facets deleted per iteration", Zprocessed);
  zdef_(zmax, Zvisfacetmax,  "    maximum", -1);
  zdef_(zadd, Zvisvertextot, "ave. visible vertices per iteration", Zprocessed);
  zdef_(zmax, Zvisvertexmax, "    maximum", -1);
  zdef_(zinc, Ztothorizon, "ave. horizon facets per iteration", Zprocessed);
  zdef_(zadd, Znewfacettot,  "ave. new or merged facets per iteration", Zprocessed);
  zdef_(zmax, Znewfacetmax,  "    maximum(includes initial simplex)", -1);
  zdef_(wadd, Wnewbalance, "average new facet balance", Zprocessed);
  zdef_(wadd, Wnewbalance2, "  standard deviation", -1);
  zdef_(wadd, Wpbalance, "average partition balance", Zpbalance);
  zdef_(wadd, Wpbalance2, "  standard deviation", -1);
  zdef_(zinc, Zpbalance, "  number of trials", -1);
  zdef_(zinc, Zsearchpoints, "searches of all points for initial simplex", -1);
  zdef_(zinc, Zdetsimplex, "determinants computed(area & initial hull)", -1);
  zdef_(zinc, Znoarea, "determinants not computed because vertex too low", -1);
  zdef_(zinc, Znotmax, "points ignored(!above max_outside)", -1);
  zdef_(zinc, Znotgood, "points ignored(!above a good facet)", -1);
  zdef_(zinc, Znotgoodnew, "points ignored(didn't create a good new facet)", -1);
  zdef_(zinc, Zgoodfacet, "good facets found", -1);
  zzdef_(zinc, Znumvisibility, "distance tests for facet visibility", -1);
  zdef_(zinc, Zdistvertex, "distance tests to report minimum vertex", -1);
  zzdef_(zinc, Ztotcheck, "points checked for facets' outer planes", -1);
  zzdef_(zinc, Zcheckpart, "  ave. distance tests per check", Ztotcheck);
}
void qh_allstatD(void) {
  zdef_(zinc, Zvisit, "resets of visit_id", -1);
  zdef_(zinc, Zvvisit, "  resets of vertex_visit", -1);
  zdef_(zmax, Zvisit2max, "  max visit_id/2", -1);
  zdef_(zmax, Zvvisit2max, "  max vertex_visit/2", -1);

  zdef_(zdoc, Zdoc4, "partitioning statistics(see previous for outer planes)", -1);
  zzdef_(zadd, Zdelvertextot, "total vertices deleted", -1);
  zdef_(zmax, Zdelvertexmax, "    maximum vertices deleted per iteration", -1);
  zdef_(zinc, Zfindbest, "calls to findbest", -1);
  zdef_(zadd, Zfindbesttot, " ave. facets tested", Zfindbest);
  zdef_(zmax, Zfindbestmax, " max. facets tested", -1);
  zdef_(zadd, Zfindcoplanar, " ave. coplanar search", Zfindbest);
  zdef_(zinc, Zfindnew, "calls to findbestnew", -1);
  zdef_(zadd, Zfindnewtot, " ave. facets tested", Zfindnew);
  zdef_(zmax, Zfindnewmax, " max. facets tested", -1);
  zdef_(zinc, Zfindnewjump, " ave. clearly better", Zfindnew);
  zdef_(zinc, Zfindnewsharp, " calls due to qh_sharpnewfacets", -1);
  zdef_(zinc, Zfindhorizon, "calls to findhorizon", -1);
  zdef_(zadd, Zfindhorizontot, " ave. facets tested", Zfindhorizon);
  zdef_(zmax, Zfindhorizonmax, " max. facets tested", -1);
  zdef_(zinc, Zfindjump,       " ave. clearly better", Zfindhorizon);
  zdef_(zinc, Zparthorizon, " horizon facets better than bestfacet", -1);
  zdef_(zinc, Zpartangle, "angle tests for repartitioned coplanar points", -1);
  zdef_(zinc, Zpartflip, "  repartitioned coplanar points for flipped orientation", -1);
}
void qh_allstatE(void) {
  zdef_(zinc, Zpartinside, "inside points", -1);
  zdef_(zinc, Zpartnear, "  inside points kept with a facet", -1);
  zdef_(zinc, Zcoplanarinside, "  inside points that were coplanar with a facet", -1);
  zdef_(zinc, Zbestlower, "calls to findbestlower", -1);
  zdef_(zinc, Zbestlowerv, "  with search of vertex neighbors", -1);
  zdef_(wadd, Wmaxout, "difference in max_outside at final check", -1);
  zzdef_(zinc, Zpartitionall, "distance tests for initial partition", -1);
  zdef_(zinc, Ztotpartition, "partitions of a point", -1);
  zzdef_(zinc, Zpartition, "distance tests for partitioning", -1);
  zzdef_(zinc, Zdistcheck, "distance tests for checking flipped facets", -1);
  zzdef_(zinc, Zdistconvex, "distance tests for checking convexity", -1);
  zdef_(zinc, Zdistgood, "distance tests for checking good point", -1);
  zdef_(zinc, Zdistio, "distance tests for output", -1);
  zdef_(zinc, Zdiststat, "distance tests for statistics", -1);
  zdef_(zinc, Zdistplane, "total number of distance tests", -1);
  zdef_(zinc, Ztotpartcoplanar, "partitions of coplanar points or deleted vertices", -1);
  zzdef_(zinc, Zpartcoplanar, "   distance tests for these partitions", -1);
  zdef_(zinc, Zcomputefurthest, "distance tests for computing furthest", -1);
}
void qh_allstatE2(void) {
  zdef_(zdoc, Zdoc5, "statistics for matching ridges", -1);
  zdef_(zinc, Zhashlookup, "total lookups for matching ridges of new facets", -1);
  zdef_(zinc, Zhashtests, "average number of tests to match a ridge", Zhashlookup);
  zdef_(zinc, Zhashridge, "total lookups of subridges(duplicates and boundary)", -1);
  zdef_(zinc, Zhashridgetest, "average number of tests per subridge", Zhashridge);
  zdef_(zinc, Zdupsame, "duplicated ridges in same merge cycle", -1);
  zdef_(zinc, Zdupflip, "duplicated ridges with flipped facets", -1);

  zdef_(zdoc, Zdoc6, "statistics for determining merges", -1);
  zdef_(zinc, Zangletests, "angles computed for ridge convexity", -1);
  zdef_(zinc, Zbestcentrum, "best merges used centrum instead of vertices",-1);
  zzdef_(zinc, Zbestdist, "distance tests for best merge", -1);
  zzdef_(zinc, Zcentrumtests, "distance tests for centrum convexity", -1);
  zzdef_(zinc, Zdistzero, "distance tests for checking simplicial convexity", -1);
  zdef_(zinc, Zcoplanarangle, "coplanar angles in getmergeset", -1);
  zdef_(zinc, Zcoplanarcentrum, "coplanar centrums in getmergeset", -1);
  zdef_(zinc, Zconcaveridge, "concave ridges in getmergeset", -1);
}
void qh_allstatF(void) {
  zdef_(zdoc, Zdoc7, "statistics for merging", -1);
  zdef_(zinc, Zpremergetot, "merge iterations", -1);
  zdef_(zadd, Zmergeinittot, "ave. initial non-convex ridges per iteration", Zpremergetot);
  zdef_(zadd, Zmergeinitmax, "  maximum", -1);
  zdef_(zadd, Zmergesettot, "  ave. additional non-convex ridges per iteration", Zpremergetot);
  zdef_(zadd, Zmergesetmax, "  maximum additional in one pass", -1);
  zdef_(zadd, Zmergeinittot2, "initial non-convex ridges for post merging", -1);
  zdef_(zadd, Zmergesettot2, "  additional non-convex ridges", -1);
  zdef_(wmax, Wmaxoutside, "max distance of vertex or coplanar point above facet(w/roundoff)", -1);
  zdef_(wmin, Wminvertex, "max distance of merged vertex below facet(or roundoff)", -1);
  zdef_(zinc, Zwidefacet, "centrums frozen due to a wide merge", -1);
  zdef_(zinc, Zwidevertices, "centrums frozen due to extra vertices", -1);
  zzdef_(zinc, Ztotmerge, "total number of facets or cycles of facets merged", -1);
  zdef_(zinc, Zmergesimplex, "merged a simplex", -1);
  zdef_(zinc, Zonehorizon, "simplices merged into coplanar horizon", -1);
  zzdef_(zinc, Zcyclehorizon, "cycles of facets merged into coplanar horizon", -1);
  zzdef_(zadd, Zcyclefacettot, "  ave. facets per cycle", Zcyclehorizon);
  zdef_(zmax, Zcyclefacetmax, "  max. facets", -1);
  zdef_(zinc, Zmergeintohorizon, "new facets merged into horizon", -1);
  zdef_(zinc, Zmergenew, "new facets merged", -1);
  zdef_(zinc, Zmergehorizon, "horizon facets merged into new facets", -1);
  zdef_(zinc, Zmergevertex, "vertices deleted by merging", -1);
  zdef_(zinc, Zcyclevertex, "vertices deleted by merging into coplanar horizon", -1);
  zdef_(zinc, Zdegenvertex, "vertices deleted by degenerate facet", -1);
  zdef_(zinc, Zmergeflipdup, "merges due to flipped facets in duplicated ridge", -1);
  zdef_(zinc, Zneighbor, "merges due to redundant neighbors", -1);
  zdef_(zadd, Ztestvneighbor, "non-convex vertex neighbors", -1);
}
void qh_allstatG(void) {
  zdef_(zinc, Zacoplanar, "merges due to angle coplanar facets", -1);
  zdef_(wadd, Wacoplanartot, "  average merge distance", Zacoplanar);
  zdef_(wmax, Wacoplanarmax, "  maximum merge distance", -1);
  zdef_(zinc, Zcoplanar, "merges due to coplanar facets", -1);
  zdef_(wadd, Wcoplanartot, "  average merge distance", Zcoplanar);
  zdef_(wmax, Wcoplanarmax, "  maximum merge distance", -1);
  zdef_(zinc, Zconcave, "merges due to concave facets", -1);
  zdef_(wadd, Wconcavetot, "  average merge distance", Zconcave);
  zdef_(wmax, Wconcavemax, "  maximum merge distance", -1);
  zdef_(zinc, Zavoidold, "coplanar/concave merges due to avoiding old merge", -1);
  zdef_(wadd, Wavoidoldtot, "  average merge distance", Zavoidold);
  zdef_(wmax, Wavoidoldmax, "  maximum merge distance", -1);
  zdef_(zinc, Zdegen, "merges due to degenerate facets", -1);
  zdef_(wadd, Wdegentot, "  average merge distance", Zdegen);
  zdef_(wmax, Wdegenmax, "  maximum merge distance", -1);
  zdef_(zinc, Zflipped, "merges due to removing flipped facets", -1);
  zdef_(wadd, Wflippedtot, "  average merge distance", Zflipped);
  zdef_(wmax, Wflippedmax, "  maximum merge distance", -1);
  zdef_(zinc, Zduplicate, "merges due to duplicated ridges", -1);
  zdef_(wadd, Wduplicatetot, "  average merge distance", Zduplicate);
  zdef_(wmax, Wduplicatemax, "  maximum merge distance", -1);
}
void qh_allstatH(void) {
  zdef_(zdoc, Zdoc8, "renamed vertex statistics", -1);
  zdef_(zinc, Zrenameshare, "renamed vertices shared by two facets", -1);
  zdef_(zinc, Zrenamepinch, "renamed vertices in a pinched facet", -1);
  zdef_(zinc, Zrenameall, "renamed vertices shared by multiple facets", -1);
  zdef_(zinc, Zfindfail, "rename failures due to duplicated ridges", -1);
  zdef_(zinc, Zdupridge, "  duplicate ridges detected", -1);
  zdef_(zinc, Zdelridge, "deleted ridges due to renamed vertices", -1);
  zdef_(zinc, Zdropneighbor, "dropped neighbors due to renamed vertices", -1);
  zdef_(zinc, Zdropdegen, "degenerate facets due to dropped neighbors", -1);
  zdef_(zinc, Zdelfacetdup, "  facets deleted because of no neighbors", -1);
  zdef_(zinc, Zremvertex, "vertices removed from facets due to no ridges", -1);
  zdef_(zinc, Zremvertexdel, "  deleted", -1);
  zdef_(zinc, Zintersectnum, "vertex intersections for locating redundant vertices", -1);
  zdef_(zinc, Zintersectfail, "intersections failed to find a redundant vertex", -1);
  zdef_(zinc, Zintersect, "intersections found redundant vertices", -1);
  zdef_(zadd, Zintersecttot, "   ave. number found per vertex", Zintersect);
  zdef_(zmax, Zintersectmax, "   max. found for a vertex", -1);
  zdef_(zinc, Zvertexridge, NULL, -1);
  zdef_(zadd, Zvertexridgetot, "  ave. number of ridges per tested vertex", Zvertexridge);
  zdef_(zmax, Zvertexridgemax, "  max. number of ridges per tested vertex", -1);

  zdef_(zdoc, Zdoc10, "memory usage statistics(in bytes)", -1);
  zdef_(zadd, Zmemfacets, "for facets and their normals, neighbor and vertex sets", -1);
  zdef_(zadd, Zmemvertices, "for vertices and their neighbor sets", -1);
  zdef_(zadd, Zmempoints, "for input points and outside and coplanar sets",-1);
  zdef_(zadd, Zmemridges, "for ridges and their vertex sets", -1);
} /* allstat */

void qh_allstatI(void) {
  qhstat vridges= qhstat next;
  zzdef_(zdoc, Zdoc11, "Voronoi ridge statistics", -1);
  zzdef_(zinc, Zridge, "non-simplicial Voronoi vertices for all ridges", -1);
  zzdef_(wadd, Wridge, "  ave. distance to ridge", Zridge);
  zzdef_(wmax, Wridgemax, "  max. distance to ridge", -1);
  zzdef_(zinc, Zridgemid, "bounded ridges", -1);
  zzdef_(wadd, Wridgemid, "  ave. distance of midpoint to ridge", Zridgemid);
  zzdef_(wmax, Wridgemidmax, "  max. distance of midpoint to ridge", -1);
  zzdef_(zinc, Zridgeok, "bounded ridges with ok normal", -1);
  zzdef_(wadd, Wridgeok, "  ave. angle to ridge", Zridgeok);
  zzdef_(wmax, Wridgeokmax, "  max. angle to ridge", -1);
  zzdef_(zinc, Zridge0, "bounded ridges with near-zero normal", -1);
  zzdef_(wadd, Wridge0, "  ave. angle to ridge", Zridge0);
  zzdef_(wmax, Wridge0max, "  max. angle to ridge", -1);

  zdef_(zdoc, Zdoc12, "Triangulation statistics(Qt)", -1);
  zdef_(zinc, Ztricoplanar, "non-simplicial facets triangulated", -1);
  zdef_(zadd, Ztricoplanartot, "  ave. new facets created(may be deleted)", Ztricoplanar);
  zdef_(zmax, Ztricoplanarmax, "  max. new facets created", -1);
  zdef_(zinc, Ztrinull, "null new facets deleted(duplicated vertex)", -1);
  zdef_(zinc, Ztrimirror, "mirrored pairs of new facets deleted(same vertices)", -1);
  zdef_(zinc, Ztridegen, "degenerate new facets in output(same ridge)", -1);
} /* allstat */

/*---------------------------------

  qh_allstatistics()
    reset printed flag for all statistics
*/
void qh_allstatistics(void) {
  int i;

  for(i=ZEND; i--; )
    qhstat printed[i]= False;
} /* allstatistics */

#if qh_KEEPstatistics
/*---------------------------------

  qh_collectstatistics()
    collect statistics for qh.facet_list

*/
void qh_collectstatistics(void) {
  facetT *facet, *neighbor, **neighborp;
  vertexT *vertex, **vertexp;
  realT dotproduct, dist;
  int sizneighbors, sizridges, sizvertices, i;

  qh old_randomdist= qh RANDOMdist;
  qh RANDOMdist= False;
  zval_(Zmempoints)= qh num_points * qh normal_size +
                             sizeof(qhT) + sizeof(qhstatT);
  zval_(Zmemfacets)= 0;
  zval_(Zmemridges)= 0;
  zval_(Zmemvertices)= 0;
  zval_(Zangle)= 0;
  wval_(Wangle)= 0.0;
  zval_(Znumridges)= 0;
  zval_(Znumfacets)= 0;
  zval_(Znumneighbors)= 0;
  zval_(Znumvertices)= 0;
  zval_(Znumvneighbors)= 0;
  zval_(Znummergetot)= 0;
  zval_(Znummergemax)= 0;
  zval_(Zvertices)= qh num_vertices - qh_setsize(qh del_vertices);
  if (qh MERGING || qh APPROXhull || qh JOGGLEmax < REALmax/2)
    wmax_(Wmaxoutside, qh max_outside);
  if (qh MERGING)
    wmin_(Wminvertex, qh min_vertex);
  FORALLfacets
    facet->seen= False;
  if (qh DELAUNAY) {
    FORALLfacets {
      if (facet->upperdelaunay != qh UPPERdelaunay)
        facet->seen= True; /* remove from angle statistics */
    }
  }
  FORALLfacets {
    if (facet->visible && qh NEWfacets)
      continue;
    sizvertices= qh_setsize(facet->vertices);
    sizneighbors= qh_setsize(facet->neighbors);
    sizridges= qh_setsize(facet->ridges);
    zinc_(Znumfacets);
    zadd_(Znumvertices, sizvertices);
    zmax_(Zmaxvertices, sizvertices);
    zadd_(Znumneighbors, sizneighbors);
    zmax_(Zmaxneighbors, sizneighbors);
    zadd_(Znummergetot, facet->nummerge);
    i= facet->nummerge; /* avoid warnings */
    zmax_(Znummergemax, i);
    if (!facet->simplicial) {
      if (sizvertices == qh hull_dim) {
        zinc_(Znowsimplicial);
      }else {
        zinc_(Znonsimplicial);
      }
    }
    if (sizridges) {
      zadd_(Znumridges, sizridges);
      zmax_(Zmaxridges, sizridges);
    }
    zadd_(Zmemfacets, sizeof(facetT) + qh normal_size + 2*sizeof(setT)
       + SETelemsize * (sizneighbors + sizvertices));
    if (facet->ridges) {
      zadd_(Zmemridges,
         sizeof(setT) + SETelemsize * sizridges + sizridges *
         (sizeof(ridgeT) + sizeof(setT) + SETelemsize * (qh hull_dim-1))/2);
    }
    if (facet->outsideset)
      zadd_(Zmempoints, sizeof(setT) + SETelemsize * qh_setsize(facet->outsideset));
    if (facet->coplanarset)
      zadd_(Zmempoints, sizeof(setT) + SETelemsize * qh_setsize(facet->coplanarset));
    if (facet->seen) /* Delaunay upper envelope */
      continue;
    facet->seen= True;
    FOREACHneighbor_(facet) {
      if (neighbor == qh_DUPLICATEridge || neighbor == qh_MERGEridge
          || neighbor->seen || !facet->normal || !neighbor->normal)
        continue;
      dotproduct= qh_getangle(facet->normal, neighbor->normal);
      zinc_(Zangle);
      wadd_(Wangle, dotproduct);
      wmax_(Wanglemax, dotproduct)
      wmin_(Wanglemin, dotproduct)
    }
    if (facet->normal) {
      FOREACHvertex_(facet->vertices) {
        zinc_(Zdiststat);
        qh_distplane(vertex->point, facet, &dist);
        wmax_(Wvertexmax, dist);
        wmin_(Wvertexmin, dist);
      }
    }
  }
  FORALLvertices {
    if (vertex->deleted)
      continue;
    zadd_(Zmemvertices, sizeof(vertexT));
    if (vertex->neighbors) {
      sizneighbors= qh_setsize(vertex->neighbors);
      zadd_(Znumvneighbors, sizneighbors);
      zmax_(Zmaxvneighbors, sizneighbors);
      zadd_(Zmemvertices, sizeof(vertexT) + SETelemsize * sizneighbors);
    }
  }
  qh RANDOMdist= qh old_randomdist;
} /* collectstatistics */
#endif /* qh_KEEPstatistics */

/*---------------------------------

  qh_freestatistics(  )
    free memory used for statistics
*/
void qh_freestatistics(void) {

#if qh_QHpointer
  qh_free(qh_qhstat);
  qh_qhstat= NULL;
#endif
} /* freestatistics */

/*---------------------------------

  qh_initstatistics(  )
    allocate and initialize statistics

  notes:
    uses qh_malloc() instead of qh_memalloc() since mem.c not set up yet
    NOerrors -- qh_initstatistics can not use qh_errexit().  One first call, qh_memalloc is not initialized.  Also invoked by QhullQh().
*/
void qh_initstatistics(void) {
  int i;
  realT realx;
  int intx;

#if qh_QHpointer
  if(qh_qhstat){  /* qh_initstatistics may be called from Qhull::resetStatistics() */
      qh_free(qh_qhstat);
      qh_qhstat= 0;
  }
  if (!(qh_qhstat= (qhstatT *)qh_malloc(sizeof(qhstatT)))) {
    qh_fprintf(qhmem.ferr, 6183, "qhull error (qh_initstatistics): insufficient memory\n");
    qh_exit(qh_ERRmem);  /* can not use qh_errexit() */
  }
#endif

  qhstat next= 0;
  qh_allstatA();
  qh_allstatB();
  qh_allstatC();
  qh_allstatD();
  qh_allstatE();
  qh_allstatE2();
  qh_allstatF();
  qh_allstatG();
  qh_allstatH();
  qh_allstatI();
  if (qhstat next > (int)sizeof(qhstat id)) {
    qh_fprintf(qhmem.ferr, 6184, "qhull error (qh_initstatistics): increase size of qhstat.id[].\n\
      qhstat.next %d should be <= sizeof(qhstat id) %d\n", qhstat next, (int)sizeof(qhstat id));
#if 0 /* for locating error, Znumridges should be duplicated */
    for(i=0; i < ZEND; i++) {
      int j;
      for(j=i+1; j < ZEND; j++) {
        if (qhstat id[i] == qhstat id[j]) {
          qh_fprintf(qhmem.ferr, 6185, "qhull error (qh_initstatistics): duplicated statistic %d at indices %d and %d\n",
              qhstat id[i], i, j);
        }
      }
    }
#endif
    qh_exit(qh_ERRqhull);  /* can not use qh_errexit() */
  }
  qhstat init[zinc].i= 0;
  qhstat init[zadd].i= 0;
  qhstat init[zmin].i= INT_MAX;
  qhstat init[zmax].i= INT_MIN;
  qhstat init[wadd].r= 0;
  qhstat init[wmin].r= REALmax;
  qhstat init[wmax].r= -REALmax;
  for(i=0; i < ZEND; i++) {
    if (qhstat type[i] > ZTYPEreal) {
      realx= qhstat init[(unsigned char)(qhstat type[i])].r;
      qhstat stats[i].r= realx;
    }else if (qhstat type[i] != zdoc) {
      intx= qhstat init[(unsigned char)(qhstat type[i])].i;
      qhstat stats[i].i= intx;
    }
  }
} /* initstatistics */

/*---------------------------------

  qh_newstats(  )
    returns True if statistics for zdoc

  returns:
    next zdoc
*/
boolT qh_newstats(int idx, int *nextindex) {
  boolT isnew= False;
  int start, i;

  if (qhstat type[qhstat id[idx]] == zdoc)
    start= idx+1;
  else
    start= idx;
  for(i= start; i < qhstat next && qhstat type[qhstat id[i]] != zdoc; i++) {
    if (!qh_nostatistic(qhstat id[i]) && !qhstat printed[qhstat id[i]])
        isnew= True;
  }
  *nextindex= i;
  return isnew;
} /* newstats */

/*---------------------------------

  qh_nostatistic( index )
    true if no statistic to print
*/
boolT qh_nostatistic(int i) {

  if ((qhstat type[i] > ZTYPEreal
       &&qhstat stats[i].r == qhstat init[(unsigned char)(qhstat type[i])].r)
      || (qhstat type[i] < ZTYPEreal
          &&qhstat stats[i].i == qhstat init[(unsigned char)(qhstat type[i])].i))
    return True;
  return False;
} /* nostatistic */

#if qh_KEEPstatistics
/*---------------------------------

  qh_printallstatistics( fp, string )
    print all statistics with header 'string'
*/
void qh_printallstatistics(FILE *fp, const char *string) {

  qh_allstatistics();
  qh_collectstatistics();
  qh_printstatistics(fp, string);
  qh_memstatistics(fp);
}


/*---------------------------------

  qh_printstatistics( fp, string )
    print statistics to a file with header 'string'
    skips statistics with qhstat.printed[] (reset with qh_allstatistics)

  see:
    qh_printallstatistics()
*/
void qh_printstatistics(FILE *fp, const char *string) {
  int i, k;
  realT ave;

  if (qh num_points != qh num_vertices) {
    wval_(Wpbalance)= 0;
    wval_(Wpbalance2)= 0;
  }else
    wval_(Wpbalance2)= qh_stddev(zval_(Zpbalance), wval_(Wpbalance),
                                 wval_(Wpbalance2), &ave);
  wval_(Wnewbalance2)= qh_stddev(zval_(Zprocessed), wval_(Wnewbalance),
                                 wval_(Wnewbalance2), &ave);
  qh_fprintf(fp, 9350, "\n\
%s\n\
 qhull invoked by: %s | %s\n%s with options:\n%s\n", string, qh rbox_command,
     qh qhull_command, qh_version, qh qhull_options);
  qh_fprintf(fp, 9351, "\nprecision constants:\n\
 %6.2g max. abs. coordinate in the (transformed) input('Qbd:n')\n\
 %6.2g max. roundoff error for distance computation('En')\n\
 %6.2g max. roundoff error for angle computations\n\
 %6.2g min. distance for outside points ('Wn')\n\
 %6.2g min. distance for visible facets ('Vn')\n\
 %6.2g max. distance for coplanar facets ('Un')\n\
 %6.2g max. facet width for recomputing centrum and area\n\
",
  qh MAXabs_coord, qh DISTround, qh ANGLEround, qh MINoutside,
        qh MINvisible, qh MAXcoplanar, qh WIDEfacet);
  if (qh KEEPnearinside)
    qh_fprintf(fp, 9352, "\
 %6.2g max. distance for near-inside points\n", qh NEARinside);
  if (qh premerge_cos < REALmax/2) qh_fprintf(fp, 9353, "\
 %6.2g max. cosine for pre-merge angle\n", qh premerge_cos);
  if (qh PREmerge) qh_fprintf(fp, 9354, "\
 %6.2g radius of pre-merge centrum\n", qh premerge_centrum);
  if (qh postmerge_cos < REALmax/2) qh_fprintf(fp, 9355, "\
 %6.2g max. cosine for post-merge angle\n", qh postmerge_cos);
  if (qh POSTmerge) qh_fprintf(fp, 9356, "\
 %6.2g radius of post-merge centrum\n", qh postmerge_centrum);
  qh_fprintf(fp, 9357, "\
 %6.2g max. distance for merging two simplicial facets\n\
 %6.2g max. roundoff error for arithmetic operations\n\
 %6.2g min. denominator for divisions\n\
  zero diagonal for Gauss: ", qh ONEmerge, REALepsilon, qh MINdenom);
  for(k=0; k < qh hull_dim; k++)
    qh_fprintf(fp, 9358, "%6.2e ", qh NEARzero[k]);
  qh_fprintf(fp, 9359, "\n\n");
  for(i=0 ; i < qhstat next; )
    qh_printstats(fp, i, &i);
} /* printstatistics */
#endif /* qh_KEEPstatistics */

/*---------------------------------

  qh_printstatlevel( fp, id )
    print level information for a statistic

  notes:
    nop if id >= ZEND, printed, or same as initial value
*/
void qh_printstatlevel(FILE *fp, int id, int start) {
#define NULLfield "       "

  if (id >= ZEND || qhstat printed[id])
    return;
  if (qhstat type[id] == zdoc) {
    qh_fprintf(fp, 9360, "%s\n", qhstat doc[id]);
    return;
  }
  start= 0; /* not used */
  if (qh_nostatistic(id) || !qhstat doc[id])
    return;
  qhstat printed[id]= True;
  if (qhstat count[id] != -1
      && qhstat stats[(unsigned char)(qhstat count[id])].i == 0)
    qh_fprintf(fp, 9361, " *0 cnt*");
  else if (qhstat type[id] >= ZTYPEreal && qhstat count[id] == -1)
    qh_fprintf(fp, 9362, "%7.2g", qhstat stats[id].r);
  else if (qhstat type[id] >= ZTYPEreal && qhstat count[id] != -1)
    qh_fprintf(fp, 9363, "%7.2g", qhstat stats[id].r/ qhstat stats[(unsigned char)(qhstat count[id])].i);
  else if (qhstat type[id] < ZTYPEreal && qhstat count[id] == -1)
    qh_fprintf(fp, 9364, "%7d", qhstat stats[id].i);
  else if (qhstat type[id] < ZTYPEreal && qhstat count[id] != -1)
    qh_fprintf(fp, 9365, "%7.3g", (realT) qhstat stats[id].i / qhstat stats[(unsigned char)(qhstat count[id])].i);
  qh_fprintf(fp, 9366, " %s\n", qhstat doc[id]);
} /* printstatlevel */


/*---------------------------------

  qh_printstats( fp, index, nextindex )
    print statistics for a zdoc group

  returns:
    next zdoc if non-null
*/
void qh_printstats(FILE *fp, int idx, int *nextindex) {
  int j, nexti;

  if (qh_newstats(idx, &nexti)) {
    qh_fprintf(fp, 9367, "\n");
    for (j=idx; j--------------------------------

  qh_stddev( num, tot, tot2, ave )
    compute the standard deviation and average from statistics

    tot2 is the sum of the squares
  notes:
    computes r.m.s.:
      (x-ave)^2
      == x^2 - 2x tot/num +   (tot/num)^2
      == tot2 - 2 tot tot/num + tot tot/num
      == tot2 - tot ave
*/
realT qh_stddev(int num, realT tot, realT tot2, realT *ave) {
  realT stddev;

  *ave= tot/num;
  stddev= sqrt(tot2/num - *ave * *ave);
  return stddev;
} /* stddev */

#endif /* qh_KEEPstatistics */

#if !qh_KEEPstatistics
void    qh_collectstatistics(void) {}
void    qh_printallstatistics(FILE *fp, char *string) {};
void    qh_printstatistics(FILE *fp, char *string) {}
#endif

qhull-2012.1/src/libqhull/stat.h0000644000076400010400000003111511710144467017641 0ustar  bbarberAdministrators/*
  ---------------------------------

   stat.h
     contains all statistics that are collected for qhull

   see qh-stat.htm and stat.c

   Copyright (c) 1993-2012 The Geometry Center.
   $Id: //main/2011/qhull/src/libqhull/stat.h#5 $$Change: 1464 $
   $DateTime: 2012/01/25 22:58:41 $$Author: bbarber $

   recompile qhull if you change this file

   Integer statistics are Z* while real statistics are W*.

   define maydebugx to call a routine at every statistic event

*/

#ifndef qhDEFstat
#define qhDEFstat 1

#include "libqhull.h"

/*---------------------------------

  qh_KEEPstatistics
    0 turns off statistic gathering (except zzdef/zzinc/zzadd/zzval/wwval)
*/
#ifndef qh_KEEPstatistics
#define qh_KEEPstatistics 1
#endif

/*---------------------------------

  Zxxx for integers, Wxxx for reals

  notes:
    be sure that all statistics are defined in stat.c
      otherwise initialization may core dump
    can pick up all statistics by:
      grep '[zw].*_[(][ZW]' *.c >z.x
    remove trailers with query">-
    remove leaders with  query-replace-regexp [ ^I]+  (
*/
#if qh_KEEPstatistics
enum statistics {     /* alphabetical after Z/W */
    Zacoplanar,
    Wacoplanarmax,
    Wacoplanartot,
    Zangle,
    Wangle,
    Wanglemax,
    Wanglemin,
    Zangletests,
    Wareatot,
    Wareamax,
    Wareamin,
    Zavoidold,
    Wavoidoldmax,
    Wavoidoldtot,
    Zback0,
    Zbestcentrum,
    Zbestdist,
    Zbestlower,
    Zbestlowerv,
    Zcentrumtests,
    Zcheckpart,
    Zcomputefurthest,
    Zconcave,
    Wconcavemax,
    Wconcavetot,
    Zconcaveridges,
    Zconcaveridge,
    Zcoplanar,
    Wcoplanarmax,
    Wcoplanartot,
    Zcoplanarangle,
    Zcoplanarcentrum,
    Zcoplanarhorizon,
    Zcoplanarinside,
    Zcoplanarpart,
    Zcoplanarridges,
    Wcpu,
    Zcyclefacetmax,
    Zcyclefacettot,
    Zcyclehorizon,
    Zcyclevertex,
    Zdegen,
    Wdegenmax,
    Wdegentot,
    Zdegenvertex,
    Zdelfacetdup,
    Zdelridge,
    Zdelvertextot,
    Zdelvertexmax,
    Zdetsimplex,
    Zdistcheck,
    Zdistconvex,
    Zdistgood,
    Zdistio,
    Zdistplane,
    Zdiststat,
    Zdistvertex,
    Zdistzero,
    Zdoc1,
    Zdoc2,
    Zdoc3,
    Zdoc4,
    Zdoc5,
    Zdoc6,
    Zdoc7,
    Zdoc8,
    Zdoc9,
    Zdoc10,
    Zdoc11,
    Zdoc12,
    Zdropdegen,
    Zdropneighbor,
    Zdupflip,
    Zduplicate,
    Wduplicatemax,
    Wduplicatetot,
    Zdupridge,
    Zdupsame,
    Zflipped,
    Wflippedmax,
    Wflippedtot,
    Zflippedfacets,
    Zfindbest,
    Zfindbestmax,
    Zfindbesttot,
    Zfindcoplanar,
    Zfindfail,
    Zfindhorizon,
    Zfindhorizonmax,
    Zfindhorizontot,
    Zfindjump,
    Zfindnew,
    Zfindnewmax,
    Zfindnewtot,
    Zfindnewjump,
    Zfindnewsharp,
    Zgauss0,
    Zgoodfacet,
    Zhashlookup,
    Zhashridge,
    Zhashridgetest,
    Zhashtests,
    Zinsidevisible,
    Zintersect,
    Zintersectfail,
    Zintersectmax,
    Zintersectnum,
    Zintersecttot,
    Zmaxneighbors,
    Wmaxout,
    Wmaxoutside,
    Zmaxridges,
    Zmaxvertex,
    Zmaxvertices,
    Zmaxvneighbors,
    Zmemfacets,
    Zmempoints,
    Zmemridges,
    Zmemvertices,
    Zmergeflipdup,
    Zmergehorizon,
    Zmergeinittot,
    Zmergeinitmax,
    Zmergeinittot2,
    Zmergeintohorizon,
    Zmergenew,
    Zmergesettot,
    Zmergesetmax,
    Zmergesettot2,
    Zmergesimplex,
    Zmergevertex,
    Wmindenom,
    Wminvertex,
    Zminnorm,
    Zmultiridge,
    Znearlysingular,
    Zneighbor,
    Wnewbalance,
    Wnewbalance2,
    Znewfacettot,
    Znewfacetmax,
    Znewvertex,
    Wnewvertex,
    Wnewvertexmax,
    Znoarea,
    Znonsimplicial,
    Znowsimplicial,
    Znotgood,
    Znotgoodnew,
    Znotmax,
    Znumfacets,
    Znummergemax,
    Znummergetot,
    Znumneighbors,
    Znumridges,
    Znumvertices,
    Znumvisibility,
    Znumvneighbors,
    Zonehorizon,
    Zpartangle,
    Zpartcoplanar,
    Zpartflip,
    Zparthorizon,
    Zpartinside,
    Zpartition,
    Zpartitionall,
    Zpartnear,
    Zpbalance,
    Wpbalance,
    Wpbalance2,
    Zpostfacets,
    Zpremergetot,
    Zprocessed,
    Zremvertex,
    Zremvertexdel,
    Zrenameall,
    Zrenamepinch,
    Zrenameshare,
    Zretry,
    Wretrymax,
    Zridge,
    Wridge,
    Wridgemax,
    Zridge0,
    Wridge0,
    Wridge0max,
    Zridgemid,
    Wridgemid,
    Wridgemidmax,
    Zridgeok,
    Wridgeok,
    Wridgeokmax,
    Zsearchpoints,
    Zsetplane,
    Ztestvneighbor,
    Ztotcheck,
    Ztothorizon,
    Ztotmerge,
    Ztotpartcoplanar,
    Ztotpartition,
    Ztotridges,
    Ztotvertices,
    Ztotvisible,
    Ztricoplanar,
    Ztricoplanarmax,
    Ztricoplanartot,
    Ztridegen,
    Ztrimirror,
    Ztrinull,
    Wvertexmax,
    Wvertexmin,
    Zvertexridge,
    Zvertexridgetot,
    Zvertexridgemax,
    Zvertices,
    Zvisfacettot,
    Zvisfacetmax,
    Zvisit,
    Zvisit2max,
    Zvisvertextot,
    Zvisvertexmax,
    Zvvisit,
    Zvvisit2max,
    Zwidefacet,
    Zwidevertices,
    ZEND};

/*---------------------------------

  Zxxx/Wxxx statistics that remain defined if qh_KEEPstatistics=0

  notes:
    be sure to use zzdef, zzinc, etc. with these statistics (no double checking!)
*/
#else
enum statistics {     /* for zzdef etc. macros */
  Zback0,
  Zbestdist,
  Zcentrumtests,
  Zcheckpart,
  Zconcaveridges,
  Zcoplanarhorizon,
  Zcoplanarpart,
  Zcoplanarridges,
  Zcyclefacettot,
  Zcyclehorizon,
  Zdelvertextot,
  Zdistcheck,
  Zdistconvex,
  Zdistzero,
  Zdoc1,
  Zdoc2,
  Zdoc3,
  Zdoc11,
  Zflippedfacets,
  Zgauss0,
  Zminnorm,
  Zmultiridge,
  Znearlysingular,
  Wnewvertexmax,
  Znumvisibility,
  Zpartcoplanar,
  Zpartition,
  Zpartitionall,
  Zprocessed,
  Zretry,
  Zridge,
  Wridge,
  Wridgemax,
  Zridge0,
  Wridge0,
  Wridge0max,
  Zridgemid,
  Wridgemid,
  Wridgemidmax,
  Zridgeok,
  Wridgeok,
  Wridgeokmax,
  Zsetplane,
  Ztotcheck,
  Ztotmerge,
    ZEND};
#endif

/*---------------------------------

  ztype
    the type of a statistic sets its initial value.

  notes:
    The type should be the same as the macro for collecting the statistic
*/
enum ztypes {zdoc,zinc,zadd,zmax,zmin,ZTYPEreal,wadd,wmax,wmin,ZTYPEend};

/*========== macros and constants =============*/

/*----------------------------------

  MAYdebugx
    define as maydebug() to be called frequently for error trapping
*/
#define MAYdebugx

/*----------------------------------

  zzdef_, zdef_( type, name, doc, -1)
    define a statistic (assumes 'qhstat.next= 0;')

  zdef_( type, name, doc, count)
    define an averaged statistic
    printed as name/count
*/
#define zzdef_(stype,name,string,cnt) qhstat id[qhstat next++]=name; \
   qhstat doc[name]= string; qhstat count[name]= cnt; qhstat type[name]= stype
#if qh_KEEPstatistics
#define zdef_(stype,name,string,cnt) qhstat id[qhstat next++]=name; \
   qhstat doc[name]= string; qhstat count[name]= cnt; qhstat type[name]= stype
#else
#define zdef_(type,name,doc,count)
#endif

/*----------------------------------

  zzinc_( name ), zinc_( name)
    increment an integer statistic
*/
#define zzinc_(id) {MAYdebugx; qhstat stats[id].i++;}
#if qh_KEEPstatistics
#define zinc_(id) {MAYdebugx; qhstat stats[id].i++;}
#else
#define zinc_(id) {}
#endif

/*----------------------------------

  zzadd_( name, value ), zadd_( name, value ), wadd_( name, value )
    add value to an integer or real statistic
*/
#define zzadd_(id, val) {MAYdebugx; qhstat stats[id].i += (val);}
#define wwadd_(id, val) {MAYdebugx; qhstat stats[id].r += (val);}
#if qh_KEEPstatistics
#define zadd_(id, val) {MAYdebugx; qhstat stats[id].i += (val);}
#define wadd_(id, val) {MAYdebugx; qhstat stats[id].r += (val);}
#else
#define zadd_(id, val) {}
#define wadd_(id, val) {}
#endif

/*----------------------------------

  zzval_( name ), zval_( name ), wwval_( name )
    set or return value of a statistic
*/
#define zzval_(id) ((qhstat stats[id]).i)
#define wwval_(id) ((qhstat stats[id]).r)
#if qh_KEEPstatistics
#define zval_(id) ((qhstat stats[id]).i)
#define wval_(id) ((qhstat stats[id]).r)
#else
#define zval_(id) qhstat tempi
#define wval_(id) qhstat tempr
#endif

/*----------------------------------

  zmax_( id, val ), wmax_( id, value )
    maximize id with val
*/
#define wwmax_(id, val) {MAYdebugx; maximize_(qhstat stats[id].r,(val));}
#if qh_KEEPstatistics
#define zmax_(id, val) {MAYdebugx; maximize_(qhstat stats[id].i,(val));}
#define wmax_(id, val) {MAYdebugx; maximize_(qhstat stats[id].r,(val));}
#else
#define zmax_(id, val) {}
#define wmax_(id, val) {}
#endif

/*----------------------------------

  zmin_( id, val ), wmin_( id, value )
    minimize id with val
*/
#if qh_KEEPstatistics
#define zmin_(id, val) {MAYdebugx; minimize_(qhstat stats[id].i,(val));}
#define wmin_(id, val) {MAYdebugx; minimize_(qhstat stats[id].r,(val));}
#else
#define zmin_(id, val) {}
#define wmin_(id, val) {}
#endif

/*================== stat.h types ==============*/


/*----------------------------------

  intrealT
    union of integer and real, used for statistics
*/
typedef union intrealT intrealT;    /* union of int and realT */
union intrealT {
    int i;
    realT r;
};

/*----------------------------------

  qhstat
    global data structure for statistics, similar to qh and qhrbox

  notes:
   access to qh_qhstat is via the "qhstat" macro.  There are two choices
   qh_QHpointer = 1     access globals via a pointer
                        enables qh_saveqhull() and qh_restoreqhull()
                = 0     qh_qhstat is a static data structure
                        only one instance of qhull() can be active at a time
                        default value
   qh_QHpointer is defined in libqhull.h
   qh_QHpointer_dllimport and qh_dllimport define qh_qh as __declspec(dllimport) [libqhull.h]

   allocated in stat.c using qh_malloc()
*/
#ifndef DEFqhstatT
#define DEFqhstatT 1
typedef struct qhstatT qhstatT;
#endif

#if qh_QHpointer_dllimport
#define qhstat qh_qhstat->
__declspec(dllimport) extern qhstatT *qh_qhstat;
#elif qh_QHpointer
#define qhstat qh_qhstat->
extern qhstatT *qh_qhstat;
#elif qh_dllimport
#define qhstat qh_qhstat.
__declspec(dllimport) extern qhstatT qh_qhstat;
#else
#define qhstat qh_qhstat.
extern qhstatT qh_qhstat;
#endif
struct qhstatT {
  intrealT   stats[ZEND];     /* integer and real statistics */
  unsigned   char id[ZEND+10]; /* id's in print order */
  const char *doc[ZEND];       /* array of documentation strings */
  short int  count[ZEND];     /* -1 if none, else index of count to use */
  char       type[ZEND];      /* type, see ztypes above */
  char       printed[ZEND];   /* true, if statistic has been printed */
  intrealT   init[ZTYPEend];  /* initial values by types, set initstatistics */

  int        next;            /* next index for zdef_ */
  int        precision;       /* index for precision problems */
  int        vridges;         /* index for Voronoi ridges */
  int        tempi;
  realT      tempr;
};

/*========== function prototypes ===========*/

void    qh_allstatA(void);
void    qh_allstatB(void);
void    qh_allstatC(void);
void    qh_allstatD(void);
void    qh_allstatE(void);
void    qh_allstatE2(void);
void    qh_allstatF(void);
void    qh_allstatG(void);
void    qh_allstatH(void);
void    qh_allstatI(void);
void    qh_allstatistics(void);
void    qh_collectstatistics(void);
void    qh_freestatistics(void);
void    qh_initstatistics(void);
boolT   qh_newstats(int idx, int *nextindex);
boolT   qh_nostatistic(int i);
void    qh_printallstatistics(FILE *fp, const char *string);
void    qh_printstatistics(FILE *fp, const char *string);
void    qh_printstatlevel(FILE *fp, int id, int start);
void    qh_printstats(FILE *fp, int idx, int *nextindex);
realT   qh_stddev(int num, realT tot, realT tot2, realT *ave);

#endif   /* qhDEFstat */
qhull-2012.1/src/libqhull/user.c0000644000076400010400000004637411720036664017654 0ustar  bbarberAdministrators/*
  ---------------------------------

   user.c
   user redefinable functions

   see user2.c for qh_fprintf, qh_malloc, qh_free

   see README.txt  see COPYING.txt for copyright information.

   see libqhull.h for data structures, macros, and user-callable functions.

   see user_eg.c, unix.c, and qhull_interface.cpp for examples.

   see user.h for user-definable constants

      use qh_NOmem in mem.h to turn off memory management
      use qh_NOmerge in user.h to turn off facet merging
      set qh_KEEPstatistics in user.h to 0 to turn off statistics

   This is unsupported software.  You're welcome to make changes,
   but you're on your own if something goes wrong.  Use 'Tc' to
   check frequently.  Usually qhull will report an error if
   a data structure becomes inconsistent.  If so, it also reports
   the last point added to the hull, e.g., 102.  You can then trace
   the execution of qhull with "T4P102".

   Please report any errors that you fix to qhull@qhull.org

   call_qhull is a template for calling qhull from within your application

   if you recompile and load this module, then user.o will not be loaded
   from qhull.a

   you can add additional quick allocation sizes in qh_user_memsizes

   if the other functions here are redefined to not use qh_print...,
   then io.o will not be loaded from qhull.a.  See user_eg.c for an
   example.  We recommend keeping io.o for the extra debugging
   information it supplies.
*/

#include "qhull_a.h"

#include 

/*---------------------------------

  qh_call_qhull( void )
    template for calling qhull from inside your program
    remove #if 0, #endif to compile

  returns:
    exit code(see qh_ERR... in libqhull.h)
    all memory freed

  notes:
    This can be called any number of times.

  see:
    qh_call_qhull_once()

*/
#if 0
{
  int dim;                  /* dimension of points */
  int numpoints;            /* number of points */
  coordT *points;           /* array of coordinates for each point */
  boolT ismalloc;           /* True if qhull should free points in qh_freeqhull() or reallocation */
  char flags[]= "qhull Tv"; /* option flags for qhull, see qh_opt.htm */
  FILE *outfile= stdout;    /* output from qh_produce_output()
                               use NULL to skip qh_produce_output() */
  FILE *errfile= stderr;    /* error messages from qhull code */
  int exitcode;             /* 0 if no error from qhull */
  facetT *facet;            /* set by FORALLfacets */
  int curlong, totlong;     /* memory remaining after qh_memfreeshort */

#if qh_QHpointer  /* see user.h */
  if (qh_qh){
      printf ("QH6238: Qhull link error.  The global variable qh_qh was not initialized\n\
              to NULL by global.c.  Please compile this program with -Dqh_QHpointer_dllimport\n\
              as well as -Dqh_QHpointer, or use libqhullstatic, or use a different tool chain.\n\n");
      exit -1;
  }
#endif

  /* initialize dim, numpoints, points[], ismalloc here */
  exitcode= qh_new_qhull(dim, numpoints, points, ismalloc,
                      flags, outfile, errfile);
  if (!exitcode) {                  /* if no error */
    /* 'qh facet_list' contains the convex hull */
    FORALLfacets {
       /* ... your code ... */
    }
  }
  qh_freeqhull(!qh_ALL);
  qh_memfreeshort(&curlong, &totlong);
  if (curlong || totlong)
    qh_fprintf(errfile, 7068, "qhull internal warning (main): did not free %d bytes of long memory(%d pieces)\n", totlong, curlong);
}
#endif

/*---------------------------------

  qh_new_qhull( dim, numpoints, points, ismalloc, qhull_cmd, outfile, errfile )
    build new qhull data structure and return exitcode (0 if no errors)

  notes:
    do not modify points until finished with results.
      The qhull data structure contains pointers into the points array.
    do not call qhull functions before qh_new_qhull().
      The qhull data structure is not initialized until qh_new_qhull().

    outfile may be null
    qhull_cmd must start with "qhull "
    projects points to a new point array for Delaunay triangulations ('d' and 'v')
    transforms points into a new point array for halfspace intersection ('H')


  To allow multiple, concurrent calls to qhull()
    - set qh_QHpointer in user.h
    - use qh_save_qhull and qh_restore_qhull to swap the global data structure between calls.
    - use qh_freeqhull(qh_ALL) to free intermediate convex hulls

  see:
    user_eg.c for an example
*/
int qh_new_qhull(int dim, int numpoints, coordT *points, boolT ismalloc,
                char *qhull_cmd, FILE *outfile, FILE *errfile) {
  int exitcode, hulldim;
  boolT new_ismalloc;
  static boolT firstcall = True;
  coordT *new_points;

  if (firstcall) {
    qh_meminit(errfile);
    firstcall= False;
  }
  if (strncmp(qhull_cmd,"qhull ", (size_t)6)) {
    qh_fprintf(errfile, 6186, "qhull error (qh_new_qhull): start qhull_cmd argument with \"qhull \"\n");
    qh_exit(qh_ERRinput);
  }
  qh_initqhull_start(NULL, outfile, errfile);
  trace1((qh ferr, 1044, "qh_new_qhull: build new Qhull for %d %d-d points with %s\n", numpoints, dim, qhull_cmd));
  exitcode = setjmp(qh errexit);
  if (!exitcode)
  {
    qh NOerrexit = False;
    qh_initflags(qhull_cmd);
    if (qh DELAUNAY)
      qh PROJECTdelaunay= True;
    if (qh HALFspace) {
      /* points is an array of halfspaces,
         the last coordinate of each halfspace is its offset */
      hulldim= dim-1;
      qh_setfeasible(hulldim);
      new_points= qh_sethalfspace_all(dim, numpoints, points, qh feasible_point);
      new_ismalloc= True;
      if (ismalloc)
        qh_free(points);
    }else {
      hulldim= dim;
      new_points= points;
      new_ismalloc= ismalloc;
    }
    qh_init_B(new_points, numpoints, hulldim, new_ismalloc);
    qh_qhull();
    qh_check_output();
    if (outfile) {
      qh_produce_output();
    }else {
      qh_prepare_output();
    }
    if (qh VERIFYoutput && !qh STOPpoint && !qh STOPcone)
      qh_check_points();
  }
  qh NOerrexit = True;
  return exitcode;
} /* new_qhull */

/*---------------------------------

  qh_errexit( exitcode, facet, ridge )
    report and exit from an error
    report facet and ridge if non-NULL
    reports useful information such as last point processed
    set qh.FORCEoutput to print neighborhood of facet

  see:
    qh_errexit2() in libqhull.c for printing 2 facets

  design:
    check for error within error processing
    compute qh.hulltime
    print facet and ridge (if any)
    report commandString, options, qh.furthest_id
    print summary and statistics (including precision statistics)
    if qh_ERRsingular
      print help text for singular data set
    exit program via long jump (if defined) or exit()
*/
void qh_errexit(int exitcode, facetT *facet, ridgeT *ridge) {

  if (qh ERREXITcalled) {
    qh_fprintf(qh ferr, 8126, "\nqhull error while processing previous error.  Exit program\n");
    qh_exit(qh_ERRqhull);
  }
  qh ERREXITcalled= True;
  if (!qh QHULLfinished)
    qh hulltime= qh_CPUclock - qh hulltime;
  qh_errprint("ERRONEOUS", facet, NULL, ridge, NULL);
  qh_fprintf(qh ferr, 8127, "\nWhile executing: %s | %s\n", qh rbox_command, qh qhull_command);
  qh_fprintf(qh ferr, 8128, "Options selected for Qhull %s:\n%s\n", qh_version, qh qhull_options);
  if (qh furthest_id >= 0) {
    qh_fprintf(qh ferr, 8129, "Last point added to hull was p%d.", qh furthest_id);
    if (zzval_(Ztotmerge))
      qh_fprintf(qh ferr, 8130, "  Last merge was #%d.", zzval_(Ztotmerge));
    if (qh QHULLfinished)
      qh_fprintf(qh ferr, 8131, "\nQhull has finished constructing the hull.");
    else if (qh POSTmerging)
      qh_fprintf(qh ferr, 8132, "\nQhull has started post-merging.");
    qh_fprintf(qh ferr, 8133, "\n");
  }
  if (qh FORCEoutput && (qh QHULLfinished || (!facet && !ridge)))
    qh_produce_output();
  else if (exitcode != qh_ERRinput) {
    if (exitcode != qh_ERRsingular && zzval_(Zsetplane) > qh hull_dim+1) {
      qh_fprintf(qh ferr, 8134, "\nAt error exit:\n");
      qh_printsummary(qh ferr);
      if (qh PRINTstatistics) {
        qh_collectstatistics();
        qh_printstatistics(qh ferr, "at error exit");
        qh_memstatistics(qh ferr);
      }
    }
    if (qh PRINTprecision)
      qh_printstats(qh ferr, qhstat precision, NULL);
  }
  if (!exitcode)
    exitcode= qh_ERRqhull;
  else if (exitcode == qh_ERRsingular)
    qh_printhelp_singular(qh ferr);
  else if (exitcode == qh_ERRprec && !qh PREmerge)
    qh_printhelp_degenerate(qh ferr);
  if (qh NOerrexit) {
    qh_fprintf(qh ferr, 6187, "qhull error while ending program.  Exit program\n");
    qh_exit(qh_ERRqhull);
  }
  qh ERREXITcalled= False;
  qh NOerrexit= True;
  longjmp(qh errexit, exitcode);
} /* errexit */


/*---------------------------------

  qh_errprint( fp, string, atfacet, otherfacet, atridge, atvertex )
    prints out the information of facets and ridges to fp
    also prints neighbors and geomview output

  notes:
    except for string, any parameter may be NULL
*/
void qh_errprint(const char *string, facetT *atfacet, facetT *otherfacet, ridgeT *atridge, vertexT *atvertex) {
  int i;

  if (atfacet) {
    qh_fprintf(qh ferr, 8135, "%s FACET:\n", string);
    qh_printfacet(qh ferr, atfacet);
  }
  if (otherfacet) {
    qh_fprintf(qh ferr, 8136, "%s OTHER FACET:\n", string);
    qh_printfacet(qh ferr, otherfacet);
  }
  if (atridge) {
    qh_fprintf(qh ferr, 8137, "%s RIDGE:\n", string);
    qh_printridge(qh ferr, atridge);
    if (atridge->top && atridge->top != atfacet && atridge->top != otherfacet)
      qh_printfacet(qh ferr, atridge->top);
    if (atridge->bottom
        && atridge->bottom != atfacet && atridge->bottom != otherfacet)
      qh_printfacet(qh ferr, atridge->bottom);
    if (!atfacet)
      atfacet= atridge->top;
    if (!otherfacet)
      otherfacet= otherfacet_(atridge, atfacet);
  }
  if (atvertex) {
    qh_fprintf(qh ferr, 8138, "%s VERTEX:\n", string);
    qh_printvertex(qh ferr, atvertex);
  }
  if (qh fout && qh FORCEoutput && atfacet && !qh QHULLfinished && !qh IStracing) {
    qh_fprintf(qh ferr, 8139, "ERRONEOUS and NEIGHBORING FACETS to output\n");
    for (i=0; i < qh_PRINTEND; i++)  /* use fout for geomview output */
      qh_printneighborhood(qh fout, qh PRINTout[i], atfacet, otherfacet,
                            !qh_ALL);
  }
} /* errprint */


/*---------------------------------

  qh_printfacetlist( fp, facetlist, facets, printall )
    print all fields for a facet list and/or set of facets to fp
    if !printall,
      only prints good facets

  notes:
    also prints all vertices
*/
void qh_printfacetlist(facetT *facetlist, setT *facets, boolT printall) {
  facetT *facet, **facetp;

  qh_printbegin(qh ferr, qh_PRINTfacets, facetlist, facets, printall);
  FORALLfacet_(facetlist)
    qh_printafacet(qh ferr, qh_PRINTfacets, facet, printall);
  FOREACHfacet_(facets)
    qh_printafacet(qh ferr, qh_PRINTfacets, facet, printall);
  qh_printend(qh ferr, qh_PRINTfacets, facetlist, facets, printall);
} /* printfacetlist */


/*---------------------------------

  qh_printhelp_degenerate( fp )
    prints descriptive message for precision error

  notes:
    no message if qh_QUICKhelp
*/
void qh_printhelp_degenerate(FILE *fp) {

  if (qh MERGEexact || qh PREmerge || qh JOGGLEmax < REALmax/2)
    qh_fprintf(fp, 9368, "\n\
A Qhull error has occurred.  Qhull should have corrected the above\n\
precision error.  Please send the input and all of the output to\n\
qhull_bug@qhull.org\n");
  else if (!qh_QUICKhelp) {
    qh_fprintf(fp, 9369, "\n\
Precision problems were detected during construction of the convex hull.\n\
This occurs because convex hull algorithms assume that calculations are\n\
exact, but floating-point arithmetic has roundoff errors.\n\
\n\
To correct for precision problems, do not use 'Q0'.  By default, Qhull\n\
selects 'C-0' or 'Qx' and merges non-convex facets.  With option 'QJ',\n\
Qhull joggles the input to prevent precision problems.  See \"Imprecision\n\
in Qhull\" (qh-impre.htm).\n\
\n\
If you use 'Q0', the output may include\n\
coplanar ridges, concave ridges, and flipped facets.  In 4-d and higher,\n\
Qhull may produce a ridge with four neighbors or two facets with the same \n\
vertices.  Qhull reports these events when they occur.  It stops when a\n\
concave ridge, flipped facet, or duplicate facet occurs.\n");
#if REALfloat
    qh_fprintf(fp, 9370, "\
\n\
Qhull is currently using single precision arithmetic.  The following\n\
will probably remove the precision problems:\n\
  - recompile qhull for realT precision(#define REALfloat 0 in user.h).\n");
#endif
    if (qh DELAUNAY && !qh SCALElast && qh MAXabs_coord > 1e4)
      qh_fprintf(fp, 9371, "\
\n\
When computing the Delaunay triangulation of coordinates > 1.0,\n\
  - use 'Qbb' to scale the last coordinate to [0,m] (max previous coordinate)\n");
    if (qh DELAUNAY && !qh ATinfinity)
      qh_fprintf(fp, 9372, "\
When computing the Delaunay triangulation:\n\
  - use 'Qz' to add a point at-infinity.  This reduces precision problems.\n");

    qh_fprintf(fp, 9373, "\
\n\
If you need triangular output:\n\
  - use option 'Qt' to triangulate the output\n\
  - use option 'QJ' to joggle the input points and remove precision errors\n\
  - use option 'Ft'.  It triangulates non-simplicial facets with added points.\n\
\n\
If you must use 'Q0',\n\
try one or more of the following options.  They can not guarantee an output.\n\
  - use 'QbB' to scale the input to a cube.\n\
  - use 'Po' to produce output and prevent partitioning for flipped facets\n\
  - use 'V0' to set min. distance to visible facet as 0 instead of roundoff\n\
  - use 'En' to specify a maximum roundoff error less than %2.2g.\n\
  - options 'Qf', 'Qbb', and 'QR0' may also help\n",
               qh DISTround);
    qh_fprintf(fp, 9374, "\
\n\
To guarantee simplicial output:\n\
  - use option 'Qt' to triangulate the output\n\
  - use option 'QJ' to joggle the input points and remove precision errors\n\
  - use option 'Ft' to triangulate the output by adding points\n\
  - use exact arithmetic (see \"Imprecision in Qhull\", qh-impre.htm)\n\
");
  }
} /* printhelp_degenerate */


/*---------------------------------

  qh_printhelp_narrowhull( minangle )
    Warn about a narrow hull

  notes:
    Alternatively, reduce qh_WARNnarrow in user.h

*/
void qh_printhelp_narrowhull(FILE *fp, realT minangle) {

    qh_fprintf(fp, 9375, "qhull precision warning: \n\
The initial hull is narrow (cosine of min. angle is %.16f).\n\
Is the input lower dimensional (e.g., on a plane in 3-d)?  Qhull may\n\
produce a wide facet.  Options 'QbB' (scale to unit box) or 'Qbb' (scale\n\
last coordinate) may remove this warning.  Use 'Pp' to skip this warning.\n\
See 'Limitations' in qh-impre.htm.\n",
          -minangle);   /* convert from angle between normals to angle between facets */
} /* printhelp_narrowhull */

/*---------------------------------

  qh_printhelp_singular( fp )
    prints descriptive message for singular input
*/
void qh_printhelp_singular(FILE *fp) {
  facetT *facet;
  vertexT *vertex, **vertexp;
  realT min, max, *coord, dist;
  int i,k;

  qh_fprintf(fp, 9376, "\n\
The input to qhull appears to be less than %d dimensional, or a\n\
computation has overflowed.\n\n\
Qhull could not construct a clearly convex simplex from points:\n",
           qh hull_dim);
  qh_printvertexlist(fp, "", qh facet_list, NULL, qh_ALL);
  if (!qh_QUICKhelp)
    qh_fprintf(fp, 9377, "\n\
The center point is coplanar with a facet, or a vertex is coplanar\n\
with a neighboring facet.  The maximum round off error for\n\
computing distances is %2.2g.  The center point, facets and distances\n\
to the center point are as follows:\n\n", qh DISTround);
  qh_printpointid(fp, "center point", qh hull_dim, qh interior_point, -1);
  qh_fprintf(fp, 9378, "\n");
  FORALLfacets {
    qh_fprintf(fp, 9379, "facet");
    FOREACHvertex_(facet->vertices)
      qh_fprintf(fp, 9380, " p%d", qh_pointid(vertex->point));
    zinc_(Zdistio);
    qh_distplane(qh interior_point, facet, &dist);
    qh_fprintf(fp, 9381, " distance= %4.2g\n", dist);
  }
  if (!qh_QUICKhelp) {
    if (qh HALFspace)
      qh_fprintf(fp, 9382, "\n\
These points are the dual of the given halfspaces.  They indicate that\n\
the intersection is degenerate.\n");
    qh_fprintf(fp, 9383,"\n\
These points either have a maximum or minimum x-coordinate, or\n\
they maximize the determinant for k coordinates.  Trial points\n\
are first selected from points that maximize a coordinate.\n");
    if (qh hull_dim >= qh_INITIALmax)
      qh_fprintf(fp, 9384, "\n\
Because of the high dimension, the min x-coordinate and max-coordinate\n\
points are used if the determinant is non-zero.  Option 'Qs' will\n\
do a better, though much slower, job.  Instead of 'Qs', you can change\n\
the points by randomly rotating the input with 'QR0'.\n");
  }
  qh_fprintf(fp, 9385, "\nThe min and max coordinates for each dimension are:\n");
  for (k=0; k < qh hull_dim; k++) {
    min= REALmax;
    max= -REALmin;
    for (i=qh num_points, coord= qh first_point+k; i--; coord += qh hull_dim) {
      maximize_(max, *coord);
      minimize_(min, *coord);
    }
    qh_fprintf(fp, 9386, "  %d:  %8.4g  %8.4g  difference= %4.4g\n", k, min, max, max-min);
  }
  if (!qh_QUICKhelp) {
    qh_fprintf(fp, 9387, "\n\
If the input should be full dimensional, you have several options that\n\
may determine an initial simplex:\n\
  - use 'QJ'  to joggle the input and make it full dimensional\n\
  - use 'QbB' to scale the points to the unit cube\n\
  - use 'QR0' to randomly rotate the input for different maximum points\n\
  - use 'Qs'  to search all points for the initial simplex\n\
  - use 'En'  to specify a maximum roundoff error less than %2.2g.\n\
  - trace execution with 'T3' to see the determinant for each point.\n",
                     qh DISTround);
#if REALfloat
    qh_fprintf(fp, 9388, "\
  - recompile qhull for realT precision(#define REALfloat 0 in libqhull.h).\n");
#endif
    qh_fprintf(fp, 9389, "\n\
If the input is lower dimensional:\n\
  - use 'QJ' to joggle the input and make it full dimensional\n\
  - use 'Qbk:0Bk:0' to delete coordinate k from the input.  You should\n\
    pick the coordinate with the least range.  The hull will have the\n\
    correct topology.\n\
  - determine the flat containing the points, rotate the points\n\
    into a coordinate plane, and delete the other coordinates.\n\
  - add one or more points to make the input full dimensional.\n\
");
  }
} /* printhelp_singular */

/*---------------------------------

  qh_user_memsizes()
    allocate up to 10 additional, quick allocation sizes

  notes:
    increase maximum number of allocations in qh_initqhull_mem()
*/
void qh_user_memsizes(void) {

  /* qh_memsize(size); */
} /* user_memsizes */


qhull-2012.1/src/libqhull/user.h0000644000076400010400000006702511720040556017650 0ustar  bbarberAdministrators/*
  ---------------------------------

   user.h
   user redefinable constants

   see qh-user.htm.  see COPYING for copyright information.

   before reading any code, review libqhull.h for data structure definitions and
   the "qh" macro.

Sections:
   ============= qhull library constants ======================
   ============= data types and configuration macros ==========
   ============= performance related constants ================
   ============= memory constants =============================
   ============= joggle constants =============================
   ============= conditional compilation ======================
   ============= -merge constants- ============================

Code flags --
  NOerrors -- the code does not call qh_errexit()
  WARN64 -- the code may be incompatible with 64-bit pointers

*/

#include 

#ifndef qhDEFuser
#define qhDEFuser 1

/*============================================================*/
/*============= qhull library constants ======================*/
/*============================================================*/

/*----------------------------------

  FILENAMElen -- max length for TI and TO filenames

*/

#define qh_FILENAMElen 500

/*----------------------------------

  msgcode -- Unique message codes for qh_fprintf

  If add new messages, assign these values and increment.

  def counters =  [27, 1047, 2059, 3025, 4068, 5003,
     6241, 7079, 8143, 9410, 10000, 11026]

  See: qh_ERR* [libqhull.h]
*/

#define MSG_TRACE0 0
#define MSG_TRACE1 1000
#define MSG_TRACE2 2000
#define MSG_TRACE3 3000
#define MSG_TRACE4 4000
#define MSG_TRACE5 5000
#define MSG_ERROR  6000   /* errors written to qh.ferr */
#define MSG_WARNING 7000
#define MSG_STDERR  8000  /* log messages Written to qh.ferr */
#define MSG_OUTPUT  9000
#define MSG_QHULL_ERROR 10000 /* errors thrown by QhullError [QhullError.h] */
#define MSG_FIXUP  11000  /* FIXUP QH11... */
#define MSG_MAXLEN  3000 /* qh_printhelp_degenerate() in user.c */


/*----------------------------------

  qh_OPTIONline -- max length of an option line 'FO'
*/
#define qh_OPTIONline 80

/*============================================================*/
/*============= data types and configuration macros ==========*/
/*============================================================*/

/*----------------------------------

  realT
    set the size of floating point numbers

  qh_REALdigits
    maximimum number of significant digits

  qh_REAL_1, qh_REAL_2n, qh_REAL_3n
    format strings for printf

  qh_REALmax, qh_REALmin
    maximum and minimum (near zero) values

  qh_REALepsilon
    machine roundoff.  Maximum roundoff error for addition and multiplication.

  notes:
   Select whether to store floating point numbers in single precision (float)
   or double precision (double).

   Use 'float' to save about 8% in time and 25% in space.  This is particularly
   helpful if high-d where convex hulls are space limited.  Using 'float' also
   reduces the printed size of Qhull's output since numbers have 8 digits of
   precision.

   Use 'double' when greater arithmetic precision is needed.  This is needed
   for Delaunay triangulations and Voronoi diagrams when you are not merging
   facets.

   If 'double' gives insufficient precision, your data probably includes
   degeneracies.  If so you should use facet merging (done by default)
   or exact arithmetic (see imprecision section of manual, qh-impre.htm).
   You may also use option 'Po' to force output despite precision errors.

   You may use 'long double', but many format statements need to be changed
   and you may need a 'long double' square root routine.  S. Grundmann
   (sg@eeiwzb.et.tu-dresden.de) has done this.  He reports that the code runs
   much slower with little gain in precision.

   WARNING: on some machines,    int f(){realT a= REALmax;return (a == REALmax);}
      returns False.  Use (a > REALmax/2) instead of (a == REALmax).

   REALfloat =   1      all numbers are 'float' type
             =   0      all numbers are 'double' type
*/
#define REALfloat 0

#if (REALfloat == 1)
#define realT float
#define REALmax FLT_MAX
#define REALmin FLT_MIN
#define REALepsilon FLT_EPSILON
#define qh_REALdigits 8   /* maximum number of significant digits */
#define qh_REAL_1 "%6.8g "
#define qh_REAL_2n "%6.8g %6.8g\n"
#define qh_REAL_3n "%6.8g %6.8g %6.8g\n"

#elif (REALfloat == 0)
#define realT double
#define REALmax DBL_MAX
#define REALmin DBL_MIN
#define REALepsilon DBL_EPSILON
#define qh_REALdigits 16    /* maximum number of significant digits */
#define qh_REAL_1 "%6.16g "
#define qh_REAL_2n "%6.16g %6.16g\n"
#define qh_REAL_3n "%6.16g %6.16g %6.16g\n"

#else
#error unknown float option
#endif

/*----------------------------------

  qh_CPUclock
    define the clock() function for reporting the total time spent by Qhull
    returns CPU ticks as a 'long int'
    qh_CPUclock is only used for reporting the total time spent by Qhull

  qh_SECticks
    the number of clock ticks per second

  notes:
    looks for CLOCKS_PER_SEC, CLOCKS_PER_SECOND, or assumes microseconds
    to define a custom clock, set qh_CLOCKtype to 0

    if your system does not use clock() to return CPU ticks, replace
    qh_CPUclock with the corresponding function.  It is converted
    to 'unsigned long' to prevent wrap-around during long runs.  By default,
     defines clock_t as 'long'

   Set qh_CLOCKtype to

     1          for CLOCKS_PER_SEC, CLOCKS_PER_SECOND, or microsecond
                Note:  may fail if more than 1 hour elapsed time

     2          use qh_clock() with POSIX times() (see global.c)
*/
#define qh_CLOCKtype 1  /* change to the desired number */

#if (qh_CLOCKtype == 1)

#if defined(CLOCKS_PER_SECOND)
#define qh_CPUclock    ((unsigned long)clock())  /* return CPU clock */
#define qh_SECticks CLOCKS_PER_SECOND

#elif defined(CLOCKS_PER_SEC)
#define qh_CPUclock    ((unsigned long)clock())  /* return CPU clock */
#define qh_SECticks CLOCKS_PER_SEC

#elif defined(CLK_TCK)
#define qh_CPUclock    ((unsigned long)clock())  /* return CPU clock */
#define qh_SECticks CLK_TCK

#else
#define qh_CPUclock    ((unsigned long)clock())  /* return CPU clock */
#define qh_SECticks 1E6
#endif

#elif (qh_CLOCKtype == 2)
#define qh_CPUclock    qh_clock()  /* return CPU clock */
#define qh_SECticks 100

#else /* qh_CLOCKtype == ? */
#error unknown clock option
#endif

/*----------------------------------

  qh_RANDOMtype, qh_RANDOMmax, qh_RANDOMseed
    define random number generator

    qh_RANDOMint generates a random integer between 0 and qh_RANDOMmax.
    qh_RANDOMseed sets the random number seed for qh_RANDOMint

  Set qh_RANDOMtype (default 5) to:
    1       for random() with 31 bits (UCB)
    2       for rand() with RAND_MAX or 15 bits (system 5)
    3       for rand() with 31 bits (Sun)
    4       for lrand48() with 31 bits (Solaris)
    5       for qh_rand() with 31 bits (included with Qhull)

  notes:
    Random numbers are used by rbox to generate point sets.  Random
    numbers are used by Qhull to rotate the input ('QRn' option),
    simulate a randomized algorithm ('Qr' option), and to simulate
    roundoff errors ('Rn' option).

    Random number generators differ between systems.  Most systems provide
    rand() but the period varies.  The period of rand() is not critical
    since qhull does not normally use random numbers.

    The default generator is Park & Miller's minimal standard random
    number generator [CACM 31:1195 '88].  It is included with Qhull.

    If qh_RANDOMmax is wrong, qhull will report a warning and Geomview
    output will likely be invisible.
*/
#define qh_RANDOMtype 5   /* *** change to the desired number *** */

#if (qh_RANDOMtype == 1)
#define qh_RANDOMmax ((realT)0x7fffffffUL)  /* 31 bits, random()/MAX */
#define qh_RANDOMint random()
#define qh_RANDOMseed_(seed) srandom(seed);

#elif (qh_RANDOMtype == 2)
#ifdef RAND_MAX
#define qh_RANDOMmax ((realT)RAND_MAX)
#else
#define qh_RANDOMmax ((realT)32767)   /* 15 bits (System 5) */
#endif
#define qh_RANDOMint  rand()
#define qh_RANDOMseed_(seed) srand((unsigned)seed);

#elif (qh_RANDOMtype == 3)
#define qh_RANDOMmax ((realT)0x7fffffffUL)  /* 31 bits, Sun */
#define qh_RANDOMint  rand()
#define qh_RANDOMseed_(seed) srand((unsigned)seed);

#elif (qh_RANDOMtype == 4)
#define qh_RANDOMmax ((realT)0x7fffffffUL)  /* 31 bits, lrand38()/MAX */
#define qh_RANDOMint lrand48()
#define qh_RANDOMseed_(seed) srand48(seed);

#elif (qh_RANDOMtype == 5)
#define qh_RANDOMmax ((realT)2147483646UL)  /* 31 bits, qh_rand/MAX */
#define qh_RANDOMint qh_rand()
#define qh_RANDOMseed_(seed) qh_srand(seed);
/* unlike rand(), never returns 0 */

#else
#error: unknown random option
#endif

/*----------------------------------

  qh_ORIENTclock
    0 for inward pointing normals by Geomview convention
*/
#define qh_ORIENTclock 0


/*============================================================*/
/*============= joggle constants =============================*/
/*============================================================*/

/*----------------------------------

qh_JOGGLEdefault
default qh.JOGGLEmax is qh.DISTround * qh_JOGGLEdefault

notes:
rbox s r 100 | qhull QJ1e-15 QR0 generates 90% faults at distround 7e-16
rbox s r 100 | qhull QJ1e-14 QR0 generates 70% faults
rbox s r 100 | qhull QJ1e-13 QR0 generates 35% faults
rbox s r 100 | qhull QJ1e-12 QR0 generates 8% faults
rbox s r 100 | qhull QJ1e-11 QR0 generates 1% faults
rbox s r 100 | qhull QJ1e-10 QR0 generates 0% faults
rbox 1000 W0 | qhull QJ1e-12 QR0 generates 86% faults
rbox 1000 W0 | qhull QJ1e-11 QR0 generates 20% faults
rbox 1000 W0 | qhull QJ1e-10 QR0 generates 2% faults
the later have about 20 points per facet, each of which may interfere

pick a value large enough to avoid retries on most inputs
*/
#define qh_JOGGLEdefault 30000.0

/*----------------------------------

qh_JOGGLEincrease
factor to increase qh.JOGGLEmax on qh_JOGGLEretry or qh_JOGGLEagain
*/
#define qh_JOGGLEincrease 10.0

/*----------------------------------

qh_JOGGLEretry
if ZZretry = qh_JOGGLEretry, increase qh.JOGGLEmax

notes:
try twice at the original value in case of bad luck the first time
*/
#define qh_JOGGLEretry 2

/*----------------------------------

qh_JOGGLEagain
every following qh_JOGGLEagain, increase qh.JOGGLEmax

notes:
1 is OK since it's already failed qh_JOGGLEretry times
*/
#define qh_JOGGLEagain 1

/*----------------------------------

qh_JOGGLEmaxincrease
maximum qh.JOGGLEmax due to qh_JOGGLEincrease
relative to qh.MAXwidth

notes:
qh.joggleinput will retry at this value until qh_JOGGLEmaxretry
*/
#define qh_JOGGLEmaxincrease 1e-2

/*----------------------------------

qh_JOGGLEmaxretry
stop after qh_JOGGLEmaxretry attempts
*/
#define qh_JOGGLEmaxretry 100

/*============================================================*/
/*============= performance related constants ================*/
/*============================================================*/

/*----------------------------------

  qh_HASHfactor
    total hash slots / used hash slots.  Must be at least 1.1.

  notes:
    =2 for at worst 50% occupancy for qh hash_table and normally 25% occupancy
*/
#define qh_HASHfactor 2

/*----------------------------------

  qh_VERIFYdirect
    with 'Tv' verify all points against all facets if op count is smaller

  notes:
    if greater, calls qh_check_bestdist() instead
*/
#define qh_VERIFYdirect 1000000

/*----------------------------------

  qh_INITIALsearch
     if qh_INITIALmax, search points up to this dimension
*/
#define qh_INITIALsearch 6

/*----------------------------------

  qh_INITIALmax
    if dim >= qh_INITIALmax, use min/max coordinate points for initial simplex

  notes:
    from points with non-zero determinants
    use option 'Qs' to override (much slower)
*/
#define qh_INITIALmax 8

/*============================================================*/
/*============= memory constants =============================*/
/*============================================================*/

/*----------------------------------

  qh_MEMalign
    memory alignment for qh_meminitbuffers() in global.c

  notes:
    to avoid bus errors, memory allocation must consider alignment requirements.
    malloc() automatically takes care of alignment.   Since mem.c manages
    its own memory, we need to explicitly specify alignment in
    qh_meminitbuffers().

    A safe choice is sizeof(double).  sizeof(float) may be used if doubles
    do not occur in data structures and pointers are the same size.  Be careful
    of machines (e.g., DEC Alpha) with large pointers.

    If using gcc, best alignment is
              #define qh_MEMalign fmax_(__alignof__(realT),__alignof__(void *))
*/
#define qh_MEMalign ((int)(fmax_(sizeof(realT), sizeof(void *))))

/*----------------------------------

  qh_MEMbufsize
    size of additional memory buffers

  notes:
    used for qh_meminitbuffers() in global.c
*/
#define qh_MEMbufsize 0x10000       /* allocate 64K memory buffers */

/*----------------------------------

  qh_MEMinitbuf
    size of initial memory buffer

  notes:
    use for qh_meminitbuffers() in global.c
*/
#define qh_MEMinitbuf 0x20000      /* initially allocate 128K buffer */

/*----------------------------------

  qh_INFINITE
    on output, indicates Voronoi center at infinity
*/
#define qh_INFINITE  -10.101

/*----------------------------------

  qh_DEFAULTbox
    default box size (Geomview expects 0.5)

  qh_DEFAULTbox
    default box size for integer coorindate (rbox only)
*/
#define qh_DEFAULTbox 0.5
#define qh_DEFAULTzbox 1e6

/*============================================================*/
/*============= conditional compilation ======================*/
/*============================================================*/

/*----------------------------------

  __cplusplus
    defined by C++ compilers

  __MSC_VER
    defined by Microsoft Visual C++

  __MWERKS__ && __POWERPC__
    defined by Metrowerks when compiling for the Power Macintosh

  __STDC__
    defined for strict ANSI C
*/

/*----------------------------------

  qh_COMPUTEfurthest
    compute furthest distance to an outside point instead of storing it with the facet
    =1 to compute furthest

  notes:
    computing furthest saves memory but costs time
      about 40% more distance tests for partitioning
      removes facet->furthestdist
*/
#define qh_COMPUTEfurthest 0

/*----------------------------------

  qh_KEEPstatistics
    =0 removes most of statistic gathering and reporting

  notes:
    if 0, code size is reduced by about 4%.
*/
#define qh_KEEPstatistics 1

/*----------------------------------

  qh_MAXoutside
    record outer plane for each facet
    =1 to record facet->maxoutside

  notes:
    this takes a realT per facet and slightly slows down qhull
    it produces better outer planes for geomview output
*/
#define qh_MAXoutside 1

/*----------------------------------

  qh_NOmerge
    disables facet merging if defined

  notes:
    This saves about 10% space.

    Unless 'Q0'
      qh_NOmerge sets 'QJ' to avoid precision errors

    #define qh_NOmerge

  see:
    qh_NOmem in mem.c

    see user.c/user_eg.c for removing io.o
*/

/*----------------------------------

  qh_NOtrace
    no tracing if defined

  notes:
    This saves about 5% space.

    #define qh_NOtrace
*/

/*----------------------------------

  qh_QHpointer
    access global data with pointer or static structure

  qh_QHpointer  = 1     access globals via a pointer to allocated memory
                        enables qh_saveqhull() and qh_restoreqhull()
                        [2010, gcc] costs about 4% in time and 4% in space
                        [2003, msvc] costs about 8% in time and 2% in space

                = 0     qh_qh and qh_qhstat are static data structures
                        only one instance of qhull() can be active at a time
                        default value

  qh_QHpointer_dllimport and qh_dllimport define qh_qh as __declspec(dllimport) [libqhull.h]
  It is required for msvc-2005.  It is not needed for gcc.

  notes:
    all global variables for qhull are in qh, qhmem, and qhstat
    qh is defined in libqhull.h
    qhmem is defined in mem.h
    qhstat is defined in stat.h
    C++ build defines qh_QHpointer [libqhullp.pro, libqhullcpp.pro]

  see:
    user_eg.c for an example
*/
#ifdef qh_QHpointer
#if qh_dllimport
#error QH6207 Qhull error: Use qh_QHpointer_dllimport instead of qh_dllimport with qh_QHpointer
#endif
#else
#define qh_QHpointer 0
#if qh_QHpointer_dllimport
#error QH6234 Qhull error: Use qh_dllimport instead of qh_QHpointer_dllimport when qh_QHpointer is not defined
#endif
#endif
#if 0  /* sample code */
    qhT *oldqhA, *oldqhB;

    exitcode= qh_new_qhull(dim, numpoints, points, ismalloc,
                      flags, outfile, errfile);
    /* use results from first call to qh_new_qhull */
    oldqhA= qh_save_qhull();
    exitcode= qh_new_qhull(dimB, numpointsB, pointsB, ismalloc,
                      flags, outfile, errfile);
    /* use results from second call to qh_new_qhull */
    oldqhB= qh_save_qhull();
    qh_restore_qhull(&oldqhA);
    /* use results from first call to qh_new_qhull */
    qh_freeqhull(qh_ALL);  /* frees all memory used by first call */
    qh_restore_qhull(&oldqhB);
    /* use results from second call to qh_new_qhull */
    qh_freeqhull(!qh_ALL); /* frees long memory used by second call */
    qh_memfreeshort(&curlong, &totlong);  /* frees short memory and memory allocator */
#endif

/*----------------------------------

  qh_QUICKhelp
    =1 to use abbreviated help messages, e.g., for degenerate inputs
*/
#define qh_QUICKhelp    0

/*============================================================*/
/*============= -merge constants- ============================*/
/*============================================================*/
/*
   These constants effect facet merging.  You probably will not need
   to modify them.  They effect the performance of facet merging.
*/

/*----------------------------------

  qh_DIMmergeVertex
    max dimension for vertex merging (it is not effective in high-d)
*/
#define qh_DIMmergeVertex 6

/*----------------------------------

  qh_DIMreduceBuild
     max dimension for vertex reduction during build (slow in high-d)
*/
#define qh_DIMreduceBuild 5

/*----------------------------------

  qh_BESTcentrum
     if > 2*dim+n vertices, qh_findbestneighbor() tests centrums (faster)
     else, qh_findbestneighbor() tests all vertices (much better merges)

  qh_BESTcentrum2
     if qh_BESTcentrum2 * DIM3 + BESTcentrum < #vertices tests centrums
*/
#define qh_BESTcentrum 20
#define qh_BESTcentrum2 2

/*----------------------------------

  qh_BESTnonconvex
    if > dim+n neighbors, qh_findbestneighbor() tests nonconvex ridges.

  notes:
    It is needed because qh_findbestneighbor is slow for large facets
*/
#define qh_BESTnonconvex 15

/*----------------------------------

  qh_MAXnewmerges
    if >n newmerges, qh_merge_nonconvex() calls qh_reducevertices_centrums.

  notes:
    It is needed because postmerge can merge many facets at once
*/
#define qh_MAXnewmerges 2

/*----------------------------------

  qh_MAXnewcentrum
    if <= dim+n vertices (n approximates the number of merges),
      reset the centrum in qh_updatetested() and qh_mergecycle_facets()

  notes:
    needed to reduce cost and because centrums may move too much if
    many vertices in high-d
*/
#define qh_MAXnewcentrum 5

/*----------------------------------

  qh_COPLANARratio
    for 3-d+ merging, qh.MINvisible is n*premerge_centrum

  notes:
    for non-merging, it's DISTround
*/
#define qh_COPLANARratio 3

/*----------------------------------

  qh_DISToutside
    When is a point clearly outside of a facet?
    Stops search in qh_findbestnew or qh_partitionall
    qh_findbest uses qh.MINoutside since since it is only called if no merges.

  notes:
    'Qf' always searches for best facet
    if !qh.MERGING, same as qh.MINoutside.
    if qh_USEfindbestnew, increase value since neighboring facets may be ill-behaved
      [Note: Zdelvertextot occurs normally with interior points]
            RBOX 1000 s Z1 G1e-13 t1001188774 | QHULL Tv
    When there is a sharp edge, need to move points to a
    clearly good facet; otherwise may be lost in another partitioning.
    if too big then O(n^2) behavior for partitioning in cone
    if very small then important points not processed
    Needed in qh_partitionall for
      RBOX 1000 s Z1 G1e-13 t1001032651 | QHULL Tv
    Needed in qh_findbestnew for many instances of
      RBOX 1000 s Z1 G1e-13 t | QHULL Tv

  See:
    qh_DISToutside -- when is a point clearly outside of a facet
    qh_SEARCHdist -- when is facet coplanar with the best facet?
    qh_USEfindbestnew -- when to use qh_findbestnew for qh_partitionpoint()
*/
#define qh_DISToutside ((qh_USEfindbestnew ? 2 : 1) * \
     fmax_((qh MERGING ? 2 : 1)*qh MINoutside, qh max_outside))

/*----------------------------------

  qh_RATIOnearinside
    ratio of qh.NEARinside to qh.ONEmerge for retaining inside points for
    qh_check_maxout().

  notes:
    This is overkill since do not know the correct value.
    It effects whether 'Qc' reports all coplanar points
    Not used for 'd' since non-extreme points are coplanar
*/
#define qh_RATIOnearinside 5

/*----------------------------------

  qh_SEARCHdist
    When is a facet coplanar with the best facet?
    qh_findbesthorizon: all coplanar facets of the best facet need to be searched.

