From a459767912fcede5b3d60b3f25b7af865535066c Mon Sep 17 00:00:00 2001
From: Brad Barber <bradb@shore.net>
Date: Wed, 6 Jan 2010 23:58:34 -0500
Subject: [PATCH] qhull 2010.1 Moved qtpro/ and vcproj/ into project/ Updated
documentation for 2010.1 Add reviewed results of q_test and qhulltest Fixed
an error message
---
Announce.txt | 2 +-
README.txt | 240 +-
eg/q_test-ok.txt | 10935 ++++++++++++++++
eg/qhulltest-ok.txt | 1059 ++
html/qh-code.htm | 9 +-
html/qh-get.htm | 16 +-
html/trolltech2.rtf | 335 -
index.htm | 4 +-
{vcproj => project}/libqhull.vcproj | 0
{qtpro => project}/libqhull/libqhull.pro | 0
.../libqhullcpp/libqhullcpp.pro | 2 +
{qtpro => project}/qconvex/qconvex.pro | 2 +
{qtpro => project}/qdelaunay/qdelaunay.pro | 2 +
{qtpro => project}/qhalf/qhalf.pro | 2 +
{qtpro => project}/qhull-all.pro | 0
{vcproj => project}/qhull.sln | 0
{vcproj => project}/qhull.vcproj | 0
{qtpro => project}/qhull/qhull.pro | 2 +
{vcproj => project}/qhullcpp.vcproj | 0
{vcproj => project}/qhulltest.vcproj | 0
{qtpro => project}/qhulltest/qhulltest.pro | 2 +
{qtpro => project}/qvoronoi/qvoronoi.pro | 2 +
{vcproj => project}/rbox.vcproj | 0
{qtpro => project}/rbox/rbox.pro | 2 +
{qtpro => project}/user_eg/user_eg.pro | 2 +
{qtpro => project}/user_eg2/user_eg2.pro | 2 +
{vcproj => project}/user_eg3.vcproj | 0
{qtpro => project}/user_eg3/user_eg3.pro | 2 +
qhull.ilk | Bin 485320 -> 0 bytes
rbox.ilk | Bin 484968 -> 0 bytes
src/Changes.txt | 34 +-
src/global.c | 6 +-
src/poly2.c | 7 +-
user_eg3.ilk | Bin 982096 -> 0 bytes
34 files changed, 12242 insertions(+), 427 deletions(-)
create mode 100644 eg/q_test-ok.txt
create mode 100644 eg/qhulltest-ok.txt
delete mode 100644 html/trolltech2.rtf
rename {vcproj => project}/libqhull.vcproj (100%)
rename {qtpro => project}/libqhull/libqhull.pro (100%)
rename {qtpro => project}/libqhullcpp/libqhullcpp.pro (96%)
rename {qtpro => project}/qconvex/qconvex.pro (90%)
rename {qtpro => project}/qdelaunay/qdelaunay.pro (90%)
rename {qtpro => project}/qhalf/qhalf.pro (90%)
rename {qtpro => project}/qhull-all.pro (100%)
rename {vcproj => project}/qhull.sln (100%)
rename {vcproj => project}/qhull.vcproj (100%)
rename {qtpro => project}/qhull/qhull.pro (90%)
rename {vcproj => project}/qhullcpp.vcproj (100%)
rename {vcproj => project}/qhulltest.vcproj (100%)
rename {qtpro => project}/qhulltest/qhulltest.pro (96%)
rename {qtpro => project}/qvoronoi/qvoronoi.pro (90%)
rename {vcproj => project}/rbox.vcproj (100%)
rename {qtpro => project}/rbox/rbox.pro (90%)
rename {qtpro => project}/user_eg/user_eg.pro (90%)
rename {qtpro => project}/user_eg2/user_eg2.pro (90%)
rename {vcproj => project}/user_eg3.vcproj (100%)
rename {qtpro => project}/user_eg3/user_eg3.pro (94%)
delete mode 100644 qhull.ilk
delete mode 100644 rbox.ilk
delete mode 100644 user_eg3.ilk
diff --git a/Announce.txt b/Announce.txt
index 86a692b..549a044 100644
--- a/Announce.txt
+++ b/Announce.txt
@@ -1,5 +1,5 @@
- Qhull 2010.0.3 2010/01/05
+ Qhull 2010.1 2010/01/06
http://www.qhull.org
git@gitorious.org:qhull/qhull.git
diff --git a/README.txt b/README.txt
index 8637e94..95207ed 100644
--- a/README.txt
+++ b/README.txt
@@ -1,6 +1,6 @@
Name
- qhull, rbox 2010.0.3 2010/01/05
+ qhull, rbox 2010.1 2010/01/06
Convex hull, Delaunay triangulation, Voronoi diagrams, Halfspace intersection
@@ -10,12 +10,10 @@ Convex hull, Delaunay triangulation, Voronoi diagrams, Halfspace intersection
Available from:
<http://www.qhull.org>
- git@gitorious.org:qhull/qhull.git
- <http://savannah.nongnu.org/projects/qhull>
+ <git@gitorious.org:qhull/qhull.git>
Version 1 (simplicial only):
<http://www.qhull.org/download/qhull-1.0.tar.gz>
- <http://www.qhull.org/download/qhull.sit.hqx>
News and a paper:
<http://www.qhull.org/news>
@@ -41,7 +39,11 @@ 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.
+ self-contained. It comes with examples and test scripts.
+
+ Qhull's C++ interface uses the STL. The C++ test program is based on
+ QTestLib from Nokia's Qt Framework. For 2010, Qhull's C++ interface
+ may change without notice.
Qhull is copyrighted software. Please read COPYING.txt and REGISTER.txt
before using or distributing Qhull.
@@ -52,11 +54,7 @@ To cite Qhull, please use
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 Savannah at http://savannah.nongnu.org/projects/qhull/
-
-Qhull on Windows 95, 98, ME, NT, 2000, XP
+Qhull on Windows
The zip file contains rbox.exe, qhull.exe, qconvex.exe, qdelaunay.exe,
qhalf.exe, qvoronoi.exe, documentation files, and source files.
@@ -65,38 +63,47 @@ Qhull on Windows 95, 98, ME, NT, 2000, XP
- Unzip the files into a directory. You may use WinZip32 <www.hotfiles.com>
- Click on QHULL-GO
+ - If you use qhull a lot, consider using
+ Road Bash (www.qhull.org/bash) or Cygwin (www.cygwin.com),
- In Windows 95, the DOS window needs improvement.
- Increase the size of the screen font to 8x12.
- If the text is too dim, fix the screen colors with shareware (e.g., crt.exe)
- - If you use qhull a lot, consider using the Cygwin Unix shell (www.cygwin.com),
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'.
- - If an error occurs, Windows 95 sends the error to stdout instead of stderr
- - use 'TO xxx' to send normal output to xxx and error output to stdout
- 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 contribute to Qhull
-Compiling with cygwin on Windows NT, 2000, XP
+ Qhull is on Gitorious (http://gitorious.org:qhull, git@gitorious.org:qhull/qhull.git)
+
+ For internal documentation, see html/qh-code.htm
+
+Compiling with cygwin on Windows
- install cygwin [www.cygwin.com] with gcc, make, ar, and ln
- cd qhull/src
- make -f Makefile.txt
-Qhull on Unix (Debian)
-
- The gzip file, qhull.tar.gz, contains documentation and source files for
- qhull and rbox. It should compile on all Unix systems, including Debian.
- You may also use the source instructions below.
+Compiling with Qt on Windows or Unix
- To unpack the gzip file
- - tar zxf qhull.tar.gz
- - cd qhull
-
- Compile with the configure Makefile [R. Laboissiere]:
- - ./configure
- - make
+ Download Qt SDK from Nokia.
+ Start Qt Creator
+ Load project/qhull-all.pro
+ Build all
+Compiling on Windows
+
+ Qhull compiles as a console application in Visual C++ 5.0 at warning
+ level 3.
+
+ Visual C++ quickstart for qhull library, qhull.exe, qconvex.exe, etc.
+ - Load project/qhull.sln
+ - Build->Build all
+
Compiling the source distribution
The gzip file, qhull-src.tgz, contains documentation and source files for
@@ -106,7 +113,7 @@ Compiling the source distribution
- tar zxf qhull-src.tgz
- cd qhull
- Compiling with Makefile (i.e., Makefile.txt)
+ Compiling qhull and rbox with Makefile (i.e., Makefile.txt)
- cd src
- in Makefile, check the CC, CCOPTS1, PRINTMAN, and PRINTC defines
- the defaults are gcc and enscript
@@ -124,8 +131,10 @@ Compiling the source distribution
- 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 is gcc-2.95.1, you need to set flag -fno-strict-aliasing.
- - This flag is set by default for other versions [Karas, Krishnaswami]
+ - if your compiler is gcc-4.3, 4.2, 4.1 or 2.95.1, set flag -fno-strict-aliasing.
+ - This flag is set by default for other versions up to 4.0 [Karas, Krishnaswami]
+ - strict-aliasing appears to work ok for gcc-4.4
+ - See news/qhull-news.html#bugs for details
- 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"
@@ -147,52 +156,81 @@ Compiling the source distribution
- define MANDIR and BINDIR
- type 'make install'
-Compiling on Windows 95, 98, NT, 2000, XP
+Qhull on Unix (Debian)
- Qhull compiles as a console application in Visual C++ 5.0 at warning
- level 3.
+ [Jan 2009] Not available yet for Qhull 2010.1
- Visual C++ quickstart for qhull.exe only:
- - create a "Win32 console application" called "qhull"
+ The gzip file, qhull.tar.gz, contains documentation and source files for
+ qhull and rbox. It should compile on all Unix systems, including Debian.
+ You may also use the source instructions below.
+
+ To unpack the gzip file
+ - tar zxf qhull.tar.gz
+ - cd qhull
+
+ Compile with the configure Makefile [R. Laboissiere]:
+ - ./configure
+ - make
+
+If you need to create a custom build, create projects as follows.
+These instructions assume Visual C++, but similar ones also apply.
+
+ For qhull.exe and rbox.exe only:
+ - create a "console application" called "qhull"
- add the following files:
- geom.c geom2.c global.c io.c mem.c merge.c poly.c poly2.c libqhull.c
- qset.c stat.c unix.c user.c
- - create a "Win32 console application" called "rbox"
- - add rbox.c
+ geom.c geom2.c global.c io.c libqhull.c mem.c merge.c
+ poly.c poly2.c qset.c random.c stat.c unix.c
+ user.c usermem.c userprintf.c
+ - create a "console application" called "rbox"
+ - add rbox.c rboxlib.c
- Visual C++ quickstart for qhull library, qhull.exe, qconvex.exe, etc.
+ For all projects
- To simplify setting up lots of projects,
- create a temporary "Win32 console application" called "source"
- add all .c files from .../src/...
+ - add all .cpp files from .../cpp/...
- In Tools::Options::Tab
Set tab size to 8 and indent size to 2
- create a "Win32 console application" called "rbox"
- - move rbox.c from "qhull source"
+ - move rbox.c rboxlib.c from "qhull source"
- for Project:Settings..., Link
you only need the default libraries
- build the project
- - create a "Win32 static library" called "library"
+ - create a "Win32 static library" called "libqhull"
- move these files from "qhull source"
geom.c geom2.c global.c io.c mem.c merge.c poly.c poly2.c libqhull.c
- qset.c stat.c user.c
+ qset.c random.c rboxlib.c stat.c user.c usermem.c userprintf.c
- set the library file (use the same for debug and release)
- build the project
- create a "Win32 console application" called "qhull"
- Move unix.c from "qhull source"
- - Add the library file created by "library"
+ - Add the library file created by "libqhull"
- Qhull does not use other libraries
- create a "Win32 console application" called "qconvex"
- Move qconvex.c from "qhull source"
- - Copy the library file from "qhull"
+ - Copy the library file from "libqhull"
- do the same for qdelaun.c, qhalf, qvoronoi.c, user_eg.c, user_eg2.c
- - delete "qhull sources" since it is no longer needed
- - use Project:Settings to make any changes
- - use batch build to rebuild everything
+
+ - create a "Win32 dynamic library" called "libqhullcpp"
+ - Move cpp sources in cpp/*.cpp from "qhull source"
+ Do not move cpp/qhulltest, road/RoadTest.cpp, or user_eg3.cpp
+
+ - create a "Win32 console application" called "user_eg3"
+ - Move user_eg3 from "qhull source"
+ - Add the library file created by "libqhullcpp"
+
+ - create a "Win32 console application" called "qhulltest"
+ - Add everything in cpp/qhulltest
+ - Add road/RoadTest.cpp
+
+ - use Project:Settings to make any changes
+ - use batch build to rebuild everything
+ - delete "qhull sources" since it is no longer needed
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
@@ -218,11 +256,6 @@ Compiling on the Power Macintosh
Windows 95'. Instead of using SIOUX, Qhull may be embedded within an
application.
- Version 1 is available for Macintosh computers by download of qhull.sit.hqx
- It reads point coordinates from a standard file and returns output
- to a standard file. There is no graphical output.