  See:
    qh_DISToutside -- when is a point clearly outside of a facet
    qh_SEARCHdist -- when is facet coplanar with the best facet?
    qh_USEfindbestnew -- when to use qh_findbestnew for qh_partitionpoint()
*/
#define qh_SEARCHdist ((qh_USEfindbestnew ? 2 : 1) * \
      (qh max_outside + 2 * qh DISTround + fmax_( qh MINvisible, qh MAXcoplanar)));

/*----------------------------------

  qh_USEfindbestnew
     Always use qh_findbestnew for qh_partitionpoint, otherwise use
     qh_findbestnew if merged new facet or sharpnewfacets.

  See:
    qh_DISToutside -- when is a point clearly outside of a facet
    qh_SEARCHdist -- when is facet coplanar with the best facet?
    qh_USEfindbestnew -- when to use qh_findbestnew for qh_partitionpoint()
*/
#define qh_USEfindbestnew (zzval_(Ztotmerge) > 50)

/*----------------------------------

  qh_WIDEcoplanar
    n*MAXcoplanar or n*MINvisible for a WIDEfacet

    if vertex is further than qh.WIDEfacet from the hyperplane
    then its ridges are not counted in computing the area, and
    the facet's centrum is frozen.

  notes:
   qh.WIDEfacet= max(qh.MAXoutside,qh_WIDEcoplanar*qh.MAXcoplanar,
      qh_WIDEcoplanar * qh.MINvisible);
*/
#define qh_WIDEcoplanar 6

/*----------------------------------

  qh_MAXnarrow
    max. cosine in initial hull that sets qh.NARROWhull

  notes:
    If qh.NARROWhull, the initial partition does not make
    coplanar points.  If narrow, a coplanar point can be
    coplanar to two facets of opposite orientations and
    distant from the exact convex hull.

    Conservative estimate.  Don't actually see problems until it is -1.0
*/
#define qh_MAXnarrow -0.99999999

/*----------------------------------

  qh_WARNnarrow
    max. cosine in initial hull to warn about qh.NARROWhull

  notes:
    this is a conservative estimate.
    Don't actually see problems until it is -1.0.  See qh-impre.htm
*/
#define qh_WARNnarrow -0.999999999999999

/*----------------------------------

  qh_ZEROdelaunay
    a zero Delaunay facet occurs for input sites coplanar with their convex hull
    the last normal coefficient of a zero Delaunay facet is within
        qh_ZEROdelaunay * qh.ANGLEround of 0

  notes:
    qh_ZEROdelaunay does not allow for joggled input ('QJ').

    You can avoid zero Delaunay facets by surrounding the input with a box.

    Use option 'PDk:-n' to explicitly define zero Delaunay facets
      k= dimension of input sites (e.g., 3 for 3-d Delaunay triangulation)
      n= the cutoff for zero Delaunay facets (e.g., 'PD3:-1e-12')
*/
#define qh_ZEROdelaunay 2

#endif /* qh_DEFuser */



qhull-2012.1/src/libqhull/usermem.c0000644000076400010400000000272711710657472020352 0ustar  bbarberAdministrators/*
  ---------------------------------

   usermem.c
   qh_exit(), qh_free(), and qh_malloc()

   See README.txt.

   If you redefine one of these functions you must redefine all of them.
   If you recompile and load this file, then usermem.o will not be loaded
   from qhull.a or qhull.lib

   See libqhull.h for data structures, macros, and user-callable functions.
   See user.c for qhull-related, redefinable functions
   see user.h for user-definable constants
   See userprintf.c for qh_fprintf and userprintf_rbox,c for qh_fprintf_rbox

   Please report any errors that you fix to qhull@qhull.org
*/

#include "libqhull.h"

#include 

/*---------------------------------

  qh_exit( exitcode )
    exit program

  notes:
    same as exit()
*/
void qh_exit(int exitcode) {
    exit(exitcode);
} /* exit */

/*---------------------------------

qh_free( mem )
free memory

notes:
same as free()
*/
void qh_free(void *mem) {
    free(mem);
} /* free */

/*---------------------------------

    qh_malloc( mem )
      allocate memory

    notes:
      same as malloc()
*/
void *qh_malloc(size_t size) {
    return malloc(size);
} /* malloc */


qhull-2012.1/src/libqhull/userprintf.c0000644000076400010400000000337611710424077021070 0ustar  bbarberAdministrators/*
  ---------------------------------

   userprintf.c
   qh_fprintf()

   see README.txt  see COPYING.txt for copyright information.

   If you recompile and load this file, then userprintf.o will not be loaded
   from qhull.a or qhull.lib

   See libqhull.h for data structures, macros, and user-callable functions.
   See user.c for qhull-related, redefinable functions
   see user.h for user-definable constants
   See usermem.c for qh_exit(), qh_free(), and qh_malloc()
   see Qhull.cpp and RboxPoints.cpp for examples.

   Please report any errors that you fix to qhull@qhull.org
*/

#include "libqhull.h"

#include 
#include 
#include 

/*---------------------------------

   qh_fprintf(fp, msgcode, format, list of args )
     print arguments to *fp according to format
     Use qh_fprintf_rbox() for rboxlib.c

   notes:
     same as fprintf()
     fgets() is not trapped like fprintf()
     exit qh_fprintf via qh_errexit()
*/

void qh_fprintf(FILE *fp, int msgcode, const char *fmt, ... ) {
    va_list args;

    if (!fp) {
        fprintf(stderr, "QH6232 Qhull internal error (userprintf.c): fp is 0.  Wrong qh_fprintf called.\n");
        qh_errexit(6232, NULL, NULL);
    }
    va_start(args, fmt);
#if qh_QHpointer
    if (qh_qh && qh ANNOTATEoutput) {
#else
    if (qh ANNOTATEoutput) {
#endif
      fprintf(fp, "[QH%.4d]", msgcode);
    }else if (msgcode >= MSG_ERROR && msgcode < MSG_STDERR ) {
      fprintf(fp, "QH%.4d ", msgcode);
    }
    vfprintf(fp, fmt, args);
    va_end(args);

    /* Place debugging traps here. Use with option 'Tn' */

} /* qh_fprintf */

qhull-2012.1/src/libqhull/userprintf_rbox.c0000644000076400010400000000312411710424161022103 0ustar  bbarberAdministrators/*
  ---------------------------------

   userprintf_rbox.c
   qh_fprintf_rbox()

   see README.txt  see COPYING.txt for copyright information.

   If you recompile and load this file, then userprintf_rbox.o will not be loaded
   from qhull.a or qhull.lib

   See libqhull.h for data structures, macros, and user-callable functions.
   See user.c for qhull-related, redefinable functions
   see user.h for user-definable constants
   See usermem.c for qh_exit(), qh_free(), and qh_malloc()
   see Qhull.cpp and RboxPoints.cpp for examples.

   Please report any errors that you fix to qhull@qhull.org
*/

#include "libqhull.h"

#include 
#include 
#include 

/*---------------------------------

   qh_fprintf_rbox(fp, msgcode, format, list of args )
     print arguments to *fp according to format
     Use qh_fprintf_rbox() for rboxlib.c

   notes:
     same as fprintf()
     fgets() is not trapped like fprintf()
     exit qh_fprintf_rbox via qh_errexit_rbox()
*/

void qh_fprintf_rbox(FILE *fp, int msgcode, const char *fmt, ... ) {
    va_list args;

    if (!fp) {
        fprintf(stderr, "QH6231 Qhull internal error (userprintf.c): fp is 0.  Wrong qh_fprintf_rbox called.\n");
        qh_errexit_rbox(6231);
    }
    if (msgcode >= MSG_ERROR && msgcode < MSG_STDERR)
      fprintf(fp, "QH%.4d ", msgcode);
    va_start(args, fmt);
    vfprintf(fp, fmt, args);
    va_end(args);
} /* qh_fprintf_rbox */

qhull-2012.1/src/libqhullcpp/0000755000076400010400000000000011721063454017215 5ustar  bbarberAdministratorsqhull-2012.1/src/libqhullcpp/Coordinates.cpp0000644000076400010400000000727111710144464022201 0ustar  bbarberAdministrators/****************************************************************************
**
** Copyright (c) 2009-2012 C.B. Barber. All rights reserved.
** $Id: //main/2011/qhull/src/libqhullcpp/Coordinates.cpp#3 $$Change: 1464 $
** $DateTime: 2012/01/25 22:58:41 $$Author: bbarber $
**
****************************************************************************/

#include "functionObjects.h"
#include "QhullError.h"
#include "Coordinates.h"

#include 
#include 
#include 

#ifdef _MSC_VER  // Microsoft Visual C++ -- warning level 4
#endif

namespace orgQhull {

#//! Coordinates -- vector of coordT (normally double)

#//Element access

// Inefficient without result-value-optimization or implicitly shared object
Coordinates Coordinates::
mid(int idx, int length) const
{
    int newLength= length;
    if(length<0 || idx+length > count()){
        newLength= count()-idx;
    }
    Coordinates result;
    if(newLength>0){
        std::copy(begin()+idx, begin()+(idx+newLength), std::back_inserter(result));
    }
    return result;
}//mid

coordT Coordinates::
value(int idx, const coordT &defaultValue) const
{
    return ((idx < 0 || idx >= count()) ? defaultValue : (*this)[idx]);
}//value

#//Operator

Coordinates Coordinates::
operator+(const Coordinates &other) const
{
    Coordinates result(*this);
    std::copy(other.begin(), other.end(), std::back_inserter(result));
    return result;
}//operator+

Coordinates & Coordinates::
operator+=(const Coordinates &other)
{
    if(&other==this){
        Coordinates clone(other);
        std::copy(clone.begin(), clone.end(), std::back_inserter(*this));
    }else{
        std::copy(other.begin(), other.end(), std::back_inserter(*this));
    }
    return *this;
}//operator+=

#//Read-write

coordT Coordinates::
takeAt(int idx)
{
    coordT c= at(idx);
    erase(begin()+idx);
    return c;
}//takeAt

coordT Coordinates::
takeLast()
{
    coordT c= last();
    removeLast();
    return c;
}//takeLast

void Coordinates::
swap(int idx, int other)
{
    coordT c= at(idx);
    at(idx)= at(other);
    at(other)= c;
}//swap

#//Search

bool Coordinates::
contains(const coordT &t) const
{
    CoordinatesIterator i(*this);
    return i.findNext(t);
}//contains

int Coordinates::
count(const coordT &t) const
{
    CoordinatesIterator i(*this);
    int result= 0;
    while(i.findNext(t)){
        ++result;
    }
    return result;
}//count

int Coordinates::
indexOf(const coordT &t, int from) const
{
    if(from<0){
        from += count();
        if(from<0){
            from= 0;
        }
    }
    if(from(i-begin())); // WARN64
            }
            ++i;
        }
    }
    return -1;
}//indexOf

int Coordinates::
lastIndexOf(const coordT &t, int from) const
{
    if(from<0){
        from += count();
    }else if(from>=count()){
        from= count()-1;
    }
    if(from>=0){
        const_iterator i= begin()+from+1;
        while(i-- != constBegin()){
            if(*i==t){
                return (static_cast(i-begin())); // WARN64
            }
        }
    }
    return -1;
}//lastIndexOf

void Coordinates::
removeAll(const coordT &t)
{
    MutableCoordinatesIterator i(*this);
    while(i.findNext(t)){
        i.remove();
    }
}//removeAll

}//namespace orgQhull

#//Global functions

using std::endl;
using std::istream;
using std::ostream;
using std::string;
using std::ws;
using orgQhull::Coordinates;

ostream &
operator<<(ostream &os, const Coordinates &cs)
{
    Coordinates::const_iterator c= cs.begin();
    for(int i=cs.count(); i--; ){
        os << *c++ << " ";
    }
    return os;
}//operator<<

qhull-2012.1/src/libqhullcpp/Coordinates.h0000644000076400010400000003626711710144464021655 0ustar  bbarberAdministrators/****************************************************************************
**
** Copyright (c) 2009-2012 C.B. Barber. All rights reserved.
** $Id: //main/2011/qhull/src/libqhullcpp/Coordinates.h#6 $$Change: 1464 $
** $DateTime: 2012/01/25 22:58:41 $$Author: bbarber $
**
****************************************************************************/

#ifndef QHCOORDINATES_H
#define QHCOORDINATES_H

#include "QhullError.h"
#include "QhullIterator.h"
extern "C" {
    #include "libqhull/qhull_a.h"
}


#include  // ptrdiff_t, size_t
#include 
#include 

namespace orgQhull {

#//Types
    //! an allocated vector of point coordinates
    //!  Used by PointCoordinates for RboxPoints
    //!  A QhullPoint refers to previously allocated coordinates
    class  Coordinates;
    class  MutableCoordinatesIterator;


class Coordinates {

private:
#//Fields
    std::vector coordinate_array;

public:
#//Subtypes

    class                       const_iterator;
    class                       iterator;
    typedef iterator Iterator;
    typedef const_iterator ConstIterator;

    typedef coordT              value_type;
    typedef const value_type   *const_pointer;
    typedef const value_type   &const_reference;
    typedef value_type         *pointer;
    typedef value_type         &reference;
    typedef ptrdiff_t           difference_type;
    typedef int                 size_type;

#//Construct
                        Coordinates() {};
    explicit            Coordinates(const std::vector &other) : coordinate_array(other) {}
                        Coordinates(const Coordinates &other) : coordinate_array(other.coordinate_array) {}
    Coordinates        &operator=(const Coordinates &other) { coordinate_array= other.coordinate_array; return *this; }
    Coordinates        &operator=(const std::vector &other) { coordinate_array= other; return *this; }
                       ~Coordinates() {}

#//Conversion

    coordT             *data() { return isEmpty() ? 0 : &at(0); }
    const coordT       *data() const { return const_cast(isEmpty() ? 0 : &at(0)); }

#ifndef QHULL_NO_STL
    std::vector toStdVector() const { return coordinate_array; }
#endif //QHULL_NO_STL
#ifdef QHULL_USES_QT
    QList      toQList() const;
#endif //QHULL_USES_QT

#//GetSet
    int                count() const { return static_cast(size()); }
    bool               empty() const { return coordinate_array.empty(); }
    bool               isEmpty() const { return empty(); }
    bool               operator==(const Coordinates &other) const  { return coordinate_array==other.coordinate_array; }
    bool               operator!=(const Coordinates &other) const  { return coordinate_array!=other.coordinate_array; }
    size_t             size() const { return coordinate_array.size(); }

#//Element access
    coordT             &at(int idx) { return coordinate_array.at(idx); }
    const coordT       &at(int idx) const { return coordinate_array.at(idx); }
    coordT             &back() { return coordinate_array.back(); }
    const coordT       &back() const { return coordinate_array.back(); }
    coordT             &first() { return front(); }
    const coordT       &first() const { return front(); }
    coordT             &front() { return coordinate_array.front(); }
    const coordT       &front() const { return coordinate_array.front(); }
    coordT             &last() { return back(); }
    const coordT       &last() const { return back(); }
    Coordinates        mid(int idx, int length= -1) const;
    coordT            &operator[](int idx) { return coordinate_array.operator[](idx); }
    const coordT      &operator[](int idx) const { return coordinate_array.operator[](idx); }
    coordT             value(int idx, const coordT &defaultValue) const;

#//Iterator
    iterator            begin() { return iterator(coordinate_array.begin()); }
    const_iterator      begin() const { return const_iterator(coordinate_array.begin()); }
    const_iterator      constBegin() const { return begin(); }
    const_iterator      constEnd() const { return end(); }
    iterator            end() { return iterator(coordinate_array.end()); }
    const_iterator      end() const { return const_iterator(coordinate_array.end()); }

#//Read-only
    Coordinates         operator+(const Coordinates &other) const;

#//Modify
    void                append(const coordT &c) { push_back(c); }
    void                clear() { coordinate_array.clear(); }
    iterator            erase(iterator idx) { return iterator(coordinate_array.erase(idx.base())); }
    iterator            erase(iterator beginIterator, iterator endIterator) { return iterator(coordinate_array.erase(beginIterator.base(), endIterator.base())); }
    void                insert(int before, const coordT &c) { insert(begin()+before, c); }
    iterator            insert(iterator before, const coordT &c) { return iterator(coordinate_array.insert(before.base(), c)); }
    void                move(int from, int to) { insert(to, takeAt(from)); }
    Coordinates        &operator+=(const Coordinates &other);
    Coordinates        &operator+=(const coordT &c) { append(c); return *this; }
    Coordinates        &operator<<(const Coordinates &other) { return *this += other; }
    Coordinates        &operator<<(const coordT &c) { return *this += c; }
    void                pop_back() { coordinate_array.pop_back(); }
    void                pop_front() { removeFirst(); }
    void                prepend(const coordT &c) { insert(begin(), c); }
    void                push_back(const coordT &c) { coordinate_array.push_back(c); }
    void                push_front(const coordT &c) { insert(begin(), c); }
                        //removeAll below
    void                removeAt(int idx) { erase(begin()+idx); }
    void                removeFirst() { erase(begin()); }
    void                removeLast() { erase(--end()); }
    void                replace(int idx, const coordT &c) { (*this)[idx]= c; }
    void                reserve(int i) { coordinate_array.reserve(i); }
    void                swap(int idx, int other);
    coordT              takeAt(int idx);
    coordT              takeFirst() { return takeAt(0); }
    coordT              takeLast();

#//Search
    bool                contains(const coordT &t) const;
    int                 count(const coordT &t) const;
    int                 indexOf(const coordT &t, int from = 0) const;
    int                 lastIndexOf(const coordT &t, int from = -1) const;
    void                removeAll(const coordT &t);

#//Coordinates::iterator -- from QhullPoints, forwarding to coordinate_array
    // before const_iterator for conversion with comparison operators
    class iterator {

    private:
        std::vector::iterator i;
        friend class    const_iterator;

    public:
        typedef std::random_access_iterator_tag  iterator_category;
        typedef coordT      value_type;
        typedef value_type *pointer;
        typedef value_type &reference;
        typedef ptrdiff_t   difference_type;

                        iterator() {}
                        iterator(const iterator &other) { i= other.i; }
        explicit        iterator(const std::vector::iterator &vi) { i= vi; }
        iterator       &operator=(const iterator &other) { i= other.i; return *this; }
        std::vector::iterator &base() { return i; }
                        // No operator-> for base types
        coordT         &operator*() const { return *i; }
        coordT         &operator[](int idx) const { return i[idx]; }

        bool            operator==(const iterator &other) const { return i==other.i; }
        bool            operator!=(const iterator &other) const { return i!=other.i; }
        bool            operator<(const iterator &other) const { return i(const iterator &other) const { return i>other.i; }
        bool            operator>=(const iterator &other) const { return i>=other.i; }
              // reinterpret_cast to break circular dependency
        bool            operator==(const Coordinates::const_iterator &other) const { return *this==reinterpret_cast(other); }
        bool            operator!=(const Coordinates::const_iterator &other) const { return *this!=reinterpret_cast(other); }
        bool            operator<(const Coordinates::const_iterator &other) const { return *this(other); }
        bool            operator<=(const Coordinates::const_iterator &other) const { return *this<=reinterpret_cast(other); }
        bool            operator>(const Coordinates::const_iterator &other) const { return *this>reinterpret_cast(other); }
        bool            operator>=(const Coordinates::const_iterator &other) const { return *this>=reinterpret_cast(other); }

        iterator        operator++() { return iterator(++i); } //FIXUP QH11012 Should return reference, but get reference to temporary
        iterator        operator++(int) { return iterator(i++); }
        iterator        operator--() { return iterator(--i); }
        iterator        operator--(int) { return iterator(i--); }
        iterator        operator+=(int idx) { return iterator(i += idx); }
        iterator        operator-=(int idx) { return iterator(i -= idx); }
        iterator        operator+(int idx) const { return iterator(i+idx); }
        iterator        operator-(int idx) const { return iterator(i-idx); }
        difference_type operator-(iterator other) const { return i-other.i; }
    };//Coordinates::iterator

#//Coordinates::const_iterator
    class const_iterator {

    private:
        std::vector::const_iterator i;

    public:
        typedef std::random_access_iterator_tag  iterator_category;
        typedef coordT            value_type;
        typedef const value_type *pointer;
        typedef const value_type &reference;
        typedef ptrdiff_t         difference_type;

                        const_iterator() {}
                        const_iterator(const const_iterator &other) { i= other.i; }
                        const_iterator(iterator o) : i(o.i) {}
        explicit        const_iterator(const std::vector::const_iterator &vi) { i= vi; }
        const_iterator &operator=(const const_iterator &other) { i= other.i; return *this; }
                        // No operator-> for base types
                        // No reference to a base type for () and []
        const coordT   &operator*() const { return *i; }
        const coordT   &operator[](int idx) const { return i[idx]; }

        bool            operator==(const const_iterator &other) const { return i==other.i; }
        bool            operator!=(const const_iterator &other) const { return i!=other.i; }
        bool            operator<(const const_iterator &other) const { return i(const const_iterator &other) const { return i>other.i; }
        bool            operator>=(const const_iterator &other) const { return i>=other.i; }

        const_iterator  operator++() { return const_iterator(++i); } //FIXUP QH11014 -- too much copying
        const_iterator  operator++(int) { return const_iterator(i++); }
        const_iterator  operator--() { return const_iterator(--i); }
        const_iterator  operator--(int) { return const_iterator(i--); }
        const_iterator  operator+=(int idx) { return const_iterator(i += idx); }
        const_iterator  operator-=(int idx) { return const_iterator(i -= idx); }
        const_iterator  operator+(int idx) const { return const_iterator(i+idx); }
        const_iterator  operator-(int idx) const { return const_iterator(i-idx); }
        difference_type operator-(const_iterator other) const { return i-other.i; }
    };//Coordinates::const_iterator

};//Coordinates

//class CoordinatesIterator
//QHULL_DECLARE_SEQUENTIAL_ITERATOR(Coordinates, coordT)

class CoordinatesIterator
{
    typedef Coordinates::const_iterator const_iterator;
    const Coordinates *c;
    const_iterator i;
    public:
    inline CoordinatesIterator(const Coordinates &container)
    : c(&container), i(c->constBegin()) {}
    inline CoordinatesIterator &operator=(const Coordinates &container)
    { c = &container; i = c->constBegin(); return *this; }
    inline void toFront() { i = c->constBegin(); }
    inline void toBack() { i = c->constEnd(); }
    inline bool hasNext() const { return i != c->constEnd(); }
    inline const coordT &next() { return *i++; }
    inline const coordT &peekNext() const { return *i; }
    inline bool hasPrevious() const { return i != c->constBegin(); }
    inline const coordT &previous() { return *--i; }
    inline const coordT &peekPrevious() const { const_iterator p = i; return *--p; }
    inline bool findNext(const coordT &t)
    { while (i != c->constEnd()) if (*i++ == t) return true; return false; }
    inline bool findPrevious(const coordT &t)
    { while (i != c->constBegin()) if (*(--i) == t) return true;
    return false;  }
};//CoordinatesIterator

//class MutableCoordinatesIterator
//QHULL_DECLARE_MUTABLE_SEQUENTIAL_ITERATOR(Coordinates, coordT)
class MutableCoordinatesIterator
{
    typedef Coordinates::iterator iterator;
    typedef Coordinates::const_iterator const_iterator;
    Coordinates *c;
    iterator i, n;
    inline bool item_exists() const { return const_iterator(n) != c->constEnd(); }
    public:
    inline MutableCoordinatesIterator(Coordinates &container)
    : c(&container)
    { i = c->begin(); n = c->end(); }
    inline ~MutableCoordinatesIterator()
    {}
    inline MutableCoordinatesIterator &operator=(Coordinates &container)
    { c = &container;
    i = c->begin(); n = c->end(); return *this; }
    inline void toFront() { i = c->begin(); n = c->end(); }
    inline void toBack() { i = c->end(); n = i; }
    inline bool hasNext() const { return c->constEnd() != const_iterator(i); }
    inline coordT &next() { n = i++; return *n; }
    inline coordT &peekNext() const { return *i; }
    inline bool hasPrevious() const { return c->constBegin() != const_iterator(i); }
    inline coordT &previous() { n = --i; return *n; }
    inline coordT &peekPrevious() const { iterator p = i; return *--p; }
    inline void remove()
    { if (c->constEnd() != const_iterator(n)) { i = c->erase(n); n = c->end(); } }
    inline void setValue(const coordT &t) const { if (c->constEnd() != const_iterator(n)) *n = t; }
    inline coordT &value() { QHULL_ASSERT(item_exists()); return *n; }
    inline const coordT &value() const { QHULL_ASSERT(item_exists()); return *n; }
    inline void insert(const coordT &t) { n = i = c->insert(i, t); ++i; }
    inline bool findNext(const coordT &t)
    { while (c->constEnd() != const_iterator(n = i)) if (*i++ == t) return true; return false; }
    inline bool findPrevious(const coordT &t)
    { while (c->constBegin() != const_iterator(i)) if (*(n = --i) == t) return true;
    n = c->end(); return false;  }
};//MutableCoordinatesIterator


}//namespace orgQhull

#//Global functions

std::ostream &operator<<(std::ostream &os, const orgQhull::Coordinates &c);

#endif // QHCOORDINATES_H
qhull-2012.1/src/libqhullcpp/functionObjects.h0000644000076400010400000000275411710144464022534 0ustar  bbarberAdministrators/****************************************************************************
**
** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
** $Id: //main/2011/qhull/src/libqhullcpp/functionObjects.h#4 $$Change: 1464 $
** $DateTime: 2012/01/25 22:58:41 $$Author: bbarber $
**
****************************************************************************/

#ifndef QHFUNCTIONOBJECTS_H
#define QHFUNCTIONOBJECTS_H

#include 
#include 

namespace orgQhull {
#//Type

    //! Sum of absolute values of the elements in a container
    class AbsoluteSumOf;
    //! Sum of the elements in a container
    class SumOf;
    //! Sum of squares of the elements in a container
    class SumSquaresOf;

#//Class

//! Absolute sum of the elements in a container
class AbsoluteSumOf
{
private:
    double sum;
public:
    inline AbsoluteSumOf() : sum(0.0) {}
    inline void operator()(double v) { sum += fabs(v); }
    inline operator double() { return sum; }
};//AbsoluteSumOf

//! Sum of the elements in a container
class SumOf
{
private:
    double sum;
public:
    inline SumOf() : sum(0.0) {}
    inline void operator()(double v) { sum += v; }
    inline operator double() { return sum; }
};//SumOf


//! Sum of squares of the elements in a container
class SumSquaresOf
{
private:
    double sum;
public:
    inline SumSquaresOf() : sum(0.0) {}
    inline void operator()(double v) { sum += v*v; }
    inline operator double() { return sum; }
};//SumSquaresOf


}//orgQhull


#endif //QHFUNCTIONOBJECTS_H

qhull-2012.1/src/libqhullcpp/libqhullcpp.pro0000644000076400010400000000336211716453152022264 0ustar  bbarberAdministrators# -------------------------------------------------
# libqhullcpp.pro -- Qt project for Qhull cpp shared library
# -------------------------------------------------

include(../qhull-warn.pri)

DESTDIR = ../../lib
TEMPLATE = lib
CONFIG += staticlib warn_on
CONFIG -= qt rtti
build_pass:CONFIG(debug, debug|release):{
   TARGET = qhullcpp_d
   OBJECTS_DIR = Debug
}else:build_pass:CONFIG(release, debug|release):{
   TARGET = qhullcpp
   OBJECTS_DIR = Release
}
MOC_DIR = moc

DEFINES += qh_QHpointer # libqhull/user.h

INCLUDEPATH += ../../src
INCLUDEPATH += $$PWD # for MOC_DIR

CONFIG += qhull_warn_shadow qhull_warn_conversion

SOURCES += Coordinates.cpp
SOURCES += PointCoordinates.cpp
SOURCES += Qhull.cpp
SOURCES += QhullFacet.cpp
SOURCES += QhullFacetList.cpp
SOURCES += QhullFacetSet.cpp
SOURCES += QhullHyperplane.cpp
SOURCES += QhullPoint.cpp
SOURCES += QhullPoints.cpp
SOURCES += QhullPointSet.cpp
SOURCES += QhullQh.cpp
SOURCES += QhullRidge.cpp
SOURCES += QhullSet.cpp
SOURCES += QhullStat.cpp
SOURCES += QhullVertex.cpp
SOURCES += QhullVertexSet.cpp
SOURCES += RboxPoints.cpp
SOURCES += RoadError.cpp
SOURCES += RoadLogEvent.cpp
SOURCES += UsingLibQhull.cpp

HEADERS += Coordinates.h
HEADERS += functionObjects.h
HEADERS += PointCoordinates.h
HEADERS += Qhull.h
HEADERS += QhullError.h
HEADERS += QhullFacet.h
HEADERS += QhullFacetList.h
HEADERS += QhullFacetSet.h
HEADERS += QhullHyperplane.h
HEADERS += QhullIterator.h
HEADERS += QhullLinkedList.h
HEADERS += QhullPoint.h
HEADERS += QhullPoints.h
HEADERS += QhullPointSet.h
HEADERS += QhullQh.h
HEADERS += QhullRidge.h
HEADERS += QhullSet.h
HEADERS += QhullSets.h
HEADERS += QhullStat.h
HEADERS += QhullVertex.h
HEADERS += RboxPoints.h
HEADERS += RoadError.h
HEADERS += RoadLogEvent.h
HEADERS += UsingLibQhull.h
qhull-2012.1/src/libqhullcpp/PointCoordinates.cpp0000644000076400010400000001776611710144464023225 0ustar  bbarberAdministrators/****************************************************************************
**
** Copyright (c) 2009-2012 C.B. Barber. All rights reserved.
** $Id: //main/2011/qhull/src/libqhullcpp/PointCoordinates.cpp#6 $$Change: 1464 $
** $DateTime: 2012/01/25 22:58:41 $$Author: bbarber $
**
****************************************************************************/

#include "QhullError.h"
#include "QhullPoint.h"
#include "PointCoordinates.h"

#include 
#include 

using std::istream;
using std::string;
using std::ws;

#ifdef _MSC_VER  // Microsoft Visual C++ -- warning level 4
#pragma warning( disable : 4996)  // function was declared deprecated(strcpy, localtime, etc.)
#endif

namespace orgQhull {

#//! PointCoordinates -- vector of PointCoordinates

#//Construct
PointCoordinates::
PointCoordinates()
: QhullPoints()
, point_coordinates()
, point_comment()
{
    makeValid();
}

#//Construct
PointCoordinates::
PointCoordinates(int pointDimension)
: QhullPoints(pointDimension)
, point_coordinates()
, point_comment()
{
    makeValid();
}

PointCoordinates::
PointCoordinates(const std::string &aComment)
: QhullPoints()
, point_coordinates()
, point_comment(aComment)
{
    makeValid();
}

PointCoordinates::
PointCoordinates(int pointDimension, const std::string &aComment)
: QhullPoints(pointDimension)
, point_coordinates()
, point_comment(aComment)
{
    makeValid();
}

PointCoordinates::
PointCoordinates(int pointDimension, const std::string &aComment, int coordinatesCount, const coordT *c)
: QhullPoints(pointDimension)
, point_coordinates()
, point_comment(aComment)
{
    append(coordinatesCount, c);
}

PointCoordinates::
PointCoordinates(const PointCoordinates &other)
: QhullPoints(other)
, point_coordinates(other.point_coordinates)
, point_comment(other.point_comment)
{
    makeValid();
}

PointCoordinates & PointCoordinates::
operator=(const PointCoordinates &other)
{
    point_coordinates= other.point_coordinates;
    point_comment= other.point_comment;
    makeValid();
    return *this;
}//operator=

PointCoordinates::
~PointCoordinates()
{ }

#//GetSet

void PointCoordinates::
checkValid() const
{
    if(getCoordinates().data()!=data()
    || getCoordinates().count()!=coordinateCount()){
        throw QhullError(10060, "Qhull error: first point (%x) is not PointCoordinates.data() or count (%d) is not PointCoordinates.count (%d)", coordinateCount(), getCoordinates().count(), 0.0, data());
    }
}//checkValid

void PointCoordinates::
setDimension(int i)
{
    if(i<0){
        throw QhullError(10062, "Qhull error: can not set PointCoordinates dimension to %d", i);
    }
    int currentDimension=QhullPoints::dimension();
    if(currentDimension!=0 && i!=currentDimension){
        throw QhullError(10063, "Qhull error: can not change PointCoordinates dimension (from %d to %d)", currentDimension, i);
    }
    QhullPoints::setDimension(i);
}//setDimension

//#Foreach

Coordinates::ConstIterator PointCoordinates::
beginCoordinates(int pointIndex) const
{
    return point_coordinates.begin()+indexOffset(pointIndex);
}

Coordinates::Iterator PointCoordinates::
beginCoordinates(int pointIndex)
{
    return point_coordinates.begin()+indexOffset(pointIndex);
}

#//Modify

void PointCoordinates::
append(int coordinatesCount, const coordT *c)
{
    if(coordinatesCount<=0){
        return;
    }
    if(includesCoordinates(c)){
        throw QhullError(10065, "Qhull error: can not append a subset of PointCoordinates to itself.  The coordinates for point %d may move.", indexOf(c, QhullError::NOthrow));
    }
    reserveCoordinates(coordinatesCount);
    std::copy(c, c+coordinatesCount, std::back_inserter(point_coordinates));
    makeValid();
}//append coordT

void PointCoordinates::
append(const PointCoordinates &other)
{
    setDimension(other.dimension());
    append(other.coordinateCount(), other.data());
}//append PointCoordinates

void PointCoordinates::
append(const QhullPoint &p)
{
    setDimension(p.dimension());
    append(p.dimension(), p.coordinates());
}//append QhullPoint

void PointCoordinates::
appendComment(const std::string &s){
    if(char c= s[0] && point_comment.empty()){
        if(c=='-' || isdigit(c)){
            throw QhullError(10028, "Qhull argument error: comments can not start with a number or minus, %s", 0, 0, 0.0, s.c_str());
        }
    }
    point_comment += s;
}//appendComment

//! Read PointCoordinates from istream.  First two numbers are dimension and count.  A non-digit starts a rboxCommand.
//! Overwrites point_comment.  See qh_readpoints [io.c]
void PointCoordinates::
appendPoints(istream &in)
{
    int inDimension, inCount;
    in >> ws >> inDimension >> ws;
    if(!in.good()){
        in.clear();
        string remainder;
        getline(in, remainder);
        throw QhullError(10005, "Qhull error: input did not start with dimension or count -- %s", 0, 0, 0, remainder.c_str());
    }
    char c= (char)in.peek();
    if(c!='-' && !isdigit(c)){         // Comments start with a non-digit
        getline(in, point_comment);
        in >> ws;
    }
    in >> inCount >> ws;
    if(!in.good()){
        in.clear();
        string remainder;
        getline(in, remainder);
        throw QhullError(10009, "Qhull error: input did not start with dimension and count -- %d %s", inDimension, 0, 0, remainder.c_str());
    }
    c= (char)in.peek();
    if(c!='-' && !isdigit(c)){         // Comments start with a non-digit
        getline(in, point_comment);
        in >> ws;
    }
    if(inCount> p >> ws;
        if(in.fail()){
            in.clear();
            string remainder;
            getline(in, remainder);
            throw QhullError(10008, "Qhull error: failed to read coordinate %d  of point %d\n   %s", coordinatesCount % inDimension, coordinatesCount/inDimension, 0, remainder.c_str());
        }else{
            point_coordinates.push_back(p);
            coordinatesCount++;
        }
    }
    if(coordinatesCount != inCount*inDimension){
        if(coordinatesCount%inDimension==0){
            throw QhullError(10006, "Qhull error: expected %d %d-d PointCoordinates but read %i PointCoordinates", int(inCount), inDimension, 0.0, int(coordinatesCount/inDimension));
        }else{
            throw QhullError(10012, "Qhull error: expected %d %d-d PointCoordinates but read %i PointCoordinates plus %f extra coordinates", inCount, inDimension, float(coordinatesCount%inDimension), coordinatesCount/inDimension);
        }
    }
    makeValid();
}//appendPoints istream

PointCoordinates PointCoordinates::
operator+(const PointCoordinates &other) const
{
    PointCoordinates pc= *this;
    pc << other;
    return pc;
}//operator+

void PointCoordinates::
reserveCoordinates(int newCoordinates)
{
    // vector::reserve is not const
    point_coordinates.reserve((int)point_coordinates.size()+newCoordinates); // WARN64
    makeValid();
}//reserveCoordinates

#//Helpers

int PointCoordinates::
indexOffset(int i) const {
    int n= i*dimension();
    int coordinatesCount= point_coordinates.count();
    if(i<0 || n>coordinatesCount){
        throw QhullError(10061, "Qhull error: point_coordinates is too short (%d) for point %d", coordinatesCount, i);
    }
    return n;
}

}//namespace orgQhull

#//Global functions

using std::endl;
using std::ostream;

using orgQhull::Coordinates;
using orgQhull::PointCoordinates;

ostream&
operator<<(ostream &os, const PointCoordinates &p)
{
    p.checkValid();
    int count= p.count();
    int dimension= p.dimension();
    string comment= p.comment();
    if(comment.empty()){
        os << dimension << endl;
    }else{
        os << dimension << " " << comment << endl;
    }
    os << count << endl;
    Coordinates::ConstIterator c= p.beginCoordinates();
    for(int i=0; i
#include 

namespace orgQhull {

#//Types
    //! Zero or more points with Coordinates, count, and dimension
    class PointCoordinates;

class PointCoordinates : public QhullPoints {

private:
#//Field
    Coordinates         point_coordinates;      //! array of point coordinates
                                                //! may have extraCoordinates()
    std::string         point_comment;          //! Comment describing PointCoordinates

public:
#//Construct
                        PointCoordinates();
    explicit            PointCoordinates(int pointDimension);
    explicit            PointCoordinates(const std::string &aComment);
                        PointCoordinates(int pointDimension, const std::string &aComment);
                        PointCoordinates(int pointDimension, const std::string &aComment, int coordinatesCount, const coordT *c); // may be invalid
                        //! Use append() and appendPoints() for Coordinates and vector
                        PointCoordinates(const PointCoordinates &other);
    PointCoordinates   &operator=(const PointCoordinates &other);
    ~PointCoordinates();

#//Convert
    //! QhullPoints coordinates, constData, data, count, size
#ifndef QHULL_NO_STL
    void                append(const std::vector &otherCoordinates) { if(!otherCoordinates.empty()){ append((int)otherCoordinates.size(), &otherCoordinates[0]); } }
    std::vector toStdVector() const { return point_coordinates.toStdVector(); }
#endif //QHULL_NO_STL
#ifdef QHULL_USES_QT
    void                append(const QList &pointCoordinates) { if(!pointCoordinates.isEmpty()){ append(pointCoordinates.count(), &pointCoordinates[0]); } }
    QList       toQList() const { return point_coordinates.toQList(); }
#endif //QHULL_USES_QT

#//GetSet
    //! See QhullPoints for coordinates, coordinateCount, dimension, empty, isEmpty, ==, !=
    void                checkValid() const;
    std::string         comment() const { return point_comment; }
    void                makeValid() { defineAs(point_coordinates.count(), point_coordinates.data()); }
    const Coordinates  &getCoordinates() const { return point_coordinates; }
    void                setComment(const std::string &s) { point_comment= s; }
    void                setDimension(int i);

private:
    void                defineAs(int coordinatesCount, coordT *c) { QhullPoints::defineAs(coordinatesCount, c); }
    //! defineAs() otherwise disabled
public:

#//ElementAccess
    //! See QhullPoints for at, back, first, front, last, mid, [], value

#//Foreach
    //! See QhullPoints for begin, constBegin, end
    Coordinates::ConstIterator  beginCoordinates() const { return point_coordinates.begin(); }
    Coordinates::Iterator       beginCoordinates() { return point_coordinates.begin(); }
    Coordinates::ConstIterator  beginCoordinates(int pointIndex) const;
    Coordinates::Iterator       beginCoordinates(int pointIndex);
    Coordinates::ConstIterator  endCoordinates() const { return point_coordinates.end(); }
    Coordinates::Iterator       endCoordinates() { return point_coordinates.end(); }

#//Search
    //! See QhullPoints for contains, count, indexOf, lastIndexOf

#//Read-only
    PointCoordinates    operator+(const PointCoordinates &other) const;

#//Modify
    //FIXUP QH11001: Add clear() and other modify operators from Coordinates.h.  Include QhullPoint::operator=()
    void                append(int coordinatesCount, const coordT *c);  //! Dimension previously defined
    void                append(const coordT &c) { append(1, &c); } //! Dimension previously defined
    void                append(const QhullPoint &p);
    //! See convert for std::vector and QList
    void                append(const Coordinates &c) { append(c.count(), c.data()); }
    void                append(const PointCoordinates &other);
    void                appendComment(const std::string &s);
    void                appendPoints(std::istream &in);
    PointCoordinates   &operator+=(const PointCoordinates &other) { append(other); return *this; }
    PointCoordinates   &operator+=(const coordT &c) { append(c); return *this; }
    PointCoordinates   &operator+=(const QhullPoint &p) { append(p); return *this; }
    PointCoordinates   &operator<<(const PointCoordinates &other) { return *this += other; }
    PointCoordinates   &operator<<(const coordT &c) { return *this += c; }
    PointCoordinates   &operator<<(const QhullPoint &p) { return *this += p; }
    // reserve() is non-const
    void                reserveCoordinates(int newCoordinates);

#//Helpers
private:
    int                 indexOffset(int i) const;

};//PointCoordinates

// No references to QhullPoint.  Prevents use of QHULL_DECLARE_SEQUENTIAL_ITERATOR(PointCoordinates, QhullPoint)
class PointCoordinatesIterator
{
    typedef PointCoordinates::const_iterator const_iterator;
    const PointCoordinates *c;
    const_iterator i;
    public:
    inline PointCoordinatesIterator(const PointCoordinates &container)
    : c(&container), i(c->constBegin()) {}
    inline PointCoordinatesIterator &operator=(const PointCoordinates &container)
    { c = &container; i = c->constBegin(); return *this; }
    inline void toFront() { i = c->constBegin(); }
    inline void toBack() { i = c->constEnd(); }
    inline bool hasNext() const { return i != c->constEnd(); }
    inline const QhullPoint next() { return *i++; }
    inline const QhullPoint peekNext() const { return *i; }
    inline bool hasPrevious() const { return i != c->constBegin(); }
    inline const QhullPoint previous() { return *--i; }
    inline const QhullPoint peekPrevious() const { const_iterator p = i; return *--p; }
    inline bool findNext(const QhullPoint &t)
    { while (i != c->constEnd()) if (*i++ == t) return true; return false; }
    inline bool findPrevious(const QhullPoint &t)
    { while (i != c->constBegin()) if (*(--i) == t) return true;
    return false;  }
};//CoordinatesIterator

// FIXUP QH11002:  Add MutablePointCoordinatesIterator after adding modify operators
\
}//namespace orgQhull

#//Global functions

std::ostream           &operator<<(std::ostream &os, const orgQhull::PointCoordinates &p);

#endif // QHPOINTCOORDINATES_H
qhull-2012.1/src/libqhullcpp/Qhull.cpp0000644000076400010400000003704311710144464021014 0ustar  bbarberAdministrators/****************************************************************************
**
** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
** $Id: //main/2011/qhull/src/libqhullcpp/Qhull.cpp#6 $$Change: 1464 $
** $DateTime: 2012/01/25 22:58:41 $$Author: bbarber $
**
****************************************************************************/

#//! Qhull -- invoke qhull from C++
#//! Compile libqhull and Qhull together due to use of setjmp/longjmp()

#include "QhullError.h"
#include "UsingLibQhull.h"
#include "RboxPoints.h"
#include "QhullQh.h"
#include "QhullFacet.h"
#include "QhullFacetList.h"
#include "Qhull.h"
extern "C" {
    #include "libqhull/qhull_a.h"
}

#include 

using std::cerr;
using std::string;
using std::vector;
using std::ostream;

#ifdef _MSC_VER  // Microsoft Visual C++ -- warning level 4
#pragma warning( disable : 4611)  // interaction between '_setjmp' and C++ object destruction is non-portable
#pragma warning( disable : 4996)  // function was declared deprecated(strcpy, localtime, etc.)
#endif

namespace orgQhull {

#//Global variables

char s_unsupported_options[]=" Fd TI ";
char s_not_output_options[]= " Fd TI A C d E H P Qb QbB Qbb Qc Qf Qg Qi Qm QJ Qr QR Qs Qt Qv Qx Qz Q0 Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 R Tc TC TM TP TR Tv TV TW U v V W ";

#//Constructor, destructor, etc.
Qhull::
Qhull()
: qhull_qh(0)
, qhull_run_id(UsingLibQhull::NOqhRunId)
, origin_point()
, qhull_status(qh_ERRnone)
, qhull_dimension(0)
, run_called(false)
, qh_active(false)
, qhull_message()
, error_stream(0)
, output_stream(0)
, feasiblePoint()
, useOutputStream(false)
{
    initializeQhull();
}//Qhull

Qhull::
Qhull(const RboxPoints &rboxPoints, const char *qhullCommand2)
: qhull_qh(0)
, qhull_run_id(UsingLibQhull::NOqhRunId)
, origin_point()
, qhull_status(qh_ERRnone)
, qhull_dimension(0)
, run_called(false)
, qh_active(false)
, qhull_message()
, error_stream(0)
, output_stream(0)
, feasiblePoint()
, useOutputStream(false)
{
    initializeQhull();
    runQhull(rboxPoints, qhullCommand2);
}//Qhull rbox

Qhull::
Qhull(const char *rboxCommand2, int pointDimension, int pointCount, const realT *pointCoordinates, const char *qhullCommand2)
: qhull_qh(0)
, qhull_run_id(UsingLibQhull::NOqhRunId)
, origin_point()
, qhull_status(qh_ERRnone)
, qhull_dimension(0)
, run_called(false)
, qh_active(false)
, qhull_message()
, error_stream(0)
, output_stream(0)
, feasiblePoint()
, useOutputStream(false)
{
    initializeQhull();
    runQhull(rboxCommand2, pointDimension, pointCount, pointCoordinates, qhullCommand2);
}//Qhull points

Qhull::
Qhull(const Qhull &other)
: qhull_qh(0)
, qhull_run_id(UsingLibQhull::NOqhRunId)
, origin_point()
, qhull_status(qh_ERRnone)
, qhull_dimension(0)
, run_called(false)
, qh_active(false)
, qhull_message(other.qhull_message)
, error_stream(other.error_stream)
, output_stream(other.output_stream)
, feasiblePoint(other.feasiblePoint)
, useOutputStream(other.useOutputStream)
{
    if(other.initialized()){
        throw QhullError(10069, "Qhull error: can not use Qhull copy constructor if initialized() is true");
    }
    initializeQhull();
}//copy constructor

Qhull & Qhull::
operator=(const Qhull &other)
{
    if(other.initialized() || initialized()){
        throw QhullError(10070, "Qhull error: can not use Qhull copy assignment if initialized() is true");
    }
    qhull_message= other.qhull_message;
    error_stream= other.error_stream;
    output_stream= other.output_stream;
    feasiblePoint= other.feasiblePoint;
    useOutputStream= other.useOutputStream;
    return *this;
}//copy constructor

void Qhull::
initializeQhull()
{
    #if qh_QHpointer
        qhull_qh= new QhullQh;
        qhull_qh->old_qhstat= qh_qhstat;
        qhull_qh->old_tempstack= qhmem.tempstack;
        qh_qh= 0;
        qh_qhstat= 0;
    #else
        qhull_qh= new (&qh_qh) QhullQh;
        qhull_qh->old_qhstat= &qh_qhstat;
        qhull_qh->old_tempstack= qhmem.tempstack;
    #endif
    qhmem.tempstack= 0;
    qhull_run_id= qhull_qh->run_id;
}//initializeQhull

Qhull::
~Qhull() throw()
{
    //! UsingLibQhull is required by ~QhullQh
    UsingLibQhull q(this, QhullError::NOthrow);
    if(q.defined()){
        int exitCode = setjmp(qh errexit);
        if(!exitCode){ // no object creation -- destructors skipped on longjmp()
#if qh_QHpointer
            delete qhull_qh;
            // clears qhull_qh and qh_qh
            qh_qh= 0;
#else
            qhull_qh->~QhullQh();
            qhull_qh= 0;
#endif
            qhull_run_id= UsingLibQhull::NOqhRunId;
            // Except for cerr, does not throw errors
            if(hasQhullMessage()){
                cerr<< "\nQhull output at end\n"; //FIXUP QH11005: where should error and log messages go on ~Qhull?
                cerr<num_points*hullDimension(), qhull_qh->first_point);
}//points

QhullPointSet Qhull::
otherPoints() const
{
    return QhullPointSet(hullDimension(), qhull_qh->other_points);
}//otherPoints

//! Return vertices of the convex hull.
QhullVertexList Qhull::
vertexList() const{
    return QhullVertexList(beginVertex(), endVertex());
}//vertexList

#//Modify

void Qhull::
outputQhull()
{
    checkIfQhullInitialized();
    UsingLibQhull q(this);
    int exitCode = setjmp(qh errexit);
    if(!exitCode){ // no object creation -- destructors skipped on longjmp()
        qh_produce_output2();
    }
    maybeThrowQhullMessage(exitCode);
}//outputQhull

void Qhull::
outputQhull(const char *outputflags)
{
    checkIfQhullInitialized();
    UsingLibQhull q(this);
    string cmd(" "); // qh_checkflags skips first word
    cmd += outputflags;
    char *command= const_cast(cmd.c_str());
    int exitCode = setjmp(qh errexit);
    if(!exitCode){ // no object creation -- destructors skipped on longjmp()
        qh_clear_outputflags();
        char *s = qh qhull_command + strlen(qh qhull_command) + 1; //space
        strncat(qh qhull_command, command, sizeof(qh qhull_command)-strlen(qh qhull_command)-1);
        qh_checkflags(command, s_not_output_options);
        qh_initflags(s);
        qh_initqhull_outputflags();
        if(qh KEEPminArea < REALmax/2
           || (0 != qh KEEParea + qh KEEPmerge + qh GOODvertex
                    + qh GOODthreshold + qh GOODpoint + qh SPLITthresholds)){
            facetT *facet;
            qh ONLYgood= False;
            FORALLfacet_(qh facet_list) {
                facet->good= True;
            }
            qh_prepare_output();
        }
        qh_produce_output2();
        if(qh VERIFYoutput && !qh STOPpoint && !qh STOPcone){
            qh_check_points();
        }
    }
    maybeThrowQhullMessage(exitCode);
}//outputQhull

void Qhull::
runQhull(const RboxPoints &rboxPoints, const char *qhullCommand2)
{
    runQhull(rboxPoints.comment().c_str(), rboxPoints.dimension(), rboxPoints.count(), &*rboxPoints.coordinates(), qhullCommand2);
}//runQhull, RboxPoints

//! points is a array of points, input sites ('d' or 'v'), or halfspaces with offset last ('H')
//! Derived from qh_new_qhull [user.c]
void Qhull::
runQhull(const char *rboxCommand2, int pointDimension, int pointCount, const realT *rboxPoints, const char *qhullCommand2)
{
    if(run_called){
        throw QhullError(10027, "Qhull error: runQhull called twice.  Only one call allowed.");
    }
    run_called= true;
    string s("qhull ");
    s += qhullCommand2;
    char *command= const_cast(s.c_str());
    UsingLibQhull q(this);
    int exitCode = setjmp(qh errexit);
    if(!exitCode){ // no object creation -- destructors skipped on longjmp()
        qh_checkflags(command, s_unsupported_options);
        qh_initflags(command);
        *qh rbox_command= '\0';
        strncat( qh rbox_command, rboxCommand2, sizeof(qh rbox_command)-1);
        if(qh DELAUNAY){
            qh PROJECTdelaunay= True;   // qh_init_B() calls qh_projectinput()
        }
        pointT *newPoints= const_cast(rboxPoints);
        int newDimension= pointDimension;
        int newIsMalloc= False;
        if(qh HALFspace){
            --newDimension;
            initializeFeasiblePoint(newDimension);
            newPoints= qh_sethalfspace_all(pointDimension, pointCount, newPoints, qh feasible_point);
            newIsMalloc= True;
        }
        qh_init_B(newPoints, pointCount, newDimension, newIsMalloc);
        qhull_dimension= (qh DELAUNAY ? qh hull_dim - 1 : qh hull_dim);
        qh_qhull();
        qh_check_output();
        qh_prepare_output();
        if(qh VERIFYoutput && !qh STOPpoint && !qh STOPcone){
            qh_check_points();
        }
    }
    for(int k= qhull_dimension; k--; ){  // Do not move up (may throw)
        origin_point << 0.0;
    }
    maybeThrowQhullMessage(exitCode);
}//runQhull

#//Helpers -- be careful of allocating C++ objects due to setjmp/longjmp() error handling by qh_... routines

void Qhull::
initializeFeasiblePoint(int hulldim)
{
    if(qh feasible_string){
        qh_setfeasible(hulldim);
    }else{
        if(feasiblePoint.empty()){
            qh_fprintf(qh ferr, 6209, "qhull error: missing feasible point for halfspace intersection.  Use option 'Hn,n' or set qh.feasiblePoint\n");
            qh_errexit(qh_ERRmem, NULL, NULL);
        }
        if(feasiblePoint.size()!=(size_t)hulldim){
            qh_fprintf(qh ferr, 6210, "qhull error: dimension of feasiblePoint should be %d.  It is %u", hulldim, feasiblePoint.size());
            qh_errexit(qh_ERRmem, NULL, NULL);
        }
        if (!(qh feasible_point= (coordT*)qh_malloc(hulldim * sizeof(coordT)))) {
            qh_fprintf(qh ferr, 6202, "qhull error: insufficient memory for feasible point\n");
            qh_errexit(qh_ERRmem, NULL, NULL);
        }
        coordT *t= qh feasible_point;
        // No qh_... routines after here -- longjmp() ignores destructor
        for(Coordinates::ConstIterator p=feasiblePoint.begin(); p--------------------------------

  qh_fprintf(fp, msgcode, format, list of args )
    fp is ignored (replaces qh_fprintf() in userprintf.c)
    s_qhull_output == Qhull

notes:
    only called from libqhull
    same as fprintf() and RboxPoints::qh_fprintf_rbox()
    fgets() is not trapped like fprintf()
    Do not throw errors from here.  Use qh_errexit;
*/
extern "C"
void qh_fprintf(FILE *fp, int msgcode, const char *fmt, ... ) {
    va_list args;

    using namespace orgQhull;

    if(!s_qhull_output){
        fprintf(stderr, "QH10025 Qhull error: UsingLibQhull not declared prior to calling qh_...().  s_qhull_output==NULL.\n");
        qh_exit(10025);
    }
    Qhull *out= s_qhull_output;
    va_start(args, fmt);
    if(msgcode=MSG_ERROR && msgcodeqhull_statusqhull_status>=MSG_WARNING){
                out->qhull_status= msgcode;
            }
        }
        char newMessage[MSG_MAXLEN];
        // RoadError will add the message tag
        vsnprintf(newMessage, sizeof(newMessage), fmt, args);
        out->appendQhullMessage(newMessage);
        va_end(args);
        return;
    }
    if(out->output_stream && out->useOutputStream){
        char newMessage[MSG_MAXLEN];
        vsnprintf(newMessage, sizeof(newMessage), fmt, args);
        *out->output_stream << newMessage;
        va_end(args);
        return;
    }
    // FIXUP QH11008: how do users trap messages and handle input?  A callback?
    char newMessage[MSG_MAXLEN];
    vsnprintf(newMessage, sizeof(newMessage), fmt, args);
    out->appendQhullMessage(newMessage);
    va_end(args);
} /* qh_fprintf */

qhull-2012.1/src/libqhullcpp/Qhull.h0000644000076400010400000001436711710144464020465 0ustar  bbarberAdministrators/****************************************************************************
**
** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
** $Id: //main/2011/qhull/src/libqhullcpp/Qhull.h#4 $$Change: 1464 $
** $DateTime: 2012/01/25 22:58:41 $$Author: bbarber $
**
****************************************************************************/

#ifndef QHULLCPP_H
#define QHULLCPP_H

#include "QhullQh.h"
#include "RboxPoints.h"
#include "QhullLinkedList.h"
#include "QhullPoint.h"
#include "QhullPoints.h"
#include "QhullVertex.h"
#include "QhullFacet.h"

#include 
#include 
#include 
#include 
#include 

#if qh_QHpointer != 1
#error  qh_QHpointer is not set.  Please set it in user.h or
#error  compile Qhull with -Dqh_QHpointer.  The C++ classes
#error  require dynamic allocation for Qhulls global data
#error  structure qhT (QhullQh).
#endif

namespace orgQhull {

/***
   Compile qhullcpp and libqhull with the same compiler.  setjmp() and longjmp() must be the same.
*/

#//Types
    //! Qhull -- run Qhull from C++
    class Qhull;

    //Defined elsewhere
    class QhullFacetList;
    class RboxPoints;

class Qhull {

private:
#//Members and friends
    QhullQh            *qhull_qh;       //! qh_qh for this instance
    int                 qhull_run_id;    //! qh.run_id at initialization (catch multiple runs if !qh_QHpointer)
    Coordinates         origin_point;   //! origin for qhull_dimension.  Set by runQhull()
    int                 qhull_status;   //! qh_ERRnone if valid
    int                 qhull_dimension; //! Dimension of result (qh.hull_dim or one less for Delaunay/Voronoi)
    bool                run_called;     //! True at start of runQhull.  Errors if call again.
    bool                qh_active;      //! True if global pointer qh_qh equals qhull_qh
    std::string         qhull_message;
    std::ostream       *error_stream;   //! overrides errorMessage, use appendQhullMessage()
    std::ostream       *output_stream;  //! send output to stream

    friend void       ::qh_fprintf(FILE *fp, int msgcode, const char *fmt, ... );
    friend class        UsingLibQhull;

#//Attribute
public:
    Coordinates         feasiblePoint;  //! feasible point for half-space intersection
    bool                useOutputStream; //! Set if using outputStream
    // FIXUP QH11003 feasiblePoint useOutputStream as field or getter?

#//constructor, assignment, destructor, invariant
                        Qhull();      //! Qhull::runQhull() must be called next
                        Qhull(const RboxPoints &rboxPoints, const char *qhullCommand2);
                        Qhull(const char *rboxCommand2, int pointDimension, int pointCount, const realT *pointCoordinates, const char *qhullCommand2);
                        // Throws error if other.initialized().  Needed for return by value and parameter passing
                        Qhull(const Qhull &other);
                        // Throws error if initialized() or other.initialized().  Needed for vector
    Qhull              &operator=(const Qhull &other);
                       ~Qhull() throw();
private:
    void                initializeQhull();

public:
#//virtual methods
    //FIXUP QH11004 -- qh_memfree, etc. as virtual?

#//Messaging
    void                appendQhullMessage(const std::string &s);
    void                clearQhullMessage();
    std::string         qhullMessage() const;
    bool                hasQhullMessage() const;
    int                 qhullStatus() const;
    void                setErrorStream(std::ostream *os);
    void                setOutputStream(std::ostream *os);

#//GetSet
    void                checkIfQhullInitialized();
    bool                initialized() const { return qhull_dimension>0; }
    int                 dimension() const { return qhull_dimension; }
    int                 hullDimension() const { return qhullQh()->hull_dim; }
                        // non-const due to QhullPoint
    QhullPoint          origin() { QHULL_ASSERT(initialized()); return QhullPoint(dimension(), origin_point.data()); }
    QhullQh            *qhullQh() const { return qhull_qh; };
    int                 runId(); // Modifies my_qhull

#//GetQh -- access to qhT (Qhull's global data structure)
    const char         *qhullCommand() const { return qhull_qh->qhull_command; }
    const char         *rboxCommand() const { return qhull_qh->rbox_command; }
    int                 facetCount() const { return qhull_qh->num_facets; }
    int                 vertexCount() const { return qhull_qh->num_vertices; }

#//GetValue
    double              area();
    double              volume();

#//ForEach
    QhullFacet          beginFacet() const { return QhullFacet(qhull_qh->facet_list); }
    QhullVertex         beginVertex() const { return QhullVertex(qhull_qh->vertex_list); }
    void                defineVertexNeighborFacets(); //!< Automatically called if merging facets or Voronoi diagram
    QhullFacet          endFacet() const { return QhullFacet(qhull_qh->facet_tail); }
    QhullVertex         endVertex() const { return QhullVertex(qhull_qh->vertex_tail); }
    QhullFacetList      facetList() const;
    QhullFacet          firstFacet() const { return beginFacet(); }
    QhullVertex         firstVertex() const { return beginVertex(); }
    QhullPoints         points() const;
    QhullPointSet       otherPoints() const;
                        //! Same as points().coordinates()
    coordT             *pointCoordinateBegin() const { return qhull_qh->first_point; }
    coordT             *pointCoordinateEnd() const { return qhull_qh->first_point + qhull_qh->num_points*qhull_qh->hull_dim; }
    QhullVertexList     vertexList() const;

#//Modify
    void                outputQhull();
    void                outputQhull(const char * outputflags);
    void                runQhull(const RboxPoints &rboxPoints, const char *qhullCommand2);
    void                runQhull(const char *rboxCommand2, int pointDimension, int pointCount, const realT *rboxPoints, const char *qhullCommand2);

private:
#//Helpers
    void                initializeFeasiblePoint(int hulldim);
    void                maybeThrowQhullMessage(int exitCode);
    void                maybeThrowQhullMessage(int exitCode, int noThrow) throw();
};//Qhull

}//namespace orgQhull

#endif // QHULLCPP_H
qhull-2012.1/src/libqhullcpp/QhullError.h0000644000076400010400000000447111716456524021503 0ustar  bbarberAdministrators/****************************************************************************
**
** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
** $Id: //main/2011/qhull/src/libqhullcpp/QhullError.h#5 $$Change: 1490 $
** $DateTime: 2012/02/19 20:27:01 $$Author: bbarber $
**
****************************************************************************/

#ifndef QHULLERROR_H
#define QHULLERROR_H

#include "RoadError.h"

#include 
#include 
#include 

namespace orgQhull {

#//Types
    //! QhullError -- std::exception class for Qhull
    class QhullError;

class QhullError : public RoadError {

public:
#//Constants
    enum {
        QHULLfirstError= 10000, //MSG_QHULL_ERROR in Qhull's user.h
        QHULLlastError= 10070,
        NOthrow= 1 //! For flag to UsingLibQhull()
    };

#//Constructors
    // default constructors
    QhullError() : RoadError() {};
    QhullError(const QhullError &other) : RoadError(other) {}
    QhullError(int code, const std::string &message) : RoadError(code, message) {};
    QhullError(int code, const char *fmt) : RoadError(code, fmt) {};
    QhullError(int code, const char *fmt, int d) : RoadError(code, fmt, d) {};
    QhullError(int code, const char *fmt, int d, int d2) : RoadError(code, fmt, d, d2) {};
    QhullError(int code, const char *fmt, int d, int d2, float f) : RoadError(code, fmt, d, d2, f) {};
    QhullError(int code, const char *fmt, int d, int d2, float f, const char *s) : RoadError(code, fmt, d, d2, f, s) {};
    QhullError(int code, const char *fmt, int d, int d2, float f, const void *x) : RoadError(code, fmt, d, d2, f, x) {};
    QhullError(int code, const char *fmt, int d, int d2, float f, int i) : RoadError(code, fmt, d, d2, f, i) {};
    QhullError(int code, const char *fmt, int d, int d2, float f, long long i) : RoadError(code, fmt, d, d2, f, i) {};
    QhullError(int code, const char *fmt, int d, int d2, float f, double e) : RoadError(code, fmt, d, d2, f, e) {};
    QhullError &operator=(const QhullError &other) { this->RoadError::operator=(other); return *this; }
    ~QhullError() throw() {}

};//class QhullError

#ifndef QHULL_1
    #define QHULL_ASSERT assert

#endif

}//namespace orgQhull

#//Global functions

inline std::ostream &operator<<(std::ostream &os, const orgQhull::QhullError &e) { return os << e.what(); }

#endif // QHULLERROR_H
qhull-2012.1/src/libqhullcpp/QhullFacet.cpp0000644000076400010400000003651311710144464021760 0ustar  bbarberAdministrators/****************************************************************************
**
** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
** $Id: //main/2011/qhull/src/libqhullcpp/QhullFacet.cpp#7 $$Change: 1464 $
** $DateTime: 2012/01/25 22:58:41 $$Author: bbarber $
**
****************************************************************************/

#//! QhullFacet -- Qhull's facet structure, facetT, as a C++ class

#include "QhullError.h"
#include "QhullSet.h"
#include "QhullPoint.h"
#include "QhullPointSet.h"
#include "QhullRidge.h"
#include "QhullFacet.h"
#include "QhullFacetSet.h"
#include "QhullVertex.h"

#include 

using std::endl;
using std::string;
using std::vector;
using std::ostream;

#ifdef _MSC_VER  // Microsoft Visual C++ -- warning level 4
#pragma warning( disable : 4611)  // interaction between '_setjmp' and C++ object destruction is non-portable
#pragma warning( disable : 4996)  // function was declared deprecated(strcpy, localtime, etc.)
#endif

namespace orgQhull {

#//class statics
facetT QhullFacet::
        s_empty_facet= {0,0,0,0,{0},
                0,0,0,0,0,
                0,0,0,0,0,
                0,0,0,0,0,
                0,0,0,0,0,
                0,0,0,0,0,
                0,0,0,0,0,
                0,0,0,0};

#//GetSet

int QhullFacet::
dimension() const
{
    if(qh_facet->ridges){
        setT *s= qh_facet->ridges;
        ridgeT *r= reinterpret_cast(SETfirst_(s));
        return r ? QhullSetBase::count(r->vertices)+1 : 0;
    }else{
        return QhullSetBase::count(qh_facet->vertices);
    }
}//dimension

//! Return voronoi center or facet centrum.  Derived from qh_printcenter [io.c]
//! printFormat=qh_PRINTtriangles if return centrum of a Delaunay facet
//! Sets center if needed
//! Code duplicated for PrintCenter and getCenter
//! .empty() if none or qh_INFINITE
QhullPoint QhullFacet::
getCenter(int qhRunId, qh_PRINT printFormat)
{
    UsingLibQhull q(qhRunId);

    if(qh CENTERtype==qh_ASvoronoi){
        if(!qh_facet->normal || !qh_facet->upperdelaunay || !qh ATinfinity){
            if(!qh_facet->center){
                int exitCode = setjmp(qh errexit);
                if(!exitCode){ // no object creation -- destructors skipped on longjmp()
                    qh_facet->center= qh_facetcenter(qh_facet->vertices);
                }
                q.maybeThrowQhullMessage(exitCode);
            }
            return QhullPoint(qh hull_dim-1, qh_facet->center);
        }
    }else if(qh CENTERtype==qh_AScentrum){
        volatile int numCoords= qh hull_dim;
        if(printFormat==qh_PRINTtriangles && qh DELAUNAY){
            numCoords--;
        }
        if(!qh_facet->center){
            int exitCode = setjmp(qh errexit);
            if(!exitCode){ // no object creation -- destructors skipped on longjmp()
                qh_facet->center= qh_getcentrum(getFacetT());
            }
            q.maybeThrowQhullMessage(exitCode);
        }
        return QhullPoint(numCoords, qh_facet->center);
    }
    return QhullPoint();
 }//getCenter

//! Return innerplane clearly below the vertices
//! from io.c[qh_PRINTinner]
QhullHyperplane QhullFacet::
innerplane(int qhRunId) const{
    UsingLibQhull q(qhRunId);
    realT inner;
    // Does not error
    qh_outerinner(const_cast(getFacetT()), NULL, &inner);
    QhullHyperplane h= hyperplane();
    h.setOffset(h.offset()-inner); //inner is negative
    return h;
}//innerplane

//! Return outerplane clearly above all points
//! from io.c[qh_PRINTouter]
QhullHyperplane QhullFacet::
outerplane(int qhRunId) const{
    UsingLibQhull q(qhRunId);
    realT outer;
    // Does not error
    qh_outerinner(const_cast(getFacetT()), &outer, NULL);
    QhullHyperplane h= hyperplane();
    h.setOffset(h.offset()-outer); //outer is positive
    return h;
}//outerplane

//! Set by qh_triangulate for option 'Qt'.
//! Errors if tricoplanar and facetArea() or qh_getarea() called first.
QhullFacet QhullFacet::
tricoplanarOwner() const
{
    if(qh_facet->tricoplanar){
        if(qh_facet->isarea){
            throw QhullError(10018, "Qhull error: facetArea() or qh_getarea() previously called.  triCoplanarOwner() is not available.");
        }
        return qh_facet->f.triowner;
    }
    return 0; // FIXUP QH11009 Should false be the NULL facet or empty facet
}//tricoplanarOwner

QhullPoint QhullFacet::
voronoiVertex(int qhRunId)
{
    if(
#if qh_QHpointer
      !qh_qh ||
#endif
      qh CENTERtype!=qh_ASvoronoi){
          throw QhullError(10052, "Error: QhullFacet.voronoiVertex() requires option 'v' (qh_ASvoronoi)");
    }
    return getCenter(qhRunId);
}//voronoiVertex

#//Value

//! Disables tricoplanarOwner()
double QhullFacet::
facetArea(int qhRunId)
{
    if(!qh_facet->isarea){
        UsingLibQhull q(qhRunId);
        int exitCode = setjmp(qh errexit);
        if(!exitCode){ // no object creation -- destructors skipped on longjmp()
            qh_facet->f.area= qh_facetarea(qh_facet);
            qh_facet->isarea= True;
        }
        q.maybeThrowQhullMessage(exitCode);
    }
    return qh_facet->f.area;
}//facetArea

#//Foreach

QhullPointSet QhullFacet::
coplanarPoints() const
{
    return QhullPointSet(dimension(), qh_facet->coplanarset);
}//coplanarPoints

QhullFacetSet QhullFacet::
neighborFacets() const
{
    return QhullFacetSet(qh_facet->neighbors);
}//neighborFacets

QhullPointSet QhullFacet::
outsidePoints() const
{
    return QhullPointSet(dimension(), qh_facet->outsideset);
}//outsidePoints

QhullRidgeSet QhullFacet::
ridges() const
{
    return QhullRidgeSet(qh_facet->ridges);
}//ridges

QhullVertexSet QhullFacet::
vertices() const
{
    return QhullVertexSet(qh_facet->vertices);
}//vertices


}//namespace orgQhull

#//operator<<

using std::ostream;

using orgQhull::QhullFacet;
using orgQhull::QhullFacetSet;
using orgQhull::QhullPoint;
using orgQhull::QhullPointSet;
using orgQhull::QhullRidge;
using orgQhull::QhullRidgeSet;
using orgQhull::QhullSetBase;
using orgQhull::QhullVertexSet;
using orgQhull::UsingLibQhull;

ostream &
operator<<(ostream &os, const QhullFacet::PrintFacet &pr)
{
    QhullFacet f= *pr.facet;
    if(f.getFacetT()==0){ // Special values from set iterator
        os << " NULLfacet" << endl;
        return os;
    }
    if(f.getFacetT()==qh_MERGEridge){
        os << " MERGEridge" << endl;
        return os;
    }
    if(f.getFacetT()==qh_DUPLICATEridge){
        os << " DUPLICATEridge" << endl;
        return os;
    }
    os << f.printHeader(pr.run_id);
    if(!f.ridges().isEmpty()){
        os << f.printRidges(pr.run_id);
    }
    return os;
}//operator<< PrintFacet

//! Print Voronoi center or facet centrum to stream.  Same as qh_printcenter [io.c]
//! Code duplicated for PrintCenter and getCenter
//! Sets center if needed
ostream &
operator<<(ostream &os, const QhullFacet::PrintCenter &pr)
{
    facetT *f= pr.facet->getFacetT();
    if(qh CENTERtype!=qh_ASvoronoi && qh CENTERtype!=qh_AScentrum){
        return os;
    }
    if (pr.message){
        os << pr.message;
    }
    int numCoords;
    if(qh CENTERtype==qh_ASvoronoi){
        numCoords= qh hull_dim-1;
        if(!f->normal || !f->upperdelaunay || !qh ATinfinity){
            if(!f->center){
                f->center= qh_facetcenter(f->vertices);
            }
            for(int k=0; kcenter[k] << " "; // FIXUP QH11010 qh_REAL_1
            }
        }else{
            for(int k=0; kcenter){
            f->center= qh_getcentrum(f);
        }
        for(int k=0; kcenter[k] << " "; // FIXUP QH11010 qh_REAL_1
        }
    }
    if(pr.print_format==qh_PRINTgeom && numCoords==2){
        os << " 0";
    }
    os << endl;
    return os;
}//operator<< PrintCenter

//! Print flags for facet to stream.  Space prefix.  From qh_printfacetheader [io.c]
ostream &
operator<<(ostream &os, const QhullFacet::PrintFlags &p)
{
    const facetT *f= p.facet->getFacetT();
    if(p.message){
        os << p.message;
    }

    os << (p.facet->isTopOrient() ? " top" : " bottom");
    if(p.facet->isSimplicial()){
        os << " simplicial";
    }
    if(p.facet->isTriCoplanar()){
        os << " tricoplanar";
    }
    if(p.facet->isUpperDelaunay()){
        os << " upperDelaunay";
    }
    if(f->visible){
        os << " visible";
    }
    if(f->newfacet){
        os << " new";
    }
    if(f->tested){
        os << " tested";
    }
    if(!f->good){
        os << " notG";
    }
    if(f->seen){
        os << " seen";
    }
    if(f->coplanar){
        os << " coplanar";
    }
    if(f->mergehorizon){
        os << " mergehorizon";
    }
    if(f->keepcentrum){
        os << " keepcentrum";
    }
    if(f->dupridge){
        os << " dupridge";
    }
    if(f->mergeridge && !f->mergeridge2){
        os << " mergeridge1";
    }
    if(f->mergeridge2){
        os << " mergeridge2";
    }
    if(f->newmerge){
        os << " newmerge";
    }
    if(f->flipped){
        os << " flipped";
    }
    if(f->notfurthest){
        os << " notfurthest";
    }
    if(f->degenerate){
        os << " degenerate";
    }
    if(f->redundant){
        os << " redundant";
    }
    os << endl;
    return os;
}//operator<< PrintFlags

//! Print header for facet to stream. Space prefix.  From qh_printfacetheader [io.c]
ostream &
operator<<(ostream &os, const QhullFacet::PrintHeader &pr)
{
    QhullFacet facet= *pr.facet;
    facetT *f= facet.getFacetT();
    os << "- f" << facet.id() << endl;
    os << facet.printFlags("    - flags:");
    if(f->isarea){
        os << "    - area: " << f->f.area << endl; //FIXUP QH11010 2.2g
    }else if(qh NEWfacets && f->visible && f->f.replace){
        os << "    - replacement: f" << f->f.replace->id << endl;
    }else if(f->newfacet){
        if(f->f.samecycle && f->f.samecycle != f){
            os << "    - shares same visible/horizon as f" << f->f.samecycle->id << endl;
        }
    }else if(f->tricoplanar /* !isarea */){
        if(f->f.triowner){
            os << "    - owner of normal & centrum is facet f" << f->f.triowner->id << endl;
        }
    }else if(f->f.newcycle){
        os << "    - was horizon to f" << f->f.newcycle->id << endl;
    }
    if(f->nummerge){
        os << "    - merges: " << f->nummerge << endl;
    }
    os << facet.hyperplane().print("    - normal: ", "\n    - offset: "); // FIXUP QH11010 %10.7g
    if(qh CENTERtype==qh_ASvoronoi || f->center){
        os << facet.printCenter(pr.run_id, qh_PRINTfacets, "    - center: ");
    }
#if qh_MAXoutside
    if(f->maxoutside > qh DISTround){
        os << "    - maxoutside: " << f->maxoutside << endl; //FIXUP QH11010 %10.7g
    }
#endif
    QhullPointSet ps= facet.outsidePoints();
    if(!ps.isEmpty()){
        QhullPoint furthest= ps.last();
        if (ps.size() < 6) {
            os << "    - outside set(furthest p" << furthest.id(pr.run_id) << "):" << endl;
            for(QhullPointSet::iterator i=ps.begin(); i!=ps.end(); ++i){
                QhullPoint p= *i;
                os << p.print(pr.run_id, "     ");
            }
        }else if(ps.size()<21){
            os << ps.print(pr.run_id, "    - outside set:");
        }else{
            os << "    - outside set:  " << ps.size() << " points.";
            os << furthest.print(pr.run_id, "  Furthest");
        }
#if !qh_COMPUTEfurthest
        os << "    - furthest distance= " << f->furthestdist << endl; //FIXUP QH11010 %2.2g
#endif
    }
    QhullPointSet cs= facet.coplanarPoints();
    if(!cs.isEmpty()){
        QhullPoint furthest= cs.last();
        if (cs.size() < 6) {
            os << "    - coplanar set(furthest p" << furthest.id(pr.run_id) << "):" << endl;
            for(QhullPointSet::iterator i=cs.begin(); i!=cs.end(); ++i){
                QhullPoint p= *i;
                os << p.print(pr.run_id, "     ");
            }
        }else if(cs.size()<21){
            os << cs.print(pr.run_id, "    - coplanar set:");
        }else{
            os << "    - coplanar set:  " << cs.size() << " points.";
            os << furthest.print(pr.run_id, "  Furthest");
        }
        zinc_(Zdistio);
        double d= facet.distance(furthest);
        os << "      furthest distance= " << d << endl; //FIXUP QH11010 %2.2g
    }
    QhullVertexSet vs= facet.vertices();
    if(!vs.isEmpty()){
        os << vs.print(pr.run_id, "    - vertices:");
    }
    QhullFacetSet fs= facet.neighborFacets();
    fs.selectAll();
    if(!fs.isEmpty()){
        os << fs.printIdentifiers("    - neighboring facets:");
    }
    return os;
}//operator<< PrintHeader


//! Print ridges of facet to stream.  Same as qh_printfacetridges [io.c]
//! If qhRunId==UsingLibQhull::NOqhRunId, does not use qh
ostream &
operator<<(ostream &os, const QhullFacet::PrintRidges &pr)
{
    const QhullFacet facet= *pr.facet;
    facetT *f= facet.getFacetT();
    QhullRidgeSet rs= facet.ridges();
    if(!rs.isEmpty()){
        if(pr.run_id!=UsingLibQhull::NOqhRunId){
            UsingLibQhull q(pr.run_id);
            // No calls to libqhull
            if(f->visible && qh NEWfacets){
                os << "    - ridges(ids may be garbage):";
                for(QhullRidgeSet::iterator i=rs.begin(); i!=rs.end(); ++i){
                    QhullRidge r= *i;
                    os << " r" << r.id();
                }
                os << endl;
            }else{
                os << "    - ridges:" << endl;
            }
        }else{
            os << "    - ridges:" << endl;
        }

        // Keep track of printed ridges
        for(QhullRidgeSet::iterator i=rs.begin(); i!=rs.end(); ++i){
            QhullRidge r= *i;
            r.getRidgeT()->seen= false;
        }
        int ridgeCount= 0;
        if(facet.dimension()==3){
            for(QhullRidge r= rs.first(); !r.getRidgeT()->seen; r= r.nextRidge3d(facet)){
                r.getRidgeT()->seen= true;
                os << r.print(pr.run_id);
                ++ridgeCount;
                if(!r.hasNextRidge3d(facet)){
                    break;
                }
            }
        }else {
            QhullFacetSet ns(facet.neighborFacets());
            for(QhullFacetSet::iterator i=ns.begin(); i!=ns.end(); ++i){
                QhullFacet neighbor= *i;
                QhullRidgeSet nrs(neighbor.ridges());
                for(QhullRidgeSet::iterator j=nrs.begin(); j!=nrs.end(); ++j){
                    QhullRidge r= *j;
                    if(r.otherFacet(neighbor)==facet){
                        r.getRidgeT()->seen= true;
                        os << r.print(pr.run_id);
                        ridgeCount++;
                    }
                }
            }
        }
        if(ridgeCount!=rs.count()){
            os << "     - all ridges:";
            for(QhullRidgeSet::iterator i=rs.begin(); i!=rs.end(); ++i){
                QhullRidge r= *i;
                os << " r" << r.id();
            }
            os << endl;
        }
        for(QhullRidgeSet::iterator i=rs.begin(); i!=rs.end(); ++i){
            QhullRidge r= *i;
            if(!r.getRidgeT()->seen){
                os << r.print(pr.run_id);
            }
        }
    }
    return os;
}//operator<< PrintRidges

// "No conversion" error if defined inline
ostream &
operator<<(ostream &os, QhullFacet &f)
{
    os << f.print(UsingLibQhull::NOqhRunId);
    return os;
}//<< QhullFacet
qhull-2012.1/src/libqhullcpp/QhullFacet.h0000644000076400010400000001531111710144465021417 0ustar  bbarberAdministrators/****************************************************************************
**
** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
** $Id: //main/2011/qhull/src/libqhullcpp/QhullFacet.h#7 $$Change: 1464 $
** $DateTime: 2012/01/25 22:58:41 $$Author: bbarber $
**
****************************************************************************/

#ifndef QHULLFACET_H
#define QHULLFACET_H

#include "Coordinates.h"
#include "QhullHyperplane.h"
#include "QhullPoint.h"
#include "QhullSet.h"
#include "QhullPointSet.h"
extern "C" {
    #include "libqhull/qhull_a.h"
}

#include 
#include 
#include 

namespace orgQhull {

#//ClassRef
    class QhullFacetSet;
    class QhullRidge;
    typedef QhullSet  QhullRidgeSet;
    class QhullVertex;
    class QhullVertexSet;

#//Types
    //! QhullFacet -- Qhull's facet structure, facetT [libqhull.h], as a C++ class
    class QhullFacet;

//! A QhullFacet is the C++ equivalent to Qhull's facetT*
class QhullFacet {

private:
#//Fields -- no additions (QhullFacetSet of facetT*)
    facetT             *qh_facet;  //! May be 0 (!isDefined) for corner cases (e.g., *facetSet.end()==0) and tricoplanarOwner()

#//Class objects
    static facetT       s_empty_facet; // needed for shallow copy

public:
#//Constants

#//Constructors
                        QhullFacet() : qh_facet(&s_empty_facet) {}
                        // Creates an alias.  Does not copy QhullFacet.  Needed for return by value and parameter passing
                        QhullFacet(const QhullFacet &o) : qh_facet(o.qh_facet ? o.qh_facet : &s_empty_facet) {}
                        // Creates an alias.  Does not copy QhullFacet.  Needed for vector
    QhullFacet         &operator=(const QhullFacet &o) { qh_facet= o.qh_facet ? o.qh_facet : &s_empty_facet; return *this; }
                       ~QhullFacet() {}

#//Conversion
                        //Implicit conversion from facetT
                        QhullFacet(facetT *f) : qh_facet(f ? f : &s_empty_facet) {}
                        // Do not define facetT().  It conflicts with return type facetT*
    facetT             *getFacetT() const { return qh_facet; }

#//QhullSet
    facetT             *getBaseT() const { return getFacetT(); }

#//getSet
    int                 dimension() const;
    QhullPoint          getCenter(int qhRunId) { return getCenter(qhRunId, qh_PRINTpoints); }
    QhullPoint          getCenter(int qhRunId, qh_PRINT printFormat);
    QhullHyperplane     hyperplane() const { return QhullHyperplane(dimension(), qh_facet->normal, qh_facet->offset); }
    int                 id() const { return qh_facet ? qh_facet->id : -1; }
    QhullHyperplane     innerplane(int qhRunId) const;
    bool                isDefined() const { return qh_facet && qh_facet != &s_empty_facet; }
    bool                isGood() const { return qh_facet && qh_facet->good; }
    bool                isSimplicial() const { return qh_facet->simplicial; }
    bool                isTopOrient() const { return qh_facet->toporient; }
    bool                isTriCoplanar() const { return qh_facet->tricoplanar; }
    bool                isUpperDelaunay() const { return qh_facet->upperdelaunay; }
    QhullFacet          next() const { return qh_facet->next; }
    bool                operator==(const QhullFacet &o) const { return qh_facet==o.qh_facet; }
    bool                operator!=(const QhullFacet &o) const { return !operator==(o); }
    QhullHyperplane     outerplane(int qhRunId) const;
    QhullFacet          previous() const { return qh_facet->previous; }
    QhullFacet          tricoplanarOwner() const;
    QhullPoint          voronoiVertex(int qhRunId);

#//value
    //! Undefined if c.size() != dimension()
    double              distance(const Coordinates &c) const { return distance(c.data()); }
    double              distance(const pointT *p) const { return distance(QhullPoint(dimension(), const_cast(p))); }
    double              distance(const QhullPoint &p) const { return hyperplane().distance(p); }
    double              facetArea(int qhRunId);

#//foreach
    // Can not inline.  Otherwise circular reference
    QhullPointSet       coplanarPoints() const;
    QhullFacetSet       neighborFacets() const;
    QhullPointSet       outsidePoints() const;
    QhullRidgeSet       ridges() const;
    QhullVertexSet      vertices() const;

#//IO
    struct PrintCenter{
        QhullFacet     *facet;  // non-const due to facet.center()
        const char     *message;
        int             run_id;
        qh_PRINT        print_format;
                        PrintCenter(int qhRunId, QhullFacet &f, qh_PRINT printFormat, const char * s) : facet(&f), message(s), run_id(qhRunId), print_format(printFormat){}
    };//PrintCenter
    PrintCenter         printCenter(int qhRunId, qh_PRINT printFormat, const char *message) { return PrintCenter(qhRunId, *this, printFormat, message); }

    struct PrintFacet{
        QhullFacet     *facet;  // non-const due to f->center()
        int             run_id;
                        PrintFacet(int qhRunId, QhullFacet &f) : facet(&f), run_id(qhRunId) {}
    };//PrintFacet
    PrintFacet          print(int qhRunId) { return PrintFacet(qhRunId, *this); }

    struct PrintFlags{
        const QhullFacet *facet;
        const char     *message;
                        PrintFlags(const QhullFacet &f, const char *s) : facet(&f), message(s) {}
    };//PrintFlags
    PrintFlags          printFlags(const char *message) const { return PrintFlags(*this, message); }

    struct PrintHeader{
        QhullFacet     *facet;  // non-const due to f->center()
        int             run_id;
                        PrintHeader(int qhRunId, QhullFacet &f) : facet(&f), run_id(qhRunId) {}
    };//PrintHeader
    PrintHeader         printHeader(int qhRunId) { return PrintHeader(qhRunId, *this); }

    struct PrintRidges{
        const QhullFacet *facet;
        int             run_id;
                        PrintRidges(int qhRunId, QhullFacet &f) : facet(&f), run_id(qhRunId) {}
    };//PrintRidges
    PrintRidges         printRidges(int qhRunId) { return PrintRidges(qhRunId, *this); }

};//class QhullFacet

}//namespace orgQhull

#//Global functions

std::ostream &operator<<(std::ostream &os, const orgQhull::QhullFacet::PrintCenter &pr);
std::ostream &operator<<(std::ostream &os, const orgQhull::QhullFacet::PrintFlags &pr);
std::ostream &operator<<(std::ostream &os, const orgQhull::QhullFacet::PrintHeader &pr);
std::ostream &operator<<(std::ostream &os, const orgQhull::QhullFacet::PrintRidges &pr);
std::ostream &operator<<(std::ostream &os, const orgQhull::QhullFacet::PrintFacet &pr);
std::ostream &operator<<(std::ostream &os, orgQhull::QhullFacet &f); // non-const due to qh_getcenter()

#endif // QHULLFACET_H
qhull-2012.1/src/libqhullcpp/QhullFacetList.cpp0000644000076400010400000001027511710144465022612 0ustar  bbarberAdministrators/****************************************************************************
**
** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
** $Id: //main/2011/qhull/src/libqhullcpp/QhullFacetList.cpp#3 $$Change: 1464 $
** $DateTime: 2012/01/25 22:58:41 $$Author: bbarber $
**
****************************************************************************/

#//! QhullFacetList -- Qhull's linked facets, as a C++ class

#include "QhullFacet.h"
#include "QhullFacetList.h"
#include "QhullPoint.h"
#include "QhullRidge.h"
#include "QhullVertex.h"

using std::string;
using std::vector;

#ifdef _MSC_VER  // Microsoft Visual C++ -- warning level 4
#pragma warning( disable : 4611)  // interaction between '_setjmp' and C++ object destruction is non-portable
#pragma warning( disable : 4996)  // function was declared deprecated(strcpy, localtime, etc.)
#endif

namespace orgQhull {

#//Conversion

// See qt_qhull.cpp for QList conversions

#ifndef QHULL_NO_STL
std::vector QhullFacetList::
toStdVector() const
{
    QhullLinkedListIterator i(*this);
    std::vector vs;
    while(i.hasNext()){
        QhullFacet f= i.next();
        if(isSelectAll() || f.isGood()){
            vs.push_back(f);
        }
    }
    return vs;
}//toStdVector
#endif //QHULL_NO_STL

#ifndef QHULL_NO_STL
//! Same as PrintVertices
std::vector QhullFacetList::
vertices_toStdVector(int qhRunId) const
{
    std::vector vs;
    QhullVertexSet qvs(qhRunId, first().getFacetT(), NULL, isSelectAll());

    for(QhullVertexSet::iterator i=qvs.begin(); i!=qvs.end(); ++i){
        vs.push_back(*i);
    }
    return vs;
}//vertices_toStdVector
#endif //QHULL_NO_STL

#//Read-only

bool QhullFacetList::
contains(const QhullFacet &facet) const
{
    if(isSelectAll()){
        return QhullLinkedList::contains(facet);
    }
    for(QhullFacetList::const_iterator i=begin(); i != end(); ++i){
        QhullFacet f= *i;
        if(f==facet && f.isGood()){
            return true;
        }
    }
    return false;
}//contains

int QhullFacetList::
count() const
{
    if(isSelectAll()){
        return QhullLinkedList::count();
    }
    int counter= 0;
    for(QhullFacetList::const_iterator i=begin(); i != end(); ++i){
        if((*i).isGood()){
            counter++;
        }
    }
    return counter;
}//count

int QhullFacetList::
count(const QhullFacet &facet) const
{
    if(isSelectAll()){
        return QhullLinkedList::count(facet);
    }
    int counter= 0;
    for(QhullFacetList::const_iterator i=begin(); i != end(); ++i){
        QhullFacet f= *i;
        if(f==facet && f.isGood()){
            counter++;
        }
    }
    return counter;
}//count

}//namespace orgQhull

#//Global functions

using std::endl;
using std::ostream;
using orgQhull::QhullFacet;
using orgQhull::QhullFacetList;
using orgQhull::QhullVertex;
using orgQhull::QhullVertexSet;
using orgQhull::UsingLibQhull;

ostream &
operator<<(ostream &os, const QhullFacetList::PrintFacetList &pr)
{
    QhullFacetList fs= *pr.facet_list;
    os << "Vertices for " << fs.count() << " facets" << endl;
    os << fs.printVertices(pr.run_id);
    os << fs.printFacets(pr.run_id);
    return os;
}//operator<<

//! Print facet list to stream.  From qh_printafacet [io.c]
ostream &
operator<<(ostream &os, const QhullFacetList::PrintFacets &pr)
{
    for(QhullFacetList::const_iterator i= pr.facet_list->begin(); i != pr.facet_list->end(); ++i){
        QhullFacet f= *i;
        if(pr.facet_list->isSelectAll() || f.isGood()){
            os << f.print(pr.run_id);
        }
    }
    return os;
}//printFacets

//! Print vertices of good faces in facet list to stream.  From qh_printvertexlist [io.c]
//! Same as vertices_toStdVector
ostream &
operator<<(ostream &os, const QhullFacetList::PrintVertices &pr)
{
    QhullVertexSet vs(pr.run_id, pr.facet_list->first().getFacetT(), NULL, pr.facet_list->isSelectAll());
    for(QhullVertexSet::iterator i=vs.begin(); i!=vs.end(); ++i){
        QhullVertex v= *i;
        os << v.print(pr.run_id);
    }
    return os;
}//printVertices

std::ostream &
operator<<(ostream &os, const QhullFacetList &fs)
{
    os << fs.printFacets(UsingLibQhull::NOqhRunId);
    return os;
}//QhullFacetList

qhull-2012.1/src/libqhullcpp/QhullFacetList.h0000644000076400010400000000776211710144465022266 0ustar  bbarberAdministrators/****************************************************************************
**
** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
** $Id: //main/2011/qhull/src/libqhullcpp/QhullFacetList.h#3 $$Change: 1464 $
** $DateTime: 2012/01/25 22:58:41 $$Author: bbarber $
**
****************************************************************************/

#ifndef QHULLFACETLIST_H
#define QHULLFACETLIST_H

#include "QhullLinkedList.h"
#include "QhullFacet.h"

#include 

namespace orgQhull {

#//ClassRef
    class               QhullFacet;

#//Types
    //! QhullFacetList -- List of Qhull facets, as a C++ class.  See QhullFacetSet.h
    class               QhullFacetList;
    //! QhullFacetListIterator -- if(f.isGood()){ ... }
    typedef QhullLinkedListIterator
                        QhullFacetListIterator;

class QhullFacetList : public QhullLinkedList {

#// Fields
private:
    bool                select_all;   //! True if include bad facets.  Default is false.

#//Constructors
public:
                        QhullFacetList(QhullFacet b, QhullFacet e) : QhullLinkedList(b, e), select_all(false) {}
                        //Copy constructor copies pointer but not contents.  Needed for return by value and parameter passing.
                        QhullFacetList(const QhullFacetList &o) : QhullLinkedList(*o.begin(), *o.end()), select_all(o.select_all) {}
                       ~QhullFacetList() {}

private:
                        //!Disable default constructor and copy assignment.  See QhullLinkedList
                        QhullFacetList();
    QhullFacetList     &operator=(const QhullFacetList &);
public:

#//Conversion
#ifndef QHULL_NO_STL
    std::vector toStdVector() const;
    std::vector vertices_toStdVector(int qhRunId) const;
#endif //QHULL_NO_STL
#ifdef QHULL_USES_QT
    QList   toQList() const;
    QList  vertices_toQList(int qhRunId) const;
#endif //QHULL_USES_QT

#//GetSet
    bool                isSelectAll() const { return select_all; }
    void                selectAll() { select_all= true; }
    void                selectGood() { select_all= false; }

#//Read-only
                        //! Filtered by facet.isGood().  May be 0 when !isEmpty().
    int                 count() const;
    bool                contains(const QhullFacet &f) const;
    int                 count(const QhullFacet &f) const;
                        //! operator==() does not depend on isGood()

#//IO
    struct PrintFacetList{
        const QhullFacetList *facet_list;
        int             run_id;
                        PrintFacetList(int qhRunId, const QhullFacetList &fl) : facet_list(&fl), run_id(qhRunId) {}
    };//PrintFacetList
    PrintFacetList     print(int qhRunId) const  { return PrintFacetList(qhRunId, *this); }

    struct PrintFacets{
        const QhullFacetList *facet_list;
        int             run_id;
                        PrintFacets(int qhRunId, const QhullFacetList &fl) : facet_list(&fl), run_id(qhRunId) {}
    };//PrintFacets
    PrintFacets     printFacets(int qhRunId) const { return PrintFacets(qhRunId, *this); }

    struct PrintVertices{
        const QhullFacetList *facet_list;
        int             run_id;   //! Can not be NOrunId due to qh_facetvertices
                        PrintVertices(int qhRunId, const QhullFacetList &fl) : facet_list(&fl), run_id(qhRunId) {}
    };//PrintVertices
    PrintVertices   printVertices(int qhRunId) const { return PrintVertices(qhRunId, *this); }
};//class QhullFacetList

}//namespace orgQhull

#//== Global namespace =========================================

std::ostream &operator<<(std::ostream &os, const orgQhull::QhullFacetList::PrintFacetList &p);
std::ostream &operator<<(std::ostream &os, const orgQhull::QhullFacetList::PrintFacets &p);
std::ostream &operator<<(std::ostream &os, const orgQhull::QhullFacetList::PrintVertices &p);
std::ostream &operator<<(std::ostream &os, const orgQhull::QhullFacetList &fs);

#endif // QHULLFACETLIST_H
qhull-2012.1/src/libqhullcpp/QhullFacetSet.cpp0000644000076400010400000000706711710144465022437 0ustar  bbarberAdministrators/****************************************************************************
**
** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
** $Id: //main/2011/qhull/src/libqhullcpp/QhullFacetSet.cpp#5 $$Change: 1464 $
** $DateTime: 2012/01/25 22:58:41 $$Author: bbarber $
**
****************************************************************************/

#//! QhullFacetSet -- Qhull's linked facets, as a C++ class

#include "QhullFacet.h"
#include "QhullFacetSet.h"
#include "QhullPoint.h"
#include "QhullRidge.h"
#include "QhullVertex.h"

using std::string;
using std::vector;

#ifdef _MSC_VER  // Microsoft Visual C++ -- warning level 4
#pragma warning( disable : 4611)  // interaction between '_setjmp' and C++ object destruction is non-portable
#pragma warning( disable : 4996)  // function was declared deprecated(strcpy, localtime, etc.)
#endif

namespace orgQhull {

#//Conversion

// See qt-qhull.cpp for QList conversions

#ifndef QHULL_NO_STL
std::vector QhullFacetSet::
toStdVector() const
{
    QhullSetIterator i(*this);
    std::vector vs;
    while(i.hasNext()){
        QhullFacet f= i.next();
        if(isSelectAll() || f.isGood()){
            vs.push_back(f);
        }
    }
    return vs;
}//toStdVector
#endif //QHULL_NO_STL

#//Read-only

bool QhullFacetSet::
contains(const QhullFacet &facet) const
{
    if(isSelectAll()){
        return QhullSet::contains(facet);
    }
    for(QhullFacetSet::const_iterator i=begin(); i != end(); ++i){
        QhullFacet f= *i;
        if(f==facet && f.isGood()){
            return true;
        }
    }
    return false;
}//contains

int QhullFacetSet::
count() const
{
    if(isSelectAll()){
        return QhullSet::count();
    }
    int counter= 0;
    for(QhullFacetSet::const_iterator i=begin(); i != end(); ++i){
        QhullFacet f= *i;
        if(f.isGood()){
            counter++;
        }
    }
    return counter;
}//count

int QhullFacetSet::
count(const QhullFacet &facet) const
{
    if(isSelectAll()){
        return QhullSet::count(facet);
    }
    int counter= 0;
    for(QhullFacetSet::const_iterator i=begin(); i != end(); ++i){
        QhullFacet f= *i;
        if(f==facet && f.isGood()){
            counter++;
        }
    }
    return counter;
}//count

}//namespace orgQhull

#//Global functions

using std::endl;
using std::ostream;
using orgQhull::QhullFacet;
using orgQhull::QhullFacetSet;
using orgQhull::UsingLibQhull;

ostream &
operator<<(ostream &os, const QhullFacetSet &fs)
{
    os << fs.print(UsingLibQhull::NOqhRunId, "");
    return os;
}//<begin(); i!=p.facet_set->end(); ++i){
        const QhullFacet f= *i;
        if(f.getFacetT()==qh_MERGEridge){
            os << " MERGE";
        }else if(f.getFacetT()==qh_DUPLICATEridge){
            os << " DUP";
        }else if(p.facet_set->isSelectAll() || f.isGood()){
            os << " f" << f.id();
        }
    }
    os << endl;
    return os;
}//<

namespace orgQhull {

#//ClassRef
    class               QhullFacet;

#//Types
    //! QhullFacetSet -- a set of Qhull facets, as a C++ class.  See QhullFacetList.h
    class               QhullFacetSet;
    typedef QhullSetIterator
                        QhullFacetSetIterator;

class QhullFacetSet : public QhullSet {

private:
#//Fields
    bool                select_all;   //! True if include bad facets.  Default is false.

public:
#//Constructor
                        //Conversion from setT* is not type-safe.  Implicit conversion for void* to T
   explicit             QhullFacetSet(setT *s) : QhullSet(s), select_all(false) {}
                        //Copy constructor copies pointer but not contents.  Needed for return by value and parameter passing.
                        QhullFacetSet(const QhullFacetSet &o) : QhullSet(o), select_all(o.select_all) {}

private:
                        //!Disable default constructor and copy assignment.  See QhullSetBase
                        QhullFacetSet();
    QhullFacetSet      &operator=(const QhullFacetSet &);
public:

#//Conversion
#ifndef QHULL_NO_STL
    std::vector toStdVector() const;
#endif //QHULL_NO_STL
#ifdef QHULL_USES_QT
    QList   toQList() const;
#endif //QHULL_USES_QT

#//GetSet
    bool                isSelectAll() const { return select_all; }
    void                selectAll() { select_all= true; }
    void                selectGood() { select_all= false; }

#//Read-only
                        //! Filtered by facet.isGood().  May be 0 when !isEmpty().
    int                 count() const;
    bool                contains(const QhullFacet &f) const;
    int                 count(const QhullFacet &f) const;
                        //! operator==() does not depend on isGood()

#//IO
    // Not same as QhullFacetList#IO.  A QhullFacetSet is a component of a QhullFacetList.

    struct PrintFacetSet{
        const QhullFacetSet *facet_set;
        const char     *print_message;
        int             run_id;
                        PrintFacetSet(int qhRunId, const char *message, const QhullFacetSet *s) : facet_set(s), print_message(message), run_id(qhRunId) {}
    };//PrintFacetSet
    const PrintFacetSet       print(int qhRunId, const char *message) const { return PrintFacetSet(qhRunId, message, this); }

    struct PrintIdentifiers{
        const QhullFacetSet *facet_set;
        const char     *print_message;
                        PrintIdentifiers(const char *message, const QhullFacetSet *s) : facet_set(s), print_message(message) {}
    };//PrintIdentifiers
    PrintIdentifiers    printIdentifiers(const char *message) const { return PrintIdentifiers(message, this); }

};//class QhullFacetSet

}//namespace orgQhull

#//== Global namespace =========================================

std::ostream &operator<<(std::ostream &os, const orgQhull::QhullFacetSet &fs);
std::ostream &operator<<(std::ostream &os, const orgQhull::QhullFacetSet::PrintFacetSet &pr);
std::ostream &operator<<(std::ostream &os, const orgQhull::QhullFacetSet::PrintIdentifiers &p);

#endif // QHULLFACETSET_H
qhull-2012.1/src/libqhullcpp/QhullHyperplane.cpp0000644000076400010400000001040511710144465023036 0ustar  bbarberAdministrators/****************************************************************************
**
** Copyright (c) 2009-2012 C.B. Barber. All rights reserved.
** $Id: //main/2011/qhull/src/libqhullcpp/QhullHyperplane.cpp#6 $$Change: 1464 $
** $DateTime: 2012/01/25 22:58:41 $$Author: bbarber $
**
****************************************************************************/

#include "QhullHyperplane.h"
#include "QhullPoint.h"

#include 


#ifdef _MSC_VER  // Microsoft Visual C++ -- warning level 4
#endif

namespace orgQhull {

#//Conversion

// See qt-qhull.cpp for QList conversions

#ifndef QHULL_NO_STL
std::vector QhullHyperplane::
toStdVector() const
{
    QhullHyperplaneIterator i(*this);
    std::vector fs;
    while(i.hasNext()){
        fs.push_back(i.next());
    }
    fs.push_back(hyperplane_offset);
    return fs;
}//toStdVector
#endif //QHULL_NO_STL

#//Value

//! Return distance from point to hyperplane.
//!   If greater than zero, the point is above the facet (i.e., outside).
// qh_distplane [geom.c], QhullFacet::distance, and QhullHyperplane::distance are copies
//    Does not support RANDOMdist or logging
double QhullHyperplane::
distance(const QhullPoint &p) const
{
    const coordT *point= p.coordinates();
    int dim= p.dimension();
    QHULL_ASSERT(dim==dimension());
    const coordT *normal= coordinates();
    double dist;

    switch (dim){
  case 2:
      dist= offset() + point[0] * normal[0] + point[1] * normal[1];
      break;
  case 3:
      dist= offset() + point[0] * normal[0] + point[1] * normal[1] + point[2] * normal[2];
      break;
  case 4:
      dist= offset()+point[0]*normal[0]+point[1]*normal[1]+point[2]*normal[2]+point[3]*normal[3];
      break;
  case 5:
      dist= offset()+point[0]*normal[0]+point[1]*normal[1]+point[2]*normal[2]+point[3]*normal[3]+point[4]*normal[4];
      break;
  case 6:
      dist= offset()+point[0]*normal[0]+point[1]*normal[1]+point[2]*normal[2]+point[3]*normal[3]+point[4]*normal[4]+point[5]*normal[5];
      break;
  case 7:
      dist= offset()+point[0]*normal[0]+point[1]*normal[1]+point[2]*normal[2]+point[3]*normal[3]+point[4]*normal[4]+point[5]*normal[5]+point[6]*normal[6];
      break;
  case 8:
      dist= offset()+point[0]*normal[0]+point[1]*normal[1]+point[2]*normal[2]+point[3]*normal[3]+point[4]*normal[4]+point[5]*normal[5]+point[6]*normal[6]+point[7]*normal[7];
      break;
  default:
      dist= offset();
      for (int k=dim; k--; )
          dist += *point++ * *normal++;
      break;
    }
    return dist;
}//distance

double QhullHyperplane::
norm() const {
    double d= 0.0;
    const coordT *c= coordinates();
    for (int k=dimension(); k--; ){
        d += *c * *c;
        ++c;
    }
    return sqrt(d);
}//norm

#//Operator

bool QhullHyperplane::
operator==(const QhullHyperplane &other) const
{
    if(hyperplane_dimension!=other.hyperplane_dimension){
        return false;
    }
    double d= fabs(hyperplane_offset-other.hyperplane_offset);
    if(d>UsingLibQhull::globalDistanceEpsilon()){
        return false;
    }
    const coordT *c= hyperplane_coordinates;
    const coordT *c2= other.hyperplane_coordinates;
    if(c==c2){
        return true;
    }
    double dist2= 0.0;
    for(int k= hyperplane_dimension; k--; ){
        double diff= *c++ - *c2++;
        dist2 += diff*diff;
    }
    if(dist2 > UsingLibQhull::globalAngleEpsilon()){
        return false;
    }
    return true;
}//operator==

#//GetSet

}//namespace orgQhull

#//Global functions

using std::ostream;
using orgQhull::QhullHyperplane;
using orgQhull::UsingLibQhull;

#//operator<<

ostream &
operator<<(ostream &os, const QhullHyperplane &p)
{
    os << p.print();
    return os;
}

ostream &
operator<<(ostream &os, const QhullHyperplane::PrintHyperplane &pr)
{
    QhullHyperplane p= *pr.hyperplane;
    if(pr.print_message){
        os << pr.print_message;
    }
    const realT *c= p.coordinates();
    for(int k=p.dimension(); k--; ){
        realT r= *c++;
        if(pr.print_message){
            os << " " << r; // FIXUP QH11010 %8.4g
        }else{
            os << " " << r; // FIXUP QH11010 qh_REAL_1
        }
    }
    if(pr.hyperplane_offset_message){
        os << pr.hyperplane_offset_message << " " << p.offset();
    }else{
        os << " " << p.offset();
    }
    os << std::endl;
    return os;
}//PrintHyperplane

qhull-2012.1/src/libqhullcpp/QhullHyperplane.h0000644000076400010400000001361111710144465022505 0ustar  bbarberAdministrators/****************************************************************************
**
** Copyright (c) 2009-2012 C.B. Barber. All rights reserved.
** $Id: //main/2011/qhull/src/libqhullcpp/QhullHyperplane.h#6 $$Change: 1464 $
** $DateTime: 2012/01/25 22:58:41 $$Author: bbarber $
**
****************************************************************************/

#ifndef QHHYPERPLANE_H
#define QHHYPERPLANE_H

#include "QhullError.h"
#include "QhullIterator.h"
#include "UsingLibQhull.h"
extern "C" {
    #include "libqhull/qhull_a.h"
}

#include 

namespace orgQhull {
#//ClassRef
    class QhullPoint;

#//Types
    //! QhullHyperplane as an offset, dimension, and pointer to coordinates
    class QhullHyperplane;
    //! Java-style iterator for QhullHyperplane coordinates
    class QhullHyperplaneIterator;

class QhullHyperplane { // Similar to QhullPoint

private:
#//Fields
    coordT             *hyperplane_coordinates;  // Keep pointers aligned
    int                 hyperplane_dimension;
    coordT              hyperplane_offset;

public:
#//Subtypes
    typedef const coordT *                  iterator;
    typedef const coordT *                  const_iterator;
    typedef QhullHyperplane::iterator       Iterator;
    typedef QhullHyperplane::const_iterator ConstIterator;

#//Construct
                        QhullHyperplane() : hyperplane_coordinates(0), hyperplane_dimension(0), hyperplane_offset(0.0) {};
                        QhullHyperplane(int hyperplaneDimension, coordT *c, coordT hyperplaneOffset) : hyperplane_coordinates(c), hyperplane_dimension(hyperplaneDimension), hyperplane_offset(hyperplaneOffset) {}
                        // Creates an alias.  Does not copy the hyperplane's coordinates.  Needed for return by value and parameter passing.
                        QhullHyperplane(const QhullHyperplane &other)  : hyperplane_coordinates(other.hyperplane_coordinates), hyperplane_dimension(other.hyperplane_dimension), hyperplane_offset(other.hyperplane_offset) {}
                        // Creates an alias.  Does not copy the hyperplane's coordinates.  Needed for vector
    QhullHyperplane    &operator=(const QhullHyperplane &other) { hyperplane_coordinates= other.hyperplane_coordinates; hyperplane_dimension= other.hyperplane_dimension; hyperplane_offset= other.hyperplane_offset; return *this; }
                       ~QhullHyperplane() {}

#//Conversions --
//! Includes offset at end
#ifndef QHULL_NO_STL
    std::vector toStdVector() const;
#endif //QHULL_NO_STL
#ifdef QHULL_USES_QT
    QList       toQList() const;
#endif //QHULL_USES_QT

#//Read-only
public:
    const coordT       *coordinates() const { return hyperplane_coordinates; }
    coordT             *coordinates() { return hyperplane_coordinates; }
    int                 dimension() const { return hyperplane_dimension; }
    bool                isDefined() const { return hyperplane_coordinates!=0 && hyperplane_dimension>0; }
    coordT              offset() const { return hyperplane_offset; }

#//Define
    void                defineAs(int hyperplaneDimension, coordT *c, coordT hyperplaneOffset) { QHULL_ASSERT(hyperplaneDimension>=0); hyperplane_coordinates= c; hyperplane_dimension= hyperplaneDimension; hyperplane_offset= hyperplaneOffset; }
    //! Creates an alias to other
    void                defineAs(QhullHyperplane &other) { hyperplane_coordinates= other.coordinates(); hyperplane_dimension= other.dimension();  hyperplane_offset= other.offset(); }
    void                setCoordinates(coordT *c) { hyperplane_coordinates= c; }
    void                setDimension(int hyperplaneDimension) { hyperplane_dimension= hyperplaneDimension; }
    void                setOffset(coordT hyperplaneOffset) { hyperplane_offset= hyperplaneOffset; }

#//value
    double              distance(const QhullPoint &p) const;
    double              norm() const;

#//iterator
    iterator            begin() { return hyperplane_coordinates; }
    const_iterator      begin() const { return hyperplane_coordinates; }
    const_iterator      constBegin() const { return hyperplane_coordinates; }
    const_iterator      constEnd() const { return hyperplane_coordinates+hyperplane_dimension; }
    int                 count() { return dimension(); }
    iterator            end() { return hyperplane_coordinates+hyperplane_dimension; }
    const_iterator      end() const { return hyperplane_coordinates+hyperplane_dimension; }
    size_t              size() { return (size_t)dimension(); }

#//Operator
    bool                operator==(const QhullHyperplane &other) const;
    bool                operator!=(const QhullHyperplane &other) const { return !operator==(other); }
    const coordT       &operator[](int idx) const { QHULL_ASSERT(idx>=0 && idx=0 && idx
#include 
#include 
//! Avoid dependence on 
namespace std { struct bidirectional_iterator_tag; struct random_access_iterator_tag; }

namespace orgQhull {

#//Defined here
    //! QHULL_DECLARE_SEQUENTIAL_ITERATOR(C) -- Declare a Java-style iterator
    //! QHULL_DECLARE_MUTABLE_SEQUENTIAL_ITERATOR(C) -- Declare a mutable Java-style iterator
    //! QHULL_DECLARE_SET_ITERATOR(C) -- Declare a set iterator
    //! QHULL_DECLARE_MUTABLE_SET_ITERATOR(C) -- Declare a mutable set iterator
    //! Derived from Qt/core/tools/qiterator.h and qset.h/FOREACHsetelement_()

// Changed c to C* as in Mutable...  Assumes c does not go away.
#define QHULL_DECLARE_SEQUENTIAL_ITERATOR(C, T) \
    \
    class C##Iterator \
    { \
        typedef C::const_iterator const_iterator; \
        const C *c; \
        const_iterator i; \
        public: \
        inline C##Iterator(const C &container) \
        : c(&container), i(c->constBegin()) {} \
        inline C##Iterator &operator=(const C &container) \
        { c = &container; i = c->constBegin(); return *this; } \
        inline void toFront() { i = c->constBegin(); } \
        inline void toBack() { i = c->constEnd(); } \
        inline bool hasNext() const { return i != c->constEnd(); } \
        inline const T &next() { return *i++; } \
        inline const T &peekNext() const { return *i; } \
        inline bool hasPrevious() const { return i != c->constBegin(); } \
        inline const T &previous() { return *--i; } \
        inline const T &peekPrevious() const { const_iterator p = i; return *--p; } \
        inline bool findNext(const T &t) \
        { while (i != c->constEnd()) if (*i++ == t) return true; return false; } \
        inline bool findPrevious(const T &t) \
        { while (i != c->constBegin()) if (*(--i) == t) return true; \
        return false;  } \
    };//C##Iterator

// Remove setShareable() from Q_DECLARE_MUTABLE_SEQUENTIAL_ITERATOR
// Uses QHULL_ASSERT (assert.h)
// Duplicated in MutablePointIterator without insert or remove
#define QHULL_DECLARE_MUTABLE_SEQUENTIAL_ITERATOR(C, T) \
    class Mutable##C##Iterator \
    { \
        typedef C::iterator iterator; \
        typedef C::const_iterator const_iterator; \
        C *c; \
        iterator i, n; \
        inline bool item_exists() const { return const_iterator(n) != c->constEnd(); } \
        public: \
        inline Mutable##C##Iterator(C &container) \
        : c(&container) \
        { i = c->begin(); n = c->end(); } \
        inline ~Mutable##C##Iterator() \
        {} \
        inline Mutable##C##Iterator &operator=(C &container) \
        { c = &container; \
        i = c->begin(); n = c->end(); return *this; } \
        inline void toFront() { i = c->begin(); n = c->end(); } \
        inline void toBack() { i = c->end(); n = i; } \
        inline bool hasNext() const { return c->constEnd() != const_iterator(i); } \
        inline T &next() { n = i++; return *n; } \
        inline T &peekNext() const { return *i; } \
        inline bool hasPrevious() const { return c->constBegin() != const_iterator(i); } \
        inline T &previous() { n = --i; return *n; } \
        inline T &peekPrevious() const { iterator p = i; return *--p; } \
        inline void remove() \
        { if (c->constEnd() != const_iterator(n)) { i = c->erase(n); n = c->end(); } } \
        inline void setValue(const T &t) const { if (c->constEnd() != const_iterator(n)) *n = t; } \
        inline T &value() { QHULL_ASSERT(item_exists()); return *n; } \
        inline const T &value() const { QHULL_ASSERT(item_exists()); return *n; } \
        inline void insert(const T &t) { n = i = c->insert(i, t); ++i; } \
        inline bool findNext(const T &t) \
        { while (c->constEnd() != const_iterator(n = i)) if (*i++ == t) return true; return false; } \
        inline bool findPrevious(const T &t) \
        { while (c->constBegin() != const_iterator(i)) if (*(n = --i) == t) return true; \
        n = c->end(); return false;  } \
    };//Mutable##C##Iterator

#define QHULL_DECLARE_SET_ITERATOR(C) \
\
    template  \
    class Qhull##C##Iterator \
    { \
        typedef typename Qhull##C::const_iterator const_iterator; \
        Qhull##C c; \
        const_iterator i; \
    public: \
        inline Qhull##C##Iterator(const Qhull##C &container) \
        : c(container), i(c.constBegin()) {} \
        inline Qhull##C##Iterator &operator=(const Qhull##C &container) \
        { c = container; i = c.constBegin(); return *this; } \
        inline void toFront() { i = c.constBegin(); } \
        inline void toBack() { i = c.constEnd(); } \
        inline bool hasNext() const { return i != c.constEnd(); } \
        inline const T &next() { return *i++; } \
        inline const T &peekNext() const { return *i; } \
        inline bool hasPrevious() const { return i != c.constBegin(); } \
        inline const T &previous() { return *--i; } \
        inline const T &peekPrevious() const { const_iterator p = i; return *--p; } \
        inline bool findNext(const T &t) \
        { while (i != c.constEnd()) if (*i++ == t) return true; return false; } \
        inline bool findPrevious(const T &t) \
        { while (i != c.constBegin()) if (*(--i) == t) return true; \
        return false;  } \
    };//Qhull##C##Iterator

#define QHULL_DECLARE_MUTABLE_SET_ITERATOR(C) \
\
template  \
class QhullMutable##C##Iterator \
{ \
    typedef typename Qhull##C::iterator iterator; \
    typedef typename Qhull##C::const_iterator const_iterator; \
    Qhull##C *c; \
    iterator i, n; \
    inline bool item_exists() const { return const_iterator(n) != c->constEnd(); } \
public: \
    inline Mutable##C##Iterator(Qhull##C &container) \
        : c(&container) \
    { c->setSharable(false); i = c->begin(); n = c->end(); } \
    inline ~Mutable##C##Iterator() \
    { c->setSharable(true); } \
    inline Mutable##C##Iterator &operator=(Qhull##C &container) \
    { c->setSharable(true); c = &container; c->setSharable(false); \
      i = c->begin(); n = c->end(); return *this; } \
    inline void toFront() { i = c->begin(); n = c->end(); } \
    inline void toBack() { i = c->end(); n = i; } \
    inline bool hasNext() const { return c->constEnd() != const_iterator(i); } \
    inline T &next() { n = i++; return *n; } \
    inline T &peekNext() const { return *i; } \
    inline bool hasPrevious() const { return c->constBegin() != const_iterator(i); } \
    inline T &previous() { n = --i; return *n; } \
    inline T &peekPrevious() const { iterator p = i; return *--p; } \
    inline void remove() \
    { if (c->constEnd() != const_iterator(n)) { i = c->erase(n); n = c->end(); } } \
    inline void setValue(const T &t) const { if (c->constEnd() != const_iterator(n)) *n = t; } \
    inline T &value() { Q_ASSERT(item_exists()); return *n; } \
    inline const T &value() const { Q_ASSERT(item_exists()); return *n; } \
    inline void insert(const T &t) { n = i = c->insert(i, t); ++i; } \
    inline bool findNext(const T &t) \
    { while (c->constEnd() != const_iterator(n = i)) if (*i++ == t) return true; return false; } \
    inline bool findPrevious(const T &t) \
    { while (c->constBegin() != const_iterator(i)) if (*(n = --i) == t) return true; \
      n = c->end(); return false;  } \
};//QhullMutable##C##Iterator

}//namespace orgQhull

#endif // QHULLITERATOR_H

qhull-2012.1/src/libqhullcpp/QhullLinkedList.h0000644000076400010400000002726411710144465022451 0ustar  bbarberAdministrators/****************************************************************************
**
** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
** $Id: //main/2011/qhull/src/libqhullcpp/QhullLinkedList.h#3 $$Change: 1464 $
** $DateTime: 2012/01/25 22:58:41 $$Author: bbarber $
**
****************************************************************************/

#ifndef QHULLLINKEDLIST_H
#define QHULLLINKEDLIST_H

namespace std { struct bidirectional_iterator_tag; struct random_access_iterator_tag; }

#include "QhullError.h"

#ifdef QHULL_USES_QT
#include 
#endif

#ifndef QHULL_NO_STL
#include 
#endif

namespace orgQhull {

#//Type
    //! QhullLinkedList -- A linked list modeled on QLinkedList.
    //!   T is an opaque type with T(B *b), b=t.getBaseT(), t=t.next(), and t=t.prev().  The end node is a sentinel.
    //!   libqhull owns the contents.
    //!   QhullLinkedList does not define erase(), clear(), removeFirst(), removeLast(), pop_back(), pop_front(), fromStdList()
    //!   Derived from Qt/core/tools/qlinkedlist.h and libqhull.h/FORALLfacets_()
    //! QhullLinkedList::const_iterator -- STL-style iterator
    //! QhullLinkedList::iterator -- STL-style iterator
    //! QhullLinkedListIterator -- Java-style iterator
    //!   Derived from Qt/core/tools/qiterator.h
    //!   Works with Qt's foreach keyword [Qt/src/corelib/global/qglobal.h]

template 
class QhullLinkedList
{
private:
#//Fields
    T                   begin_node;
    T                   end_node;     //! Sentinel node at end of list

public:
#//Subtypes and types
    class               const_iterator;
    class               iterator;
    typedef const_iterator  ConstIterator;
    typedef iterator    Iterator;
    typedef ptrdiff_t   difference_type;
    typedef int         size_type;
    typedef T           value_type;
    typedef const value_type *const_pointer;
    typedef const value_type &const_reference;
    typedef value_type *pointer;
    typedef value_type &reference;

#//Constructors
                        QhullLinkedList(T b, T e) : begin_node(b), end_node(e) {}
                        //Copy constructor copies pointer but not contents.  Needed for return by value and parameter passing.
                        QhullLinkedList(const QhullLinkedList &o) : begin_node(o.begin_node), end_node(o.end_node) {}
                       ~QhullLinkedList() {}

private:
                        //!disabled since a sentinel must be allocated as the private type
                        QhullLinkedList() {}
                        //!disabled since qs= qs2 is ambiguous (pointer vs. contents)
    QhullLinkedList &operator=(const QhullLinkedList &l) {}
public:

#//Conversions
#ifndef QHULL_NO_STL
    std::vector      toStdVector() const;
#endif
#ifdef QHULL_USES_QT
    QList            toQList() const;
#endif

#//Read-only
    int                 count() const;
                        //count(t) under #//Search
    bool                empty() const { return isEmpty(); }
    bool                isEmpty() const { return (begin_node==end_node); }
    bool                operator==(const QhullLinkedList &o) const;
    bool                operator!=(const QhullLinkedList &o) const { return !operator==(o); }
    size_t              size() const { return count(); }

#//Element access
    //! Return by value which contains a pointer (e.g., typedef vertexT * QhullVertex).  A reference does not make sense.
    T                   back() const { return last(); }
    T                   first() const { QHULL_ASSERT(!isEmpty()); return *begin(); }
    T                   front() const { return first(); }
    T                   last() const { QHULL_ASSERT(!isEmpty()); return *--end(); }

#//Modify -- Allocation of opaque types not implemented.

#//Search
    bool                contains(const T &t) const;
    int                 count(const T &t) const;

#//Iterator
    iterator            begin() { return begin_node; }
    const_iterator      begin() const { return begin_node; }
    const_iterator      constBegin() const { return begin_node; }
    const_iterator      constEnd() const { return end_node; }
    iterator            end() { return end_node; }
    const_iterator      end() const { return end_node; }

    class iterator {

    private:
        T               i;
        friend class    const_iterator;

    public:
        typedef std::bidirectional_iterator_tag  iterator_category;
        typedef T           value_type;
        typedef value_type *pointer;
        typedef value_type &reference;
        typedef ptrdiff_t   difference_type;

                        iterator() : i() {}
                        iterator(T t) : i(t) {}
                        iterator(const iterator &o) : i(o.i) {}
        iterator       &operator=(const iterator &o) { i= o.i; return *this; }

        T               operator*() const { return i; }
        T               operator->() const { return i; }
        bool            operator==(const iterator &o) const { return i == o.i; }
        bool            operator!=(const iterator &o) const { return !operator==(o); }
        bool            operator==(const const_iterator &o) const { return i==reinterpret_cast(o).i; }
        bool            operator!=(const const_iterator &o) const { return !operator==(o); }
        iterator       &operator++() { i= i.next(); return *this; }
        iterator        operator++(int) { iterator o= i; i= i.next(); return o; }
        iterator       &operator--() { i= i.previous(); return *this; }
        iterator        operator--(int) { iterator o= i; i= i.previous(); return o; }
        iterator        operator+(int j) const;
        iterator        operator-(int j) const { return operator+(-j); }
        iterator       &operator+=(int j) { return *this= *this + j; }
        iterator       &operator-=(int j) { return *this= *this - j; }
    };//QhullLinkedList::iterator

    class const_iterator {

    private:
        T               i;

    public:
        typedef std::bidirectional_iterator_tag  iterator_category;
        typedef T                 value_type;
        typedef const value_type *pointer;
        typedef const value_type &reference;
        typedef ptrdiff_t         difference_type;

                        const_iterator() : i() {}
                        const_iterator(T t) : i(t) {}
                        const_iterator(const const_iterator &o) : i(o.i) {}
                        const_iterator(iterator o) : i(o.i) {}
        const_iterator &operator=(const const_iterator &o) { i= o.i; return *this; }

        T               operator*() const { return i; }
        T               operator->() const { return i; }
        bool            operator==(const const_iterator &o) const { return i == o.i; }
        bool            operator!=(const const_iterator &o) const { return !operator==(o); }
                        // No comparisons or iterator diff
        const_iterator &operator++() { i= i.next(); return *this; }
        const_iterator  operator++(int) { const_iterator o= i; i= i.next(); return o; }
        const_iterator &operator--() { i= i.previous(); return *this; }
        const_iterator  operator--(int) { const_iterator o= i; i= i.previous(); return o; }
        const_iterator  operator+(int j) const;
        const_iterator  operator-(int j) const { return operator+(-j); }
        const_iterator &operator+=(int j) { return *this= *this + j; }
        const_iterator &operator-=(int j) { return *this= *this - j; }
    };//QhullLinkedList::const_iterator

};//QhullLinkedList

template 
class QhullLinkedListIterator // FIXUP QH11016 define QhullMutableLinkedListIterator
{
    typedef typename QhullLinkedList::const_iterator const_iterator;
    const QhullLinkedList *c;
    const_iterator      i;

public:
                        QhullLinkedListIterator(const QhullLinkedList &container) : c(&container), i(c->constBegin()) {}
                        QhullLinkedListIterator &operator=(const QhullLinkedList &container) { c= &container; i= c->constBegin(); return *this; }
    bool                findNext(const T &t);
    bool                findPrevious(const T &t);
    bool                hasNext() const { return i != c->constEnd(); }
    bool                hasPrevious() const { return i != c->constBegin(); }
    T                   next() { return *i++; }
    T                   peekNext() const { return *i; }
    T                   peekPrevious() const { const_iterator p= i; return *--p; }
    T                   previous() { return *--i; }
    void                toFront() { i= c->constBegin(); }
    void                toBack() { i= c->constEnd(); }
};//QhullLinkedListIterator

#//== Definitions =========================================

#//Conversion

#ifndef QHULL_NO_STL
template 
std::vector QhullLinkedList::
toStdVector() const
{
    std::vector tmp;
    std::copy(constBegin(), constEnd(), std::back_inserter(tmp));
    return tmp;
}//toStdVector
#endif

#ifdef QHULL_USES_QT
template 
QList  QhullLinkedList::
toQList() const
{
    QhullLinkedListIterator i(*this);
    QList ls;
    while(i.hasNext()){
        ls.append(i.next());
    }
    return ls;
}//toQList
#endif

#//Read-only

template 
int QhullLinkedList::
count() const
{
    const_iterator i= begin_node;
    int c= 0;
    while(i != end_node){
        c++;
        i++;
    }
    return c;
}//count

#//Search

template 
bool QhullLinkedList::
contains(const T &t) const
{
    const_iterator i= begin_node;
    while(i != end_node){
        if(i==t){
            return true;
        }
        i++;
    }
    return false;
}//contains

template 
int QhullLinkedList::
count(const T &t) const
{
    const_iterator i= begin_node;
    int c= 0;
    while(i != end_node){
        if(i==t){
            c++;
        }
        i++;
    }
    return c;
}//count

template 
bool QhullLinkedList::
operator==(const QhullLinkedList &l) const
{
    if(begin_node==l.begin_node){
        return (end_node==l.end_node);
    }
    T i= begin_node;
    T il= l.begin_node;
    while(i != end_node){
        if(i != il){
            return false;
        }
        i= static_cast(i.next());
        il= static_cast(il.next());
    }
    if(il != l.end_node){
        return false;
    }
    return true;
}//operator==

#//Iterator

template 
typename QhullLinkedList::iterator  QhullLinkedList::iterator::
operator+(int j) const
{
    T n= i;
    if(j>0){
        while(j--){
            n= n.next();
        }
    }else{
        while(j++){
            n= n.previous();
        }
    }
    return iterator(n);
}//operator+

template 
typename QhullLinkedList::const_iterator  QhullLinkedList::const_iterator::
operator+(int j) const
{
    T n= i;
    if(j>0){
        while(j--){
            n= n.next();
        }
    }else{
        while(j++){
            n= n.previous();
        }
    }
    return const_iterator(n);
}//operator+

#//QhullLinkedListIterator

template 
bool QhullLinkedListIterator::
findNext(const T &t)
{
    while(i != c->constEnd()){
        if (*i++ == t){
            return true;
        }
    }
    return false;
}//findNext

template 
bool QhullLinkedListIterator::
findPrevious(const T &t)
{
    while(i!=c->constBegin()){
        if(*(--i)==t){
            return true;
        }
    }
    return false;
}//findNext

}//namespace orgQhull

#//Global functions

template 
std::ostream &
operator<<(std::ostream &os, const orgQhull::QhullLinkedList &qs)
{
    typename orgQhull::QhullLinkedList::const_iterator i;
    for(i= qs.begin(); i != qs.end(); ++i){
        os << *i;
    }
    return os;
}//operator<<

#endif // QHULLLINKEDLIST_H

qhull-2012.1/src/libqhullcpp/QhullPoint.cpp0000644000076400010400000001152111710144465022020 0ustar  bbarberAdministrators/****************************************************************************
**
** Copyright (c) 2009-2012 C.B. Barber. All rights reserved.
** $Id: //main/2011/qhull/src/libqhullcpp/QhullPoint.cpp#4 $$Change: 1464 $
** $DateTime: 2012/01/25 22:58:41 $$Author: bbarber $
**
****************************************************************************/

#include "UsingLibQhull.h"
#include "QhullPoint.h"

#include 
#include 

#ifdef _MSC_VER  // Microsoft Visual C++ -- warning level 4
#endif

namespace orgQhull {

#//Class public variables and methods

//! If qhRundID undefined uses QhullPoint::s_points_begin and dimension
int QhullPoint::
id(int qhRunId, int dimension, const coordT *c)
{
    QHULL_UNUSED(dimension);

    if(UsingLibQhull::hasPoints()){
        if(qhRunId==UsingLibQhull::NOqhRunId){
            const coordT *pointsEnd;
            int dim;
            const coordT *points= UsingLibQhull::globalPoints(&dim, &pointsEnd);
            if(c>=points && c(c));
        }
    }
    long long i=(long long)c;
    return (int)i; // WARN64
}//id

#//Conversion

// See qt-qhull.cpp for QList conversion

#ifndef QHULL_NO_STL
std::vector QhullPoint::
toStdVector() const
{
    QhullPointIterator i(*this);
    std::vector vs;
    while(i.hasNext()){
        vs.push_back(i.next());
    }
    return vs;
}//toStdVector
#endif //QHULL_NO_STL

#//Operator

bool QhullPoint::
operator==(const QhullPoint &other) const
{
    if(point_dimension!=other.point_dimension){
        return false;
    }
    const coordT *c= point_coordinates;
    const coordT *c2= other.point_coordinates;
    if(c==c2){
        return true;
    }
    double dist2= 0.0;
    for(int k= point_dimension; k--; ){
        double diff= *c++ - *c2++;
        dist2 += diff*diff;
    }
    double epsilon= UsingLibQhull::globalDistanceEpsilon();
    // std::cout << "DEBUG dist2 " << dist2 << " epsilon^2 " << epsilon*epsilon << std::endl;
    return (dist2<=(epsilon*epsilon));
}//operator==


#//Value

//! Return distance betweeen two points.
double QhullPoint::
distance(const QhullPoint &p) const
{
    const coordT *c= coordinates();
    const coordT *c2= p.coordinates();
    int dim= dimension();
    QHULL_ASSERT(dim==p.dimension());
    double dist;

    switch(dim){
  case 2:
      dist= (c[0]-c2[0])*(c[0]-c2[0]) + (c[1]-c2[1])*(c[1]-c2[1]);
      break;
  case 3:
      dist= (c[0]-c2[0])*(c[0]-c2[0]) + (c[1]-c2[1])*(c[1]-c2[1]) + (c[2]-c2[2])*(c[2]-c2[2]);
      break;
  case 4:
      dist= (c[0]-c2[0])*(c[0]-c2[0]) + (c[1]-c2[1])*(c[1]-c2[1]) + (c[2]-c2[2])*(c[2]-c2[2]) + (c[3]-c2[3])*(c[3]-c2[3]);
      break;
  case 5:
      dist= (c[0]-c2[0])*(c[0]-c2[0]) + (c[1]-c2[1])*(c[1]-c2[1]) + (c[2]-c2[2])*(c[2]-c2[2]) + (c[3]-c2[3])*(c[3]-c2[3]) + (c[4]-c2[4])*(c[4]-c2[4]);
      break;
  case 6:
      dist= (c[0]-c2[0])*(c[0]-c2[0]) + (c[1]-c2[1])*(c[1]-c2[1]) + (c[2]-c2[2])*(c[2]-c2[2]) + (c[3]-c2[3])*(c[3]-c2[3]) + (c[4]-c2[4])*(c[4]-c2[4]) + (c[5]-c2[5])*(c[5]-c2[5]);
      break;
  case 7:
      dist= (c[0]-c2[0])*(c[0]-c2[0]) + (c[1]-c2[1])*(c[1]-c2[1]) + (c[2]-c2[2])*(c[2]-c2[2]) + (c[3]-c2[3])*(c[3]-c2[3]) + (c[4]-c2[4])*(c[4]-c2[4]) + (c[5]-c2[5])*(c[5]-c2[5]) + (c[6]-c2[6])*(c[6]-c2[6]);
      break;
  case 8:
      dist= (c[0]-c2[0])*(c[0]-c2[0]) + (c[1]-c2[1])*(c[1]-c2[1]) + (c[2]-c2[2])*(c[2]-c2[2]) + (c[3]-c2[3])*(c[3]-c2[3]) + (c[4]-c2[4])*(c[4]-c2[4]) + (c[5]-c2[5])*(c[5]-c2[5]) + (c[6]-c2[6])*(c[6]-c2[6]) + (c[7]-c2[7])*(c[7]-c2[7]);
      break;
  default:
      dist= 0.0;
      for(int k=dim; k--; ){
          dist += (*c - *c2) * (*c - *c2);
          ++c;
          ++c2;
      }
      break;
    }
    return sqrt(dist);
}//distance

}//namespace orgQhull

#//Global functions

using std::ostream;
using orgQhull::QhullPoint;
using orgQhull::UsingLibQhull;

#//operator<<

ostream &
operator<<(ostream &os, const QhullPoint &p)
{
    os << p.printWithIdentifier(UsingLibQhull::NOqhRunId, "");
    return os;
}

//! Same as qh_printpointid [io.c]
ostream &
operator<<(ostream &os, const QhullPoint::PrintPoint &pr)
{
    QhullPoint p= *pr.point; 
    int i= p.id(pr.run_id);
    if(pr.point_message){
        if(*pr.point_message){
            os << pr.point_message << " ";
        }
        if(pr.with_identifier && (i!=-1)){
            os << "p" << i << ": ";
        }
    }
    const realT *c= p.coordinates();
    for(int k=p.dimension(); k--; ){
        realT r= *c++;
        if(pr.point_message){
            os << " " << r; // FIXUP QH11010 %8.4g
        }else{
            os << " " << r; // FIXUP QH11010 qh_REAL_1
        }
    }
    os << std::endl;
    return os;
}//printPoint

qhull-2012.1/src/libqhullcpp/QhullPoint.h0000644000076400010400000001401711710144465021470 0ustar  bbarberAdministrators/****************************************************************************
**
** Copyright (c) 2009-2012 C.B. Barber. All rights reserved.
** $Id: //main/2011/qhull/src/libqhullcpp/QhullPoint.h#6 $$Change: 1464 $
** $DateTime: 2012/01/25 22:58:41 $$Author: bbarber $
**
****************************************************************************/

#ifndef QHPOINT_H
#define QHPOINT_H

#include "QhullError.h"
#include "QhullIterator.h"
#include "UsingLibQhull.h"
#include "Coordinates.h"
extern "C" {
    #include "libqhull/qhull_a.h"
}

#include 

namespace orgQhull {

#//Types
    //! QhullPoint as a pointer and dimension to shared memory
    class QhullPoint;
    //! Java-style iterator for QhullPoint coordinates
    class QhullPointIterator;

class QhullPoint {

    //! A point is a pointer into an array of coordinates.

private:
#//Fields
    coordT             *point_coordinates;  // Keep pointers aligned
    int                 point_dimension;

public:
#//Subtypes
    typedef const coordT *              iterator;
    typedef const coordT *              const_iterator;
    typedef QhullPoint::iterator        Iterator;
    typedef QhullPoint::const_iterator  ConstIterator;

#//Class methods -- Convert point to id w/o QhullQh data structure
    static int          id(const coordT *c) { return QhullPoint::id(UsingLibQhull::NOqhRunId, 0, c); }
    static int          id(int qhRunId, const coordT *c) { return QhullPoint::id(qhRunId, 0, c); }
    static int          id(int qhRunId, int dimension, const coordT *c);

#//Construct
                        QhullPoint() : point_coordinates(0), point_dimension(0) {};
                        QhullPoint(int pointDimension, coordT *c) : point_coordinates(c), point_dimension(pointDimension) {}
    explicit            QhullPoint(Coordinates &c) : point_coordinates(c.data()), point_dimension(c.count()) {}
                        // Creates an alias.  Does not copy the point.  Needed for return by value and parameter passing.
                        QhullPoint(const QhullPoint &other)  : point_coordinates(other.point_coordinates), point_dimension(other.point_dimension) {}
                        // Creates an alias.  Does not copy the point.  Needed for vector
    QhullPoint         &operator=(const QhullPoint &other) { point_coordinates= other.point_coordinates; point_dimension= other.point_dimension; return *this; }
                       ~QhullPoint() {}

#//Conversions
    // see coordinates()
#ifndef QHULL_NO_STL
    std::vector toStdVector() const;
#endif //QHULL_NO_STL
#ifdef QHULL_USES_QT
    QList       toQList() const;
#endif //QHULL_USES_QT

#//Read-only
public:
    const coordT       *coordinates() const { return point_coordinates; }
    coordT             *coordinates() { return point_coordinates; }
    int                 dimension() const { return point_dimension; }
    int                 id(int qhRunId) const { return id(qhRunId, dimension(), coordinates()); }
    int                 id() const { return id(UsingLibQhull::NOqhRunId, dimension(), coordinates()); }
    bool                isDefined() const { return point_coordinates!=0 && point_dimension>0; }

#//Define
    void                advancePoint(int idx) { point_coordinates += idx*point_dimension; }
    void                defineAs(int pointDimension, coordT *c) { QHULL_ASSERT(pointDimension>=0); point_coordinates= c; point_dimension= pointDimension; }
    //! Creates an alias to other
    void                defineAs(QhullPoint &other) { point_coordinates= other.coordinates(); point_dimension= other.dimension(); }
    void                setCoordinates(coordT *c) { point_coordinates= c; }
    void                setDimension(int pointDimension) { point_dimension= pointDimension; }

#//value
    double              distance(const QhullPoint &p) const;

#//iterator
    iterator            begin() { return point_coordinates; }
    const_iterator      begin() const { return point_coordinates; }
    const_iterator      constBegin() const { return point_coordinates; }
    const_iterator      constEnd() const { return point_coordinates+point_dimension; }
    int                 count() { return dimension(); }
    iterator            end() { return point_coordinates+point_dimension; }
    const_iterator      end() const { return point_coordinates+point_dimension; }
    size_t              size() { return (size_t)dimension(); }

#//Operator
    bool                operator==(const QhullPoint &other) const;
    bool                operator!=(const QhullPoint &other) const { return !operator==(other); }
    const coordT       &operator[](int idx) const { QHULL_ASSERT(idx>=0 && idx=0 && idx
#include 

#ifdef _MSC_VER  // Microsoft Visual C++ -- warning level 4
#endif

namespace orgQhull {

#//Conversion
// See qt-qhull.cpp for QList conversion

#ifndef QHULL_NO_STL
std::vector QhullPoints::
toStdVector() const
{
    QhullPointsIterator i(*this);
    std::vector vs;
    while(i.hasNext()){
        vs.push_back(i.next());
    }
    return vs;
}//toStdVector
#endif //QHULL_NO_STL

#//Read-only

bool QhullPoints::
operator==(const QhullPoints &other) const
{
    if(point_dimension!=other.point_dimension || (point_end-point_first) != (other.point_end-other.point_first)){
        return false;
    }
    const coordT *c= point_first;
    const coordT *c2= other.point_first;
    while(c=n){
        n= 0;
    }else if(length<0 || idx+length>=n){
        n -= idx;
    }else{
        n -= idx+length;
    }
    return QhullPoints(point_dimension, n*point_dimension, point_first+idx*point_dimension);
}//mid

QhullPoint QhullPoints::
value(int idx) const
{
    QhullPoint p;
    if(idx>=0 && idx=0 && idxconstEnd()){
        if(*i++ == p){
            return true;
        }
    }
    return false;
}//findNext

bool QhullPointsIterator::
findPrevious(const QhullPoint &p)
{
    while(i!=ps->constBegin()){
        if(*--i == p){
            return true;
        }
    }
    return false;
}//findPrevious

}//namespace orgQhull

#//Global functions

using std::ostream;
using orgQhull::QhullPoint;
using orgQhull::QhullPoints;
using orgQhull::QhullPointsIterator;

ostream &
operator<<(ostream &os, const QhullPoints &p)
{
    QhullPointsIterator i(p);
    while(i.hasNext()){
        os << i.next();
    }
    return os;
}//operator<

namespace orgQhull {

#//Types
    //! coordinate pointer with dimension
    // with const_iterator and iterator
    class QhullPoints;
    //! Java-style iterator
    class QhullPointsIterator;

class QhullPoints {

    // QhullPoints consists of pointers into an array of coordinates.

private:
#//Field
    coordT             *point_first;
    coordT             *point_end;  // end>=first.  Trailing coordinates ignored
    int                 point_dimension;  // >= 0

public:
#//Subtypes
    class               const_iterator;
    class               iterator;
    typedef QhullPoints::const_iterator ConstIterator;
    typedef QhullPoints::iterator Iterator;

#//Construct
                        QhullPoints() : point_first(0), point_end(0), point_dimension(0) {};
                        QhullPoints(int pointDimension) : point_first(0), point_end(0), point_dimension(pointDimension) { QHULL_ASSERT(pointDimension>=0); }
                        QhullPoints(int pointDimension, int coordinateCount2, coordT *c) : point_first(c), point_end(c+coordinateCount2), point_dimension(pointDimension) { QHULL_ASSERT(pointDimension>=0 && coordinateCount2>=0 ); }
                        //Copy constructor copies pointers but not contents.  Needed for return by value and parameter passing.
                        QhullPoints(const QhullPoints &other)  : point_first(other.point_first), point_end(other.point_end), point_dimension(other.point_dimension) {}
                       ~QhullPoints() {}

//disabled since p= p2 is ambiguous (coord* vs coord)
private:
    QhullPoints        &operator=(const QhullPoints &other) { point_first= other.point_first; point_end= other.point_end; point_dimension= other.point_dimension; return *this; }
public:

#//Conversion
    const coordT       *constData() const { return coordinates(); }
    // See coordinates()
    coordT             *data() { return coordinates(); }
    const coordT       *data() const { return coordinates(); }
#ifndef QHULL_NO_STL
    std::vector toStdVector() const;
#endif //QHULL_NO_STL
#ifdef QHULL_USES_QT
    QList   toQList() const;
#endif //QHULL_USES_QT

#//GetSet
    coordT             *coordinates() const { return point_first; }
    int                 coordinateCount() const { return (int)(point_end-point_first); } // WARN64
    int                 count() const { return (int)size(); } // WARN64
    void                defineAs(int pointDimension, int coordinatesCount, coordT *c) { QHULL_ASSERT(pointDimension>=0 && coordinatesCount>=0 && c!=0); point_first= c; point_end= c+coordinatesCount; point_dimension= pointDimension; }
    void                defineAs(int coordinatesCount, coordT *c) { QHULL_ASSERT((coordinatesCount>=0 && c!=0) || (c==0 && coordinatesCount==0)); point_first= c; point_end= c+coordinatesCount; }
    void                defineAs(const QhullPoints &other) { point_first= other.point_first; point_end= other.point_end; point_dimension= other.point_dimension; }
    int                 dimension() const { return point_dimension; }
    bool                empty() const { return point_end==point_first; }
    coordT             *extraCoordinates() const { return extraCoordinatesCount() ? (point_end-extraCoordinatesCount()) : 0; }
    int                 extraCoordinatesCount() const { return point_dimension>0 ? (int)((point_end-point_first)%(size_t)point_dimension) : 0; }  // WARN64
    bool                includesCoordinates(const coordT *c) const { return c>=point_first && c=0); point_dimension= pointDimension; }
    size_t              size() const { return (point_dimension ? (point_end-point_first)/point_dimension : 0); }

#//ElementAccess -- can not return references to QhullPoint
    QhullPoint          at(int idx) const { coordT *p= point_first+idx*point_dimension; QHULL_ASSERT(p(other)); return *this; }
        QhullPoint     *operator->() { return this; }
        // value instead of reference since advancePoint() modifies self
        QhullPoint      operator*() const { return *this; }
        QhullPoint      operator[](int idx) const { QhullPoint n= *this; n.advancePoint(idx); return n; }
        bool            operator==(const iterator &other) const { QHULL_ASSERT(dimension()==other.dimension()); return coordinates()==other.coordinates(); }
        bool            operator!=(const iterator &other) const { return !operator==(other); }
        bool            operator<(const iterator &other) const  { QHULL_ASSERT(dimension()==other.dimension()); return coordinates() < other.coordinates(); }
        bool            operator<=(const iterator &other) const { QHULL_ASSERT(dimension()==other.dimension()); return coordinates() <= other.coordinates(); }
        bool            operator>(const iterator &other) const  { QHULL_ASSERT(dimension()==other.dimension()); return coordinates() > other.coordinates(); }
        bool            operator>=(const iterator &other) const { QHULL_ASSERT(dimension()==other.dimension()); return coordinates() >= other.coordinates(); }
        // reinterpret_cast to break circular dependency
        bool            operator==(const QhullPoints::const_iterator &other) const { QHULL_ASSERT(dimension()==reinterpret_cast(other).dimension()); return coordinates()==reinterpret_cast(other).coordinates(); }
        bool            operator!=(const QhullPoints::const_iterator &other) const { return !operator==(reinterpret_cast(other)); }
        bool            operator<(const QhullPoints::const_iterator &other) const  { QHULL_ASSERT(dimension()==reinterpret_cast(other).dimension()); return coordinates() < reinterpret_cast(other).coordinates(); }
        bool            operator<=(const QhullPoints::const_iterator &other) const { QHULL_ASSERT(dimension()==reinterpret_cast(other).dimension()); return coordinates() <= reinterpret_cast(other).coordinates(); }
        bool            operator>(const QhullPoints::const_iterator &other) const  { QHULL_ASSERT(dimension()==reinterpret_cast(other).dimension()); return coordinates() > reinterpret_cast(other).coordinates(); }
        bool            operator>=(const QhullPoints::const_iterator &other) const { QHULL_ASSERT(dimension()==reinterpret_cast(other).dimension()); return coordinates() >= reinterpret_cast(other).coordinates(); }
        iterator       &operator++() { advancePoint(1); return *this; }
        iterator        operator++(int) { iterator n= *this; operator++(); return iterator(n); }
        iterator       &operator--() { advancePoint(-1); return *this; }
        iterator        operator--(int) { iterator n= *this; operator--(); return iterator(n); }
        iterator       &operator+=(int idx) { advancePoint(idx); return *this; }
        iterator       &operator-=(int idx) { advancePoint(-idx); return *this; }
        iterator        operator+(int idx) const { iterator n= *this; n.advancePoint(idx); return n; }
        iterator        operator-(int idx) const { iterator n= *this; n.advancePoint(-idx); return n; }
        difference_type operator-(iterator other) const { QHULL_ASSERT(dimension()==other.dimension()); return (coordinates()-other.coordinates())/dimension(); }
    };//QhullPoints::iterator

#//QhullPoints::const_iterator -- FIXUP QH11018 const_iterator same as iterator
    class const_iterator : public QhullPoint {

    public:
        typedef std::random_access_iterator_tag  iterator_category;
        typedef QhullPoint          value_type;
        typedef const value_type   *pointer;
        typedef const value_type   &reference;
        typedef ptrdiff_t           difference_type;

                        const_iterator() : QhullPoint() {}
                        const_iterator(const const_iterator &other) : QhullPoint(*other) {}
                        const_iterator(const QhullPoints::iterator &other) : QhullPoint(*other) {}
        explicit        const_iterator(const QhullPoints &ps) : QhullPoint(ps.dimension(), ps.coordinates()) {}
        explicit        const_iterator(int pointDimension, coordT *c): QhullPoint(pointDimension, c) {}
        const_iterator &operator=(const const_iterator &other) { defineAs(const_cast(other)); return *this; }
        // value/non-const since advancePoint(1), etc. modifies self
        QhullPoint      operator*() const { return *this; }
        QhullPoint     *operator->() { return this; }
        QhullPoint      operator[](int idx) const { QhullPoint n= *this; n.advancePoint(idx); return n; }
        bool            operator==(const const_iterator &other) const { QHULL_ASSERT(dimension()==other.dimension()); return coordinates()==other.coordinates(); }
        bool            operator!=(const const_iterator &other) const { return !operator==(other); }
        bool            operator<(const const_iterator &other) const  { QHULL_ASSERT(dimension()==other.dimension()); return coordinates() < other.coordinates(); }
        bool            operator<=(const const_iterator &other) const { QHULL_ASSERT(dimension()==other.dimension()); return coordinates() <= other.coordinates(); }
        bool            operator>(const const_iterator &other) const  { QHULL_ASSERT(dimension()==other.dimension()); return coordinates() > other.coordinates(); }
        bool            operator>=(const const_iterator &other) const { QHULL_ASSERT(dimension()==other.dimension()); return coordinates() >= other.coordinates(); }
        const_iterator &operator++() { advancePoint(1); return *this; }
        const_iterator  operator++(int) { const_iterator n= *this; operator++(); return const_iterator(n); }
        const_iterator &operator--() { advancePoint(-1); return *this; }
        const_iterator  operator--(int) { const_iterator n= *this; operator--(); return const_iterator(n); }
        const_iterator &operator+=(int idx) { advancePoint(idx); return *this; }
        const_iterator &operator-=(int idx) { advancePoint(-idx); return *this; }
        const_iterator  operator+(int idx) const { const_iterator n= *this; n.advancePoint(idx); return n; }
        const_iterator  operator-(int idx) const { const_iterator n= *this; n.advancePoint(-idx); return n; }
        difference_type operator-(const_iterator other) const { QHULL_ASSERT(dimension()==other.dimension()); return (coordinates()-other.coordinates())/dimension(); }
    };//QhullPoints::const_iterator

#//IO
    struct PrintPoints{
        const QhullPoints  *points;
        const char     *point_message;
        int             run_id;
        bool            with_identifier;
        PrintPoints(int qhRunId, const char *message, bool withIdentifier, const QhullPoints &ps) : points(&ps), point_message(message), run_id(qhRunId), with_identifier(withIdentifier) {}
    };//PrintPoints
    PrintPoints          print() const { return  PrintPoints(UsingLibQhull::NOqhRunId, "", false, *this); }
    PrintPoints          print(int qhRunId) const { return PrintPoints(qhRunId, "", true, *this); }
    PrintPoints          print(int qhRunId, const char *message) const { return PrintPoints(qhRunId, message, false, *this); }
    PrintPoints          printWithIdentifier(int qhRunId, const char *message) const { return PrintPoints(qhRunId, message, true, *this); }
    //FIXUP remove message for print()?
};//QhullPoints

// can't use QHULL_DECLARE_SEQUENTIAL_ITERATOR because next(),etc would return a reference to a temporary
class QhullPointsIterator
{
    typedef QhullPoints::const_iterator const_iterator;

private:
#//Fields
    const QhullPoints  *ps;
    const_iterator      i;

public:
                        QhullPointsIterator(const QhullPoints &other) : ps(&other), i(ps->constBegin()) {}
    QhullPointsIterator &operator=(const QhullPoints &other) { ps = &other; i = ps->constBegin(); return *this; }
    bool                findNext(const QhullPoint &t);
    bool                findPrevious(const QhullPoint &t);
    bool                hasNext() const { return i != ps->constEnd(); }
    bool                hasPrevious() const { return i != ps->constBegin(); }
    QhullPoint          next() { return *i++; }
    QhullPoint          peekNext() const { return *i; }
    QhullPoint          peekPrevious() const { const_iterator p = i; return *--p; }
    QhullPoint          previous() { return *--i; }
    void                toBack() { i = ps->constEnd(); }
    void                toFront() { i = ps->constBegin(); }
};//QhullPointsIterator

}//namespace orgQhull

#//Global functions

std::ostream           &operator<<(std::ostream &os, const orgQhull::QhullPoints &p);
std::ostream           &operator<<(std::ostream &os, const orgQhull::QhullPoints::PrintPoints &pr);

#endif // QHULLPOINTS_H
qhull-2012.1/src/libqhullcpp/QhullPointSet.cpp0000644000076400010400000001112311710144465022472 0ustar  bbarberAdministrators/****************************************************************************
**
** Copyright (c) 2009-2012 C.B. Barber. All rights reserved.
** $Id: //main/2011/qhull/src/libqhullcpp/QhullPointSet.cpp#5 $$Change: 1464 $
** $DateTime: 2012/01/25 22:58:41 $$Author: bbarber $
**
****************************************************************************/

#include "QhullPointSet.h"

#include 
#include 

#ifdef _MSC_VER  // Microsoft Visual C++ -- warning level 4
#endif

namespace orgQhull {

#// Conversion

// See qt-qhull.cpp for QList conversion

#ifndef QHULL_NO_STL
std::vector QhullPointSet::
toStdVector() const
{
    QhullPointSetIterator i(*this);
    std::vector vs;
    while(i.hasNext()){
        vs.push_back(i.next());
    }
    return vs;
}//toStdVector
#endif //QHULL_NO_STL

#//Element-access
//! Derived from QhullSet::value
QhullPoint QhullPointSet::
value(int idx) const
{
    // Avoid call to qh_setsize() and assert in elementPointer()
    //const T *n= reinterpret_cast(&SETelem_(getSetT(), idx));
    void **n= reinterpret_cast(&SETelem_(getSetT(), idx));
    coordT **n2= reinterpret_cast(n);
    if(idx>=0 && n(&SETelem_(getSetT(), idx));
    coordT **n2= reinterpret_cast(n);
    if(idx>=0 && nconstEnd()){
        if(*i++ == p){
            return true;
        }
    }
    return false;
}//findNext

bool QhullPointSetIterator::
findPrevious(const QhullPoint &p)
{
    while(i!=c->constBegin()){
        if(*(--i) == p){
            return true;
        }
    }
    return false;
}//findPrevious

}//namespace orgQhull

#//Global functions

using std::endl;
using std::ostream;
using orgQhull::QhullPoint;
using orgQhull::QhullPointSet;
using orgQhull::UsingLibQhull;

#//operator<<

ostream &
operator<<(ostream &os, const QhullPointSet &ps)
{
    os << ps.print(UsingLibQhull::NOqhRunId);
    return os;
}//<

namespace orgQhull {

#//Types
    //! QhullPointSet -- a set of coordinate pointers with dimension
    // with const_iterator and iterator
    class               QhullPointSet;
    //! Java-style iterator
    class QhullPointsIterator;

#//Classref
    class               QhullPoint;

class QhullPointSet : public QhullSet {

private:
#//Field
    int                 point_dimension;

public:
#//Subtypes and types
    class               const_iterator;
    class               iterator;
    typedef QhullPointSet::const_iterator ConstIterator;
    typedef QhullPointSet::iterator Iterator;

    typedef QhullPoint  value_type;
    typedef ptrdiff_t   difference_type;
    typedef int         size_type;
    //typedef const value_type *const_pointer;    // FIXUP QH11019: QhullPointSet does not define pointer or reference due to point_dimension
    //typedef const value_type &const_reference;
    //typedef value_type *pointer;
    //typedef value_type &reference;

#//Construct
                        //Conversion from setT* is not type-safe.  Implicit conversion for void* to T
                        QhullPointSet(int pointDimension, setT *s) : QhullSet(s), point_dimension(pointDimension) {}
                        //Copy constructor copies pointer but not contents.  Needed for return by value and parameter passing.
                        QhullPointSet(const QhullPointSet &o) : QhullSet(o), point_dimension(o.point_dimension) {}
                       ~QhullPointSet() {}

//Default constructor and copy assignment disabled since p= p2 is ambiguous (coord* vs coord)
private:
                        QhullPointSet();
    QhullPointSet      &operator=(const QhullPointSet &);
public:

#//Conversions
    // inherited -- constData, data
#ifndef QHULL_NO_STL
    std::vector toStdVector() const;
#endif
#ifdef QHULL_USES_QT
    QList   toQList() const;
#endif

#//Read-only
    //inherits count, empty, isEmpty, size
    using QhullSetBase::count;
    int                 dimension() const { return point_dimension; }
    bool                operator==(const QhullPointSet &o) const;
    bool                operator!=(const QhullPointSet &o) const { return !operator==(o); }

#//Element access -- can not return references since QhullPoint must be generated
    QhullPoint          at(int idx) const { return operator[](idx); }
    QhullPoint          back() const { return last(); }
    //! end element is NULL
    QhullPoint          first() const { QHULL_ASSERT(!isEmpty()); return *begin(); }
    QhullPoint          front() const { return first(); }
    QhullPoint          last() const { QHULL_ASSERT(!isEmpty()); return *(end()-1); }
    // mid() not available.  No setT constructor
    QhullPoint          operator[](int idx) const { return QhullPoint(dimension(), QhullSet::operator[](idx)); }
    QhullPoint          second()  const { return operator[](1); }
    QhullPoint          value(int idx) const;
    // Non-const since copy is an alias
    QhullPoint          value(int idx, QhullPoint &defaultValue) const;

#//iterator
    iterator            begin() { return iterator(dimension(), reinterpret_cast(beginPointer())); }
    const_iterator      begin() const { return const_iterator(dimension(), reinterpret_cast(beginPointer())); }
    const_iterator      constBegin() const { return const_iterator(dimension(), reinterpret_cast(beginPointer())); }
    const_iterator      constEnd() const { return const_iterator(dimension(), reinterpret_cast(endPointer())); }
    iterator            end() { return iterator(dimension(), reinterpret_cast(endPointer())); }
    const_iterator      end() const { return const_iterator(dimension(), reinterpret_cast(endPointer())); }

//Read-write -- Not available, no setT constructor

#//Search
    bool                contains(const QhullPoint &t) const;
    int                 count(const QhullPoint &t) const;
    int                 indexOf(const QhullPoint &t) const;
    int                 lastIndexOf(const QhullPoint &t) const;

    // before const_iterator for conversion with comparison operators
    class iterator {
        friend class    const_iterator;

    private:
        coordT        **i;
        int             point_dimension;

    public:
        typedef ptrdiff_t   difference_type;
        typedef std::bidirectional_iterator_tag  iterator_category;
        typedef QhullPoint *pointer;
        typedef QhullPoint &reference;
        typedef QhullPoint  value_type;

                        iterator() : i(0), point_dimension(0) {}
                        iterator(int dimension, coordT **c) : i(c), point_dimension(dimension) {}
                        iterator(const iterator &o) : i(o.i), point_dimension(o.point_dimension) {}
        iterator       &operator=(const iterator &o) { i= o.i; point_dimension= o.point_dimension; return *this; }

        QhullPoint      operator*() const { return QhullPoint(point_dimension, *i); }
                      //operator->() n/a, value-type
        QhullPoint      operator[](int idx) { return QhullPoint(point_dimension, *(i+idx)); }
        bool            operator==(const iterator &o) const { return i == o.i && point_dimension == o.point_dimension; }
        bool            operator!=(const iterator &o) const { return !operator==(o); }
        bool            operator==(const const_iterator &o) const
        { return i == reinterpret_cast(o).i && point_dimension == reinterpret_cast(o).point_dimension; }
        bool            operator!=(const const_iterator &o) const { return !operator==(o); }

        //! Assumes same point set
        int             operator-(const iterator &o) { return (int)(i-o.i); } //WARN64
        bool            operator>(const iterator &o) const { return i>o.i; }
        bool            operator<=(const iterator &o) const { return !operator>(o); }
        bool            operator<(const iterator &o) const { return i=(const iterator &o) const { return !operator<(o); }
        bool            operator>(const const_iterator &o) const
        { return i > reinterpret_cast(o).i; }
        bool            operator<=(const const_iterator &o) const { return !operator>(o); }
        bool            operator<(const const_iterator &o) const
        { return i < reinterpret_cast(o).i; }
        bool            operator>=(const const_iterator &o) const { return !operator<(o); }

        iterator       &operator++() { ++i; return *this; }
        iterator        operator++(int) { iterator o= *this; ++i; return o; }
        iterator       &operator--() { --i; return *this; }
        iterator        operator--(int) { iterator o= *this; --i; return o; }
        iterator        operator+(int j) const { return iterator(point_dimension, i+j); }
        iterator        operator-(int j) const { return operator+(-j); }
        iterator       &operator+=(int j) { i += j; return *this; }
        iterator       &operator-=(int j) { i -= j; return *this; }
    };//QhullPointSet::iterator

    class const_iterator {
    private:
        coordT        **i;
        int             point_dimension;

    public:
        typedef std::random_access_iterator_tag  iterator_category;
        typedef QhullPoint value_type;
        typedef value_type *pointer;
        typedef value_type &reference;
        typedef ptrdiff_t  difference_type;

                        const_iterator() : i(0), point_dimension(0) {}
                        const_iterator(int dimension, coordT **c) : i(c), point_dimension(dimension) {}
                        const_iterator(const const_iterator &o) : i(o.i), point_dimension(o.point_dimension) {}
                        const_iterator(iterator o) : i(o.i), point_dimension(o.point_dimension) {}
        const_iterator &operator=(const const_iterator &o) { i= o.i; point_dimension= o.point_dimension; return *this; }

        QhullPoint      operator*() const { return QhullPoint(point_dimension, *i); }
        QhullPoint      operator[](int idx) { return QhullPoint(point_dimension, *(i+idx)); }
                      //operator->() n/a, value-type
        bool            operator==(const const_iterator &o) const { return i == o.i && point_dimension == o.point_dimension; }
        bool            operator!=(const const_iterator &o) const { return !operator==(o); }

        //! Assumes same point set
        int             operator-(const const_iterator &o) { return (int)(i-o.i); } //WARN64
        bool            operator>(const const_iterator &o) const { return i>o.i; }
        bool            operator<=(const const_iterator &o) const { return !operator>(o); }
        bool            operator<(const const_iterator &o) const { return i=(const const_iterator &o) const { return !operator<(o); }

        const_iterator &operator++() { ++i; return *this; }
        const_iterator  operator++(int) { const_iterator o= *this; ++i; return o; }
        const_iterator &operator--() { --i; return *this; }
        const_iterator  operator--(int) { const_iterator o= *this; --i; return o; }
        const_iterator  operator+(int j) const { return const_iterator(point_dimension, i+j); }
        const_iterator  operator-(int j) const { return operator+(-j); }
        const_iterator &operator+=(int j) { i += j; return *this; }
        const_iterator &operator-=(int j) { i -= j; return *this; }
    };//QhullPointSet::const_iterator

#//IO
    struct PrintIdentifiers{
        const QhullPointSet *point_set;
        const char     *print_message;
        int             run_id;
        PrintIdentifiers(const char *message, const QhullPointSet *s) : point_set(s), print_message(message) {}
    };//PrintIdentifiers
    PrintIdentifiers printIdentifiers(const char *message) const { return PrintIdentifiers(message, this); }

    struct PrintPointSet{
        const QhullPointSet *point_set;
        const char     *print_message;
        int             run_id;
        PrintPointSet(int qhRunId, const char *message, const QhullPointSet &s) : point_set(&s), print_message(message), run_id(qhRunId) {}
    };//PrintPointSet
    PrintPointSet       print(int qhRunId) const { return PrintPointSet(qhRunId, 0, *this); }
    PrintPointSet       print(int qhRunId, const char *message) const { return PrintPointSet(qhRunId, message, *this); }

};//QhullPointSet

//derived from qiterator.h
class QhullPointSetIterator { // FIXUP QH11020 define QhullMutablePointSetIterator
    typedef QhullPointSet::const_iterator const_iterator;
    const QhullPointSet *c;
    const_iterator      i;

public:
                        QhullPointSetIterator(const QhullPointSet &container) : c(&container), i(c->constBegin()) {}
    QhullPointSetIterator &operator=(const QhullPointSet &container) { c= &container; i= c->constBegin(); return *this; }
    bool                findNext(const QhullPoint &p);
    bool                findPrevious(const QhullPoint &p);
    bool                hasNext() const { return i != c->constEnd(); }
    bool                hasPrevious() const { return i != c->constBegin(); }
    QhullPoint          next() { return *i++; }
    QhullPoint          peekNext() const { return *i; }
    QhullPoint          peekPrevious() const { const_iterator p= i; return *--p; }
    QhullPoint          previous() { return *--i; }
    void                toBack() { i= c->constEnd(); }
    void                toFront() { i= c->constBegin(); }
};//QhullPointSetIterator

}//namespace orgQhull

#//Global functions

std::ostream &operator<<(std::ostream &os, const orgQhull::QhullPointSet &fs); // Not inline to avoid using statement
std::ostream &operator<<(std::ostream &os, const orgQhull::QhullPointSet::PrintIdentifiers &pr);
std::ostream &operator<<(std::ostream &os, const orgQhull::QhullPointSet::PrintPointSet &pr);

#endif // QHULLPOINTSET_H
qhull-2012.1/src/libqhullcpp/QhullQh.cpp0000644000076400010400000000646011710144465021305 0ustar  bbarberAdministrators/****************************************************************************
**
** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
** $Id: //main/2011/qhull/src/libqhullcpp/QhullQh.cpp#3 $$Change: 1464 $
** $DateTime: 2012/01/25 22:58:41 $$Author: bbarber $
**
****************************************************************************/

#//! QhullQh -- Qhull's global data structure, qhT, as a C++ class



#include "QhullError.h"
#include "QhullQh.h"
#include "QhullStat.h"

#include 
#include 

using std::cerr;
using std::string;
using std::vector;
using std::ostream;

#ifdef _MSC_VER  // Microsoft Visual C++ -- warning level 4
#pragma warning( disable : 4611)  // interaction between '_setjmp' and C++ object destruction is non-portable
#pragma warning( disable : 4996)  // function was declared deprecated(strcpy, localtime, etc.)
#endif

namespace orgQhull {

#//Global variables

#//Constructor, destructor, etc.

//! If qh_QHpointer==0, invoke with placement new on qh_qh;
//! Sets qh_qh and qh_qhstat.  Need to reset before UsingLibQhull.
//! Derived from qh_new_qhull[user.c]
QhullQh::
QhullQh()
{
    static boolT firstcall = True;

    if(firstcall){
        if(qhmem.BUFinit!=0){
            throw QhullError(10017, "Qhull error: qhmem already initialized by another class.");
        }
        qh_meminit(NULL);
        firstcall= False;
    }
    // QhullQh() and UsingLibQhull() are the same
#if qh_QHpointer
    if(qh_qh){
        if(qh old_qhstat){
            throw QhullError(10041, "Qhull internal error: qh_qh.old_qhstat defined (%x) but qh_qh is active.  qh_qh not restored correctly.", 0, 0, 0.0, qh old_qhstat);
        }
        qh old_qhstat= qh_qhstat;
        qh old_tempstack= qhmem.tempstack;
        qh_qhstat= 0;
        qhmem.tempstack= 0;
    }
    qh_qh= static_cast(this);
#else
    if(strncmp(qh qhull, "qhull", 5) == 0){
        throw QhullError(10022, "Qhull error: Qhull already initialized as run %d", qh run_id);
    }
#endif
    // NOerrors -- Does not call qh_errexit()
    qh_initstatistics();
    // NOerrors -- Does not call qh_errexit()
    qh_initqhull_start2(NULL, NULL, qh_FILEstderr);
}//QhullQh

//! UsingLibQhull must be declared along with QhullQh
QhullQh::
~QhullQh()
{
#if qh_QHpointer
    if(!qh_qh){
        QhullError e(10042, "Qhull internal error: qh_qh undefined.  Was ~QhullQh() invoked independent of UsingLibQhull?", qh run_id, 0, 0, qh_qh);
        e.logError();
    }else if(!qh_qhstat){
        QhullError e(10043, "Qhull internal error: qh_qhstat null.  Is another thread running?");
        e.logError();
    }else if(qh_qh!=this){
        QhullError e(10044, "Qhull error: ~QhullQh() invoked independent of UsingLibQhull. qh_qh %x (runId %d) vs. QhullQh.runId %d.", qh run_id, run_id, 0.0, qh_qh);
        e.logError();
    }else{
        qh_freeqhull2(qh_ALL); // sets qh.NOerrexit.  Clears struct *qh_qh including run_id, but not qh_qh itself
    }
#else
    if(&qh_qh!=this){
        QhullError e(10045, "Qhull error: ~QhullQh() invoked independent of UsingLibQhull. qh_qh %x (runId %d) vs. QhullQh.runId %d.", qh run_id, run_id, 0.0, qh_qh);
        e.logError();
    }else{
        qh_freeqhull2(qh_ALL); // sets qh.NOerrexit.  Clears struct *qh_qh including run_id, but not qh_qh itself
    }
#endif
}//~QhullQh

#//Parallel Access

}//namespace orgQhull

qhull-2012.1/src/libqhullcpp/QhullQh.h0000644000076400010400000000244211710144465020746 0ustar  bbarberAdministrators/****************************************************************************
**
** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
** $Id: //main/2011/qhull/src/libqhullcpp/QhullQh.h#6 $$Change: 1464 $
** $DateTime: 2012/01/25 22:58:41 $$Author: bbarber $
**
****************************************************************************/

#ifndef QHULLQH_H
#define QHULLQH_H

extern "C" {
    #include "libqhull/qhull_a.h"
}

#include 
#include 

namespace orgQhull {

#//defined here
    //! QhullQh -- Qhull's global data structure, qhT, as a C++ class
    //! See UsingLibQhull.h for C++/C interface to qhT
    class QhullQh;

class QhullQh : public qhT {

#//Constants
    // Set ignored.  PointSet needs explicit dimension
    // Facet from vertices or ridges.vertices.count
    // Ridge from vertices.count
    // Vertex stored in vertexT?  1->16?
    // QhullPoint needs explicit dimension

#//members (empty) -- POD type equivalent to qhT.  No data or virtual members

public:
#//constructor, assignment, destructor, invariant
    QhullQh();
    ~QhullQh();

private:
    //!disable copy constructor and assignment
                        QhullQh(const QhullQh &);
    QhullQh            &operator=(const QhullQh &);

};//class QhullQh

}//namespace orgQhull

#endif // QHULLQH_H
qhull-2012.1/src/libqhullcpp/QhullRidge.cpp0000644000076400010400000000564311710144465021771 0ustar  bbarberAdministrators/****************************************************************************
**
** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
** $Id: //main/2011/qhull/src/libqhullcpp/QhullRidge.cpp#4 $$Change: 1464 $
** $DateTime: 2012/01/25 22:58:41 $$Author: bbarber $
**
****************************************************************************/

#//! QhullRidge -- Qhull's ridge structure, ridgeT, as a C++ class

#include "QhullSets.h"
#include "QhullVertex.h"
#include "QhullRidge.h"

#ifdef _MSC_VER  // Microsoft Visual C++ -- warning level 4
#pragma warning( disable : 4611)  // interaction between '_setjmp' and C++ object destruction is non-portable
#pragma warning( disable : 4996)  // function was declared deprecated(strcpy, localtime, etc.)
#endif

namespace orgQhull {

#//class statics
ridgeT QhullRidge::
s_empty_ridge= {0,0,0,0,0,
                0,0};

#//Constructor, destructor, etc.