-
-
Compiling on other machines
Some users have reported problems with compiling Qhull under Irix 5.1. It
@@ -258,6 +291,7 @@ src/
rbox.man // Unix man page
rbox.txt
rbox.c // source program
+ rboxlib.c
qhull consists of:
qhull.exe // Win32 executables (.zip only)
@@ -291,11 +325,16 @@ src/
user.h // header file of user definable constants
libqhull.h // header file for qhull
unix.c // Unix front end to qhull
- libqhull.c // Quickhull algorithm with partitioning
+ qconvex.c
+ qhalf.c
+ qdelaunay.c
+ qvoronoi.c
+ libqhull.c // Quickhull algorithm with partitioning
user.c // user re-definable functions
+ usermem.c
+ userprintf.c
user_eg.c // example of incorporating qhull into a user program
user_eg2.c // more complex example
- qhull_interface.cpp // call Qhull from C++
other source files:
qhull_a.h // include file for *.c
@@ -317,6 +356,99 @@ src/
stat.c // statistics
stat.h
+project/
+ projects for building Qhull
+ qhull.sln // Solution for Visual C++ 2005 and higher
+ qhull-all.pro // Project for Qt
+ */*.pro // Qt projects for each component
+ *.vcproj // Temporary Visual C++ projects
+
+cpp/
+ cpp interface to Qhull
+ Qhull.cpp // calls libqhull.c
+ Qhull.h
+ user_eg3.cpp // sample program
+
+ input classes
+ Coordinates.cpp
+ Coordinates.h
+ PointCoordinates.cpp
+ PointCoordinates.h
+ PointIterator.h
+ RboxPoints.cpp // calls rboxlib.c
+ RboxPoints.h
+
+ data structure classes
+ QhullFacet.cpp
+ QhullFacet.h
+ QhullHyperplane.cpp
+ QhullHyperplane.h
+ QhullPoint.cpp
+ QhullPoint.h
+ QhullQh.cpp
+ QhullQh.h
+ QhullStat.cpp
+ QhullStat.h
+
+ collection classes
+ QhullFacetList.cpp
+ 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
+
+ supporting classes
+ functionObjects.h
+ QhullError.cpp
+ QhullError.h
+ QhullEvent.cpp
+ QhullEvent.h
+ QhullLog.cpp
+ QhullLog.h
+ UsingLibQhull.cpp
+ UsingLibQhull.h
+
+cpp/qhulltest/
+ Tests for each class
+ Coordinates_test.cpp
+ 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
+ qhulltest.cpp
+ QhullVertexSet_test.cpp
+ QhullVertex_test.cpp
+ Qhull_test.cpp
+ RboxPoints_test.cpp
+ UsingLibQhull_test.cpp
+
+cpp/road/
+ Supporting base classes
+ RoadError.cpp
+ RoadError.h
+ RoadLogEvent.cpp
+ RoadLogEvent.h
+ RoadTest.cpp
+ RoadTest.h
+
Authors:
C. Bradford Barber Hannu Huhdanpaa
diff --git a/eg/q_test-ok.txt b/eg/q_test-ok.txt
new file mode 100644
index 0000000..d6d7486
--- /dev/null
+++ b/eg/q_test-ok.txt
@@ -0,0 +1,10935 @@
+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 Wed Jan 6 20:32:58 EST 2010 =====================
+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. 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
+0.9124763375291642 1.390833937612013 -0.4826674750136242
+-0.5764091147442416 0.565375258822974 -1.532352227508615
+-0.1847368907548404 1.250953879569599 1.183632828365285
+-1.673622343028246 0.4254952007805603 0.1339480758702938
+1.673622343028246 -0.4254952007805603 -0.1339480758702938
+0.1847368907548404 -1.250953879569599 -1.183632828365285
+0.5764091147442416 -0.565375258822974 1.532352227508615
+-0.9124763375291642 -1.390833937612013 0.4826674750136242
+4
+12
+-0.5486066141420023 -0.06994002902120682 0.8331501516894545 -1
+-0.5486066141420023 -0.06994002902120682 0.8331501516894545 -1
+0.7444427261367029 0.4127293393945192 0.5248423762474955 -1
+0.7444427261367029 0.4127293393945192 0.5248423762474955 -1
+-0.380573002749541 0.9081645691962864 -0.1743596995716651 -0.9999999999999999
+-0.380573002749541 0.9081645691962864 -0.1743596995716651 -0.9999999999999999
+0.380573002749541 -0.9081645691962864 0.1743596995716652 -1
+0.380573002749541 -0.9081645691962864 0.1743596995716652 -1
+0.5486066141420023 0.06994002902120682 -0.8331501516894545 -1
+0.5486066141420023 0.06994002902120682 -0.8331501516894545 -1
+-0.7444427261367029 -0.4127293393945192 -0.5248423762474955 -0.9999999999999999
+-0.7444427261367029 -0.4127293393945192 -0.5248423762474955 -0.9999999999999999
+
+8 vertices and 12 facets with normals:
+ -0.55 -0.07 0.83
+ -0.55 -0.07 0.83
+ 0.74 0.41 0.52
+ 0.74 0.41 0.52
+ -0.38 0.91 -0.17
+ -0.38 0.91 -0.17
+ 0.38 -0.91 0.17
+ 0.38 -0.91 0.17
+ 0.55 0.07 -0.83
+ 0.55 0.07 -0.83
+ -0.74 -0.41 -0.52
+ -0.74 -0.41 -0.52
+
+compute 3-d Delaunay triangulation
+seed: 1262827978
+input
+-0.284 -0.937 -0.613
+ 0.413 -0.668 0.0705
+ 0.14 0.477 0.291
+ 0.664 -0.849 0.757
+ 0.638 -0.135 -0.0323
+-0.809 0.26 0.855
+ 0.953 0.301 0.936
+ 0.392 0.976 -0.411
+3
+11
+-0.107122721676714 4.642012758895731 2.594014131991853
+-1.143432268087588 0.4673409800796297 -0.7502417401774856
+0.07333064744704747 -0.1241567200549079 1.069448053241315
+-0.4868070746917165 -0.2575061767744242 0.07616537619949211
+-0.7890761620126147 -1.242379665518076 0.7718258022524666
+-0.07233986329948129 -0.2903874968351289 0.7606758488539565
+0.3709567557844827 -0.1400449796017737 0.6901497505936796
+0.29614179471238 -0.1821717507120503 0.6544496282833386
+0.9785991222438674 0.6464362793808945 0.1386495456450708
+-0.1831649785520406 0.1182376164616292 -0.6542706771096271
+-0.2244108981135336 -0.134229004898564 -0.2398235548629705
+
+8 vertices and 17 facets with normals:
+ -0.21 0.13 -0.26 0.93
+ -0.02 0.87 0.49 -0.094
+ -0.75 0.31 -0.49 -0.33
+ -0.22 -0.04 -0.12 0.97
+ 0.062 -0.1 0.9 -0.42
+ 0.58 -0.13 -0.56 0.58
+ -0.65 -0.34 0.1 -0.67
+ -0.45 -0.72 0.44 -0.29
+-0.075 -0.3 0.79 -0.52
+ 0.39 -0.15 0.73 -0.53
+ 0.33 -0.2 0.73 -0.56
+ 0.76 0.5 0.11 -0.39
+ 0.82 -0.15 -0.51 0.21
+ -0.22 0.14 -0.77 -0.59
+ -0.37 -0.22 -0.39 -0.82
+ 0.76 -0.2 -0.58 0.22
+ 0.75 -0.39 -0.52 0.09
+
+find 3-d Delaunay triangle closest to [0.5, 0.5, ...]
+ 0.64 -0.13 -0.03
+ 0.14 0.48 0.29
+ 0.39 0.98 -0.41
+ 0.95 0.30 0.94
+
+save first triangulation and compute a new triangulation
+seed: 1262827979
+input
+-0.284 -0.674 0.898
+ -0.67 0.397 0.508
+ 0.234 -0.166 -0.351
+ 0.533 -0.0824 -0.204
+ 0.3 -0.0657 0.0746
+ 0.251 -0.397 0.87
+ -0.28 0.435 -0.229
+-0.235 0.154 -0.55
+3
+12
+-0.5318247905139241 -0.3789926222692477 0.09689119901402704
+14.18050906035933 21.00050920804131 10.19021100269239
+-0.2449106218239875 -0.1362278031044013 0.4796146924436587
+6.019740682265416 9.657431965223601 4.040955175646227
+-0.4938454908232109 -0.2962072559865082 0.09349513909119164
+-0.5160164454199128 -0.4430209930311082 0.06081216810905762
+1.125944674473549 -2.857784804064876 -0.2416058095684987
+0.5088821308870263 -1.206486240607808 0.08033463171387149
+0.2430625208148472 -1.117527237379534 0.1008723020956014
+0.3063880070395068 0.4482640498873325 -0.4440151470058987
+0.2353123883968058 0.3463716540105546 -0.2415762868804195
+-0.1774340847016189 -0.03860147353887491 -0.08688633319034281
+
+8 vertices and 16 facets with normals:
+ 0.31 0.36 -0.33 0.82
+ -0.64 -0.46 0.12 -0.6
+ 0.34 0.38 -0.29 0.81
+ 0.52 0.77 0.37 -0.018
+ -0.33 -0.18 0.64 -0.67
+ 0.35 0.55 -0.3 0.69
+ 0.5 0.8 0.33 -0.041
+ -0.64 -0.39 0.12 -0.65
+ 0.19 -0.45 -0.64 0.59
+ -0.61 -0.52 0.072 -0.59
+ 0.36 -0.92 -0.077 -0.16
+ 0.36 -0.86 0.057 -0.36
+ 0.19 -0.89 0.081 -0.4
+ 0.36 0.52 -0.52 -0.58
+ 0.34 0.5 -0.35 -0.72
+ -0.33 -0.072 -0.16 -0.93
+
+save second triangulation and restore first one
+
+8 vertices and 17 facets with normals:
+ -0.21 0.13 -0.26 0.93
+ -0.02 0.87 0.49 -0.094
+ -0.75 0.31 -0.49 -0.33
+ -0.22 -0.04 -0.12 0.97
+ 0.062 -0.1 0.9 -0.42
+ 0.58 -0.13 -0.56 0.58
+ -0.65 -0.34 0.1 -0.67
+ -0.45 -0.72 0.44 -0.29
+-0.075 -0.3 0.79 -0.52
+ 0.39 -0.15 0.73 -0.53
+ 0.33 -0.2 0.73 -0.56
+ 0.76 0.5 0.11 -0.39
+ 0.82 -0.15 -0.51 0.21
+ -0.22 0.14 -0.77 -0.59
+ -0.37 -0.22 -0.39 -0.82
+ 0.76 -0.2 -0.58 0.22
+ 0.75 -0.39 -0.52 0.09
+
+free first triangulation and restore second one.
+
+8 vertices and 16 facets with normals:
+ 0.31 0.36 -0.33 0.82
+ -0.64 -0.46 0.12 -0.6
+ 0.34 0.38 -0.29 0.81
+ 0.52 0.77 0.37 -0.018
+ -0.33 -0.18 0.64 -0.67
+ 0.35 0.55 -0.3 0.69
+ 0.5 0.8 0.33 -0.041
+ -0.64 -0.39 0.12 -0.65
+ 0.19 -0.45 -0.64 0.59
+ -0.61 -0.52 0.072 -0.59
+ 0.36 -0.92 -0.077 -0.16
+ 0.36 -0.86 0.057 -0.36
+ 0.19 -0.89 0.081 -0.4
+ 0.36 0.52 -0.52 -0.58
+ 0.34 0.5 -0.35 -0.72
+ -0.33 -0.072 -0.16 -0.93
+
+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: 26
+ 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: 17
+ Number of distance tests for qhull: 35
+ CPU seconds to compute hull (after input): 0
+
+
+Output completed. Verifying that all points are below 1.1e-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: 12
+
+Statistics for: | qhull s d Tcv v p
+
+ Number of points processed: 8
+ Number of hyperplanes created: 22
+ Number of facets in hull: 16
+ Number of distance tests for qhull: 29
+ CPU seconds to compute hull (after input): 0
+
+
+Output completed. Verifying that all points are below 8.1e-015 of
+all facets. Will make 96 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. 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:
+ -0.55 -0.07 0.83
+ -0.55 -0.07 0.83
+ 0.74 0.41 0.52
+ 0.74 0.41 0.52
+ -0.38 0.91 -0.17
+ -0.38 0.91 -0.17
+ 0.38 -0.91 0.17
+ 0.38 -0.91 0.17
+ 0.55 0.07 -0.83
+ 0.55 0.07 -0.83
+ -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
+ -0.65 -0.65 -0.41
+ -0.62 -0.62 -0.49
+ -0.1 -0.71 0.7
+ 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
+ -0.63 0.7 0.34
+ -0.65 0.66 -0.37
+ -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
+0.9124763375291642 1.390833937612013 -0.4826674750136242
+-0.5764091147442416 0.565375258822974 -1.532352227508615
+-0.1847368907548404 1.250953879569599 1.183632828365285
+-1.673622343028246 0.4254952007805603 0.1339480758702938
+1.673622343028246 -0.4254952007805603 -0.1339480758702938
+0.1847368907548404 -1.250953879569599 -1.183632828365285
+0.5764091147442416 -0.565375258822974 1.532352227508615
+-0.9124763375291642 -1.390833937612013 0.4826674750136242
+ -2 0 0
+ 2 0 0
+ 0 -2 0
+ 0 2 0
+ 0 0 -2
+ 0 0 2
+
+compute 2-d Delaunay triangulation
+seed: 1262827978
+
+8 vertices and 12 facets with normals:
+ 0.5 -0.0036 0.86
+ -0.94 -0.33 0.064
+ 0.56 0.14 0.81
+ -0.23 0.86 -0.45
+ 0.69 0.38 -0.62
+ -0.26 0.84 -0.47
+ -0.88 0.25 -0.39
+ -0.37 0.3 -0.88
+-0.025 -0.3 -0.95
+-0.096 -0.29 -0.95
+ 0.72 -0.6 0.34
+ -0.53 -0.53 -0.66
+2
+8
+-0.259496361687563 0.9528344385574261
+0.5490224770006654 0.3013148093005802
+-0.2750696212613971 0.8979367376368015
+-1.118619090455706 0.3190511096405528
+-0.2132915806472766 0.1722858731592264
+-0.01329395930930872 -0.1570034641305634
+-0.0502384878542752 -0.1520557268483896
+-0.397780133553935 -0.4034732257626989
+
+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
+19
+-0.259496361687563 0.9528344385574261
+-0.2750696212613971 0.8979367376368015
+-0.5353825561212637 -0.455971672228587
+0.7851077816595146 0.4040843218587615
+0.5190447766192479 0.3254714019535874
+0.84981005407999 -1.015913517586868
+0.4322617492664664 -0.456162908166885
+-0.322530648104052 -0.5508484793660541
+-1.244818200732448 -0.1645143912873466
+-0.7893133737607369 0.5450370815051274
+-0.7353291925675684 0.2569148861247563
+-0.2589451145556475 0.9595553589764398
+1.059639137937667 0.5235896578957147
+-0.2341685629474075 0.417508934673909
+-0.4394328223799044 0.2089462777768801
+0.1565429254891246 0.08483328287170187
+0.1161835094406035 -0.1623083804984112
+-0.4863784325856633 -0.4372754871757206
+-0.4419604743424794 -0.4395906521601979
+
+find Delaunay triangle closest to [0.5, 0.5, ...]
+ 0.36 0.87
+ 0.29 0.66
+ 0.64 -0.13
+
+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: 70
+ 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: 8
+
+Statistics for: user_eg Delaunay | qhull s d Tcv v p
+
+ Number of points processed: 8
+ Number of hyperplanes created: 19
+ Number of facets in hull: 12
+ Number of distance tests for qhull: 30
+ CPU seconds to compute hull (after input): 0
+
+
+Output completed. Verifying that all points are below 5.4e-015 of
+all facets. Will make 64 distance computations.
+
+Voronoi diagram by the convex hull of 14 points in 3-d:
+
+ Number of Voronoi regions: 14
+ Number of Voronoi vertices: 19
+
+Statistics for: user_eg Delaunay | qhull s d Tcv v p
+
+ Number of points processed: 14
+ Number of hyperplanes created: 49
+ Number of facets in hull: 24
+ Number of distance tests for qhull: 71
+ CPU seconds to compute hull (after input): 0
+
+
+Output completed. Verifying that all points are below 5.4e-015 of
+all facets. Will make 266 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.
+echo === check front ends ${d:-`date`} ==================
+date
+=== check front ends Wed Jan 6 20:32:58 EST 2010 ==================
+qconvex -
+
+qconvex- compute the convex hull
+ http://www.qhull.org 2010.0.3 2010/01/05
+
+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 2010.0.3 2010/01/05.
+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 2010.0.3 2010/01/05
+ 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 - 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): 1.5e-005
+
+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
+0.2135848119563836 0.1168704340428168 0.9699086708284445 -0.09806074564261894
+0.08553875579270354 -0.8316435307282576 -0.5486822022403076 -0.1234144150397865
+-0.749541668500822 -0.02779445272382557 -0.6613733859014792 -0.2159556159595279
+0.3120013537900506 0.9498158823230657 -0.02247097950761923 -0.02453689035981484
+
+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 QR1262827979
+
+ 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: 98328
+ Number of merged facets: 2036
+ CPU seconds to compute hull (after input): 6.2e-005
+ 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): 1.5e-005
+ Approximate facet area: 12
+ Approximate volume: 1
+
+
+At 20:32:59 & 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 20:32:59 & 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 20:32:59 & 1.5e-005 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 20:32:59 & 1.5e-005 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 20:32:59 & 1.5e-005 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 2010.0.3 2010/01/05:
+ run-id 768959753
+qvoronoi -
+
+qvoronoi- compute the Voronoi diagram
+ http://www.qhull.org 2010.0.3 2010/01/05
+
+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
+ Qt - triangulated output
+ QJ - joggled input instead of merged facets
+
+Qhull control options:
+ Qz - add point-at-infinity to Voronoi diagram
+ QJn - randomly joggle input in range [-n,n]
+ 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 2010.0.3 2010/01/05.
+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 QJoggle Qsearch_1st Qtriangulate 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 2010.0.3 2010/01/05
+ input (stdin): dimension, number of points, point coordinates
+ comments start with a non-numeric character
+
+options (qvoronoi.htm):
+ Qu - compute furthest-site Voronoi diagram
+ 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)
+ 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 G1 d D2 | qvoronoi QJ 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 0.7071067811865476 -0.7071067811865476 -0.3535533905932738
+5 0 1 -0.7071067811865476 -0.7071067811865476 -0.3535533905932738
+5 0 2 -0.7071067811865476 0.7071067811865476 -0.3535533905932738
+5 0 4 0.7071067811865476 0.7071067811865476 -0.3535533905932738
+
+Voronoi ridge statistics
+ 4 bounded ridges
+ 0 max. distance of midpoint to ridge
+ 4 bounded ridges with ok normal
+ 0 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: 160
+ Number of merged facets: 3
+ CPU seconds to compute hull (after input): 0
+
+rbox c G1 d D2 | qvoronoi QJ p
+2
+10
+-2.572789203902914e-011 1.749999999802917
+-2.0546373700981e-011 -1.750000000331276
+0.5833333333083517 -0.5833333333052267
+1.862263126909194e-011 -7.815055220092851e-011
+1.750000000002628 3.498097972106761e-011
+0.5833333333132078 0.5833333333796981
+-0.5833333332888888 0.5833333333317836
+-7.592296236147433e-011 -7.815050692933325e-011
+-1.750000000049026 2.293199654852279e-011
+-0.5833333333977308 -0.583333333322986
+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 2010.0.3 2010/01/05
+
+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 2010.0.3 2010/01/05.
+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 2010.0.3 2010/01/05
+ 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: 160
+ 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
+-7.74859240079281e-011 -0.5000000000743411
+2.849349704487492e-011 0.49999999991804
+-0.5000000000721135 -1.373719891421591e-011
+0.5000000000148132 7.166044474310068e-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: 260
+ Number of facets in hull: 86
+ Number of distance tests for qhull: 1726
+ Number of distance tests for merging: 2755
+ Number of distance tests for checking: 1348
+ Number of merged facets: 151
+ 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 2010.0.3 2010/01/05
+
+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 2010.0.3 2010/01/05.
+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 2010.0.3 2010/01/05
+ 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 0.5000000000000001
+ 0 0 0.5000000000000001
+ 0 0.5000000000000001 0
+ 0 0.5000000000000001 0
+-0.5000000000000001 0 0
+-0.5000000000000001 0 0
+0.5000000000000001 0 0
+0.5000000000000001 0 0
+ 0 -0.5000000000000001 0
+ 0 -0.5000000000000001 0
+ 0 0 -0.5000000000000001
+ 0 0 -0.5000000000000001
+
+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 Wed Jan 6 20:33:00 EST 2010
+rbox 1000 W0 | qhull QR2 QJ s Fs Tv
+10 3 1000 144 284 144 284 0 0 33 0
+2 5.045982607091334e-011 -5.045982607091334e-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: 33563
+ CPU seconds to compute hull (after input): 1.5e-005
+ 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 -1.036131500307862e-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
+
+
+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: 83897
+ 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): 3.1e-005
+ 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: 41366
+ Number of distance tests for merging: 162691
+ Number of distance tests for checking: 10420
+ Number of merged facets: 2809
+ CPU seconds to compute hull (after input): 4.6e-005
+ 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
+ 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 | 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
+ 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): 3.1e-005
+ 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): 6.2e-005
+ 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): 0.000109
+ 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: 182077
+ 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): 3.1e-005
+ 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): 9.3e-005
+ 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. Wed Jan 6 20:33:01 EST 2010
+qhull <<EOF
+
+Convex hull of 4 points in 2-d:
+
+ Number of vertices: 3
+ Number of facets: 3
+
+Statistics for: #;laskdjf | qhull
+
+ Number of points processed: 3
+ Number of hyperplanes created: 4
+ Number of distance tests for qhull: 9
+ CPU seconds to compute hull (after input): 0
+
+qhull <<EOF
+
+Convex hull of 4 points in 2-d:
+
+ Number of vertices: 3
+ Number of facets: 3
+
+Statistics for: #;laskdjf | qhull
+
+ Number of points processed: 3
+ Number of hyperplanes created: 4
+ Number of distance tests for qhull: 9
+ CPU seconds to compute hull (after input): 0
+
+QH7073 qhull warning: instead of 4 2-dimensional points, input contains
+4 points and 1 extra coordinates. Line 2 is the first
+point, line 1 is the first comment, line 2 is the first long line. Continue with 4 points.
+qhull <<EOF
+QH7073 qhull warning: instead of 4 2-dimensional points, input contains
+3 points and 1 extra coordinates. Line 2 is the first
+point, line 1 is the first comment, line 2 is the first long line. Continue with 3 points.
+QH6013 qhull input error: input is less than 2-dimensional since it has the same x coordinate
+
+While executing: #;laskdjf | qhull
+Options selected for Qhull 2010.0.3 2010/01/05:
+ run-id 768993367 _pre-merge _zero-centrum _max-width 2
+ Error-roundoff 1.7e-015 _one-merge 8.6e-015 _near-inside 4.3e-014
+ Visible-distance 3.4e-015 U-coplanar-distance 3.4e-015
+ Width-outside 6.9e-015 _wide-facet 2.1e-014
+qhull <<EOF
+QH7073 qhull warning: instead of 4 2-dimensional points, input contains
+3 points and 1 extra coordinates. Line 3 is the first
+point, line 2 is the first comment, line 3 is the first short
+line, line 4 is the first long line. Continue with 3 points.
+QH6013 qhull input error: input is less than 2-dimensional since it has the same x coordinate
+
+While executing: #;laskdjf | qhull
+Options selected for Qhull 2010.0.3 2010/01/05:
+ run-id 768993367 _pre-merge _zero-centrum _max-width 2
+ Error-roundoff 1.7e-015 _one-merge 8.6e-015 _near-inside 4.3e-014
+ Visible-distance 3.4e-015 U-coplanar-distance 3.4e-015
+ Width-outside 6.9e-015 _wide-facet 2.1e-014
+qhull <<EOF
+
+Convex hull of 4 points in 2-d:
+
+ Number of vertices: 3
+ Number of facets: 3
+
+Statistics for: | qhull
+
+ Number of points processed: 3
+ Number of hyperplanes created: 4
+ Number of distance tests for qhull: 9
+ CPU seconds to compute hull (after input): 0
+
+qhull d Qz <<EOF
+
+Delaunay triangulation by the convex hull of 5 points in 3-d:
+
+ Number of input sites and at-infinity: 5
+ Number of Delaunay regions: 1
+ Number of non-simplicial Delaunay regions: 1
+
+Statistics for: | qhull d Qz
+
+ Number of points processed: 5
+ Number of hyperplanes created: 7
+ Number of facets in hull: 5
+ Number of distance tests for qhull: 6
+ 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
+
+QH7073 qhull warning: instead of 5 2-dimensional points, input contains
+4 points and 1 extra coordinates. Line 1 is the first
+point, line 1 is the first long line. Continue with 4 points.
+qhull d Q8 Qz <<EOF
+
+Delaunay triangulation by the convex hull of 5 points in 3-d:
+
+ Number of input sites and at-infinity: 5
+ Number of Delaunay regions: 1
+ Number of non-simplicial Delaunay regions: 1
+
+Statistics for: | qhull d Q8 Qz
+
+ Number of points processed: 5
+ Number of hyperplanes created: 7
+ Number of facets in hull: 5
+ Number of distance tests for qhull: 6
+ 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
+
+QH7073 qhull warning: instead of 5 2-dimensional points, input contains
+4 points and 1 extra coordinates. Line 1 is the first
+point, line 1 is the first long line. Continue with 4 points.