#//Accessors

//! Return True if nextRidge3d
//! Simplicial facets may have incomplete ridgeSets
//! Does not use qh_qh or qh_errexit()
bool QhullRidge::
hasNextRidge3d(const QhullFacet f) const
{
    vertexT *v= 0;
    ridgeT *ridge= qh_nextridge3d(getRidgeT(), f.getFacetT(), &v);
    return (ridge!=0);
}//hasNextRidge3d



//! Return next ridge and optional vertex for a 3d facet and ridge
//! Does not use qh_qh or qh_errexit()
QhullRidge QhullRidge::
nextRidge3d(const QhullFacet f, QhullVertex *nextVertex) const
{
    vertexT *v= 0;
    ridgeT *ridge= qh_nextridge3d(getRidgeT(), f.getFacetT(), &v);
    if(!ridge){
        throw QhullError(10030, "Qhull error nextRidge3d:  missing next ridge for facet %d ridge %d.  Does facet contain ridge?", f.id(), id());
    }
    if(nextVertex!=0){
        *nextVertex= QhullVertex(v);
    }
    return QhullRidge(ridge);
}//nextRidge3d


}//namespace orgQhull

#//Global functions

using std::endl;
using std::ostream;
using orgQhull::QhullRidge;
using orgQhull::QhullVertex;
using orgQhull::UsingLibQhull;

ostream &
operator<<(ostream &os, const QhullRidge &r)
{
    os << r.print(UsingLibQhull::NOqhRunId);
    return os;
}//<< QhullRidge

//! Duplicate of qh_printridge [io.c]
//!  if pr.run_id==UsingLibQhull::NOqhRunId, no access to qh [needed for QhullVertex/QhullPoint]
ostream &
operator<<(ostream &os, const QhullRidge::PrintRidge &pr)
{
    QhullRidge r= *pr.ridge;
    os << "     - r" << r.id();
    if(r.getRidgeT()->tested){
        os << " tested";
    }
    if(r.getRidgeT()->nonconvex){
        os << " nonconvex";
    }
    os << endl;
    os << r.vertices().print(pr.run_id, "           vertices:");
    if(r.getRidgeT()->top && r.getRidgeT()->bottom){
        os << "           between f" << r.topFacet().id() << " and f" << r.bottomFacet().id() << endl;
    }else if(r.getRidgeT()->top){
        os << "           top f" << r.topFacet().id() << endl;
    }else if(r.getRidgeT()->bottom){
        os << "           bottom f" << r.bottomFacet().id() << endl;
    }

    return os;
}//<< PrintRidge
qhull-2012.1/src/libqhullcpp/QhullRidge.h0000644000076400010400000001002511710144465021424 0ustar  bbarberAdministrators/****************************************************************************
**
** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
** $Id: //main/2011/qhull/src/libqhullcpp/QhullRidge.h#6 $$Change: 1464 $
** $DateTime: 2012/01/25 22:58:41 $$Author: bbarber $
**
****************************************************************************/

#ifndef QHULLRIDGE_H
#define QHULLRIDGE_H

#include "QhullSet.h"
#include "QhullVertex.h"
#include "QhullVertexSet.h"
#include "QhullFacet.h"
extern "C" {
    #include "libqhull/qhull_a.h"
}

#include 

namespace orgQhull {

#//ClassRef
    class QhullVertex;
    class QhullVertexSet;
    class QhullFacet;

#//Types
    //! QhullRidge -- Qhull's ridge structure, ridgeT [libqhull.h], as a C++ class
    class QhullRidge;
    typedef QhullSet  QhullRidgeSet;
    typedef QhullSetIterator  QhullRidgeSetIterator;

    // see QhullSets.h for QhullRidgeSet and QhullRidgeSetIterator -- avoids circular references

/************************
a ridge is hull_dim-1 simplex between two neighboring facets.  If the
facets are non-simplicial, there may be more than one ridge between
two facets.  E.G. a 4-d hypercube has two triangles between each pair
of neighboring facets.

topological information:
    vertices            a set of vertices
    top,bottom          neighboring facets with orientation

geometric information:
    tested              True if ridge is clearly convex
    nonconvex           True if ridge is non-convex
*/

class QhullRidge {

#//Fields
    ridgeT             *qh_ridge;

#//Class objects
    static ridgeT       s_empty_ridge;

public:
#//Constants

#//Constructors
                        QhullRidge() : qh_ridge(&s_empty_ridge) {}
                        // Creates an alias.  Does not copy QhullRidge.  Needed for return by value and parameter passing
                        QhullRidge(const QhullRidge &o) : qh_ridge(o.qh_ridge) {}
                        // Creates an alias.  Does not copy QhullRidge.  Needed for vector
    QhullRidge         &operator=(const QhullRidge &o) { qh_ridge= o.qh_ridge; return *this; }
                       ~QhullRidge() {}

#//Conversion
                        //Implicit conversion from ridgeT
                        QhullRidge(ridgeT *r) : qh_ridge(r ? r : &s_empty_ridge) {}
    ridgeT             *getRidgeT() const { return qh_ridge; }

#//QhullSet
    ridgeT             *getBaseT() const { return getRidgeT(); }

#//getSet
    QhullFacet          bottomFacet() const { return QhullFacet(qh_ridge->bottom); }
    int                 dimension() const { return QhullSetBase::count(qh_ridge->vertices); }
    int                 id() const { return qh_ridge->id; }
    bool                isDefined() const { return qh_ridge != &s_empty_ridge; }
    bool                operator==(const QhullRidge &o) const { return qh_ridge==o.qh_ridge; }
    bool                operator!=(const QhullRidge &o) const { return !operator==(o); }
    QhullFacet          otherFacet(QhullFacet f) const { return QhullFacet(qh_ridge->top==f.getFacetT() ? qh_ridge->bottom : qh_ridge->top); }
    QhullFacet          topFacet() const { return QhullFacet(qh_ridge->top); }

#//forEach
    bool                hasNextRidge3d(const QhullFacet f) const;
    QhullRidge          nextRidge3d(const QhullFacet f) const { return nextRidge3d(f, 0); }
    QhullRidge          nextRidge3d(const QhullFacet f, QhullVertex *nextVertex) const;
    QhullVertexSet      vertices() const { return QhullVertexSet(qh_ridge->vertices); }

#//IO

    struct PrintRidge{
        const QhullRidge *ridge;
        int             run_id;
                        PrintRidge(int qhRunId, const QhullRidge &r) : ridge(&r), run_id(qhRunId) {}
    };//PrintRidge
    PrintRidge          print(int qhRunId) const { return PrintRidge(qhRunId, *this); }
};//class QhullRidge

}//namespace orgQhull

std::ostream &operator<<(std::ostream &os, const orgQhull::QhullRidge &r); 
std::ostream &operator<<(std::ostream &os, const orgQhull::QhullRidge::PrintRidge &pr);

#endif // QHULLRIDGE_H
qhull-2012.1/src/libqhullcpp/QhullSet.cpp0000644000076400010400000000234711710144465021470 0ustar  bbarberAdministrators/****************************************************************************
**
** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
** $Id: //main/2011/qhull/src/libqhullcpp/QhullSet.cpp#4 $$Change: 1464 $
** $DateTime: 2012/01/25 22:58:41 $$Author: bbarber $
**
****************************************************************************/

#//! QhullSet -- Qhull's facet structure, facetT, as a C++ class

#include "QhullError.h"
#include "QhullSet.h"

#ifdef _MSC_VER  // Microsoft Visual C++ -- warning level 4
#endif

namespace orgQhull {

#//static members

setT QhullSetBase::
s_empty_set;

// Same code for qh_setsize [qset.c] and QhullSetBase::count
int QhullSetBase::count(const setT *set)
{
    int size;
    const setelemT *sizep;

    if (!set)
        return(0);
    sizep= SETsizeaddr_(set);
    if ((size= sizep->i)) {
        size--;
        if (size > set->maxsize) {
            // FIXUP QH11022 How to add additional output to a error? -- qh_setprint(qhmem.ferr, "set: ", set);
            throw QhullError(10032, "QhullSet internal error: current set size %d is greater than maximum size %d\n",
                size, set->maxsize);
        }
    }else
        size= set->maxsize;
    return size;
}


}//namespace orgQhull

qhull-2012.1/src/libqhullcpp/QhullSet.h0000644000076400010400000002654711710144465021145 0ustar  bbarberAdministrators/****************************************************************************
**
** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
** $Id: //main/2011/qhull/src/libqhullcpp/QhullSet.h#7 $$Change: 1464 $
** $DateTime: 2012/01/25 22:58:41 $$Author: bbarber $
**
****************************************************************************/

#ifndef QhullSet_H
#define QhullSet_H

#include "QhullError.h"
extern "C" {
    #include "libqhull/qhull_a.h"
}


#ifndef QHULL_NO_STL
#include 
#endif

#ifdef QHULL_USES_QT
 #include 
#endif

namespace orgQhull {

#//Type
    class QhullSetBase;  //! Base class for QhullSet
    //! QhullSet -- A read-only wrapper to Qhull's collection class, setT.
    //!  QhullSet is similar to STL's  and Qt's QVector.
    //!  QhullSet is unrelated to STL and Qt's set and map types (e.g., QSet and QMap)
    //!  For STL efficiency, QhullSet caches endPointer()
    //!  T must be a pointer type
    //!  A QhullSet does not own its contents -- erase(), clear(), removeFirst(), removeLast(), pop_back(), pop_front(), fromStdList() not defined
    //!  Qhull's FOREACHelement_() [qset.h] is more efficient than QhullSet.  It uses a NULL terminator instead of an end pointer.  STL requires an end pointer.
    //!  Derived from QhullLinkedList.h and Qt/core/tools/qvector.h

    //! QhullSetIterator defined below
    //See: QhullPointSet, QhullLinkedList

class QhullSetBase {

private:
#//Fields --
    setT               *qh_set;

#//Class objects
    static setT         s_empty_set;  //! Workaround for no setT allocator.  Used if setT* is NULL

public:
#//Class methods
    static int          count(const setT *set);
    //s may be null
    static bool         isEmpty(const setT *s) { return SETempty_(s); }


#//Constructors
                        //! Copy constructor copies the pointer but not the set.  Needed for return by value and parameter passing.
                        QhullSetBase(const QhullSetBase &o) : qh_set(o.qh_set) {}
    explicit            QhullSetBase(setT *s) : qh_set(s ? s : &s_empty_set) {}
                       ~QhullSetBase() {}

private:
                        //!disabled since memory allocation for QhullSet not defined
                        QhullSetBase() {}
                        //!disabled since qs= qs2 is ambiguous (pointer vs. contents)
    QhullSetBase       &operator=(const QhullSetBase &);
public:

#//Conversions
                        //! Not type-safe since setT may contain any type
    void                defineAs(setT *s) { qh_set= s ? s : &s_empty_set; }
    setT               *getSetT() const { return qh_set; }
    setT              **referenceSetT() { return &qh_set; }

#//Read-only
    int                 count() const { return QhullSetBase::count(qh_set); }
    bool                empty() const { return SETfirst_(qh_set)==0; }
    bool                isEmpty() const { return empty(); }
    size_t              size() const { return count(); }

#//Element
protected:
    void              **beginPointer() const { return &qh_set->e[0].p; }
    void              **elementPointer(int idx) const { QHULL_ASSERT(idx>=0 && idxmaxsize); return &SETelem_(qh_set, idx); }
                        //! Always points to 0
    void              **endPointer() const { return qh_setendpointer(qh_set); }
};//QhullSetBase


//! set of pointers to baseT, T.getBaseT()
template 
class QhullSet : public QhullSetBase {

private:
#//Fields -- see QhullSetBase

#//Class objects
    static setT         s_empty_set;  //! Workaround for no setT allocator.  Used if setT* is NULL

public:
#//Subtypes
    typedef T         *iterator;
    typedef const T   *const_iterator;
    typedef typename QhullSet::iterator Iterator;
    typedef typename QhullSet::const_iterator ConstIterator;

#//Class methods
    static int          count(const setT *set);
                        //s may be null
    static bool         isEmpty(const setT *s) { return SETempty_(s); }

#//Constructors
                        //Copy constructor copies pointer but not contents.  Needed for return by value.
                        QhullSet(const QhullSet &o) : QhullSetBase(o) {}
                        //Conversion from setT* is not type-safe.  Implicit conversion for void* to T
    explicit            QhullSet(setT *s) : QhullSetBase(s) { QHULL_ASSERT(sizeof(T)==sizeof(void *)); }
                       ~QhullSet() {}

private:
                        //!Disable default constructor and copy assignment.  See QhullSetBase
                        QhullSet();
    QhullSet        &operator=(const QhullSet &);
public:

#//Conversion

#ifndef QHULL_NO_STL
    std::vector      toStdVector() const;
#endif
#ifdef QHULL_USES_QT
    QList            toQList() const;
#endif

#//Read-only -- see QhullSetBase for count(), empty(), isEmpty(), size()
    using QhullSetBase::count;
    using QhullSetBase::isEmpty;
    // operator== defined for QhullSets of the same type
    bool                operator==(const QhullSet &other) const { return qh_setequal(getSetT(), other.getSetT()); }
    bool                operator!=(const QhullSet &other) const { return !operator==(other); }

#//Element access
    const T            &at(int idx) const { return operator[](idx); }
    T                  &back() { return last(); }
    T                  &back() const { return last(); }
    //! end element is NULL
    const T            *constData() const { return constBegin(); }
    T                  *data() { return begin(); }
    const T            *data() const { return begin(); }
    T                  &first() { QHULL_ASSERT(!isEmpty()); return *begin(); }
    const T            &first() const { QHULL_ASSERT(!isEmpty()); return *begin(); }
    T                  &front() { return first(); }
    const T            &front() const { return first(); }
    T                  &last() { QHULL_ASSERT(!isEmpty()); return *(end()-1); }
    const T            &last() const {  QHULL_ASSERT(!isEmpty()); return *(end()-1); }
    // mid() not available.  No setT constructor
    T                  &operator[](int idx) { T *n= reinterpret_cast(elementPointer(idx)); QHULL_ASSERT(idx>=0 && n < reinterpret_cast(endPointer())); return *n; }
    const T            &operator[](int idx) const { const T *n= reinterpret_cast(elementPointer(idx)); QHULL_ASSERT(idx>=0 && n < reinterpret_cast(endPointer())); return *n; }
    T                  &second() { return operator[](1); }
    const T            &second() const { return operator[](1); }
    T                   value(int idx) const;
    T                   value(int idx, const T &defaultValue) const;

#//Read-write -- Not available, no setT constructor

#//iterator
    iterator            begin() { return iterator(beginPointer()); }
    const_iterator      begin() const { return const_iterator(beginPointer()); }
    const_iterator      constBegin() const { return const_iterator(beginPointer()); }
    const_iterator      constEnd() const { return const_iterator(endPointer()); }
    iterator            end() { return iterator(endPointer()); }
    const_iterator      end() const { return const_iterator(endPointer()); }

#//Search
    bool                contains(const T &t) const;
    int                 count(const T &t) const;
    int                 indexOf(const T &t) const { /* no qh_qh */ return qh_setindex(getSetT(), t.getBaseT()); }
    int                 lastIndexOf(const T &t) const;

};//class QhullSet

// FIXUP? can't use QHULL_DECLARE_SEQUENTIAL_ITERATOR because it is not a template

template 
class QhullSetIterator {

#//Subtypes
    typedef typename QhullSet::const_iterator const_iterator;

private:
#//Fields
    const_iterator      i;
    const_iterator      begin_i;
    const_iterator      end_i;

public:
#//Constructors
                        QhullSetIterator(const QhullSet &s) : i(s.begin()), begin_i(i), end_i(s.end()) {}
                        QhullSetIterator(const QhullSetIterator &o) : i(o.i), begin_i(o.begin_i), end_i(o.end_i) {}
    QhullSetIterator &operator=(const QhullSetIterator &o) { i= o.i; begin_i= o.begin_i; end_i= o.end_i; return *this; }

#//ReadOnly
    int                 countRemaining() { return (int)(end_i-begin_i); } // WARN64

#//Search
    bool                findNext(const T &t);
    bool                findPrevious(const T &t);

#//Foreach
    bool                hasNext() const { return i != end_i; }
    bool                hasPrevious() const { return i != begin_i; }
    T                   next() { return *i++; }
    T                   peekNext() const { return *i; }
    T                   peekPrevious() const { const_iterator p = i; return *--p; }
    T                   previous() { return *--i; }
    void                toBack() { i = end_i; }
    void                toFront() { i = begin_i; }
};//class QhullSetIterator

#//== Definitions =========================================

#//Conversion

#ifndef QHULL_NO_STL
template 
std::vector QhullSet::
toStdVector() const
{
    QhullSetIterator i(*this);
    std::vector vs;
    vs.reserve(i.countRemaining());
    while(i.hasNext()){
        vs.push_back(i.next());
    }
    return vs;
}//toStdVector
#endif

#ifdef QHULL_USES_QT
template 
QList QhullSet::
toQList() const
{
    QhullSetIterator i(*this);
    QList vs;
    while(i.hasNext()){
        vs.append(i.next());
    }
    return vs;
}//toQList
#endif

#//Element

template 
T QhullSet::
value(int idx) const
{
    // Avoid call to qh_setsize() and assert in elementPointer()
    const T *n= reinterpret_cast(&SETelem_(getSetT(), idx));
    return (idx>=0 && n
T QhullSet::
value(int idx, const T &defaultValue) const
{
    // Avoid call to qh_setsize() and assert in elementPointer()
    const T *n= reinterpret_cast(&SETelem_(getSetT(), idx));
    return (idx>=0 && n
bool QhullSet::
contains(const T &t) const
{
    setT *s= getSetT();
    void *e= t.getBaseT();  // contains() is not inline for better error reporting
    int result= qh_setin(s, e);
    return result!=0;
}//contains

template 
int QhullSet::
count(const T &t) const
{
    int c= 0;
    const T *i= data();
    const T *e= end();
    while(i
int QhullSet::
lastIndexOf(const T &t) const
{
    const T *b= begin();
    const T *i= end();
    while(--i>=b){
        if(*i==t){
            break;
        }
    }
    return (int)(i-b); // WARN64
}//lastIndexOf

#//QhullSetIterator

template 
bool QhullSetIterator::
findNext(const T &t)
{
    while(i!=end_i){
        if(*(++i)==t){
            return true;
        }
    }
    return false;
}//findNext

template 
bool QhullSetIterator::
findPrevious(const T &t)
{
    while(i!=begin_i){
        if(*(--i)==t){
            return true;
        }
    }
    return false;
}//findPrevious

}//namespace orgQhull


#//== Global namespace =========================================

template 
std::ostream &
operator<<(std::ostream &os, const orgQhull::QhullSet &qs)
{
    const T *i= qs.begin();
    const T *e= qs.end();
    while(i!=e){
        os << *i;
        ++i;
    }
    return os;
}//operator<<

#endif // QhullSet_H
qhull-2012.1/src/libqhullcpp/QhullSets.h0000644000076400010400000000141711710144465021315 0ustar  bbarberAdministrators/****************************************************************************
**
** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
** $Id: //main/2011/qhull/src/libqhullcpp/QhullSets.h#3 $$Change: 1464 $
** $DateTime: 2012/01/25 22:58:41 $$Author: bbarber $
**
****************************************************************************/

#ifndef QHULLSETS_H
#define QHULLSETS_H

#include "QhullSet.h"

namespace orgQhull {

    //See: QhullFacetSet.h
    //See: QhullPointSet.h
    //See: QhullVertexSet.h

    // Avoid circular references between QhullFacet, QhullRidge, and QhullVertex
    class QhullRidge;
    typedef QhullSet  QhullRidgeSet;
    typedef QhullSetIterator  QhullRidgeSetIterator;

}//namespace orgQhull

#endif // QHULLSETS_H
qhull-2012.1/src/libqhullcpp/QhullStat.cpp0000644000076400010400000000156111710144465021645 0ustar  bbarberAdministrators/****************************************************************************
**
** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
** $Id: //main/2011/qhull/src/libqhullcpp/QhullStat.cpp#3 $$Change: 1464 $
** $DateTime: 2012/01/25 22:58:41 $$Author: bbarber $
**
****************************************************************************/

#//! QhullStat -- Qhull's global data structure, statT, as a C++ class


#include "QhullError.h"
#include "QhullStat.h"

#include 
#include 

using std::cerr;
using std::string;
using std::vector;
using std::ostream;

#ifdef _MSC_VER  // Microsoft Visual C++ -- warning level 4
#endif

namespace orgQhull {

#//Constructor, destructor, etc.

//! If qh_QHpointer==0, invoke with placement new on qh_stat;
QhullStat::
QhullStat()
{
}//QhullStat

QhullStat::
~QhullStat()
{
}//~QhullStat

}//namespace orgQhull

qhull-2012.1/src/libqhullcpp/QhullStat.h0000644000076400010400000000243411710144465021312 0ustar  bbarberAdministrators/****************************************************************************
**
** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
** $Id: //main/2011/qhull/src/libqhullcpp/QhullStat.h#6 $$Change: 1464 $
** $DateTime: 2012/01/25 22:58:41 $$Author: bbarber $
**
****************************************************************************/

#ifndef QHULLSTAT_H
#define QHULLSTAT_H

extern "C" {
    #include "libqhull/qhull_a.h"
}

#include 
#include 

namespace orgQhull {

#//defined here
    //! QhullStat -- Qhull's statistics, qhstatT, as a C++ class
    //! Statistics defined with zzdef_() control Qhull's behavior, summarize its result, and report precision problems.
    class QhullStat;

class QhullStat : public qhstatT {

private:
#//Fields (empty) -- POD type equivalent to qhstatT.  No data or virtual members

public:
#//Constants

#//class methods
    static void         clearStatistics();

#//constructor, assignment, destructor, invariant
                        QhullStat();
                       ~QhullStat();

private:
    //!disable copy constructor and assignment
                        QhullStat(const QhullStat &);
    QhullStat          &operator=(const QhullStat &);
public:

#//Access
};//class QhullStat

}//namespace orgQhull

#endif // QHULLSTAT_H
qhull-2012.1/src/libqhullcpp/QhullVertex.cpp0000644000076400010400000000532511710144465022211 0ustar  bbarberAdministrators/****************************************************************************
**
** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
** $Id: //main/2011/qhull/src/libqhullcpp/QhullVertex.cpp#3 $$Change: 1464 $
** $DateTime: 2012/01/25 22:58:41 $$Author: bbarber $
**
****************************************************************************/

#//! QhullVertex -- Qhull's vertex structure, vertexT, as a C++ class

#include "UsingLibQhull.h"
#include "QhullPoint.h"
#include "QhullFacetSet.h"
#include "QhullVertex.h"
#include "QhullVertexSet.h"
#include "QhullFacet.h"

#ifdef _MSC_VER  // Microsoft Visual C++ -- warning level 4
#pragma warning( disable : 4611)  // interaction between '_setjmp' and C++ object destruction is non-portable
#pragma warning( disable : 4996)  // function was declared deprecated(strcpy, localtime, etc.)
#endif

namespace orgQhull {

#//class statics
vertexT QhullVertex::
s_empty_vertex= {0,0,0,0,0,
                 0,0,0,0,0,
                 0,0};

#//ForEach

//! Return neighboring facets for a vertex
//! If neither merging nor Voronoi diagram, requires Qhull::defineVertexNeighborFacets() beforehand.
QhullFacetSet QhullVertex::
neighborFacets() const
{
    if(!neighborFacetsDefined()){
        throw QhullError(10034, "Qhull error: neighboring facets of vertex %d not defined.  Please call Qhull::defineVertexNeighborFacets() beforehand.", id());
    }
    return QhullFacetSet(qh_vertex->neighbors);
}//neighborFacets

}//namespace orgQhull

#//Global functions

using std::endl;
using std::ostream;
using std::string;
using std::vector;
using orgQhull::QhullPoint;
using orgQhull::QhullFacet;
using orgQhull::QhullFacetSet;
using orgQhull::QhullFacetSetIterator;
using orgQhull::QhullVertex;
using orgQhull::UsingLibQhull;

//! Duplicate of qh_printvertex [io.c]
ostream &
operator<<(ostream &os, const QhullVertex::PrintVertex &pr)
{
    QhullVertex v= *pr.vertex;
    QhullPoint p= v.point();
    os << "- p" << p.id(pr.run_id) << " (v" << v.id() << "): ";
    const realT *c= p.coordinates();
    for(int k= p.dimension(); k--; ){
        os << " " << *c++; // FIXUP QH11010 %5.2g
    }
    if(v.getVertexT()->deleted){
        os << " deleted";
    }
    if(v.getVertexT()->delridge){
        os << " ridgedeleted";
    }
    os << endl;
    if(v.neighborFacetsDefined()){
        QhullFacetSetIterator i= v.neighborFacets();
        if(i.hasNext()){
            os << " neighborFacets:";
            int count= 0;
            while(i.hasNext()){
                if(++count % 100 == 0){
                    os << endl << "     ";
                }
                QhullFacet f= i.next();
                os << " f" << f.id();
            }
            os << endl;
        }
    }
    return os;
}//<< PrintVertex

qhull-2012.1/src/libqhullcpp/QhullVertex.h0000644000076400010400000000742611710144465021662 0ustar  bbarberAdministrators/****************************************************************************
**
** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
** $Id: //main/2011/qhull/src/libqhullcpp/QhullVertex.h#6 $$Change: 1464 $
** $DateTime: 2012/01/25 22:58:41 $$Author: bbarber $
**
****************************************************************************/

#ifndef QHULLVERTEX_H
#define QHULLVERTEX_H

#include "UsingLibQhull.h"
#include "QhullPoint.h"
#include "QhullLinkedList.h"
#include "QhullSet.h"
extern "C" {
    #include "libqhull/qhull_a.h"
}

#include 

namespace orgQhull {

#//ClassRef
    class QhullFacetSet;

#//Types
    //! QhullVertex -- Qhull's vertex structure, vertexT [libqhull.h], as a C++ class
    class QhullVertex;
    typedef QhullLinkedList QhullVertexList;
    typedef QhullLinkedListIterator QhullVertexListIterator;


/*********************
  topological information:
    next,previous       doubly-linked list of all vertices
    neighborFacets           set of adjacent facets (only if qh.VERTEXneighbors)

  geometric information:
    point               array of DIM coordinates
*/

class QhullVertex {

private:
#//Fields
    vertexT            *qh_vertex;

#//Class objects
    static vertexT      s_empty_vertex;  // needed for shallow copy

public:
#//Constants

#//Constructors
                        QhullVertex() : qh_vertex(&s_empty_vertex) {}
                        // Creates an alias.  Does not copy QhullVertex.  Needed for return by value and parameter passing
                        QhullVertex(const QhullVertex &o) : qh_vertex(o.qh_vertex) {}
                        // Creates an alias.  Does not copy QhullVertex.  Needed for vector
    QhullVertex        &operator=(const QhullVertex &o) { qh_vertex= o.qh_vertex; return *this; }
                       ~QhullVertex() {}

#//Conversion
                        //Implicit conversion from vertexT
                        QhullVertex(vertexT *v) : qh_vertex(v ? v : &s_empty_vertex) {}
    vertexT            *getVertexT() const { return qh_vertex; }

#//QhullSet
    vertexT            *getBaseT() const { return getVertexT(); }

#//getSet
    int                 dimension() const { return (qh_vertex->dim || !isDefined()) ? qh_vertex->dim : UsingLibQhull::globalVertexDimension(); }
    int                 id() const { return qh_vertex->id; }
    bool                isDefined() const { return qh_vertex != &s_empty_vertex; }
                        //! True if defineVertexNeighborFacets() already called.  Auotomatically set for facet merging, Voronoi diagrams
    bool                neighborFacetsDefined() const { return qh_vertex->neighbors != 0; }
    QhullVertex         next() const { return qh_vertex->next; }
    bool                operator==(const QhullVertex &o) const { return qh_vertex==o.qh_vertex; }
    bool                operator!=(const QhullVertex &o) const { return !operator==(o); }
    QhullPoint          point() const { return QhullPoint(dimension(), qh_vertex->point); }
    QhullVertex         previous() const { return qh_vertex->previous; }

#//ForEach
    //See also QhullVertexList
    QhullFacetSet       neighborFacets() const;

#//IO
    struct PrintVertex{
        const QhullVertex *vertex;
        int             run_id;
                        PrintVertex(int qhRunId, const QhullVertex &v) : vertex(&v), run_id(qhRunId) {}
    };//PrintVertex
    PrintVertex         print(int qhRunId) const { return PrintVertex(qhRunId, *this); }
};//class QhullVertex

}//namespace orgQhull

#//GLobal

std::ostream &operator<<(std::ostream &os, const orgQhull::QhullVertex::PrintVertex &pr);
inline std::ostream &operator<<(std::ostream &os, const orgQhull::QhullVertex &v) { os << v.print(orgQhull::UsingLibQhull::NOqhRunId); return os; }

#endif // QHULLVERTEX_H
qhull-2012.1/src/libqhullcpp/QhullVertexSet.cpp0000644000076400010400000000635611710144466022673 0ustar  bbarberAdministrators/****************************************************************************
**
** Copyright (c) 2009-2012 C.B. Barber. All rights reserved.
** $Id: //main/2011/qhull/src/libqhullcpp/QhullVertexSet.cpp#5 $$Change: 1464 $
** $DateTime: 2012/01/25 22:58:41 $$Author: bbarber $
**
****************************************************************************/

#//! QhullVertexSet -- Qhull's linked Vertexs, as a C++ class

#include "QhullVertex.h"
#include "QhullVertexSet.h"
#include "QhullPoint.h"
#include "QhullRidge.h"
#include "QhullVertex.h"

using std::string;
using std::vector;

#ifdef _MSC_VER  // Microsoft Visual C++ -- warning level 4
#pragma warning( disable : 4611)  /* interaction between '_setjmp' and C++ object destruction is non-portable */
                                    /* setjmp should not be implemented with 'catch' */
#endif

namespace orgQhull {

QhullVertexSet::
QhullVertexSet(int qhRunId, facetT *facetlist, setT *facetset, bool allfacets)
: QhullSet(0)
, qhsettemp_qhull(0)
, qhsettemp_defined(false)
{
    UsingLibQhull q(qhRunId);
    int exitCode = setjmp(qh errexit);
    if(!exitCode){ // no object creation -- destructors skipped on longjmp()
        setT *vertices= qh_facetvertices(facetlist, facetset, allfacets);
        defineAs(vertices);
        qhsettemp_qhull= s_qhull_output;
        qhsettemp_defined= true;
    }
    q.maybeThrowQhullMessage(exitCode);
}//QhullVertexSet facetlist facetset

void QhullVertexSet::
freeQhSetTemp()
{
    if(qhsettemp_defined){
        UsingLibQhull q(qhsettemp_qhull, QhullError::NOthrow);
        if(q.defined()){
            int exitCode = setjmp(qh errexit);
            if(!exitCode){ // no object creation -- destructors skipped on longjmp()
                qh_settempfree(referenceSetT()); // errors if not top of tempstack or if qhmem corrupted
            }
            q.maybeThrowQhullMessage(exitCode, QhullError::NOthrow);
        }
    }
}//freeQhSetTemp

QhullVertexSet::
~QhullVertexSet()
{
    freeQhSetTemp();
}//~QhullVertexSet

}//namespace orgQhull

#//Global functions

using std::endl;
using std::ostream;
using orgQhull::QhullPoint;
using orgQhull::QhullVertex;
using orgQhull::QhullVertexSet;
using orgQhull::QhullVertexSetIterator;
using orgQhull::UsingLibQhull;

//! Print Vertex identifiers to stream.  Space prefix.  From qh_printVertexheader [io.c]
ostream &
operator<<(ostream &os, const QhullVertexSet::PrintIdentifiers &pr)
{
    if(pr.print_message && *pr.print_message){
        os << pr.print_message;
    }
    for(QhullVertexSet::const_iterator i=pr.Vertex_set->begin(); i!=pr.Vertex_set->end(); ++i){
        const QhullVertex v= *i;
        os << " v" << v.id();
    }
    os << endl;
    return os;
}//<

namespace orgQhull {

#//ClassRef
    class               QhullVertex;

#//Types
    //! QhullVertexSet -- a set of Qhull Vertices, as a C++ class.
    //! See Qhull
    class               QhullVertexSet;
    typedef QhullSetIterator
                        QhullVertexSetIterator;

class QhullVertexSet : public QhullSet {

private:
#//Fields
    Qhull              *qhsettemp_qhull; //! For sets allocated with qh_settemp()
    bool                qhsettemp_defined;  //! Set was allocated with q_memalloc()

public:
#//Constructor
                        //Conversion from setT* is not type-safe.  Implicit conversion for void* to T
   explicit             QhullVertexSet(setT *s) : QhullSet(s), qhsettemp_qhull(0), qhsettemp_defined(false) {}
                        QhullVertexSet(int qhRunId, facetT *facetlist, setT *facetset, bool allfacets);
                        //Copy constructor copies pointer but not contents.  Needed for return by value.
                        QhullVertexSet(const QhullVertexSet &o) : QhullSet(o), qhsettemp_qhull(o.qhsettemp_qhull), qhsettemp_defined(o.qhsettemp_defined) {}
                       ~QhullVertexSet();

private:
                        //!Disable default constructor and copy assignment.  See QhullSetBase
                        QhullVertexSet();
    QhullVertexSet      &operator=(const QhullVertexSet &);
public:

#//Constructor, destructor
    void                freeQhSetTemp();

#//IO
    struct PrintVertexSet{
        const QhullVertexSet *Vertex_set;
        const char     *print_message;
        int             run_id;
                        PrintVertexSet(int qhRunId, const char *message, const QhullVertexSet *s) : Vertex_set(s), print_message(message), run_id(qhRunId) {}
    };//PrintVertexSet
    const PrintVertexSet       print(int qhRunId, const char *message) const { return PrintVertexSet(qhRunId, message, this); }

    struct PrintIdentifiers{
        const QhullVertexSet *Vertex_set;
        const char     *print_message;
                        PrintIdentifiers(const char *message, const QhullVertexSet *s) : Vertex_set(s), print_message(message) {}
    };//PrintIdentifiers
    PrintIdentifiers    printIdentifiers(const char *message) const { return PrintIdentifiers(message, this); }

};//class QhullVertexSet

}//namespace orgQhull

#//== Global namespace =========================================

std::ostream &operator<<(std::ostream &os, const orgQhull::QhullVertexSet::PrintVertexSet &pr);
std::ostream &operator<<(std::ostream &os, const orgQhull::QhullVertexSet::PrintIdentifiers &p);
inline std::ostream &operator<<(std::ostream &os, const orgQhull::QhullVertexSet &vs) { os << vs.print(orgQhull::UsingLibQhull::NOqhRunId, ""); return os; }

#endif // QHULLVERTEXSET_H
qhull-2012.1/src/libqhullcpp/qhull_interface.cpp0000644000076400010400000000675511552665572023116 0ustar  bbarberAdministrators/*
  ---------------------------------
*/

#include 
#include 

//--- Include qhull, so it works from with in a C++ source file
//---
//--- In MVC one cannot just do:
//---
//---    extern "C"
//---    {
//---      #include "qhull_a.h"
//---    }
//---
//--- Because qhull_a.h includes math.h, which can not appear
//--- inside a extern "C" declaration.
//---
//--- Maybe that why Numerical recipes in C avoid this problem, by removing
//--- standard include headers from its header files and add them in the
//--- respective source files instead.
//---
//--- [K. Erleben]

#if defined(__cplusplus)
extern "C"
{
#endif
#include 
#include 
#include 
#include 
#include 
#include 
#include 
#include 
#include 
#include 
#if defined(__cplusplus)
}
#endif

/*********************************************************************/
/*                                                                   */
/*                                                                   */
/*                                                                   */
/*                                                                   */
/*********************************************************************/

void compute_convex_hull(void)
{
        int dim;                      /* dimension of points */
        int numpoints;            /* number of points */
        coordT *points;           /* array of coordinates for each point */
        boolT ismalloc;           /* True if qhull should free points in qh_freeqhull() or reallocation */
        char flags[]= "qhull Tv"; /* option flags for qhull, see qh_opt.htm */
        FILE *outfile= stdout;    /* output from qh_produce_output()
                                     use NULL to skip qh_produce_output() */
        FILE *errfile= stderr;    /* error messages from qhull code */
        int exitcode;             /* 0 if no error from qhull */
        facetT *facet;            /* set by FORALLfacets */
        int curlong, totlong;     /* memory remaining after qh_memfreeshort */

        /* initialize dim, numpoints, points[], ismalloc here */
        exitcode= qh_new_qhull(dim, numpoints, points, ismalloc,
                                                        flags, outfile, errfile);
        if (!exitcode) { /* if no error */
                /* 'qh facet_list' contains the convex hull */
                FORALLfacets {
                        /* ... your code ... */
                }
        }
        qh_freeqhull(!qh_ALL);
        qh_memfreeshort(&curlong, &totlong);
        if (curlong || totlong)
                fprintf(errfile, "qhull internal warning (main): did not free %d bytes of long memory(%d pieces)\n",
                             totlong, curlong);
};

/*********************************************************************/
/*                                                                   */
/*                                                                   */
/*                                                                   */
/*                                                                   */
/*********************************************************************/

void main()
{
        cout << "Hello world" << endl;

        cout << "Press any key..." << endl;

        while (!_kbhit());

};
qhull-2012.1/src/libqhullcpp/qt-qhull.cpp0000644000076400010400000000521411720052005021457 0ustar  bbarberAdministrators/****************************************************************************
**
** Copyright (c) 2009-2012 C.B. Barber. All rights reserved.
** $Id: //main/2011/qhull/src/libqhullcpp/qt-qhull.cpp#4 $$Change: 1490 $
** $DateTime: 2012/02/19 20:27:01 $$Author: bbarber $
**
****************************************************************************/

#include 
#include "RoadTest.h"

#ifndef QHULL_USES_QT
#define QHULL_USES_QT 1
#endif

#include "Coordinates.h"
#include "QhullFacetList.h"
#include "QhullFacetSet.h"
#include "QhullHyperplane.h"
#include "QhullPoint.h"
#include "QhullPoints.h"
#include "QhullPointSet.h"
#include "QhullVertex.h"
#include "QhullVertexSet.h"

namespace orgQhull {

#//Conversions

QList Coordinates::
toQList() const
{
    CoordinatesIterator i(*this);
    QList cs;
    while(i.hasNext()){
        cs.append(i.next());
    }
    return cs;
}//toQList

QList QhullFacetList::
toQList() const
{
    QhullLinkedListIterator i(*this);
    QList vs;
    while(i.hasNext()){
        QhullFacet f= i.next();
        if(isSelectAll() || f.isGood()){
            vs.append(f);
        }
    }
    return vs;
}//toQList

//! Same as PrintVertices
QList QhullFacetList::
vertices_toQList(int qhRunId) const
{
    QList vs;
    QhullVertexSet qvs(qhRunId, first().getFacetT(), NULL, isSelectAll());
    for(QhullVertexSet::iterator i=qvs.begin(); i!=qvs.end(); ++i){
        vs.push_back(*i);
    }
    return vs;
}//vertices_toQList

QList QhullFacetSet::
toQList() const
{
    QhullSetIterator i(*this);
    QList vs;
    while(i.hasNext()){
        QhullFacet f= i.next();
        if(isSelectAll() || f.isGood()){
            vs.append(f);
        }
    }
    return vs;
}//toQList

#ifdef QHULL_USES_QT
QList QhullHyperplane::
toQList() const
{
    QhullHyperplaneIterator i(*this);
    QList fs;
    while(i.hasNext()){
        fs.append(i.next());
    }
    fs.append(hyperplane_offset);
    return fs;
}//toQList
#endif //QHULL_USES_QT

QList QhullPoint::
toQList() const
{
    QhullPointIterator i(*this);
    QList vs;
    while(i.hasNext()){
        vs.append(i.next());
    }
    return vs;
}//toQList

QList QhullPoints::
toQList() const
{
    QhullPointsIterator i(*this);
    QList vs;
    while(i.hasNext()){
        vs.append(i.next());
    }
    return vs;
}//toQList

QList QhullPointSet::
toQList() const
{
    QhullPointSetIterator i(*this);
    QList vs;
    while(i.hasNext()){
        vs.append(i.next());
    }
    return vs;
}//toQList

}//orgQhull

qhull-2012.1/src/libqhullcpp/RboxPoints.cpp0000644000076400010400000001323311710144466022033 0ustar  bbarberAdministrators/****************************************************************************
**
** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
** $Id: //main/2011/qhull/src/libqhullcpp/RboxPoints.cpp#4 $$Change: 1464 $
** $DateTime: 2012/01/25 22:58:41 $$Author: bbarber $
**
****************************************************************************/

#include "QhullError.h"
#include "RboxPoints.h"

#include 

using std::cerr;
using std::endl;
using std::istream;
using std::ostream;
using std::ostringstream;
using std::string;
using std::vector;
using std::ws;

#ifdef _MSC_VER  // Microsoft Visual C++ -- warning level 4
#pragma warning( disable : 4996)  // function was declared deprecated(strcpy, localtime, etc.)
#endif

namespace orgQhull {

#//! RboxPoints -- generate random PointCoordinates for qhull (rbox)

#//Global

//! pointer to RboxPoints for qh_fprintf callback
RboxPoints *rbox_output= 0;

#//Construct
RboxPoints::
RboxPoints()
: PointCoordinates("rbox")
, rbox_new_count(0)
, rbox_status(qh_ERRnone)
, rbox_message()
{}

RboxPoints::
RboxPoints(const char *rboxCommand)
: PointCoordinates("rbox")
, rbox_new_count(0)
, rbox_status(qh_ERRnone)
, rbox_message()
{
    appendPoints(rboxCommand);
}

RboxPoints::
RboxPoints(const RboxPoints &other)
: PointCoordinates(other)
, rbox_new_count(0)
, rbox_status(other.rbox_status)
, rbox_message(other.rbox_message)
{}

RboxPoints & RboxPoints::
operator=(const RboxPoints &other)
{
    PointCoordinates::operator=(other);
    rbox_new_count= other.rbox_new_count;
    rbox_status= other.rbox_status;
    rbox_message= other.rbox_message;
    return *this;
}//operator=


RboxPoints::
~RboxPoints()
{}

#//Error

void RboxPoints::
clearRboxMessage()
{
    rbox_status= qh_ERRnone;
    rbox_message.clear();
}//clearRboxMessage

std::string RboxPoints::
rboxMessage() const
{
    if(rbox_status!=qh_ERRnone){
        return rbox_message;
    }
    if(isEmpty()){
        return "rbox warning: no points generated\n";
    }
    return "rbox: OK\n";
}//rboxMessage

int RboxPoints::
rboxStatus() const
{
    return rbox_status;
}

bool RboxPoints::
hasRboxMessage() const
{
    return (rbox_status!=qh_ERRnone);
}

#//Modify

void RboxPoints::
appendPoints(const char *rboxCommand)
{
    string s("rbox ");
    s += rboxCommand;
    char *command= const_cast(s.c_str());
    if(rbox_output){
        throw QhullError(10001, "Qhull error: Two simultaneous calls to RboxPoints::appendPoints().  Prevent two processes calling appendPoints() at the same time.  Other RboxPoints '%s'", 0, 0, 0, rbox_output->comment().c_str());
    }
    if(extraCoordinatesCount()!=0){
        throw QhullError(10067, "Qhull error: Extra coordinates (%d) prior to calling RboxPoints::appendPoints.  Was %s", extraCoordinatesCount(), 0, 0.0, comment().c_str());
    }
    int previousCount= count();
    rbox_output= this;              // set rbox_output for qh_fprintf()
    int status= ::qh_rboxpoints(0, 0, command);
    rbox_output= 0;
    if(rbox_status==qh_ERRnone){
        rbox_status= status;
    }
    if(rbox_status!=qh_ERRnone){
        throw QhullError(rbox_status, rbox_message);
    }
    if(extraCoordinatesCount()!=0){
        throw QhullError(10002, "Qhull error: extra coordinates (%d) for PointCoordinates (%x)", extraCoordinatesCount(), 0, 0.0, coordinates());
    }
    if(previousCount+newCount()!=count()){
        throw QhullError(10068, "Qhull error: rbox specified %d points but got %d points for command '%s'", newCount(), count()-previousCount, 0.0, comment().c_str());
    }
}//appendPoints

}//namespace orgQhull

#//Global functions

/*---------------------------------

  qh_fprintf_rbox(fp, msgcode, format, list of args )
    fp is ignored (replaces qh_fprintf_rbox() in userprintf_rbox.c)
    rbox_output == RboxPoints

notes:
    only called from qh_rboxpoints()
    same as fprintf() and Qhull::qh_fprintf()
    fgets() is not trapped like fprintf()
    Do not throw errors from here.  Use qh_errexit_rbox;
*/
extern "C"
void qh_fprintf_rbox(FILE*, int msgcode, const char *fmt, ... ) {
    va_list args;

    using namespace orgQhull;

    RboxPoints *out= rbox_output;
    va_start(args, fmt);
    if(msgcoderbox_message += newMessage;
        if(out->rbox_statusrbox_status>=MSG_STDERR){
            out->rbox_status= msgcode;
        }
        va_end(args);
        return;
    }
    switch(msgcode){
    case 9391:
    case 9392:
        out->rbox_message += "RboxPoints error: options 'h', 'n' not supported.\n";
        qh_errexit_rbox(10010);
        /* never returns */
    case 9393:
        {
            int dimension= va_arg(args, int);
            string command(va_arg(args, char*));
            int count= va_arg(args, int);
            out->setDimension(dimension);
            out->appendComment(" \"");
            out->appendComment(command.substr(command.find(' ')+1));
            out->appendComment("\"");
            out->setNewCount(count);
            out->reservePoints();
        }
        break;
    case 9407:
        *out << va_arg(args, int);
        // fall through
    case 9405:
        *out << va_arg(args, int);
        // fall through
    case 9403:
        *out << va_arg(args, int);
        break;
    case 9408:
        *out << va_arg(args, double);
        // fall through
    case 9406:
        *out << va_arg(args, double);
        // fall through
    case 9404:
        *out << va_arg(args, double);
        break;
    }
    va_end(args);
} /* qh_fprintf_rbox */

qhull-2012.1/src/libqhullcpp/RboxPoints.h0000644000076400010400000000407511710144466021504 0ustar  bbarberAdministrators/****************************************************************************
**
** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
** $Id: //main/2011/qhull/src/libqhullcpp/RboxPoints.h#6 $$Change: 1464 $
** $DateTime: 2012/01/25 22:58:41 $$Author: bbarber $
**
****************************************************************************/

#ifndef RBOXPOINTS_H
#define RBOXPOINTS_H

#include "QhullPoint.h"
#include "PointCoordinates.h"
extern "C" {
#include "libqhull/libqhull.h"
}

#include 
#include 
#include 
#include 
#include 
#include 

namespace orgQhull {

#//Types
    //! RboxPoints -- generate random PointCoordinates for Qhull
    class RboxPoints;

    class RboxPoints : public PointCoordinates {

private:
#//Fields and friends
    int                 rbox_new_count;     //! Number of points for PointCoordinates
    int                 rbox_status;    //! error status from rboxpoints.  qh_ERRnone if none.
    std::string         rbox_message;   //! stderr from rboxpoints

    friend void ::qh_fprintf_rbox(FILE *fp, int msgcode, const char *fmt, ... );

public:
#//Construct
                        RboxPoints();
    explicit            RboxPoints(const char *rboxCommand);
                        RboxPoints(const RboxPoints &other);
                        RboxPoints &operator=(const RboxPoints &other);
                       ~RboxPoints();

public:
#//GetSet
    void                clearRboxMessage();
    int                 newCount() const { return rbox_new_count; }
    std::string         rboxMessage() const;
    int                 rboxStatus() const;
    bool                hasRboxMessage() const;
    void                setNewCount(int pointCount) { QHULL_ASSERT(pointCount>=0); rbox_new_count= pointCount; }

#//Modify
    void                appendPoints(const char* rboxCommand);
    using               PointCoordinates::appendPoints;
    void                reservePoints() { reserveCoordinates((count()+newCount())*dimension()); }
};//class RboxPoints

}//namespace orgQhull

#endif // RBOXPOINTS_H
qhull-2012.1/src/libqhullcpp/RoadError.cpp0000644000076400010400000000642611710144466021631 0ustar  bbarberAdministrators/****************************************************************************
**
** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
** $Id: //main/2011/qhull/src/libqhullcpp/RoadError.cpp#1 $$Change: 1490 $
** $DateTime: 2012/02/19 20:27:01 $$Author: bbarber $
**
****************************************************************************/

#//! RoadError -- All exceptions thrown by Qhull are RoadErrors
#//! Do not throw RoadError's from destructors.  Use e.logError() instead.

#include "RoadError.h"

#include 
#include 
#include 

using std::cerr;
using std::cout;
using std::string;

#ifdef _MSC_VER  // Microsoft Visual C++ -- warning level 4
#endif

namespace orgQhull {

#//Class fields

//! Identifies error messages from Qhull and Road for web searches.
//! See QhullError.h#QHULLlastError and user.h#MSG_ERROR
const char * RoadError::
ROADtag= "QH";

std::ostringstream RoadError::
global_log;

#//Constructor

RoadError::
RoadError()
: error_code(0)
, log_event()
, error_message()
{ }

RoadError::
RoadError(const RoadError &other)
: error_code(other.error_code)
, log_event(other.log_event)
, error_message(other.error_message)
{
}//copy construct

RoadError::
RoadError(int code, const std::string &message)
: error_code(code)
, log_event(message.c_str())
, error_message(log_event.toString(ROADtag, error_code))
{
    log_event.cstr_1= error_message.c_str(); // overwrites initial value
}

RoadError::
RoadError(int code, const char *fmt)
: error_code(code)
, log_event(fmt)
, error_message()
{ }

RoadError::
RoadError(int code, const char *fmt, int d)
: error_code(code)
, log_event(fmt, d)
, error_message()
{ }

RoadError::
RoadError(int code, const char *fmt, int d, int d2)
: error_code(code)
, log_event(fmt, d, d2)
, error_message()
{ }

RoadError::
RoadError(int code, const char *fmt, int d, int d2, float f)
: error_code(code)
, log_event(fmt, d, d2, f)
, error_message()
{ }

RoadError::
RoadError(int code, const char *fmt, int d, int d2, float f, const char *s)
: error_code(code)
, log_event(fmt, d, d2, f, s)
, error_message(log_event.toString(ROADtag, code)) // char * may go out of scope
{ }

RoadError::
RoadError(int code, const char *fmt, int d, int d2, float f, const void *x)
: error_code(code)
, log_event(fmt, d, d2, f, x)
, error_message()
{ }

RoadError::
RoadError(int code, const char *fmt, int d, int d2, float f, int i)
: error_code(code)
, log_event(fmt, d, d2, f, i)
, error_message()
{ }

RoadError::
RoadError(int code, const char *fmt, int d, int d2, float f, long long i)
: error_code(code)
, log_event(fmt, d, d2, f, i)
, error_message()
{ }

RoadError::
RoadError(int code, const char *fmt, int d, int d2, float f, double e)
: error_code(code)
, log_event(fmt, d, d2, f, e)
, error_message()
{ }

RoadError & RoadError::
operator=(const RoadError &other)
{
    error_code= other.error_code;
    error_message= other.error_message;
    log_event= other.log_event;
    return *this;
}//operator=

#//Virtual
const char * RoadError::
what() const throw()
{
    if(error_message.empty()){
        error_message= log_event.toString(ROADtag, error_code);
    }
    return error_message.c_str();
}//what

#//Updates

//! Log error instead of throwing it.
void RoadError::
logError() const
{
    global_log << what() << endl;
}//logError


}//namespace orgQhull

qhull-2012.1/src/libqhullcpp/RoadError.h0000644000076400010400000000607711710144466021300 0ustar  bbarberAdministrators/****************************************************************************
**
** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
** $Id: //main/2011/qhull/src/libqhullcpp/RoadError.h#1 $$Change: 1490 $
** $DateTime: 2012/02/19 20:27:01 $$Author: bbarber $
**
****************************************************************************/

#ifndef ROADERROR_H
#define ROADERROR_H

#include "RoadLogEvent.h"

#include 
#include 
#include 
#include 

using std::endl;

namespace orgQhull {

#//Types
    //! RoadError -- Report and log errors
    //!  See discussion in Saylan, G., "Practical C++ error handling in hybrid environments," Dr. Dobb's Journal, p. 50-55, March 2007.
    //!   He uses an auto_ptr to track a stringstream.  It constructs a string on the fly.  RoadError uses the copy constructor to transform RoadLogEvent into a string
    class RoadError;

class RoadError : public std::exception {

private:
#//Fields
    int                 error_code;  //! Non-zero code (not logged), maybe returned as program status
    RoadLogEvent        log_event;   //! Format string w/ arguments
    mutable std::string error_message;  //! Formated error message.  Must be after log_event.

#//Class fields
    static const char  *  ROADtag;
    static std::ostringstream  global_log; //! May be replaced with any ostream object

public:
#//Constants

#//Constructors
    RoadError();
    RoadError(const RoadError &other);  //! Called on throw, generates error_message
    RoadError(int code, const std::string &message);
    RoadError(int code, const char *fmt);
    RoadError(int code, const char *fmt, int d);
    RoadError(int code, const char *fmt, int d, int d2);
    RoadError(int code, const char *fmt, int d, int d2, float f);
    RoadError(int code, const char *fmt, int d, int d2, float f, const char *s);
    RoadError(int code, const char *fmt, int d, int d2, float f, const void *x);
    RoadError(int code, const char *fmt, int d, int d2, float f, int i);
    RoadError(int code, const char *fmt, int d, int d2, float f, long long i);
    RoadError(int code, const char *fmt, int d, int d2, float f, double e);

    RoadError          &operator=(const RoadError &other);
                       ~RoadError() throw() {};

#//Class methods

    static void         clearGlobalLog() { global_log.seekp(0); }
    static bool         emptyGlobalLog() { return global_log.tellp()<=0; }
    static const char  *stringGlobalLog() { return global_log.str().c_str(); }

#//Virtual
    virtual const char *what() const throw();

#//GetSet
    bool                isDefined() const { return log_event.isDefined(); }
    int                 errorCode() const { return error_code; };
   // FIXUP QH11021 should RoadError provide errorMessage().  Currently what()
    RoadLogEvent        roadLogEvent() const { return log_event; };

#//Update
    void                logError() const;
};//class RoadError

}//namespace orgQhull

#//Global functions

inline std::ostream    &operator<<(std::ostream &os, const orgQhull::RoadError &e) { return os << e.what(); }

#endif // ROADERROR_H
qhull-2012.1/src/libqhullcpp/RoadLogEvent.cpp0000644000076400010400000000607511710144466022263 0ustar  bbarberAdministrators/****************************************************************************
**
** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
** $Id: //main/2011/qhull/src/libqhullcpp/RoadLogEvent.cpp#1 $$Change: 1490 $
** $Date: 2012/02/19 $$Author: bbarber $
**
****************************************************************************/

#//! RoadError -- All exceptions thrown by Qhull are RoadErrors

#include "RoadError.h"

#include 
#include 
#include 

using std::cout;
using std::endl;
using std::ostringstream;
using std::string;

#ifdef _MSC_VER  // Microsoft Visual C++ -- warning level 4
#endif

namespace orgQhull {

#//!\name Conversion
string RoadLogEvent::
toString(const char *tag, int code) const
{
    ostringstream os;
    if(tag && code){
        os << tag << code;
        if(format_string){
            os << " ";
        }
    }
    if(!format_string){
        return os.str();
    }
    const char *s= format_string;
    int dCount= 0;  // Count of %d
    int fCount= 0;  // Count of %f
    char extraCode= '\0';
    while(*s){
        if(*s!='%'){
            os << *s++;
        }else{
            char c= *++s;
            s++;
            switch(c){
            case 'd':
                if(++dCount>2){
                    os << " ERROR_three_%d_in_format ";
                }else if(dCount==2){
                    os << int_2;
                }else{
                    os << int_1;
                }
                break;
            case 'e':
                if(firstExtraCode(os, c, &extraCode)){
                    os << double_1;
                }
                break;
            case 'f':
                if(++fCount>1){
                    os << " ERROR_two_%f_in_format ";
                }else{
                    os << float_1;
                }
                break;
            case 'i':
                if(firstExtraCode(os, c, &extraCode)){
                    os << int64_1;
                }
                break;
            case 's':
                if(firstExtraCode(os, c, &extraCode)){
                    os << cstr_1;
                }
                break;
            case 'u':
                if(firstExtraCode(os, c, &extraCode)){
                    os << "0x" << std::hex << int64_1 << std::dec;
                }
                break;
            case 'x':
                if(firstExtraCode(os, c, &extraCode)){
                    os << void_1;
                }
                break;
            case '%':
                os << c;
                break;
            default:
                os << " ERROR_%" << c << "_not_defined_in_format";
                break;
            }
        }
    }
    if(s[-1]!='\n'){
        os << endl;
    }
    return os.str();
}//toString

#//Class helpers (static)

//! True if this char is the first extra code
bool RoadLogEvent::
firstExtraCode(std::ostream &os, char c, char *extraCode){
    if(*extraCode){
        os << " ERROR_%" << *extraCode << "_and_%" << c << "_in_format ";
        return false;
    }
    *extraCode= c;
    return true;
}//firstExtraCode

}//namespace orgQhull

qhull-2012.1/src/libqhullcpp/RoadLogEvent.h0000644000076400010400000000672011710144466021725 0ustar  bbarberAdministrators/****************************************************************************
**
** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
** $Id: //main/2011/qhull/src/libqhullcpp/RoadLogEvent.h#1 $$Change: 1490 $
** $DateTime: 2012/02/19 20:27:01 $$Author: bbarber $
**
****************************************************************************/

#ifndef ROADLOGEVENT_H
#define ROADLOGEVENT_H

#include 
#include 
#include 

namespace orgQhull {

#//Types
    //! RoadLogEvent -- Record an event for the RoadLog
    struct RoadLogEvent;

struct RoadLogEvent {

public:
#//Fields
    const char     *format_string; //! Format string (a literal with format codes, for logging)
    int             int_1;       //! Integer argument (%d, for logging)
    int             int_2;       //! Integer argument (%d, for logging)
    float           float_1;     //! Float argument (%f, for logging)
    union {                      //! One additional argument (for logging)
        const char *cstr_1;      //!   Cstr argument (%s) -- type checked at construct-time
        const void *void_1;      //!   Void* argument (%x) -- Use upper-case codes for object types
        long long   int64_1;     //!   signed int64 (%i).  Ambiguous if unsigned is also defined.
        double      double_1;    //!   Double argument (%e)
    };

#//Constants

#//Constructors
    RoadLogEvent() : format_string(0), int_1(0), int_2(0), float_1(0), int64_1(0) {};
    explicit RoadLogEvent(const char *fmt) : format_string(fmt), int_1(0), int_2(0), float_1(0), int64_1(0) {};
    RoadLogEvent(const char *fmt, int d) : format_string(fmt), int_1(d), int_2(0), float_1(0), int64_1(0) {};
    RoadLogEvent(const char *fmt, int d, int d2) : format_string(fmt), int_1(d), int_2(d2), float_1(0), int64_1(0) {};
    RoadLogEvent(const char *fmt, int d, int d2, float f) : format_string(fmt), int_1(d), int_2(d2), float_1(f), int64_1(0) {};
    RoadLogEvent(const char *fmt, int d, int d2, float f, const char *s) : format_string(fmt), int_1(d), int_2(d2), float_1(f), cstr_1(s) {};
    RoadLogEvent(const char *fmt, int d, int d2, float f, const void *x) : format_string(fmt), int_1(d), int_2(d2), float_1(f), void_1(x) {};
    RoadLogEvent(const char *fmt, int d, int d2, float f, int i) : format_string(fmt), int_1(d), int_2(d2), float_1(f), int64_1(i) {};
    RoadLogEvent(const char *fmt, int d, int d2, float f, long long i) : format_string(fmt), int_1(d), int_2(d2), float_1(f), int64_1(i) {};
    RoadLogEvent(const char *fmt, int d, int d2, float f, double g) : format_string(fmt), int_1(d), int_2(d2), float_1(f), double_1(g) {};
    ~RoadLogEvent() {};
    //! Default copy constructor and assignment

#//GetSet
    bool                isDefined() const { return format_string!=0; }
    int                 int1() const { return int_1; };
    int                 int2() const { return int_2; };
    float               float1() const { return float_1; };
    const char         *format() const { return format_string; };
    const char         *cstr1() const { return cstr_1; };
    const void         *void1() const { return void_1; };
    long long           int64() const { return int64_1; };
    double              double1() const { return double_1; };

#//Conversion

    std::string        toString(const char* tag, int code) const;

private:
#//Class helpers
    static bool         firstExtraCode(std::ostream &os, char c, char *extraCode);


};//class RoadLogEvent

}//namespace orgQhull

#endif // ROADLOGEVENT_H
qhull-2012.1/src/libqhullcpp/UsingLibQhull.cpp0000644000076400010400000002674511710144466022462 0ustar  bbarberAdministrators/****************************************************************************
**
** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
** $Id: //main/2011/qhull/src/libqhullcpp/UsingLibQhull.cpp#4 $$Change: 1464 $
** $DateTime: 2012/01/25 22:58:41 $$Author: bbarber $
**
****************************************************************************/

#//! UsingLibQhull -- Set up qhull C code from C++

#include "Qhull.h"
#include "UsingLibQhull.h"
#include "QhullError.h"
#include "QhullQh.h"

#ifdef _MSC_VER  // Microsoft Visual C++ -- warning level 4
#endif

namespace orgQhull {

#//Class objects

const double UsingLibQhull::
DEFAULTdistanceEpsilon= 1e-15*FACTORepsilon; //! ~DISTround*FACTORepsilon for unit cube

const double UsingLibQhull::
DEFAULTangleEpsilon= 1e-15*FACTORepsilon; //! ~ANGLEround*FACTORepsilon for unit cube

    //! Global pointer to Qhull for qh_fprintf callback and QhullError
Qhull *
s_qhull_output= 0;

double UsingLibQhull::
s_angle_epsilon= 0;

double UsingLibQhull::
s_distance_epsilon= 0;

//! For QhullPoint.id() w/o qhRunId.  Initialized by Qhull
const coordT *UsingLibQhull::
s_points_begin= 0;
const coordT *UsingLibQhull::
s_points_end= 0;
int UsingLibQhull::
s_points_dimension= 0;

int UsingLibQhull::
s_vertex_dimension= 0;  // FIXUP QH11023: s_vertex_dimension is required if dimension>15.  Cannot store in QhullVertex

bool UsingLibQhull::
s_has_points= false;

bool UsingLibQhull::
s_has_angle_epsilon= false;

bool UsingLibQhull::
s_has_vertex_dimension= false;

bool UsingLibQhull::
s_has_distance_epsilon= false;

bool UsingLibQhull::
s_using_libqhull= false;

#//Constructors

//! Grabs global state (qh_qh, qh_qhstat, qhmem.tempstack)
//! Follow immediately with setjmp(qh errexit), otherwise errors in libqhull are not caught properly
//! See qh_restore_qhull [global.c]
UsingLibQhull::
UsingLibQhull(Qhull *q)
: my_qhull(q)
, qh_exitcode(0)
{
    checkUsingLibQhull();
    QhullQh *qhullqh= q->qhullQh();
    if(!qhullqh){
        throw QhullError(10014, "Qhull internal error: Qhull.qhullQh() not defined. initializeQhull() not called.");
    }
    if(qhullqh->run_id != q->qhull_run_id){
        throw QhullError(10015, "Qhull error: QhullQh.runId %d != Qhull.runId %d.  Overwritten?", qhullqh->run_id, q->qhull_run_id);
    }
    // qh.old_qhstat is zero at initialization
    // qh.old_tempstack is zero when empty
    // QhullQh() and UsingLibQhull() are the same
#if qh_QHpointer
    if(qh_qh){
        qh old_qhstat= qh_qhstat;
        qh old_tempstack= qhmem.tempstack;
    }
    qh_qh= qhullqh;
    qh_qhstat= qhullqh->old_qhstat;
    qhmem.tempstack= qhullqh->old_tempstack;
    qhullqh->old_qhstat= 0;
    qhullqh->old_tempstack= 0;
#else
    #error FIXUP QH11024 static qh_qh not tested.  Delete the line to try.
    if(qhullqh!=&qh_qh){
        throw QhullError(10040, "Qhull internal error: Qhull.qhullQh() is not qh_qh (%x, static).  Overwrite?", 0,0,0.0, &qh_qh);
    }
#endif
    s_qhull_output= q;      // set s_qhull_output for qh_fprintf()
    qh NOerrexit= False;   // assumes setjmp called next
}//UsingLibQhull qhull

//! Same as UsingLibQhull but does not throw exceptions
//! !defined() on failure.  For use in destructors
UsingLibQhull::
UsingLibQhull(Qhull *q, int noThrow)
: my_qhull(0)  // Fail by default
, qh_exitcode(0)
{
    QHULL_UNUSED(noThrow);

    QhullQh *qhullqh= q->qhullQh();
    if(s_using_libqhull){
        QhullError e(10050, "Qhull error: UsingLibQhull already in use");
        e.logError();
    }else if(!qhullqh || qhullqh->run_id != q->qhull_run_id){
        QhullError e(10051, "Qhull error: Qhull.qhullQh (%x) undefined or QhullQh.runId %d != Qhull.runId %d.  Overwritten?", (qhullqh ? qhullqh->run_id : -1), q->qhull_run_id, 0.0, qhullqh);
        e.logError();
    }else{
        // qh.old_qhstat is zero at initialization
        // qh.old_tempstack is zero when empty
        // QhullQh() and UsingLibQhull() are the same
#if qh_QHpointer
        if(qh_qh){
            qh old_qhstat= qh_qhstat;
            qh old_tempstack= qhmem.tempstack;
        }
        qh_qh= qhullqh;
        qh_qhstat= qhullqh->old_qhstat;
        qhmem.tempstack= qhullqh->old_tempstack;
        qhullqh->old_qhstat= 0;
        qhullqh->old_tempstack= 0;
#endif
        my_qhull= q;
        s_qhull_output= q;          // set s_qhull_output for qh_fprintf()
        qh NOerrexit= False;   // assumes setjmp called next
    }
}//UsingLibQhull qhull noThrow

//! Reuses current global state (qh_qh) from prior UsingQhull
//! Errors if runId is not the same
UsingLibQhull::
UsingLibQhull(int qhRunId)
: my_qhull(0)
, qh_exitcode(0)
{
    checkUsingLibQhull();
#if qh_QHpointer
    if(!qh_qh || !qh_qhstat){
        throw QhullError(10024, "Qhull error: UsingLibQhull is not active (qh_qh %x or qh_qhstat is not defined)", 0,0,0.0, qh_qh);
    }
#endif
    if(qh run_id!=qhRunId){
        throw QhullError(10036, "Qhull error: qhRunId %d != qh_qh.runId %d.  Is another Qhull active?", qhRunId, qh run_id);
    }
    if(!s_qhull_output){
        throw QhullError(10037, "Qhull error: UsingLibQhull not active(s_qhull_output undefined).  Invoke UsingLibQhull before this call");
    }
    if(s_qhull_output->qhull_run_id!=qhRunId){
        throw QhullError(10046, "Qhull error: qhRunId %d != s_qhull_output.runId %d.  Is another Qhull active", qhRunId, s_qhull_output->qhull_run_id);
    }
    my_qhull= s_qhull_output;
    qh NOerrexit= False;   // assumes setjmp called next
}//UsingLibQhull runId

//Leaves libqhull active for runId access
UsingLibQhull::
~UsingLibQhull()
{
    QhullError e= checkRunId();
    if(e.isDefined()){
        e.logError();
    }else{
#if qh_QHpointer
        if(qh_qh){
            qh NOerrexit= true;
        }
#else
        qh NOerrexit= true;
#endif
    }
    s_using_libqhull= false;
}//~UsingLibQhull

#//Class methods

void UsingLibQhull::
checkQhullMemoryEmpty()
{
    int curlong, totlong, curshort, totshort, maxlong, totbuffer;
    // qh_memtotal does not error
    qh_memtotal(&curlong, &totlong, &curshort, &totshort, &maxlong, &totbuffer);
    if (curlong || totlong){
        throw QhullError(10026, "Qhull error: qhull did not free %d bytes of long memory (%d pieces).", totlong, curlong);
    }
    if (curshort || totshort){
        throw QhullError(10035, "Qhull error: qhull did not free %d bytes of short memory (%d pieces).", totshort, curshort);
    }
}//checkQhullMemoryEmpty

double UsingLibQhull::
currentAngleEpsilon()
{
    if(s_qhull_output && s_qhull_output->initialized()){
        return s_qhull_output->qhullQh()->ANGLEround*FACTORepsilon;
    }else if(s_has_angle_epsilon){
        return s_angle_epsilon;
    }
    return UsingLibQhull::DEFAULTangleEpsilon;
}//currentAngleEpsilon

double UsingLibQhull::
currentDistanceEpsilon()
{
    if(s_qhull_output && s_qhull_output->initialized()){
        return s_qhull_output->qhullQh()->DISTround*FACTORepsilon;
    }else if(s_has_distance_epsilon){
        return s_distance_epsilon;
    }
    return UsingLibQhull::DEFAULTdistanceEpsilon;
}//currentDistanceEpsilon

const coordT *UsingLibQhull::
currentPoints(int *dimension, const coordT **pointsEnd)
{
    if(s_qhull_output && s_qhull_output->initialized()){
        *dimension= qh hull_dim;
        *pointsEnd= qh first_point+qh num_points*qh hull_dim;
        return qh first_point;
    }else if(s_has_points){
        *dimension= s_points_dimension;
        *pointsEnd= s_points_end;
        return s_points_begin;
    }
    throw QhullError(10059, "Qhull error: missing definition for currentPoints().  Need currentQhull() or setGlobalDistanceEpsilon()");
}//currentPoints

Qhull &UsingLibQhull::
currentQhull()
{
    if(!s_qhull_output){
        throw QhullError(10055, "Qhull error: currentQhull not defined.  Run qhull first.");
    }
    return *s_qhull_output;
}//currentQhull

// for QhullVertex::dimension() when >= 16
int UsingLibQhull::
currentVertexDimension()
{
    if(s_qhull_output && s_qhull_output->initialized()){
        return s_qhull_output->dimension();
    }else if(s_has_vertex_dimension){
        return s_vertex_dimension;
    }
    throw QhullError(10057, "Qhull error: missing definition for currentVertexDimension().  Need currentQhull() or setGlobalVertexDimension()");
}//currentVertexDimension

const coordT *UsingLibQhull::
globalPoints(int *dimension, const coordT **pointsEnd)
{
    if(s_has_points){
        *dimension= s_points_dimension;
        *pointsEnd= s_points_end;
        return s_points_begin;
    }else{
        return currentPoints(dimension, pointsEnd);
    }
}//globalPoints

bool UsingLibQhull::
hasPoints()
{
    return s_has_points || (s_qhull_output && s_qhull_output->initialized());
}

bool UsingLibQhull::
hasVertexDimension()
{
    return s_has_vertex_dimension || (s_qhull_output && s_qhull_output->initialized());
}

void UsingLibQhull::
setGlobals()
{
    if(s_qhull_output && s_qhull_output->initialized()){
        QhullQh *qqh= s_qhull_output->qhullQh();
        s_angle_epsilon= qqh->ANGLEround*FACTORepsilon;
        s_distance_epsilon= qqh->DISTround*FACTORepsilon;
        s_points_begin= qqh->first_point;
        s_points_dimension= qqh->hull_dim;
        s_points_end= s_points_begin+qqh->num_points*s_points_dimension;
        s_vertex_dimension= qqh->hull_dim;
        s_has_angle_epsilon= true;
        s_has_distance_epsilon= true;
        s_has_points= true;
        s_has_vertex_dimension= true;
    }else{
        throw QhullError(10058, "Qhull error: setGlobals can only be called for currentQhull().  Run qhull first.");
    }
 }//setGlobals

void UsingLibQhull::
unsetGlobals()
{
    s_has_angle_epsilon= false;
    s_has_distance_epsilon= false;
    s_has_points= false;
    s_has_vertex_dimension= false;
}//unsetGlobals

#// Methods

void UsingLibQhull::
maybeThrowQhullMessage(int exitCode) const
{
    my_qhull->maybeThrowQhullMessage(exitCode);
    QhullError e= checkRunId(); // Check for qhRunId after libqhull returns. For convenience, ought to be at end of libqhull try block
    if(e.isDefined()){
        throw e;
    }
}//maybeThrowQhullMessage

void UsingLibQhull::
maybeThrowQhullMessage(int exitCode, int noThrow) const
{
    my_qhull->maybeThrowQhullMessage(exitCode, noThrow);
    QhullError e= checkRunId(); // Check for qhRunId after libqhull returns. For convenience, ought to be at end of libqhull try block
    if(e.isDefined()){
        e.logError();
    }
}//maybeThrowQhullMessage

#//Helpers

//! Return QhullError for maybeThrowFromDestructor()
QhullError UsingLibQhull::
checkRunId() const
{
    // Predeclaring QhullError results in four copy constructors, none used here
#if qh_QHpointer
    if(qh_qh){ // 0 if ~Qhull
        if(my_qhull->qhull_run_id!=qh run_id){
            return QhullError(10047, "Qhull internal error: Global state (qh_qh, run_id %d) changed.  Should be runId %d.  Another thread?", qh run_id, my_qhull->qhull_run_id);
        }
    }
#else
    if(qh run_id!=0 && my_qhull->qhull_run_id!=qh run_id){
        return QhullError(10048, "Qhull internal error: Global state (qh_qh, run_id %d) changed.  Should be runId %d.  Another thread?", qh run_id, my_qhull->qhull_run_id);
    }
#endif
    return QhullError();
}//checkRunId

//! Can not embed UsingLibQhull.  Otherwise allocated a C++ object missed by qh_errexit
void UsingLibQhull::
checkUsingLibQhull() const
{
    if(s_using_libqhull){
        if(s_qhull_output){
            throw QhullError(10049, "Qhull error: UsingLibQhull already in use by QhullQh.runId %d", s_qhull_output->qhull_run_id);
        }else{
            throw QhullError(10050, "Qhull error: UsingLibQhull already in use.  No s_qhull_output");
        }
    }
    s_using_libqhull= true;
}//checkUsingLibQhull

}//namespace orgQhull

qhull-2012.1/src/libqhullcpp/UsingLibQhull.h0000644000076400010400000001403411710144466022113 0ustar  bbarberAdministrators/****************************************************************************
**
** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
** $Id: //main/2011/qhull/src/libqhullcpp/UsingLibQhull.h#6 $$Change: 1464 $
** $DateTime: 2012/01/25 22:58:41 $$Author: bbarber $
**
****************************************************************************/

#ifndef USINGlibqhull_H
#define USINGlibqhull_H

#include "QhullError.h"
extern "C" {
#include "libqhull/libqhull.h"
}

namespace orgQhull {

#//Types
    //! UsingLibQhull -- Interface into libqhull and its 'qh' and 'qhstat' macros
    //! Always use with setjmp() for libqhull error handling.

/*******************************

UsingLibQhull is stack based, but as a call
Qhull declarations are stack-based.  But can't define a
setjmp environment, since the target goes away.  So must be UsingLibQhull, but can only have one
setjmp at a time? Can embedded another Using as long as save/restore
longjmp on exit.
*/
    class UsingLibQhull;

    // Defined elsewhere
    class Qhull;

#// Global variables
extern Qhull           *s_qhull_output; //! Provide qh_fprintf (Qhull.cpp) access to Qhull

class UsingLibQhull {

private:
#//Fields
    Qhull              *my_qhull;
    int                 qh_exitcode;

#//Class globals
    //! Global flags
    static bool         s_using_libqhull; //! True if UsingLibQhull is in scope

    //! Use global values if s_has_... is set
    static bool         s_has_angle_epsilon; //! True if s_angle_epsilon defined
    static bool         s_has_distance_epsilon; //! True if s_distance_epsilon defined
    static bool         s_has_points;        //! If False (default), Qhull() runs setPointBase()
    static bool         s_has_vertex_dimension; //! True if s_vertex_dimension defined

    //! Global values
    static double       s_angle_epsilon;   //! Epsilon for angle equality
    static double       s_distance_epsilon;   //! Epsilon for distance equality
    static const coordT *s_points_begin;            //! For QhullPoint::id() w/o qhRunId.
    static const coordT *s_points_end;            //! For QhullPoint::id() w/o qhRunId.
    static int          s_points_dimension;
    static int          s_vertex_dimension; //! Default dimension (e.g., if Vertex::dimension() >= 16)

public:
#//Class constants
    static const int    NOqhRunId= 0;   //! qh_qh is not available
    static const int    NOthrow= 1;     //! Do not throw from maybeThrowQhullMessage
    static const int    FACTORepsilon= 10;  //!
    static const double DEFAULTdistanceEpsilon; //! ~DISTround*FACTORepsilon for unit cube
    static const double DEFAULTangleEpsilon;    //! ~ANGLEround*FACTORepsilon for unit cube

#//Class members
    static void         checkQhullMemoryEmpty();
    static double       currentAngleEpsilon();
    static double       currentDistanceEpsilon();
    static const coordT *currentPoints(int *dimension, const coordT **pointsEnd);
    static Qhull       ¤tQhull();
    static int          currentVertexDimension();
    static double       globalAngleEpsilon() { return s_has_angle_epsilon ? s_angle_epsilon : currentAngleEpsilon(); }
    static double       globalDistanceEpsilon() { return s_has_distance_epsilon ? s_distance_epsilon : currentDistanceEpsilon(); }
    static double       globalMachineEpsilon() { return REALepsilon; }
    static const coordT *globalPoints(int *dimension, const coordT **pointsEnd);
    static int          globalVertexDimension() { return s_has_vertex_dimension ? s_vertex_dimension : currentVertexDimension(); }
    static bool         hasPoints();        // inline would require Qhull.h
    static bool         hasVertexDimension();
    static void         setGlobalAngleEpsilon(double d) { s_angle_epsilon=d; s_has_angle_epsilon= true; }
    static void         setGlobalDistanceEpsilon(double d) { s_distance_epsilon= d; s_has_distance_epsilon= true; }
    static void         setGlobalPoints(int dimension, const coordT *pointsBegin, const coordT *pointsEnd) { s_points_dimension= dimension; s_points_begin= pointsBegin; s_points_end= pointsEnd; s_has_points= true; }
    static void         setGlobalVertexDimension(int i) { s_vertex_dimension= i; s_has_vertex_dimension= true; }
    static void         setGlobals();
    static void         unsetGlobalAngleEpsilon() { s_has_angle_epsilon= false; }
    static void         unsetGlobalDistanceEpsilon() { s_has_distance_epsilon= false; }
    static void         unsetGlobalPoints() { s_has_points= false; }
    static void         unsetGlobalVertexDimension() { s_has_vertex_dimension= false; }
    static void         unsetGlobals();

#//Constructors
                        UsingLibQhull(Qhull *p);
                        UsingLibQhull(Qhull *p, int noThrow);
                        UsingLibQhull(int qhRunId);
                       ~UsingLibQhull();

private:                //! disable default constructor, copy constructor, and copy assignment
                        UsingLibQhull();
                        UsingLibQhull(const UsingLibQhull &);
   UsingLibQhull       &operator=(const UsingLibQhull &);
public:

#//Methods
#//Access
    bool                defined() const { return my_qhull!=0; }
    void                maybeThrowQhullMessage(int exitCode) const;
    void                maybeThrowQhullMessage(int exitCode, int noThrow) const;

#//Helpers
private:
   QhullError           checkRunId() const;
   void                 checkUsingLibQhull() const;

/***********************************
You may use global variables in 'qh' after declaring UsingLibQhull.  For example

  UsingLibQhull q(qhRunId);
  // NOerrors -- no calls that throw libqhull errors
  cout << "Delaunay Mode: " << qh DELAUNAY;

To trap errors from libqhull, UsingLibQhull must be followed by

UsingLibQhull q(qhRunId);
int exitCode = setjmp(qh errexit);
if(!exitCode){ // no object creation -- destructors skipped on longjmp()
    calls to libqhull
}
q.maybeThrowQhullMessage(exitCode);

The call to setjmp() can not be moved to a method.  The stack must be preserved for error exits from libqhull.