+rbox d h | qhull Fd FV n FD Tcv | qhull Fd H Fp Tcv
+
+Output completed. Verifying that all points are below outer planes of
+all facets. Will make 48 distance computations.
+3
+6
+ 0 0 0.5000000000000001
+ 0 0.5000000000000001 0
+-0.5000000000000001 0 0
+0.5000000000000001 0 0
+ 0 -0.5000000000000001 0
+ 0 0 -0.5000000000000001
+
+Output completed. Verifying that all points are below outer planes of
+all facets. Will make 48 distance computations.
+rbox 10 h | qhull Fd FD p Tcv | qhull Fd d Tcv
+
+Output completed. Verifying that all points are below 1.7e-015 of
+all facets. Will make 140 distance computations.
+
+Delaunay triangulation by the convex hull of 9 points in 4-d:
+
+ Number of input sites: 9
+ Number of Delaunay regions: 11
+
+Statistics for: rbox 10 h | qhull Fd FD p Tcv | qhull Fd d Tcv
+
+ Number of points processed: 9
+ Number of hyperplanes created: 34
+ Number of facets in hull: 22
+ Number of distance tests for qhull: 46
+ CPU seconds to compute hull (after input): 0
+
+
+Output completed. Verifying that all points are below 2.5e-015 of
+all facets. Will make 99 distance computations.
+echo === check rbox ${d:-`date`}
+date
+=== check rbox Wed Jan 6 20:33:01 EST 2010
+rbox 3 n D2
+2
+3
+0.2234321234034674 0.2236923805658635
+-0.4021654933711192 -0.1954478539484068
+0.1079163058734651 -0.2506519423338137
+rbox 3 D2
+2 rbox 3 D2
+3
+-0.3570490315156514 0.07692619792830777
+-0.1013959339832849 -0.1614655765345931
+0.2480525339469803 0.01893219260399434
+rbox 3 h D2
+rbox 3 h D2
+begin
+ 3 3 real
+ 1 0.16093073846859 -0.2370837309743126
+ 1 0.3337314574362072 0.02459860548805316
+ 1 0.4287583324394732 0.1412860417191741
+end
+hull
+rbox 3 z D2
+2 rbox 3 z D2
+3
+696870 290489
+252081 728918
+932465 -69056
+rbox 3 z h D2
+rbox 3 z h D2
+begin
+ 3 3 integer
+1 -951655 -464136
+1 -741320 630989
+1 -964370 -171508
+end
+hull
+rbox 3 B10 D2
+2 rbox 3 B10 D2
+3
+6.077775206489279 9.167769643634344
+2.704250554278727 -9.661033665445665
+7.007182209759188 9.711266327380452
+rbox 3 z B10 D2
+2 rbox 3 z B10 D2
+3
+5 2
+5 -1
+3 9
+rbox 4 L2 r D2
+2 rbox 4 L2 r D2
+6
+ 0.5 0
+0.1736481776669304 0.1187823492277694
+0.1736481776669304 -0.1187823492277694
+-0.1736481776669304 0.1187823492277694
+-0.1736481776669304 -0.1187823492277694
+ -0.5 0
+rbox 8 L2 D2
+2 rbox 8 L2 D2
+8
+-9.037112801233254e-006 -0.1339745961747267
+-0.4680200990905804 0.01769241704257363
+-0.05424246984329754 -0.1325023897522756
+0.0751966408142334 -0.1311433207603373
+0.1915694083864337 0.1154536646477271
+0.4772264523261766 0.01275495170842944
+-0.4048291575354194 0.04836693717712182
+0.3401207718037282 -0.07435635943071239
+rbox 4 L4 r D3
+3 rbox 4 L4 r D3
+12
+ 0.5 0 0
+ 0.25 0 0.04782181019473443
+ 0.25 0 -0.04782181019473443
+3.061515884555943e-017 0.5 0
+1.530757942277972e-017 0.25 0.04782181019473443
+1.530757942277972e-017 0.25 -0.04782181019473443
+ -0.5 6.123031769111886e-017 0
+ -0.25 3.061515884555943e-017 0.04782181019473443
+ -0.25 3.061515884555943e-017 -0.04782181019473443
+-9.184547653667829e-017 -0.5 0
+-4.592273826833915e-017 -0.25 0.04782181019473443
+-4.592273826833915e-017 -0.25 -0.04782181019473443
+rbox 4 L4 s D5 W1e-3
+5 rbox 4 L4 s D5 W1e-3
+4
+-0.1779876601833929 -0.1311655069863711 0.09099061083332424 -0.0147197628642461 0.04910076644488379
+0.08530477699633815 0.08551065958609008 0.2073152333839906 -0.05556059038062113 0.04824638578429845
+-0.2043906348252541 0.01359444539903208 0.07833891569611257 -0.2253375927975145 0.03863248544102459
+0.07678497944972421 0.03657959246981073 0.1769587053753909 0.142314245066564 -0.04874898497507386
+rbox y
+3 rbox y
+4
+-0.3062920647731908 0.1492658412542808 -0.2890111205997049
+-0.4099055704752966 -0.2829236833219637 -0.09834729097629645
+0.07707741817187278 0.4401626986825492 -0.1855306003107974
+-0.2128018845923262 0.4387234094913335 -0.3756640258949847
+rbox 10 M3,4
+3 rbox 10 M3,4
+10
+ 0 0 0
+ 3 4 0
+ 6 8 0
+ -4 3 0
+ -1 7 0
+ 2 11 0
+ -8 6 0
+ -5 10 0
+ -2 14 0
+ 0 0 5
+rbox 10 L2 s D3 | qhull Tcv
+
+Convex hull of 10 points in 3-d:
+
+ Number of vertices: 10
+ Number of facets: 16
+
+Statistics for: rbox 10 L2 s D3 | qhull Tcv
+
+ Number of points processed: 10
+ Number of hyperplanes created: 29
+ Number of distance tests for qhull: 50
+ CPU seconds to compute hull (after input): 0
+
+
+Output completed. Verifying that all points are below 1.5e-015 of
+all facets. Will make 160 distance computations.
+rbox 10 L4 s W1e-3 D3 | qhull Tcv
+
+Convex hull of 10 points in 3-d:
+
+ Number of vertices: 10
+ Number of facets: 16
+
+Statistics for: rbox 10 L4 s W1e-3 D3 | qhull Tcv
+
+ Number of points processed: 10
+ Number of hyperplanes created: 27
+ Number of distance tests for qhull: 43
+ CPU seconds to compute hull (after input): 0
+
+
+Output completed. Verifying that all points are below 1.9e-015 of
+all facets. Will make 160 distance computations.
+rbox 10 L6 D3 | qhull Tcv
+
+Convex hull of 10 points in 3-d:
+
+ Number of vertices: 10
+ Number of facets: 16
+
+Statistics for: rbox 10 L6 D3 | qhull Tcv
+
+ Number of points processed: 10
+ Number of hyperplanes created: 29
+ Number of distance tests for qhull: 48
+ CPU seconds to compute hull (after input): 0
+
+
+Output completed. Verifying that all points are below 1.7e-015 of
+all facets. Will make 160 distance computations.
+rbox 10 L1.1 s D4 | qhull Tcv
+
+Convex hull of 10 points in 4-d:
+
+ Number of vertices: 10
+ Number of facets: 26
+
+Statistics for: rbox 10 L1.1 s D4 | qhull Tcv
+
+ Number of points processed: 10
+ Number of hyperplanes created: 44
+ Number of distance tests for qhull: 53
+ CPU seconds to compute hull (after input): 0
+
+
+Output completed. Verifying that all points are below 2.4e-015 of
+all facets. Will make 260 distance computations.
+rbox y r 100 W0 O0.5 | qhull s p Tcv
+3
+4
+ 1 0.5 0.5
+ 0.5 1 0.5
+ 0.5 0.5 1
+ 0 0 0
+
+Convex hull of 104 points in 3-d:
+
+ Number of vertices: 4
+ Number of facets: 4
+
+Statistics for: rbox y r 100 W0 O0.5 | qhull s p Tcv
+
+ Number of points processed: 4
+ Number of hyperplanes created: 5
+ Number of distance tests for qhull: 1101
+ CPU seconds to compute hull (after input): 0
+
+
+Output completed. Verifying that all points are below outer planes of
+all facets. Will make 416 distance computations.
+rbox x r 100 W0 O0.5 | qhull s Tcv
+
+Convex hull of 100 points in 3-d:
+
+ Number of vertices: 27
+ Number of facets: 35
+ Number of non-simplicial facets: 4
+
+Statistics for: rbox x r 100 W0 O0.5 | qhull s Tcv
+
+ Number of points processed: 27
+ Number of hyperplanes created: 77
+ Number of distance tests for qhull: 1287
+ Number of distance tests for merging: 779
+ Number of distance tests for checking: 905
+ Number of merged facets: 15
+ CPU seconds to compute hull (after input): 0
+
+
+Output completed. Verifying that all points are below outer planes of
+all facets. Will make 3500 distance computations.
+rbox 12 D8 | qhull Tcv
+
+Convex hull of 12 points in 8-d:
+
+ Number of vertices: 12
+ Number of facets: 92
+
+Statistics for: rbox 12 D8 | qhull Tcv
+
+ Number of points processed: 12
+ Number of hyperplanes created: 132
+ Number of distance tests for qhull: 91
+ 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 7.9e-015 of
+all facets. Will make 1104 distance computations.
+rbox 12 D9 | qhull Tcv
+
+Convex hull of 12 points in 9-d:
+
+ Number of vertices: 12
+ Number of facets: 70
+
+Statistics for: rbox 12 D9 | qhull Tcv
+
+ Number of points processed: 12
+ Number of hyperplanes created: 89
+ Number of distance tests for qhull: 47
+ 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 9e-015 of
+all facets. Will make 840 distance computations.
+rbox 1000 D4 | qhull s i A-0.97 C0.2 A0.7 Tcv
+48
+117 111 263 638
+117 263 111 146
+117 263 146 638
+117 146 111 638
+118 111 771 456
+118 111 146 638
+118 146 111 456
+118 771 146 456
+118 771 430 465
+118 771 465 638
+118 771 111 638
+118 146 771 638
+118 465 430 638
+118 430 771 638
+119 771 263 299
+119 430 465 638
+119 111 263 771
+119 771 430 638
+119 465 299 638
+119 263 111 638
+119 430 771 299
+119 111 771 638
+119 299 263 638
+119 430 299 465
+120 430 771 465
+120 299 465 638
+120 263 771 299
+120 146 263 638
+120 299 430 465
+120 465 771 638
+120 263 146 299
+120 771 263 456
+120 299 771 456
+120 771 430 299
+120 771 146 638
+120 146 771 299
+120 263 299 456
+120 263 299 638
+121 111 146 456
+121 146 263 299
+121 771 299 456
+121 771 146 299
+121 263 111 771
+121 146 771 456
+121 299 263 456
+121 111 263 146
+121 771 111 456
+121 263 771 456
+
+Convex hull of 1000 points in 4-d:
+
+ Number of vertices: 9
+ Number of facets: 5
+ Number of non-simplicial facets: 4
+
+Statistics for: rbox 1000 D4 | qhull s i A-0.97 C0.2 A0.7 Tcv
+
+ Number of points processed: 116
+ Number of hyperplanes created: 2284
+ Number of distance tests for qhull: 518897
+ Number of distance tests for merging: 76094
+ Number of distance tests for checking: 5989
+ Number of merged facets: 1889
+ CPU seconds to compute hull (after input): 4.7e-005
+ Maximum distance of point above facet: 0.07
+ Maximum distance of vertex below facet: -0.92 (0.6x)
+
+
+Output completed. Verifying that all points are below outer planes of
+all facets. Will make 5000 distance computations.
+rbox 3 D2 | qhull Qb0B1:-2 p
+2
+3
+ -0.5 -2
+-0.1839506649197531 -0.1614655765345931
+0.2480525339469803 -1.552736350137872
+rbox 100 r D2 | qhull Pd0:0.7 PD0:0.8 n Tcv
+3
+6
+0.7501110696304588 0.6613118653236527 -0.4997532801828658
+0.7071067811865485 0.7071067811865467 -0.4997532801828658
+0.7501110696304542 -0.6613118653236579 -0.4997532801828658
+0.7901550123756913 0.6129070536529753 -0.4997532801828658
+0.7901550123756885 -0.6129070536529789 -0.4997532801828659
+0.707106781186544 -0.707106781186551 -0.4997532801828657
+
+Output completed. Verifying that all points are below 1.3e-015 of
+all facets. Will make 600 distance computations.
+rbox 1000 s | qhull C0.05 Tcv
+
+Convex hull of 1000 points in 3-d:
+
+ Number of vertices: 48
+ Number of facets: 26
+ Number of non-simplicial facets: 26
+
+Statistics for: rbox 1000 s | qhull C0.05 Tcv
+
+ Number of points processed: 1000
+ Number of hyperplanes created: 5545
+ Number of distance tests for qhull: 55680
+ Number of distance tests for merging: 100391
+ Number of distance tests for checking: 6790
+ Number of merged facets: 1970
+ CPU seconds to compute hull (after input): 3.1e-005
+ Maximum distance of vertex below facet: -0.21 (1.4x)
+
+
+Output completed. Verifying that all points are below outer planes of
+all facets. Will make 26000 distance computations.
+rbox 1000 s t | qhull Qm C0.05 Tcv
+
+Convex hull of 1000 points in 3-d:
+
+ Number of vertices: 48
+ Number of facets: 26
+ Number of non-simplicial facets: 26
+
+Statistics for: rbox 1000 s t1262827982 | qhull Qm C0.05 Tcv
+
+ Number of points processed: 1000
+ Number of hyperplanes created: 5484
+ Number of distance tests for qhull: 56825
+ Number of distance tests for merging: 99361
+ Number of distance tests for checking: 6742
+ Number of merged facets: 1970
+ CPU seconds to compute hull (after input): 3.1e-005
+ Maximum distance of vertex below facet: -0.17 (1.2x)
+
+
+Output completed. Verifying that all points are below outer planes of
+all facets. Will make 26000 distance computations.
+rbox 500 D2 | qhull n A-0.95 C0.1 Tcv
+3
+4
+0.004814116480453834 0.9999884120741163 -0.4852084337990874
+-0.9999815737204624 -0.00607060289818463 -0.4913197370926179
+-0.006423098021811922 -0.9999793716931376 -0.4958250456626818
+0.9999972817907392 0.002331611273993356 -0.4974344499395051
+
+Output completed. Verifying that all points are below outer planes of
+all facets. Will make 2000 distance computations.
+rbox 500 s P1,1,1 | qhull QgG0 Pp Tcv
+
+Convex hull of 500 points in 3-d:
+
+ Number of vertices: 226
+ Number of facets: 448
+ Number of 'good' facets: 340
+
+Statistics for: rbox 500 s P1,1,1 | qhull QgG0 Pp Tcv
+
+ Number of points processed: 294
+ Number of hyperplanes created: 1612
+ Number of distance tests for qhull: 9968
+ CPU seconds to compute hull (after input): 0
+
+
+rbox d | qhull m
+{
+Polygon[{{ 0.00000000, 0.50000000, 0.00000000},
+{ 0.00000000, 0.00000000, 0.50000000},
+{ -0.50000000, 0.00000000, 0.00000000}}],
+Polygon[{{ 0.00000000, 0.00000000, 0.50000000},
+{ 0.00000000, 0.50000000, 0.00000000},
+{ 0.50000000, 0.00000000, 0.00000000}}],
+Polygon[{{ 0.00000000, 0.00000000, -0.50000000},
+{ 0.00000000, 0.50000000, 0.00000000},
+{ -0.50000000, 0.00000000, 0.00000000}}],
+Polygon[{{ 0.00000000, 0.50000000, 0.00000000},
+{ 0.00000000, 0.00000000, -0.50000000},
+{ 0.50000000, 0.00000000, 0.00000000}}],
+Polygon[{{ 0.00000000, -0.50000000, 0.00000000},
+{ 0.00000000, 0.00000000, 0.50000000},
+{ 0.50000000, 0.00000000, 0.00000000}}],
+Polygon[{{ 0.00000000, 0.00000000, 0.50000000},
+{ 0.00000000, -0.50000000, 0.00000000},
+{ -0.50000000, 0.00000000, 0.00000000}}],
+Polygon[{{ 0.00000000, -0.50000000, 0.00000000},
+{ 0.00000000, 0.00000000, -0.50000000},
+{ -0.50000000, 0.00000000, 0.00000000}}],
+Polygon[{{ 0.00000000, 0.00000000, -0.50000000},
+{ 0.00000000, -0.50000000, 0.00000000},
+{ 0.50000000, 0.00000000, 0.00000000}}]}
+rbox d | qhull FM
+PLOT3D(POLYGONS(
+[[ 0.00000000, 0.50000000, 0.00000000],
+[ 0.00000000, 0.00000000, 0.50000000],
+[ -0.50000000, 0.00000000, 0.00000000]],
+[[ 0.00000000, 0.00000000, 0.50000000],
+[ 0.00000000, 0.50000000, 0.00000000],
+[ 0.50000000, 0.00000000, 0.00000000]],
+[[ 0.00000000, 0.00000000, -0.50000000],
+[ 0.00000000, 0.50000000, 0.00000000],
+[ -0.50000000, 0.00000000, 0.00000000]],
+[[ 0.00000000, 0.50000000, 0.00000000],
+[ 0.00000000, 0.00000000, -0.50000000],
+[ 0.50000000, 0.00000000, 0.00000000]],
+[[ 0.00000000, -0.50000000, 0.00000000],
+[ 0.00000000, 0.00000000, 0.50000000],
+[ 0.50000000, 0.00000000, 0.00000000]],
+[[ 0.00000000, 0.00000000, 0.50000000],
+[ 0.00000000, -0.50000000, 0.00000000],
+[ -0.50000000, 0.00000000, 0.00000000]],
+[[ 0.00000000, -0.50000000, 0.00000000],
+[ 0.00000000, 0.00000000, -0.50000000],
+[ -0.50000000, 0.00000000, 0.00000000]],
+[[ 0.00000000, 0.00000000, -0.50000000],
+[ 0.00000000, -0.50000000, 0.00000000],
+[ 0.50000000, 0.00000000, 0.00000000]]));
+rbox c D2 | qhull Tcv Q0
+
+Convex hull of 4 points in 2-d:
+
+ Number of vertices: 4
+ Number of facets: 4
+
+Statistics for: rbox c D2 | qhull Tcv Q0
+
+ 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
+
+
+Output completed. Verifying that all points are below 1.3e-015 of
+all facets. Will make 16 distance computations.
+rbox d D2 | qhull Tcv
+
+Convex hull of 4 points in 2-d:
+
+ Number of vertices: 4
+ Number of facets: 4
+
+Statistics for: rbox d D2 | qhull Tcv
+
+ 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 D3 | qhull Tcv Q0
+
+Convex hull of 8 points in 3-d:
+
+ Number of vertices: 8
+ Number of facets: 12
+
+Statistics for: rbox c D3 | qhull Tcv Q0
+
+ Number of points processed: 8
+ Number of hyperplanes created: 17
+ Number of distance tests for qhull: 35
+ CPU seconds to compute hull (after input): 0
+
+
+precision problems (corrected unless 'Q0' or an error)
+ 12 coplanar half ridges in output
+ 6 coplanar horizon facets for new vertices
+
+Output completed. Verifying that all points are below 2.1e-015 of
+all facets. Will make 96 distance computations.
+rbox d D3 | qhull Tcv
+
+Convex hull of 6 points in 3-d:
+
+ Number of vertices: 6
+ Number of facets: 8
+
+Statistics for: rbox d D3 | qhull Tcv
+
+ 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 c D4 | qhull Tcv Q0
+
+Convex hull of 16 points in 4-d:
+
+ Number of vertices: 16
+ Number of facets: 44
+
+Statistics for: rbox c D4 | qhull Tcv Q0
+
+ Number of points processed: 16
+ Number of hyperplanes created: 62
+ Number of distance tests for qhull: 163
+ CPU seconds to compute hull (after input): 0
+
+
+precision problems (corrected unless 'Q0' or an error)
+ 80 coplanar half ridges in output
+ 32 coplanar horizon facets for new vertices
+
+Output completed. Verifying that all points are below 3e-015 of
+all facets. Will make 704 distance computations.
+rbox d D4 | qhull Tcv
+
+Convex hull of 8 points in 4-d:
+
+ Number of vertices: 8
+ Number of facets: 16
+
+Statistics for: rbox d D4 | qhull Tcv
+
+ Number of points processed: 8
+ Number of hyperplanes created: 20
+ Number of distance tests for qhull: 24
+ Number of distance tests for merging: 165
+ Number of distance tests for checking: 136
+ Number of merged facets: 4
+ CPU seconds to compute hull (after input): 0
+
+
+Output completed. Verifying that all points are below outer planes of
+all facets. Will make 128 distance computations.
+rbox c D5 | qhull Tcv Q0
+
+Convex hull of 32 points in 5-d:
+
+ Number of vertices: 32
+ Number of facets: 210
+
+Statistics for: rbox c D5 | qhull Tcv Q0
+
+ Number of points processed: 32
+ Number of hyperplanes created: 297
+ Number of distance tests for qhull: 856
+ CPU seconds to compute hull (after input): 1.5e-005
+
+
+precision problems (corrected unless 'Q0' or an error)
+ 590 coplanar half ridges in output
+ 200 coplanar horizon facets for new vertices
+ 190 nearly singular or axis-parallel hyperplanes
+ 190 zero divisors during back substitute
+ 246 zero divisors during gaussian elimination
+
+Output completed. Verifying that all points are below 4.1e-015 of
+all facets. Will make 6720 distance computations.
+rbox d D5 | qhull Tcv
+
+Convex hull of 10 points in 5-d:
+
+ Number of vertices: 10
+ Number of facets: 32
+
+Statistics for: rbox d D5 | qhull Tcv
+
+ Number of points processed: 10
+ Number of hyperplanes created: 37
+ Number of distance tests for qhull: 47
+ Number of distance tests for merging: 510
+ Number of distance tests for checking: 330
+ Number of merged facets: 11
+ 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 320 distance computations.
+rbox c D6 | qhull Tcv Q0
+
+Convex hull of 64 points in 6-d:
+
+ Number of vertices: 64
+ Number of facets: 1242
+
+Statistics for: rbox c D6 | qhull Tcv Q0
+
+ Number of points processed: 64
+ Number of hyperplanes created: 1760
+ Number of distance tests for qhull: 5986
+ CPU seconds to compute hull (after input): 0
+
+
+precision problems (corrected unless 'Q0' or an error)
+ 4752 coplanar half ridges in output
+ 1382 coplanar horizon facets for new vertices
+ 1180 nearly singular or axis-parallel hyperplanes
+ 1180 zero divisors during back substitute
+ 1593 zero divisors during gaussian elimination
+
+Output completed. Verifying that all points are below 5.3e-015 of
+all facets. Will make 79488 distance computations.
+rbox d D6 | qhull Tcv
+
+Convex hull of 12 points in 6-d:
+
+ Number of vertices: 12
+ Number of facets: 64
+
+Statistics for: rbox d D6 | qhull Tcv
+
+ Number of points processed: 12
+ Number of hyperplanes created: 70
+ Number of distance tests for qhull: 88
+ Number of distance tests for merging: 1176
+ Number of distance tests for checking: 780
+ Number of merged facets: 26
+ 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 768 distance computations.
+rbox d D7 | qhull Tcv
+
+Convex hull of 14 points in 7-d:
+
+ Number of vertices: 14
+ Number of facets: 128
+
+Statistics for: rbox d D7 | qhull Tcv
+
+ Number of points processed: 14
+ Number of hyperplanes created: 135
+ Number of distance tests for qhull: 163
+ Number of distance tests for merging: 2635
+ Number of distance tests for checking: 1806
+ Number of merged facets: 57
+ 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 1792 distance computations.
+rbox c D2 | qhull Tcv C-0
+
+Convex hull of 4 points in 2-d:
+
+ Number of vertices: 4
+ Number of facets: 4
+
+Statistics for: rbox c D2 | qhull Tcv C-0
+
+ 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
+
+
+Output completed. Verifying that all points are below 1.3e-015 of
+all facets. Will make 16 distance computations.
+rbox c D3 | qhull Tcv C-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 D3 | qhull Tcv C-0
+
+ 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.
+rbox c D4 | qhull Tcv C-0
+
+Convex hull of 16 points in 4-d:
+
+ Number of vertices: 16
+ Number of facets: 8
+ Number of non-simplicial facets: 8
+
+Statistics for: rbox c D4 | qhull Tcv C-0
+
+ 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 128 distance computations.
+rbox c D5 | qhull Tcv C-0
+
+Convex hull of 32 points in 5-d:
+
+ Number of vertices: 32
+ Number of facets: 10
+ Number of non-simplicial facets: 10
+
+Statistics for: rbox c D5 | qhull Tcv C-0
+
+ Number of points processed: 32
+ Number of hyperplanes created: 87
+ Number of distance tests for qhull: 722
+ Number of distance tests for merging: 4130
+ Number of distance tests for checking: 352
+ Number of merged facets: 210
+ CPU seconds to compute hull (after input): 1.5e-005
+
+
+Output completed. Verifying that all points are below outer planes of
+all facets. Will make 320 distance computations.
+rbox c D6 | qhull Tcv C-0
+
+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 | qhull Tcv C-0
+
+ Number of points processed: 64
+ Number of hyperplanes created: 354
+ Number of distance tests for qhull: 2474
+ Number of distance tests for merging: 22065
+ Number of distance tests for checking: 832
+ Number of merged facets: 1488
+ CPU seconds to compute hull (after input): 4.6e-005
+
+
+Output completed. Verifying that all points are below outer planes of
+all facets. Will make 768 distance computations.