*/

};//UsingLibQhull

}//namespace orgQhull

#endif // USINGlibqhull_H
qhull-2012.1/src/libqhullp/0000755000076400010400000000000011721063454016672 5ustar  bbarberAdministratorsqhull-2012.1/src/libqhullp/libqhullp.pro0000644000076400010400000000130511720334706021407 0ustar  bbarberAdministrators# -------------------------------------------------
# libqhull.pro -- Qt project for Qhull shared library with qh_QHpointer
#   Built with qh_QHpointer=1
# -------------------------------------------------

include(../qhull-warn.pri)
include(../qhull-libqhull-src.pri)

DESTDIR = ../../lib
DLLDESTDIR = ../../bin
TEMPLATE = lib
CONFIG += shared warn_on
CONFIG -= qt

build_pass:CONFIG(debug, debug|release):{
    TARGET = qhull_pd
    OBJECTS_DIR = Debug
}else:build_pass:CONFIG(release, debug|release):{
    TARGET = qhull_p
    OBJECTS_DIR = Release
}
win32-msvc* : QMAKE_LFLAGS += /INCREMENTAL:NO
win32-msvc* : DEF_FILE += ../../src/libqhullp/qhull_p-exports.def

DEFINES += qh_QHpointer # libqhull/user.h
qhull-2012.1/src/libqhullp/qhull_p-exports.def0000644000076400010400000001650011707662251022526 0ustar  bbarberAdministrators; qhull_p-exports.def -- msvc module-definition file
;
;   Generated from depends.exe by cut-and-paste of exported symbols by mingw gcc
;   [mar'11] 399 symbols 
;   Annotate as DATA qh_qh qh_qhstat qhmem qhull_inuse rbox_inuse
;
; $Id: //main/2011/qhull/src/libqhull/qhull-exports.def#2 $$Change: 1368 $
; $DateTime: 2011/04/16 08:12:32 $$Author: bbarber $
;
; Define qhull_VERSION in CMakeLists.txt, Makefile, qhull-exports.def, qhull_p-exports.def, and qhull-warn.pri
VERSION 6.3
EXPORTS
dfacet
dvertex
out1
out2n
out3n
qh_addhash
qh_addpoint
qh_all_merges
qh_allstatA
qh_allstatB
qh_allstatC
qh_allstatD
qh_allstatE
qh_allstatE2
qh_allstatF
qh_allstatG
qh_allstatH
qh_allstatI
qh_allstatistics
qh_appendfacet
qh_appendmergeset
qh_appendprint
qh_appendvertex
qh_argv_to_command
qh_argv_to_command_size
qh_attachnewfacets
qh_backnormal
qh_basevertices
qh_build_withrestart
qh_buildhull
qh_buildtracing
qh_check_bestdist
qh_check_maxout
qh_check_output
qh_check_point
qh_check_points
qh_checkconnect
qh_checkconvex
qh_checkfacet
qh_checkflags
qh_checkflipped
qh_checkflipped_all
qh_checkpolygon
qh_checkvertex
qh_checkzero
qh_clear_outputflags
qh_clearcenters
qh_clock
qh_collectstatistics
qh_compare_facetarea
qh_compare_facetmerge
qh_compare_facetvisit
qh_compare_vertexpoint
qh_compareangle
qh_comparemerge
qh_comparevisit
qh_copyfilename
qh_copynonconvex
qh_copypoints
qh_countfacets
qh_createsimplex
qh_crossproduct
qh_degen_redundant_facet
qh_degen_redundant_neighbors
qh_deletevisible
qh_delfacet
qh_delridge
qh_delvertex
qh_determinant
qh_detjoggle
qh_detroundoff
qh_detsimplex
qh_detvnorm
qh_detvridge
qh_detvridge3
qh_distnorm
qh_distplane
qh_distround
qh_divzero
qh_eachvoronoi
qh_eachvoronoi_all
qh_errexit
qh_errexit2
qh_errexit_rbox
qh_errprint
qh_exit
qh_facet2point
qh_facet3vertex
qh_facetarea
qh_facetarea_simplex
qh_facetcenter
qh_facetintersect
qh_facetvertices
qh_find_newvertex
qh_findbest
qh_findbest_test
qh_findbestfacet
qh_findbesthorizon
qh_findbestlower
qh_findbestneighbor
qh_findbestnew
qh_findfacet_all
qh_findgood
qh_findgood_all
qh_findgooddist
qh_findhorizon
qh_flippedmerges
qh_forcedmerges
qh_fprintf
qh_fprintf_rbox
qh_free
qh_freebuffers
qh_freebuild
qh_freeqhull
qh_freeqhull2
qh_freestatistics
qh_furthestnext
qh_furthestout
qh_gausselim
qh_geomplanes
qh_getangle
qh_getarea
qh_getcenter
qh_getcentrum
qh_getdistance
qh_gethash
qh_getmergeset
qh_getmergeset_initial
qh_gram_schmidt
qh_hashridge
qh_hashridge_find
qh_infiniteloop
qh_init_A
qh_init_B
qh_init_qhull_command
qh_initbuild
qh_initflags
qh_initialhull
qh_initialvertices
qh_initqhull_buffers
qh_initqhull_globals
qh_initqhull_mem
qh_initqhull_outputflags
qh_initqhull_start
qh_initqhull_start2
qh_initstatistics
qh_initthresholds
qh_inthresholds
qh_isvertex
qh_joggleinput
qh_makenew_nonsimplicial
qh_makenew_simplicial
qh_makenewfacet
qh_makenewfacets
qh_makenewplanes
qh_makeridges
qh_malloc
qh_mark_dupridges
qh_markkeep
qh_markvoronoi
qh_matchduplicates
qh_matchneighbor
qh_matchnewfacets
qh_matchvertices
qh_maxabsval
qh_maxmin
qh_maxouter
qh_maxsimplex
qh_maydropneighbor
qh_memalloc
qh_memfree
qh_memfreeshort
qh_meminit
qh_meminitbuffers
qh_memsetup
qh_memsize
qh_memstatistics
qh_memtotal
qh_merge_degenredundant
qh_merge_nonconvex
qh_mergecycle
qh_mergecycle_all
qh_mergecycle_facets
qh_mergecycle_neighbors
qh_mergecycle_ridges
qh_mergecycle_vneighbors
qh_mergefacet
qh_mergefacet2d
qh_mergeneighbors
qh_mergeridges
qh_mergesimplex
qh_mergevertex_del
qh_mergevertex_neighbors
qh_mergevertices
qh_minabsval
qh_mindiff
qh_nearcoplanar
qh_nearvertex
qh_neighbor_intersections
qh_new_qhull
qh_newfacet
qh_newhashtable
qh_newridge
qh_newstats
qh_newvertex
qh_newvertices
qh_nextfurthest
qh_nextridge3d
qh_normalize
qh_normalize2
qh_nostatistic
qh_option
qh_order_vertexneighbors
qh_orientoutside
qh_outcoplanar
qh_outerinner
qh_partitionall
qh_partitioncoplanar
qh_partitionpoint
qh_partitionvisible
qh_point
qh_point_add
qh_pointdist
qh_pointfacet
qh_pointid
qh_pointvertex
qh_postmerge
qh_precision
qh_premerge
qh_prepare_output
qh_prependfacet
qh_printafacet
qh_printallstatistics
qh_printbegin
qh_printcenter
qh_printcentrum
qh_printend
qh_printend4geom
qh_printextremes
qh_printextremes_2d
qh_printextremes_d
qh_printfacet
qh_printfacet2geom
qh_printfacet2geom_points
qh_printfacet2math
qh_printfacet3geom_nonsimplicial
qh_printfacet3geom_points
qh_printfacet3geom_simplicial
qh_printfacet3math
qh_printfacet3vertex
qh_printfacet4geom_nonsimplicial
qh_printfacet4geom_simplicial
qh_printfacetNvertex_nonsimplicial
qh_printfacetNvertex_simplicial
qh_printfacetheader
qh_printfacetlist
qh_printfacetridges
qh_printfacets
qh_printhashtable
qh_printhelp_degenerate
qh_printhelp_narrowhull
qh_printhelp_singular
qh_printhyperplaneintersection
qh_printline3geom
qh_printlists
qh_printmatrix
qh_printneighborhood
qh_printpoint
qh_printpoint3
qh_printpointid
qh_printpoints
qh_printpoints_out
qh_printpointvect
qh_printpointvect2
qh_printridge
qh_printspheres
qh_printstatistics
qh_printstatlevel
qh_printstats
qh_printsummary
qh_printvdiagram
qh_printvdiagram2
qh_printvertex
qh_printvertexlist
qh_printvertices
qh_printvneighbors
qh_printvnorm
qh_printvoronoi
qh_printvridge
qh_produce_output
qh_produce_output2
qh_projectdim3
qh_projectinput
qh_projectpoint
qh_projectpoints
; Mark as DATA, otherwise links a separate qh_qh.  Requires __dcelspec
qh_qh               DATA
qh_qhstat           DATA
qh_qhull
qh_rand
qh_rand_seed
qh_randomfactor
qh_randommatrix
qh_rboxpoints
qh_readfeasible
qh_readpoints
qh_reducevertices
qh_redundant_vertex
qh_remove_extravertices
qh_removefacet
qh_removevertex
qh_rename_sharedvertex
qh_renameridgevertex
qh_renamevertex
qh_resetlists
qh_restore_qhull
qh_rotateinput
qh_rotatepoints
qh_save_qhull
qh_scaleinput
qh_scalelast
qh_scalepoints
qh_setaddnth
qh_setaddsorted
qh_setappend
qh_setappend2ndlast
qh_setappend_set
qh_setcheck
qh_setcompact
qh_setcopy
qh_setdel
qh_setdelaunay
qh_setdellast
qh_setdelnth
qh_setdelnthsorted
qh_setdelsorted
qh_setduplicate
qh_setequal
qh_setequal_except
qh_setequal_skip
qh_setfacetplane
qh_setfeasible
qh_setfree
qh_setfree2
qh_setfreelong
qh_sethalfspace
qh_sethalfspace_all
qh_sethyperplane_det
qh_sethyperplane_gauss
qh_setin
qh_setindex
qh_setlarger
qh_setlast
qh_setnew
qh_setnew_delnthsorted
qh_setprint
qh_setreplace
qh_setsize
qh_settemp
qh_settempfree
qh_settempfree_all
qh_settemppop
qh_settemppush
qh_settruncate
qh_setunique
qh_setvoronoi_all
qh_setzero
qh_sharpnewfacets
qh_skipfacet
qh_skipfilename
qh_srand
qh_stddev
qh_strtod
qh_strtol
qh_test_appendmerge
qh_test_vneighbors
qh_tracemerge
qh_tracemerging
qh_triangulate
qh_triangulate_facet
qh_triangulate_link
qh_triangulate_mirror
qh_triangulate_null
qh_updatetested
qh_updatevertices
qh_user_memsizes
qh_version
qh_vertexintersect
qh_vertexintersect_new
qh_vertexneighbors
qh_vertexridges
qh_vertexridges_facet
qh_vertexsubset
qh_voronoi_center
qh_willdelete
; Mark as DATA, otherwise links a separate qhmem.  Requires __dcelspec
qhmem                   DATA
qhull_inuse             DATA
rbox
rbox_inuse              DATA
roundi
qhull-2012.1/src/libqhullstatic/0000755000076400010400000000000011721063454017722 5ustar  bbarberAdministratorsqhull-2012.1/src/libqhullstatic/libqhullstatic.pro0000644000076400010400000000104611710650027023465 0ustar  bbarberAdministrators# -------------------------------------------------
# libqhullstatic.pro -- Qt project for Qhull static library
#   Built with qh_QHpointer=0.  See libqhullp.pro
# -------------------------------------------------

include(../qhull-warn.pri)
include(../qhull-libqhull-src.pri)

DESTDIR = ../../lib
TEMPLATE = lib
CONFIG += staticlib warn_on
CONFIG -= qt
build_pass:CONFIG(debug, debug|release):{
    TARGET = qhullstatic_d
    OBJECTS_DIR = Debug
}else:build_pass:CONFIG(release, debug|release):{
    TARGET = qhullstatic
    OBJECTS_DIR = Release
}
qhull-2012.1/src/libqhullstaticp/0000755000076400010400000000000011721063454020102 5ustar  bbarberAdministratorsqhull-2012.1/src/libqhullstaticp/libqhullstaticp.pro0000644000076400010400000000104711710650041024022 0ustar  bbarberAdministrators# -------------------------------------------------
# libqhullstaticp.pro -- Qhull static library with qh_qhPointer
# -------------------------------------------------

include(../qhull-warn.pri)
include(../qhull-libqhull-src.pri)

DESTDIR = ../../lib
TEMPLATE = lib
CONFIG += staticlib warn_on
CONFIG -= qt
build_pass:CONFIG(debug, debug|release) {
    TARGET = qhullstatic_pd
    OBJECTS_DIR = Debug
}else:build_pass:CONFIG(release, debug|release) {
    TARGET = qhullstatic_p
    OBJECTS_DIR = Release
}

DEFINES += qh_QHpointer # libqhull/user.h

qhull-2012.1/src/qconvex/0000755000076400010400000000000011721063454016361 5ustar  bbarberAdministratorsqhull-2012.1/src/qconvex/qconvex.c0000644000076400010400000003011311710144464020205 0ustar  bbarberAdministrators/*
  ---------------------------------

   qconvex.c
      compute convex hulls using qhull

   see unix.c for full interface

   Copyright (c) 1993-2012, The Geometry Center
*/

#include 
#include 
#include 
#include 
#include 
#include "libqhull.h"
#include "mem.h"
#include "qset.h"

#if __MWERKS__ && __POWERPC__
#include 
#include 
#include 
#include 

#elif __cplusplus
extern "C" {
  int isatty(int);
}

#elif _MSC_VER
#include 
#define isatty _isatty
int _isatty(int);

#else
int isatty(int);  /* returns 1 if stdin is a tty
                   if "Undefined symbol" this can be deleted along with call in main() */
#endif

/*---------------------------------

  qh_prompt
    long prompt for qconvex

  notes:
    restricted version of libqhull.c

  see:
    concise prompt below
*/

/* duplicated in qconvex.htm */
char hidden_options[]=" d v H Qbb Qf Qg Qm Qr Qu Qv Qx Qz TR E V Fp Gt Q0 Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 ";

char qh_prompta[]= "\n\
qconvex- compute the convex hull\n\
    http://www.qhull.org  %s\n\
\n\
input (stdin):\n\
    first lines: dimension and number of points (or vice-versa).\n\
    other lines: point coordinates, best if one point per line\n\
    comments:    start with a non-numeric character\n\
\n\
options:\n\
    Qt   - triangulated output\n\
    QJ   - joggled input instead of merged facets\n\
    Qc   - keep coplanar points with nearest facet\n\
    Qi   - keep interior points with nearest facet\n\
\n\
Qhull control options:\n\
    Qbk:n   - scale coord k so that low bound is n\n\
      QBk:n - scale coord k so that upper bound is n (QBk is %2.2g)\n\
    QbB  - scale input to unit cube centered at the origin\n\
    Qbk:0Bk:0 - remove k-th coordinate from input\n\
    QJn  - randomly joggle input in range [-n,n]\n\
    QRn  - random rotation (n=seed, n=0 time, n=-1 time/no rotate)\n\
%s%s%s%s";  /* split up qh_prompt for Visual C++ */
char qh_promptb[]= "\
    Qs   - search all points for the initial simplex\n\
    QGn  - good facet if visible from point n, -n for not visible\n\
    QVn  - good facet if it includes point n, -n if not\n\
\n\
";
char qh_promptc[]= "\
Trace options:\n\
    T4   - trace at level n, 4=all, 5=mem/gauss, -1= events\n\
    Tc   - check frequently during execution\n\
    Ts   - print statistics\n\
    Tv   - verify result: structure, convexity, and point inclusion\n\
    Tz   - send all output to stdout\n\
    TFn  - report summary when n or more facets created\n\
    TI file - input data from file, no spaces or single quotes\n\
    TO file - output results to file, may be enclosed in single quotes\n\
    TPn  - turn on tracing when point n added to hull\n\
     TMn - turn on tracing at merge n\n\
     TWn - trace merge facets when width > n\n\
    TVn  - stop qhull after adding point n, -n for before (see TCn)\n\
     TCn - stop qhull after building cone for point n (see TVn)\n\
\n\
Precision options:\n\
    Cn   - radius of centrum (roundoff added).  Merge facets if non-convex\n\
     An  - cosine of maximum angle.  Merge facets if cosine > n or non-convex\n\
           C-0 roundoff, A-0.99/C-0.01 pre-merge, A0.99/C0.01 post-merge\n\
    Rn   - randomly perturb computations by a factor of [1-n,1+n]\n\
    Un   - max distance below plane for a new, coplanar point\n\
    Wn   - min facet width for outside point (before roundoff)\n\
\n\
Output formats (may be combined; if none, produces a summary to stdout):\n\
    f    - facet dump\n\
    G    - Geomview output (see below)\n\
    i    - vertices incident to each facet\n\
    m    - Mathematica output (2-d and 3-d)\n\
    n    - normals with offsets\n\
    o    - OFF file format (dim, points and facets; Voronoi regions)\n\
    p    - point coordinates \n\
    s    - summary (stderr)\n\
\n\
";
char qh_promptd[]= "\
More formats:\n\
    Fa   - area for each facet\n\
    FA   - compute total area and volume for option 's'\n\
    Fc   - count plus coplanar points for each facet\n\
           use 'Qc' (default) for coplanar and 'Qi' for interior\n\
    FC   - centrum for each facet\n\
    Fd   - use cdd format for input (homogeneous with offset first)\n\
    FD   - use cdd format for numeric output (offset first)\n\
    FF   - facet dump without ridges\n\
    Fi   - inner plane for each facet\n\
    FI   - ID for each facet\n\
    Fm   - merge count for each facet (511 max)\n\
    Fn   - count plus neighboring facets for each facet\n\
    FN   - count plus neighboring facets for each point\n\
    Fo   - outer plane (or max_outside) for each facet\n\
    FO   - options and precision constants\n\
    FP   - nearest vertex for each coplanar point\n\
    FQ   - command used for qconvex\n\
    Fs   - summary: #int (8), dimension, #points, tot vertices, tot facets,\n\
                      for output: #vertices, #facets,\n\
                                  #coplanar points, #non-simplicial facets\n\
                    #real (2), max outer plane, min vertex\n\
    FS   - sizes:   #int (0) \n\
                    #real (2) tot area, tot volume\n\
    Ft   - triangulation with centrums for non-simplicial facets (OFF format)\n\
    Fv   - count plus vertices for each facet\n\
    FV   - average of vertices (a feasible point for 'H')\n\
    Fx   - extreme points (in order for 2-d)\n\
\n\
";
char qh_prompte[]= "\
Geomview output (2-d, 3-d, and 4-d)\n\
    Ga   - all points as dots\n\
     Gp  -  coplanar points and vertices as radii\n\
     Gv  -  vertices as spheres\n\
    Gi   - inner planes only\n\
     Gn  -  no planes\n\
     Go  -  outer planes only\n\
    Gc   - centrums\n\
    Gh   - hyperplane intersections\n\
    Gr   - ridges\n\
    GDn  - drop dimension n in 3-d and 4-d output\n\
\n\
Print options:\n\
    PAn  - keep n largest facets by area\n\
    Pdk:n - drop facet if normal[k] <= n (default 0.0)\n\
    PDk:n - drop facet if normal[k] >= n\n\
    Pg   - print good facets (needs 'QGn' or 'QVn')\n\
    PFn  - keep facets whose area is at least n\n\
    PG   - print neighbors of good facets\n\
    PMn  - keep n facets with most merges\n\
    Po   - force output.  If error, output neighborhood of facet\n\
    Pp   - do not report precision problems\n\
\n\
    .    - list of all options\n\
    -    - one line descriptions of all options\n\
";
/* for opts, don't assign 'e' or 'E' to a flag (already used for exponent) */

/*---------------------------------

  qh_prompt2
    synopsis for qhull
*/
char qh_prompt2[]= "\n\
qconvex- compute the convex hull.  Qhull %s\n\
    input (stdin): dimension, number of points, point coordinates\n\
    comments start with a non-numeric character\n\
\n\
options (qconvex.htm):\n\
    Qt   - triangulated output\n\
    QJ   - joggled input instead of merged facets\n\
    Tv   - verify result: structure, convexity, and point inclusion\n\
    .    - concise list of all options\n\
    -    - one-line description of all options\n\
\n\
output options (subset):\n\
    s    - summary of results (default)\n\
    i    - vertices incident to each facet\n\
    n    - normals with offsets\n\
    p    - vertex coordinates (includes coplanar points if 'Qc')\n\
    Fx   - extreme points (convex hull vertices)\n\
    FA   - report total area and volume\n\
    FS   - compute total area and volume\n\
    o    - OFF format (dim, n, points, facets)\n\
    G    - Geomview output (2-d, 3-d, and 4-d)\n\
    m    - Mathematica output (2-d and 3-d)\n\
    QVn  - print facets that include point n, -n if not\n\
    TO file- output results to file, may be enclosed in single quotes\n\
\n\
examples:\n\
    rbox c D2 | qconvex s n                    rbox c D2 | qconvex i\n\
    rbox c D2 | qconvex o                      rbox 1000 s | qconvex s Tv FA\n\
    rbox c d D2 | qconvex s Qc Fx              rbox y 1000 W0 | qconvex s n\n\
    rbox y 1000 W0 | qconvex s QJ              rbox d G1 D12 | qconvex QR0 FA Pp\n\
    rbox c D7 | qconvex FA TF1000\n\
\n\
";
/* for opts, don't assign 'e' or 'E' to a flag (already used for exponent) */

/*---------------------------------

  qh_prompt3
    concise prompt for qhull
*/
char qh_prompt3[]= "\n\
Qhull %s.\n\
Except for 'F.' and 'PG', upper-case options take an argument.\n\
\n\
 incidences     mathematica    normals        OFF_format     points\n\
 summary        facet_dump\n\
\n\
 Farea          FArea_total    Fcoplanars     FCentrums      Fd_cdd_in\n\
 FD_cdd_out     FFacet_xridge  Finner         FIDs           Fmerges\n\
 Fneighbors     FNeigh_vertex  Fouter         FOptions       FPoint_near\n\
 FQhull         Fsummary       FSize          Fvertices      FVertex_ave\n\
 Fxtremes       FMaple\n\
\n\
 Gvertices      Gpoints        Gall_points    Gno_planes     Ginner\n\
 Gcentrums      Ghyperplanes   Gridges        Gouter         GDrop_dim\n\
\n\
 PArea_keep     Pdrop d0:0D0   PFacet_area_keep Pgood        PGood_neighbors\n\
 PMerge_keep    Poutput_forced Pprecision_not\n\
\n\
 QbBound 0:0.5  QbB_scale_box  Qcoplanar      QGood_point    Qinterior\n\
 QJoggle        Qrandom        QRotate        Qsearch_1st    Qtriangulate\n\
 QVertex_good\n\
\n\
 T4_trace       Tcheck_often   Tstatistics    Tverify        Tz_stdout\n\
 TFacet_log     TInput_file    TPoint_trace   TMerge_trace   TOutput_file\n\
 TWide_trace    TVertex_stop   TCone_stop\n\
\n\
 Angle_max      Centrum_size   Random_dist    Ucoplanar_max  Wide_outside\n\
";

/*---------------------------------

  main( argc, argv )
    processes the command line, calls qhull() to do the work, and exits

  design:
    initializes data structures
    reads points
    finishes initialization
    computes convex hull and other structures
    checks the result
    writes the output
    frees memory
*/
int main(int argc, char *argv[]) {
  int curlong, totlong; /* used !qh_NOmem */
  int exitcode, numpoints, dim;
  coordT *points;
  boolT ismalloc;

#if __MWERKS__ && __POWERPC__
  char inBuf[BUFSIZ], outBuf[BUFSIZ], errBuf[BUFSIZ];
  SIOUXSettings.showstatusline= false;
  SIOUXSettings.tabspaces= 1;
  SIOUXSettings.rows= 40;
  if (setvbuf(stdin, inBuf, _IOFBF, sizeof(inBuf)) < 0   /* w/o, SIOUX I/O is slow*/
  || setvbuf(stdout, outBuf, _IOFBF, sizeof(outBuf)) < 0
  || (stdout != stderr && setvbuf(stderr, errBuf, _IOFBF, sizeof(errBuf)) < 0))
    fprintf(stderr, "qhull internal warning (main): could not change stdio to fully buffered.\n");
  argc= ccommand(&argv);
#endif

  if ((argc == 1) && isatty( 0 /*stdin*/)) {
    fprintf(stdout, qh_prompt2, qh_version);
    exit(qh_ERRnone);
  }
  if (argc > 1 && *argv[1] == '-' && !*(argv[1]+1)) {
    fprintf(stdout, qh_prompta, qh_version, qh_DEFAULTbox,
                qh_promptb, qh_promptc, qh_promptd, qh_prompte);
    exit(qh_ERRnone);
  }
  if (argc >1 && *argv[1] == '.' && !*(argv[1]+1)) {
    fprintf(stdout, qh_prompt3, qh_version);
    exit(qh_ERRnone);
  }
  qh_init_A(stdin, stdout, stderr, argc, argv);  /* sets qh qhull_command */
  exitcode= setjmp(qh errexit); /* simple statement for CRAY J916 */
  if (!exitcode) {
    qh_checkflags(qh qhull_command, hidden_options);
    qh_initflags(qh qhull_command);
    points= qh_readpoints(&numpoints, &dim, &ismalloc);
    if (dim >= 5) {
      qh_option("Qxact_merge", NULL, NULL);
      qh MERGEexact= True; /* 'Qx' always */
    }
    qh_init_B(points, numpoints, dim, ismalloc);
    qh_qhull();
    qh_check_output();
    qh_produce_output();
    if (qh VERIFYoutput && !qh FORCEoutput && !qh STOPpoint && !qh STOPcone)
      qh_check_points();
    exitcode= qh_ERRnone;
  }
  qh NOerrexit= True;  /* no more setjmp */
#ifdef qh_NOmem
  qh_freeqhull( True);
#else
  qh_freeqhull( False);
  qh_memfreeshort(&curlong, &totlong);
  if (curlong || totlong)
    fprintf(stderr, "qhull internal warning (main): did not free %d bytes of long memory(%d pieces)\n",
       totlong, curlong);
#endif
  return exitcode;
} /* main */

qhull-2012.1/src/qconvex/qconvex.pro0000644000076400010400000000033611545641040020565 0ustar  bbarberAdministrators# -------------------------------------------------
# qconvex.pro -- Qt project file for qconvex.exe
# -------------------------------------------------

include(../qhull-app-c.pri)

TARGET = qconvex

SOURCES += qconvex.c
qhull-2012.1/src/qdelaunay/0000755000076400010400000000000011721063454016661 5ustar  bbarberAdministratorsqhull-2012.1/src/qdelaunay/qdelaun.c0000644000076400010400000002740011710144464020460 0ustar  bbarberAdministrators/*
  ---------------------------------

   qdelaun.c
     compute Delaunay triangulations and furthest-point Delaunay
     triangulations using qhull

   see unix.c for full interface

   Copyright (c) 1993-2012, The Geometry Center
*/

#include 
#include 
#include 
#include 
#include 
#include "libqhull.h"
#include "mem.h"
#include "qset.h"

#if __MWERKS__ && __POWERPC__
#include 
#include 
#include 
#include 

#elif __cplusplus
extern "C" {
  int isatty(int);
}

#elif _MSC_VER
#include 
#define isatty _isatty
int _isatty(int);

#else
int isatty(int);  /* returns 1 if stdin is a tty
                   if "Undefined symbol" this can be deleted along with call in main() */
#endif

/*---------------------------------

  qh_prompt
    long prompt for qhull

  notes:
    restricted version of libqhull.c

  see:
    concise prompt below
*/

/* duplicated in qdelau_f.htm and qdelaun.htm */
char hidden_options[]=" d n v H U Qb QB Qc Qf Qg Qi Qm Qr QR Qv Qx TR E V FC Fi Fo Ft Fp FV Q0 Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 ";

char qh_prompta[]= "\n\
qdelaunay- compute the Delaunay triangulation\n\
    http://www.qhull.org  %s\n\
\n\
input (stdin):\n\
    first lines: dimension and number of points (or vice-versa).\n\
    other lines: point coordinates, best if one point per line\n\
    comments:    start with a non-numeric character\n\
\n\
options:\n\
    Qu   - compute furthest-site Delaunay triangulation\n\
    Qt   - triangulated output\n\
    QJ   - joggled input instead of merged facets\n\
\n\
Qhull control options:\n\
    QJn  - randomly joggle input in range [-n,n]\n\
%s%s%s%s";  /* split up qh_prompt for Visual C++ */
char qh_promptb[]= "\
    Qs   - search all points for the initial simplex\n\
    Qz   - add point-at-infinity to Delaunay triangulation\n\
    QGn  - print Delaunay region if visible from point n, -n if not\n\
    QVn  - print Delaunay regions that include point n, -n if not\n\
\n\
";
char qh_promptc[]= "\
Trace options:\n\
    T4   - trace at level n, 4=all, 5=mem/gauss, -1= events\n\
    Tc   - check frequently during execution\n\
    Ts   - print statistics\n\
    Tv   - verify result: structure, convexity, and in-circle test\n\
    Tz   - send all output to stdout\n\
    TFn  - report summary when n or more facets created\n\
    TI file - input data from file, no spaces or single quotes\n\
    TO file - output results to file, may be enclosed in single quotes\n\
    TPn  - turn on tracing when point n added to hull\n\
     TMn - turn on tracing at merge n\n\
     TWn - trace merge facets when width > n\n\
    TVn  - stop qhull after adding point n, -n for before (see TCn)\n\
     TCn - stop qhull after building cone for point n (see TVn)\n\
\n\
Precision options:\n\
    Cn   - radius of centrum (roundoff added).  Merge facets if non-convex\n\
     An  - cosine of maximum angle.  Merge facets if cosine > n or non-convex\n\
           C-0 roundoff, A-0.99/C-0.01 pre-merge, A0.99/C0.01 post-merge\n\
    Rn   - randomly perturb computations by a factor of [1-n,1+n]\n\
    Wn   - min facet width for outside point (before roundoff)\n\
\n\
Output formats (may be combined; if none, produces a summary to stdout):\n\
    f    - facet dump\n\
    G    - Geomview output (see below)\n\
    i    - vertices incident to each Delaunay region\n\
    m    - Mathematica output (2-d only, lifted to a paraboloid)\n\
    o    - OFF format (dim, points, and facets as a paraboloid)\n\
    p    - point coordinates (lifted to a paraboloid)\n\
    s    - summary (stderr)\n\
\n\
";
char qh_promptd[]= "\
More formats:\n\
    Fa   - area for each Delaunay region\n\
    FA   - compute total area for option 's'\n\
    Fc   - count plus coincident points for each Delaunay region\n\
    Fd   - use cdd format for input (homogeneous with offset first)\n\
    FD   - use cdd format for numeric output (offset first)\n\
    FF   - facet dump without ridges\n\
    FI   - ID of each Delaunay region\n\
    Fm   - merge count for each Delaunay region (511 max)\n\
    FM   - Maple output (2-d only, lifted to a paraboloid)\n\
    Fn   - count plus neighboring region for each Delaunay region\n\
    FN   - count plus neighboring region for each point\n\
    FO   - options and precision constants\n\
    FP   - nearest point and distance for each coincident point\n\
    FQ   - command used for qdelaunay\n\
    Fs   - summary: #int (8), dimension, #points, tot vertices, tot facets,\n\
                    for output: #vertices, #Delaunay regions,\n\
                                #coincident points, #non-simplicial regions\n\
                    #real (2), max outer plane, min vertex\n\
    FS   - sizes:   #int (0)\n\
                    #real (2), tot area, 0\n\
    Fv   - count plus vertices for each Delaunay region\n\
    Fx   - extreme points of Delaunay triangulation (on convex hull)\n\
\n\
";
char qh_prompte[]= "\
Geomview options (2-d and 3-d)\n\
    Ga   - all points as dots\n\
     Gp  -  coplanar points and vertices as radii\n\
     Gv  -  vertices as spheres\n\
    Gi   - inner planes only\n\
     Gn  -  no planes\n\
     Go  -  outer planes only\n\
    Gc     - centrums\n\
    Gh   - hyperplane intersections\n\
    Gr   - ridges\n\
    GDn  - drop dimension n in 3-d and 4-d output\n\
    Gt   - transparent outer ridges to view 3-d Delaunay\n\
\n\
Print options:\n\
    PAn  - keep n largest Delaunay regions by area\n\
    Pdk:n - drop facet if normal[k] <= n (default 0.0)\n\
    PDk:n - drop facet if normal[k] >= n\n\
    Pg   - print good Delaunay regions (needs 'QGn' or 'QVn')\n\
    PFn  - keep Delaunay regions whose area is at least n\n\
    PG   - print neighbors of good regions (needs 'QGn' or 'QVn')\n\
    PMn  - keep n Delaunay regions with most merges\n\
    Po   - force output.  If error, output neighborhood of facet\n\
    Pp   - do not report precision problems\n\
\n\
    .    - list of all options\n\
    -    - one line descriptions of all options\n\
";
/* for opts, don't assign 'e' or 'E' to a flag (already used for exponent) */

/*---------------------------------

  qh_prompt2
    synopsis for qhull
*/
char qh_prompt2[]= "\n\
qdelaunay- compute the Delaunay triangulation.  Qhull %s\n\
    input (stdin): dimension, number of points, point coordinates\n\
    comments start with a non-numeric character\n\
\n\
options (qdelaun.htm):\n\
    Qu   - furthest-site Delaunay triangulation\n\
    Qt   - triangulated output\n\
    QJ   - joggled input instead of merged facets\n\
    Tv   - verify result: structure, convexity, and in-circle test\n\
    .    - concise list of all options\n\
    -    - one-line description of all options\n\
\n\
output options (subset):\n\
    s    - summary of results (default)\n\
    i    - vertices incident to each Delaunay region\n\
    Fx   - extreme points (vertices of the convex hull)\n\
    o    - OFF format (shows the points lifted to a paraboloid)\n\
    G    - Geomview output (2-d and 3-d points lifted to a paraboloid)\n\
    m    - Mathematica output (2-d inputs lifted to a paraboloid)\n\
    QVn  - print Delaunay regions that include point n, -n if not\n\
    TO file- output results to file, may be enclosed in single quotes\n\
\n\
examples:\n\
    rbox c P0 D2 | qdelaunay s o          rbox c P0 D2 | qdelaunay i\n\
    rbox c P0 D2 | qdelaunay Fv           rbox c P0 D2 | qdelaunay s Qu Fv\n\
    rbox c G1 d D2 | qdelaunay s i        rbox c G1 d D2 | qdelaunay Qt\n\
    rbox M3,4 z 100 D2 | qdelaunay s      rbox M3,4 z 100 D2 | qdelaunay s Qt\n\
\n\
";
/* for opts, don't assign 'e' or 'E' to a flag (already used for exponent) */

/*---------------------------------

  qh_prompt3
    concise prompt for qhull
*/
char qh_prompt3[]= "\n\
Qhull %s.\n\
Except for 'F.' and 'PG', upper-case options take an argument.\n\
\n\
 incidences     mathematica    OFF_format     points_lifted  summary\n\
 facet_dump\n\
\n\
 Farea          FArea_total    Fcoincident    Fd_cdd_in      FD_cdd_out\n\
 FF_dump_xridge FIDs           Fmerges        Fneighbors     FNeigh_vertex\n\
 FOptions       FPoint_near    FQdelaun       Fsummary       FSize\n\
 Fvertices      Fxtremes       FMaple\n\
\n\
 Gvertices      Gpoints        Gall_points    Gno_planes     Ginner\n\
 Gcentrums      Ghyperplanes   Gridges        Gouter         GDrop_dim\n\
 Gtransparent\n\
\n\
 PArea_keep     Pdrop d0:0D0   Pgood          PFacet_area_keep\n\
 PGood_neighbors PMerge_keep   Poutput_forced Pprecision_not\n\
\n\
 QGood_point    QJoggle        Qsearch_1st    Qtriangulate   QupperDelaunay\n\
 QVertex_good   Qzinfinite\n\
\n\
 T4_trace       Tcheck_often   Tstatistics    Tverify        Tz_stdout\n\
 TFacet_log     TInput_file    TPoint_trace   TMerge_trace   TOutput_file\n\
 TWide_trace    TVertex_stop   TCone_stop\n\
\n\
 Angle_max      Centrum_size   Random_dist    Wide_outside\n\
";

/*---------------------------------

  main( argc, argv )
    processes the command line, calls qhull() to do the work, and exits

  design:
    initializes data structures
    reads points
    finishes initialization
    computes convex hull and other structures
    checks the result
    writes the output
    frees memory
*/
int main(int argc, char *argv[]) {
  int curlong, totlong; /* used !qh_NOmem */
  int exitcode, numpoints, dim;
  coordT *points;
  boolT ismalloc;

#if __MWERKS__ && __POWERPC__
  char inBuf[BUFSIZ], outBuf[BUFSIZ], errBuf[BUFSIZ];
  SIOUXSettings.showstatusline= false;
  SIOUXSettings.tabspaces= 1;
  SIOUXSettings.rows= 40;
  if (setvbuf(stdin, inBuf, _IOFBF, sizeof(inBuf)) < 0   /* w/o, SIOUX I/O is slow*/
  || setvbuf(stdout, outBuf, _IOFBF, sizeof(outBuf)) < 0
  || (stdout != stderr && setvbuf(stderr, errBuf, _IOFBF, sizeof(errBuf)) < 0))
    fprintf(stderr, "qhull internal warning (main): could not change stdio to fully buffered.\n");
  argc= ccommand(&argv);
#endif

  if ((argc == 1) && isatty( 0 /*stdin*/)) {
    fprintf(stdout, qh_prompt2, qh_version);
    exit(qh_ERRnone);
  }
  if (argc > 1 && *argv[1] == '-' && !*(argv[1]+1)) {
    fprintf(stdout, qh_prompta, qh_version,
                qh_promptb, qh_promptc, qh_promptd, qh_prompte);
    exit(qh_ERRnone);
  }
  if (argc >1 && *argv[1] == '.' && !*(argv[1]+1)) {
    fprintf(stdout, qh_prompt3, qh_version);
    exit(qh_ERRnone);
  }
  qh_init_A(stdin, stdout, stderr, argc, argv);  /* sets qh qhull_command */
  exitcode= setjmp(qh errexit); /* simple statement for CRAY J916 */
  if (!exitcode) {
    qh_option("delaunay  Qbbound-last", NULL, NULL);
    qh DELAUNAY= True;     /* 'd'   */
    qh SCALElast= True;    /* 'Qbb' */
    qh KEEPcoplanar= True; /* 'Qc', to keep coplanars in 'p' */
    qh_checkflags(qh qhull_command, hidden_options);
    qh_initflags(qh qhull_command);
    points= qh_readpoints(&numpoints, &dim, &ismalloc);
    if (dim >= 5) {
      qh_option("Qxact_merge", NULL, NULL);
      qh MERGEexact= True; /* 'Qx' always */
    }
    qh_init_B(points, numpoints, dim, ismalloc);
    qh_qhull();
    qh_check_output();
    qh_produce_output();
    if (qh VERIFYoutput && !qh FORCEoutput && !qh STOPpoint && !qh STOPcone)
      qh_check_points();
    exitcode= qh_ERRnone;
  }
  qh NOerrexit= True;  /* no more setjmp */
#ifdef qh_NOmem
  qh_freeqhull( True);
#else
  qh_freeqhull( False);
  qh_memfreeshort(&curlong, &totlong);
  if (curlong || totlong)
    fprintf(stderr, "qhull internal warning (main): did not free %d bytes of long memory(%d pieces)\n",
       totlong, curlong);
#endif
  return exitcode;
} /* main */

qhull-2012.1/src/qdelaunay/qdelaunay.pro0000644000076400010400000000034311545641040021363 0ustar  bbarberAdministrators# -------------------------------------------------
# qdelaunay.pro -- Qt project file for qvoronoi.exe
# -------------------------------------------------

include(../qhull-app-c.pri)

TARGET = qdelaunay

SOURCES += qdelaun.c
qhull-2012.1/src/qhalf/0000755000076400010400000000000011721063454015771 5ustar  bbarberAdministratorsqhull-2012.1/src/qhalf/qhalf.c0000644000076400010400000002734511710144471017240 0ustar  bbarberAdministrators/*
  ---------------------------------

   qhalf.c
     compute the intersection of halfspaces about a point

   see unix.c for full interface

   Copyright (c) 1993-2012, The Geometry Center
*/

#include 
#include 
#include 
#include 
#include 
#include "libqhull.h"
#include "mem.h"
#include "qset.h"

#if __MWERKS__ && __POWERPC__
#include 
#include 
#include 
#include 

#elif __cplusplus
extern "C" {
  int isatty(int);
}

#elif _MSC_VER
#include 
#define isatty _isatty
int _isatty(int);

#else
int isatty(int);  /* returns 1 if stdin is a tty
                   if "Undefined symbol" this can be deleted along with call in main() */
#endif

/*---------------------------------

  qh_prompt
    long prompt for qhull

  notes:
    restricted version of libqhull.c

  see:
    concise prompt below
*/

/* duplicated in qhalf.htm */
char hidden_options[]=" d n v Qbb QbB Qf Qg Qm Qr QR Qv Qx Qz TR E V Fa FA FC FD FS Ft FV Gt Q0 Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 ";

char qh_prompta[]= "\n\
qhalf- compute the intersection of halfspaces about a point\n\
    http://www.qhull.org  %s\n\
\n\
input (stdin):\n\
    optional interior point: dimension, 1, coordinates\n\
    first lines: dimension+1 and number of halfspaces\n\
    other lines: halfspace coefficients followed by offset\n\
    comments:    start with a non-numeric character\n\
\n\
options:\n\
    Hn,n - specify coordinates of interior point\n\
    Qt   - triangulated output\n\
    QJ   - joggled input instead of merged facets\n\
    Qc   - keep coplanar halfspaces\n\
    Qi   - keep other redundant halfspaces\n\
\n\
Qhull control options:\n\
    QJn  - randomly joggle input in range [-n,n]\n\
%s%s%s%s";  /* split up qh_prompt for Visual C++ */
char qh_promptb[]= "\
    Qbk:0Bk:0 - remove k-th coordinate from input\n\
    Qs   - search all halfspaces for the initial simplex\n\
    QGn  - print intersection if visible to halfspace n, -n for not\n\
    QVn  - print intersections for halfspace n, -n if not\n\
\n\
";
char qh_promptc[]= "\
Trace options:\n\
    T4   - trace at level n, 4=all, 5=mem/gauss, -1= events\n\
    Tc   - check frequently during execution\n\
    Ts   - print statistics\n\
    Tv   - verify result: structure, convexity, and redundancy\n\
    Tz   - send all output to stdout\n\
    TFn  - report summary when n or more facets created\n\
    TI file - input data from file, no spaces or single quotes\n\
    TO file - output results to file, may be enclosed in single quotes\n\
    TPn  - turn on tracing when halfspace n added to intersection\n\
    TMn  - turn on tracing at merge n\n\
    TWn  - trace merge facets when width > n\n\
    TVn  - stop qhull after adding halfspace n, -n for before (see TCn)\n\
    TCn  - stop qhull after building cone for halfspace n (see TVn)\n\
\n\
Precision options:\n\
    Cn   - radius of centrum (roundoff added).  Merge facets if non-convex\n\
     An  - cosine of maximum angle.  Merge facets if cosine > n or non-convex\n\
           C-0 roundoff, A-0.99/C-0.01 pre-merge, A0.99/C0.01 post-merge\n\
    Rn   - randomly perturb computations by a factor of [1-n,1+n]\n\
    Un   - max distance below plane for a new, coplanar halfspace\n\
    Wn   - min facet width for outside halfspace (before roundoff)\n\
\n\
Output formats (may be combined; if none, produces a summary to stdout):\n\
    f    - facet dump\n\
    G    - Geomview output (dual convex hull)\n\
    i    - non-redundant halfspaces incident to each intersection\n\
    m    - Mathematica output (dual convex hull)\n\
    o    - OFF format (dual convex hull: dimension, points, and facets)\n\
    p    - vertex coordinates of dual convex hull (coplanars if 'Qc' or 'Qi')\n\
    s    - summary (stderr)\n\
\n\
";
char qh_promptd[]= "\
More formats:\n\
    Fc   - count plus redundant halfspaces for each intersection\n\
         -   Qc (default) for coplanar and Qi for other redundant\n\
    Fd   - use cdd format for input (homogeneous with offset first)\n\
    FF   - facet dump without ridges\n\
    FI   - ID of each intersection\n\
    Fm   - merge count for each intersection (511 max)\n\
    FM   - Maple output (dual convex hull)\n\
    Fn   - count plus neighboring intersections for each intersection\n\
    FN   - count plus intersections for each non-redundant halfspace\n\
    FO   - options and precision constants\n\
    Fp   - dim, count, and intersection coordinates\n\
    FP   - nearest halfspace and distance for each redundant halfspace\n\
    FQ   - command used for qhalf\n\
    Fs   - summary: #int (8), dim, #halfspaces, #non-redundant, #intersections\n\
                      for output: #non-redundant, #intersections, #coplanar\n\
                                  halfspaces, #non-simplicial intersections\n\
                    #real (2), max outer plane, min vertex\n\
    Fv   - count plus non-redundant halfspaces for each intersection\n\
    Fx   - non-redundant halfspaces\n\
\n\
";
char qh_prompte[]= "\
Geomview output (2-d, 3-d and 4-d; dual convex hull)\n\
    Ga   - all points (i.e., transformed halfspaces) as dots\n\
     Gp  -  coplanar points and vertices as radii\n\
     Gv  -  vertices (i.e., non-redundant halfspaces) as spheres\n\
    Gi   - inner planes (i.e., halfspace intersections) only\n\
     Gn  -  no planes\n\
     Go  -  outer planes only\n\
    Gc   - centrums\n\
    Gh   - hyperplane intersections\n\
    Gr   - ridges\n\
    GDn  - drop dimension n in 3-d and 4-d output\n\
\n\
Print options:\n\
    PAn  - keep n largest facets (i.e., intersections) by area\n\
    Pdk:n- drop facet if normal[k] <= n (default 0.0)\n\
    PDk:n- drop facet if normal[k] >= n\n\
    Pg   - print good facets (needs 'QGn' or 'QVn')\n\
    PFn  - keep facets whose area is at least n\n\
    PG   - print neighbors of good facets\n\
    PMn  - keep n facets with most merges\n\
    Po   - force output.  If error, output neighborhood of facet\n\
    Pp   - do not report precision problems\n\
\n\
    .    - list of all options\n\
    -    - one line descriptions of all options\n\
";
/* for opts, don't assign 'e' or 'E' to a flag (already used for exponent) */

/*---------------------------------

  qh_prompt2
    synopsis for qhull
*/
char qh_prompt2[]= "\n\
qhalf- halfspace intersection about a point.  Qhull %s\n\
    input (stdin): [dim, 1, interior point], dim+1, n, coefficients+offset\n\
    comments start with a non-numeric character\n\
\n\
options (qhalf.htm):\n\
    Hn,n - specify coordinates of interior point\n\
    Qt   - triangulated output\n\
    QJ   - joggled input instead of merged facets\n\
    Tv   - verify result: structure, convexity, and redundancy\n\
    .    - concise list of all options\n\
    -    - one-line description of all options\n\
\n\
output options (subset):\n\
    s    - summary of results (default)\n\
    Fp   - intersection coordinates\n\
    Fv   - non-redundant halfspaces incident to each intersection\n\
    Fx   - non-redundant halfspaces\n\
    o    - OFF file format (dual convex hull)\n\
    G    - Geomview output (dual convex hull)\n\
    m    - Mathematica output (dual convex hull)\n\
    QVn  - print intersections for halfspace n, -n if not\n\
    TO file - output results to file, may be enclosed in single quotes\n\
\n\
examples:\n\
    rbox d | qconvex FQ n | qhalf s H0,0,0 Fp\n\
    rbox c | qconvex FQ FV n | qhalf s i\n\
    rbox c | qconvex FQ FV n | qhalf s o\n\
\n\
";
/* for opts, don't assign 'e' or 'E' to a flag (already used for exponent) */

/*---------------------------------

  qh_prompt3
    concise prompt for qhull
*/
char qh_prompt3[]= "\n\
Qhull %s.\n\
Except for 'F.' and 'PG', upper_case options take an argument.\n\
\n\
 incidences     Geomview       mathematica    OFF_format     point_dual\n\
 summary        facet_dump\n\
\n\
 Fc_redundant   Fd_cdd_in      FF_dump_xridge FIDs           Fmerges\n\
 Fneighbors     FN_intersect   FOptions       Fp_coordinates FP_nearest\n\
 FQhalf         Fsummary       Fv_halfspace   FMaple         Fx_non_redundant\n\
\n\
 Gvertices      Gpoints        Gall_points    Gno_planes     Ginner\n\
 Gcentrums      Ghyperplanes   Gridges        Gouter         GDrop_dim\n\
\n\
 PArea_keep     Pdrop d0:0D0   Pgood          PFacet_area_keep\n\
 PGood_neighbors PMerge_keep   Poutput_forced Pprecision_not\n\
\n\
 Qbk:0Bk:0_drop Qcoplanar      QG_half_good   Qi_redundant   QJoggle\n\
 Qsearch_1st    Qtriangulate   QVertex_good\n\
\n\
 T4_trace       Tcheck_often   Tstatistics    Tverify        Tz_stdout\n\
 TFacet_log     TInput_file    TPoint_trace   TMerge_trace   TOutput_file\n\
 TWide_trace    TVertex_stop   TCone_stop\n\
\n\
 Angle_max      Centrum_size   Random_dist    Ucoplanar_max  Wide_outside\n\
";

/*---------------------------------

  main( argc, argv )
    processes the command line, calls qhull() to do the work, and exits

  design:
    initializes data structures
    reads points
    finishes initialization
    computes convex hull and other structures
    checks the result
    writes the output
    frees memory
*/
int main(int argc, char *argv[]) {
  int curlong, totlong; /* used !qh_NOmem */
  int exitcode, numpoints, dim;
  coordT *points;
  boolT ismalloc;

#if __MWERKS__ && __POWERPC__
  char inBuf[BUFSIZ], outBuf[BUFSIZ], errBuf[BUFSIZ];
  SIOUXSettings.showstatusline= false;
  SIOUXSettings.tabspaces= 1;
  SIOUXSettings.rows= 40;
  if (setvbuf(stdin, inBuf, _IOFBF, sizeof(inBuf)) < 0   /* w/o, SIOUX I/O is slow*/
  || setvbuf(stdout, outBuf, _IOFBF, sizeof(outBuf)) < 0
  || (stdout != stderr && setvbuf(stderr, errBuf, _IOFBF, sizeof(errBuf)) < 0))
    fprintf(stderr, "qhull internal warning (main): could not change stdio to fully buffered.\n");
  argc= ccommand(&argv);
#endif

  if ((argc == 1) && isatty( 0 /*stdin*/)) {
    fprintf(stdout, qh_prompt2, qh_version);
    exit(qh_ERRnone);
  }
  if (argc > 1 && *argv[1] == '-' && !*(argv[1]+1)) {
    fprintf(stdout, qh_prompta, qh_version,
        qh_promptb, qh_promptc, qh_promptd, qh_prompte);
    exit(qh_ERRnone);
  }
  if (argc >1 && *argv[1] == '.' && !*(argv[1]+1)) {
    fprintf(stdout, qh_prompt3, qh_version);
    exit(qh_ERRnone);
  }
  qh_init_A(stdin, stdout, stderr, argc, argv);  /* sets qh qhull_command */
  exitcode= setjmp(qh errexit); /* simple statement for CRAY J916 */
  if (!exitcode) {
    qh_option("Halfspace", NULL, NULL);
    qh HALFspace= True;    /* 'H'   */
    qh_checkflags(qh qhull_command, hidden_options);
    qh_initflags(qh qhull_command);
    if (qh SCALEinput) {
      fprintf(qh ferr, "\
qhull error: options 'Qbk:n' and 'QBk:n' are not used with qhalf.\n\
             Use 'Qbk:0Bk:0 to drop dimension k.\n");
      qh_errexit(qh_ERRinput, NULL, NULL);
    }
    points= qh_readpoints(&numpoints, &dim, &ismalloc);
    if (dim >= 5) {
      qh_option("Qxact_merge", NULL, NULL);
      qh MERGEexact= True; /* 'Qx' always */
    }
    qh_init_B(points, numpoints, dim, ismalloc);
    qh_qhull();
    qh_check_output();
    qh_produce_output();
    if (qh VERIFYoutput && !qh FORCEoutput && !qh STOPpoint && !qh STOPcone)
      qh_check_points();
    exitcode= qh_ERRnone;
  }
  qh NOerrexit= True;  /* no more setjmp */
#ifdef qh_NOmem
  qh_freeqhull( True);
#else
  qh_freeqhull( False);
  qh_memfreeshort(&curlong, &totlong);
  if (curlong || totlong)
    fprintf(stderr, "qhull internal warning (main): did not free %d bytes of long memory(%d pieces)\n",
       totlong, curlong);
#endif
  return exitcode;
} /* main */

qhull-2012.1/src/qhalf/qhalf.pro0000644000076400010400000000033011545641040017577 0ustar  bbarberAdministrators# -------------------------------------------------
# qhalf.pro -- Qt project file for qconvex.exe
# -------------------------------------------------

include(../qhull-app-c.pri)

TARGET = qhalf

SOURCES += qhalf.c
qhull-2012.1/src/qhull/0000755000076400010400000000000011721063454016023 5ustar  bbarberAdministratorsqhull-2012.1/src/qhull/qhull.pro0000644000076400010400000000032511545640614017675 0ustar  bbarberAdministrators# -------------------------------------------------
# qhull.pro -- Qt project file for qhull.exe
# -------------------------------------------------

include(../qhull-app-c.pri)

TARGET = qhull

SOURCES += unix.c
qhull-2012.1/src/qhull/unix.c0000644000076400010400000003655411710144464017166 0ustar  bbarberAdministrators/*
  ---------------------------------

   unix.c
     command line interface to qhull
         includes SIOUX interface for Macintoshes

   see qh-qhull.htm

   Copyright (c) 1993-2012 The Geometry Center.
   $Id: //main/2011/qhull/src/qhull/unix.c#5 $$Change: 1464 $
   $DateTime: 2012/01/25 22:58:41 $$Author: bbarber $
*/

#include "mem.h"
#include "qset.h"
#include "libqhull.h"

#include 
#include 
#include 
#include 
#include 

#if __MWERKS__ && __POWERPC__
#include 
#include 
#include 
#include 

#elif __cplusplus
extern "C" {
  int isatty(int);
}

#elif _MSC_VER
#include 
#define isatty _isatty
int _isatty(int);

#else
int isatty(int);  /* returns 1 if stdin is a tty
                   if "Undefined symbol" this can be deleted along with call in main() */
#endif

/*---------------------------------

  qh_prompt
    long prompt for qhull

  see:
    concise prompt below
*/
char qh_prompta[]= "\n\
qhull- compute convex hulls and related structures.\n\
    http://www.qhull.org  %s\n\
\n\
input (stdin):\n\
    first lines: dimension and number of points (or vice-versa).\n\
    other lines: point coordinates, best if one point per line\n\
    comments:    start with a non-numeric character\n\
    halfspaces:  use dim plus one and put offset after coefficients.\n\
                 May be preceeded by a single interior point ('H').\n\
\n\
options:\n\
    d    - Delaunay triangulation by lifting points to a paraboloid\n\
    d Qu - furthest-site Delaunay triangulation (upper convex hull)\n\
    v    - Voronoi diagram (dual of the Delaunay triangulation)\n\
    v Qu - furthest-site Voronoi diagram\n\
    Hn,n,... - halfspace intersection about point [n,n,0,...]\n\
    Qt   - triangulated output\n\
    QJ   - joggled input instead of merged facets\n\
    Qc   - keep coplanar points with nearest facet\n\
    Qi   - keep interior points with nearest facet\n\
\n\
Qhull control options:\n\
    Qbk:n   - scale coord k so that low bound is n\n\
      QBk:n - scale coord k so that upper bound is n (QBk is %2.2g)\n\
    QbB  - scale input to unit cube centered at the origin\n\
    Qbb  - scale last coordinate to [0,m] for Delaunay triangulations\n\
    Qbk:0Bk:0 - remove k-th coordinate from input\n\
    QJn  - randomly joggle input in range [-n,n]\n\
    QRn  - random rotation (n=seed, n=0 time, n=-1 time/no rotate)\n\
%s%s%s%s";  /* split up qh_prompt for Visual C++ */
char qh_promptb[]= "\
    Qf   - partition point to furthest outside facet\n\
    Qg   - only build good facets (needs 'QGn', 'QVn', or 'PdD')\n\
    Qm   - only process points that would increase max_outside\n\
    Qr   - process random outside points instead of furthest ones\n\
    Qs   - search all points for the initial simplex\n\
    Qu   - for 'd' or 'v', compute upper hull without point at-infinity\n\
              returns furthest-site Delaunay triangulation\n\
    Qv   - test vertex neighbors for convexity\n\
    Qx   - exact pre-merges (skips coplanar and angle-coplanar facets)\n\
    Qz   - add point-at-infinity to Delaunay triangulation\n\
    QGn  - good facet if visible from point n, -n for not visible\n\
    QVn  - good facet if it includes point n, -n if not\n\
    Q0   - turn off default premerge with 'C-0'/'Qx'\n\
    Q1     - sort merges by type instead of angle\n\
    Q2   - merge all non-convex at once instead of independent sets\n\
    Q3   - do not merge redundant vertices\n\
    Q4   - avoid old->new merges\n\
    Q5   - do not correct outer planes at end of qhull\n\
    Q6   - do not pre-merge concave or coplanar facets\n\
    Q7   - depth-first processing instead of breadth-first\n\
    Q8   - do not process near-inside points\n\
    Q9   - process furthest of furthest points\n\
    Q10  - no special processing for narrow distributions\n\
    Q11  - copy normals and recompute centrums for tricoplanar facets\n\
\n\
";
char qh_promptc[]= "\
Topts- Trace options:\n\
    T4   - trace at level n, 4=all, 5=mem/gauss, -1= events\n\
    Ta   - annotate output with message codes\n\
    Tc   - check frequently during execution\n\
    Ts   - print statistics\n\
    Tv   - verify result: structure, convexity, and point inclusion\n\
    Tz   - send all output to stdout\n\
    TFn  - report summary when n or more facets created\n\
    TI file - input data from file, no spaces or single quotes\n\
    TO file - output results to file, may be enclosed in single quotes\n\
    TPn  - turn on tracing when point n added to hull\n\
     TMn - turn on tracing at merge n\n\
     TWn - trace merge facets when width > n\n\
    TRn  - rerun qhull n times.  Use with 'QJn'\n\
    TVn  - stop qhull after adding point n, -n for before (see TCn)\n\
     TCn - stop qhull after building cone for point n (see TVn)\n\
\n\
Precision options:\n\
    Cn   - radius of centrum (roundoff added).  Merge facets if non-convex\n\
     An  - cosine of maximum angle.  Merge facets if cosine > n or non-convex\n\
           C-0 roundoff, A-0.99/C-0.01 pre-merge, A0.99/C0.01 post-merge\n\
    En   - max roundoff error for distance computation\n\
    Rn   - randomly perturb computations by a factor of [1-n,1+n]\n\
    Vn   - min distance above plane for a visible facet (default 3C-n or En)\n\
    Un   - max distance below plane for a new, coplanar point (default Vn)\n\
    Wn   - min facet width for outside point (before roundoff, default 2Vn)\n\
\n\
Output formats (may be combined; if none, produces a summary to stdout):\n\
    f    - facet dump\n\
    G    - Geomview output (see below)\n\
    i    - vertices incident to each facet\n\
    m    - Mathematica output (2-d and 3-d)\n\
    o    - OFF format (dim, points and facets; Voronoi regions)\n\
    n    - normals with offsets\n\
    p    - vertex coordinates or Voronoi vertices (coplanar points if 'Qc')\n\
    s    - summary (stderr)\n\
\n\
";
char qh_promptd[]= "\
More formats:\n\
    Fa   - area for each facet\n\
    FA   - compute total area and volume for option 's'\n\
    Fc   - count plus coplanar points for each facet\n\
           use 'Qc' (default) for coplanar and 'Qi' for interior\n\
    FC   - centrum or Voronoi center for each facet\n\
    Fd   - use cdd format for input (homogeneous with offset first)\n\
    FD   - use cdd format for numeric output (offset first)\n\
    FF   - facet dump without ridges\n\
    Fi   - inner plane for each facet\n\
           for 'v', separating hyperplanes for bounded Voronoi regions\n\
    FI   - ID of each facet\n\
    Fm   - merge count for each facet (511 max)\n\
    FM   - Maple output (2-d and 3-d)\n\
    Fn   - count plus neighboring facets for each facet\n\
    FN   - count plus neighboring facets for each point\n\
    Fo   - outer plane (or max_outside) for each facet\n\
           for 'v', separating hyperplanes for unbounded Voronoi regions\n\
    FO   - options and precision constants\n\
    Fp   - dim, count, and intersection coordinates (halfspace only)\n\
    FP   - nearest vertex and distance for each coplanar point\n\
    FQ   - command used for qhull\n\
    Fs   - summary: #int (8), dimension, #points, tot vertices, tot facets,\n\
                      output: #vertices, #facets, #coplanars, #nonsimplicial\n\
                    #real (2), max outer plane, min vertex\n\
    FS   - sizes:   #int (0)\n\
                    #real (2) tot area, tot volume\n\
    Ft   - triangulation with centrums for non-simplicial facets (OFF format)\n\
    Fv   - count plus vertices for each facet\n\
           for 'v', Voronoi diagram as Voronoi vertices for pairs of sites\n\
    FV   - average of vertices (a feasible point for 'H')\n\
    Fx   - extreme points (in order for 2-d)\n\
\n\
";
char qh_prompte[]= "\
Geomview options (2-d, 3-d, and 4-d; 2-d Voronoi)\n\
    Ga   - all points as dots\n\
     Gp  -  coplanar points and vertices as radii\n\
     Gv  -  vertices as spheres\n\
    Gi   - inner planes only\n\
     Gn  -  no planes\n\
     Go  -  outer planes only\n\
    Gc   - centrums\n\
    Gh   - hyperplane intersections\n\
    Gr   - ridges\n\
    GDn  - drop dimension n in 3-d and 4-d output\n\
    Gt   - for 3-d 'd', transparent outer ridges\n\
\n\
Print options:\n\
    PAn  - keep n largest facets by area\n\
    Pdk:n - drop facet if normal[k] <= n (default 0.0)\n\
    PDk:n - drop facet if normal[k] >= n\n\
    Pg   - print good facets (needs 'QGn' or 'QVn')\n\
    PFn  - keep facets whose area is at least n\n\
    PG   - print neighbors of good facets\n\
    PMn  - keep n facets with most merges\n\
    Po   - force output.  If error, output neighborhood of facet\n\
    Pp   - do not report precision problems\n\
\n\
    .    - list of all options\n\
    -    - one line descriptions of all options\n\
";
/* for opts, don't assign 'e' or 'E' to a flag (already used for exponent) */

/*---------------------------------

  qh_prompt2
    synopsis for qhull
*/
char qh_prompt2[]= "\n\
qhull- compute convex hulls and related structures.  Qhull %s\n\
    input (stdin): dimension, n, point coordinates\n\
    comments start with a non-numeric character\n\
    halfspace: use dim+1 and put offsets after coefficients\n\
\n\
options (qh-quick.htm):\n\
    d    - Delaunay triangulation by lifting points to a paraboloid\n\
    d Qu - furthest-site Delaunay triangulation (upper convex hull)\n\
    v    - Voronoi diagram as the dual of the Delaunay triangulation\n\
    v Qu - furthest-site Voronoi diagram\n\
    H1,1 - Halfspace intersection about [1,1,0,...] via polar duality\n\
    Qt   - triangulated output\n\
    QJ   - joggled input instead of merged facets\n\
    Tv   - verify result: structure, convexity, and point inclusion\n\
    .    - concise list of all options\n\
    -    - one-line description of each option\n\
\n\
Output options (subset):\n\
    s    - summary of results (default)\n\
    i    - vertices incident to each facet\n\
    n    - normals with offsets\n\
    p    - vertex coordinates (if 'Qc', includes coplanar points)\n\
           if 'v', Voronoi vertices\n\
    Fp   - halfspace intersections\n\
    Fx   - extreme points (convex hull vertices)\n\
    FA   - compute total area and volume\n\
    o    - OFF format (if 'v', outputs Voronoi regions)\n\
    G    - Geomview output (2-d, 3-d and 4-d)\n\
    m    - Mathematica output (2-d and 3-d)\n\
    QVn  - print facets that include point n, -n if not\n\
    TO file- output results to file, may be enclosed in single quotes\n\
\n\
examples:\n\
    rbox c d D2 | qhull Qc s f Fx | more      rbox 1000 s | qhull Tv s FA\n\
    rbox 10 D2 | qhull d QJ s i TO result     rbox 10 D2 | qhull v Qbb Qt p\n\
    rbox 10 D2 | qhull d Qu QJ m              rbox 10 D2 | qhull v Qu QJ o\n\
    rbox c | qhull n                          rbox c | qhull FV n | qhull H Fp\n\
    rbox d D12 | qhull QR0 FA                 rbox c D7 | qhull FA TF1000\n\
    rbox y 1000 W0 | qhull                    rbox 10 | qhull v QJ o Fv\n\
\n\
";
/* for opts, don't assign 'e' or 'E' to a flag (already used for exponent) */

/*---------------------------------

  qh_prompt3
    concise prompt for qhull
*/
char qh_prompt3[]= "\n\
Qhull %s.\n\
Except for 'F.' and 'PG', upper-case options take an argument.\n\
\n\
 delaunay       voronoi        Geomview       Halfspace      facet_dump\n\
 incidences     mathematica    normals        OFF_format     points\n\
 summary\n\
\n\
 Farea          FArea-total    Fcoplanars     FCentrums      Fd-cdd-in\n\
 FD-cdd-out     FF-dump-xridge Finner         FIDs           Fmerges\n\
 Fneighbors     FNeigh-vertex  Fouter         FOptions       Fpoint-intersect\n\
 FPoint_near    FQhull         Fsummary       FSize          Ftriangles\n\
 Fvertices      Fvoronoi       FVertex-ave    Fxtremes       FMaple\n\
\n\
 Gvertices      Gpoints        Gall_points    Gno_planes     Ginner\n\
 Gcentrums      Ghyperplanes   Gridges        Gouter         GDrop_dim\n\
 Gtransparent\n\
\n\
 PArea-keep     Pdrop d0:0D0   Pgood          PFacet_area_keep\n\
 PGood_neighbors PMerge-keep   Poutput_forced Pprecision_not\n\
\n\
 QbBound 0:0.5  Qbk:0Bk:0_drop QbB-scale-box  Qbb-scale-last Qcoplanar\n\
 Qfurthest      Qgood_only     QGood_point    Qinterior      Qmax_out\n\
 QJoggle        Qrandom        QRotate        Qsearch_1st    Qtriangulate\n\
 QupperDelaunay QVertex_good   Qvneighbors    Qxact_merge    Qzinfinite\n\
\n\
 Q0_no_premerge Q1_no_angle    Q2_no_independ Q3_no_redundant Q4_no_old\n\
 Q5_no_check_out Q6_no_concave Q7_depth_first Q8_no_near_in  Q9_pick_furthest\n\
 Q10_no_narrow  Q11_trinormals\n\
\n\
 T4_trace       Tannotate      Tcheck_often   Tstatistics    Tverify\n\
 Tz_stdout      TFacet_log     TInput_file    TPoint_trace   TMerge_trace\n\
 TOutput_file   TRerun         TWide_trace    TVertex_stop   TCone_stop\n\
\n\
 Angle_max      Centrum_size   Error_round    Random_dist    Visible_min\n\
 Ucoplanar_max  Wide_outside\n\
";

/*---------------------------------

  main( argc, argv )
    processes the command line, calls qhull() to do the work, and exits

  design:
    initializes data structures
    reads points
    finishes initialization
    computes convex hull and other structures
    checks the result
    writes the output
    frees memory
*/
int main(int argc, char *argv[]) {
  int curlong, totlong; /* used !qh_NOmem */
  int exitcode, numpoints, dim;
  coordT *points;
  boolT ismalloc;

#if __MWERKS__ && __POWERPC__
  char inBuf[BUFSIZ], outBuf[BUFSIZ], errBuf[BUFSIZ];
  SIOUXSettings.showstatusline= false;
  SIOUXSettings.tabspaces= 1;
  SIOUXSettings.rows= 40;
  if (setvbuf(stdin, inBuf, _IOFBF, sizeof(inBuf)) < 0   /* w/o, SIOUX I/O is slow*/
  || setvbuf(stdout, outBuf, _IOFBF, sizeof(outBuf)) < 0
  || (stdout != stderr && setvbuf(stderr, errBuf, _IOFBF, sizeof(errBuf)) < 0))
    fprintf(stderr, "qhull internal warning (main): could not change stdio to fully buffered.\n");
  argc= ccommand(&argv);
#endif

  if ((argc == 1) && isatty( 0 /*stdin*/)) {
    fprintf(stdout, qh_prompt2, qh_version);
    exit(qh_ERRnone);
  }
  if (argc > 1 && *argv[1] == '-' && !*(argv[1]+1)) {
    fprintf(stdout, qh_prompta, qh_version, qh_DEFAULTbox,
                qh_promptb, qh_promptc, qh_promptd, qh_prompte);
    exit(qh_ERRnone);
  }
  if (argc >1 && *argv[1] == '.' && !*(argv[1]+1)) {
    fprintf(stdout, qh_prompt3, qh_version);
    exit(qh_ERRnone);
  }
  qh_init_A(stdin, stdout, stderr, argc, argv);  /* sets qh qhull_command */
  exitcode= setjmp(qh errexit); /* simple statement for CRAY J916 */
  if (!exitcode) {
    qh_initflags(qh qhull_command);
    points= qh_readpoints(&numpoints, &dim, &ismalloc);
    qh_init_B(points, numpoints, dim, ismalloc);
    qh_qhull();
    qh_check_output();
    qh_produce_output();
    if (qh VERIFYoutput && !qh FORCEoutput && !qh STOPpoint && !qh STOPcone)
      qh_check_points();
    exitcode= qh_ERRnone;
  }
  qh NOerrexit= True;  /* no more setjmp */
#ifdef qh_NOmem
  qh_freeqhull( True);
#else
  qh_freeqhull( False);
  qh_memfreeshort(&curlong, &totlong);
  if (curlong || totlong)
    fprintf(stderr, "qhull internal warning (main): did not free %d bytes of long memory(%d pieces)\n",
       totlong, curlong);
#endif
  return exitcode;
} /* main */

qhull-2012.1/src/qhull-all.pro0000644000076400010400000000536311707146137017326 0ustar  bbarberAdministrators# -------------------------------------------------
# qhull-all.pro -- Qt project to build executables and static libraries
#
# To build with Qt on mingw
#   Download Qt SDK, install Perl
#   /c/qt/2010.05/qt> ./configure -static -platform win32-g++ -fast -no-qt3support
#
# To build DevStudio sln and proj files (Qhull ships with cmake derived files)
# qmake is in Qt's bin directory
# ../build> qmake -tp vc -r ../src/qhull-all.pro
# Need to add Build Dependencies, disable rtti, rename targets to qhull.dll, qhull6_p.dll and qhull6_pd.dll
# -------------------------------------------------

TEMPLATE = subdirs
CONFIG += ordered

SUBDIRS += libqhull        #shared library
SUBDIRS += libqhullp       #shared library with qh_QHpointer (libqhull/user.h)
SUBDIRS += user_eg         #user program linked to libqhull6_p (libqhullp)

SUBDIRS += libqhullstatic  #static library
SUBDIRS += libqhullstaticp #static library with qh_QHpointer
SUBDIRS += qhull           #qhull programs linked to libqhullstatic
SUBDIRS += qconvex
SUBDIRS += qdelaunay
SUBDIRS += qhalf
SUBDIRS += qvoronoi
SUBDIRS += rbox
SUBDIRS += user_eg2        #user program linked to libqhull
SUBDIRS += testqset        #test program for qset.c with mem.c

SUBDIRS += libqhullcpp     #static library for C++ interface with libqhullstaticp
SUBDIRS += user_eg3        #user program with libqhullcpp and libqhullstaticp
SUBDIRS += qhulltest       #test program with Qt, libqhullcpp, and libqhullstaticp

OTHER_FILES += Changes.txt
OTHER_FILES += CMakeLists.txt
OTHER_FILES += Make-config.sh
OTHER_FILES += ../Announce.txt
OTHER_FILES += ../CMakeLists.txt
OTHER_FILES += ../COPYING.txt
OTHER_FILES += ../File_id.diz
OTHER_FILES += ../index.htm
OTHER_FILES += ../Makefile
OTHER_FILES += ../README.txt
OTHER_FILES += ../REGISTER.txt
OTHER_FILES += ../eg/q_eg
OTHER_FILES += ../eg/q_egtest
OTHER_FILES += ../eg/q_test
OTHER_FILES += ../html/index.htm
OTHER_FILES += ../html/qconvex.htm
OTHER_FILES += ../html/qdelau_f.htm
OTHER_FILES += ../html/qdelaun.htm
OTHER_FILES += ../html/qhalf.htm
OTHER_FILES += ../html/qh-code.htm
OTHER_FILES += ../html/qh-eg.htm
OTHER_FILES += ../html/qh-faq.htm
OTHER_FILES += ../html/qh-get.htm
OTHER_FILES += ../html/qh-impre.htm
OTHER_FILES += ../html/qh-optc.htm
OTHER_FILES += ../html/qh-optf.htm
OTHER_FILES += ../html/qh-optg.htm
OTHER_FILES += ../html/qh-opto.htm
OTHER_FILES += ../html/qh-optp.htm
OTHER_FILES += ../html/qh-optq.htm
OTHER_FILES += ../html/qh-optt.htm
OTHER_FILES += ../html/qh-quick.htm
OTHER_FILES += ../html/qhull.htm
OTHER_FILES += ../html/qhull.man
OTHER_FILES += ../html/qhull.txt
OTHER_FILES += ../html/qhull-cpp.xml
OTHER_FILES += ../html/qvoron_f.htm
OTHER_FILES += ../html/qvoronoi.htm
OTHER_FILES += ../html/rbox.htm
OTHER_FILES += ../html/rbox.man
OTHER_FILES += ../html/rbox.txt
qhull-2012.1/src/qhull-app-c.pri0000644000076400010400000000114011547730627017542 0ustar  bbarberAdministrators# -------------------------------------------------
# qhull-app-c.pri -- Qt include project for C qhull applications linked to libqhull
# -------------------------------------------------

include(qhull-warn.pri)

DESTDIR = ../../bin
TEMPLATE = app
CONFIG += console warn_on
CONFIG -= qt

LIBS += -L../../lib
build_pass:CONFIG(debug, debug|release){
   LIBS += -lqhullstatic_d
   OBJECTS_DIR = Debug
}else:build_pass:CONFIG(release, debug|release){
   LIBS += -lqhullstatic
   OBJECTS_DIR = Release
}
win32-msvc* : QMAKE_LFLAGS += /INCREMENTAL:NO

INCLUDEPATH += ../libqhull
CONFIG += qhull_warn_conversion

qhull-2012.1/src/qhull-app-cpp.pri0000644000076400010400000000160211720334551020072 0ustar  bbarberAdministrators# -------------------------------------------------
# qhull-app-cpp.pri -- Qt include project for static CPP qhull applications using Qt
# -------------------------------------------------

include(qhull-warn.pri)

DESTDIR = ../../bin
TEMPLATE = app
CONFIG += console warn_on
CONFIG -= rtti
LIBS += -L../../lib
build_pass:CONFIG(debug, debug|release){
   LIBS += -lqhullcpp_d
   LIBS += -lqhullstatic_pd  # Must be last, otherwise qh_fprintf,etc. are loaded from here instead of qhullcpp-d.lib
   OBJECTS_DIR = Debug
}else:build_pass:CONFIG(release, debug|release){
   LIBS += -lqhullcpp
   LIBS += -lqhullstatic_p  # Must be last, otherwise qh_fprintf,etc. are loaded from here instead of qhullcpp.lib
   OBJECTS_DIR = Release
}
win32-msvc* : QMAKE_LFLAGS += /INCREMENTAL:NO

DEFINES += qh_QHpointer # libqhull/user.h

INCLUDEPATH += ../libqhullcpp
INCLUDEPATH += ../../src # "libqhull/qhull_a.h"
qhull-2012.1/src/qhull-app-shared.pri0000644000076400010400000000124611710647015020563 0ustar  bbarberAdministrators# -------------------------------------------------
# qhull-app-shared.pri -- Qt include project for C qhull applications linked with libqhull (shared library)
# -------------------------------------------------

include(qhull-warn.pri)

DESTDIR = ../../bin
TEMPLATE = app
CONFIG += console warn_on
CONFIG -= qt

LIBS += -L../../lib
build_pass:CONFIG(debug, debug|release){
   LIBS += -lqhull_d
   OBJECTS_DIR = Debug
}else:build_pass:CONFIG(release, debug|release){
   LIBS += -lqhull
   OBJECTS_DIR = Release
}
win32-msvc* : QMAKE_LFLAGS += /INCREMENTAL:NO

win32-msvc* : DEFINES += qh_dllimport # libqhull/user.h

INCLUDEPATH += ../libqhull
CONFIG += qhull_warn_conversion


qhull-2012.1/src/qhull-app-sharedp.pri0000644000076400010400000000136711720335101020736 0ustar  bbarberAdministrators# -------------------------------------------------
# qhull-app-sharedp.pri -- Qt include project for C qhull applications linked with libqhull6_p 
#   Compile code with -Dqh_QHpointer 
# -------------------------------------------------

include(qhull-warn.pri)

DESTDIR = ../../bin
TEMPLATE = app
CONFIG += console warn_on
CONFIG -= qt

LIBS += -L../../lib
build_pass:CONFIG(debug, debug|release){
   LIBS += -lqhull_pd
   OBJECTS_DIR = Debug
}else:build_pass:CONFIG(release, debug|release){
   LIBS += -lqhull_p
   OBJECTS_DIR = Release
}
win32-msvc* : QMAKE_LFLAGS += /INCREMENTAL:NO

DEFINES += qh_QHpointer # libqhull/user.h
win32-msvc* : DEFINES += qh_QHpointer_dllimport # libqhull/user.h

INCLUDEPATH += ../libqhull
CONFIG += qhull_warn_conversion


qhull-2012.1/src/qhull-libqhull-src.pri0000644000076400010400000000234511710647745021153 0ustar  bbarberAdministrators# -------------------------------------------------
# qhull-libqhull-src.pri -- Qt include project for libqhull sources and headers
#   libqhull.pro, libqhullp.pro, and libqhulldll.pro are the same for SOURCES and HEADERS
# -------------------------------------------------

# Order object files by frequency of execution.  Small files at end.
# Current directory is caller
SOURCES += ../libqhull/global.c
SOURCES += ../libqhull/stat.c
SOURCES += ../libqhull/geom2.c
SOURCES += ../libqhull/poly2.c
SOURCES += ../libqhull/merge.c
SOURCES += ../libqhull/libqhull.c
SOURCES += ../libqhull/geom.c
SOURCES += ../libqhull/poly.c
SOURCES += ../libqhull/qset.c
SOURCES += ../libqhull/mem.c
SOURCES += ../libqhull/random.c
SOURCES += ../libqhull/usermem.c
SOURCES += ../libqhull/userprintf.c
SOURCES += ../libqhull/io.c
SOURCES += ../libqhull/user.c
SOURCES += ../libqhull/rboxlib.c
SOURCES += ../libqhull/userprintf_rbox.c

HEADERS += ../libqhull/geom.h
HEADERS += ../libqhull/io.h
HEADERS += ../libqhull/libqhull.h
HEADERS += ../libqhull/mem.h
HEADERS += ../libqhull/merge.h
HEADERS += ../libqhull/poly.h
HEADERS += ../libqhull/random.h
HEADERS += ../libqhull/qhull_a.h
HEADERS += ../libqhull/qset.h
HEADERS += ../libqhull/stat.h
HEADERS += ../libqhull/user.h
qhull-2012.1/src/qhull-warn.pri0000644000076400010400000000613411720335155017507 0ustar  bbarberAdministrators# -------------------------------------------------
# qhull-warn.pri -- Qt project warnings for warn_on
#   CONFIG += qhull_warn_all        # Qhull compiles with all warnings except for qhull_warn_shadow and qhull_warn_conversion
#   CONFIG += qhull_warn_conversion # Warn in Qt and Qhull about conversion errors
#   CONFIG += qhull_warn_error      # Turn warnings into errors
#   CONFIG += qhull_warn_shadow     # Warn in Qt about shadowing of functions and fields
# -------------------------------------------------

# [apr'11] VERSION works erratically for msvc builds
# VERSION = 6.3.1
qhull_SOVERSION = 6

# Uncomment to report warnings as errors
#CONFIG += qhull_warn_error

*g++{
    qhull_warn_error{
        QMAKE_CFLAGS_WARN_ON += -Werror
        QMAKE_CXXFLAGS_WARN_ON += -Werror
    }

    QMAKE_CFLAGS_WARN_ON += -Wcast-qual -Wextra -Wshadow -Wwrite-strings

    QMAKE_CXXFLAGS_WARN_ON += -Wcast-qual -Wextra -Wwrite-strings
    QMAKE_CXXFLAGS_WARN_ON += -Wno-sign-conversion

    qhull_warn_shadow{
        QMAKE_CXXFLAGS_WARN_ON += -Wshadow     # Shadowing occurs in Qt, e.g., nested foreach
    }

    qhull_warn_conversion{
        QMAKE_CFLAGS_WARN_ON += -Wno-sign-conversion   # libqhullstatic has many size_t vs. int warnings
        QMAKE_CFLAGS_WARN_ON += -Wconversion           # libqhullstatic has no workaround for bit-field conversions
        QMAKE_CXXFLAGS_WARN_ON += -Wconversion         # Qt has conversion errors for qbitarray and qpalette
    }

    qhull_warn_all{
        QMAKE_CFLAGS_WARN_ON += -Waddress -Warray-bounds -Wchar-subscripts -Wclobbered -Wcomment -Wempty-body
        QMAKE_CFLAGS_WARN_ON += -Wformat -Wignored-qualifiers -Wimplicit-function-declaration -Wimplicit-int
        QMAKE_CFLAGS_WARN_ON += -Wmain -Wmissing-braces -Wmissing-field-initializers -Wmissing-parameter-type
        QMAKE_CFLAGS_WARN_ON += -Wnonnull -Wold-style-declaration -Woverride-init -Wparentheses
        QMAKE_CFLAGS_WARN_ON += -Wpointer-sign -Wreturn-type -Wsequence-point -Wsign-compare
        QMAKE_CFLAGS_WARN_ON += -Wsign-compare -Wstrict-aliasing -Wstrict-overflow=1 -Wswitch
        QMAKE_CFLAGS_WARN_ON += -Wtrigraphs -Wtype-limits -Wuninitialized -Wuninitialized
        QMAKE_CFLAGS_WARN_ON += -Wunknown-pragmas -Wunused-function -Wunused-label -Wunused-parameter
        QMAKE_CFLAGS_WARN_ON += -Wunused-value -Wunused-variable -Wvolatile-register-var

        QMAKE_CXXFLAGS_WARN_ON += -Waddress -Warray-bounds -Wc++0x-compat -Wchar-subscripts
        QMAKE_CXXFLAGS_WARN_ON += -Wclobbered -Wcomment -Wempty-body -Wenum-compare
        QMAKE_CXXFLAGS_WARN_ON += -Wformat -Wignored-qualifiers -Wmain -Wmissing-braces
        QMAKE_CXXFLAGS_WARN_ON += -Wmissing-field-initializers -Wparentheses -Wreorder -Wreturn-type
        QMAKE_CXXFLAGS_WARN_ON += -Wsequence-point -Wsign-compare -Wsign-compare -Wstrict-aliasing
        QMAKE_CXXFLAGS_WARN_ON += -Wstrict-overflow=1 -Wswitch -Wtrigraphs -Wtype-limits
        QMAKE_CXXFLAGS_WARN_ON += -Wuninitialized -Wunknown-pragmas -Wunused-function -Wunused-label
        QMAKE_CXXFLAGS_WARN_ON += -Wunused-parameter -Wunused-value -Wunused-variable -Wvolatile-register-var
    }
}
qhull-2012.1/src/qhulltest/0000755000076400010400000000000011721063455016724 5ustar  bbarberAdministratorsqhull-2012.1/src/qhulltest/Coordinates_test.cpp0000644000076400010400000003234011716456524022752 0ustar  bbarberAdministrators/****************************************************************************
**
** Copyright (c) 2009-2012 C.B. Barber. All rights reserved.
** $Id: //main/2011/qhull/src/qhulltest/Coordinates_test.cpp#4 $$Change: 1490 $
** $DateTime: 2012/02/19 20:27:01 $$Author: bbarber $
**
****************************************************************************/

//pre-compiled headers
#include 
#include "RoadTest.h" // QT_VERSION

#include "Coordinates.h"
#include "QhullError.h"
#include "RboxPoints.h"
#include "Qhull.h"

using std::cout;
using std::endl;
using std::ostringstream;
using std::ostream;
using std::string;

namespace orgQhull {

class Coordinates_test : public RoadTest
{
    Q_OBJECT

#//Test slots
private slots:
    void t_construct();
    void t_convert();
    void t_element();
    void t_readonly();
    void t_operator();
    void t_const_iterator();
    void t_iterator();
    void t_coord_iterator();
    void t_mutable_coord_iterator();
    void t_readwrite();
    void t_search();
    void t_io();
};//Coordinates_test

void
add_Coordinates_test()
{
    new Coordinates_test();
}

void Coordinates_test::
t_construct()
{
    Coordinates c;
    QCOMPARE(c.size(), 0U);
    QVERIFY(c.isEmpty());
    c << 1.0;
    QCOMPARE(c.count(), 1);
    Coordinates c2(c);
    c2 << 2.0;
    QCOMPARE(c2.count(), 2);
    Coordinates c3;
    c3 = c2;
    QCOMPARE(c3.count(), 2);
    QCOMPARE(c3[0]+c3[1], 3.0);
    QVERIFY(c2==c3);
    std::vector vc;
    vc.push_back(3.0);
    vc.push_back(4.0);
    Coordinates c4(vc);
    QCOMPARE(c4[0]+c4[1], 7.0);
    Coordinates c5(c3);
    QVERIFY(c5==c3);
    c5= vc;
    QVERIFY(c5!=c3);
    QVERIFY(c5==c4);
}//t_construct

void Coordinates_test::
t_convert()
{
    Coordinates c;
    c << 1.0 << 3.0;
    QCOMPARE(c.data()[1], 3.0);
    coordT *c2= c.data();
    const coordT *c3= c.data();
    QCOMPARE(c2, c3);
    std::vector vc= c.toStdVector();
    QCOMPARE(vc.size(), c.size());
    for(size_t k= vc.size(); k--; ){
        QCOMPARE(vc[k], c[k]);
    }
    QList qc= c.toQList();
    QCOMPARE(qc.count(), c.count());
    for(int k= qc.count(); k--; ){
        QCOMPARE(qc[k], c[k]);
    }
    Coordinates c4;
    c4= std::vector(2, 0.0);
    QCOMPARE(c4.back(), 0.0);
    Coordinates c5(std::vector(2, 0.0));
    QCOMPARE(c4.size(), c5.size());
    QVERIFY(c4==c5);
}//t_convert

void Coordinates_test::
t_element()
{
    Coordinates c;
    c << 1.0 << -2.0;
    c.at(1)= -3;
    QCOMPARE(c.at(1), -3.0);
    QCOMPARE(c.back(), -3.0);
    QCOMPARE(c.front(), 1.0);
    c[1]= -2.0;
    QCOMPARE(c[1],-2.0);
    QCOMPARE(c.first(), 1.0);
    c.first()= 2.0;
    QCOMPARE(c.first(), 2.0);
    QCOMPARE(c.last(), -2.0);
    c.last()= 0.0;
    QCOMPARE(c.first()+c.last(), 2.0);
    coordT *c4= &c.first();
    const coordT *c5= &c.first();
    QCOMPARE(c4, c5);
    coordT *c6= &c.last();
    const coordT *c7= &c.last();
    QCOMPARE(c6, c7);
    Coordinates c2= c.mid(1);
    QCOMPARE(c2.count(), 1);
    c << 3.0;
    Coordinates c3= c.mid(1,1);
    QCOMPARE(c2, c3);
    QCOMPARE(c3.value(-1, -1.0), -1.0);
    QCOMPARE(c3.value(3, 4.0), 4.0);
    QCOMPARE(c.value(2, 4.0), 3.0);
}//t_element

void Coordinates_test::
t_readonly()
{
    Coordinates c;
    QCOMPARE(c.size(), 0u);
    QCOMPARE(c.count(), 0);
    QVERIFY(c.empty());
    QVERIFY(c.isEmpty());
    c << 1.0 << -2.0;
    QCOMPARE(c.size(), 2u);
    QCOMPARE(c.count(), 2);
    QVERIFY(!c.empty());
    QVERIFY(!c.isEmpty());
}//t_readonly

void Coordinates_test::
t_operator()
{
    Coordinates c;
    Coordinates c2(c);
    QVERIFY(c==c2);
    QVERIFY(!(c!=c2));
    c << 1.0;
    QVERIFY(!(c==c2));
    QVERIFY(c!=c2);
    c2 << 1.0;
    QVERIFY(c==c2);
    QVERIFY(!(c!=c2));
    c[0]= 0.0;
    QVERIFY(c!=c2);
    Coordinates c3= c+c2;
    QCOMPARE(c3.count(), 2);
    QCOMPARE(c3[0], 0.0);
    QCOMPARE(c3[1], 1.0);
    c3 += c3;
    QCOMPARE(c3.count(), 4);
    QCOMPARE(c3[2], 0.0);
    QCOMPARE(c3[3], 1.0);
    c3 += c2;
    QCOMPARE(c3[4], 1.0);
    c3 += 5.0;
    QCOMPARE(c3.count(), 6);
    QCOMPARE(c3[5], 5.0);
    // << checked above
}//t_operator

void Coordinates_test::
t_const_iterator()
{
    Coordinates c;
    QCOMPARE(c.begin(), c.end());
    // begin and end checked elsewhere
    c << 1.0 << 3.0;
    Coordinates::const_iterator i= c.begin();
    QCOMPARE(*i, 1.0);
    QCOMPARE(i[1], 3.0);
    // i[1]= -3.0; // compiler error
    // operator-> is not applicable to double
    QCOMPARE(*i++, 1.0);
    QCOMPARE(*i, 3.0);
    QCOMPARE(*i--, 3.0);
    QCOMPARE(*i, 1.0);
    QCOMPARE(*(i+1), 3.0);
    QCOMPARE(*++i, 3.0);
    QCOMPARE(*(i-1), 1.0);
    QCOMPARE(*--i, 1.0);
    QVERIFY(i==c.begin());
    QVERIFY(i==c.constBegin());
    QVERIFY(i!=c.end());
    QVERIFY(i!=c.constEnd());
    QVERIFY(i=c.begin());
    QVERIFY(i+1<=c.end());
    QVERIFY(i+1>c.begin());
    Coordinates::iterator i2= c.begin();
    Coordinates::const_iterator i3(i2);
    QCOMPARE(*i3, 1.0);
    QCOMPARE(i3[1], 3.0);
}//t_const_iterator

void Coordinates_test::
t_iterator()
{
    Coordinates c;
    QCOMPARE(c.begin(), c.end());
    // begin and end checked elsewhere
    c << 1.0 << 3.0;
    Coordinates::iterator i= c.begin();
    QCOMPARE(*i, 1.0);
    QCOMPARE(i[1], 3.0);
    *i= -1.0;
    QCOMPARE(*i, -1.0);
    i[1]= -3.0;
    QCOMPARE(i[1], -3.0);
    *i= 1.0;
    // operator-> is not applicable to double
    QCOMPARE(*i++, 1.0);
    QCOMPARE(*i, -3.0);
    *i= 3.0;
    QCOMPARE(*i--, 3.0);
    QCOMPARE(*i, 1.0);
    QCOMPARE(*(i+1), 3.0);
    QCOMPARE(*++i, 3.0);
    QCOMPARE(*(i-1), 1.0);
    QCOMPARE(*--i, 1.0);
    QVERIFY(i==c.begin());
    QVERIFY(i==c.constBegin());
    QVERIFY(i!=c.end());
    QVERIFY(i!=c.constEnd());
    QVERIFY(i=c.begin());
    QVERIFY(i+1<=c.end());
    QVERIFY(i+1>c.begin());
}//t_iterator

void Coordinates_test::
t_coord_iterator()
{
    Coordinates c;
    c << 1.0 << 3.0;
    CoordinatesIterator i(c);
    CoordinatesIterator i2= c;
    QVERIFY(i.findNext(1.0));
    QVERIFY(!i.findNext(2.0));
    QVERIFY(!i.findNext(3.0));
    QVERIFY(i.findPrevious(3.0));
    QVERIFY(!i.findPrevious(2.0));
    QVERIFY(!i.findPrevious(1.0));
    QVERIFY(i2.findNext(3.0));
    QVERIFY(i2.findPrevious(3.0));
    QVERIFY(i2.findNext(3.0));
    QVERIFY(i2.findPrevious(1.0));
    QVERIFY(i2.hasNext());
    QVERIFY(!i2.hasPrevious());
    QVERIFY(i.hasNext());
    QVERIFY(!i.hasPrevious());
    i.toBack();
    i2.toFront();
    QVERIFY(!i.hasNext());
    QVERIFY(i.hasPrevious());
    QVERIFY(i2.hasNext());
    QVERIFY(!i2.hasPrevious());
    Coordinates c2;
    i2= c2;
    QVERIFY(!i2.hasNext());
    QVERIFY(!i2.hasPrevious());
    i2.toBack();
    QVERIFY(!i2.hasNext());
    QVERIFY(!i2.hasPrevious());
    QCOMPARE(i.peekPrevious(), 3.0);
    QCOMPARE(i.previous(), 3.0);
    QCOMPARE(i.previous(), 1.0);
    QVERIFY(!i.hasPrevious());
    QCOMPARE(i.peekNext(), 1.0);
    // i.peekNext()= 1.0; // compiler error
    QCOMPARE(i.next(), 1.0);
    QCOMPARE(i.peekNext(), 3.0);
    QCOMPARE(i.next(), 3.0);
    QVERIFY(!i.hasNext());
    i.toFront();
    QCOMPARE(i.next(), 1.0);
}//t_coord_iterator

void Coordinates_test::
t_mutable_coord_iterator()
{
    // Same tests as CoordinatesIterator
    Coordinates c;
    c << 1.0 << 3.0;
    MutableCoordinatesIterator i(c);
    MutableCoordinatesIterator i2= c;
    QVERIFY(i.findNext(1.0));
    QVERIFY(!i.findNext(2.0));
    QVERIFY(!i.findNext(3.0));
    QVERIFY(i.findPrevious(3.0));
    QVERIFY(!i.findPrevious(2.0));
    QVERIFY(!i.findPrevious(1.0));
    QVERIFY(i2.findNext(3.0));
    QVERIFY(i2.findPrevious(3.0));
    QVERIFY(i2.findNext(3.0));
    QVERIFY(i2.findPrevious(1.0));
    QVERIFY(i2.hasNext());
    QVERIFY(!i2.hasPrevious());
    QVERIFY(i.hasNext());
    QVERIFY(!i.hasPrevious());
    i.toBack();
    i2.toFront();
    QVERIFY(!i.hasNext());
    QVERIFY(i.hasPrevious());
    QVERIFY(i2.hasNext());
    QVERIFY(!i2.hasPrevious());
    Coordinates c2;
    i2= c2;
    QVERIFY(!i2.hasNext());
    QVERIFY(!i2.hasPrevious());
    i2.toBack();
    QVERIFY(!i2.hasNext());
    QVERIFY(!i2.hasPrevious());
    QCOMPARE(i.peekPrevious(), 3.0);
    QCOMPARE(i.peekPrevious(), 3.0);
    QCOMPARE(i.previous(), 3.0);
    QCOMPARE(i.previous(), 1.0);
    QVERIFY(!i.hasPrevious());
    QCOMPARE(i.peekNext(), 1.0);
    QCOMPARE(i.next(), 1.0);
    QCOMPARE(i.peekNext(), 3.0);
    QCOMPARE(i.next(), 3.0);
    QVERIFY(!i.hasNext());
    i.toFront();
    QCOMPARE(i.next(), 1.0);

    // Mutable tests
    i.toFront();
    i.peekNext()= -1.0;
    QCOMPARE(i.peekNext(), -1.0);
    QCOMPARE((i.next()= 1.0), 1.0);
    QCOMPARE(i.peekPrevious(), 1.0);
    i.remove();
    QCOMPARE(c.count(), 1);
    i.remove();
    QCOMPARE(c.count(), 1);
    QCOMPARE(i.peekNext(), 3.0);
    i.insert(1.0);
    i.insert(2.0);
    QCOMPARE(c.count(), 3);
    QCOMPARE(i.peekNext(), 3.0);
    QCOMPARE(i.peekPrevious(), 2.0);
    i.peekPrevious()= -2.0;
    QCOMPARE(i.peekPrevious(), -2.0);
    QCOMPARE((i.previous()= 2.0), 2.0);
    QCOMPARE(i.peekNext(), 2.0);
    i.toBack();
    i.remove();
    QCOMPARE(c.count(), 3); // unchanged
    i.toFront();
    i.remove();
    QCOMPARE(c.count(), 3); // unchanged
    QCOMPARE(i.peekNext(), 1.0);
    i.remove();
    QCOMPARE(c.count(), 3); // unchanged
    i.insert(0.0);
    QCOMPARE(c.count(), 4);
    QCOMPARE(i.value(), 0.0);
    QCOMPARE(i.peekPrevious(), 0.0);
    i.setValue(-10.0);
    QCOMPARE(c.count(), 4); // unchanged
    QCOMPARE(i.peekNext(), 1.0);
    QCOMPARE(i.peekPrevious(), -10.0);
    i.findNext(1.0);
    i.setValue(-1.0);
    QCOMPARE(i.peekPrevious(), -1.0);
    i.setValue(1.0);
    QCOMPARE(i.peekPrevious(), 1.0);
    QCOMPARE(i.value(), 1.0);
    i.findPrevious(1.0);
    i.setValue(-1.0);
    QCOMPARE(i.peekNext(), -1.0);
    i.toBack();
    QCOMPARE(i.previous(), 3.0);
    i.setValue(-3.0);
    QCOMPARE(i.peekNext(), -3.0);
    double d= i.value();
    QCOMPARE(d, -3.0);
    QCOMPARE(i.previous(), 2.0);
}//t_mutable_coord_iterator

void Coordinates_test::
t_readwrite()
{
    Coordinates c;
    c.clear();
    QCOMPARE(c.count(), 0);
    c << 1.0 << 3.0;
    c.clear();
    QCOMPARE(c.count(), 0);
    c << 1.0 << 3.0;
    c.erase(c.begin(), c.end());
    QCOMPARE(c.count(), 0);
    c << 1.0 << 0.0;
    Coordinates::iterator i= c.erase(c.begin());
    QCOMPARE(*i, 0.0);
    i= c.insert(c.end(), 1.0);
    QCOMPARE(*i, 1.0);
    QCOMPARE(c.count(), 2);
    c.pop_back();
    QCOMPARE(c.count(), 1);   // 0
    QCOMPARE(c[0], 0.0);
    c.push_back(2.0);
    QCOMPARE(c.count(), 2);
    c.append(3.0);
    QCOMPARE(c.count(), 3);   // 0, 2, 3
    QCOMPARE(c[2], 3.0);
    c.insert(0, 4.0);
    QCOMPARE(c[0], 4.0);
    QCOMPARE(c[3], 3.0);
    c.insert(c.count(), 5.0);
    QCOMPARE(c.count(), 5);   // 4, 0, 2, 3, 5
    QCOMPARE(c[4], 5.0);
    c.move(4, 0);
    QCOMPARE(c.count(), 5);   // 5, 4, 0, 2, 3
    QCOMPARE(c[0], 5.0);
    c.pop_front();
    QCOMPARE(c.count(), 4);
    QCOMPARE(c[0], 4.0);
    c.prepend(6.0);
    QCOMPARE(c.count(), 5);   // 6, 4, 0, 2, 3
    QCOMPARE(c[0], 6.0);
    c.push_front(7.0);
    QCOMPARE(c.count(), 6);
    QCOMPARE(c[0], 7.0);
    c.removeAt(1);
    QCOMPARE(c.count(), 5);   // 7, 4, 0, 2, 3
    QCOMPARE(c[1], 4.0);
    c.removeFirst();
    QCOMPARE(c.count(), 4);   // 4, 0, 2, 3
    QCOMPARE(c[0], 4.0);
    c.removeLast();
    QCOMPARE(c.count(), 3);
    QCOMPARE(c.last(), 2.0);
    c.replace(2, 8.0);
    QCOMPARE(c.count(), 3);   // 4, 0, 8
    QCOMPARE(c[2], 8.0);
    c.swap(0, 2);
    QCOMPARE(c[2], 4.0);
    double d= c.takeAt(2);
    QCOMPARE(c.count(), 2);   // 8, 0
    QCOMPARE(d, 4.0);
    double d2= c.takeFirst();
    QCOMPARE(c.count(), 1);   // 0
    QCOMPARE(d2, 8.0);
    double d3= c.takeLast();
    QVERIFY(c.isEmpty()); \
    QCOMPARE(d3, 0.0);
}//t_readwrite

void Coordinates_test::
t_search()
{
    Coordinates c;
    c << 1.0 << 3.0 << 1.0;
    QVERIFY(c.contains(1.0));
    QVERIFY(c.contains(3.0));
    QVERIFY(!c.contains(0.0));
    QCOMPARE(c.count(1.0), 2);
    QCOMPARE(c.count(3.0), 1);
    QCOMPARE(c.count(0.0), 0);
    QCOMPARE(c.indexOf(1.0), 0);
    QCOMPARE(c.indexOf(3.0), 1);
    QCOMPARE(c.indexOf(1.0, -1), 2);
    QCOMPARE(c.indexOf(3.0, -1), -1);
    QCOMPARE(c.indexOf(3.0, -2), 1);
    QCOMPARE(c.indexOf(1.0, -3), 0);
    QCOMPARE(c.indexOf(1.0, -4), 0);
    QCOMPARE(c.indexOf(1.0, 1), 2);
    QCOMPARE(c.indexOf(3.0, 2), -1);
    QCOMPARE(c.indexOf(1.0, 2), 2);
    QCOMPARE(c.indexOf(1.0, 3), -1);
    QCOMPARE(c.indexOf(1.0, 4), -1);
    QCOMPARE(c.lastIndexOf(1.0), 2);
    QCOMPARE(c.lastIndexOf(3.0), 1);
    QCOMPARE(c.lastIndexOf(1.0, -1), 2);
    QCOMPARE(c.lastIndexOf(3.0, -1), 1);
    QCOMPARE(c.lastIndexOf(3.0, -2), 1);
    QCOMPARE(c.lastIndexOf(1.0, -3), 0);
    QCOMPARE(c.lastIndexOf(1.0, -4), -1);
    QCOMPARE(c.lastIndexOf(1.0, 1), 0);
    QCOMPARE(c.lastIndexOf(3.0, 2), 1);
    QCOMPARE(c.lastIndexOf(1.0, 2), 2);
    QCOMPARE(c.lastIndexOf(1.0, 3), 2);
    QCOMPARE(c.lastIndexOf(1.0, 4), 2);
    c.removeAll(3.0);
    QCOMPARE(c.count(), 2);
    c.removeAll(4.0);
    QCOMPARE(c.count(), 2);
    c.removeAll(1.0);
    QCOMPARE(c.count(), 0);
    c.removeAll(4.0);
    QCOMPARE(c.count(), 0);
}//t_search

void Coordinates_test::
t_io()
{
    Coordinates c;
    c << 1.0 << 2.0 << 3.0;
    ostringstream os;
    os << "Coordinates 1-2-3\n" << c;
    cout << os.str();
    QString s= QString::fromStdString(os.str());
    QCOMPARE(s.count("2"), 2);
}//t_io

}//orgQhull

#include "moc/Coordinates_test.moc"
qhull-2012.1/src/qhulltest/PointCoordinates_test.cpp0000644000076400010400000002552211716456524023770 0ustar  bbarberAdministrators/****************************************************************************
**
** Copyright (c) 2009-2012 C.B. Barber. All rights reserved.
** $Id: //main/2011/qhull/src/qhulltest/PointCoordinates_test.cpp#6 $$Change: 1490 $
** $DateTime: 2012/02/19 20:27:01 $$Author: bbarber $
**
****************************************************************************/

//pre-compiled headers
#include 
#include "RoadTest.h" // QT_VERSION

#include "PointCoordinates.h"
#include "QhullError.h"
#include "RboxPoints.h"
#include "Qhull.h"

using std::cout;
using std::endl;
using std::ostringstream;
using std::ostream;
using std::string;
using std::stringstream;

namespace orgQhull {

class PointCoordinates_test : public RoadTest
{
    Q_OBJECT

#//Test slots
private slots:
    void t_construct();
    void t_convert();
    void t_getset();
    void t_element();
    void t_foreach();
    void t_search();
    void t_modify();
    void t_append_points();
    void t_coord_iterator();
    void t_io();
};//PointCoordinates_test

void
add_PointCoordinates_test()
{
    new PointCoordinates_test();
}

void PointCoordinates_test::
t_construct()
{
    PointCoordinates pc;
    QCOMPARE(pc.size(), 0U);
    QCOMPARE(pc.coordinateCount(), 0);
    QCOMPARE(pc.dimension(), 0);
    QCOMPARE(pc.coordinates(), (coordT *)0);
    QVERIFY(pc.isEmpty());
    pc.checkValid();
    PointCoordinates pc7(2);
    QCOMPARE(pc7.dimension(), 2);
    QCOMPARE(pc7.count(), 0);
    QVERIFY(pc7.isEmpty());
    QVERIFY(pc7.comment().empty());
    pc7.checkValid();
    PointCoordinates pc2("Test pc2");
    QCOMPARE(pc2.count(), 0);
    QVERIFY(pc2.isEmpty());
    QCOMPARE(pc2.comment(), std::string("Test pc2"));
    pc2.checkValid();
    PointCoordinates pc3(3, "Test 3-d pc3");
    QCOMPARE(pc3.dimension(), 3);
    QVERIFY(pc3.isEmpty());
    pc3.checkValid();
    coordT c[]= { 0.0, 1.0, 2.0, 3.0, 4.0, 5.0 };
    PointCoordinates pc4(2, "Test 2-d pc4", 6, c);
    QCOMPARE(pc4.dimension(), 2);
    QCOMPARE(pc4.count(), 3);
    QCOMPARE(pc4.size(), 3u);
    QVERIFY(!pc4.isEmpty());
    QVERIFY(!pc4.empty());
    pc4.checkValid();
    QhullPoint p= pc4[2];
    QCOMPARE(p[1], 5.0);
    // QhullPoint refers to PointCoordinates
    p[1] += 1.0;
    QCOMPARE(pc4[2][1], 6.0);
    PointCoordinates pc5(4, "Test 4-d pc5 with insufficient coordinates", 6, c);
    QCOMPARE(pc5.dimension(), 4);
    QCOMPARE(pc5.count(), 1);
    QCOMPARE(pc5.extraCoordinatesCount(), 2);
    QCOMPARE(pc5.extraCoordinates()[1], 5.0);
    QVERIFY(!pc5.isEmpty());;
    std::vector vc;
    vc.push_back(3.0);
    vc.push_back(4.0);
    vc.push_back(5.0);
    vc.push_back(6.0);
    vc.push_back(7.0);
    vc.push_back(9.0);
    pc5.append(2, &vc[3]); // Copy of vc[]
    pc5.checkValid();
    QhullPoint p5(4, &vc[1]);
    QCOMPARE(pc5[1], p5);
    PointCoordinates pc6(pc5); // Makes copy of point_coordinates
    QCOMPARE(pc6[1], p5);
    QVERIFY(pc6==pc5);
    QhullPoint p6= pc5[1];  // Refers to pc5.coordinates
    pc5[1][0] += 1.0;
    QCOMPARE(pc5[1], p6);
    QVERIFY(pc5[1]!=p5);
    QVERIFY(pc6!=pc5);
    pc6= pc5;
    QVERIFY(pc6==pc5);
    PointCoordinates pc8;
    pc6= pc8;
    QVERIFY(pc6!=pc5);
    QVERIFY(pc6.isEmpty());
}//t_construct

void PointCoordinates_test::
t_convert()
{
    //defineAs tested above
    coordT c[]= {0.0, 1.0, 2.0, 3.0, 4.0, 5.0};
    PointCoordinates ps(3, "two 3-d points", 6, c);
    QCOMPARE(ps.dimension(), 3);
    QCOMPARE(ps.size(), 2u);
    const coordT *c2= ps.constData();
    QVERIFY(c!=c2);
    QCOMPARE(c[0], c2[0]);
    const coordT *c3= ps.data();
    QCOMPARE(c3, c2);
    coordT *c4= ps.data();
    QCOMPARE(c4, c2);
    std::vector vs= ps.toStdVector();
    QCOMPARE(vs.size(), 6u);
    QCOMPARE(vs[5], 5.0);
    QList qs= ps.toQList();
    QCOMPARE(qs.size(), 6);
    QCOMPARE(qs[5], 5.0);
}//t_convert

void PointCoordinates_test::
t_getset()
{
    // See t_construct() for test of coordinates, coordinateCount, dimension, empty, isEmpty, ==, !=
    // See t_construct() for test of checkValid, comment, setDimension
    PointCoordinates pc("Coordinates c");
    pc.setComment("New comment");
    QCOMPARE(pc.comment(), std::string("New comment"));
    pc.checkValid();
    pc.makeValid();  // A no-op
    pc.checkValid();
    Coordinates cs= pc.getCoordinates();
    QVERIFY(cs.isEmpty());
    PointCoordinates pc2(pc);
    pc.setDimension(3);
    QVERIFY(pc2!=pc);
    coordT c[]= {0.0, 1.0, 2.0, 3.0, 4.0, 5.0};
    pc.append(6, c);
    pc.checkValid();
    pc.makeValid();  // A no-op
    QhullPoint p= pc[0];
    QCOMPARE(p[2], 2.0);
    try{
        pc.setDimension(2);
        QFAIL("setDimension(2) did not fail for 3-d.");
    }catch (const std::exception &e) {
        const char *s= e.what();
        cout << "INFO   : Caught " << s;
    }
}//t_getset

void PointCoordinates_test::
t_element()
{
    coordT c[]= {0.0, 1.0, 2.0, 3.0, 4.0, 5.0};
    PointCoordinates pc(2, "2-d points", 6, c);
    QhullPoint p= pc.at(0);
    QCOMPARE(p, pc[0]);
    QCOMPARE(p, pc.first());
    QCOMPARE(p, pc.value(0));
    p= pc.back();
    QCOMPARE(p, pc[2]);
    QCOMPARE(p, pc.last());
    QCOMPARE(p, pc.value(2));
    QhullPoints ps= pc.mid(1, 2);
    QCOMPARE(ps[1], p);
}//t_element

void PointCoordinates_test::
t_foreach()
{
    coordT c[]= {0.0, 1.0, 2.0, 3.0, 4.0, 5.0};
    PointCoordinates pc(2, "2-d points", 6, c);
    QhullPoints::Iterator i= pc.begin();
    QhullPoint p= pc[0];
    QCOMPARE(*i, p);
    QCOMPARE((*i)[0], 0.0);
    QhullPoint p3= pc[2];
    i= pc.end();
    QCOMPARE(i[-1], p3);
    const PointCoordinates pc2(2, "2-d points", 6, c);
    QhullPoints::ConstIterator i2= pc.begin();
    const QhullPoint p0= pc2[0];
    QCOMPARE(*i2, p0);
    QCOMPARE((*i2)[0], 0.0);
    QhullPoints::ConstIterator i3= i2;
    QCOMPARE(i3, i2);
    QCOMPARE((*i3)[0], 0.0);
    i3= pc.constEnd();
    --i3;
    QhullPoint p2= pc2[2];
    QCOMPARE(*i3, p2);
    i= pc.end();
    QVERIFY(i-1==i3);
    i2= pc2.end();
    QVERIFY(i2-1!=i3);
    QCOMPARE(*(i2-1), *i3);
    foreach(QhullPoint p3, pc){ //Qt only
        QVERIFY(p3[0]>=0.0);
        QVERIFY(p3[0]<=5.0);
    }
    Coordinates::ConstIterator i4= pc.beginCoordinates();
    QCOMPARE(*i4, 0.0);
    Coordinates::Iterator i5= pc.beginCoordinates();
    QCOMPARE(*i5, 0.0);
    i4= pc.beginCoordinates(1);
    QCOMPARE(*i4, 2.0);
    i5= pc.beginCoordinates(1);
    QCOMPARE(*i5, 2.0);
    i4= pc.endCoordinates();
    QCOMPARE(*--i4, 5.0);
    i5= pc.endCoordinates();
    QCOMPARE(*--i5, 5.0);
}//t_foreach

void PointCoordinates_test::
t_search()
{
    coordT c[]= {0.0, 1.0, 2.0, 3.0, 4.0, 5.0};
    PointCoordinates pc(2, "2-d points", 6, c);
    QhullPoint p0= pc[0];
    QhullPoint p2= pc[2];
    QVERIFY(pc.contains(p0));
    QVERIFY(pc.contains(p2));
    QCOMPARE(pc.count(p0), 1);
    QCOMPARE(pc.indexOf(p2), 2);
    QCOMPARE(pc.lastIndexOf(p0), 0);
}//t_search

void PointCoordinates_test::
t_modify()
{
    coordT c[]= {0.0, 1.0, 2.0, 3.0, 4.0, 5.0};
    PointCoordinates pc(2, "2-d points", 6, c);
    coordT c3[]= {0.0, 1.0, 2.0, 3.0, 4.0, 5.0};
    PointCoordinates pc5(2);
    pc5.append(6, c3); // 0-5
    QVERIFY(pc5==pc);
    PointCoordinates pc2(2, "2-d");
    coordT c2[]= {6.0, 7.0, 8.0, 9.0, 10.0, 11.0};
    pc2.append(6, c2);
    QCOMPARE(pc2.count(), 3);
    pc2.append(14.0);
    QCOMPARE(pc2.count(), 3);
    QCOMPARE(pc2.extraCoordinatesCount(), 1);
    pc2.append(15.0); // 6-11, 14,15
    QCOMPARE(pc2.count(), 4);
    QCOMPARE(pc2.extraCoordinatesCount(), 0);
    QhullPoint p(pc[0]);
    pc2.append(p); // 6-11, 14,15, 0,1
    QCOMPARE(pc2.count(), 5);
    QCOMPARE(pc2.extraCoordinatesCount(), 0);
    QCOMPARE(pc2.lastIndexOf(p), 4);
    pc.append(pc2); // Invalidates p
    QCOMPARE(pc.count(), 8); // 0-11, 14,15, 0,1
    QCOMPARE(pc.extraCoordinatesCount(), 0);
    QCOMPARE(pc.lastIndexOf(pc[0]), 7);
    pc.appendComment(" operators");
    QCOMPARE(pc.comment(), std::string("2-d points operators"));
    pc.checkValid();
    // see t_append_points for appendPoints
    PointCoordinates pc3= pc+pc2;
    pc3.checkValid();
    QCOMPARE(pc3.count(), 13);
    QCOMPARE(pc3[6][0], 14.0);
    QCOMPARE(pc3[8][0], 6.0);
    pc3 += pc;
    QCOMPARE(pc3.count(), 21);
    QCOMPARE(pc3[14][0], 2.0);
    pc3 += 12.0;
    pc3 += 14.0;
    QCOMPARE(pc3.count(), 22);
    QCOMPARE(pc3.last()[0], 12.0);
    // QhullPoint p3= pc3.first(); // += throws error because append may move the data
    QhullPoint p3= pc2.first();
    pc3 += p3;
    QCOMPARE(pc3.count(), 23);
    QCOMPARE(pc3.last()[0], 6.0);
    pc3 << pc;
    QCOMPARE(pc3.count(), 31);
    QCOMPARE(pc3.last()[0], 0.0);
    pc3 << 12.0 << 14.0;
    QCOMPARE(pc3.count(), 32);
    QCOMPARE(pc3.last()[0], 12.0);
    PointCoordinates pc4(pc3);
    pc4.reserveCoordinates(100);
    QVERIFY(pc3==pc4);
}//t_modify

void PointCoordinates_test::
t_append_points()
{
    PointCoordinates pc(2, "stringstream");
    stringstream s("2 3 1 2 3 4 5 6");
    pc.appendPoints(s);
    QCOMPARE(pc.count(), 3);
}//t_append_points

void PointCoordinates_test::
t_coord_iterator()
{
    PointCoordinates c(2);
    c << 0.0 << 1.0 << 2.0 << 3.0 << 4.0 << 5.0;
    PointCoordinatesIterator i(c);
    QhullPoint p0(c[0]);
    QhullPoint p1(c[1]);
    QhullPoint p2(c[2]);
    coordT c2[] = {-1.0, -2.0};
    QhullPoint p3(2, c2);
    PointCoordinatesIterator i2= c;
    QVERIFY(i.findNext(p1));
    QVERIFY(!i.findNext(p1));
    QVERIFY(!i.findNext(p2));
    QVERIFY(!i.findNext(p3));
    QVERIFY(i.findPrevious(p2));
    QVERIFY(!i.findPrevious(p2));
    QVERIFY(!i.findPrevious(p0));
    QVERIFY(!i.findPrevious(p3));
    QVERIFY(i2.findNext(p2));
    QVERIFY(i2.findPrevious(p0));
    QVERIFY(i2.findNext(p1));
    QVERIFY(i2.findPrevious(p0));
    QVERIFY(i2.hasNext());
    QVERIFY(!i2.hasPrevious());
    QVERIFY(i.hasNext());
    QVERIFY(!i.hasPrevious());
    i.toBack();
    i2.toFront();
    QVERIFY(!i.hasNext());
    QVERIFY(i.hasPrevious());
    QVERIFY(i2.hasNext());
    QVERIFY(!i2.hasPrevious());
    PointCoordinates c3;
    PointCoordinatesIterator i3= c3;
    QVERIFY(!i3.hasNext());
    QVERIFY(!i3.hasPrevious());
    i3.toBack();
    QVERIFY(!i3.hasNext());
    QVERIFY(!i3.hasPrevious());
    QCOMPARE(i.peekPrevious(), p2);
    QCOMPARE(i.previous(), p2);
    QCOMPARE(i.previous(), p1);
    QCOMPARE(i.previous(), p0);
    QVERIFY(!i.hasPrevious());
    QCOMPARE(i.peekNext(), p0);
    // i.peekNext()= 1.0; // compiler error
    QCOMPARE(i.next(), p0);
    QCOMPARE(i.peekNext(), p1);
    QCOMPARE(i.next(), p1);
    QCOMPARE(i.next(), p2);
    QVERIFY(!i.hasNext());
    i.toFront();
    QCOMPARE(i.next(), p0);
}//t_coord_iterator

void PointCoordinates_test::
t_io()
{
    PointCoordinates c;
    c << 1.0 << 2.0 << 3.0 << 1.0 << 2.0 << 3.0;
    ostringstream os;
    os << "PointCoordinates 0-d\n" << c;
    c.setDimension(2);
    os << "PointCoordinates 1-3-2\n" << c;
    cout << os.str();
    QString s= QString::fromStdString(os.str());
    QCOMPARE(s.count("0"), 3);
    QCOMPARE(s.count("2"), 4);
}//t_io

}//orgQhull

#include "moc/PointCoordinates_test.moc"
qhull-2012.1/src/qhulltest/Point_test.cpp0000644000076400010400000001315611716456524021575 0ustar  bbarberAdministrators/****************************************************************************
**
** Copyright (C) 2009-2012 C.B. Barber. All rights reserved.
** $Id: //main/2011/qhull/src/qhulltest/Point_test.cpp#4 $$Change: 1490 $
** $DateTime: 2012/02/19 20:27:01 $$Author: bbarber $
**
****************************************************************************/

#include 
using std::cout;
using std::endl;
#include "RoadTest.h" // QT_VERSION

#include "QhullPoint.h"

#include "Qhull.h"

namespace orgQhull {

class Point_test : public RoadTest
{
    Q_OBJECT

#//Test slots
private slots:
    void initTestCase();
    void t_construct();
    void t_getset();
    void t_operator();
    void t_const_iterator();
    void t_iterator();
    void t_point_iterator();
    // void t_mutable_point_iterator();
    // void t_io();
};//Point_test

void
add_Point_test()
{
    new Point_test();
}

void Point_test::
initTestCase(){
    RboxPoints rcube("c");
    Qhull q(rcube, "");
    UsingQhullLib::setGlobals();
}//initTestCase

void Point_test::
t_construct()
{
    QhullPoint p;
    QCOMPARE(p.dimension(), 0);
    coordT c[]= {0.0, 1.0, 2.0};
    QhullPoint p2;
    p2.defineAs(3, c);
    QCOMPARE(p2.dimension(), 3);
    QCOMPARE(p2.coordinates(), c);
    coordT c2[]= {0.0, 1.0, 2.0};
    QhullPoint p3(3, c2);
    QVERIFY(p3==p2);
    QhullPoint p5(p3);
    QVERIFY(p5==p3);
}//t_construct

void Point_test::
t_getset()
{
    coordT c[]= {0.0, 1.0, 2.0};
    QhullPoint p(3, c);
    QCOMPARE(p.coordinates(), c);
    QCOMPARE(p.dimension(), 3);
    QCOMPARE(p[2], 2.0);
    QhullPoint p2(p);
    p2.defineAs(p);
    QVERIFY(p2==p);
    QVERIFY(p2.coordinates()==p.coordinates());
    QVERIFY(p2.dimension()==p.dimension());
    p2.setDimension(2);
    QCOMPARE(p2.dimension(), 2);
    QVERIFY(p2!=p);
    coordT c2[]= {0.0, 1.0};
    p2.setCoordinates(c2);
    QCOMPARE(p2.coordinates(), c2);
    p.defineAs(2, c);
    QVERIFY(p2==p);
    QCOMPARE(p[1], 1.0);
}//t_getset

void Point_test::
t_operator()
{
    QhullPoint p;
    QhullPoint p2(p);
    QVERIFY(p==p2);
    QVERIFY(!(p!=p2));
    coordT c[]= {0.0, 1.0, 2.0};
    QhullPoint p3(3, c);
    QVERIFY(p3!=p2);
    QhullPoint p4(p3);
    QVERIFY(p4==p3);
    coordT c5[]= {5.0, 6.0, 7.0};
    QhullPoint p5(3, c5);
    QVERIFY(p5!=p3);
    QCOMPARE(p5[1], 6.0);
    QCOMPARE(p5[0], 5.0);
    const coordT *c0= &p5[0];
    QCOMPARE(*c0, 5.0);
}//t_operator

void Point_test::
t_const_iterator()
{
    coordT c[]= {1.0, 2.0, 3.0};
    QhullPoint p(3, c);
    QhullPoint::const_iterator i(p.coordinates());
    QhullPoint::const_iterator i2= p.coordinates();
    QVERIFY(i==i2);
    QVERIFY(i>=i2);
    QVERIFY(i<=i2);
    QCOMPARE(*i, 1.0);
    QCOMPARE(*(i+1), 2.0);
    QCOMPARE(*(i+1), i[1]);
    i= p.end();
    QVERIFY(i!=i2);
    i= i2;
    QVERIFY(i==i2);
    i= p.end();
    i= p.begin();
    QCOMPARE(*i, 1.0);
    QhullPoint::ConstIterator i3= p.end();
    QCOMPARE(*(i3-1), 3.0);
    QCOMPARE(*(i3-1), i3[-1]);
    QVERIFY(i!=i3);
    QVERIFY(ii);
    QVERIFY(i3>=i);
}//t_const_iterator


void Point_test::
t_iterator()
{
    coordT c[]= {1.0, 2.0, 3.0};
    QhullPoint p(3, c);
    QhullPoint::Iterator i(p.coordinates());
    QhullPoint::iterator i2= p.coordinates();
    QVERIFY(i==i2);
    QVERIFY(i>=i2);
    QVERIFY(i<=i2);
    QCOMPARE(*i, 1.0);
    QCOMPARE(*(i+1), 2.0);
    QCOMPARE(*(i+1), i[1]);
    i= p.end();
    QVERIFY(i!=i2);
    i= i2;
    QVERIFY(i==i2);
    i= p.end();
    i= p.begin();
    QCOMPARE(*i, 1.0);
    QhullPoint::Iterator i3= p.end();
    QCOMPARE(*(i3-1), 3.0);
    QCOMPARE(*(i3-1), i3[-1]);
    QVERIFY(i!=i3);
    QVERIFY(ii);
    QVERIFY(i3>=i);
    // compiler errors -- QhullPoint is const-only
    // QCOMPARE((i[0]= -10.0), -10.0);
    // coordT *c3= &i3[1];
}//t_iterator

void Point_test::
t_point_iterator()
{
    coordT c[]= {1.0, 3.0, 4.0};
    QhullPoint p(3, c);
    QhullPointIterator i(p);
    QhullPointIterator i2= p;
    QVERIFY(i2.hasNext());
    QVERIFY(!i2.hasPrevious());
    QVERIFY(i.hasNext());
    QVERIFY(!i.hasPrevious());
    i.toBack();
    i2.toFront();
    QVERIFY(!i.hasNext());
    QVERIFY(i.hasPrevious());
    QVERIFY(i2.hasNext());
    QVERIFY(!i2.hasPrevious());

    coordT c2[]= {1.0, 3.0, 4.0};
    QhullPoint p2(0, c2); // 0-dimensional
    i2= p2;
    QVERIFY(!i2.hasNext());
    QVERIFY(!i2.hasPrevious());
    i2.toBack();
    QVERIFY(!i2.hasNext());
    QVERIFY(!i2.hasPrevious());
    QCOMPARE(i.peekPrevious(), 4.0);
    QCOMPARE(i.previous(), 4.0);
    QCOMPARE(i.previous(), 3.0);
    QCOMPARE(i.previous(), 1.0);
    QVERIFY(!i.hasPrevious());
    QCOMPARE(i.peekNext(), 1.0);
    // i.peekNext()= 1.0; // compiler error
    QCOMPARE(i.next(), 1.0);
    QCOMPARE(i.peekNext(), 3.0);
    QCOMPARE(i.next(), 3.0);
    QCOMPARE(i.next(), 4.0);
    QVERIFY(!i.hasNext());
    i.toFront();
    QCOMPARE(i.next(), 1.0);
}//t_point_iterator

// No MutableQhullPointIterator since QhullPoint is const-only

#if 0

void Point_test::
t_io()
{
    QhullPoint p;
    cout<< "INFO:     empty point" << p << endl;
    const coordT c[]= {1.0, 3.0, 4.0};
    QhullPoint p2(2, c); // 2-dimensional
    cout<< "INFO:   " << p2 << endl;
}//t_io

error LNK2019: unresolved external symbol "class std::basic_ostream > & __cdecl operator<<(class std::basic_ostream > &,class orgQhull::QhullPoint &)" (??6@YAAAV?$basic_ostream@DU?$char_traits@D@std@@@std@@AAV01@AAVPoint@orgQhull@@@Z) referenced in function "private: void __thiscall orgQhull::Point_test::t_io(void)" (?t_io@Point_test@orgQhull@@AAEXXZ)

#endif

}//orgQhull

#include "moc/Point_test.moc"
qhull-2012.1/src/qhulltest/QhullFacetList_test.cpp0000644000076400010400000001140511716456524023363 0ustar  bbarberAdministrators/****************************************************************************
**
** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
** $Id: //main/2011/qhull/src/qhulltest/QhullFacetList_test.cpp#4 $$Change: 1490 $
** $DateTime: 2012/02/19 20:27:01 $$Author: bbarber $
**
****************************************************************************/

//pre-compiled headers
#include 
#include "RoadTest.h" // QT_VERSION

#include "QhullFacetList.h"
#include "QhullError.h"
#include "QhullFacet.h"
#include "QhullVertexSet.h"
#include "Qhull.h"

using std::cout;
using std::endl;
using std::ostringstream;
using std::ostream;
using std::string;

namespace orgQhull {

class QhullFacetList_test : public RoadTest
{
    Q_OBJECT

#//Test slots
private slots:
    void cleanup();
    void t_construct();
    void t_convert();
    void t_readonly();
    void t_foreach();
    void t_io();
};//QhullFacetList_test

void
add_QhullFacetList_test()
{
    new QhullFacetList_test();
}

//Executed after each testcase
void QhullFacetList_test::
cleanup()
{
    UsingLibQhull::checkQhullMemoryEmpty();
    RoadTest::cleanup();
}

void QhullFacetList_test::
t_construct()
{
    RboxPoints rcube("c");
    Qhull q(rcube,"QR0");  // rotated unit cube
    QhullFacetList fs2= q.facetList();
    QVERIFY(!fs2.isEmpty());
    QCOMPARE(fs2.count(),6);
    QhullFacetList fs3(q.endFacet(), q.endFacet());
    QVERIFY(fs3.isEmpty());
    QhullFacetList fs4(q.endFacet().previous(), q.endFacet());
    QCOMPARE(fs4.count(), 1);
    QhullFacetList fs5(q.beginFacet(), q.endFacet());
    QCOMPARE(fs2.count(), fs5.count());
    QVERIFY(fs2==fs5);
    QhullFacetList fs6= fs2; // copy constructor
    QVERIFY(fs6==fs2);
    std::vector fv= fs2.toStdVector();
    QCOMPARE(fv.size(), 6u);
}//t_construct

void QhullFacetList_test::
t_convert()
{
    RboxPoints rcube("c");
    Qhull q(rcube,"QR0 QV2");  // rotated unit cube
    QhullFacetList fs2= q.facetList();
    QVERIFY(!fs2.isSelectAll());
    QVERIFY(!fs2.isEmpty());
    QCOMPARE(fs2.count(),3);
    std::vector fv= fs2.toStdVector();
    QCOMPARE(fv.size(), 3u);
    QList fv2= fs2.toQList();
    QCOMPARE(fv2.size(), 3);
    std::vector fv5= fs2.vertices_toStdVector(q.runId());
    QCOMPARE(fv5.size(), 7u);
    QList fv6= fs2.vertices_toQList(q.runId());
    QCOMPARE(fv6.size(), 7);
    fs2.selectAll();
    QVERIFY(fs2.isSelectAll());
    std::vector fv3= fs2.toStdVector();
    QCOMPARE(fv3.size(), 6u);
    QList fv4= fs2.toQList();
    QCOMPARE(fv4.size(), 6);
    std::vector fv7= fs2.vertices_toStdVector(q.runId());
    QCOMPARE(fv7.size(), 8u);
    QList fv8= fs2.vertices_toQList(q.runId());
    QCOMPARE(fv8.size(), 8);
}//t_convert

//! Spot check properties and read-only.  See QhullLinkedList_test
void QhullFacetList_test::
t_readonly()
{
    RboxPoints rcube("c");
    Qhull q(rcube,"QV0");  // good facets are adjacent to point 0
    QhullFacetList fs= q.facetList();
    QVERIFY(!fs.isSelectAll());
    QCOMPARE(fs.count(), 3);
    QCOMPARE(fs.first(), q.firstFacet());
    fs.selectAll();
    QVERIFY(fs.isSelectAll());
    QCOMPARE(fs.count(), 6);
    fs.selectGood();
    QVERIFY(!fs.isSelectAll());
    QCOMPARE(fs.count(), 3);
    fs.selectAll();
    QVERIFY(fs.isSelectAll());
    QCOMPARE(fs.count(), 6);
    QhullFacet f= fs.first();
    QhullFacet f2= fs.last();
    fs.selectAll();
    QVERIFY(fs.contains(f));
    QVERIFY(fs.contains(f2));
    QVERIFY(f.isGood());
    QVERIFY(!f2.isGood());
    fs.selectGood();
    QVERIFY(fs.contains(f));
    QVERIFY(!fs.contains(f2));
}//t_readonly

void QhullFacetList_test::
t_foreach()
{
    RboxPoints rcube("c");
    // Spot check predicates and accessors.  See QhullLinkedList_test
    Qhull q(rcube,"Qt QR0");  // triangulation of rotated unit cube
    QhullFacetList fs= q.facetList();
    QVERIFY(fs.contains(q.firstFacet()));
    QhullFacet f= q.firstFacet().next();
    QVERIFY(fs.contains(f));
    QCOMPARE(fs.first(), *fs.begin());
    QCOMPARE(*(fs.end()-1), fs.last());
    QCOMPARE(fs.first(), q.firstFacet());
    QCOMPARE(*fs.begin(), q.beginFacet());
    QCOMPARE(*fs.end(), q.endFacet());
}//t_foreach

void QhullFacetList_test::
t_io()
{
    RboxPoints rcube("c");
    {
        Qhull q(rcube,"QR0 QV0");   // good facets are adjacent to point 0
        QhullFacetList fs= q.facetList();
        ostringstream os;
        os << fs.print(q.runId()); // Runs all print options
        os << "\nFacets only\n" << fs; // printVertices() requires a runId
        cout << os.str();
        QString facets= QString::fromStdString(os.str());
        QCOMPARE(facets.count("(v"), 7+12*3*2);
        QCOMPARE(facets.count(QRegExp("f\\d")), 3*7 + 13*3*2);
    }
}//t_io

}//orgQhull

#include "moc/QhullFacetList_test.moc"
qhull-2012.1/src/qhulltest/QhullFacetSet_test.cpp0000644000076400010400000000765211716456524023214 0ustar  bbarberAdministrators/****************************************************************************
**
** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
** $Id: //main/2011/qhull/src/qhulltest/QhullFacetSet_test.cpp#4 $$Change: 1490 $
** $DateTime: 2012/02/19 20:27:01 $$Author: bbarber $
**
****************************************************************************/

//pre-compiled headers
#include 
#include "RoadTest.h"

#include "QhullFacetSet.h"
#include "QhullError.h"
#include "QhullFacet.h"
#include "Qhull.h"

using std::cout;
using std::endl;
using std::ostringstream;
using std::ostream;
using std::string;

namespace orgQhull {

class QhullFacetSet_test : public RoadTest
{
    Q_OBJECT

#//Test slots
private slots:
    void cleanup();
    void t_construct();
    void t_convert();
    void t_readonly();
    void t_foreach();
    void t_io();
};//QhullFacetSet_test

void
add_QhullFacetSet_test()
{
    new QhullFacetSet_test();
}

//Executed after each testcase
void QhullFacetSet_test::
cleanup()
{
    RoadTest::cleanup();
    UsingLibQhull::checkQhullMemoryEmpty();
}

void QhullFacetSet_test::
t_construct()
{
    RboxPoints rcube("c");
    Qhull q(rcube,"QR0");  // rotated unit cube
    QhullFacet f= q.firstFacet();
    QhullFacetSet fs2= f.neighborFacets();
    QVERIFY(!fs2.isEmpty());
    QCOMPARE(fs2.count(),4);
    QhullFacetSet fs4= fs2; // copy constructor
    QVERIFY(fs4==fs2);
    QhullFacetSet fs3(q.qhullQh()->facet_mergeset);
    QVERIFY(fs3.isEmpty());
}//t_construct

void QhullFacetSet_test::
t_convert()
{
    RboxPoints rcube("c");
    Qhull q2(rcube,"QR0 QV2");  // rotated unit cube
    QhullFacet f2= q2.firstFacet();
    QhullFacetSet fs2= f2.neighborFacets();
    QVERIFY(!fs2.isSelectAll());
    QCOMPARE(fs2.count(),2);
    std::vector fv= fs2.toStdVector();
    QCOMPARE(fv.size(), 2u);
    QList fv2= fs2.toQList();
    QCOMPARE(fv2.size(), 2);
    fs2.selectAll();
    QVERIFY(fs2.isSelectAll());
    std::vector fv3= fs2.toStdVector();
    QCOMPARE(fv3.size(), 4u);
    QList fv4= fs2.toQList();
    QCOMPARE(fv4.size(), 4);
}//t_convert

//! Spot check properties and read-only.  See QhullSet_test
void QhullFacetSet_test::
t_readonly()
{
    RboxPoints rcube("c");
    Qhull q(rcube,"QV0");  // good facets are adjacent to point 0
    QhullFacetSet fs= q.firstFacet().neighborFacets();
    QVERIFY(!fs.isSelectAll());
    QCOMPARE(fs.count(), 2);
    fs.selectAll();
    QVERIFY(fs.isSelectAll());
    QCOMPARE(fs.count(), 4);
    fs.selectGood();
    QVERIFY(!fs.isSelectAll());
    QCOMPARE(fs.count(), 2);
    QhullFacet f= fs.first();
    QhullFacet f2= fs.last();
    fs.selectAll();
    QVERIFY(fs.contains(f));
    QVERIFY(fs.contains(f2));
    QVERIFY(f.isGood());
    QVERIFY(!f2.isGood());
    fs.selectGood();
    QVERIFY(fs.contains(f));
    QVERIFY(!fs.contains(f2));
}//t_readonly

void QhullFacetSet_test::
t_foreach()
{
    RboxPoints rcube("c");
    // Spot check predicates and accessors.  See QhullLinkedList_test
    Qhull q(rcube,"QR0");  // rotated unit cube
    QhullFacetSet fs= q.firstFacet().neighborFacets();
    QVERIFY(!fs.contains(q.firstFacet()));
    QVERIFY(fs.contains(fs.first()));
    QhullFacet f= q.firstFacet().next();
    if(!fs.contains(f)){
        f= f.next();
    }
    QVERIFY(fs.contains(f));
    QCOMPARE(fs.first(), *fs.begin());
    QCOMPARE(*(fs.end()-1), fs.last());
}//t_foreach

void QhullFacetSet_test::
t_io()
{
    RboxPoints rcube("c");
    {
        Qhull q(rcube,"QR0 QV0");   // good facets are adjacent to point 0
        QhullFacetSet fs= q.firstFacet().neighborFacets();
        ostringstream os;
        os << fs.print(q.runId(), "Neighbors of first facet with point 0");
        os << fs.printIdentifiers("\nFacet identifiers: ");
        cout << os.str();
        QString facets= QString::fromStdString(os.str());
        QCOMPARE(facets.count(QRegExp(" f[0-9]")), 2+13*2);
    }
}//t_io

}//orgQhull

#include "moc/QhullFacetSet_test.moc"
qhull-2012.1/src/qhulltest/QhullFacet_test.cpp0000644000076400010400000002067011716456524022533 0ustar  bbarberAdministrators/****************************************************************************
**
** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
** $Id: //main/2011/qhull/src/qhulltest/QhullFacet_test.cpp#6 $$Change: 1490 $
** $DateTime: 2012/02/19 20:27:01 $$Author: bbarber $
**
****************************************************************************/

//pre-compiled headers
#include 
#include "RoadTest.h"

#include "QhullFacet.h"
#include "QhullError.h"
#include "Coordinates.h"
#include "RboxPoints.h"
#include "QhullFacetList.h"
#include "QhullFacetSet.h"
#include "QhullPointSet.h"
#include "QhullRidge.h"
#include "Qhull.h"

using std::cout;
using std::endl;
using std::ostringstream;
using std::ostream;
using std::string;

namespace orgQhull {

class QhullFacet_test : public RoadTest
{
    Q_OBJECT

#//Test slots
private slots:
    void cleanup();
    void t_constructConvert();
    void t_getSet();
    void t_value();
    void t_foreach();
    void t_io();
};//QhullFacet_test

void
add_QhullFacet_test()
{
    new QhullFacet_test();
}

//Executed after each testcase
void QhullFacet_test::
cleanup()
{
    UsingLibQhull::checkQhullMemoryEmpty();
    RoadTest::cleanup();
}

void QhullFacet_test::
t_constructConvert()
{
    // Qhull.runQhull() constructs QhullFacets as facetT
    QhullFacet f;
    QVERIFY(!f.isDefined());
    QCOMPARE(f.dimension(),0);
    RboxPoints rcube("c");
    Qhull q(rcube,"Qt QR0");  // triangulation of rotated unit cube
    QhullFacet f2(q.beginFacet());
    QCOMPARE(f2.dimension(),3);
    f= f2; // copy assignment
    QVERIFY(f.isDefined());
    QCOMPARE(f.dimension(),3);
    QhullFacet f5= f2;
    QVERIFY(f5==f2);
    QVERIFY(f5==f);
    QhullFacet f3= f2.getFacetT();
    QCOMPARE(f,f3);
    QhullFacet f4= f2.getBaseT();
    QCOMPARE(f,f4);
}//t_constructConvert

void QhullFacet_test::
t_getSet()
{
    RboxPoints rcube("c");
    {
        Qhull q(rcube,"Qt QR0");  // triangulation of rotated unit cube
        QCOMPARE(q.facetCount(), 12);
        QCOMPARE(q.vertexCount(), 8);
        QhullFacetListIterator i(q.facetList());
        while(i.hasNext()){
            const QhullFacet f= i.next();
            cout << f.id() << endl;
            QCOMPARE(f.dimension(),3);
            QVERIFY(f.id()>0 && f.id()<=39);
            QVERIFY(f.isDefined());
            if(i.hasNext()){
                QCOMPARE(f.next(), i.peekNext());
                QVERIFY(f.next()!=f);
            }
            QVERIFY(i.hasPrevious());
            QCOMPARE(f, i.peekPrevious());
        }
        QhullFacetListIterator i2(i);
        QEXPECT_FAIL("", "ListIterator copy constructor not reset to BOT", Continue);
        QVERIFY(!i2.hasPrevious());

        // test tricoplanarOwner
        QhullFacet facet = q.beginFacet();
        QhullFacet tricoplanarOwner = facet.tricoplanarOwner();
        int tricoplanarCount= 0;
        i.toFront();
        while(i.hasNext()){
            const QhullFacet f= i.next();
            if(f.tricoplanarOwner()==tricoplanarOwner){
                tricoplanarCount++;
            }
        }
        QCOMPARE(tricoplanarCount, 2);
        int tricoplanarCount2= 0;
        foreach (QhullFacet f, q.facetList()){  // Qt only
            QhullHyperplane h= f.hyperplane();
            cout << "Hyperplane: " << h << endl;
            QCOMPARE(h.count(), 3);
            QCOMPARE(h.offset(), -0.5);
            double n= h.norm();
            QCOMPARE(n, 1.0);
            QhullHyperplane hi= f.innerplane(q.runId());
            QCOMPARE(hi.count(), 3);
            double innerOffset= hi.offset()+0.5;
            cout << "InnerPlane: " << hi << "innerOffset+0.5 " << innerOffset << endl;
            QVERIFY(innerOffset >= 0.0);
            QhullHyperplane ho= f.outerplane(q.runId());
            QCOMPARE(ho.count(), 3);
            double outerOffset= ho.offset()+0.5;
            cout << "OuterPlane: " << ho << "outerOffset+0.5 " << outerOffset << endl;
            QVERIFY(outerOffset <= 0.0);
            QVERIFY(outerOffset-innerOffset < 1e-7);
            for(int k= 0; k<3; k++){
                QVERIFY(ho[k]==hi[k]);
                QVERIFY(ho[k]==h[k]);
            }
            QhullPoint center= f.getCenter(q.runId());
            cout << "Center: " << center << endl;
            double d= f.distance(center);
            QVERIFY(d < innerOffset-outerOffset);
            QhullPoint center2= f.getCenter(q.runId(), qh_PRINTcentrums);
            QCOMPARE(center, center2);
            if(f.tricoplanarOwner()==tricoplanarOwner){
                tricoplanarCount2++;
            }
        }
        QCOMPARE(tricoplanarCount2, 2);
        Qhull q2(rcube,"d Qz Qt QR0");  // 3-d triangulation of Delaunay triangulation (the cube)
        QhullFacet f2= q2.firstFacet();
        QhullPoint center3= f2.getCenter(q.runId(), qh_PRINTtriangles);
        QCOMPARE(center3.dimension(), 3);
        QhullPoint center4= f2.getCenter(q.runId());
        QCOMPARE(center4.dimension(), 3);
        for(int k= 0; k<3; k++){
            QVERIFY(center4[k]==center3[k]);
        }
        Qhull q3(rcube,"v Qz QR0");  // Voronoi diagram of a cube (one vertex)

        UsingLibQhull::setGlobalDistanceEpsilon(1e-12); // Voronoi vertices are not necessarily within distance episilon
        foreach(QhullFacet f, q3.facetList()){ //Qt only
            if(f.isGood()){
                QhullPoint p= f.voronoiVertex(q3.runId());
                cout << p.print(q3.runId(), "Voronoi vertex: ")
                    << " DistanceEpsilon " << UsingLibQhull::globalDistanceEpsilon() << endl;
                QCOMPARE(p, q3.origin());
            }
        }
    }
}//t_getSet

void QhullFacet_test::
t_value()
{
    RboxPoints rcube("c");
    {
        Qhull q(rcube, "");
        coordT c[]= {0.0, 0.0, 0.0};
        foreach (QhullFacet f, q.facetList()){  // Qt only
            double d= f.distance(q.origin());
            QCOMPARE(d, -0.5);
            double d0= f.distance(c);
            QCOMPARE(d0, -0.5);
            double facetArea= f.facetArea(q.runId());
            QCOMPARE(facetArea, 1.0);
            #if qh_MAXoutside
                double maxoutside= f.getFacetT()->maxoutside;
                QVERIFY(maxoutside<1e-7);
            #endif
        }
    }
}//t_value

void QhullFacet_test::
t_foreach()
{
    RboxPoints rcube("c W0 300");  // cube plus 300 points on its surface
    {
        Qhull q(rcube, "QR0 Qc"); // keep coplanars, thick facet, and rotate the cube
        int coplanarCount= 0;
        foreach(const QhullFacet f, q.facetList()){
            QhullPointSet coplanars= f.coplanarPoints();
            coplanarCount += coplanars.count();
            QhullFacetSet neighbors= f.neighborFacets();
            QCOMPARE(neighbors.count(), 4);
            QhullPointSet outsides= f.outsidePoints();
            QCOMPARE(outsides.count(), 0);
            QhullRidgeSet ridges= f.ridges();
            QCOMPARE(ridges.count(), 4);
            QhullVertexSet vertices= f.vertices();
            QCOMPARE(vertices.count(), 4);
            int ridgeCount= 0;
            QhullRidge r= ridges.first();
            for(int r0= r.id(); ridgeCount==0 || r.id()!=r0; r= r.nextRidge3d(f)){
                ++ridgeCount;
                if(!r.hasNextRidge3d(f)){
                    QFAIL("Unexpected simplicial facet.  They only have ridges to non-simplicial neighbors.");
                }
            }
            QCOMPARE(ridgeCount, 4);
        }
        QCOMPARE(coplanarCount, 300);
    }
}//t_foreach

void QhullFacet_test::
t_io()
{
    RboxPoints rcube("c");
    {
        Qhull q(rcube, "");
        QhullFacet f= q.beginFacet();
        cout << f;
        ostringstream os;
        os << f.printHeader(q.runId());
        os << f.printFlags("    - flags:");
        os << f.printCenter(q.runId(), qh_PRINTfacets, "    - center:");
        os << f.printRidges(q.runId());
        cout << os.str();
        ostringstream os2;
        os2 << f.print(q.runId());  // invokes print*()
        QString facetString2= QString::fromStdString(os2.str());
        facetString2.replace(QRegExp("\\s\\s+"), " ");
        ostringstream os3;
        q.setOutputStream(&os3);
        q.outputQhull("f");
        QString facetsString= QString::fromStdString(os3.str());
        QString facetString3= facetsString.mid(facetsString.indexOf("- f1\n"));
        facetString3= facetString3.left(facetString3.indexOf("\n- f")+1);
        facetString3.replace(QRegExp("\\s\\s+"), " ");
        QCOMPARE(facetString2, facetString3);
    }
}//t_io

// toQhullFacet is static_cast only

}//orgQhull

#include "moc/QhullFacet_test.moc"
qhull-2012.1/src/qhulltest/QhullHyperplane_test.cpp0000644000076400010400000002576011716456524023625 0ustar  bbarberAdministrators/****************************************************************************
**
** Copyright (c) 2009-2012 C.B. Barber. All rights reserved.
** $Id: //main/2011/qhull/src/qhulltest/QhullHyperplane_test.cpp#6 $$Change: 1490 $
** $DateTime: 2012/02/19 20:27:01 $$Author: bbarber $
**
****************************************************************************/

//pre-compiled headers
#include 
#include 
#include "RoadTest.h"

#include "QhullHyperplane.h"
#include "QhullError.h"
#include "RboxPoints.h"
#include "QhullFacet.h"
#include "QhullFacetList.h"
#include "Qhull.h"
#include 

using std::cout;
using std::endl;
using std::ostringstream;
using std::ostream;
using std::string;

namespace orgQhull {

class QhullHyperplane_test : public RoadTest
{
    Q_OBJECT

#//Test slots
private slots:
    void cleanup();
    void t_construct();
    void t_convert();
    void t_readonly();
    void t_define();
    void t_value();
    void t_operator();
    void t_iterator();
    void t_const_iterator();
    void t_qhullHyperplane_iterator();
    void t_io();
};//QhullHyperplane_test

void
add_QhullHyperplane_test()
{
    new QhullHyperplane_test();
}

//Executed after each testcase
void QhullHyperplane_test::
cleanup()
{
    UsingLibQhull::checkQhullMemoryEmpty();
    RoadTest::cleanup();
}

void QhullHyperplane_test::
t_construct()
{
    // Qhull.runQhull() constructs QhullFacets as facetT
    QhullHyperplane h;
    QVERIFY(!h.isDefined());
    QCOMPARE(h.dimension(),0);
    QCOMPARE(h.coordinates(),static_cast(0));
    RboxPoints rcube("c");
    Qhull q(rcube,"Qt QR0");  // triangulation of rotated unit cube
    QhullFacet f= q.firstFacet();
    QhullHyperplane h2(f.hyperplane());
    QVERIFY(h2.isDefined());
    QCOMPARE(h2.dimension(),3);
    // h= h2;  // copy assignment disabled, ambiguous
    QhullHyperplane h3(h2.dimension(), h2.coordinates(), h2.offset());
    QCOMPARE(h2, h3);
    QhullHyperplane h5= h2; // copy constructor
    QVERIFY(h5==h2);
}//t_construct

void QhullHyperplane_test::
t_convert()
{
    RboxPoints rcube("c");
    Qhull q(rcube,"Qt QR0");  // triangulation of rotated unit cube
    QhullHyperplane h= q.firstFacet().hyperplane();
    std::vector fs= h.toStdVector();
    QCOMPARE(fs.size(), 4u);
    double offset= fs.back();
    fs.pop_back();
    QCOMPARE(offset, -0.5);

    double squareNorm= inner_product(fs.begin(), fs.end(), fs.begin(), 0.0);
    QCOMPARE(squareNorm, 1.0);
    QList qs= h.toQList();
    QCOMPARE(qs.size(), 4);
    double offset2= qs.takeLast();
    QCOMPARE(offset2, -0.5);
    double squareNorm2= std::inner_product(qs.begin(), qs.end(), qs.begin(), 0.0);
    QCOMPARE(squareNorm2, 1.0);
}//t_convert

void QhullHyperplane_test::
t_readonly()
{
    RboxPoints rcube("c");
    {
        Qhull q(rcube,"Qt QR0");  // triangulation of rotated unit cube
        QhullFacetList fs= q.facetList();
        QhullFacetListIterator i(fs);
        while(i.hasNext()){
            QhullFacet f= i.next();
            QhullHyperplane h= f.hyperplane();
            int id= f.id();
            cout << "h" << id << endl;
            QVERIFY(h.isDefined());
            QCOMPARE(h.dimension(),3);
            const coordT *c= h.coordinates();
            coordT *c2= h.coordinates();
            QCOMPARE(c, c2);
            const coordT *c3= h.begin();
            QCOMPARE(c, c3);
            QCOMPARE(h.offset(), -0.5);
            int j= h.end()-h.begin();
            QCOMPARE(j, 3);
            double squareNorm= std::inner_product(h.begin(), h.end(), h.begin(), 0.0);
            QCOMPARE(squareNorm, 1.0);
        }
        QhullHyperplane h2= fs.first().hyperplane();
        QhullHyperplane h3= fs.last().hyperplane();
        QVERIFY(h2!=h3);
        QVERIFY(h3.coordinates()!=h2.coordinates());
    }
}//t_readonly

void QhullHyperplane_test::
t_define()
{
    RboxPoints rcube("c");
    {
        Qhull q(rcube,"Qt QR0");  // triangulation of rotated unit cube
        QhullFacetList fs= q.facetList();
        QhullHyperplane h= fs.first().hyperplane();
        QhullHyperplane h2= h;
        QVERIFY(h==h2);
        QhullHyperplane h3= fs.last().hyperplane();
        QVERIFY(h2!=h3);

        QhullHyperplane h4= h3;
        h4.defineAs(h2);
        QVERIFY(h2==h4);
        QhullHyperplane p5= h3;
        p5.defineAs(h2.dimension(), h2.coordinates(), h2.offset());
        QVERIFY(h2==p5);
        QhullHyperplane h6= h3;
        h6.setCoordinates(h2.coordinates());
        QCOMPARE(h2.coordinates(), h6.coordinates());
        h6.setOffset(h2.offset());
        QCOMPARE(h2.offset(), h6.offset());
        QVERIFY(h2==h6);
        h6.setDimension(2);
        QCOMPARE(h6.dimension(), 2);
        QVERIFY(h2!=h6);
    }
}//t_define

void QhullHyperplane_test::
t_value()
{
    RboxPoints rcube("c G1");
    Qhull q(rcube,"Qt QR0");  // triangulation of rotated unit cube
    const QhullHyperplane h= q.firstFacet().hyperplane();
    double dist= h.distance(q.origin());
    QCOMPARE(dist, -1.0);
    double norm= h.norm();
    QCOMPARE(norm, 1.0);
}//t_value

void QhullHyperplane_test::
t_operator()
{
    RboxPoints rcube("c");
    Qhull q(rcube,"Qt QR0");  // triangulation of rotated unit cube
    const QhullHyperplane h= q.firstFacet().hyperplane();
    //operator== and operator!= tested elsewhere
    const coordT *c= h.coordinates();
    for(int k=h.dimension(); k--; ){
        QCOMPARE(c[k], h[k]);
    }
    //h[0]= 10.0; // compiler error, const
    QhullHyperplane h2= q.firstFacet().hyperplane();
    h2[0]= 10.0;  // Overwrites Hyperplane coordinate!
    QCOMPARE(h2[0], 10.0);
}//t_operator

void QhullHyperplane_test::
t_iterator()
{
    RboxPoints rcube("c");
    {
        QhullHyperplane h2;
        QCOMPARE(h2.begin(), h2.end());
        QCOMPARE(h2.count(), 0);
        QCOMPARE(h2.size(), 0u);
        Qhull q(rcube,"QR0");  // rotated unit cube
        QhullHyperplane h= q.firstFacet().hyperplane();
        QCOMPARE(h.count(), 3);
        QCOMPARE(h.size(), 3u);
        QhullHyperplane::Iterator i= h.begin();
        QhullHyperplane::iterator i2= h.begin();
        QVERIFY(i==i2);
        QVERIFY(i>=i2);
        QVERIFY(i<=i2);
        i= h.begin();
        QVERIFY(i==i2);
        i2= h.end();
        QVERIFY(i!=i2);
        double d3= *i;
        i2--;
        double d2= *i2;
        QCOMPARE(d3, h[0]);
        QCOMPARE(d2, h[2]);
        QhullHyperplane::Iterator i3(i2);
        QCOMPARE(*i2, *i3);

        (i3= i)++;
        QCOMPARE((*i3), h[1]);
        QVERIFY(i==i);
        QVERIFY(i!=i2);
        QVERIFY(ii);
        QVERIFY(i2>=i);

        QhullHyperplane::ConstIterator i4= h.begin();
        QVERIFY(i==i4); // iterator COMP const_iterator
        QVERIFY(i<=i4);
        QVERIFY(i>=i4);
        QVERIFY(i4==i); // const_iterator COMP iterator
        QVERIFY(i4<=i);
        QVERIFY(i4>=i);
        QVERIFY(i>=i4);
        QVERIFY(i4<=i);
        QVERIFY(i2!=i4);
        QVERIFY(i2>i4);
        QVERIFY(i2>=i4);
        QVERIFY(i4!=i2);
        QVERIFY(i4i);
        QVERIFY(i4>=i);

        i= h.begin();
        i2= h.begin();
        QCOMPARE(i, i2++);
        QCOMPARE(*i2, h[1]);
        QCOMPARE(++i, i2);
        QCOMPARE(i, i2--);
        QCOMPARE(i2, h.begin());
        QCOMPARE(--i, i2);
        QCOMPARE(i2 += 3, h.end());
        QCOMPARE(i2 -= 3, h.begin());
        QCOMPARE(i2+0, h.begin());
        QCOMPARE(i2+3, h.end());
        i2 += 3;
        i= i2-0;
        QCOMPARE(i, i2);
        i= i2-3;
        QCOMPARE(i, h.begin());
        QCOMPARE(i2-i, 3);

        //h.begin end tested above

        // QhullHyperplane is const-only
    }
}//t_iterator

void QhullHyperplane_test::
t_const_iterator()
{
    RboxPoints rcube("c");
    {
        Qhull q(rcube,"QR0");  // rotated unit cube
        QhullHyperplane h= q.firstFacet().hyperplane();
        QhullHyperplane::ConstIterator i= h.begin();
        QhullHyperplane::const_iterator i2= h.begin();
        QVERIFY(i==i2);
        QVERIFY(i>=i2);
        QVERIFY(i<=i2);
        i= h.begin();
        QVERIFY(i==i2);
        i2= h.end();
        QVERIFY(i!=i2);
        double d3= *i;
        i2--;
        double d2= *i2;
        QCOMPARE(d3, h[0]);
        QCOMPARE(d2, h[2]);
        QhullHyperplane::ConstIterator i3(i2);
        QCOMPARE(*i2, *i3);

        (i3= i)++;
        QCOMPARE((*i3), h[1]);
        QVERIFY(i==i);
        QVERIFY(i!=i2);
        QVERIFY(ii);
        QVERIFY(i2>=i);

        // See t_iterator for const_iterator COMP iterator

        i= h.begin();
        i2= h.constBegin();
        QCOMPARE(i, i2++);
        QCOMPARE(*i2, h[1]);
        QCOMPARE(++i, i2);
        QCOMPARE(i, i2--);
        QCOMPARE(i2, h.constBegin());
        QCOMPARE(--i, i2);
        QCOMPARE(i2+=3, h.constEnd());
        QCOMPARE(i2-=3, h.constBegin());
        QCOMPARE(i2+0, h.constBegin());
        QCOMPARE(i2+3, h.constEnd());
        i2 += 3;
        i= i2-0;
        QCOMPARE(i, i2);
        i= i2-3;
        QCOMPARE(i, h.constBegin());
        QCOMPARE(i2-i, 3);

        // QhullHyperplane is const-only
    }
}//t_const_iterator

void QhullHyperplane_test::
t_qhullHyperplane_iterator()
{
    QhullHyperplane h2;
    QhullHyperplaneIterator i= h2;
    QCOMPARE(h2.dimension(), 0);
    QVERIFY(!i.hasNext());
    QVERIFY(!i.hasPrevious());
    i.toBack();
    QVERIFY(!i.hasNext());
    QVERIFY(!i.hasPrevious());

    RboxPoints rcube("c");
    Qhull q(rcube,"QR0");  // rotated unit cube
    QhullHyperplane h = q.firstFacet().hyperplane();
    QhullHyperplaneIterator i2(h);
    QCOMPARE(h.dimension(), 3);
    i= h;
    QVERIFY(i2.hasNext());
    QVERIFY(!i2.hasPrevious());
    QVERIFY(i.hasNext());
    QVERIFY(!i.hasPrevious());
    i2.toBack();
    i.toFront();
    QVERIFY(!i2.hasNext());
    QVERIFY(i2.hasPrevious());
    QVERIFY(i.hasNext());
    QVERIFY(!i.hasPrevious());

    // i at front, i2 at end/back, 3 coordinates
    QCOMPARE(i.peekNext(), h[0]);
    QCOMPARE(i2.peekPrevious(), h[2]);
    QCOMPARE(i2.previous(), h[2]);
    QCOMPARE(i2.previous(), h[1]);
    QCOMPARE(i2.previous(), h[0]);
    QVERIFY(!i2.hasPrevious());
    QCOMPARE(i.peekNext(), h[0]);
    // i.peekNext()= 1.0; // compiler error, i is const
    QCOMPARE(i.next(), h[0]);
    QCOMPARE(i.peekNext(), h[1]);
    QCOMPARE(i.next(), h[1]);
    QCOMPARE(i.next(), h[2]);
    QVERIFY(!i.hasNext());
    i.toFront();
    QCOMPARE(i.next(), h[0]);
}//t_qhullHyperplane_iterator

void QhullHyperplane_test::
t_io()
{
    RboxPoints rcube("c");
    {
        Qhull q(rcube, "");
        QhullHyperplane h= q.firstFacet().hyperplane();
        ostringstream os;
        os << "Hyperplane:\n";
        os << h;
        os << "Hyperplane w/ runId:\n";
        os << h.print();
        os << h.print(" and a message ", " offset ");
        cout << os.str();
        QString s= QString::fromStdString(os.str());
        QCOMPARE(s.count("1"), 3);
        // QCOMPARE(s.count(QRegExp("f\\d")), 3*7 + 13*3*2);
    }
}//t_io


}//orgQhull

#include "moc/QhullHyperplane_test.moc"
qhull-2012.1/src/qhulltest/QhullLinkedList_test.cpp0000644000076400010400000002140511716456524023550 0ustar  bbarberAdministrators/****************************************************************************
**
** Copyright (c) 2009-2012 C.B. Barber. All rights reserved.
** $Id: //main/2011/qhull/src/qhulltest/QhullLinkedList_test.cpp#4 $$Change: 1490 $
** $DateTime: 2012/02/19 20:27:01 $$Author: bbarber $
**
****************************************************************************/

//pre-compiled headers
#include 
#include "RoadTest.h"

#include "QhullLinkedList.h"
#include "Qhull.h"

namespace orgQhull {

class QhullLinkedList_test : public RoadTest
{
    Q_OBJECT

#//Test slots
private slots:
    void cleanup();
    void t_construct();
    void t_convert();
    void t_element();
    void t_search();
    void t_iterator();
    void t_const_iterator();
    void t_QhullLinkedList_iterator();
    void t_io();
};//QhullLinkedList_test

void
add_QhullLinkedList_test()
{
    new QhullLinkedList_test();
}

//Executed after each testcase
void QhullLinkedList_test::
cleanup()
{
    UsingLibQhull::checkQhullMemoryEmpty();
    RoadTest::cleanup();
}

void QhullLinkedList_test::
t_construct()
{
    // QhullLinkedList vs; //private (compiler error).  No memory allocation
    RboxPoints rcube("c");
    {
        Qhull q(rcube,"Qt QR0");  // triangulation of rotated unit cube
        QCOMPARE(q.facetCount(), 12);
        QhullVertexList vs = QhullVertexList(q.beginVertex(), q.endVertex());
        QCOMPARE(vs.count(), 8);
        QCOMPARE(vs.size(), 8u);
        QVERIFY(!vs.isEmpty());
        QhullVertexList vs2 = q.vertexList();
        QCOMPARE(vs2.count(), 8);
        QCOMPARE(vs2.size(),8u);
        QVERIFY(!vs2.isEmpty());
        QVERIFY(!vs2.empty());
        QVERIFY(vs==vs2);
        // vs= vs2; // disabled.  Would not copy the vertices
        QhullVertexList vs3= vs2; // copy constructor
        QVERIFY(vs3==vs2);
    }
}//t_construct

void QhullLinkedList_test::
t_convert()
{
    RboxPoints rcube("c");
    {
        Qhull q(rcube,"Qt QR0");  // triangulation of rotated unit cube
        QCOMPARE(q.facetCount(), 12);
        QhullVertexList vs = q.vertexList();
        QCOMPARE(vs.size(), 8u);
        QVERIFY(!vs.isEmpty());
        QVERIFY(!vs.empty());
        std::vector vs2= vs.toStdVector();
        QCOMPARE(vs2.size(), vs.size());
        QhullVertexList::Iterator i= vs.begin();
        for(int k= 0; k<(int)vs2.size(); k++){
            QCOMPARE(vs2[k], *i++);
        }
        QList vs3= vs.toQList();
        QCOMPARE(vs3.count(), vs.count());
        i= vs.begin();
        for(int k= 0; k
#include "RoadTest.h" // QT_VERSION

#include "QhullPointSet.h"
#include "RboxPoints.h"
#include "QhullPoint.h"
#include "QhullFacet.h"
#include "QhullFacetList.h"
#include "Qhull.h"

using std::cout;
using std::endl;
using std::ostringstream;

namespace orgQhull {

class QhullPointSet_test : public RoadTest
{
    Q_OBJECT

#//Test slots
private slots:
    void cleanup();
    void t_construct();
    void t_convert();
    void t_element();
    void t_iterator();
    void t_const_iterator();
    void t_search();
    void t_pointset_iterator();
    void t_io();
};//QhullPointSet_test

void
add_QhullPointSet_test()
{
    new QhullPointSet_test();
}

//Executed after each testcase
void QhullPointSet_test::
cleanup()
{
    UsingLibQhull::checkQhullMemoryEmpty();
    RoadTest::cleanup();
}

void QhullPointSet_test::
t_construct()
{
    RboxPoints rcube("c W0 1000");
    Qhull q(rcube,"Qc");  // cube with 1000 coplanar points
    int coplanarCount= 0;
    foreach(QhullFacet f, q.facetList()){
        QhullPointSet ps(q.dimension(), f.getFacetT()->outsideset);
        QCOMPARE(ps.dimension(), 3);
        QVERIFY(ps.isEmpty());
        QVERIFY(ps.empty());
        QCOMPARE(ps.count(), 0);
        QCOMPARE(ps.size(), 0u);
        QhullPointSet ps2(q.dimension(), f.getFacetT()->coplanarset);
        QCOMPARE(ps2.dimension(), 3);
        QVERIFY(!ps2.isEmpty());
        QVERIFY(!ps2.empty());
        coplanarCount += ps2.count();
        QCOMPARE(ps2.count(), (int)ps2.size());
        QhullPointSet ps3(ps2);
        QCOMPARE(ps3.dimension(), 3);
        QVERIFY(!ps3.isEmpty());
        QCOMPARE(ps3.count(), ps2.count());
        QVERIFY(ps3==ps2);
        QVERIFY(ps3!=ps);
        // ps4= ps3; //compiler error
    }
    QCOMPARE(coplanarCount, 1000);
}//t_construct

void QhullPointSet_test::
t_convert()
{
    RboxPoints rcube("c W0 1000");
    Qhull q(rcube,"Qc");  // cube with 1000 coplanar points
    QhullFacet f= q.firstFacet();
    QhullPointSet ps= f.coplanarPoints();
    QCOMPARE(ps.dimension(), 3);
    QVERIFY(ps.count()>=1);   // Sometimes no coplanar points
    std::vector vs= ps.toStdVector();
    QCOMPARE(vs.size(), ps.size());
    QhullPoint p= ps[0];
    QhullPoint p2= vs[0];
    QCOMPARE(p, p2);
    QList qs= ps.toQList();
    QCOMPARE(qs.size(), static_cast(ps.size()));
    QhullPoint p3= qs[0];
    QCOMPARE(p3, p);
}//t_convert

// readonly tested in t_construct
//   dimension, empty, isEmpty, ==, !=, size

void QhullPointSet_test::
t_element()
{
    RboxPoints rcube("c W0 1000");
    Qhull q(rcube,"Qc");  // cube with 1000 coplanar points
    QhullFacet f= q.firstFacet();
    QhullPointSet ps= f.coplanarPoints();
    QVERIFY(ps.count()>=3);  // Sometimes no coplanar points
    QhullPoint p= ps[0];
    QCOMPARE(p, ps[0]);
    QhullPoint p2= ps[ps.count()-1];
    QCOMPARE(ps.at(1), ps[1]);
    QCOMPARE(ps.first(), p);
    QCOMPARE(ps.front(), ps.first());
    QCOMPARE(ps.last(), p2);
    QCOMPARE(ps.back(), ps.last());
    QhullPoint p8;
    QCOMPARE(ps.value(2), ps[2]);
    QCOMPARE(ps.value(-1), p8);
    QCOMPARE(ps.value(ps.count()), p8);
    QCOMPARE(ps.value(ps.count(), p), p);
    QVERIFY(ps.value(1, p)!=p);
    QhullPointSet ps8= f.coplanarPoints();
    QhullPointSet::Iterator i= ps8.begin();
    foreach(QhullPoint p9, ps){  // Qt only
        QCOMPARE(p9.dimension(), 3);
        QCOMPARE(p9, *i++);
    }
}//t_element

void QhullPointSet_test::
t_iterator()
{
    RboxPoints rcube("c W0 1000");
    Qhull q(rcube,"Qc");  // cube with 1000 coplanar points
    QhullFacet f= q.firstFacet();
    QhullPointSet ps= f.coplanarPoints();
    QVERIFY(ps.count()>=3);  // Sometimes no coplanar points
    QhullPointSet::Iterator i= ps.begin();
    QhullPointSet::iterator i2= ps.begin();
    QVERIFY(i==i2);
    QVERIFY(i>=i2);
    QVERIFY(i<=i2);
    i= ps.begin();
    QVERIFY(i==i2);
    i2= ps.end();
    QVERIFY(i!=i2);
    QhullPoint p= *i;
    QCOMPARE(p.dimension(), ps.dimension());
    QCOMPARE(p, ps[0]);
    i2--;
    QhullPoint p2= *i2;
    QCOMPARE(p2.dimension(), ps.dimension());
    QCOMPARE(p2, ps.last());
    QhullPointSet::Iterator i5(i2);
    QCOMPARE(*i2, *i5);
    QhullPointSet::Iterator i3= i+1;
    QVERIFY(i!=i3);
    QCOMPARE(i[1], *i3);
    (i3= i)++;
    QCOMPARE((*i3)[0], ps[1][0]);
    QCOMPARE((*i3).dimension(), 3);

    QVERIFY(i==i);
    QVERIFY(i!=i3);
    QVERIFY(ii);
    QVERIFY(i3>=i);

    QhullPointSet::ConstIterator i4= ps.begin();
    QVERIFY(i==i4); // iterator COMP const_iterator
    QVERIFY(i<=i4);
    QVERIFY(i>=i4);
    QVERIFY(i4==i); // const_iterator COMP iterator
    QVERIFY(i4<=i);
    QVERIFY(i4>=i);
    QVERIFY(i>=i4);
    QVERIFY(i4<=i);
    QVERIFY(i2!=i4);
    QVERIFY(i2>i4);
    QVERIFY(i2>=i4);
    QVERIFY(i4!=i2);
    QVERIFY(i4i);
    QVERIFY(i4>=i);

    i= ps.begin();
    i2= ps.begin();
    QCOMPARE(i, i2++);
    QCOMPARE(*i2, ps[1]);
    QCOMPARE(++i, i2);
    QCOMPARE(i, i2--);
    QCOMPARE(i2, ps.begin());
    QCOMPARE(--i, i2);
    QCOMPARE(i2+=ps.count(), ps.end());
    QCOMPARE(i2-=ps.count(), ps.begin());
    QCOMPARE(i2+0, ps.begin());
    QCOMPARE(i2+ps.count(), ps.end());
    i2 += ps.count();
    i= i2-0;
    QCOMPARE(i, i2);
    i= i2-ps.count();
    QCOMPARE(i, ps.begin());
    QCOMPARE(i2-i, ps.count());

    //ps.begin end tested above

    // QhullPointSet is const-only
}//t_iterator

void QhullPointSet_test::
t_const_iterator()
{
    RboxPoints rcube("c W0 1000");
    Qhull q(rcube,"Qc");  // cube with 1000 coplanar points
    QhullFacet f= q.firstFacet();
    QhullPointSet ps= f.coplanarPoints();
    QVERIFY(ps.count()>=3);  // Sometimes no coplanar points
    QhullPointSet::ConstIterator i= ps.begin();
    QhullPointSet::const_iterator i2= ps.begin();
    QVERIFY(i==i2);
    QVERIFY(i>=i2);
    QVERIFY(i<=i2);

    // See t_iterator for const_iterator COMP iterator

    i= ps.begin();
    QVERIFY(i==i2);
    i2= ps.end();
    QVERIFY(i!=i2);
    QhullPoint p= *i; // QhullPoint is the base class for QhullPointSet::iterator
    QCOMPARE(p.dimension(), ps.dimension());
    QCOMPARE(p, ps[0]);
    i2--;
    QhullPoint p2= *i2;
    QCOMPARE(p2.dimension(), ps.dimension());
    QCOMPARE(p2, ps.last());
    QhullPointSet::ConstIterator i5(i2);
    QCOMPARE(*i2, *i5);


    QhullPointSet::ConstIterator i3= i+1;
    QVERIFY(i!=i3);
    QCOMPARE(i[1], *i3);

    QVERIFY(i==i);
    QVERIFY(i!=i3);
    QVERIFY(ii);
    QVERIFY(i3>=i);

    // QhullPointSet is const-only
}//t_const_iterator


void QhullPointSet_test::
t_search()
{
    RboxPoints rcube("c W0 1000");
    Qhull q(rcube,"Qc");  // cube with 1000 coplanar points
    QhullFacet f= q.firstFacet();
    QhullPointSet ps= f.coplanarPoints();
    QVERIFY(ps.count()>=3);  // Sometimes no coplanar points
    QhullPoint p= ps.first();
    QhullPoint p2= ps.last();
    QVERIFY(ps.contains(p));
    QVERIFY(ps.contains(p2));
    QVERIFY(p!=p2);
    QhullPoint p3= ps[2];
    QVERIFY(ps.contains(p3));
    QVERIFY(p!=p3);
    QhullPoint p4;
    QCOMPARE(ps.indexOf(p), 0);
    QCOMPARE(ps.indexOf(p2), ps.count()-1);
    QCOMPARE(ps.indexOf(p3), 2);
    QCOMPARE(ps.indexOf(p4), -1);
    QCOMPARE(ps.lastIndexOf(p), 0);
    QCOMPARE(ps.lastIndexOf(p2), ps.count()-1);
    QCOMPARE(ps.lastIndexOf(p3), 2);
    QCOMPARE(ps.lastIndexOf(p4), -1);
}//t_search

void QhullPointSet_test::
t_pointset_iterator()
{
    RboxPoints rcube("c W0 1000");
    Qhull q(rcube,"Qc");  // cube with 1000 coplanar points
    QhullFacet f= q.firstFacet();
    QhullPointSet ps2= f.outsidePoints();
    QVERIFY(ps2.count()==0); // No outside points after constructing the convex hull
    QhullPointSetIterator i2= ps2;
    QVERIFY(!i2.hasNext());
    QVERIFY(!i2.hasPrevious());
    i2.toBack();
    QVERIFY(!i2.hasNext());
    QVERIFY(!i2.hasPrevious());

    QhullPointSet ps= f.coplanarPoints();
    QVERIFY(ps.count()>=3);  // Sometimes no coplanar points
    QhullPointSetIterator i(ps);
    i2= ps;
    QVERIFY(i2.hasNext());
    QVERIFY(!i2.hasPrevious());
    QVERIFY(i.hasNext());
    QVERIFY(!i.hasPrevious());
    i2.toBack();
    i.toFront();
    QVERIFY(!i2.hasNext());
    QVERIFY(i2.hasPrevious());
    QVERIFY(i.hasNext());
    QVERIFY(!i.hasPrevious());

    QhullPoint p= ps[0];
    QhullPoint p2(ps[0]);
    QCOMPARE(p, p2);
    QVERIFY(p==p2);
    QhullPoint p3(ps.last());
 // p2[0]= 0.0;
    QVERIFY(p==p2);
    QCOMPARE(i2.peekPrevious(), p3);
    QCOMPARE(i2.previous(), p3);
    QCOMPARE(i2.previous(), ps[ps.count()-2]);
    QVERIFY(i2.hasPrevious());
    QCOMPARE(i.peekNext(), p);
    // i.peekNext()= 1.0; // compiler error
    QCOMPARE(i.next(), p);
    QhullPoint p4= i.peekNext();
    QVERIFY(p4!=p3);
    QCOMPARE(i.next(), p4);
    QVERIFY(i.hasNext());
    i.toFront();
    QCOMPARE(i.next(), p);
}//t_pointset_iterator

void QhullPointSet_test::
t_io()
{
    ostringstream os;
    RboxPoints rcube("c W0 120");
    Qhull q(rcube,"Qc");  // cube with 100 coplanar points
    QhullFacet f= q.firstFacet();
    QhullPointSet ps= f.coplanarPoints();
    QVERIFY(ps.count()>=3);  // Sometimes no coplanar points
    os << "QhullPointSet from coplanarPoints\n" << ps << endl;
    os << "\nRunId\n" << ps.print(q.runId());
    os << ps.print(q.runId(), "\nRunId w/ message\n");
    cout << os.str();
    QString s= QString::fromStdString(os.str());
    QCOMPARE(s.count("p"), 3*ps.count()+1);
    // QCOMPARE(s.count(QRegExp("f\\d")), 3*7 + 13*3*2);
}//t_io

}//orgQhull

#include "moc/QhullPointSet_test.moc"
qhull-2012.1/src/qhulltest/QhullPoints_test.cpp0000644000076400010400000003131311716456524022761 0ustar  bbarberAdministrators/****************************************************************************
**
** Copyright (p) 2009-2012 C.B. Barber. All rights reserved.
** $Id: //main/2011/qhull/src/qhulltest/QhullPoints_test.cpp#6 $$Change: 1490 $
** $DateTime: 2012/02/19 20:27:01 $$Author: bbarber $
**
****************************************************************************/