+rbox c D7 | qhull Tv C-0
+
+Convex hull of 128 points in 7-d:
+
+ Number of vertices: 128
+ Number of facets: 14
+ Number of non-simplicial facets: 14
+
+Statistics for: rbox c D7 | qhull Tv C-0
+
+ Number of points processed: 128
+ Number of hyperplanes created: 1778
+ Number of distance tests for qhull: 9437
+ Number of distance tests for merging: 88829
+ Number of distance tests for checking: 1920
+ Number of merged facets: 11466
+ CPU seconds to compute hull (after input): 6.2e-005
+
+
+Output completed. Verifying that all points are below outer planes of
+all facets. Will make 1792 distance computations.
+rbox 20 l D3 | qhull Tcv
+
+Convex hull of 20 points in 3-d:
+
+ Number of vertices: 20
+ Number of facets: 36
+
+Statistics for: rbox 20 l D3 | qhull Tcv
+
+ Number of points processed: 20
+ Number of hyperplanes created: 64
+ Number of distance tests for qhull: 139
+ CPU seconds to compute hull (after input): 0
+
+
+Output completed. Verifying that all points are below 2.1e-015 of
+all facets. Will make 720 distance computations.
+rbox 100 s D2 | qhull Tcv
+
+Convex hull of 100 points in 2-d:
+
+ Number of vertices: 100
+ Number of facets: 100
+
+Statistics for: rbox 100 s D2 | qhull Tcv
+
+ Number of points processed: 100
+ Number of hyperplanes created: 198
+ Number of distance tests for qhull: 898
+ CPU seconds to compute hull (after input): 0
+
+
+Output completed. Verifying that all points are below 1.3e-015 of
+all facets. Will make 10000 distance computations.
+rbox 100 s D3 | qhull Tcv
+
+Convex hull of 100 points in 3-d:
+
+ Number of vertices: 100
+ Number of facets: 196
+
+Statistics for: rbox 100 s D3 | qhull Tcv
+
+ 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
+
+
+Output completed. Verifying that all points are below 2e-015 of
+all facets. Will make 19600 distance computations.
+rbox 100 s D4 | qhull Tcv
+
+Convex hull of 100 points in 4-d:
+
+ Number of vertices: 100
+ Number of facets: 584
+
+Statistics for: rbox 100 s D4 | qhull Tcv
+
+ Number of points processed: 100
+ Number of hyperplanes created: 1718
+ Number of distance tests for qhull: 4091
+ CPU seconds to compute hull (after input): 0
+
+
+Output completed. Verifying that all points are below 2.8e-015 of
+all facets. Will make 58400 distance computations.
+rbox 100 s c D4 | qhull Tcv
+
+Convex hull of 116 points in 4-d:
+
+ Number of vertices: 16
+ Number of facets: 8
+ Number of non-simplicial facets: 8
+
+Statistics for: rbox 100 s c D4 | qhull Tcv
+
+ Number of points processed: 16
+ Number of hyperplanes created: 26
+ Number of distance tests for qhull: 2028
+ 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 928 distance computations.
+rbox 100 s d G1.5 D4 | qhull Tcv
+
+Convex hull of 108 points in 4-d:
+
+ Number of vertices: 8
+ Number of facets: 16
+
+Statistics for: rbox 100 s d G1.5 D4 | qhull Tcv
+
+ Number of points processed: 8
+ Number of hyperplanes created: 20
+ Number of distance tests for qhull: 1457
+ Number of distance tests for merging: 165
+ Number of distance tests for checking: 136
+ Number of merged facets: 4
+ CPU seconds to compute hull (after input): 0
+
+
+Output completed. Verifying that all points are below outer planes of
+all facets. Will make 1728 distance computations.
+rbox 100 s W1e-2 | qhull Tcv
+
+Convex hull of 100 points in 3-d:
+
+ Number of vertices: 100
+ Number of facets: 196
+
+Statistics for: rbox 100 s W1e-2 | qhull Tcv
+
+ Number of points processed: 100
+ Number of hyperplanes created: 493
+ Number of distance tests for qhull: 1582
+ CPU seconds to compute hull (after input): 0
+
+
+Output completed. Verifying that all points are below 2.1e-015 of
+all facets. Will make 19600 distance computations.
+rbox 100 | qhull Tcv
+
+Convex hull of 100 points in 3-d:
+
+ Number of vertices: 30
+ Number of facets: 56
+
+Statistics for: rbox 100 | qhull Tcv
+
+ Number of points processed: 31
+ Number of hyperplanes created: 117
+ Number of distance tests for qhull: 1211
+ CPU seconds to compute hull (after input): 0
+
+
+Output completed. Verifying that all points are below outer planes of
+all facets. Will make 5600 distance computations.
+rbox 100 W1e-3 | qhull Tcv
+
+Convex hull of 100 points in 3-d:
+
+ Number of vertices: 60
+ Number of facets: 116
+
+Statistics for: rbox 100 W1e-3 | qhull Tcv
+
+ Number of points processed: 65
+ Number of hyperplanes created: 298
+ Number of distance tests for qhull: 1753
+ CPU seconds to compute hull (after input): 0
+
+
+Output completed. Verifying that all points are below outer planes of
+all facets. Will make 11600 distance computations.
+rbox 100 r D2 | qhull Tcv
+
+Convex hull of 100 points in 2-d:
+
+ Number of vertices: 100
+ Number of facets: 100
+
+Statistics for: rbox 100 r D2 | qhull Tcv
+
+ Number of points processed: 100
+ Number of hyperplanes created: 198
+ Number of distance tests for qhull: 852
+ CPU seconds to compute hull (after input): 0
+
+
+Output completed. Verifying that all points are below 1.3e-015 of
+all facets. Will make 10000 distance computations.
+rbox 100 r s Z1 | qhull Tcv
+
+Convex hull of 102 points in 3-d:
+
+ Number of vertices: 102
+ Number of facets: 200
+
+Statistics for: rbox 100 r s Z1 | qhull Tcv
+
+ Number of points processed: 102
+ Number of hyperplanes created: 299
+ Number of distance tests for qhull: 1455
+ Number of distance tests for merging: 16912
+ Number of distance tests for checking: 2604
+ Number of merged facets: 97
+ CPU seconds to compute hull (after input): 1.5e-005
+
+
+Output completed. Verifying that all points are below outer planes of
+all facets. Will make 20400 distance computations.
+rbox 100 r s Z1 G0.1 | qhull Tcv C-0
+
+Convex hull of 201 points in 3-d:
+
+ Number of vertices: 201
+ Number of facets: 201
+ Number of non-simplicial facets: 101
+
+Statistics for: rbox 100 r s Z1 G0.1 | qhull Tcv C-0
+
+ Number of points processed: 201
+ Number of hyperplanes created: 1020
+ Number of distance tests for qhull: 6621
+ Number of distance tests for merging: 38388
+ Number of distance tests for checking: 11601
+ Number of merged facets: 328
+ CPU seconds to compute hull (after input): 4.6e-005
+
+
+Output completed. Verifying that all points are below outer planes of
+all facets. Will make 40401 distance computations.
+rbox 100 s Z1 G0.1 | qhull Tcv
+
+Convex hull of 101 points in 3-d:
+
+ Number of vertices: 101
+ Number of facets: 198
+
+Statistics for: rbox 100 s Z1 G0.1 | qhull Tcv
+
+ Number of points processed: 101
+ Number of hyperplanes created: 460
+ Number of distance tests for qhull: 1622
+ CPU seconds to compute hull (after input): 0
+
+
+Output completed. Verifying that all points are below 2.1e-015 of
+all facets. Will make 19998 distance computations.
+rbox 100 s Z1e-5 G0.1 | qhull Tc Pp
+
+Convex hull of 101 points in 3-d:
+
+ Number of vertices: 101
+ Number of facets: 196
+ Number of non-simplicial facets: 2
+
+Statistics for: rbox 100 s Z1e-5 G0.1 | qhull Tc Pp
+
+ Number of points processed: 101
+ Number of hyperplanes created: 453
+ Number of distance tests for qhull: 1848
+ Number of distance tests for merging: 2108
+ Number of distance tests for checking: 1274
+ Number of merged facets: 3
+ CPU seconds to compute hull (after input): 1.5e-005
+ Maximum distance of vertex below facet: -1.1e-015 (0.3x)
+
+
+echo === check qhull output formats ${d:-`date`}
+date
+=== check qhull output formats Wed Jan 6 20:33:03 EST 2010
+rbox 5 r s D2 | qhull Tcv
+
+Convex hull of 5 points in 2-d:
+
+ Number of vertices: 5
+ Number of facets: 5
+
+Statistics for: rbox 5 r s D2 | qhull Tcv
+
+ Number of points processed: 5
+ Number of hyperplanes created: 8
+ Number of distance tests for qhull: 8
+ CPU seconds to compute hull (after input): 0
+
+
+Output completed. Verifying that all points are below 1.3e-015 of
+all facets. Will make 25 distance computations.
+rbox 5 r s D2 | qhull s
+
+Convex hull of 5 points in 2-d:
+
+ Number of vertices: 5
+ Number of facets: 5
+
+Statistics for: rbox 5 r s D2 | qhull s
+
+ Number of points processed: 5
+ Number of hyperplanes created: 8
+ Number of distance tests for qhull: 8
+ CPU seconds to compute hull (after input): 0
+
+rbox 5 r s D2 | qhull s o
+2
+5 5 5
+0.1545084971874737 0.4755282581475768
+-0.4045084971874737 0.2938926261462366
+-0.4045084971874738 -0.2938926261462365
+0.1545084971874736 -0.4755282581475768
+ 0.5 -1.224606353822377e-016
+2 4 0
+2 2 3
+2 3 4
+2 1 2
+2 0 1
+
+Convex hull of 5 points in 2-d:
+
+ Number of vertices: 5
+ Number of facets: 5
+
+Statistics for: rbox 5 r s D2 | qhull s o
+
+ Number of points processed: 5
+ Number of hyperplanes created: 8
+ Number of distance tests for qhull: 8
+ CPU seconds to compute hull (after input): 0
+
+rbox 5 r s D2 | qhull f
+Vertices and facets:
+- p0(v2): 0.15 0.48
+- p4(v1): 0.5 -1.2e-016
+- p3(v4): 0.15 -0.48
+- p2(v0): -0.4 -0.29
+- p1(v5): -0.4 0.29
+- f3
+ - flags: bottom simplicial
+ - normal: 0.809 0.5878
+ - offset: -0.4045085
+ - vertices: p0(v2) p4(v1)
+ - neighboring facets: f5 f7
+- f4
+ - flags: bottom simplicial
+ - normal: -0.309 -0.9511
+ - offset: -0.4045085
+ - vertices: p3(v4) p2(v0)
+ - neighboring facets: f6 f5
+- f5
+ - flags: top simplicial
+ - normal: 0.809 -0.5878
+ - offset: -0.4045085
+ - vertices: p3(v4) p4(v1)
+ - neighboring facets: f3 f4
+- f6
+ - flags: top simplicial
+ - normal: -1 9.444e-017
+ - offset: -0.4045085
+ - vertices: p1(v5) p2(v0)
+ - neighboring facets: f4 f7
+- f7
+ - flags: bottom simplicial
+ - normal: -0.309 0.9511
+ - offset: -0.4045085
+ - vertices: p1(v5) p0(v2)
+ - neighboring facets: f3 f6
+rbox 5 r s D2 | qhull i
+5
+4 0
+2 3
+3 4
+1 2
+0 1
+rbox 5 r s D2 | qhull m
+{
+Line[{{ 0.50000000, -0.00000000}, { 0.15450850, 0.47552826}}]
+,Line[{{ -0.40450850, -0.29389263}, { 0.15450850, -0.47552826}}]