//pre-compiled header
#include 
#include "RoadTest.h" // QT_VERSION

#include "QhullPoints.h"
#include "RboxPoints.h"
#include "Qhull.h"

using std::cout;
using std::endl;
using std::ostringstream;

namespace orgQhull {

class QhullPoints_test : public RoadTest
{
    Q_OBJECT

#//Test slots
private slots:
    void cleanup();
    void t_construct();
    void t_convert();
    void t_getset();
    void t_element();
    void t_iterator();
    void t_const_iterator();
    void t_search();
    void t_points_iterator();
    void t_io();
};//QhullPoints_test

void
add_QhullPoints_test()
{
    new QhullPoints_test();
}

//Executed after each testcase
void QhullPoints_test::
cleanup()
{
    UsingLibQhull::checkQhullMemoryEmpty();
    RoadTest::cleanup();
}

void QhullPoints_test::
t_construct()
{
    QhullPoints ps;
    QCOMPARE(ps.dimension(), 0);
    QVERIFY(ps.isEmpty());
    QVERIFY(ps.empty());
    QCOMPARE(ps.count(), 0);
    QCOMPARE(ps.size(), 0u);
    QCOMPARE(ps.coordinateCount(), 0);
    coordT c[]= {0.0, 1.0, 2.0, 3.0, 4.0, 5.0};
    QhullPoints ps2;
    ps2.defineAs(2, 6, c);
    QCOMPARE(ps2.dimension(), 2);
    QVERIFY(!ps2.isEmpty());
    QVERIFY(!ps2.empty());
    QCOMPARE(ps2.count(), 3);
    QCOMPARE(ps2.size(), 3u);
    QCOMPARE(ps2.coordinates(), c);
    QhullPoints ps7(3);
    QCOMPARE(ps7.dimension(), 3);
    QVERIFY(ps7.isEmpty());
    QhullPoints ps3(2, 6, c);
    QCOMPARE(ps3.dimension(), 2);
    QVERIFY(!ps3.isEmpty());
    QCOMPARE(ps3.coordinates(), ps2.coordinates());
    QVERIFY(ps3==ps2);
    QVERIFY(ps3!=ps);
    QhullPoints ps4= ps3;
    QVERIFY(ps4==ps3);
    // ps4= ps3; //compiler error
    QhullPoints ps5(ps4);
    QVERIFY(ps5==ps4);
    QVERIFY(!(ps5!=ps4));
    coordT c2[]= {0.0, 1.0, 2.0, 3.0, 4.0, 5.0};
    QhullPoints ps6(2, 6, c2);
    QVERIFY(ps6==ps2);
}//t_construct

void QhullPoints_test::
t_convert()
{
    //defineAs tested above
    coordT c[]= {0.0, 1.0, 2.0, 3.0, 4.0, 5.0};
    QhullPoints ps(3, 6, c);
    QCOMPARE(ps.dimension(), 3);
    QCOMPARE(ps.size(), 2u);
    const coordT *c2= ps.constData();
    QCOMPARE(c, c2);
    const coordT *c3= ps.data();
    QCOMPARE(c, c3);
    coordT *c4= ps.data();
    QCOMPARE(c, c4);
    std::vector vs= ps.toStdVector();
    QCOMPARE(vs.size(), 2u);
    QhullPoint p= vs[1];
    QCOMPARE(p[2], 5.0);
    QList qs= ps.toQList();
    QCOMPARE(qs.size(), 2);
    QhullPoint p2= qs[1];
    QCOMPARE(p2[2], 5.0);
}//t_convert

void QhullPoints_test::
t_getset()
{
    //See t_construct for coordinates, count, defineAs, dimension, empty, isempty, ==, !=, size
    coordT c[]= {0.0, 1.0, 2.0, 3.0, 4.0, 5.0};
    QhullPoints ps(3, 6, c);
    QhullPoints ps2(3, 6, c);
    QCOMPARE(ps2.dimension(), 3);
    QCOMPARE(ps2.coordinates(), c);
    QCOMPARE(ps2.count(), 2);
    QCOMPARE(ps2.coordinateCount(), 6);
    coordT c2[]= {-1.0, -2.0, -3.0, -4.0, -5.0, -6.0};
    ps2.defineAs(6, c2);
    QCOMPARE(ps2.coordinates(), c2);
    QCOMPARE(ps2.count(), 2);
    QCOMPARE(ps2.size(), 2u);
    QCOMPARE(ps2.dimension(), 3);
    QVERIFY(!ps2.isEmpty());
    QVERIFY(ps!=ps2);
    // ps2= ps; // assignment not available, compiler error
    ps2.defineAs(ps);
    QVERIFY(ps==ps2);
    ps2.setDimension(2);
    QCOMPARE(ps2.dimension(), 2);
    QCOMPARE(ps2.coordinates(), c);
    QVERIFY(!ps2.isEmpty());
    QCOMPARE(ps2.count(), 3);
    QCOMPARE(ps2.size(), 3u);
    QVERIFY(ps!=ps2);
    QhullPoints ps3(3);
    ps3.defineAs(5, c2);
    QCOMPARE(ps3.count(), 1);
    QCOMPARE(ps3.extraCoordinatesCount(), 2);
    QCOMPARE(ps3.extraCoordinates()[0], -4.0);
    QVERIFY(ps3.includesCoordinates(ps3.data()));
    QVERIFY(ps3.includesCoordinates(ps3.data()+ps3.count()-1));
    QVERIFY(!ps3.includesCoordinates(ps3.data()-1));
    QVERIFY(!ps3.includesCoordinates(ps3.data()+ps3.coordinateCount()));
}//t_getset


void QhullPoints_test::
t_element()
{
    coordT c[]= {0.0, 1.0, 2.0, 3.0, 4.0, 5.0};
    QhullPoints ps(2, 6, c);
    QhullPoint p(2, c);
    QCOMPARE(ps[0], p);
    QCOMPARE(ps.at(1), ps[1]);
    QCOMPARE(ps.first(), p);
    QCOMPARE(ps.front(), ps.first());
    QCOMPARE(ps.last(), ps.at(2));
    QCOMPARE(ps.back(), ps.last());
    QhullPoints ps2= ps.mid(2);
    QCOMPARE(ps2.count(), 1);
    QhullPoints ps3= ps.mid(3);
    QVERIFY(ps3.isEmpty());
    QVERIFY(ps3.empty());
    QhullPoints ps4= ps.mid(10);
    QVERIFY(ps4.isEmpty());
    QhullPoints ps5= ps.mid(-1);
    QVERIFY(ps5.isEmpty());
    QhullPoints ps6= ps.mid(1, 1);
    QCOMPARE(ps6.count(), 1);
    QCOMPARE(ps6[0], ps[1]);
    QhullPoints ps7= ps.mid(1, 10);
    QCOMPARE(ps7.count(), 2);
    QCOMPARE(ps7[1], ps[2]);
    QhullPoint p8;
    QCOMPARE(ps.value(2), ps[2]);
    QCOMPARE(ps.value(-1), p8);
    QCOMPARE(ps.value(3), p8);
    QCOMPARE(ps.value(3, p), p);
    QVERIFY(ps.value(1, p)!=p);
    foreach(QhullPoint p9, ps){  // Qt only
        QCOMPARE(p9.dimension(), 2);
        QVERIFY(p9[0]==0.0 || p9[0]==2.0 || p9[0]==4.0);
    }
}//t_element

void QhullPoints_test::
t_iterator()
{
    coordT c[]= {0.0, 1.0, 2.0};
    QhullPoints ps(1, 3, c);
    QhullPoints::Iterator i(ps);
    QhullPoints::iterator i2= ps.begin();
    QVERIFY(i==i2);
    QVERIFY(i>=i2);
    QVERIFY(i<=i2);
    i= ps.begin();
    QVERIFY(i==i2);
    i2= ps.end();
    QVERIFY(i!=i2);
    QhullPoint p(i); // QhullPoint is the base class for QhullPoints::iterator
    QCOMPARE(p.dimension(), ps.dimension());
    QCOMPARE(p.coordinates(), ps.coordinates());
    i2--;
    QhullPoint p2= *i2;
    QCOMPARE(p[0], 0.0);
    QCOMPARE(p2[0], 2.0);
    QhullPoints::Iterator i5(i2);
    QCOMPARE(*i2, *i5);
    coordT c3[]= {0.0, -1.0, -2.0};
    QhullPoints::Iterator i3(1, c3);
    QVERIFY(i!=i3);
    QCOMPARE(*i, *i3);

    (i3= i)++;
    QCOMPARE((*i3)[0], 1.0);
    QCOMPARE(i3->dimension(), 1);
    QCOMPARE(i3[0][0], 1.0);
    QCOMPARE(i3[0], ps[1]);

    QVERIFY(i==i);
    QVERIFY(i!=i2);
    QVERIFY(ii);
    QVERIFY(i2>=i);

    QhullPoints::ConstIterator i4(1, c);
    QVERIFY(i==i4); // iterator COMP const_iterator
    QVERIFY(i<=i4);
    QVERIFY(i>=i4);
    QVERIFY(i4==i); // const_iterator COMP iterator
    QVERIFY(i4<=i);
    QVERIFY(i4>=i);
    QVERIFY(i>=i4);
    QVERIFY(i4<=i);
    QVERIFY(i2!=i4);
    QVERIFY(i2>i4);
    QVERIFY(i2>=i4);
    QVERIFY(i4!=i2);
    QVERIFY(i4i);
    QVERIFY(i4>=i);

    i= ps.begin();
    i2= ps.begin();
    QCOMPARE(i, i2++);
    QCOMPARE(*i2, ps[1]);
    QCOMPARE(++i, i2);
    QCOMPARE(i, i2--);
    QCOMPARE(i2, ps.begin());
    QCOMPARE(--i, i2);
    QCOMPARE(i2+=3, ps.end());
    QCOMPARE(i2-=3, ps.begin());
    QCOMPARE(i2+0, ps.begin());
    QCOMPARE(i2+3, ps.end());
    i2 += 3;
    i= i2-0;
    QCOMPARE(i, i2);
    i= i2-3;
    QCOMPARE(i, ps.begin());
    QCOMPARE(i2-i, 3);

    //ps.begin end tested above

    // QhullPoints is const-only
}//t_iterator

void QhullPoints_test::
t_const_iterator()
{
    coordT c[]= {0.0, 1.0, 2.0};
    const QhullPoints ps(1, 3, c);
    QhullPoints::ConstIterator i(ps);
    QhullPoints::const_iterator i2= ps.begin();
    QVERIFY(i==i2);
    QVERIFY(i>=i2);
    QVERIFY(i<=i2);
    i= ps.begin();
    QVERIFY(i==i2);
    i2= ps.end();
    QVERIFY(i!=i2);
    QhullPoint p(i);
    QCOMPARE(p.dimension(), ps.dimension());
    QCOMPARE(p.coordinates(), ps.coordinates());
    i2--;
    QhullPoint p2= *i2;
    QCOMPARE(p[0], 0.0);
    QCOMPARE(p2[0], 2.0);
    QhullPoints::ConstIterator i5(i2);
    QCOMPARE(*i2, *i5);
    coordT c3[]= {0.0, -1.0, -2.0};
    QhullPoints::ConstIterator i3(1, c3);
    QVERIFY(i!=i3);
    QCOMPARE(*i, *i3);

    (i3= i)++;
    QCOMPARE((*i3)[0], 1.0);
    QCOMPARE(i3->dimension(), 1);
    QCOMPARE(i3[0][0], 1.0);
    QCOMPARE(i3[0][0], 1.0);
    QCOMPARE(i3[0], ps[1]);

    QVERIFY(i==i);
    QVERIFY(i!=i2);
    QVERIFY(ii);
    QVERIFY(i2>=i);

    // See t_iterator for const_iterator COMP iterator

    i= ps.begin();
    i2= ps.constBegin();
    QCOMPARE(i, i2++);
    QCOMPARE(*i2, ps[1]);
    QCOMPARE(++i, i2);
    QCOMPARE(i, i2--);
    QCOMPARE(i2, ps.constBegin());
    QCOMPARE(--i, i2);
    QCOMPARE(i2+=3, ps.constEnd());
    QCOMPARE(i2-=3, ps.constBegin());
    QCOMPARE(i2+0, ps.constBegin());
    QCOMPARE(i2+3, ps.constEnd());
    i2 += 3;
    i= i2-0;
    QCOMPARE(i, i2);
    i= i2-3;
    QCOMPARE(i, ps.constBegin());
    QCOMPARE(i2-i, 3);

    // QhullPoints is const-only
}//t_const_iterator


void QhullPoints_test::
t_search()
{
    coordT c[]= {0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 0, 1};
    QhullPoints ps(2, 8, c); //2-d array of 4 points
    QhullPoint p= ps.first();
    QhullPoint p2= ps.last();
    QVERIFY(ps.contains(p));
    QVERIFY(ps.contains(p2));
    QVERIFY(p==p2);
    QhullPoint p5= ps[2];
    QVERIFY(p!=p5);
    QVERIFY(ps.contains(p5));
    coordT c2[]= {0.0, 1.0, 2.0, 3.0};
    QhullPoint p3(2, c2); //2-d point
    QVERIFY(ps.contains(p3));
    QhullPoint p4(3, c2); //3-d point
    QVERIFY(!ps.contains(p4));
    p4.defineAs(2, c); //2-d point
    QVERIFY(ps.contains(p4));
    p4.defineAs(2, c+1); //2-d point
    QVERIFY(!ps.contains(p4));
    QhullPoint p6(2, c2+2); //2-d point
    QCOMPARE(ps.count(p), 2);
    QCOMPARE(ps.count(p2), 2);
    QCOMPARE(ps.count(p3), 2);
    QCOMPARE(ps.count(p4), 0);
    QCOMPARE(ps.count(p6), 1);
    QCOMPARE(ps.indexOf(&ps[0][0]), 0);
    //QCOMPARE(ps.indexOf(ps.end()), -1); //ps.end() is a QhullPoint which may match
    QCOMPARE(ps.indexOf(0), -1);
    QCOMPARE(ps.indexOf(&ps[3][0]), 3);
    QCOMPARE(ps.indexOf(&ps[3][1], QhullError::NOthrow), 3);
    QCOMPARE(ps.indexOf(ps.data()+ps.coordinateCount(), QhullError::NOthrow), -1);
    QCOMPARE(ps.indexOf(p), 0);
    QCOMPARE(ps.indexOf(p2), 0);
    QCOMPARE(ps.indexOf(p3), 0);
    QCOMPARE(ps.indexOf(p4), -1);
    QCOMPARE(ps.indexOf(p5), 2);
    QCOMPARE(ps.indexOf(p6), 1);
    QCOMPARE(ps.lastIndexOf(p), 3);
    QCOMPARE(ps.lastIndexOf(p4), -1);
    QCOMPARE(ps.lastIndexOf(p6), 1);
    QhullPoints ps2(3);
    QCOMPARE(ps2.indexOf(ps2.data()), -1);
    QCOMPARE(ps2.indexOf(ps2.data()+1, QhullError::NOthrow), -1);
    QCOMPARE(ps2.indexOf(p), -1);
    QCOMPARE(ps2.lastIndexOf(p), -1);
    QhullPoints ps3;
    QCOMPARE(ps3.indexOf(ps3.data()), -1);
    QCOMPARE(ps3.indexOf(ps3.data()+1, QhullError::NOthrow), -1);
    QCOMPARE(ps3.indexOf(p), -1);
    QCOMPARE(ps3.lastIndexOf(p), -1);
    QhullPoints ps4(2, 0, c);
    QCOMPARE(ps4.indexOf(p), -1);
    QCOMPARE(ps4.lastIndexOf(p), -1);
}//t_search

void QhullPoints_test::
t_points_iterator()
{
    coordT c2[]= {0.0};
    QhullPoints ps2(0, 0, c2); // 0-dimensional
    QhullPointsIterator i2= ps2;
    QVERIFY(!i2.hasNext());
    QVERIFY(!i2.hasPrevious());
    i2.toBack();
    QVERIFY(!i2.hasNext());
    QVERIFY(!i2.hasPrevious());

    coordT c[]= {0.0, 1.0, 2.0, 3.0, 4.0, 5.0};
    QhullPoints ps(3, 6, c); // 3-dimensional
    QhullPointsIterator i(ps);
    i2= ps;
    QVERIFY(i2.hasNext());
    QVERIFY(!i2.hasPrevious());
    QVERIFY(i.hasNext());
    QVERIFY(!i.hasPrevious());
    i2.toBack();
    i.toFront();
    QVERIFY(!i2.hasNext());
    QVERIFY(i2.hasPrevious());
    QVERIFY(i.hasNext());
    QVERIFY(!i.hasPrevious());

    QhullPoint p= ps[0];
    QhullPoint p2(ps[0]);
    QCOMPARE(p, p2);
    QVERIFY(p==p2);
    QhullPoint p3(ps[1]);
 // p2[0]= 0.0;
    QVERIFY(p==p2);
    QCOMPARE(i2.peekPrevious(), p3);
    QCOMPARE(i2.previous(), p3);
    QCOMPARE(i2.previous(), p);
    QVERIFY(!i2.hasPrevious());
    QCOMPARE(i.peekNext(), p);
    // i.peekNext()= 1.0; // compiler error
    QCOMPARE(i.next(), p);
    QCOMPARE(i.peekNext(), p3);
    QCOMPARE(i.next(), p3);
    QVERIFY(!i.hasNext());
    i.toFront();
    QCOMPARE(i.next(), p);
}//t_points_iterator

void QhullPoints_test::
t_io()
{
    QhullPoints ps;
    ostringstream os;
    os << "Empty QhullPoints\n" << ps << endl;
    coordT c[]= {0.0, 1.0, 2.0, 3.0, 4.0, 5.0};
    QhullPoints ps2(3, 6, c); // 3-dimensional explicit
    os << "QhullPoints from c[]\n" << ps2 << endl;
    RboxPoints rcube("c");
    Qhull q(rcube,"Qt QR0");  // triangulation of rotated unit cube
    QhullPoints ps3= q.points();
    os << "QhullPoints\n" << ps3;
    os << "RunId\n" << ps3.print(q.runId());
    os << ps3.print(q.runId(), "RunId w/ message\n");
    os << ps3.printWithIdentifier(q.runId(), "RunId w/ identifiers\n");
    cout << os.str();
    QString s= QString::fromStdString(os.str());
    QCOMPARE(s.count("p"), 3*8+3);
    // QCOMPARE(s.count(QRegExp("f\\d")), 3*7 + 13*3*2);
}//t_io

}//orgQhull

#include "moc/QhullPoints_test.moc"
qhull-2012.1/src/qhulltest/QhullPoint_test.cpp0000644000076400010400000002417311716456524022604 0ustar  bbarberAdministrators/****************************************************************************
**
** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
** $Id: //main/2011/qhull/src/qhulltest/QhullPoint_test.cpp#4 $$Change: 1490 $
** $DateTime: 2012/02/19 20:27:01 $$Author: bbarber $
**
****************************************************************************/

//pre-compiled headers
#include 
#include "RoadTest.h"

#include "QhullPoint.h"
#include "Coordinates.h"
#include "RboxPoints.h"
#include "QhullError.h"
#include "QhullFacet.h"
#include "QhullPoint.h"
#include "Qhull.h"

#include 

using std::cout;
using std::endl;
using std::ostringstream;
using std::ostream;
using std::string;

namespace orgQhull {

class QhullPoint_test : public RoadTest
{
    Q_OBJECT

#//Test slots
private slots:
    void cleanup();
    void t_construct();
    void t_convert();
    void t_readonly();
    void t_define();
    void t_operator();
    void t_iterator();
    void t_const_iterator();
    void t_qhullpoint_iterator();
    void t_io();
};//QhullPoint_test

void
add_QhullPoint_test()
{
    new QhullPoint_test();
}

//Executed after each test
void QhullPoint_test::
cleanup()
{
    UsingLibQhull::checkQhullMemoryEmpty();
    RoadTest::cleanup();
}

void QhullPoint_test::
t_construct()
{
    // Qhull.runQhull() constructs QhullFacets as facetT
    QhullPoint p;
    QVERIFY(!p.isDefined());
    QCOMPARE(p.dimension(),0);
    QCOMPARE(p.coordinates(),static_cast(0));
    RboxPoints rcube("c");
    Qhull q(rcube,"Qt QR0");  // triangulation of rotated unit cube
    QhullVertex v2(q.beginVertex());
    QhullPoint p2(v2.point());
    QVERIFY(p2.isDefined());
    QCOMPARE(p2.dimension(),3);
    // p= p2;  // copy assignment disabled, ambiguous
    QhullPoint p3(p2.dimension(), p2.coordinates());
    QCOMPARE(p2, p3);
    Coordinates c;
    c << 0.0 << 0.0 << 0.0;
    QhullPoint p6(c);
    QCOMPARE(p6, q.origin());
    QhullPoint p5= p2; // copy constructor
    QVERIFY(p5==p2);
}//t_construct

void QhullPoint_test::
t_convert()
{
    RboxPoints rcube("c");
    Qhull q(rcube,"Qt QR0");  // triangulation of rotated unit cube
    QhullVertex v= q.firstVertex();
    QhullPoint p= v.point();
    std::vector vs= p.toStdVector();
    QCOMPARE(vs.size(), 3u);
    for(int k=3; k--; ){
        QCOMPARE(vs[k], p[k]);
    }
    QList qs= p.toQList();
    QCOMPARE(qs.size(), 3);
    for(int k=3; k--; ){
        QCOMPARE(qs[k], p[k]);
    }
}//t_convert

void QhullPoint_test::
t_readonly()
{
    RboxPoints rcube("c");
    {
        Qhull q(rcube,"Qt QR0");  // triangulation of rotated unit cube
        QhullVertexList vs= q.vertexList();
        QhullVertexListIterator i(vs);
        while(i.hasNext()){
            QhullPoint p= i.next().point();
            int id= p.id(q.runId());
            cout << "p" << id << endl;
            QVERIFY(p.isDefined());
            QCOMPARE(p.dimension(),3);
            QCOMPARE(id, p.id());
            QVERIFY(p.id()>=0 && p.id()<9);
            const coordT *c= p.coordinates();
            coordT *c2= p.coordinates();
            QCOMPARE(c, c2);
            QCOMPARE(p.dimension(), 3);
        }
        QhullPoint p2= vs.first().point();
        QhullPoint p3= vs.last().point();
        QVERIFY(p2!=p3);
        QVERIFY(p3.coordinates()!=p2.coordinates());
    }
}//t_readonly

void QhullPoint_test::
t_define()
{
    RboxPoints rcube("c");
    {
        Qhull q(rcube,"Qt QR0");  // triangulation of rotated unit cube
        QhullVertexList vs= q.vertexList();
        QhullPoint p= vs.first().point();
        QhullPoint p2= p;
        QVERIFY(p==p2);
        QhullPoint p3= vs.last().point();
        QVERIFY(p2!=p3);
        int idx= (p3.coordinates()-p2.coordinates())/p2.dimension();
        QVERIFY(idx>-8 && idx<8);
        p2.advancePoint(idx);
        QVERIFY(p2==p3);
        p2.advancePoint(-idx);
        QVERIFY(p2==p);
        p2.advancePoint(0);
        QVERIFY(p2==p);

        QhullPoint p4= p3;
        p4.defineAs(p2);
        QVERIFY(p2==p4);
        QhullPoint p5= p3;
        p5.defineAs(p2.dimension(), p2.coordinates());
        QVERIFY(p2==p5);
        QhullPoint p6= p3;
        p6.setCoordinates(p2.coordinates());
        QCOMPARE(p2.coordinates(), p6.coordinates());
        QVERIFY(p2==p6);
        p6.setDimension(2);
        QCOMPARE(p6.dimension(), 2);
        QVERIFY(p2!=p6);
    }
}//t_define

void QhullPoint_test::
t_operator()
{
    RboxPoints rcube("c");
    Qhull q(rcube,"Qt QR0");  // triangulation of rotated unit cube
    const QhullPoint p= q.firstVertex().point();
    //operator== and operator!= tested elsewhere
    const coordT *c= p.coordinates();
    for(int k=p.dimension(); k--; ){
        QCOMPARE(c[k], p[k]);
    }
    //p[0]= 10.0; // compiler error, const
    QhullPoint p2= q.firstVertex().point();
    p2[0]= 10.0;  // Overwrites point coordinate
    QCOMPARE(p2[0], 10.0);
}//t_operator

void QhullPoint_test::
t_iterator()
{
    RboxPoints rcube("c");
    {
        QhullPoint p2;
        QCOMPARE(p2.begin(), p2.end());
        Qhull q(rcube,"QR0");  // rotated unit cube
        QhullPoint p= q.firstVertex().point();
        QhullPoint::Iterator i= p.begin();
        QhullPoint::iterator i2= p.begin();
        QVERIFY(i==i2);
        QVERIFY(i>=i2);
        QVERIFY(i<=i2);
        i= p.begin();
        QVERIFY(i==i2);
        i2= p.end();
        QVERIFY(i!=i2);
        double d3= *i;
        i2--;
        double d2= *i2;
        QCOMPARE(d3, p[0]);
        QCOMPARE(d2, p[2]);
        QhullPoint::Iterator i3(i2);
        QCOMPARE(*i2, *i3);

        (i3= i)++;
        QCOMPARE((*i3), p[1]);
        QVERIFY(i==i);
        QVERIFY(i!=i2);
        QVERIFY(ii);
        QVERIFY(i2>=i);

        QhullPoint::ConstIterator i4= p.begin();
        QVERIFY(i==i4); // iterator COMP const_iterator
        QVERIFY(i<=i4);
        QVERIFY(i>=i4);
        QVERIFY(i4==i); // const_iterator COMP iterator
        QVERIFY(i4<=i);
        QVERIFY(i4>=i);
        QVERIFY(i>=i4);
        QVERIFY(i4<=i);
        QVERIFY(i2!=i4);
        QVERIFY(i2>i4);
        QVERIFY(i2>=i4);
        QVERIFY(i4!=i2);
        QVERIFY(i4i);
        QVERIFY(i4>=i);

        i= p.begin();
        i2= p.begin();
        QCOMPARE(i, i2++);
        QCOMPARE(*i2, p[1]);
        QCOMPARE(++i, i2);
        QCOMPARE(i, i2--);
        QCOMPARE(i2, p.begin());
        QCOMPARE(--i, i2);
        QCOMPARE(i2 += 3, p.end());
        QCOMPARE(i2 -= 3, p.begin());
        QCOMPARE(i2+0, p.begin());
        QCOMPARE(i2+3, p.end());
        i2 += 3;
        i= i2-0;
        QCOMPARE(i, i2);
        i= i2-3;
        QCOMPARE(i, p.begin());
        QCOMPARE(i2-i, 3);

        //p.begin end tested above

        // QhullPoint is const-only
    }
}//t_iterator

void QhullPoint_test::
t_const_iterator()
{
    RboxPoints rcube("c");
    {
        Qhull q(rcube,"QR0");  // rotated unit cube
        QhullPoint p= q.firstVertex().point();
        QhullPoint::ConstIterator i= p.begin();
        QhullPoint::const_iterator i2= p.begin();
        QVERIFY(i==i2);
        QVERIFY(i>=i2);
        QVERIFY(i<=i2);
        i= p.begin();
        QVERIFY(i==i2);
        i2= p.end();
        QVERIFY(i!=i2);
        double d3= *i;
        i2--;
        double d2= *i2;
        QCOMPARE(d3, p[0]);
        QCOMPARE(d2, p[2]);
        QhullPoint::ConstIterator i3(i2);
        QCOMPARE(*i2, *i3);

        (i3= i)++;
        QCOMPARE((*i3), p[1]);
        QVERIFY(i==i);
        QVERIFY(i!=i2);
        QVERIFY(ii);
        QVERIFY(i2>=i);

        // See t_iterator for const_iterator COMP iterator

        i= p.begin();
        i2= p.constBegin();
        QCOMPARE(i, i2++);
        QCOMPARE(*i2, p[1]);
        QCOMPARE(++i, i2);
        QCOMPARE(i, i2--);
        QCOMPARE(i2, p.constBegin());
        QCOMPARE(--i, i2);
        QCOMPARE(i2+=3, p.constEnd());
        QCOMPARE(i2-=3, p.constBegin());
        QCOMPARE(i2+0, p.constBegin());
        QCOMPARE(i2+3, p.constEnd());
        i2 += 3;
        i= i2-0;
        QCOMPARE(i, i2);
        i= i2-3;
        QCOMPARE(i, p.constBegin());
        QCOMPARE(i2-i, 3);

        // QhullPoint is const-only
    }
}//t_const_iterator

void QhullPoint_test::
t_qhullpoint_iterator()
{
    QhullPoint p2;
    QhullPointIterator i= p2;
    QCOMPARE(p2.dimension(), 0);
    QVERIFY(!i.hasNext());
    QVERIFY(!i.hasPrevious());
    i.toBack();
    QVERIFY(!i.hasNext());
    QVERIFY(!i.hasPrevious());

    RboxPoints rcube("c");
    Qhull q(rcube,"QR0");  // rotated unit cube
    QhullPoint p = q.firstVertex().point();
    QhullPointIterator i2(p);
    QCOMPARE(p.dimension(), 3);
    i= p;
    QVERIFY(i2.hasNext());
    QVERIFY(!i2.hasPrevious());
    QVERIFY(i.hasNext());
    QVERIFY(!i.hasPrevious());
    i2.toBack();
    i.toFront();
    QVERIFY(!i2.hasNext());
    QVERIFY(i2.hasPrevious());
    QVERIFY(i.hasNext());
    QVERIFY(!i.hasPrevious());

    // i at front, i2 at end/back, 3 coordinates
    QCOMPARE(i.peekNext(), p[0]);
    QCOMPARE(i2.peekPrevious(), p[2]);
    QCOMPARE(i2.previous(), p[2]);
    QCOMPARE(i2.previous(), p[1]);
    QCOMPARE(i2.previous(), p[0]);
    QVERIFY(!i2.hasPrevious());
    QCOMPARE(i.peekNext(), p[0]);
    // i.peekNext()= 1.0; // compiler error, i is const
    QCOMPARE(i.next(), p[0]);
    QCOMPARE(i.peekNext(), p[1]);
    QCOMPARE(i.next(), p[1]);
    QCOMPARE(i.next(), p[2]);
    QVERIFY(!i.hasNext());
    i.toFront();
    QCOMPARE(i.next(), p[0]);
}//t_qhullpoint_iterator

void QhullPoint_test::
t_io()
{
    RboxPoints rcube("c");
    {
        Qhull q(rcube, "");
        QhullPoint p= q.beginVertex().point();
        ostringstream os;
        os << "Point w/o runId:\n";
        os << p;
        os << "Point w/ runId:\n";
        os << p.print(q.runId()) << p.print(q.runId(), " and a message ");
        os << p.printWithIdentifier(q.runId(), " Point with id and a message ");
        cout << os.str();
        QString s= QString::fromStdString(os.str());
        QCOMPARE(s.count("p"), 3);
        // QCOMPARE(s.count(QRegExp("f\\d")), 3*7 + 13*3*2);
    }
}//t_io

}//orgQhull

#include "moc/QhullPoint_test.moc"
qhull-2012.1/src/qhulltest/QhullRidge_test.cpp0000644000076400010400000001055011716456524022537 0ustar  bbarberAdministrators/****************************************************************************
**
** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
** $Id: //main/2011/qhull/src/qhulltest/QhullRidge_test.cpp#5 $$Change: 1490 $
** $DateTime: 2012/02/19 20:27:01 $$Author: bbarber $
**
****************************************************************************/

//pre-compiled headers
#include 
#include "RoadTest.h"

#include "QhullRidge.h"
#include "QhullError.h"
#include "RboxPoints.h"
#include "QhullFacet.h"
#include "Qhull.h"

using std::cout;
using std::endl;
using std::ostringstream;
using std::ostream;
using std::string;

namespace orgQhull {

class QhullRidge_test : public RoadTest
{
    Q_OBJECT

#//Test slots
private slots:
    void cleanup();
    void t_construct();
    void t_getSet();
    void t_foreach();
    void t_io();
};//QhullRidge_test

void
add_QhullRidge_test()
{
    new QhullRidge_test();
}

//Executed after each testcase
void QhullRidge_test::
cleanup()
{
    UsingLibQhull::checkQhullMemoryEmpty();
    RoadTest::cleanup();
}

void QhullRidge_test::
t_construct()
{
    // Qhull.runQhull() constructs QhullFacets as facetT
    QhullRidge r;
    QVERIFY(!r.isDefined());
    QCOMPARE(r.dimension(),0);
    RboxPoints rcube("c");
    Qhull q(rcube,"QR0");  // triangulation of rotated unit cube
    QhullFacet f(q.firstFacet());
    QhullRidgeSet rs(f.ridges());
    QVERIFY(!rs.isEmpty()); // Simplicial facets do not have ridges()
    QhullRidge r2(rs.first());
    QCOMPARE(r2.dimension(), 2); // One dimension lower than the facet
    r= r2;
    QVERIFY(r.isDefined());
    QCOMPARE(r.dimension(), 2);
    QhullRidge r3= r2.getRidgeT();
    QCOMPARE(r,r3);
    QhullRidge r4= r2.getBaseT();
    QCOMPARE(r,r4);
    QhullRidge r5= r2; // copy constructor
    QVERIFY(r5==r2);
    QVERIFY(r5==r);
}//t_construct

void QhullRidge_test::
t_getSet()
{
    RboxPoints rcube("c");
    {
        Qhull q(rcube,"QR0");  // triangulation of rotated unit cube
        QCOMPARE(q.facetCount(), 6);
        QCOMPARE(q.vertexCount(), 8);
        QhullFacet f(q.firstFacet());
        QhullRidgeSet rs= f.ridges();
        QhullRidgeSetIterator i(rs);
        while(i.hasNext()){
            const QhullRidge r= i.next();
            cout << r.id() << endl;
            QVERIFY(r.bottomFacet()!=r.topFacet());
            QCOMPARE(r.dimension(), 2); // Ridge one-dimension less than facet
            QVERIFY(r.id()>=0 && r.id()<9*27);
            QVERIFY(r.isDefined());
            QVERIFY(r==r);
            QVERIFY(r==i.peekPrevious());
            QCOMPARE(r.otherFacet(r.bottomFacet()),r.topFacet());
            QCOMPARE(r.otherFacet(r.topFacet()),r.bottomFacet());
        }
        QhullRidgeSetIterator i2(i);
        QEXPECT_FAIL("", "SetIterator copy constructor not reset to BOT", Continue);
        QVERIFY(!i2.hasPrevious());
    }
}//t_getSet

void QhullRidge_test::
t_foreach()
{
    RboxPoints rcube("c");  // cube
    {
        Qhull q(rcube, "QR0"); // rotated cube
        QhullFacet f(q.firstFacet());
        foreach (QhullRidge r, f.ridges()){  // Qt only
            QhullVertexSet vs= r.vertices();
            QCOMPARE(vs.count(), 2);
            foreach (QhullVertex v, vs){  // Qt only
                QVERIFY(f.vertices().contains(v));
            }
        }
        QhullRidgeSet rs= f.ridges();
        QhullRidge r= rs.first();
        QhullRidge r2= r;
        QList vs;
        int count= 0;
        while(!count || r2!=r){
            ++count;
            QhullVertex v;
            QVERIFY2(r2.hasNextRidge3d(f),"A cube should only have non-simplicial facets.");
            QhullRidge r3= r2.nextRidge3d(f, &v);
            QVERIFY(!vs.contains(v));
            vs << v;
            r2= r2.nextRidge3d(f);
            QCOMPARE(r3, r2);
        }
        QCOMPARE(vs.count(), rs.count());
        QCOMPARE(count, rs.count());
    }
}//t_foreach

void QhullRidge_test::
t_io()
{
    RboxPoints rcube("c");
    {
        Qhull q(rcube, "");
        QhullFacet f(q.firstFacet());
        QhullRidgeSet rs= f.ridges();
        QhullRidge r= rs.first();
        ostringstream os;
        os << "Ridges Without runId\n" << rs << "Ridge\n" << r;
        os << "Ridge with runId\n" << r.print(q.runId());
        cout << os.str();
        QString s= QString::fromStdString(os.str());
        QCOMPARE(s.count(" r"), 6+2);
    }
}//t_io

}//orgQhull

#include "moc/QhullRidge_test.moc"
qhull-2012.1/src/qhulltest/QhullSet_test.cpp0000644000076400010400000002755211716456524022252 0ustar  bbarberAdministrators/****************************************************************************
**
** Copyright (c) 2009-2012 C.B. Barber. All rights reserved.
** $Id: //main/2011/qhull/src/qhulltest/QhullSet_test.cpp#4 $$Change: 1490 $
** $DateTime: 2012/02/19 20:27:01 $$Author: bbarber $
**
****************************************************************************/

//pre-compiled headers
#include 
#include 
#include "RoadTest.h" // QT_VERSION

#include "QhullRidge.h"
#include "QhullFacetSet.h"
#include "Qhull.h"

using std::cout;
using std::endl;

namespace orgQhull {

class QhullSet_test : public RoadTest
{
    Q_OBJECT

#//Test slots
private slots:
    void cleanup();
    void t_qhullsetbase();
    void t_convert();
    void t_element();
    void t_search();
    void t_iterator();
    void t_const_iterator();
    void t_qhullset_iterator();
    void t_io();
};//QhullSet_test

void
add_QhullSet_test()
{
    new QhullSet_test();
}

//Executed after each testcase
void QhullSet_test::
cleanup()
{
    UsingLibQhull::checkQhullMemoryEmpty();
    RoadTest::cleanup();
}

// Test QhullFacetSet and QhullSet.
// Use QhullRidgeSet to test methods overloaded by QhullFacetSet

void QhullSet_test::
t_qhullsetbase()
{
    RboxPoints rcube("c");
    {
        Qhull q(rcube,"QR0");  // triangulation of rotated unit cube
        // Fake an empty set.  Default constructor not defined.  No memory allocation.
        QhullFacet f4 = q.beginFacet();
        QhullFacetSet fs = f4.neighborFacets();
        fs.defineAs(q.qhullQh()->other_points); // Force an empty set
        QVERIFY(fs.isEmpty());
        QVERIFY(fs.empty());
        QCOMPARE(fs.count(), 0);
        QCOMPARE(fs.size(), 0u);
        QCOMPARE(fs.begin(), fs.end()); // beginPointer(), endPointer()
        QVERIFY(QhullSetBase::isEmpty(fs.getSetT()));

        QhullRidgeSet rs = f4.ridges();
        QVERIFY(!rs.isEmpty());
        QVERIFY(!rs.empty());
        QCOMPARE(rs.count(), 4);
        QCOMPARE(rs.size(), 4u);
        QVERIFY(rs.begin()!=rs.end());
        QVERIFY(!QhullSetBase::isEmpty(rs.getSetT()));
        QhullRidgeSet rs2= rs; // copy constructor
        // rs= rs2; // disabled.  Would not copy ridges
        QCOMPARE(rs2, rs);

        QCOMPARE(q.facetCount(), 6);
        QhullFacet f = q.beginFacet();
        QhullFacetSet fs2 = f.neighborFacets();
        QCOMPARE(fs2.count(), 4);
        QCOMPARE(fs2.size(), 4u);
        QVERIFY(!fs2.isEmpty());
        QVERIFY(!QhullSetBase::isEmpty(fs2.getSetT()));
        QVERIFY(!fs2.empty());
        QVERIFY(fs!=fs2);
        setT *s= fs2.getSetT();
        fs.defineAs(s);
        QVERIFY(fs==fs2);
        QCOMPARE(fs[1], fs2[1]); // elementPointer
        QhullFacetSet fs3(fs2);
        QVERIFY(fs3==fs);
        // fs= fs2; // disabled.  Would not copy facets
        QhullFacetSet fs4= fs2; // copy constructor
        QVERIFY(fs4==fs2);
    }
}//t_qhullsetbase

// constructors tested by t_qhullsetbase

void QhullSet_test::
t_convert()
{
    RboxPoints rcube("c");
    {
        Qhull q(rcube,"QR0");  // rotated unit cube
        QhullFacet f= q.firstFacet();
        f= f.next();
        QhullRidgeSet rs= f.ridges();
        QCOMPARE(rs.count(),4);
        std::vector rv= rs.toStdVector();
        QCOMPARE(rv.size(), 4u);
        QList rv2= rs.toQList();
        QCOMPARE(rv2.size(), 4);
        std::vector::iterator i= rv.begin();
        foreach(QhullRidge r, rv2){  // Qt only
            QhullRidge r2= *i++;
            QCOMPARE(r, r2);
        }

        Qhull q2(rcube,"Qt QR0");  // triangulation of rotated unit cube
        QCOMPARE(q2.facetCount(), 12);
        QhullFacet f2 = q2.beginFacet();
        QhullFacetSet fs = f2.neighborFacets();
        QCOMPARE(fs.size(), 3U);
        std::vector vs= fs.toStdVector();
        QCOMPARE(vs.size(), fs.size());
        for(int k= fs.count(); k--; ){
            QCOMPARE(vs[k], fs[k]);
        }
        QList qv= fs.toQList();
        QCOMPARE(qv.count(), fs.count());
        for(int k= fs.count(); k--; ){
            QCOMPARE(qv[k], fs[k]);
        }
    }
}//t_convert

//ReadOnly (count, isEmpty) tested by t_convert
//  operator== tested by t_search

void QhullSet_test::
t_element()
{
    RboxPoints rcube("c");
    Qhull q(rcube,"QR0");  // rotated unit cube
    QhullFacet f = q.beginFacet();
    QhullFacetSet fs = f.neighborFacets();

    QCOMPARE(fs.at(1), fs[1]);
    QCOMPARE(fs.first(), fs[0]);
    QCOMPARE(fs.front(), fs.first());
    QCOMPARE(fs.last(), fs.at(3));
    QCOMPARE(fs.back(), fs.last());
    QhullFacet *d= fs.data();
    const QhullFacet *d2= fs.data();
    const QhullFacet *d3= fs.constData();
    QVERIFY(d==d2);
    QVERIFY(d2==d3);
    QCOMPARE(*d, fs.first());
    QCOMPARE(d+4, fs.end());
    QCOMPARE((d+4)->getFacetT(), static_cast(0));
    QhullFacet f4= *(d+4);
    QVERIFY(!f4.isDefined());
    QCOMPARE(fs.second(), fs[1]);
    const QhullFacet f2= fs.second();
    QVERIFY(f2==fs[1]);
    const QhullFacet f3= fs[1];
    QCOMPARE(f2, f3);

    QCOMPARE(fs.value(2), fs[2]);
    QCOMPARE(fs.value(-1), QhullFacet());
    QCOMPARE(fs.value(10), QhullFacet());
    QCOMPARE(fs.value(2, f), fs[2]);
    QCOMPARE(fs.value(4, f), f);
    // mid() not available (read-only)
}//t_element

void QhullSet_test::
t_search()
{
    RboxPoints rcube("c");
    Qhull q(rcube,"QR0");  // rotated unit cube
    QhullFacet f = q.beginFacet();
    QhullFacetSet fs = f.neighborFacets();
    QhullFacet f2= *fs.begin();
    QhullFacet f3= fs.last();
    QVERIFY(fs.contains(f2));
    QVERIFY(fs.contains(f3));
    QVERIFY(!fs.contains(f));

    QhullFacetSet fs2= f2.neighborFacets();
    QVERIFY(fs==fs);
    QVERIFY(fs!=fs2);
    QCOMPARE(fs.count(f2), 1);
    QCOMPARE(fs.count(f3), 1);
    QCOMPARE(fs.count(f), 0);
    QCOMPARE(fs.indexOf(f2), 0);
    QCOMPARE(fs.indexOf(f3), 3);
    QCOMPARE(fs.indexOf(f), -1);
    QCOMPARE(fs.lastIndexOf(f2), 0);
    QCOMPARE(fs.lastIndexOf(f3), 3);
    QCOMPARE(fs.lastIndexOf(f), -1);
}//t_search

void QhullSet_test::
t_iterator()
{
    RboxPoints rcube("c");
    {
        Qhull q(rcube,"QR0");  // rotated unit cube
        QhullFacet f = q.beginFacet();
        QhullFacetSet fs = f.neighborFacets();
        QhullFacetSet::Iterator i= fs.begin();
        QhullFacetSet::iterator i2= fs.begin();
        QVERIFY(i==i2);
        QVERIFY(i>=i2);
        QVERIFY(i<=i2);
        i= fs.begin();
        QVERIFY(i==i2);
        i2= fs.end();
        QVERIFY(i!=i2);
        QhullFacet f3(*i);
        i2--;
        QhullFacet f2= *i2;
        QCOMPARE(f3.id(), fs[0].id());
        QCOMPARE(f2.id(), fs[3].id());
        QhullFacetSet::Iterator i3(i2);
        QCOMPARE(*i2, *i3);

        (i3= i)++;
        QCOMPARE((*i3).id(), fs[1].id());
        QVERIFY(i==i);
        QVERIFY(i!=i2);
        QVERIFY(ii);
        QVERIFY(i2>=i);

        QhullFacetSet::ConstIterator i4= fs.begin();
        QVERIFY(i==i4); // iterator COMP const_iterator
        QVERIFY(i<=i4);
        QVERIFY(i>=i4);
        QVERIFY(i4==i); // const_iterator COMP iterator
        QVERIFY(i4<=i);
        QVERIFY(i4>=i);
        QVERIFY(i>=i4);
        QVERIFY(i4<=i);
        QVERIFY(i2!=i4);
        QVERIFY(i2>i4);
        QVERIFY(i2>=i4);
        QVERIFY(i4!=i2);
        QVERIFY(i4i);
        QVERIFY(i4>=i);

        i= fs.begin();
        i2= fs.begin();
        QCOMPARE(i, i2++);
        QCOMPARE(*i2, fs[1]);
        QCOMPARE(++i, i2);
        QCOMPARE(i, i2--);
        QCOMPARE(i2, fs.begin());
        QCOMPARE(--i, i2);
        QCOMPARE(i2 += 4, fs.end());
        QCOMPARE(i2 -= 4, fs.begin());
        QCOMPARE(i2+0, fs.begin());
        QCOMPARE(i2+4, fs.end());
        i2 += 4;
        i= i2-0;
        QCOMPARE(i, i2);
        i= i2-4;
        QCOMPARE(i, fs.begin());
        QCOMPARE(i2-i, 4);

        //fs.begin end tested above

        // QhullFacetSet is const-only
    }
}//t_iterator

void QhullSet_test::
t_const_iterator()
{
    RboxPoints rcube("c");
    {
        Qhull q(rcube,"QR0");  // rotated unit cube
        QhullFacet f = q.beginFacet();
        QhullFacetSet fs = f.neighborFacets();
        QhullFacetSet::ConstIterator i= fs.begin();
        QhullFacetSet::const_iterator i2= fs.begin();
        QVERIFY(i==i2);
        QVERIFY(i>=i2);
        QVERIFY(i<=i2);
        i= fs.begin();
        QVERIFY(i==i2);
        i2= fs.end();
        QVERIFY(i!=i2);
        QhullFacet f3(*i);
        i2--;
        QhullFacet f2= *i2;
        QCOMPARE(f3.id(), fs[0].id());
        QCOMPARE(f2.id(), fs[3].id());
        QhullFacetSet::ConstIterator i3(i2);
        QCOMPARE(*i2, *i3);

        (i3= i)++;
        QCOMPARE((*i3).id(), fs[1].id());
        QVERIFY(i==i);
        QVERIFY(i!=i2);
        QVERIFY(ii);
        QVERIFY(i2>=i);

        // See t_iterator for const_iterator COMP iterator

        i= fs.begin();
        i2= fs.constBegin();
        QCOMPARE(i, i2++);
        QCOMPARE(*i2, fs[1]);
        QCOMPARE(++i, i2);
        QCOMPARE(i, i2--);
        QCOMPARE(i2, fs.constBegin());
        QCOMPARE(--i, i2);
        QCOMPARE(i2+=4, fs.constEnd());
        QCOMPARE(i2-=4, fs.constBegin());
        QCOMPARE(i2+0, fs.constBegin());
        QCOMPARE(i2+4, fs.constEnd());
        i2 += 4;
        i= i2-0;
        QCOMPARE(i, i2);
        i= i2-4;
        QCOMPARE(i, fs.constBegin());
        QCOMPARE(i2-i, 4);

        // QhullFacetSet is const-only
    }
}//t_const_iterator

void QhullSet_test::
t_qhullset_iterator()
{
    RboxPoints rcube("c");
    Qhull q(rcube,"QR0");  // rotated unit cube
    // Fake an empty set.  Default constructor not defined.  No memory allocation.
    QhullFacet f = q.beginFacet();
    QhullFacetSet fs = f.neighborFacets();
    fs.defineAs(q.qhullQh()->other_points);
    QhullFacetSetIterator i= fs;
    QCOMPARE(fs.count(), 0);
    QVERIFY(!i.hasNext());
    QVERIFY(!i.hasPrevious());
    i.toBack();
    QVERIFY(!i.hasNext());
    QVERIFY(!i.hasPrevious());

    QhullFacet f2 = q.beginFacet();
    QhullFacetSet fs2 = f2.neighborFacets();
    QhullFacetSetIterator i2(fs2);
    QCOMPARE(fs2.count(), 4);
    i= fs2;
    QVERIFY(i2.hasNext());
    QVERIFY(!i2.hasPrevious());
    QVERIFY(i.hasNext());
    QVERIFY(!i.hasPrevious());
    i2.toBack();
    i.toFront();
    QVERIFY(!i2.hasNext());
    QVERIFY(i2.hasPrevious());
    QVERIFY(i.hasNext());
    QVERIFY(!i.hasPrevious());

    // i at front, i2 at end/back, 4 neighbors
    QhullFacetSet fs3 = f2.neighborFacets(); // same as fs2
    QhullFacet f3(fs2[0]);
    QhullFacet f4= fs3[0];
    QCOMPARE(f3, f4);
    QVERIFY(f3==f4);
    QhullFacet f5(fs3[1]);
    QVERIFY(f4!=f5);
    QhullFacet f6(fs3[2]);
    QhullFacet f7(fs3[3]);
    QCOMPARE(i2.peekPrevious(), f7);
    QCOMPARE(i2.previous(), f7);
    QCOMPARE(i2.previous(), f6);
    QCOMPARE(i2.previous(), f5);
    QCOMPARE(i2.previous(), f4);
    QVERIFY(!i2.hasPrevious());
    QCOMPARE(i.peekNext(), f4);
    // i.peekNext()= 1.0; // compiler error
    QCOMPARE(i.next(), f4);
    QCOMPARE(i.peekNext(), f5);
    QCOMPARE(i.next(), f5);
    QCOMPARE(i.next(), f6);
    QCOMPARE(i.next(), f7);
    QVERIFY(!i.hasNext());
    i.toFront();
    QCOMPARE(i.next(), f4);
}//t_qhullset_iterator

void QhullSet_test::
t_io()
{
    RboxPoints rcube("c");
    Qhull q(rcube,"QR0");  // rotated unit cube
    // Fake an empty set.  Default constructor not defined.  No memory allocation.
    QhullFacet f= q.beginFacet();
    QhullFacetSet fs= f.neighborFacets();
    fs.defineAs(q.qhullQh()->other_points);
    cout << "INFO:     empty set" << fs << std::endl;
    QhullFacet f2= q.beginFacet();
    QhullFacetSet fs2= f2.neighborFacets();
    cout << "INFO:   Neighboring facets\n";
    cout << fs2 << std::endl;

    QhullRidgeSet rs= f.ridges();
    cout << "INFO:   Ridges for a facet\n";
    cout << rs << std::endl;
}//t_io

}//namespace orgQhull

#include "moc/QhullSet_test.moc"
qhull-2012.1/src/qhulltest/qhulltest.cpp0000644000076400010400000000471611716456524021474 0ustar  bbarberAdministrators/****************************************************************************
**
** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
** $Id: //main/2011/qhull/src/qhulltest/qhulltest.cpp#5 $$Change: 1490 $
** $DateTime: 2012/02/19 20:27:01 $$Author: bbarber $
**
****************************************************************************/

//pre-compiled headers
#include 
#include 
#include 
#include 
#include "RoadTest.h"

#include "../libqhullcpp/RoadError.h"

using std::cout;
using std::endl;

namespace orgQhull {

void addQhullTests(QStringList &args)
{
    TESTadd_(add_QhullVertex_test); //copy

    if(args.contains("--all")){
        args.removeAll("--all");
        // up-to-date
        TESTadd_(add_Coordinates_test);
        TESTadd_(add_PointCoordinates_test);
        TESTadd_(add_QhullFacet_test);
        TESTadd_(add_QhullFacetList_test);
        TESTadd_(add_QhullFacetSet_test);
        TESTadd_(add_QhullHyperplane_test);
        TESTadd_(add_QhullLinkedList_test);
        TESTadd_(add_QhullPoint_test);
        TESTadd_(add_QhullPoints_test);
        TESTadd_(add_QhullPointSet_test);
        TESTadd_(add_QhullRidge_test);
        TESTadd_(add_QhullSet_test);
        TESTadd_(add_QhullVertex_test);
        TESTadd_(add_RboxPoints_test);
        TESTadd_(add_UsingLibQhull_test);
        // needs review
        // qhullStat
        TESTadd_(add_Qhull_test);
    }//--all
}//addQhullTests

int main(int argc, char *argv[])
{
    QCoreApplication app(argc, argv);
    QStringList args= app.arguments();
    bool isAll= args.contains("--all");
    addQhullTests(args);
    int status=1010;
    try{
        status= RoadTest::runTests(args);
    }catch(const std::exception &e){
        cout << "FAIL!  : runTests() did not catch error\n";
        cout << e.what() << endl;
        if(!RoadError::emptyGlobalLog()){
            cout << RoadError::stringGlobalLog() << endl;
            RoadError::clearGlobalLog();
        }
    }
    if(!RoadError::emptyGlobalLog()){
        cout << RoadError::stringGlobalLog() << endl;
        RoadError::clearGlobalLog();
    }
    if(isAll){
        cout << "Finished test of libqhullcpp.  Test libqhull with eg/q_test" << endl;
    }else{
        cout << "Finished test of one class.  Test all classes with 'qhulltest --all'" << endl;
    }
    return status;
}

}//orgQhull

int main(int argc, char *argv[])
{
    return orgQhull::main(argc, argv); // Needs RoadTest:: for TESTadd_() linkage
}

qhull-2012.1/src/qhulltest/qhulltest.pro0000644000076400010400000000166211716455560021506 0ustar  bbarberAdministrators# -------------------------------------------------
# qhulltest.pro -- Qt project for qhulltest.exe (QTestLib)
# -------------------------------------------------

include(../qhull-app-cpp.pri)

TARGET = qhulltest
CONFIG += qtestlib
MOC_DIR = moc
INCLUDEPATH += ..  # for MOC_DIR

PRECOMPILED_HEADER = RoadTest.h

SOURCES += ../libqhullcpp/qt-qhull.cpp
SOURCES += Coordinates_test.cpp
SOURCES += PointCoordinates_test.cpp
SOURCES += Qhull_test.cpp
SOURCES += QhullFacet_test.cpp
SOURCES += QhullFacetList_test.cpp
SOURCES += QhullFacetSet_test.cpp
SOURCES += QhullHyperplane_test.cpp
SOURCES += QhullLinkedList_test.cpp
SOURCES += QhullPoint_test.cpp
SOURCES += QhullPoints_test.cpp
SOURCES += QhullPointSet_test.cpp
SOURCES += QhullRidge_test.cpp
SOURCES += QhullSet_test.cpp
SOURCES += qhulltest.cpp
SOURCES += QhullVertex_test.cpp
SOURCES += RboxPoints_test.cpp
SOURCES += RoadTest.cpp
SOURCES += UsingLibQhull_test.cpp

HEADERS += RoadTest.h
qhull-2012.1/src/qhulltest/QhullVertexSet_test.cpp0000644000076400010400000001125111710144471023422 0ustar  bbarberAdministrators/****************************************************************************
**
** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
** $Id: //main/2011/qhull/src/qhulltest/QhullVertexSet_test.cpp#3 $$Change: 1464 $
** $DateTime: 2012/01/25 22:58:41 $$Author: bbarber $
**
****************************************************************************/

#include 
#include "../road/RoadTest.h" // FIXUP First for QHULL_USES_QT

#include "Qhull.h"
#include "QhullError.h"
#include "QhullFacet.h"
#include "QhullFacetSet.h"

using std::cout;
using std::endl;
using std::ostringstream;
using std::ostream;
using std::string;

namespace orgQhull {

class QhullFacetSet_test : public RoadTest
{
    Q_OBJECT

#//Test slots
private slots:
    void cleanup();
    void t_construct();
    void t_convert();
    void t_readonly();
    void t_foreach();
    void t_io();
};//QhullFacetSet_test

void
add_QhullFacetSet_test()
{
    new QhullFacetSet_test();
}

//Executed after each testcase
void QhullFacetSet_test::
cleanup()
{
    RoadTest::cleanup();
    UsingQhullLib::checkQhullMemoryEmpty();
}

void QhullFacetSet_test::
t_construct()
{
    RboxPoints rcube("c");
    Qhull q(rcube,"QR0");  // rotated unit cube
    QhullFacet f= q.firstFacet();
    QhullFacetSet fs2= f.neighborFacets();
    QVERIFY(!fs2.isEmpty());
    QCOMPARE(fs2.count(),4);
    QhullFacetSet fs4= fs2; // copy constructor
    QVERIFY(fs4==fs2);
    QhullFacetSet fs3(q.qhullQh()->facet_mergeset);
    QVERIFY(fs3.isEmpty());
}//t_construct

void QhullFacetSet_test::
t_convert()
{
    RboxPoints rcube("c");
    Qhull q(rcube,"QR0 QV2");  // rotated unit cube
    QhullFacet f= q.firstFacet();
    QhullFacetSet fs2= f.neighborFacets();
    QVERIFY(!fs2.isSelectAll());
    QCOMPARE(fs2.count(),2);
    std::vector fv= fs2.toStdVector();
    QCOMPARE(fv.size(), 2u);
    QList fv2= fs2.toQList();
    QCOMPARE(fv2.size(), 2);
    fs2.selectAll();
    QVERIFY(fs2.isSelectAll());
    std::vector fv3= fs2.toStdVector();
    QCOMPARE(fv3.size(), 4u);
    QList fv4= fs2.toQList();
    QCOMPARE(fv4.size(), 4);
}//t_convert

//! Spot check properties and read-only.  See QhullSet_test
void QhullFacetSet_test::
t_readonly()
{
    RboxPoints rcube("c");
    Qhull q(rcube,"QV0");  // good facets are adjacent to point 0
    QhullFacetSet fs= q.firstFacet().neighborFacets();
    QVERIFY(!fs.isSelectAll());
    QCOMPARE(fs.count(), 2);
    fs.selectAll();
    QVERIFY(fs.isSelectAll());
    QCOMPARE(fs.count(), 4);
    fs.selectGood();
    QVERIFY(!fs.isSelectAll());
    QCOMPARE(fs.count(), 2);
    QhullFacet f= fs.first();
    QhullFacet f2= fs.last();
    fs.selectAll();
    QVERIFY(fs.contains(f));
    QVERIFY(fs.contains(f2));
    QVERIFY(f.isGood());
    QVERIFY(!f2.isGood());
    fs.selectGood();
    QVERIFY(fs.contains(f));
    QVERIFY(!fs.contains(f2));
}//t_readonly

void QhullFacetSet_test::
t_foreach()
{
    RboxPoints rcube("c");
    // Spot check predicates and accessors.  See QhullLinkedList_test
    Qhull q(rcube,"QR0");  // rotated unit cube
    QhullFacetSet fs= q.firstFacet().neighborFacets();
    QVERIFY(!fs.contains(q.firstFacet()));
    QVERIFY(fs.contains(fs.first()));
    QhullFacet f= q.firstFacet().next();
    if(!fs.contains(f)){
        f= f.next();
    }
    QVERIFY(fs.contains(f));
    QCOMPARE(fs.first(), *fs.begin());
    QCOMPARE(*(fs.end()-1), fs.last());
}//t_foreach

void QhullFacetSet_test::
t_io()
{
    RboxPoints rcube("c");
    {
        Qhull q(rcube,"QR0 QV0");   // good facets are adjacent to point 0
        QhullFacetSet fs= q.firstFacet().neighborFacets();
        ostringstream os;
        os << fs.print(q.runId(), "Neighbors of first facet with point 0");
        os << fs.printIdentifiers("\nFacet identifiers: ");
        cout<< os.str();
        QString facets= QString::fromStdString(os.str());
        QCOMPARE(facets.count(QRegExp(" f[0-9]")), 2+13*2);
    }
}//t_io

//FIXUP -- Move conditional, QhullFacetSet code to QhullFacetSet.cpp
#ifndef QHULL_NO_STL
std::vector QhullFacetSet::
toStdVector() const
{
    QhullSetIterator i(*this);
    std::vector vs;
    while(i.hasNext()){
        QhullFacet f= i.next();
        if(isSelectAll() || f.isGood()){
            vs.push_back(f);
        }
    }
    return vs;
}//toStdVector
#endif //QHULL_NO_STL

#ifdef QHULL_USES_QT
QList QhullFacetSet::
toQList() const
{
    QhullSetIterator i(*this);
    QList vs;
    while(i.hasNext()){
        QhullFacet f= i.next();
        if(isSelectAll() || f.isGood()){
            vs.append(f);
        }
    }
    return vs;
}//toQList
#endif //QHULL_USES_QT

}//orgQhull

#include "moc/QhullFacetSet_test.moc"
qhull-2012.1/src/qhulltest/QhullVertex_test.cpp0000644000076400010400000001230211720052005022734 0ustar  bbarberAdministrators/****************************************************************************
**
** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
** $Id: //main/2011/qhull/src/qhulltest/QhullVertex_test.cpp#6 $$Change: 1490 $
** $DateTime: 2012/02/19 20:27:01 $$Author: bbarber $
**
****************************************************************************/
//pre-compiled headers
#include 
#include "RoadTest.h"

#include "QhullVertex.h"
#include "Coordinates.h"
#include "QhullError.h"
#include "RboxPoints.h"
#include "QhullFacet.h"
#include "QhullFacetSet.h"
#include "QhullVertexSet.h"
#include "Qhull.h"

using std::cout;
using std::endl;
using std::ostringstream;
using std::ostream;
using std::string;

namespace orgQhull {

class QhullVertex_test : public RoadTest
{
    Q_OBJECT

#//Test slots
private slots:
    void cleanup();
    void t_constructConvert();
    void t_getSet();
    void t_foreach();
    void t_io();
};//QhullVertex_test

void
add_QhullVertex_test()
{
    new QhullVertex_test();
}

//Executed after each testcase
void QhullVertex_test::
cleanup()
{
    UsingLibQhull::checkQhullMemoryEmpty();
    RoadTest::cleanup();
}

void QhullVertex_test::
t_constructConvert()
{
    // Qhull.runQhull() constructs QhullFacets as facetT
    QhullVertex v;
    QVERIFY(!v.isDefined());
    QCOMPARE(v.dimension(),0);
    RboxPoints rcube("c");
    Qhull q(rcube,"Qt QR0");  // triangulation of rotated unit cube
    QhullVertex v2(q.beginVertex());
    QCOMPARE(v2.dimension(),3);
    v= v2;  // copy assignment
    QVERIFY(v.isDefined());
    QCOMPARE(v.dimension(),3);
    QhullVertex v5= v2; // copy constructor
    QVERIFY(v5==v2);
    QVERIFY(v5==v);
    QhullVertex v3= v2.getVertexT();
    QCOMPARE(v,v3);
    QhullVertex v4= v2.getBaseT();
    QCOMPARE(v,v4);
}//t_constructConvert

void QhullVertex_test::
t_getSet()
{
    RboxPoints rcube("c");
    {
        Qhull q(rcube,"Qt QR0");  // triangulation of rotated unit cube
        QCOMPARE(q.facetCount(), 12);
        QCOMPARE(q.vertexCount(), 8);

        // Also spot-test QhullVertexList.  See QhullLinkedList_test.cpp
        QhullVertexList vs= q.vertexList();
        QhullVertexListIterator i(vs);
        while(i.hasNext()){
            const QhullVertex v= i.next();
            cout << v.id() << endl;
            QCOMPARE(v.dimension(),3);
            QVERIFY(v.id()>=0 && v.id()<9);
            QVERIFY(v.isDefined());
            if(i.hasNext()){
                QCOMPARE(v.next(), i.peekNext());
                QVERIFY(v.next()!=v);
                QVERIFY(v.next().previous()==v);
            }
            QVERIFY(i.hasPrevious());
            QCOMPARE(v, i.peekPrevious());
        }
        QhullVertexListIterator i2(i);
        QEXPECT_FAIL("", "ListIterator copy constructor not reset to BOT", Continue);
        QVERIFY(!i2.hasPrevious());

        // test point()
        foreach (QhullVertex v, q.vertexList()){  // Qt only
            QhullPoint p= v.point();
            int j= p.id(q.runId());
            cout << "Point " << j << ":\n" << p.print(q.runId()) << endl;
            QVERIFY(j>=0 && j<8);
        }
    }
}//t_getSet

void QhullVertex_test::
t_foreach()
{
    RboxPoints rcube("c W0 300");  // 300 points on surface of cube
    {
        Qhull q(rcube, "QR0 Qc"); // keep coplanars, thick facet, and rotate the cube
        foreach (QhullVertex v, q.vertexList()){  // Qt only
            QhullFacetSet fs= v.neighborFacets();
            QCOMPARE(fs.count(), 3);
            foreach (QhullFacet f, fs){  // Qt only
                QVERIFY(f.vertices().contains(v));
            }
        }
    }
}//t_foreach

void QhullVertex_test::
t_io()
{
    RboxPoints rcube("c");
    {
        Qhull q(rcube, "");
        QhullVertex v= q.beginVertex();
        ostringstream os;
        os << "Vertex and vertices w/o runId:\n";
        os << v;
        QhullVertexSet vs= q.firstFacet().vertices();
        os << vs;
        os << "Vertex and vertices w/ runId:\n";
        os << v.print(q.runId());
        os << vs.print(q.runId(), "vertices:");
        cout << os.str();
        QString s= QString::fromStdString(os.str());
        QCOMPARE(s.count("(v"), 10);
        QCOMPARE(s.count(": f"), 2);
    }
    RboxPoints r10("10 D3");  // Without QhullVertex::facetNeighbors
    {
        Qhull q(r10, "");
        QhullVertex v= q.beginVertex();
        ostringstream os;
        os << "\nTry again with simplicial facets.  No neighboring facets listed for vertices.\n";
        os << "Vertex and vertices w/o runId:\n";
        os << v;
        q.defineVertexNeighborFacets();
        os << "This time with neighborFacets() defined for all vertices:\n";
        os << v;
        cout << os.str();
        QString s= QString::fromStdString(os.str());
        QCOMPARE(s.count(": f"), 1);

        Qhull q2(r10, "v"); // Voronoi diagram
        QhullVertex v2= q2.beginVertex();
        ostringstream os2;
        os2 << "\nTry again with Voronoi diagram of simplicial facets.  Neighboring facets automatically defined for vertices.\n";
        os2 << "Vertex and vertices w/o runId:\n";
        os2 << v2;
        cout << os2.str();
        QString s2= QString::fromStdString(os2.str());
        QCOMPARE(s2.count(": f"), 1);
    }
}//t_io

}//orgQhull

#include "moc/QhullVertex_test.moc"
qhull-2012.1/src/qhulltest/Qhull_test.cpp0000644000076400010400000002677711716456524021606 0ustar  bbarberAdministrators/****************************************************************************
**
** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
** $Id: //main/2011/qhull/src/qhulltest/Qhull_test.cpp#5 $$Change: 1490 $
** $DateTime: 2012/02/19 20:27:01 $$Author: bbarber $
**
****************************************************************************/

//pre-compiled headers
#include 
#include "RoadTest.h" // QT_VERSION

#include "Qhull.h"
#include "QhullError.h"
#include "RboxPoints.h"
#include "QhullFacetList.h"

using std::cout;
using std::endl;
using std::string;

namespace orgQhull {

//! Test C++ interface to Qhull
//! See eg/q_test for tests of Qhull commands
class Qhull_test : public RoadTest
{
    Q_OBJECT

#//Test slots
private slots:
    void cleanup();
    void t_construct();
    void t_attribute();
    void t_message();
    void t_getSet();
    void t_getQh();
    void t_getValue();
    void t_foreach();
    void t_modify();
};//Qhull_test

void
add_Qhull_test()
{
    new Qhull_test();
}

//Executed after each testcase
void Qhull_test::
cleanup()
{
    UsingLibQhull::checkQhullMemoryEmpty();
    RoadTest::cleanup();
}

void Qhull_test::
t_construct()
{
    {
        Qhull q;
        QCOMPARE(q.dimension(),0);
        QVERIFY(q.qhullQh()!=0);
        QVERIFY(q.runId()!=0);
        QCOMPARE(QString(q.qhullCommand()),QString(""));
        QCOMPARE(QString(q.rboxCommand()),QString(""));
        try{
            QCOMPARE(q.area(),0.0);
            QFAIL("area() did not fail.");
        }catch (const std::exception &e) {
            cout << "INFO   : Caught " << e.what();
        }
        Qhull q2(q);  // Copy constructor and copy assignment OK if not q.initialized()
        QCOMPARE(q2.dimension(),0);
        q= q2;
        QCOMPARE(q.dimension(),0);
    }
    {
        RboxPoints rbox("10000");
        Qhull q(rbox, "QR0"); // Random points in a randomly rotated cube.
        QCOMPARE(q.dimension(),3);
        QVERIFY(q.volume() < 1.0);
        QVERIFY(q.volume() > 0.99);
        try{
            Qhull q2(q);
            QFAIL("Copy constructor did not fail for initialized Qhull.");
        }catch (const std::exception &e) {
            cout << "INFO   : Caught " << e.what();
        }
        try{
            Qhull q3;
            q3= q;
            QFAIL("Copy assignment did not fail for initialized Qhull source.");
        }catch (const std::exception &e) {
            cout << "INFO   : Caught " << e.what();
        }
        QCOMPARE(q.dimension(),3);
        try{
            Qhull q4;
            q= q4;
            QFAIL("Copy assignment did not fail for initialized Qhull destination.");
        }catch (const std::exception &e) {
            cout << "INFO   : Caught " << e.what();
        }
        QCOMPARE(q.dimension(),3);
    }
    {
        double points[] = {
            0, 0,
            1, 0,
            1, 1
        };
        Qhull q("triangle", 2, 3, points, "");
        QCOMPARE(q.dimension(),2);
        QCOMPARE(q.facetCount(),3);
        QCOMPARE(q.vertexCount(),3);
        QCOMPARE(q.dimension(),2);
        QCOMPARE(q.area(), 2.0+sqrt(2.0)); // length of boundary
        QCOMPARE(q.volume(), 0.5);        // the 2-d area
    }
}//t_construct

void Qhull_test::
t_attribute()
{
    RboxPoints rcube("c");
    {
        double normals[] = {
            0,  -1, -0.5,
           -1,   0, -0.5,
            1,   0, -0.5,
            0,   1, -0.5
        };
        Qhull q;
        q.feasiblePoint << 0.0 << 0.0;
        Coordinates c(std::vector(2, 0.0));
        QVERIFY(q.feasiblePoint==c);
        q.setOutputStream(&cout);
        q.runQhull("normals of square", 3, 4, normals, "H"); // halfspace intersect
        QCOMPARE(q.facetList().count(), 4); // Vertices of square
        cout << "Expecting summary of halfspace intersect\n";
        q.outputQhull();
        q.useOutputStream= false;
        cout << "Expecting no output from qh_fprintf() in Qhull.cpp\n";
        q.outputQhull();
    }
}//t_attribute

//! No QhullMessage for errors outside of qhull
void Qhull_test::
t_message()
{
    RboxPoints rcube("c");
    {
        Qhull q;
        QCOMPARE(q.qhullMessage(), string(""));
        QCOMPARE(q.qhullStatus(), qh_ERRnone);
        QVERIFY(!q.hasQhullMessage());
        try{
            q.runQhull(rcube, "Fd");
            QFAIL("runQhull Fd did not fail.");
        }catch (const std::exception &e) {
            const char *s= e.what();
            cout << "INFO   : Caught " << s;
            QCOMPARE(QString::fromStdString(s).left(6), QString("QH6029"));
            // FIXUP QH11025 -- review decision to clearQhullMessage at QhullError()            // Cleared when copied to QhullError
            QVERIFY(!q.hasQhullMessage());
            // QCOMPARE(q.qhullMessage(), QString::fromStdString(s).remove(0, 7));
            // QCOMPARE(q.qhullStatus(), 6029);
            q.clearQhullMessage();
            QVERIFY(!q.hasQhullMessage());
        }
        q.appendQhullMessage("Append 1");
        QVERIFY(q.hasQhullMessage());
        QCOMPARE(QString::fromStdString(q.qhullMessage()), QString("Append 1"));
        q.appendQhullMessage("\nAppend 2\n");
        QCOMPARE(QString::fromStdString(q.qhullMessage()), QString("Append 1\nAppend 2\n"));
        q.clearQhullMessage();
        QVERIFY(!q.hasQhullMessage());
        QCOMPARE(QString::fromStdString(q.qhullMessage()), QString(""));
    }
    {
        cout << "INFO   : Error stream without output stream\n";
        Qhull q;
        q.setErrorStream(&cout);
        q.setOutputStream(0);
        try{
            q.runQhull(rcube, "Fd");
            QFAIL("runQhull Fd did not fail.");
        }catch (const QhullError &e) {
            cout << "INFO   : Caught " << e;
            QCOMPARE(e.errorCode(), 6029);
        }
        //FIXUP QH11026 Qhullmessage cleared when QhullError thrown.  Switched to e
        //QVERIFY(q.hasQhullMessage());
        //QCOMPARE(QString::fromStdString(q.qhullMessage()).left(6), QString("QH6029"));
        q.clearQhullMessage();
        QVERIFY(!q.hasQhullMessage());
    }
    {
        cout << "INFO   : Error output sent to output stream without error stream\n";
        Qhull q;
        q.setErrorStream(0);
        q.setOutputStream(&cout);
        try{
            q.runQhull(rcube, "Tz H0");
            QFAIL("runQhull TZ did not fail.");
        }catch (const std::exception &e) {
            const char *s= e.what();
            cout << "INFO   : Caught " << s;
            QCOMPARE(QString::fromAscii(s).left(6), QString("QH6023"));
        }
        //FIXUP QH11026 Qhullmessage cleared when QhullError thrown.  Switched to e
        //QVERIFY(q.hasQhullMessage());
        //QCOMPARE(QString::fromStdString(q.qhullMessage()).left(17), QString("qhull: no message"));
        //QCOMPARE(q.qhullStatus(), 6023);
        q.clearQhullMessage();
        QVERIFY(!q.hasQhullMessage());
    }
    {
        cout << "INFO   : No error stream or output stream\n";
        Qhull q;
        q.setErrorStream(0);
        q.setOutputStream(0);
        try{
            q.runQhull(rcube, "Fd");
            QFAIL("outputQhull did not fail.");
        }catch (const std::exception &e) {
            const char *s= e.what();
            cout << "INFO   : Caught " << s;
            QCOMPARE(QString::fromAscii(s).left(6), QString("QH6029"));
        }
        //FIXUP QH11026 Qhullmessage cleared when QhullError thrown.  Switched to e
        //QVERIFY(q.hasQhullMessage());
        //QCOMPARE(QString::fromStdString(q.qhullMessage()).left(9), QString("qhull err"));
        //QCOMPARE(q.qhullStatus(), 6029);
        q.clearQhullMessage();
        QVERIFY(!q.hasQhullMessage());
    }
}//t_message

void Qhull_test::
t_getSet()
{
    RboxPoints rcube("c");
    {
        Qhull q;
        QVERIFY(!q.initialized());
        q.runQhull(rcube, "s");
        QVERIFY(q.initialized());
        QCOMPARE(q.dimension(), 3);
        QhullPoint p= q.origin();
        QCOMPARE(p.dimension(), 3);
        QCOMPARE(p[0]+p[1]+p[2], 0.0);
        QVERIFY(q.runId()!=0);
        q.setErrorStream(&cout);
        q.outputQhull();
    }
    {
        Qhull q;
        q.runQhull(rcube, "");
        q.setOutputStream(&cout);
        q.outputQhull();
    }
    // qhullQh -- UsingLibQhull [Qhull.cpp]
    // runId -- UsingLibQhull [Qhull.cpp]
}//t_getSet

void Qhull_test::
t_getQh()
{
    RboxPoints rcube("c");
    {
        Qhull q;
        q.runQhull(rcube, "s");
        QCOMPARE(QString(q.qhullCommand()), QString("qhull s"));
        QCOMPARE(QString(q.rboxCommand()), QString("rbox \"c\""));
        QCOMPARE(q.facetCount(), 6);
        QCOMPARE(q.vertexCount(), 8);
        // Sample fields from Qhull's qhT [libqhull.h]
        QCOMPARE(q.qhullQh()->ALLpoints, 0u);
        QCOMPARE(q.qhullQh()->GOODpoint, 0);
        QCOMPARE(q.qhullQh()->IStracing, 0);
        QCOMPARE(q.qhullQh()->MAXcoplanar+1.0, 1.0); // fuzzy compare
        QCOMPARE(q.qhullQh()->MERGING, 1u);
        QCOMPARE(q.qhullQh()->input_dim, 3);
        QCOMPARE(QString(q.qhullQh()->qhull_options).left(8), QString("  run-id"));
        QCOMPARE(q.qhullQh()->run_id, q.runId());
        QCOMPARE(q.qhullQh()->num_facets, 6);
        QCOMPARE(q.qhullQh()->hasTriangulation, 0u);
        QCOMPARE(q.qhullQh()->max_outside - q.qhullQh()->min_vertex + 1.0, 1.0); // fuzzy compare
        QCOMPARE(*q.qhullQh()->gm_matrix+1.0, 1.0); // fuzzy compare
    }
}//t_getQh

void Qhull_test::
t_getValue()
{
    RboxPoints rcube("c");
    {
        Qhull q;
        q.runQhull(rcube, "");
        QCOMPARE(q.area(), 6.0);
        QCOMPARE(q.volume(), 1.0);
    }
}//t_getValue

void Qhull_test::
t_foreach()
{
    RboxPoints rcube("c");
    {
        Qhull q;
        QCOMPARE(q.beginFacet(),q.endFacet());
        QCOMPARE(q.beginVertex(),q.endVertex());
        q.runQhull(rcube, "");
        QCOMPARE(q.facetList().count(), 6);

        // defineVertexNeighborFacets() tested in QhullVertex_test::t_io()

        QhullFacetList facets(q.beginFacet(), q.endFacet());
        QCOMPARE(facets.count(), 6);
        QCOMPARE(q.firstFacet(), q.beginFacet());
        QhullVertexList vertices(q.beginVertex(), q.endVertex());
        QCOMPARE(vertices.count(), 8);
        QCOMPARE(q.firstVertex(), q.beginVertex());
        QhullPoints ps= q.points();
        QCOMPARE(ps.count(), 8);
        QhullPointSet ps2= q.otherPoints();
        QCOMPARE(ps2.count(), 0);
        // ps2= q.otherPoints(); //disabled, would not copy the points
        QCOMPARE(q.facetCount(), 6);
        QCOMPARE(q.vertexCount(), 8);
        coordT *c= q.pointCoordinateBegin(); // of q.points()
        QVERIFY(*c==0.5 || *c==-0.5);
        coordT *c3= q.pointCoordinateEnd();
        QVERIFY(c3[-1]==0.5 || c3[-1]==-0.5);
        QCOMPARE(c3-c, 8*3);
        QCOMPARE(q.vertexList().count(), 8);
    }
}//t_foreach

void Qhull_test::
t_modify()
{
    //addPoint() tested in t_foreach
    RboxPoints diamond("d");
    Qhull q(diamond, "o");
    q.setOutputStream(&cout);
    cout << "Expecting vertexList and facetList of a 3-d diamond.\n";
    q.outputQhull();
    cout << "Expecting normals of a 3-d diamond.\n";
    q.outputQhull("n");
    // runQhull tested in t_attribute(), t_message(), etc.
}//t_modify

}//orgQhull

// Redefine Qhull's usermem.c
void qh_exit(int exitcode) {
    cout << "FAIL!  : Qhull called qh_exit().  Qhull's error handling not available.\n.. See the corresponding Qhull:qhull_message or setErrorStream().\n";
    exit(exitcode);
}
void qh_free(void *mem) {
    free(mem);
}
void *qh_malloc(size_t size) {
    return malloc(size);
}

#if 0
template<> char * QTest::
toString(const std::string &s)
{
    QByteArray ba = s.c_str();
    return qstrdup(ba.data());
}
#endif

#include "moc/Qhull_test.moc"
qhull-2012.1/src/qhulltest/RboxPoints_test.cpp0000644000076400010400000001364411720052005022572 0ustar  bbarberAdministrators/****************************************************************************
**
** Copyright (c) 2006-2012 C.B. Barber. All rights reserved.
** $Id: //main/2011/qhull/src/qhulltest/RboxPoints_test.cpp#4 $$Change: 1490 $
** $DateTime: 2012/02/19 20:27:01 $$Author: bbarber $
**
****************************************************************************/
//pre-compiled headers
#include 
#include "RoadTest.h" // QT_VERSION

#include "RboxPoints.h"
#include "QhullError.h"

using std::cout;
using std::endl;
using std::ostringstream;
using std::string;
using std::stringstream;

namespace orgQhull {

//! Test C++ interface to Rbox
//! See eg/q_test for tests of rbox commands
class RboxPoints_test : public RoadTest
{
    Q_OBJECT

#//Test slots
private slots:
    void t_construct();
    void t_error();
    void t_test();
    void t_getSet();
    void t_foreach();
    void t_change();
    void t_ostream();
};

void
add_RboxPoints_test()
{
    new RboxPoints_test();
}

void RboxPoints_test::
t_construct()
{
    RboxPoints rp;
    QCOMPARE(rp.dimension(), 0);
    QCOMPARE(rp.count(), 0);
    QVERIFY(QString::fromStdString(rp.comment()) != QString(""));
    QVERIFY(rp.isEmpty());
    QVERIFY(!rp.hasRboxMessage());
    QCOMPARE(rp.rboxStatus(), qh_ERRnone);
    QCOMPARE(QString::fromStdString(rp.rboxMessage()), QString("rbox warning: no points generated\n"));

    RboxPoints rp2("c"); // 3-d cube
    QCOMPARE(rp2.dimension(), 3);
    QCOMPARE(rp2.count(), 8);
    QCOMPARE(QString::fromStdString(rp2.comment()), QString("rbox \"c\""));
    QVERIFY(!rp2.isEmpty());
    QVERIFY(!rp2.hasRboxMessage());
    QCOMPARE(rp2.rboxStatus(), qh_ERRnone);
    QCOMPARE(QString::fromStdString(rp2.rboxMessage()), QString("rbox: OK\n"));
}//t_construct

void RboxPoints_test::
t_error()
{
    RboxPoints rp;
    try{
        rp.appendPoints("D0 c");
        QFAIL("'D0 c' did not fail.");
    }catch (const std::exception &e) {
        const char *s= e.what();
        cout << "INFO   : Caught " << s;
        QCOMPARE(QString(s).left(6), QString("QH6189"));
        QVERIFY(rp.hasRboxMessage());
        QCOMPARE(QString::fromStdString(rp.rboxMessage()).left(8), QString("rbox err"));
        QCOMPARE(rp.rboxStatus(), 6189);
        rp.clearRboxMessage();
        QVERIFY(!rp.hasRboxMessage());
    }
    try{
        RboxPoints rp2;
        rp2.setDimension(-1);
        QFAIL("setDimension(-1) did not fail.");
    }catch (const RoadError &e) {
        const char *s= e.what();
        cout << "INFO   : Caught " << s;
        QCOMPARE(QString(s).left(7), QString("QH10062"));
        QCOMPARE(e.errorCode(), 10062);
        QCOMPARE(QString::fromStdString(e.what()), QString(s));
        RoadLogEvent logEvent= e.roadLogEvent();
        QCOMPARE(logEvent.int1(), -1);
    }
}//t_error

void RboxPoints_test::
t_test()
{
    // isEmpty -- t_construct
}//t_test

void RboxPoints_test::
t_getSet()
{
    // comment -- t_construct
    // count -- t_construct
    // dimension -- t_construct

    RboxPoints rp;
    QCOMPARE(rp.dimension(), 0);
    rp.setDimension(2);
    QCOMPARE(rp.dimension(), 2);
    rp.setDimension(2);
    QCOMPARE(rp.dimension(), 2);
    try{
        rp.setDimension(102);
        QFAIL("setDimension(102) did not fail.");
    }catch (const std::exception &e) {
        cout << "INFO   : Caught " << e.what();
    }
    QCOMPARE(rp.newCount(), 0);
    rp.appendPoints("D2 P1 P2");
    QCOMPARE(rp.count(), 2);
    QCOMPARE(rp.newCount(), 2); // From previous appendPoints();
    PointCoordinates pc(2);
    pc << 1.0 << 0.0 << 2.0 << 0.0;
    QCOMPARE(pc.dimension(), 2);
    QCOMPARE(pc.count(), 2);
    QVERIFY(rp==pc);
    rp.setNewCount(10);  // Normally only used by appendPoints for rbox processing
    QCOMPARE(rp.newCount(), 10);
    rp.reservePoints();
    QVERIFY(rp==pc);
}//t_getSet

void RboxPoints_test::
t_foreach()
{
    RboxPoints rp("c");
    Coordinates::ConstIterator cci= rp.beginCoordinates();
    orgQhull::Coordinates::Iterator ci= rp.beginCoordinates();
    QCOMPARE(*cci, -0.5);
    QCOMPARE(*ci, *cci);
    int i=1;
    while(++cci
#include 
#include "RoadTest.h"

using std::cout;
using std::endl;

namespace orgQhull {

#//class variable

QList RoadTest::
s_testcases;

int RoadTest::
s_test_count= 0;

int RoadTest::
s_test_fail= 0;

QStringList RoadTest::
s_failed_tests;

#//Slot

//! Executed after each test
void RoadTest::
cleanup()
{
    s_test_count++;
    if(QTest::currentTestFailed()){
        recordFailedTest();
    }
}//cleanup

#//Helper

void RoadTest::
recordFailedTest()
{
    s_test_fail++;
    QString className= metaObject()->className();
    s_failed_tests << className + "::" + QTest::currentTestFunction();
}

#//class function

int RoadTest::
runTests(QStringList arguments)
{
    int result= 0; // assume success

    foreach(RoadTest *testcase, s_testcases){
        try{
            result += QTest::qExec(testcase, arguments);
        }catch(const std::exception &e){
            cout << "FAIL!  : Threw error ";
            cout << e.what() << endl;
    s_test_count++;
            testcase->recordFailedTest();
            // Qt 4.5.2 OK.  In Qt 4.3.3, qtestcase did not clear currentTestObject
        }
    }
    if(s_test_fail){
        cout << "Failed " << s_test_fail << " of " << s_test_count << " tests.\n";
        cout << s_failed_tests.join("\n").toLocal8Bit().constData() << std::endl;
    }else{
        cout << "Passed " << s_test_count << " tests.\n";
    }
    return result;
}//runTests

}//orgQhull

#include "moc/moc_RoadTest.cpp"
qhull-2012.1/src/qhulltest/RoadTest.h0000644000076400010400000000404411710144466020624 0ustar  bbarberAdministrators/****************************************************************************
**
** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
** $Id: //main/2011/qhull/src/qhulltest/RoadTest.h#1 $$Change: 1490 $
** $Date: 2012/02/19 $$Author: bbarber $
**
****************************************************************************/

#ifndef ROADTEST_H
#define ROADTEST_H

//pre-compiled with RoadTest.h
#include     // Qt C++ Framework
#include 

#define QHULL_USES_QT 1

namespace orgQhull {

#//!\name Defined here

    //! RoadTest -- Generic test for Qt's QTest
    class RoadTest;
    //! TESTadd_(t) -- Add a RoadTest

/** Test Name objects using Qt's QTestLib

Template:

class Name_test : public RoadTest
{
    Q_OBJECT
#//Test slot
private slots:
    void t_name();
    //Executed before any test
    void initTestCase();
    void init();          // Each test
    //Executed after each test
    void cleanup(); //RoadTest::cleanup();
    // Executed after last test
    void cleanupTestCase();
};

void
add_Name_test()
{
    new Name_test();
}

Send additional output to cout
*/

class RoadTest : public QObject
{
    Q_OBJECT

#//!\name Class globals
protected:
    static QList
                        s_testcases; ///! List of testcases to execute.  Initialized via add_...()
    static int          s_test_count; ///! Total number of tests executed
    static int          s_test_fail; ///! Number of failed tests
    static QStringList  s_failed_tests; ///! List of failed tests

#//!\name Test slots
public slots:
    void cleanup();

public:
#//!\name Constructors, etc.
    RoadTest()  { s_testcases.append(this); }
    ~RoadTest() { s_testcases.removeAll(this); }