+,Line[{{ 0.15450850, -0.47552826}, { 0.50000000, -0.00000000}}]
+,Line[{{ -0.40450850, 0.29389263}, { -0.40450850, -0.29389263}}]
+,Line[{{ 0.15450850, 0.47552826}, { -0.40450850, 0.29389263}}]
+}
+rbox 5 r s D2 | qhull FM
+PLOT(CURVES(
+[[ 0.50000000, -0.00000000], [ 0.15450850, 0.47552826]]
+,[[ -0.40450850, -0.29389263], [ 0.15450850, -0.47552826]]
+,[[ 0.15450850, -0.47552826], [ 0.50000000, -0.00000000]]
+,[[ -0.40450850, 0.29389263], [ -0.40450850, -0.29389263]]
+,[[ 0.15450850, 0.47552826], [ -0.40450850, 0.29389263]]
+));
+rbox 5 r s D2 | qhull n
+3
+5
+0.8090169943749476 0.587785252292473 -0.4045084971874737
+-0.3090169943749476 -0.9510565162951535 -0.4045084971874737
+0.8090169943749473 -0.5877852522924733 -0.4045084971874737
+ -1 9.444121133484361e-017 -0.4045084971874737
+-0.3090169943749474 0.9510565162951536 -0.4045084971874738
+rbox 5 r s D2 | qhull p
+2
+5
+0.1545084971874737 0.4755282581475768
+-0.4045084971874737 0.2938926261462366
+-0.4045084971874738 -0.2938926261462365
+0.1545084971874736 -0.4755282581475768
+ 0.5 -1.224606353822377e-016
+rbox 5 r s D2 | qhull o
+2
+5 5 5
+0.1545084971874737 0.4755282581475768
+-0.4045084971874737 0.2938926261462366
+-0.4045084971874738 -0.2938926261462365
+0.1545084971874736 -0.4755282581475768
+ 0.5 -1.224606353822377e-016
+2 4 0
+2 2 3
+2 3 4
+2 1 2
+2 0 1
+rbox 5 r s D2 | qhull Ft
+2
+5 5 5
+0.1545084971874737 0.4755282581475768
+-0.4045084971874737 0.2938926261462366
+-0.4045084971874738 -0.2938926261462365
+0.1545084971874736 -0.4755282581475768
+ 0.5 -1.224606353822377e-016
+2 4 0
+2 2 3
+2 3 4
+2 1 2
+2 0 1
+rbox 5 r s D2 | qhull Fx
+5
+4
+0
+1
+2
+3
+rbox 5 r s D2 | qhull p n i p p
+2
+5
+0.1545084971874737 0.4755282581475768
+-0.4045084971874737 0.2938926261462366
+-0.4045084971874738 -0.2938926261462365
+0.1545084971874736 -0.4755282581475768
+ 0.5 -1.224606353822377e-016
+3
+5
+0.8090169943749476 0.587785252292473 -0.4045084971874737
+-0.3090169943749476 -0.9510565162951535 -0.4045084971874737
+0.8090169943749473 -0.5877852522924733 -0.4045084971874737
+ -1 9.444121133484361e-017 -0.4045084971874737
+-0.3090169943749474 0.9510565162951536 -0.4045084971874738
+5
+4 0
+2 3
+3 4
+1 2
+0 1
+rbox 10 D3 | qhull f Tcv
+Vertices and facets:
+- p0(v5): -0.022 -0.37 0.33
+- p9(v2): 0.38 -0.47 -0.22
+- p6(v0): -0.31 -0.011 -0.49
+- p1(v3): -0.067 -0.16 0.46
+- p7(v1): 0.39 0.045 0.12
+- p3(v6): 0.31 0.084 -0.1
+- p4(v7): 0.18 0.12 0.049
+- p5(v8): -0.12 0.015 -0.14
+- p2(v9): 0.028 0.042 0.058
+- f5
+ - flags: top simplicial
+ - normal: -0.4934 -0.8471 -0.1973
+ - offset: -0.2568231
+ - vertices: p0(v5) p9(v2) p6(v0)
+ - neighboring facets: f9 f6 f7
+- f6
+ - flags: bottom simplicial
+ - normal: -0.9301 -0.3157 0.1877
+ - offset: -0.1977325
+ - vertices: p0(v5) p1(v3) p6(v0)
+ - neighboring facets: f17 f5 f8
+- f7
+ - flags: bottom simplicial
+ - normal: 0.7008 -0.3956 0.5936
+ - offset: -0.323519
+ - vertices: p0(v5) p9(v2) p7(v1)
+ - neighboring facets: f10 f8 f5
+- f8
+ - flags: top simplicial
+ - normal: 0.6544 -0.298 0.6949
+ - offset: -0.3219447
+ - vertices: p0(v5) p1(v3) p7(v1)
+ - neighboring facets: f13 f7 f6
+- f9
+ - flags: bottom simplicial
+ - normal: 0.4866 0.2316 -0.8424
+ - offset: -0.2582907
+ - vertices: p3(v6) p9(v2) p6(v0)
+ - neighboring facets: f5 f16 f10
+- f10
+ - flags: top simplicial
+ - normal: 0.943 0.1711 -0.2855
+ - offset: -0.3386013
+ - vertices: p3(v6) p9(v2) p7(v1)
+ - neighboring facets: f7 f14 f9
+- f13
+ - flags: bottom simplicial
+ - normal: 0.08536 0.8035 0.5892
+ - offset: -0.1388354
+ - vertices: p4(v7) p1(v3) p7(v1)
+ - neighboring facets: f8 f14 f20
+- f14
+ - flags: top simplicial
+ - normal: 0.3121 0.948 0.06295
+ - offset: -0.1707289
+ - vertices: p4(v7) p3(v6) p7(v1)
+ - neighboring facets: f10 f13 f16
+- f16
+ - flags: bottom simplicial
+ - normal: -0.008104 0.9738 -0.2271
+ - offset: -0.1026508
+ - vertices: p4(v7) p3(v6) p6(v0)
+ - neighboring facets: f9 f18 f14
+- f17
+ - flags: top simplicial
+ - normal: -0.6179 0.7381 0.2709
+ - offset: -0.04995414
+ - vertices: p5(v8) p1(v3) p6(v0)
+ - neighboring facets: f6 f18 f21
+- f18
+ - flags: bottom simplicial
+ - normal: -0.3978 0.9064 0.1423
+ - offset: -0.04320607
+ - vertices: p5(v8) p4(v7) p6(v0)
+ - neighboring facets: f16 f17 f22
+- f20
+ - flags: top simplicial
+ - normal: -0.4124 0.8514 0.3242
+ - offset: -0.04294297
+ - vertices: p2(v9) p4(v7) p1(v3)
+ - neighboring facets: f13 f21 f22
+- f21
+ - flags: bottom simplicial
+ - normal: -0.5086 0.8133 0.2826
+ - offset: -0.03620543
+ - vertices: p2(v9) p5(v8) p1(v3)
+ - neighboring facets: f17 f20 f22
+- f22
+ - flags: top simplicial
+ - normal: -0.432 0.8759 0.2148
+ - offset: -0.03703814
+ - vertices: p2(v9) p5(v8) p4(v7)
+ - neighboring facets: f18 f20 f21
+
+Output completed. Verifying that all points are below 2e-015 of
+all facets. Will make 140 distance computations.
+rbox 10 D3 | qhull i
+14
+0 9 6
+1 0 6
+9 0 7
+0 1 7
+9 3 6
+3 9 7
+1 4 7
+4 3 7
+3 4 6
+5 1 6
+4 5 6
+2 4 1
+5 2 1
+2 5 4
+rbox 10 D3 | qhull p
+3
+9
+-0.02221493611318519 -0.366434993563625 0.3270621312102882
+-0.06676722137887703 -0.1566931052661437 0.4589771055234383
+0.02820502736438534 0.04189077954915425 0.05832764185809311
+0.3126723396709862 0.08400649026409396 -0.1029227018383543
+0.1781470954214662 0.1182274414396169 0.04860343742054276
+-0.1220315663349177 0.01546165115708639 -0.1360330368727753
+-0.3072535691850386 -0.01073880122111999 -0.4870359524963758
+0.3867462923626847 0.04492879989084676 0.118335500935405
+0.3789805913148267 -0.4732086509216658 -0.2177962499836425
+rbox 10 D3 | qhull o
+3
+10 14 21
+-0.02221493611318519 -0.366434993563625 0.3270621312102882
+-0.06676722137887703 -0.1566931052661437 0.4589771055234383
+0.02820502736438534 0.04189077954915425 0.05832764185809311
+0.3126723396709862 0.08400649026409396 -0.1029227018383543
+0.1781470954214662 0.1182274414396169 0.04860343742054276
+-0.1220315663349177 0.01546165115708639 -0.1360330368727753
+-0.3072535691850386 -0.01073880122111999 -0.4870359524963758
+0.3867462923626847 0.04492879989084676 0.118335500935405
+-0.1352406177997967 0.01093378431250694 -0.2358910583293913
+0.3789805913148267 -0.4732086509216658 -0.2177962499836425
+3 0 9 6
+3 1 0 6
+3 9 0 7
+3 0 1 7
+3 9 3 6
+3 3 9 7
+3 1 4 7
+3 4 3 7
+3 3 4 6
+3 5 1 6
+3 4 5 6
+3 2 4 1
+3 5 2 1
+3 2 5 4
+rbox 10 D3 | qhull Fx
+9
+0
+1
+2
+3
+4
+5
+6
+7
+9
+rbox 27 M1,0,1 | qhull Qc
+
+Convex hull of 27 points in 3-d:
+
+ Number of vertices: 8
+ Number of coplanar points: 18
+ Number of facets: 6
+ Number of non-simplicial facets: 6
+
+Statistics for: rbox 27 M1,0,1 | qhull Qc
+
+ Number of points processed: 8
+ Number of hyperplanes created: 11
+ Number of distance tests for qhull: 316
+ Number of distance tests for merging: 84
+ Number of distance tests for checking: 188
+ Number of merged facets: 6
+ CPU seconds to compute hull (after input): 0
+
+rbox 50 D3 s | qhull C0.1 Qc Pd0d1d2 s p Tcv
+3
+7
+0.1955434141942995 0.09315491718098737 0.4506494586374647
+0.3786694231678469 0.2419725568326128 -0.2192230592287638
+0.1164290160865212 0.2250749615572271 0.4310284745734756
+0.3010852516984067 0.3425921496145067 0.2048860420629442
+0.4995640899182717 0.005583735684776694 0.02011322848106415
+0.4035338761538299 0.1419567271683243 0.2588603840063664
+0.3642936952899508 -0.2163723184172344 -0.2654677445467591
+
+Convex hull of 50 points in 3-d:
+
+ Number of vertices: 19
+ Number of coplanar points: 31
+ Number of facets: 12
+ Number of 'good' facets: 1
+ Number of 'good' non-simplicial facets: 1
+
+Statistics for: rbox 50 D3 s | qhull C0.1 Qc Pd0d1d2 s p Tcv
+
+ Number of points processed: 50
+ Number of hyperplanes created: 237
+ Number of distance tests for qhull: 1177
+ Number of distance tests for merging: 3999
+ Number of distance tests for checking: 367
+ Number of merged facets: 84
+ CPU seconds to compute hull (after input): 0
+ Maximum distance of vertex below facet: -0.24 (0.8x)
+
+
+Output completed. Verifying that all points are below outer planes of
+all facets. Will make 50 distance computations.
+rbox 10 D2 P0 P1e-15 | qhull d Qc FP s Tcv
+1
+0 1 12 1e-015
+
+Delaunay triangulation by the convex hull of 12 points in 3-d:
+
+ Number of input sites: 11
+ Number of nearly incident points: 1
+ Number of Delaunay regions: 16
+
+Statistics for: rbox 10 D2 P0 P1e-15 | qhull d Qc FP s Tcv
+
+ Number of points processed: 11
+ Number of hyperplanes created: 33
+ Number of facets in hull: 18
+ Number of distance tests for qhull: 111
+ 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.
+rbox 100 s | qhull C-0.003 Qc FP s
+10
+29 92 222 0.05221620842442
+49 2 292 0.03790045221711881
+99 9 338 0.02993864679572153
+54 84 341 0.06479664045626413
+54 72 226 0.03827167959574594
+96 6 368 0.02282529175708783
+19 1 372 0.01048228658130248
+69 26 409 0.04998878658421265
+19 66 371 0.008281093788857857
+19 45 371 0.04608027722786205
+
+Convex hull of 100 points in 3-d:
+
+ Number of vertices: 90
+ Number of coplanar points: 10
+ Number of facets: 118
+ Number of non-simplicial facets: 46
+
+Statistics for: rbox 100 s | qhull C-0.003 Qc FP s
+
+ Number of points processed: 90
+ Number of hyperplanes created: 400
+ Number of distance tests for qhull: 2016
+ Number of distance tests for merging: 3695
+ Number of distance tests for checking: 1469
+ Number of merged facets: 102
+ CPU seconds to compute hull (after input): 0
+ Maximum distance of point above facet: 0.0057 (0.6x)
+ Maximum distance of vertex below facet: -0.0087 (1.0x)
+
+rbox 100 s D2 | qhull C0.1 i Fx Tcv
+6
+4 28
+70 27
+77 70
+68 4
+27 68
+28 77
+6
+4
+28
+77
+70
+27
+68
+
+Output completed. Verifying that all points are below outer planes of
+all facets. Will make 600 distance computations.