#//Helper
    void                recordFailedTest();


#//!\name Class functions
    static int          runTests(QStringList arguments);

};//RoadTest

#define TESTadd_(t) extern void t(); t();


}//orgQhull

namespace QTest{

template<>
inline char *
toString(const std::string &s)
{
    return qstrdup(s.c_str());
}

}//namespace QTest

#endif //ROADTEST_H

qhull-2012.1/src/qhulltest/UsingLibQhull_test.cpp0000644000076400010400000001720611720052005023203 0ustar  bbarberAdministrators/****************************************************************************
**
** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
** $Id: //main/2011/qhull/src/qhulltest/UsingLibQhull_test.cpp#4 $$Change: 1490 $
** $DateTime: 2012/02/19 20:27:01 $$Author: bbarber $
**
****************************************************************************/

//pre-compiled headers
#include 
#include "RoadTest.h" // QT_VERSION

#include "UsingLibQhull.h"
#include "QhullError.h"
#include "Qhull.h"

using std::cout;
using std::endl;
using std::string;

namespace orgQhull {

//! Test C++ interface to Qhull
//! See eg/q_test for tests of Qhull commands
class UsingLibQhull_test : public RoadTest
{
    Q_OBJECT

#//Test slots
private slots:
    void cleanup();
    void t_classMembers();
    void t_globalPoints();
    void t_UsingLibQhull();
    void t_methods();
    void t_cleanuptestcase();
};//UsingLibQhull_test

void
add_UsingLibQhull_test()
{
    new UsingLibQhull_test();
}

//Executed after each testcase
void UsingLibQhull_test::
cleanup()
{
    UsingLibQhull::checkQhullMemoryEmpty();
    RoadTest::cleanup();
}

void UsingLibQhull_test::
t_classMembers()
{
    {
        //checkQhullMemoryEmpty tested by cleanup()
        QCOMPARE(UsingLibQhull::globalMachineEpsilon()+1.0, 1.0);
        RboxPoints r10("10");
        Qhull q(r10,"v");  // voronoi diagram of 10 points
        UsingLibQhull::unsetGlobalAngleEpsilon();
        UsingLibQhull::unsetGlobalDistanceEpsilon();
        cout << "MachineEpsilon " << UsingLibQhull::globalMachineEpsilon()
            << " angleEpsilon " << UsingLibQhull::globalAngleEpsilon()
            << " distanceEpsilon " << UsingLibQhull::globalDistanceEpsilon()
            << endl;
        QCOMPARE(UsingLibQhull::currentAngleEpsilon()+1.0, 1.0);
        QVERIFY(UsingLibQhull::currentAngleEpsilon() > UsingLibQhull::globalMachineEpsilon());
        QCOMPARE(UsingLibQhull::currentDistanceEpsilon()+1.0, 1.0);
        QVERIFY(UsingLibQhull::currentDistanceEpsilon() >= UsingLibQhull::currentAngleEpsilon());
        QCOMPARE(UsingLibQhull::currentQhull().runId(), q.runId());
        QCOMPARE(UsingLibQhull::globalAngleEpsilon()+1.0, UsingLibQhull::currentAngleEpsilon()+1.0);
        QCOMPARE(UsingLibQhull::currentVertexDimension(), q.dimension());
        QCOMPARE(UsingLibQhull::globalDistanceEpsilon()+1.0, UsingLibQhull::currentDistanceEpsilon()+1.0);
        UsingLibQhull::setGlobalAngleEpsilon(1.0);
        UsingLibQhull::setGlobalDistanceEpsilon(1.0);
        cout << " Global angleEpsilon " << UsingLibQhull::globalAngleEpsilon()
            << " distanceEpsilon " << UsingLibQhull::globalDistanceEpsilon()
            << endl;
        QCOMPARE(UsingLibQhull::globalAngleEpsilon(), UsingLibQhull::globalDistanceEpsilon());
        QVERIFY(UsingLibQhull::currentAngleEpsilon() != UsingLibQhull::globalAngleEpsilon());
        UsingLibQhull::setGlobalVertexDimension(3);
        QCOMPARE(UsingLibQhull::globalVertexDimension(), UsingLibQhull::currentVertexDimension());
        UsingLibQhull::setGlobalVertexDimension(2);
        QCOMPARE(UsingLibQhull::globalVertexDimension(), 2);
        QCOMPARE(UsingLibQhull::currentVertexDimension(), q.dimension());
        QVERIFY(UsingLibQhull::currentDistanceEpsilon() != UsingLibQhull::globalDistanceEpsilon());
        UsingLibQhull::unsetGlobalAngleEpsilon();
        UsingLibQhull::unsetGlobalVertexDimension();
        UsingLibQhull::unsetGlobalDistanceEpsilon();
        QCOMPARE(UsingLibQhull::currentAngleEpsilon()+1.0, UsingLibQhull::globalAngleEpsilon()+1.0);
        QCOMPARE(UsingLibQhull::globalVertexDimension(), UsingLibQhull::currentVertexDimension());
        QCOMPARE(UsingLibQhull::currentDistanceEpsilon()+1.0, UsingLibQhull::globalDistanceEpsilon()+1.0);
        UsingLibQhull::setGlobals();
    }
    QCOMPARE(UsingLibQhull::globalAngleEpsilon()+1.0, 1.0);
    QCOMPARE(UsingLibQhull::globalVertexDimension(), 4); // 'v'.  VertexDimension is only used for QhullVertex where dim>15
    QCOMPARE(UsingLibQhull::globalDistanceEpsilon()+1.0, 1.0);
    UsingLibQhull::unsetGlobals();
    try{
        cout << UsingLibQhull::globalVertexDimension();
        QFAIL("Did not throw error for undefined dimension.");
    }catch(const std::exception &e){
        cout << "INFO     Caught error -- " << e.what() << endl;
    }
}//t_classMembers

void UsingLibQhull_test::
t_globalPoints()
{
    const coordT *r10PointsBegin;
    {
        RboxPoints r10("10");
        Qhull q(r10,"v");  // voronoi diagram of 10 points
        UsingLibQhull::unsetGlobalPoints();
        int dimension;
        const coordT *pointsEnd;
        const coordT *pointsBegin= UsingLibQhull::globalPoints(&dimension, &pointsEnd);
        cout << "pointsBegin " << pointsBegin
            << " pointsEnd " << pointsEnd
            << " dimension " << dimension
            << endl;
        int dimension2;
        const coordT *pointsEnd2;
        const coordT *pointsBegin2= UsingLibQhull::currentPoints(&dimension2, &pointsEnd2);
        QCOMPARE(pointsBegin2, pointsBegin);
        QCOMPARE(pointsEnd2, pointsEnd);
        QCOMPARE(dimension2, dimension);
        coordT c[]= { 1.0,2.0, 3.0,4.0, 5.0,6.0 };
        UsingLibQhull::setGlobalPoints(2, c, c+3*2);
        pointsBegin= UsingLibQhull::globalPoints(&dimension, &pointsEnd);
        QCOMPARE(pointsBegin, c);
        QCOMPARE(pointsEnd[-1], 6.0);
        QCOMPARE(dimension, 2);
        UsingLibQhull::unsetGlobalPoints();
        pointsBegin= UsingLibQhull::globalPoints(&dimension, &pointsEnd);
        QCOMPARE(pointsBegin, pointsBegin2);
        QCOMPARE(pointsEnd, pointsEnd2);
        QCOMPARE(dimension, dimension2);
        UsingLibQhull::setGlobals();
        r10PointsBegin= pointsBegin;
    }
    int dimension3;
    const coordT *pointsEnd3;
    const coordT *pointsBegin3= UsingLibQhull::currentPoints(&dimension3, &pointsEnd3);
    QCOMPARE(pointsBegin3, r10PointsBegin); // Memory was freed
    QCOMPARE(pointsEnd3, r10PointsBegin+10*4);
    QCOMPARE(dimension3, 4);
    UsingLibQhull::unsetGlobals();
    try{
        pointsBegin3= UsingLibQhull::globalPoints(&dimension3, &pointsEnd3);
        QFAIL("Did not throw error for undefined global points.");
    }catch(const std::exception &e){
        cout << "INFO     Caught error -- " << e.what() << endl;
    }
}//t_globalPoints

void UsingLibQhull_test::
t_UsingLibQhull()
{
    {
        Qhull q;
        UsingLibQhull uq(&q); // Normally created in a method using 'this'

        try{
            Qhull q2; // If qh_QHpointer, QhullQh() calls usinlibqhull()
            UsingLibQhull uq2(&q2);
            QFAIL("UsingLibQhull did not fail.");
        }catch (const std::exception &e) {
            cout << "INFO   : Caught " << e.what();
        }
    }
    Qhull q3;
    UsingLibQhull uq3(&q3);
    // UsingLibQhull uq4; // Default constructors disabled.
}//t_UsingLibQhull

void UsingLibQhull_test::
t_methods()
{
    Qhull q;
    UsingLibQhull u(&q); // Normally created in a method using 'this'
    QVERIFY(u.defined());
    u.maybeThrowQhullMessage(0);  // Nothing thrown
    try{
        u.maybeThrowQhullMessage(1);
        QFAIL("maybeThrowQhullMessage(1) did not fail.");
    }catch (const std::exception &e) {
        cout << "INFO   : Caught " << e.what();
    }
    // Can not check checkRunId() in maybeThrowQhullMessage().  Requires another thread.
    u.maybeThrowQhullMessage(2, UsingLibQhull::NOthrow);
    try{
        throw QhullError(10054, "Report previous NOthrow error");
    }catch (const std::exception &e) {
        cout << "INFO   : " << e.what();
    }
}//t_methods

// Executed after last test
void UsingLibQhull_test::
t_cleanuptestcase()
{
    UsingLibQhull::unsetGlobals();
}//t_cleanuptestcase

}//orgQhull

#include "moc/UsingLibQhull_test.moc"

qhull-2012.1/src/qvoronoi/0000755000076400010400000000000011721063455016553 5ustar  bbarberAdministratorsqhull-2012.1/src/qvoronoi/qvoronoi.c0000644000076400010400000002625111710144471020575 0ustar  bbarberAdministrators/*
  ---------------------------------

   qvoronoi.c
     compute Voronoi diagrams and furthest-point Voronoi
     diagrams using qhull

   see unix.c for full interface

   Copyright (c) 1993-2012, The Geometry Center
*/

#include 
#include 
#include 
#include 
#include 
#include "libqhull.h"
#include "mem.h"
#include "qset.h"

#if __MWERKS__ && __POWERPC__
#include 
#include 
#include 
#include 

#elif __cplusplus
extern "C" {
  int isatty(int);
}

#elif _MSC_VER
#include 
#define isatty _isatty
int _isatty(int);

#else
int isatty(int);  /* returns 1 if stdin is a tty
                   if "Undefined symbol" this can be deleted along with call in main() */
#endif

/*---------------------------------

  qh_prompt
    long prompt for qhull

  notes:
    restricted version of libqhull.c

  see:
    concise prompt below
*/

/* duplicated in qvoron_f.htm and qvoronoi.htm
   QJ and Qt are deprecated, but allowed for backwards compatibility
*/
char hidden_options[]=" d n m v H U Qb QB Qc Qf Qg Qi Qm Qr QR Qv Qx TR E V Fa FA FC Fp FS Ft FV Pv Gt Q0 Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 ";

char qh_prompta[]= "\n\
qvoronoi- compute the Voronoi diagram\n\
    http://www.qhull.org  %s\n\
\n\
input (stdin):\n\
    first lines: dimension and number of points (or vice-versa).\n\
    other lines: point coordinates, best if one point per line\n\
    comments:    start with a non-numeric character\n\
\n\
options:\n\
    Qu   - compute furthest-site Voronoi diagram\n\
\n\
Qhull control options:\n\
    Qz   - add point-at-infinity to Voronoi diagram\n\
%s%s%s%s";  /* split up qh_prompt for Visual C++ */
char qh_promptb[]= "\
    Qs   - search all points for the initial simplex\n\
    QGn  - Voronoi vertices if visible from point n, -n if not\n\
    QVn  - Voronoi vertices for input point n, -n if not\n\
\n\
";
char qh_promptc[]= "\
Trace options:\n\
    T4   - trace at level n, 4=all, 5=mem/gauss, -1= events\n\
    Tc   - check frequently during execution\n\
    Ts   - statistics\n\
    Tv   - verify result: structure, convexity, and in-circle test\n\
    Tz   - send all output to stdout\n\
    TFn  - report summary when n or more facets created\n\
    TI file - input data from file, no spaces or single quotes\n\
    TO file - output results to file, may be enclosed in single quotes\n\
    TPn  - turn on tracing when point n added to hull\n\
     TMn - turn on tracing at merge n\n\
     TWn - trace merge facets when width > n\n\
    TVn  - stop qhull after adding point n, -n for before (see TCn)\n\
     TCn - stop qhull after building cone for point n (see TVn)\n\
\n\
Precision options:\n\
    Cn   - radius of centrum (roundoff added).  Merge facets if non-convex\n\
     An  - cosine of maximum angle.  Merge facets if cosine > n or non-convex\n\
           C-0 roundoff, A-0.99/C-0.01 pre-merge, A0.99/C0.01 post-merge\n\
    Rn   - randomly perturb computations by a factor of [1-n,1+n]\n\
    Wn   - min facet width for non-coincident point (before roundoff)\n\
\n\
Output formats (may be combined; if none, produces a summary to stdout):\n\
    s    - summary to stderr\n\
    p    - Voronoi vertices\n\
    o    - OFF format (dim, Voronoi vertices, and Voronoi regions)\n\
    i    - Delaunay regions (use 'Pp' to avoid warning)\n\
    f    - facet dump\n\
\n\
";
char qh_promptd[]= "\
More formats:\n\
    Fc   - count plus coincident points (by Voronoi vertex)\n\
    Fd   - use cdd format for input (homogeneous with offset first)\n\
    FD   - use cdd format for output (offset first)\n\
    FF   - facet dump without ridges\n\
    Fi   - separating hyperplanes for bounded Voronoi regions\n\
    FI   - ID for each Voronoi vertex\n\
    Fm   - merge count for each Voronoi vertex (511 max)\n\
    Fn   - count plus neighboring Voronoi vertices for each Voronoi vertex\n\
    FN   - count and Voronoi vertices for each Voronoi region\n\
    Fo   - separating hyperplanes for unbounded Voronoi regions\n\
    FO   - options and precision constants\n\
    FP   - nearest point and distance for each coincident point\n\
    FQ   - command used for qvoronoi\n\
    Fs   - summary: #int (8), dimension, #points, tot vertices, tot facets,\n\
                    for output: #Voronoi regions, #Voronoi vertices,\n\
                                #coincident points, #non-simplicial regions\n\
                    #real (2), max outer plane and min vertex\n\
    Fv   - Voronoi diagram as Voronoi vertices between adjacent input sites\n\
    Fx   - extreme points of Delaunay triangulation (on convex hull)\n\
\n\
";
char qh_prompte[]= "\
Geomview options (2-d only)\n\
    Ga   - all points as dots\n\
     Gp  -  coplanar points and vertices as radii\n\
     Gv  -  vertices as spheres\n\
    Gi   - inner planes only\n\
     Gn  -  no planes\n\
     Go  -  outer planes only\n\
    Gc   - centrums\n\
    Gh   - hyperplane intersections\n\
    Gr   - ridges\n\
    GDn  - drop dimension n in 3-d and 4-d output\n\
\n\
Print options:\n\
    PAn  - keep n largest Voronoi vertices by 'area'\n\
    Pdk:n - drop facet if normal[k] <= n (default 0.0)\n\
    PDk:n - drop facet if normal[k] >= n\n\
    Pg   - print good Voronoi vertices (needs 'QGn' or 'QVn')\n\
    PFn  - keep Voronoi vertices whose 'area' is at least n\n\
    PG   - print neighbors of good Voronoi vertices\n\
    PMn  - keep n Voronoi vertices with most merges\n\
    Po   - force output.  If error, output neighborhood of facet\n\
    Pp   - do not report precision problems\n\
\n\
    .    - list of all options\n\
    -    - one line descriptions of all options\n\
";
/* for opts, don't assign 'e' or 'E' to a flag (already used for exponent) */

/*---------------------------------

  qh_prompt2
    synopsis for qhull
*/
char qh_prompt2[]= "\n\
qvoronoi- compute the Voronoi diagram.  Qhull %s\n\
    input (stdin): dimension, number of points, point coordinates\n\
    comments start with a non-numeric character\n\
\n\
options (qvoronoi.htm):\n\
    Qu   - compute furthest-site Voronoi diagram\n\
    Tv   - verify result: structure, convexity, and in-circle test\n\
    .    - concise list of all options\n\
    -    - one-line description of all options\n\
\n\
output options (subset):\n\
    s    - summary of results (default)\n\
    p    - Voronoi vertices\n\
    o    - OFF file format (dim, Voronoi vertices, and Voronoi regions)\n\
    FN   - count and Voronoi vertices for each Voronoi region\n\
    Fv   - Voronoi diagram as Voronoi vertices between adjacent input sites\n\
    Fi   - separating hyperplanes for bounded regions, 'Fo' for unbounded\n\
    G    - Geomview output (2-d only)\n\
    QVn  - Voronoi vertices for input point n, -n if not\n\
    TO file- output results to file, may be enclosed in single quotes\n\
\n\
examples:\n\
rbox c P0 D2 | qvoronoi s o         rbox c P0 D2 | qvoronoi Fi\n\
rbox c P0 D2 | qvoronoi Fo          rbox c P0 D2 | qvoronoi Fv\n\
rbox c P0 D2 | qvoronoi s Qu Fv     rbox c P0 D2 | qvoronoi Qu Fo\n\
rbox c G1 d D2 | qvoronoi s p       rbox c P0 D2 | qvoronoi s Fv QV0\n\
\n\
";
/* for opts, don't assign 'e' or 'E' to a flag (already used for exponent) */

/*---------------------------------

  qh_prompt3
    concise prompt for qhull
*/
char qh_prompt3[]= "\n\
Qhull %s.\n\
Except for 'F.' and 'PG', upper-case options take an argument.\n\
\n\
 OFF_format     p_vertices     i_delaunay     summary        facet_dump\n\
\n\
 Fcoincident    Fd_cdd_in      FD_cdd_out     FF-dump-xridge Fi_bounded\n\
 Fxtremes       Fmerges        Fneighbors     FNeigh_region  FOptions\n\
 Fo_unbounded   FPoint_near    FQvoronoi      Fsummary       Fvoronoi\n\
 FIDs\n\
\n\
 Gvertices      Gpoints        Gall_points    Gno_planes     Ginner\n\
 Gcentrums      Ghyperplanes   Gridges        Gouter         GDrop_dim\n\
\n\
 PArea_keep     Pdrop d0:0D0   Pgood          PFacet_area_keep\n\
 PGood_neighbors PMerge_keep   Poutput_forced Pprecision_not\n\
\n\
 QG_vertex_good Qsearch_1st    Qupper_voronoi QV_point_good  Qzinfinite\n\
 T4_trace       Tcheck_often   Tstatistics    Tverify        Tz_stdout\n\
 TFacet_log     TInput_file    TPoint_trace   TMerge_trace   TOutput_file\n\
 TWide_trace    TVertex_stop   TCone_stop\n\
\n\
 Angle_max      Centrum_size   Random_dist    Wide_outside\n\
";

/*---------------------------------

  main( argc, argv )
    processes the command line, calls qhull() to do the work, and exits

  design:
    initializes data structures
    reads points
    finishes initialization
    computes convex hull and other structures
    checks the result
    writes the output
    frees memory
*/
int main(int argc, char *argv[]) {
  int curlong, totlong; /* used !qh_NOmem */
  int exitcode, numpoints, dim;
  coordT *points;
  boolT ismalloc;

#if __MWERKS__ && __POWERPC__
  char inBuf[BUFSIZ], outBuf[BUFSIZ], errBuf[BUFSIZ];
  SIOUXSettings.showstatusline= false;
  SIOUXSettings.tabspaces= 1;
  SIOUXSettings.rows= 40;
  if (setvbuf(stdin, inBuf, _IOFBF, sizeof(inBuf)) < 0   /* w/o, SIOUX I/O is slow*/
  || setvbuf(stdout, outBuf, _IOFBF, sizeof(outBuf)) < 0
  || (stdout != stderr && setvbuf(stderr, errBuf, _IOFBF, sizeof(errBuf)) < 0))
    fprintf(stderr, "qhull internal warning (main): could not change stdio to fully buffered.\n");
  argc= ccommand(&argv);
#endif

  if ((argc == 1) && isatty( 0 /*stdin*/)) {
    fprintf(stdout, qh_prompt2, qh_version);
    exit(qh_ERRnone);
  }
  if (argc > 1 && *argv[1] == '-' && !*(argv[1]+1)) {
    fprintf(stdout, qh_prompta, qh_version,
                qh_promptb, qh_promptc, qh_promptd, qh_prompte);
    exit(qh_ERRnone);
  }
  if (argc >1 && *argv[1] == '.' && !*(argv[1]+1)) {
    fprintf(stdout, qh_prompt3, qh_version);
    exit(qh_ERRnone);
  }
  qh_init_A(stdin, stdout, stderr, argc, argv);  /* sets qh qhull_command */
  exitcode= setjmp(qh errexit); /* simple statement for CRAY J916 */
  if (!exitcode) {
    qh_option("voronoi  _bbound-last  _coplanar-keep", NULL, NULL);
    qh DELAUNAY= True;     /* 'v'   */
    qh VORONOI= True;
    qh SCALElast= True;    /* 'Qbb' */
    qh_checkflags(qh qhull_command, hidden_options);
    qh_initflags(qh qhull_command);
    points= qh_readpoints(&numpoints, &dim, &ismalloc);
    if (dim >= 5) {
      qh_option("_merge-exact", NULL, NULL);
      qh MERGEexact= True; /* 'Qx' always */
    }
    qh_init_B(points, numpoints, dim, ismalloc);
    qh_qhull();
    qh_check_output();
    qh_produce_output();
    if (qh VERIFYoutput && !qh FORCEoutput && !qh STOPpoint && !qh STOPcone)
      qh_check_points();
    exitcode= qh_ERRnone;
  }
  qh NOerrexit= True;  /* no more setjmp */
#ifdef qh_NOmem
  qh_freeqhull( True);
#else
  qh_freeqhull( False);
  qh_memfreeshort(&curlong, &totlong);
  if (curlong || totlong)
    fprintf(stderr, "qhull internal warning (main): did not free %d bytes of long memory(%d pieces)\n",
       totlong, curlong);
#endif
  return exitcode;
} /* main */

qhull-2012.1/src/qvoronoi/qvoronoi.pro0000644000076400010400000000034211545640672021156 0ustar  bbarberAdministrators# -------------------------------------------------
# qvoronoi.pro -- Qt project file for qvoronoi.exe
# -------------------------------------------------

include(../qhull-app-c.pri)

TARGET = qvoronoi

SOURCES += qvoronoi.c
qhull-2012.1/src/rbox/0000755000076400010400000000000011721063455015651 5ustar  bbarberAdministratorsqhull-2012.1/src/rbox/rbox.c0000644000076400010400000000673311710423732016774 0ustar  bbarberAdministrators/*
  ---------------------------------

   rbox.c
     rbox program for generating input points for qhull.

   notes:
     50 points generated for 'rbox D4'

*/

#include "random.h"
#include "libqhull.h"

#include 
#include 
#include 

#if __MWERKS__ && __POWERPC__
#include 
#include 
#include 
#include 
#endif

#ifdef _MSC_VER  /* Microsoft Visual C++ -- warning level 4 */
#pragma warning( disable : 4706)  /* assignment within conditional function */
#endif

char prompt[]= "\n\
-rbox- generate various point distributions.  Default is random in cube.\n\
\n\
args (any order, space separated):                    Version: 2001/06/24\n\
  3000    number of random points in cube, lens, spiral, sphere or grid\n\
  D3      dimension 3-d\n\
  c       add a unit cube to the output ('c G2.0' sets size)\n\
  d       add a unit diamond to the output ('d G2.0' sets size)\n\
  l       generate a regular 3-d spiral\n\
  r       generate a regular polygon, ('r s Z1 G0.1' makes a cone)\n\
  s       generate cospherical points\n\
  x       generate random points in simplex, may use 'r' or 'Wn'\n\
  y       same as 'x', plus simplex\n\
  Pn,m,r  add point [n,m,r] first, pads with 0\n\
\n\
  Ln      lens distribution of radius n.  Also 's', 'r', 'G', 'W'.\n\
  Mn,m,r  lattice(Mesh) rotated by [n,-m,0], [m,n,0], [0,0,r], ...\n\
          '27 M1,0,1' is {0,1,2} x {0,1,2} x {0,1,2}.  Try 'M3,4 z'.\n\
  W0.1    random distribution within 0.1 of the cube's or sphere's surface\n\
  Z0.5 s  random points in a 0.5 disk projected to a sphere\n\
  Z0.5 s G0.6 same as Z0.5 within a 0.6 gap\n\
\n\
  Bn      bounding box coordinates, default %2.2g\n\
  h       output as homogeneous coordinates for cdd\n\
  n       remove command line from the first line of output\n\
  On      offset coordinates by n\n\
  t       use time as the random number seed(default is command line)\n\
  tn      use n as the random number seed\n\
  z       print integer coordinates, default 'Bn' is %2.2g\n\
";

/*--------------------------------------------
-rbox-  main procedure of rbox application
*/
int main(int argc, char **argv) {
  char *command;
  int command_size;
  int return_status;

#if __MWERKS__ && __POWERPC__
  char inBuf[BUFSIZ], outBuf[BUFSIZ], errBuf[BUFSIZ];
  SIOUXSettings.showstatusline= False;
  SIOUXSettings.tabspaces= 1;
  SIOUXSettings.rows= 40;
  if (setvbuf(stdin, inBuf, _IOFBF, sizeof(inBuf)) < 0   /* w/o, SIOUX I/O is slow*/
  || setvbuf(stdout, outBuf, _IOFBF, sizeof(outBuf)) < 0
  || (stdout != stderr && setvbuf(stderr, errBuf, _IOFBF, sizeof(errBuf)) < 0))
    fprintf(stderr, "qhull internal warning (main): could not change stdio to fully buffered.\n");
  argc= ccommand(&argv);
#endif

  if (argc == 1) {
    printf(prompt, qh_DEFAULTbox, qh_DEFAULTzbox);
    return 1;
  }

  command_size= qh_argv_to_command_size(argc, argv);
  if ((command= (char *)qh_malloc((size_t)command_size))) {
    if (!qh_argv_to_command(argc, argv, command, command_size)) {
      fprintf(stderr, "rbox internal error: allocated insufficient memory (%d) for arguments\n", command_size);
      return_status= qh_ERRinput;
    }else{
      return_status= qh_rboxpoints(stdout, stderr, command);
    }
    qh_free(command);
  }else {
    fprintf(stderr, "rbox error: insufficient memory for %d bytes\n", command_size);
    return_status= qh_ERRmem;
  }
  return return_status;
}/*main*/

qhull-2012.1/src/rbox/rbox.pro0000644000076400010400000000031511545640710017343 0ustar  bbarberAdministrators# -------------------------------------------------
# rbox.pro -- Qt project for rbox.exe
# -------------------------------------------------

include(../qhull-app-c.pri)

TARGET = rbox

SOURCES += rbox.c
qhull-2012.1/src/testqset/0000755000076400010400000000000011721063455016553 5ustar  bbarberAdministratorsqhull-2012.1/src/testqset/testqset.c0000644000076400010400000007733011710140235020573 0ustar  bbarberAdministrators/*
  ---------------------------------

   testset.c -- test qset.c and its use of mem.c

   The test sets are pointers to int.  Normally a set is a pointer to a type (e.g., facetT, ridgeT, etc.).
   For consistency in notation, an "int" is typedef'd to i2T

Functions and macros from qset.h.  Counts occurrences in this test.  Does not correspond to thoroughness.
    qh_setaddsorted -- 4 tests
    qh_setaddnth -- 1 test
    qh_setappend -- 7 tests
    qh_setappend_set -- 1 test
    qh_setappend2ndlast -- 1 test
    qh_setcheck -- lots of tests
    qh_setcompact -- 7 tests
    qh_setcopy -- 3 tests
    qh_setdel -- 1 tests
    qh_setdellast -- 1 tests
    qh_setdelnth -- 2 tests
    qh_setdelnthsorted -- 2 tests
    qh_setdelsorted -- 1 test
    qh_setduplicate -- not testable here
    qh_setequal -- 4 tests
    qh_setequal_except -- 2 tests
    qh_setequal_skip -- 2 tests
    qh_setfree -- 11+ tests
    qh_setfree2 -- not testable here
    qh_setfreelong -- 2 tests
    qh_setin -- 3 tests
    qh_setindex -- 4 tests
    qh_setlarger -- 1 test
    qh_setlast -- 2 tests
    qh_setnew -- 6 tests
    qh_setnew_delnthsorted
    qh_setprint -- tested elsewhere
    qh_setreplace -- 1 test
    qh_setsize -- 9+ tests
    qh_settemp -- 2 tests
    qh_settempfree -- 1 test
    qh_settempfree_all -- 1 test
    qh_settemppop -- 1 test
    qh_settemppush -- 1 test
    qh_settruncate -- 3 tests
    qh_setunique -- 3 tests
    qh_setzero -- 1 test
    FOREACHint_ -- 2 test
    FOREACHint4_
    FOREACHint_i_ -- 1 test
    FOREACHintreverse_
    FOREACHintreverse12_
    FOREACHsetelement_ -- 1 test
    FOREACHsetelement_i_ -- 1 test
    FOREACHsetelementreverse_ -- 1 test
    FOREACHsetelementreverse12_ -- 1 test
    SETelem_ -- 3 tests
    SETelemaddr_ -- 2 tests
    SETelemt_ -- not tested (generic)
    SETempty_ -- 1 test
    SETfirst_ -- 4 tests
    SETfirstt_ -- 2 tests
    SETindex_ -- 2 tests
    SETref_ -- 2 tests
    SETreturnsize_ -- 2 tests
    SETsecond_ -- 1 test
    SETsecondt_ -- 2 tests
    SETtruncate_ -- 2 tests
*/

#include 
#include 
#include 
#include 

#include "qset.h"
#include "mem.h"

typedef int i2T;
#define MAXerrorCount 100 /* quit after n errors */

#define FOREACHint_( ints ) FOREACHsetelement_( i2T, ints, i2)
#define FOREACHint4_( ints ) FOREACHsetelement_( i2T, ints, i4)
#define FOREACHint_i_( ints ) FOREACHsetelement_i_( i2T, ints, i2)
#define FOREACHintreverse_( ints ) FOREACHsetelementreverse_( i2T, ints, i2)
#define FOREACHintreverse12_( ints ) FOREACHsetelementreverse12_( i2T, ints, i2)

enum {
    MAXint= 0x7fffffff,
};

char prompt[]= "testqset N [M] -- Test qset.c and mem.c\n\
  Test qsets of 0..N integers with a check every M iterations (default ~log10)\n\
  Additional checking and logging if M is 1\n\
  For example:\n\
    testqset 10000\n\
";

int error_count= 0;  /* Global error_count.  checkSetContents() keeps its own error count.  It exits on too many errors */

/* Macros normally defined in user.h */

#define qh_MEMalign ((int)(sizeof(void *)))
#define qh_MEMbufsize 0x10000       /* allocate 64K memory buffers */
#define qh_MEMinitbuf 0x20000      /* initially allocate 128K buffer */

/* Macros normally defined in QhullSet.h */


/* Functions normally defined in usermem.h */

void qh_exit(int exitcode) {
    exit(exitcode);
} /* exit */

void qh_free(void *mem) {
    free(mem);
} /* free */

void *qh_malloc(size_t size) {
    return malloc(size);
} /* malloc */

void    qh_errexit(int exitcode, void *f, void *r)
{
    f= r; /* unused */
    qh_exit(exitcode);
}

void    qh_fprintf(FILE *fp, int msgcode, const char *fmt, ... )
{
    static int needs_cr= 0;  /* True if qh_fprintf needs a CR */

    size_t fmtlen= strlen(fmt);
    va_list args;

    if (!fp) {
        fprintf(stderr, "qh_fprintf: fp not defined for '%s'", fmt);
        qh_errexit(6232, NULL, NULL);
    }
    if(fmtlen>0){
        if(fmt[fmtlen-1]=='\n'){
            if(needs_cr && fmtlen>1){
                fprintf(fp, "\n");
            }
            needs_cr= 0;
        }else{
            needs_cr= 1;
        }
    }
    if(msgcode>=6000 && msgcode<7000){
        fprintf(fp, "Error TQ%d ", msgcode);
    }
    va_start(args, fmt);
    vfprintf(fp, fmt, args);
    va_end(args);
}

/* Defined below in order of use */
int main(int argc, char **argv);
void readOptions(int argc, char **argv, const char *promptstr, int *numInts, int *checkEvery);
void setupMemory(int tracelevel, int numInts, int **intarray);

void testSetappendSettruncate(int numInts, int *intarray, int checkEvery);
void testSetdelSetadd(int numInts, int *intarray, int checkEvery);
void testSetappendSet(int numInts, int *intarray, int checkEvery);
void testSetcompactCopy(int numInts, int *intarray, int checkEvery);
void testSetequalInEtc(int numInts, int *intarray, int checkEvery);
void testSettemp(int numInts, int *intarray, int checkEvery);
void testSetlastEtc(int numInts, int *intarray, int checkEvery);
void testSetdelsortedEtc(int numInts, int *intarray, int checkEvery);

int log_i(setT *set, const char *s, int i, int numInts, int checkEvery);
void checkSetContents(const char *name, setT *set, int count, int rangeA, int rangeB, int rangeC);

int main(int argc, char **argv) {
    int *intarray= NULL;
    int numInts;
    int checkEvery= MAXint;
    int curlong, totlong;
    int tracelevel= 4; /* 4 normally.  5 for memory tracing */

    readOptions(argc, argv, prompt, &numInts, &checkEvery);
    setupMemory(tracelevel, numInts, &intarray);

    testSetappendSettruncate(numInts, intarray, checkEvery);
    testSetdelSetadd(numInts, intarray, checkEvery);
    testSetappendSet(numInts, intarray, checkEvery);
    testSetcompactCopy(numInts, intarray, checkEvery);
    testSetequalInEtc(numInts, intarray, checkEvery);
    testSettemp(numInts, intarray, checkEvery);
    testSetlastEtc(numInts, intarray, checkEvery);
    testSetdelsortedEtc(numInts, intarray, checkEvery);
    printf("\n\nNot testing qh_setduplicate and qh_setfree2.\n  These routines use heap-allocated set contents.  See qhull tests.\n");

    qh_memstatistics(stdout);
    qh_memfreeshort(&curlong, &totlong);
    if (curlong || totlong){
        qh_fprintf(stderr, 8043, "qh_memfreeshort: did not free %d bytes of long memory(%d pieces)\n", totlong, curlong);
        error_count++;
    }
    if(error_count){
        qh_fprintf(stderr, 8012, "testqset: %d errors\n\n", error_count);
        exit(1);
    }else{
        printf("testqset: OK\n\n");
    }
    return 0;
}/*main*/

void readOptions(int argc, char **argv, const char *promptstr, int *numInts, int *checkEvery)
{
    long numIntsArg;
    long checkEveryArg;
    char *endp;

    if (argc != 2 && argc != 3) {
        printf(promptstr);
        exit(0);
    }
    numIntsArg= strtol(argv[1], &endp, 10);
    if(numIntsArg<1){
        qh_fprintf(stderr, 6301, "First argument should be 1 or greater.  Got '%s'\n", argv[1]);
        exit(1);
    }
    if(numIntsArg>MAXint){
        qh_fprintf(stderr, 6302, "qset does not currently support 64-bit ints.  Maximum count is %d\n", MAXint);
        exit(1);
    }
    *numInts= (int)numIntsArg;

    if(argc>2){
        checkEveryArg= strtol(argv[2], &endp, 10);
        if(checkEveryArg<1){
            qh_fprintf(stderr, 6321, "checkEvery argument should be 1 or greater.  Got '%s'\n", argv[2]);
            exit(1);
        }
        if(checkEveryArg>MAXint){
            qh_fprintf(stderr, 6322, "qset does not currently support 64-bit ints.  Maximum checkEvery is %d\n", MAXint);
            exit(1);
        }
        *checkEvery= (int)checkEveryArg;
    }
}/*readOptions*/

void setupMemory(int tracelevel, int numInts, int **intarray)
{
    int i;
    if(numInts<0 || numInts*(int)sizeof(int)<0){
        qh_fprintf(stderr, 6303, "qset does not currently support 64-bit ints.  Integer overflow\n");
        exit(1);
    }
    *intarray= qh_malloc(numInts * sizeof(int));
    if(!*intarray){
        qh_fprintf(stderr, 6304, "Failed to allocate %d bytes of memory\n", numInts * sizeof(int));
        exit(1);
    }
    for(i= 0; i=2){
        isCheck= log_i(ints, "n", numInts/2, numInts, checkEvery);
        qh_settruncate(ints, numInts/2);
        checkSetContents("qh_settruncate by half", ints, numInts/2, 0, -1, -1);
    }
    isCheck= log_i(ints, "n", 0, numInts, checkEvery);
    qh_settruncate(ints, 0);
    checkSetContents("qh_settruncate", ints, 0, -1, -1, -1);

    qh_fprintf(stderr, 8003, "\n\nTesting qh_setappend2ndlast 0,0..%d.  Test 0", numInts-1);
    qh_setfree(&ints);
    ints= qh_setnew(4);
    qh_setappend(&ints, intarray+0);
    for(i= 0; i=2){
        isCheck= log_i(ints, "n", numInts/2, numInts, checkEvery);
        SETtruncate_(ints, numInts/2);
        checkSetContents("SETtruncate_ by half", ints, numInts/2, 0, -1, -1);
    }
    isCheck= log_i(ints, "n", 0, numInts, checkEvery);
    SETtruncate_(ints, 0);
    checkSetContents("SETtruncate_", ints, 0, -1, -1, -1);

    qh_setfree(&ints);
}/*testSetappendSettruncate*/

void testSetdelSetadd(int numInts, int *intarray, int checkEvery)
{
    setT *ints=qh_setnew(1);
    int i,j, isCheck;

    qh_fprintf(stderr, 8003, "\n\nTesting qh_setdelnthsorted and qh_setaddnth 1..%d. Test", numInts-1);
    for(j=1; j3){
                qh_setdelsorted(ints, intarray+i/2);
                checkSetContents("qh_setdelsorted", ints, j-1, 0, i/2+1, -1);
                qh_setaddsorted(&ints, intarray+i/2);
                checkSetContents("qh_setaddsorted i/2", ints, j, 0, 0, -1);
            }
            qh_setdellast(ints);
            checkSetContents("qh_setdellast", ints, (j ? j-1 : 0), 0, -1, -1);
            if(j>0){
                qh_setaddsorted(&ints, intarray+j-1);
                checkSetContents("qh_setaddsorted j-1", ints, j, 0, -1, -1);
            }
            if(j>4){
                qh_setdelnthsorted(ints, i/2);
                if (checkEvery==1)
                  checkSetContents("qh_setdelnthsorted", ints, j-1, 0, i/2+1, -1);
                /* FIXUP qh_setdelnth  move-to-front */
                qh_setdelsorted(ints, intarray+i/2+1);
                checkSetContents("qh_setdelsorted 2", ints, j-2, 0, i/2+2, -1);
                qh_setaddsorted(&ints, intarray+i/2+1);
                if (checkEvery==1)
                  checkSetContents("qh_setaddsorted i/2+1", ints, j-1, 0, i/2+1, -1);
                qh_setaddsorted(&ints, intarray+i/2);
                checkSetContents("qh_setaddsorted i/2 again", ints, j, 0, -1, -1);
            }
            qh_setfree(&ints2);
            ints2= qh_setcopy(ints, 0);
            qh_setcompact(ints);
            qh_setcompact(ints2);
            checkSetContents("qh_setcompact", ints, j, 0, 0, -1);
            checkSetContents("qh_setcompact 2", ints2, j, 0, 0, -1);
            qh_setcompact(ints);
            checkSetContents("qh_setcompact 3", ints, j, 0, 0, -1);
            qh_setfree(&ints2);
        }
    }
    qh_setfreelong(&ints);
    if(ints){
        qh_setfree(&ints); /* Was quick memory */
    }
}/*testSetdelsortedEtc*/

void testSetequalInEtc(int numInts, int *intarray, int checkEvery)
{
    setT *ints= NULL;
    setT *ints2= NULL;
    setT *ints3= NULL;
    int i,j,n;

    qh_fprintf(stderr, 8019, "\n\nTesting qh_setequal*, qh_setin*, qh_setdel, qh_setdelnth, and qh_setlarger 0..%d. Test", numInts-1);
    for(j=0; j0){
                if(qh_setequal(ints, ints2)){
                    qh_fprintf(stderr, 6324, "testSetequalInEtc: non-empty set equal to empty set\n", j);
                    error_count++;
                }
                qh_setfree(&ints3);
                ints3= qh_setcopy(ints, 0);
                checkSetContents("qh_setreplace", ints3, j, 0, -1, -1);
                qh_setreplace(ints3, intarray+j/2, intarray+j/2+1);
                if(j==1){
                    checkSetContents("qh_setreplace 2", ints3, j, j/2+1, -1, -1);
                }else if(j==2){
                    checkSetContents("qh_setreplace 3", ints3, j, 0, j/2+1, -1);
                }else{
                    checkSetContents("qh_setreplace 3", ints3, j, 0, j/2+1, j/2+1);
                }
                if(qh_setequal(ints, ints3)){
                    qh_fprintf(stderr, 6325, "testSetequalInEtc: modified set equal to original set at %d/2\n", j);
                    error_count++;
                }
                if(!qh_setequal_except(ints, intarray+j/2, ints3, intarray+j/2+1)){
                    qh_fprintf(stderr, 6326, "qh_setequal_except: modified set not equal to original set except modified\n", j);
                    error_count++;
                }
                if(qh_setequal_except(ints, intarray+j/2, ints3, intarray)){
                    qh_fprintf(stderr, 6327, "qh_setequal_except: modified set equal to original set with wrong excepts\n", j);
                    error_count++;
                }
                if(!qh_setequal_skip(ints, j/2, ints3, j/2)){
                    qh_fprintf(stderr, 6328, "qh_setequal_skip: modified set not equal to original set except modified\n", j);
                    error_count++;
                }
                if(j>2 && qh_setequal_skip(ints, j/2, ints3, 0)){
                    qh_fprintf(stderr, 6329, "qh_setequal_skip: modified set equal to original set with wrong excepts\n", j);
                    error_count++;
                }
                if(intarray+j/2+1!=qh_setdel(ints3, intarray+j/2+1)){
                    qh_fprintf(stderr, 6330, "qh_setdel: failed to find added element\n", j);
                    error_count++;
                }
                checkSetContents("qh_setdel", ints3, j-1, 0, j-1, (j==1 ? -1 : j/2+1));  /* swaps last element with deleted element */
                if(j>3){
                    qh_setdelnth(ints3, j/2); /* Delete at the same location as the original replace, for only one out-of-order element */
                    checkSetContents("qh_setdelnth", ints3, j-2, 0, j-2, (j==2 ? -1 : j/2+1));
                }
                if(qh_setin(ints3, intarray+j/2)){
                    qh_fprintf(stderr, 6331, "qh_setin: found deleted element\n");
                    error_count++;
                }
                if(j>4 && !qh_setin(ints3, intarray+1)){
                    qh_fprintf(stderr, 6332, "qh_setin: did not find second element\n");
                    error_count++;
                }
                if(j>4 && !qh_setin(ints3, intarray+j-2)){
                    qh_fprintf(stderr, 6333, "qh_setin: did not find last element\n");
                    error_count++;
                }
                if(-1!=qh_setindex(ints2, intarray)){
                    qh_fprintf(stderr, 6334, "qh_setindex: found element in empty set\n");
                    error_count++;
                }
                if(-1!=qh_setindex(ints3, intarray+j/2)){
                    qh_fprintf(stderr, 6335, "qh_setindex: found deleted element in set\n");
                    error_count++;
                }
                if(0!=qh_setindex(ints, intarray)){
                    qh_fprintf(stderr, 6336, "qh_setindex: did not find first in set\n");
                    error_count++;
                }
                if(j-1!=qh_setindex(ints, intarray+j-1)){
                    qh_fprintf(stderr, 6337, "qh_setindex: did not find last in set\n");
                    error_count++;
                }
            }
            qh_setfree(&ints2);
        }
    }
    qh_setfree(&ints3);
    qh_setfreelong(&ints);
    if(ints){
        qh_setfree(&ints); /* Was quick memory */
    }
}/*testSetequalInEtc*/


void testSetlastEtc(int numInts, int *intarray, int checkEvery)
{
    setT *ints= NULL;
    setT *ints2= NULL;
    int i,j,prepend;

    qh_fprintf(stderr, 8020, "\n\nTesting qh_setlast, qh_setnew_delnthsorted, qh_setunique, and qh_setzero 0..%d. Test", numInts-1);
    for(j=0; j0){
                if(intarray+j-1!=qh_setlast(ints)){
                    qh_fprintf(stderr, 6338, "qh_setlast: wrong last element\n");
                    error_count++;
                }
                prepend= (j<100 ? j/4 : 0);
                ints2= qh_setnew_delnthsorted(ints, qh_setsize(ints), j/2, prepend);
                if(qh_setsize(ints2)!=j+prepend-1){
                    qh_fprintf(stderr, 6345, "qh_setnew_delnthsorted: Expecting %d elements, got %d\n", j+prepend-1, qh_setsize(ints2));
                    error_count++;
                }
                /* Define prepended elements.  Otherwise qh_setdelnthsorted may fail */
                for(i= 0; i2){
                    qh_setzero(ints2, j/2, j-1);  /* max size may be j-1 */
                    if(qh_setsize(ints2)!=j-1){
                        qh_fprintf(stderr, 6342, "qh_setzero: Expecting %d elements, got %d\n", j, qh_setsize(ints2));
                        error_count++;
                    }
                    qh_setcompact(ints2);
                    checkSetContents("qh_setzero", ints2, j/2, 0, -1, -1);
                }
            }
            qh_setfree(&ints2);
        }
    }
    qh_setfreelong(&ints);
    if(ints){
        qh_setfree(&ints); /* Was quick memory */
    }
}/*testSetlastEtc*/

void testSettemp(int numInts, int *intarray, int checkEvery)
{
    setT *ints= NULL;
    setT *ints2= NULL;
    setT *ints3= NULL;
    int i,j;

    qh_fprintf(stderr, 8021, "\n\nTesting qh_settemp* 0..%d. Test", numInts-1);
    for(j=0; j0){
                qh_settemppush(ints);
                ints3= qh_settemppop();
                if(ints!=ints3){
                    qh_fprintf(stderr, 6343, "qh_settemppop: didn't pop the push\n");
                    error_count++;
                }
            }
            qh_settempfree(&ints2);
        }
    }
    qh_setfreelong(&ints);
    if(ints){
        qh_setfree(&ints); /* Was quick memory */
    }
}/*testSettemp*/

/* Check that a set contains count elements
   Ranges are consecutive (e.g., 1,2,3,...) starting with first, mid, and last
   Use -1 for missing ranges
   Returns -1 if should check results
*/
int log_i(setT *set, const char *s, int i, int numInts, int checkEvery)
{
    int j= i;
    int scale= 1;
    int e= 0;
    int *i2, **i2p;

    if(*s || checkEvery==1){
        if(i<10){
            qh_fprintf(stderr, 8004, " %s%d", s, i);
        }else{
            if(i==11 && checkEvery==1){
                qh_fprintf(stderr, 8005, "\nResults after 10: ");
                FOREACHint_(set){
                    qh_fprintf(stderr, 8006, " %d", *i2);
                }
                qh_fprintf(stderr, 8007, " Continue");
            }
            while((j= j/10)>=1){
                scale *= 10;
                e++;
            }
            if(i==numInts-1){
                qh_fprintf(stderr, 8008, " %s%d", s, i);
            }else if(i==scale){
                if(i<=1000){
                    qh_fprintf(stderr, 8010, " %s%d", s, i);
                }else{
                    qh_fprintf(stderr, 8009, " %s1e%d", s, e);
                }
            }
        }
    }
    if(i<1000 || i%checkEvery==0 || i== scale || i==numInts-1){
        return 1;
    }
    return 0;
}/*log_i*/

/* Check that a set contains count elements
   Ranges are consecutive (e.g., 1,2,3,...) starting with first, mid, and last
   Use -1 for missing ranges
*/
void checkSetContents(const char *name, setT *set, int count, int rangeA, int rangeB, int rangeC)
{

    i2T *i2, **i2p;
    int i2_i, i2_n;
    int prev= -1; /* avoid warning */
    int i;
    int first= -3;
    int second= -3;
    int rangeCount=1;
    int actualSize= 0;

    qh_setcheck(set, name, 0);
    if(set){
        SETreturnsize_(set, actualSize);  /* normally used only when speed is critical */
        if(*qh_setendpointer(set)!=NULL){
            qh_fprintf(stderr, 6344, "%s: qh_setendpointer(), 0x%x, is not NULL terminator of set 0x%x", name, qh_setendpointer(set), set);
            error_count++;
        }
    }
    if(actualSize!=qh_setsize(set)){
        qh_fprintf(stderr, 6305, "%s: SETreturnsize_() returned %d while qh_setsize() returns %d\n", name, actualSize, qh_setsize(set));
        error_count++;
    }else if(actualSize!=count){
        qh_fprintf(stderr, 6306, "%s: Expecting %d elements for set.  Got %d elements\n", name, count, actualSize);
        error_count++;
    }
    if(SETempty_(set)){
        if(count!=0){
            qh_fprintf(stderr, 6307, "%s: Got empty set instead of count %d, rangeA %d, rangeB %d, rangeC %d\n", name, count, rangeA, rangeB, rangeC);
            error_count++;
        }
    }else{
        /* Must be first, otherwise trips msvc 8 */
        i2T **p= SETaddr_(set, i2T);
        if(*p!=SETfirstt_(set, i2T)){
            qh_fprintf(stderr, 6309, "%s: SETaddr_(set, i2t) [%p] is not the same as SETfirst_(set) [%p]\n", name, SETaddr_(set, i2T), SETfirst_(set));
            error_count++;
        }
        first= *(int *)SETfirst_(set);
        if(SETfirst_(set)!=SETfirstt_(set, i2T)){
            qh_fprintf(stderr, 6308, "%s: SETfirst_(set) [%p] is not the same as SETfirstt_(set, i2T [%p]\n", name, SETfirst_(set), SETfirstt_(set, i2T));
            error_count++;
        }
        if(qh_setsize(set)>1){
            second= *(int *)SETsecond_(set);
            if(SETsecond_(set)!=SETsecondt_(set, i2T)){
                qh_fprintf(stderr, 6310, "%s: SETsecond_(set) [%p] is not the same as SETsecondt_(set, i2T) [%p]\n", name, SETsecond_(set), SETsecondt_(set, i2T));
                error_count++;
            }
        }
    }
    /* Test first run of ints in set*/
    i= 0;
    FOREACHint_(set){
        if(i2!=SETfirst_(set) && *i2!=prev+1){
            break;
        }
        prev= *i2;
        if(SETindex_(set, i2)!=i){
            qh_fprintf(stderr, 6311, "%s: Expecting SETIndex_(set, pointer-to-%d) to be %d.  Got %d\n", name, *i2, i, SETindex_(set, i2));
            error_count++;;
        }
        if(i2!=SETref_(i2)){
            qh_fprintf(stderr, 6312, "%s: SETref_(i2) [%p] does not point to i2 (the %d'th element)\n", name, SETref_(i2), i);
            error_count++;;
        }
        i++;
    }
    FOREACHint_i_(set){
        /* Must be first conditional, otherwise it trips up msvc 8 */
        i2T **p= SETelemaddr_(set, i2_i, i2T);
        if(i2!=*p){
            qh_fprintf(stderr, 6320, "%s: SETelemaddr_(set, %d, i2T) [%p] does not point to i2\n", name, i2_i, SETelemaddr_(set, i2_i, int));
            error_count++;;
        }
        if(i2_i==0){
            if(first!=*i2){
                qh_fprintf(stderr, 6314, "%s: First element is %d instead of SETfirst %d\n", name, *i2, first);
                error_count++;;
            }
            if(rangeA!=*i2){
                qh_fprintf(stderr, 6315, "%s: starts with %d instead of rangeA %d\n", name, *i2, rangeA);
                error_count++;;
            }
            prev= rangeA;
        }else{
            if(i2_i==1 && second!=*i2){
                qh_fprintf(stderr, 6316, "%s: Second element is %d instead of SETsecond %d\n", name, *i2, second);
                error_count++;;
            }
            if(prev+1==*i2){
                prev++;
            }else{
                if(*i2==rangeB){
                    prev= rangeB;
                    rangeB= -1;
                    rangeCount++;
                }else if(rangeB==-1 && *i2==rangeC){
                    prev= rangeC;
                    rangeC= -1;
                    rangeCount++;
                }else{
                    prev++;
                    qh_fprintf(stderr, 6317, "%s: Expecting %d'th element to be %d.  Got %d\n", name, i2_i, prev, *i2);
                    error_count++;
                }
            }
        }
        if(i2!=SETelem_(set, i2_i)){
            qh_fprintf(stderr, 6318, "%s: SETelem_(set, %d) [%p] is not i2 [%p] (the %d'th element)\n", name, i2_i, SETelem_(set, i2_i), i2, i2_i);
            error_count++;;
        }
        if(SETelemt_(set, i2_i, i2T)!=SETelem_(set, i2_i)){   /* Normally SETelemt_ is used for generic sets */
            qh_fprintf(stderr, 6319, "%s: SETelemt_(set, %d, i2T) [%p] is not SETelem_(set, %d) [%p] (the %d'th element)\n", name, i2_i, SETelemt_(set, i2_i, int), i2_i, SETelem_(set, i2_i), i2_i);
            error_count++;;
        }
    }
    if(error_count>=MAXerrorCount){
        qh_fprintf(stderr, 8011, "testqset: Stop testing after %d errors\n", error_count);
        exit(1);
    }
}/*checkSetContents*/

qhull-2012.1/src/testqset/testqset.pro0000644000076400010400000000115511707650567021165 0ustar  bbarberAdministrators# -------------------------------------------------
# testqset.pro -- Qt project file for testqset.exe
# -------------------------------------------------

include(../qhull-warn.pri)

TARGET = testqset

DESTDIR = ../../bin
TEMPLATE = app
CONFIG += console warn_on
CONFIG -= qt
CONFIG += qhull_warn_conversion

build_pass:CONFIG(debug, debug|release){
   OBJECTS_DIR = Debug
}else:build_pass:CONFIG(release, debug|release){
   OBJECTS_DIR = Release
}

INCLUDEPATH += ../libqhull

SOURCES += testqset.c
SOURCES += ../libqhull/qset.c
SOURCES += ../libqhull/mem.c

HEADERS += ../libqhull/mem.h
HEADERS += ../libqhull/qset.h

qhull-2012.1/src/user_eg/0000755000076400010400000000000011721063455016330 5ustar  bbarberAdministratorsqhull-2012.1/src/user_eg/user_eg.c0000644000076400010400000002552111563521251020127 0ustar  bbarberAdministrators/*
  ---------------------------------

  user_eg.c
  sample code for calling qhull() from an application

  call with:

     user_eg "cube/diamond options" "delaunay options" "halfspace options"

  for example:

     user_eg                             # return summaries

     user_eg "n" "o" "Fp"                # return normals, OFF, points

     user_eg "n Qt" "o" "Fp"             # triangulated cube

     user_eg "QR0 p" "QR0 v p" "QR0 Fp"  # rotate input and return points
                                         # 'v' returns Voronoi
                                         # transform is rotated for halfspaces

   main() makes three runs of qhull.

     1) compute the convex hull of a cube

     2a) compute the Delaunay triangulation of random points

     2b) find the Delaunay triangle closest to a point.

     3) compute the halfspace intersection of a diamond

 notes:

   For another example, see main() in unix.c and user_eg2.c.
   These examples, call qh_qhull() directly.  They allow
   tighter control on the code loaded with Qhull.

   For a C++ example, see user_eg3.cpp

   Summaries are sent to stderr if other output formats are used

   compiled by 'make user_eg'

   see libqhull.h for data structures, macros, and user-callable functions.
*/

#define qh_QHimport
#include "qhull_a.h"

/*-------------------------------------------------
-internal function prototypes
*/
void print_summary (void);
void makecube (coordT *points, int numpoints, int dim);
void makeDelaunay (coordT *points, int numpoints, int dim, int seed);
void findDelaunay (int dim);
void makehalf (coordT *points, int numpoints, int dim);

/*-------------------------------------------------
-print_summary()
*/
void print_summary (void) {
  facetT *facet;
  int k;

  printf ("\n%d vertices and %d facets with normals:\n",
                 qh num_vertices, qh num_facets);
  FORALLfacets {
    for (k=0; k < qh hull_dim; k++)
      printf ("%6.2g ", facet->normal[k]);
    printf ("\n");
  }
}

/*--------------------------------------------------
-makecube- set points to vertices of cube
  points is numpoints X dim
*/
void makecube (coordT *points, int numpoints, int dim) {
  int j,k;
  coordT *point;

  for (j=0; jlocate a facet with qh_findbestfacet()
*/
void findDelaunay (int dim) {
  int k;
  coordT point[ 100];
  boolT isoutside;
  realT bestdist;
  facetT *facet;
  vertexT *vertex, **vertexp;

  for (k= 0; k < dim; k++)
    point[k]= 0.5;
  qh_setdelaunay (dim+1, 1, point);
  facet= qh_findbestfacet (point, qh_ALL, &bestdist, &isoutside);
  if (facet->tricoplanar) {
    fprintf(stderr, "findDelaunay: not implemented for triangulated, non-simplicial Delaunay regions (tricoplanar facet, f%d).\n",
       facet->id);
    qh_errexit (qh_ERRqhull, facet, NULL);
  }
  FOREACHvertex_(facet->vertices) {
    for (k=0; k < dim; k++)
      printf ("%5.2f ", vertex->point[k]);
    printf ("\n");
  }
} /*.findDelaunay.*/

/*--------------------------------------------------
-makehalf- set points to halfspaces for a (dim)-dimensional diamond
  points is numpoints X dim+1

  each halfspace consists of dim coefficients followed by an offset
*/
void makehalf (coordT *points, int numpoints, int dim) {
  int j,k;
  coordT *point;

  for (j=0; j= 2 ? argv[1] : "");
  numpoints= SIZEcube;
  makecube (points, numpoints, DIM);
  for (i=numpoints; i--; )
    rows[i]= points+dim*i;
  qh_printmatrix (outfile, "input", rows, numpoints, dim);
  exitcode= qh_new_qhull (dim, numpoints, points, ismalloc,
                      flags, outfile, errfile);
  if (!exitcode) {                  /* if no error */
    /* 'qh facet_list' contains the convex hull */
    print_summary();
    FORALLfacets {
       /* ... your code ... */
    }
  }
  qh_freeqhull(!qh_ALL);                   /* free long memory  */
  qh_memfreeshort (&curlong, &totlong);    /* free short memory and memory allocator */
  if (curlong || totlong)
    fprintf (errfile, "qhull internal warning (user_eg, #1): did not free %d bytes of long memory (%d pieces)\n", totlong, curlong);

  /*
    Run 2: Delaunay triangulation
  */

  printf( "\ncompute %d-d Delaunay triangulation\n", dim);
  sprintf (flags, "qhull s d Tcv %s", argc >= 3 ? argv[2] : "");
  numpoints= SIZEcube;
  makeDelaunay (points, numpoints, dim, (int)time(NULL));
  for (i=numpoints; i--; )
    rows[i]= points+dim*i;
  qh_printmatrix (outfile, "input", rows, numpoints, dim);
  exitcode= qh_new_qhull (dim, numpoints, points, ismalloc,
                      flags, outfile, errfile);
  if (!exitcode) {                  /* if no error */
    /* 'qh facet_list' contains the convex hull */
    /* If you want a Voronoi diagram ('v') and do not request output (i.e., outfile=NULL),
       call qh_setvoronoi_all() after qh_new_qhull(). */
    print_summary();
    FORALLfacets {
       /* ... your code ... */
    }
    printf( "\nfind %d-d Delaunay triangle closest to [0.5, 0.5, ...]\n", dim);
    exitcode= setjmp (qh errexit);
    if (!exitcode) {
      /* Trap Qhull errors in findDelaunay().  Without the setjmp(), Qhull
         will exit() after reporting an error */
      qh NOerrexit= False;
      findDelaunay (DIM);
    }
    qh NOerrexit= True;
  }
#if qh_QHpointer  /* see user.h */
  {
    qhT *oldqhA, *oldqhB;
    coordT pointsB[DIM*TOTpoints]; /* array of coordinates for each point */


    printf( "\nsave first triangulation and compute a new triangulation\n");
    oldqhA= qh_save_qhull();
    sprintf (flags, "qhull s d Tcv %s", argc >= 3 ? argv[2] : "");
    numpoints= SIZEcube;
    makeDelaunay (pointsB, numpoints, dim, (int)time(NULL)+1);
    for (i=numpoints; i--; )
      rows[i]= pointsB+dim*i;
    qh_printmatrix (outfile, "input", rows, numpoints, dim);
    exitcode= qh_new_qhull (dim, numpoints, pointsB, ismalloc,
                      flags, outfile, errfile);
    if (!exitcode)
      print_summary();
    printf( "\nsave second triangulation and restore first one\n");
    oldqhB= qh_save_qhull();
    qh_restore_qhull (&oldqhA);
    print_summary();
    printf( "\nfree first triangulation and restore second one.\n");
    qh_freeqhull (qh_ALL);               /* free short and long memory used by first call */
                                         /* do not use qh_memfreeshort */
    qh_restore_qhull (&oldqhB);
    print_summary();
  }
#endif
  qh_freeqhull(!qh_ALL);                 /* free long memory */
  qh_memfreeshort (&curlong, &totlong);  /* free short memory and memory allocator */
  if (curlong || totlong)
    fprintf (errfile, "qhull internal warning (user_eg, #2): did not free %d bytes of long memory (%d pieces)\n", totlong, curlong);

  /*
    Run 3: halfspace intersection about the origin
  */
  printf( "\ncompute halfspace intersection about the origin for a diamond\n");
  sprintf (flags, "qhull H0 s Tcv %s", argc >= 4 ? argv[3] : "Fp");
  numpoints= SIZEcube;
  makehalf (points, numpoints, dim);
  for (i=numpoints; i--; )
    rows[i]= points+(dim+1)*i;
  qh_printmatrix (outfile, "input as halfspace coefficients + offsets", rows, numpoints, dim+1);
  /* use qh_sethalfspace_all to transform the halfspaces yourself.
     If so, set 'qh feasible_point and do not use option 'Hn,...' [it would retransform the halfspaces]
  */
  exitcode= qh_new_qhull (dim+1, numpoints, points, ismalloc,
                      flags, outfile, errfile);
  if (!exitcode)
    print_summary();
  qh_freeqhull (!qh_ALL);
  qh_memfreeshort (&curlong, &totlong);
  if (curlong || totlong)  /* could also check previous runs */
    fprintf (stderr, "qhull internal warning (user_eg, #3): did not free %d bytes of long memory (%d pieces)\n",
       totlong, curlong);
  return exitcode;
} /* main */

qhull-2012.1/src/user_eg/user_eg.pro0000644000076400010400000000034711706636655020522 0ustar  bbarberAdministrators# -------------------------------------------------
# user_eg.pro -- Qt project for Qhull demonstration
# -------------------------------------------------

include(../qhull-app-sharedp.pri)

TARGET = user_eg

SOURCES += user_eg.c
qhull-2012.1/src/user_eg2/0000755000076400010400000000000011721063455016412 5ustar  bbarberAdministratorsqhull-2012.1/src/user_eg2/user_eg2.c0000644000076400010400000006404611710423660020277 0ustar  bbarberAdministrators/*
  ---------------------------------

  user_eg2.c

  sample code for calling qhull() from an application.

  See user_eg.c for a simpler method using qh_new_qhull().
  The method used here and in unix.c gives you additional
  control over Qhull.

  See user_eg3.cpp for a C++ example

  call with:

     user_eg2 "triangulated cube/diamond options" "delaunay options" "halfspace options"

  for example:

     user_eg2                             # return summaries

     user_eg2 "n" "o" "Fp"                # return normals, OFF, points

     user_eg2 "QR0 p" "QR0 v p" "QR0 Fp"  # rotate input and return points
                                         # 'v' returns Voronoi
                                         # transform is rotated for halfspaces

   main() makes three runs of qhull.

     1) compute the convex hull of a cube, and incrementally add a diamond

     2a) compute the Delaunay triangulation of random points, and add points.

     2b) find the Delaunay triangle closest to a point.

     3) compute the halfspace intersection of a diamond, and add a cube

 notes:

   summaries are sent to stderr if other output formats are used

   derived from unix.c and compiled by 'make user_eg2'

   see libqhull.h for data structures, macros, and user-callable functions.

   If you want to control all output to stdio and input to stdin,
   set the #if below to "1" and delete all lines that contain "io.c".
   This prevents the loading of io.o.  Qhull will
   still write to 'qh ferr' (stderr) for error reporting and tracing.

   Defining #if 1, also prevents user.o from being loaded.
*/

#include "qhull_a.h"

/*-------------------------------------------------
-internal function prototypes
*/
void print_summary (void);
void makecube (coordT *points, int numpoints, int dim);
void adddiamond (coordT *points, int numpoints, int numnew, int dim);
void makeDelaunay (coordT *points, int numpoints, int dim);
void addDelaunay (coordT *points, int numpoints, int numnew, int dim);
void findDelaunay (int dim);
void makehalf (coordT *points, int numpoints, int dim);
void addhalf (coordT *points, int numpoints, int numnew, int dim, coordT *feasible);

/*-------------------------------------------------
-print_summary()
*/
void print_summary (void) {
  facetT *facet;
  int k;

  printf ("\n%d vertices and %d facets with normals:\n",
                 qh num_vertices, qh num_facets);
  FORALLfacets {
    for (k=0; k < qh hull_dim; k++)
      printf ("%6.2g ", facet->normal[k]);
    printf ("\n");
  }
}

/*--------------------------------------------------
-makecube- set points to vertices of cube
  points is numpoints X dim
*/
void makecube (coordT *points, int numpoints, int dim) {
  int j,k;
  coordT *point;

  for (j=0; jlocate a facet with qh_findbestfacet()
*/
void findDelaunay (int dim) {
  int k;
  coordT point[ 100];
  boolT isoutside;
  realT bestdist;
  facetT *facet;
  vertexT *vertex, **vertexp;

  for (k= 0; k < dim-1; k++)
    point[k]= 0.5;
  qh_setdelaunay (dim, 1, point);
  facet= qh_findbestfacet (point, qh_ALL, &bestdist, &isoutside);
  if (facet->tricoplanar) {
    fprintf(stderr, "findDelaunay: not implemented for triangulated, non-simplicial Delaunay regions (tricoplanar facet, f%d).\n",
       facet->id);
    qh_errexit (qh_ERRqhull, facet, NULL);
  }
  FOREACHvertex_(facet->vertices) {
    for (k=0; k < dim-1; k++)
      printf ("%5.2f ", vertex->point[k]);
    printf ("\n");
  }
} /*.findDelaunay.*/

/*--------------------------------------------------
-makehalf- set points to halfspaces for a (dim)-d diamond
  points is numpoints X dim+1

  each halfspace consists of dim coefficients followed by an offset
*/
void makehalf (coordT *points, int numpoints, int dim) {
  int j,k;
  coordT *point;

  for (j=0; j= 2 ? argv[1] : "");
    qh_initflags (options);
    printf( "\ncompute triangulated convex hull of cube after rotating input\n");
    makecube (array[0], SIZEcube, DIM);
    qh_init_B (array[0], SIZEcube, DIM, ismalloc);
    qh_qhull();
    qh_check_output();
    qh_triangulate();  /* requires option 'Q11' if want to add points */
    print_summary ();
    if (qh VERIFYoutput && !qh STOPpoint && !qh STOPcone)
      qh_check_points ();
    printf( "\nadd points in a diamond\n");
    adddiamond (array[0], SIZEcube, SIZEdiamond, DIM);
    qh_check_output();
    print_summary ();
    qh_produce_output();  /* delete this line to help avoid io.c */
    if (qh VERIFYoutput && !qh STOPpoint && !qh STOPcone)
      qh_check_points ();
  }
  qh NOerrexit= True;
  qh_freeqhull (!qh_ALL);
  qh_memfreeshort (&curlong, &totlong);
  /*
    Run 2: Delaunay triangulation
  */
  qh_init_A (stdin, stdout, stderr, 0, NULL);
  exitcode= setjmp (qh errexit);
  if (!exitcode) {
    coordT array[TOTpoints][DIM];

    strcat (qh rbox_command, "user_eg Delaunay");
    sprintf (options, "qhull s d Tcv %s", argc >= 3 ? argv[2] : "");
    qh_initflags (options);
    printf( "\ncompute %d-d Delaunay triangulation\n", DIM-1);
    makeDelaunay (array[0], SIZEcube, DIM);
    /* Instead of makeDelaunay with qh_setdelaunay, you may
       produce a 2-d array of points, set DIM to 2, and set
       qh PROJECTdelaunay to True.  qh_init_B will call
       qh_projectinput to project the points to the paraboloid
       and add a point "at-infinity".
    */
    qh_init_B (array[0], SIZEcube, DIM, ismalloc);
    qh_qhull();
    /* If you want Voronoi ('v') without qh_produce_output(), call
       qh_setvoronoi_all() after qh_qhull() */
    qh_check_output();
    print_summary ();
    qh_produce_output();  /* delete this line to help avoid io.c */
    if (qh VERIFYoutput && !qh STOPpoint && !qh STOPcone)
      qh_check_points ();
    printf( "\nadd points to triangulation\n");
    addDelaunay (array[0], SIZEcube, SIZEdiamond, DIM);
    qh_check_output();
    qh_produce_output();  /* delete this line to help avoid io.c */
    if (qh VERIFYoutput && !qh STOPpoint && !qh STOPcone)
      qh_check_points ();
    printf( "\nfind Delaunay triangle closest to [0.5, 0.5, ...]\n");
    findDelaunay (DIM);
  }
  qh NOerrexit= True;
  qh_freeqhull (!qh_ALL);
  qh_memfreeshort (&curlong, &totlong);
  /*
    Run 3: halfspace intersection
  */
  qh_init_A (stdin, stdout, stderr, 0, NULL);
  exitcode= setjmp (qh errexit);
  if (!exitcode) {
    coordT array[TOTpoints][DIM+1];  /* +1 for halfspace offset */
    pointT *points;

    strcat (qh rbox_command, "user_eg halfspaces");
    sprintf (options, "qhull H0 s Tcv %s", argc >= 4 ? argv[3] : "");
    qh_initflags (options);
    printf( "\ncompute halfspace intersection about the origin for a diamond\n");
    makehalf (array[0], SIZEcube, DIM);
    qh_setfeasible (DIM); /* from io.c, sets qh feasible_point from 'Hn,n' */
    /* you may malloc and set qh feasible_point directly.  It is only used for
       option 'Fp' */
    points= qh_sethalfspace_all ( DIM+1, SIZEcube, array[0], qh feasible_point);
    qh_init_B (points, SIZEcube, DIM, True); /* qh_freeqhull frees points */
    qh_qhull();
    qh_check_output();
    qh_produce_output();  /* delete this line to help avoid io.c */
    if (qh VERIFYoutput && !qh STOPpoint && !qh STOPcone)
      qh_check_points ();
    printf( "\nadd halfspaces for cube to intersection\n");
    addhalf (array[0], SIZEcube, SIZEdiamond, DIM, qh feasible_point);
    qh_check_output();
    qh_produce_output();  /* delete this line to help avoid io.c */
    if (qh VERIFYoutput && !qh STOPpoint && !qh STOPcone)
      qh_check_points ();
  }
  qh NOerrexit= True;
  qh NOerrexit= True;
  qh_freeqhull (!qh_ALL);
  qh_memfreeshort (&curlong, &totlong);
  if (curlong || totlong)  /* could also check previous runs */
    fprintf (stderr, "qhull internal warning (main): did not free %d bytes of long memory (%d pieces)\n",
       totlong, curlong);
  return exitcode;
} /* main */

#if 1    /* use 1 to prevent loading of io.o and user.o */
/*-------------------------------------------
-errexit- return exitcode to system after an error
  assumes exitcode non-zero
  prints useful information
  see qh_errexit2() in libqhull.c for 2 facets
*/
void qh_errexit(int exitcode, facetT *facet, ridgeT *ridge) {
  QHULL_UNUSED(facet);
  QHULL_UNUSED(ridge);

  if (qh ERREXITcalled) {
    fprintf (qh ferr, "qhull error while processing previous error.  Exit program\n");
    exit(1);
  }
  qh ERREXITcalled= True;
  if (!qh QHULLfinished)
    qh hulltime= (unsigned)clock() - qh hulltime;
  fprintf (qh ferr, "\nWhile executing: %s | %s\n", qh rbox_command, qh qhull_command);
  fprintf(qh ferr, "Options selected:\n%s\n", qh qhull_options);
  if (qh furthest_id >= 0) {
    fprintf(qh ferr, "\nLast point added to hull was p%d", qh furthest_id);
    if (zzval_(Ztotmerge))
      fprintf(qh ferr, "  Last merge was #%d.", zzval_(Ztotmerge));
    if (qh QHULLfinished)
      fprintf(qh ferr, "\nQhull has finished constructing the hull.");
    else if (qh POSTmerging)
      fprintf(qh ferr, "\nQhull has started post-merging");
    fprintf(qh ferr, "\n\n");
  }
  if (qh NOerrexit) {
    fprintf (qh ferr, "qhull error while ending program.  Exit program\n");
    exit(1);
  }
  if (!exitcode)
    exitcode= qh_ERRqhull;
  qh NOerrexit= True;
  longjmp(qh errexit, exitcode);
} /* errexit */


/*-------------------------------------------
-errprint- prints out the information of the erroneous object
    any parameter may be NULL, also prints neighbors and geomview output
*/
void qh_errprint(const char *string, facetT *atfacet, facetT *otherfacet, ridgeT *atridge, vertexT *atvertex) {

  fprintf (qh ferr, "%s facets f%d f%d ridge r%d vertex v%d\n",
           string, getid_(atfacet), getid_(otherfacet), getid_(atridge),
           getid_(atvertex));
} /* errprint */


void qh_printfacetlist(facetT *facetlist, setT *facets, boolT printall) {
  facetT *facet, **facetp;

  /* remove these calls to help avoid io.c */
  qh_printbegin (qh ferr, qh_PRINTfacets, facetlist, facets, printall);/*io.c*/
  FORALLfacet_(facetlist)                                              /*io.c*/
    qh_printafacet(qh ferr, qh_PRINTfacets, facet, printall);          /*io.c*/
  FOREACHfacet_(facets)                                                /*io.c*/
    qh_printafacet(qh ferr, qh_PRINTfacets, facet, printall);          /*io.c*/
  qh_printend (qh ferr, qh_PRINTfacets, facetlist, facets, printall);  /*io.c*/

  FORALLfacet_(facetlist)
    fprintf( qh ferr, "facet f%d\n", facet->id);
} /* printfacetlist */

/* qh_printhelp_degenerate( fp )
    prints descriptive message for precision error

  notes:
    no message if qh_QUICKhelp
*/
void qh_printhelp_degenerate(FILE *fp) {

  if (qh MERGEexact || qh PREmerge || qh JOGGLEmax < REALmax/2)
    qh_fprintf(fp, 9368, "\n\
A Qhull error has occurred.  Qhull should have corrected the above\n\
precision error.  Please send the input and all of the output to\n\
qhull_bug@qhull.org\n");
  else if (!qh_QUICKhelp) {
    qh_fprintf(fp, 9369, "\n\
Precision problems were detected during construction of the convex hull.\n\
This occurs because convex hull algorithms assume that calculations are\n\
exact, but floating-point arithmetic has roundoff errors.\n\
\n\
To correct for precision problems, do not use 'Q0'.  By default, Qhull\n\
selects 'C-0' or 'Qx' and merges non-convex facets.  With option 'QJ',\n\
Qhull joggles the input to prevent precision problems.  See \"Imprecision\n\
in Qhull\" (qh-impre.htm).\n\
\n\
If you use 'Q0', the output may include\n\
coplanar ridges, concave ridges, and flipped facets.  In 4-d and higher,\n\
Qhull may produce a ridge with four neighbors or two facets with the same \n\
vertices.  Qhull reports these events when they occur.  It stops when a\n\
concave ridge, flipped facet, or duplicate facet occurs.\n");
#if REALfloat
    qh_fprintf(fp, 9370, "\
\n\
Qhull is currently using single precision arithmetic.  The following\n\
will probably remove the precision problems:\n\
  - recompile qhull for realT precision(#define REALfloat 0 in user.h).\n");
#endif
    if (qh DELAUNAY && !qh SCALElast && qh MAXabs_coord > 1e4)
      qh_fprintf(fp, 9371, "\
\n\
When computing the Delaunay triangulation of coordinates > 1.0,\n\
  - use 'Qbb' to scale the last coordinate to [0,m] (max previous coordinate)\n");
    if (qh DELAUNAY && !qh ATinfinity)
      qh_fprintf(fp, 9372, "\
When computing the Delaunay triangulation:\n\
  - use 'Qz' to add a point at-infinity.  This reduces precision problems.\n");

    qh_fprintf(fp, 9373, "\
\n\
If you need triangular output:\n\
  - use option 'Qt' to triangulate the output\n\
  - use option 'QJ' to joggle the input points and remove precision errors\n\
  - use option 'Ft'.  It triangulates non-simplicial facets with added points.\n\
\n\
If you must use 'Q0',\n\
try one or more of the following options.  They can not guarantee an output.\n\
  - use 'QbB' to scale the input to a cube.\n\
  - use 'Po' to produce output and prevent partitioning for flipped facets\n\
  - use 'V0' to set min. distance to visible facet as 0 instead of roundoff\n\
  - use 'En' to specify a maximum roundoff error less than %2.2g.\n\
  - options 'Qf', 'Qbb', and 'QR0' may also help\n",
               qh DISTround);
    qh_fprintf(fp, 9374, "\
\n\
To guarantee simplicial output:\n\
  - use option 'Qt' to triangulate the output\n\
  - use option 'QJ' to joggle the input points and remove precision errors\n\
  - use option 'Ft' to triangulate the output by adding points\n\
  - use exact arithmetic (see \"Imprecision in Qhull\", qh-impre.htm)\n\
");
  }
} /* printhelp_degenerate */


/* qh_printhelp_narrowhull( minangle )
     Warn about a narrow hull

  notes:
    Alternatively, reduce qh_WARNnarrow in user.h

*/
void qh_printhelp_narrowhull(FILE *fp, realT minangle) {

    qh_fprintf(fp, 9375, "qhull precision warning: \n\
The initial hull is narrow (cosine of min. angle is %.16f).\n\
A coplanar point may lead to a wide facet.  Options 'QbB' (scale to unit box)\n\
or 'Qbb' (scale last coordinate) may remove this warning.  Use 'Pp' to skip\n\
this warning.  See 'Limitations' in qh-impre.htm.\n",
          -minangle);   /* convert from angle between normals to angle between facets */
} /* printhelp_narrowhull */

/* qh_printhelp_singular
      prints descriptive message for singular input
*/
void qh_printhelp_singular(FILE *fp) {
  facetT *facet;
  vertexT *vertex, **vertexp;
  realT min, max, *coord, dist;
  int i,k;

  qh_fprintf(fp, 9376, "\n\
The input to qhull appears to be less than %d dimensional, or a\n\
computation has overflowed.\n\n\
Qhull could not construct a clearly convex simplex from points:\n",
           qh hull_dim);
  qh_printvertexlist(fp, "", qh facet_list, NULL, qh_ALL);
  if (!qh_QUICKhelp)
    qh_fprintf(fp, 9377, "\n\
The center point is coplanar with a facet, or a vertex is coplanar\n\
with a neighboring facet.  The maximum round off error for\n\
computing distances is %2.2g.  The center point, facets and distances\n\
to the center point are as follows:\n\n", qh DISTround);
  qh_printpointid(fp, "center point", qh hull_dim, qh interior_point, -1);
  qh_fprintf(fp, 9378, "\n");
  FORALLfacets {
    qh_fprintf(fp, 9379, "facet");
    FOREACHvertex_(facet->vertices)
      qh_fprintf(fp, 9380, " p%d", qh_pointid(vertex->point));
    zinc_(Zdistio);
    qh_distplane(qh interior_point, facet, &dist);
    qh_fprintf(fp, 9381, " distance= %4.2g\n", dist);
  }
  if (!qh_QUICKhelp) {
    if (qh HALFspace)
      qh_fprintf(fp, 9382, "\n\
These points are the dual of the given halfspaces.  They indicate that\n\
the intersection is degenerate.\n");
    qh_fprintf(fp, 9383,"\n\
These points either have a maximum or minimum x-coordinate, or\n\
they maximize the determinant for k coordinates.  Trial points\n\
are first selected from points that maximize a coordinate.\n");
    if (qh hull_dim >= qh_INITIALmax)
      qh_fprintf(fp, 9384, "\n\
Because of the high dimension, the min x-coordinate and max-coordinate\n\
points are used if the determinant is non-zero.  Option 'Qs' will\n\
do a better, though much slower, job.  Instead of 'Qs', you can change\n\
the points by randomly rotating the input with 'QR0'.\n");
  }
  qh_fprintf(fp, 9385, "\nThe min and max coordinates for each dimension are:\n");
  for (k=0; k < qh hull_dim; k++) {
    min= REALmax;
    max= -REALmin;
    for (i=qh num_points, coord= qh first_point+k; i--; coord += qh hull_dim) {
      maximize_(max, *coord);
      minimize_(min, *coord);
    }
    qh_fprintf(fp, 9386, "  %d:  %8.4g  %8.4g  difference= %4.4g\n", k, min, max, max-min);
  }
  if (!qh_QUICKhelp) {
    qh_fprintf(fp, 9387, "\n\
If the input should be full dimensional, you have several options that\n\
may determine an initial simplex:\n\
  - use 'QJ'  to joggle the input and make it full dimensional\n\
  - use 'QbB' to scale the points to the unit cube\n\
  - use 'QR0' to randomly rotate the input for different maximum points\n\
  - use 'Qs'  to search all points for the initial simplex\n\
  - use 'En'  to specify a maximum roundoff error less than %2.2g.\n\
  - trace execution with 'T3' to see the determinant for each point.\n",
                     qh DISTround);
#if REALfloat
    qh_fprintf(fp, 9388, "\
  - recompile qhull for realT precision(#define REALfloat 0 in libqhull.h).\n");
#endif
    qh_fprintf(fp, 9389, "\n\
If the input is lower dimensional:\n\
  - use 'QJ' to joggle the input and make it full dimensional\n\
  - use 'Qbk:0Bk:0' to delete coordinate k from the input.  You should\n\
    pick the coordinate with the least range.  The hull will have the\n\
    correct topology.\n\
  - determine the flat containing the points, rotate the points\n\
    into a coordinate plane, and delete the other coordinates.\n\
  - add one or more points to make the input full dimensional.\n\
");
    if (qh DELAUNAY && !qh ATinfinity)
      qh_fprintf(fp, 9390, "\n\n\
This is a Delaunay triangulation and the input is co-circular or co-spherical:\n\
  - use 'Qz' to add a point \"at infinity\" (i.e., above the paraboloid)\n\
  - or use 'QJ' to joggle the input and avoid co-circular data\n");
  }
} /* printhelp_singular */


/*-----------------------------------------
-user_memsizes- allocate up to 10 additional, quick allocation sizes
*/
void qh_user_memsizes (void) {

  /* qh_memsize (size); */
} /* user_memsizes */

#endif
qhull-2012.1/src/user_eg2/user_eg2.pro0000644000076400010400000000040011706621207020637 0ustar  bbarberAdministrators# -------------------------------------------------
# user_eg2.pro -- Qt project for Qhull demonstration using shared Qhull dll
# -------------------------------------------------

include(../qhull-app-shared.pri)

TARGET = user_eg2

SOURCES += user_eg2.c
qhull-2012.1/src/user_eg3/0000755000076400010400000000000011721063455016413 5ustar  bbarberAdministratorsqhull-2012.1/src/user_eg3/user_eg3.cpp0000644000076400010400000001072411710423630020630 0ustar  bbarberAdministrators#//! user_eg3.cpp -- Invoke rbox and qhull from C++

#include "RboxPoints.h"
#include "QhullError.h"
#include "QhullQh.h"
#include "QhullFacet.h"
#include "QhullFacetList.h"
#include "QhullLinkedList.h"
#include "QhullVertex.h"
#include "Qhull.h"

#include    /* for printf() of help message */
#include 

using std::cerr;
using std::cin;
using std::cout;
using std::endl;

using orgQhull::Qhull;
using orgQhull::QhullError;
using orgQhull::QhullFacet;
using orgQhull::QhullFacetList;
using orgQhull::QhullQh;
using orgQhull::RboxPoints;
using orgQhull::QhullVertex;
using orgQhull::QhullVertexSet;

int main(int argc, char **argv);
int user_eg3(int argc, char **argv);

char prompt[]= "\n\
user_eg3 -- demonstrate calling rbox and qhull from C++.\n\
\n\
  eg-100                       Run the example in qh-code.htm\n\
  rbox \"200 D4\" ...            Generate points from rbox\n\
  qhull \"d p\" ...              Run qhull and produce output\n\
  qhull-cout \"o\" ...           Run qhull and produce output to cout\n\
  facets                       Print facets when done\n\
\n\
For example\n\
  user_eg3 rbox qhull\n\
  user_eg3 rbox qhull d\n\
  user_eg3 rbox \"10 D2\"  \"2 D2\" qhull  \"s p\" facets\n\
\n\
";


/*--------------------------------------------
-user_eg3-  main procedure of user_eg3 application
*/
int main(int argc, char **argv) {

    if(argc==1){
        cout << prompt;
        return 1;
    }
    try{
        return user_eg3(argc, argv);
    }catch(QhullError &e){
        cerr << e.what() << std::endl;
        return e.errorCode();
    }
}//main

int user_eg3(int argc, char **argv)
{
    bool printFacets= false;
    if(strcmp(argv[1], "eg-100")==0){
        RboxPoints rbox;
        rbox.appendPoints("100");
        Qhull qhull;
        qhull.runQhull(rbox, "");
        QhullFacetList facets= qhull.facetList();
        cout << facets;
        return 0;
    }
    RboxPoints rbox;
    Qhull qhull;
    int readingRbox= 0;
    int readingQhull= 0;
    for(int i=1; i