+rbox 4 s D3 | qhull Qc Ghipv Tcv
+{appearance {+edge -evert linewidth 2} LIST # rbox 4 s D3 | qhull Qc Ghipv Tcv
+{appearance {-edge -normal normscale 0} {
+INST geom {define vsphere OFF
+18 32 48
+
+0 0 1
+1 0 0
+0 1 0
+-1 0 0
+0 -1 0
+0 0 -1
+0.707107 0 0.707107
+0 -0.707107 0.707107
+0.707107 -0.707107 0
+-0.707107 0 0.707107
+-0.707107 -0.707107 0
+0 0.707107 0.707107
+-0.707107 0.707107 0
+0.707107 0.707107 0
+0.707107 0 -0.707107
+0 0.707107 -0.707107
+-0.707107 0 -0.707107
+0 -0.707107 -0.707107
+
+3 0 6 11
+3 0 7 6
+3 0 9 7
+3 0 11 9
+3 1 6 8
+3 1 8 14
+3 1 13 6
+3 1 14 13
+3 2 11 13
+3 2 12 11
+3 2 13 15
+3 2 15 12
+3 3 9 12
+3 3 10 9
+3 3 12 16
+3 3 16 10
+3 4 7 10
+3 4 8 7
+3 4 10 17
+3 4 17 8
+3 5 14 17
+3 5 15 14
+3 5 16 15
+3 5 17 16
+3 6 13 11
+3 7 8 6
+3 9 10 7
+3 11 12 9
+3 14 8 17
+3 15 13 14
+3 16 12 15
+3 17 10 16
+} transforms { TLIST
+0.009951 0 0 0 # v2
+ 0 0.009951 0 0
+0 0 0.009951 0
+-0.04234 -0.2077 -0.4529 # p3
+1
+0.009951 0 0 0 # v1
+ 0 0.009951 0 0
+0 0 0.009951 0
+0.004313 -0.4976 0.04904 # p2
+1
+0.009951 0 0 0 # v0
+ 0 0.009951 0 0
+0 0 0.009951 0
+ -0.4876 0.03313 -0.1055 # p0
+1
+0.009951 0 0 0 # v3
+ 0 0.009951 0 0
+0 0 0.009951 0
+ -0.3939 -0.1068 -0.2889 # p1
+1
+}}}
+{ OFF 3 1 1 # f1
+-0.04933 -0.2152 -0.4566
+-0.002675 -0.5051 0.04532
+ -0.4946 0.02557 -0.1092
+3 0 1 2 0.1808 0.1547 0.3302 1.0 }
+VECT 1 2 1 2 1 # intersect f1 f2
+0.004313 -0.4976 0.04904 # projected p2
+ -0.4876 0.03313 -0.1055 # projected p0
+ 0 0 0 1.0
+VECT 1 2 1 2 1 # intersect f1 f3
+-0.04234 -0.2077 -0.4529 # projected p3
+ -0.4876 0.03313 -0.1055 # projected p0
+ 0 0 0 1.0
+VECT 1 2 1 2 1 # intersect f1 f4
+-0.04234 -0.2077 -0.4529 # projected p3
+0.004313 -0.4976 0.04904 # projected p2
+ 0 0 0 1.0
+{ OFF 3 1 1 # f2
+ 0.01247 -0.4904 0.04773
+ -0.3857 -0.09961 -0.2902
+ -0.4795 0.04031 -0.1068
+3 0 1 2 0.8726 0.828 0.4402 1.0 }
+VECT 1 2 1 2 1 # intersect f2 f3
+ -0.3939 -0.1068 -0.2889 # projected p1
+ -0.4876 0.03313 -0.1055 # projected p0
+ 0 0 0 1.0
+VECT 1 2 1 2 1 # intersect f2 f4
+ -0.3939 -0.1068 -0.2889 # projected p1
+0.004313 -0.4976 0.04904 # projected p2
+ 0 0 0 1.0
+{ OFF 3 1 1 # f3
+ -0.3931 -0.1153 -0.282
+-0.04157 -0.2162 -0.446
+ -0.4869 0.02464 -0.09863
+3 0 1 2 0.5351 0.1123 0.8138 1.0 }
+VECT 1 2 1 2 1 # intersect f3 f4
+ -0.3939 -0.1068 -0.2889 # projected p1
+-0.04234 -0.2077 -0.4529 # projected p3
+ 0 0 0 1.0
+{ OFF 3 1 1 # f4
+-0.03767 -0.1989 -0.4482
+ -0.3892 -0.09803 -0.2843
+0.008983 -0.4888 0.05366
+3 0 1 2 0.7133 0.8999 0.7112 1.0 }
+}
+
+Output completed. Verifying that all points are below 2.1e-015 of
+all facets. Will make 16 distance computations.
+rbox 6 D4 | qhull f Tcv
+Vertices and facets:
+- p3(v4): 0.1 -0.13 -0.17 -0.42
+- p0(v3): -0.33 -0.43 -0.46 0.15
+- p2(v2): 0.11 0.4 -0.063 -0.18
+- p1(v0): -0.35 -0.24 0.14 -0.18
+- p4(v1): 0.14 -0.34 -0.084 0.087
+- p5(v6): -0.25 -0.5 0.22 -0.033
+- f4
+ - flags: bottom simplicial
+ - normal: -0.6536 0.3379 -0.424 -0.5281
+ - offset: -0.1850304
+ - vertices: p3(v4) p0(v3) p2(v2) p1(v0)
+ - neighboring facets: f6 f8 f10 f5
+- f5
+ - flags: top simplicial
+ - normal: 0.6142 0.09488 -0.7743 0.1197
+ - offset: -0.1313181
+ - vertices: p3(v4) p0(v3) p2(v2) p4(v1)
+ - neighboring facets: f7 f9 f11 f4
+- f6
+ - flags: top simplicial
+ - normal: -0.4209 0.3853 0.2879 0.7691
+ - offset: 0.04819078
+ - vertices: p5(v6) p0(v3) p2(v2) p1(v0)
+ - neighboring facets: f4 f8 f10 f7
+- f7
+ - flags: bottom simplicial
+ - normal: -0.1759 0.3066 0.2842 0.8912
+ - offset: 0.07466537
+ - vertices: p5(v6) p0(v3) p2(v2) p4(v1)
+ - neighboring facets: f5 f9 f11 f6
+- f8
+ - flags: bottom simplicial
+ - normal: 0.2584 0.07433 0.814 -0.515
+ - offset: -0.09844114
+ - vertices: p5(v6) p3(v4) p2(v2) p1(v0)
+ - neighboring facets: f4 f6 f10 f9
+- f9
+ - flags: top simplicial
+ - normal: 0.6576 -0.06072 0.7252 -0.195
+ - offset: -0.03612816
+ - vertices: p5(v6) p3(v4) p2(v2) p4(v1)
+ - neighboring facets: f5 f7 f11 f8
+- f10
+ - flags: top simplicial
+ - normal: -0.3537 -0.6003 -0.2017 -0.6883
+ - offset: -0.3651888
+ - vertices: p5(v6) p3(v4) p0(v3) p1(v0)
+ - neighboring facets: f4 f6 f8 f11
+- f11
+ - flags: bottom simplicial
+ - normal: 0.2962 -0.865 -0.2123 -0.3449
+ - offset: -0.3220787
+ - vertices: p5(v6) p3(v4) p0(v3) p4(v1)
+ - neighboring facets: f5 f7 f9 f10
+
+Output completed. Verifying that all points are below 3e-015 of
+all facets. Will make 48 distance computations.
+rbox 6 D4 | qhull i
+8
+0 3 2 1
+3 0 2 4
+5 0 2 1
+0 5 2 4
+3 5 2 1
+5 3 2 4
+5 3 0 1
+3 5 0 4
+rbox 6 D4 | qhull p
+4
+6
+-0.3257826863096865 -0.4296101703584289 -0.4581337649916613 0.1458114577883961
+-0.3468340047139991 -0.2391184267952279 0.1365988111464296 -0.1837860440684352
+0.107954867284703 0.397449696341017 -0.062960620096848 -0.1791453880063681
+0.1034612661259819 -0.1265049433582509 -0.1685859450777862 -0.4239815160855479
+0.1426585555473888 -0.3376619446442108 -0.08430490557505274 0.08744874697872321
+-0.2489141260729303 -0.4997188728300099 0.224904344160952 -0.03269336003129684
+rbox 6 D4 | qhull o
+4
+6 8 16
+-0.3257826863096865 -0.4296101703584289 -0.4581337649916613 0.1458114577883961
+-0.3468340047139991 -0.2391184267952279 0.1365988111464296 -0.1837860440684352
+0.107954867284703 0.397449696341017 -0.062960620096848 -0.1791453880063681
+0.1034612661259819 -0.1265049433582509 -0.1685859450777862 -0.4239815160855479
+0.1426585555473888 -0.3376619446442108 -0.08430490557505274 0.08744874697872321
+-0.2489141260729303 -0.4997188728300099 0.224904344160952 -0.03269336003129684
+4 0 3 2 1
+4 3 0 2 4
+4 5 0 2 1
+4 0 5 2 4
+4 3 5 2 1
+4 5 3 2 4
+4 5 3 0 1
+4 3 5 0 4
+rbox 1000 s D2 | qhull FA Tcv
+
+Convex hull of 1000 points in 2-d:
+
+ Number of vertices: 1000
+ Number of facets: 1000
+
+Statistics for: rbox 1000 s D2 | qhull FA Tcv
+
+ Number of points processed: 1000
+ Number of hyperplanes created: 1998
+ Number of distance tests for qhull: 13978
+ CPU seconds to compute hull (after input): 0
+ Total facet area: 3.1415592
+ Total volume: 0.7853647
+
+
+qhull output completed. Verifying that 1000 points are
+below 1.3e-015 of the nearest facet.
+rbox 1000 s | qhull FA Tcv
+
+Convex hull of 1000 points in 3-d:
+
+ Number of vertices: 1000
+ Number of facets: 1996
+
+Statistics for: rbox 1000 s | qhull FA Tcv
+
+ 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 D4 | qhull FA Tcv
+
+Convex hull of 16 points in 4-d:
+
+ Number of vertices: 16
+ Number of facets: 8
+ Number of non-simplicial facets: 8
+
+Statistics for: rbox c D4 | qhull FA Tcv
+
+ 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
+ Approximate facet area: 8
+ Approximate volume: 1
+
+
+Output completed. Verifying that all points are below outer planes of
+all facets. Will make 128 distance computations.
+rbox c D5 | qhull FA Tcv
+
+Convex hull of 32 points in 5-d:
+
+ Number of vertices: 32
+ Number of facets: 10
+ Number of non-simplicial facets: 10
+
+Statistics for: rbox c D5 | qhull FA Tcv
+
+ Number of points processed: 32
+ Number of hyperplanes created: 87
+ Number of distance tests for qhull: 722
+ Number of distance tests for merging: 2775
+ Number of distance tests for checking: 352
+ Number of merged facets: 210
+ CPU seconds to compute hull (after input): 0
+ Approximate facet area: 10
+ Approximate volume: 1
+
+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 320 distance computations.
+rbox c D5 | qhull FA Qt Tcv
+
+Convex hull of 32 points in 5-d:
+
+ Number of vertices: 32
+ Number of facets: 316
+ Number of triangulated facets: 10
+
+Statistics for: rbox c D5 | qhull FA Qt Tcv
+
+ Number of points processed: 32
+ Number of hyperplanes created: 87
+ Number of distance tests for qhull: 722
+ Number of distance tests for merging: 3235
+ Number of distance tests for checking: 352
+ Number of merged facets: 210
+ CPU seconds to compute hull (after input): 0
+ Approximate facet area: 10
+ Approximate volume: 1
+
+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 10112 distance computations.
+rbox 10 D2 | qhull d FA Tcv
+
+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 D2 | qhull d FA Tcv
+
+ Number of points processed: 10
+ Number of hyperplanes created: 28
+ Number of facets in hull: 16
+ Number of distance tests for qhull: 48
+ CPU seconds to compute hull (after input): 0
+ Total facet area: 0.46254269
+
+
+Output completed. Verifying that all points are below 2.1e-015 of
+all facets. Will make 140 distance computations.
+rbox 10 D2 | qhull d Qu FA Tcv
+
+Furthest-site Delaunay triangulation by the convex hull of 10 points in 3-d:
+
+ Number of input sites: 10
+ Number of Delaunay regions: 2
+
+Statistics for: rbox 10 D2 | qhull d Qu FA Tcv
+
+ Number of points processed: 10
+ Number of hyperplanes created: 28
+ Number of facets in hull: 16
+ Number of distance tests for qhull: 48
+ CPU seconds to compute hull (after input): 0
+ Total facet area: 0.46254269
+
+
+Output completed. Verifying that all points are below 2.1e-015 of
+all facets. Will make 20 distance computations.
+rbox 10 D2 | qhull FA Tcv
+
+Convex hull of 10 points in 2-d:
+
+ Number of vertices: 4
+ Number of facets: 4
+
+Statistics for: rbox 10 D2 | qhull FA Tcv
+
+ Number of points processed: 4
+ Number of hyperplanes created: 6
+ Number of distance tests for qhull: 52
+ CPU seconds to compute hull (after input): 0
+ Total facet area: 2.8999576
+ Total volume: 0.46254269
+
+
+Output completed. Verifying that all points are below 1.3e-015 of
+all facets. Will make 40 distance computations.
+rbox 10 c D2 | qhull Fx Tcv
+4
+10
+12
+13
+11
+
+Output completed. Verifying that all points are below 1.3e-015 of
+all facets. Will make 56 distance computations.
+rbox 1000 s | qhull FS Tcv
+0
+2 3.120195135077459 0.5165027368863381
+
+qhull output completed. Verifying that 1000 points are
+below 2.1e-015 of the nearest facet.
+rbox 10 W0 D2 | qhull p Qc FcC Tcv
+2
+10
+-0.3863076515368257 0.5
+-0.05259535978789941 0.5
+0.2626424396993988 0.5
+0.3748708151978169 0.5
+-0.01474997775140216 0.5
+0.1582814042067914 0.5
+ -0.5 0.45089279622854
+ -0.5 -0.003085198815060033
+-0.3688616616361418 -0.5
+-0.2798755283280048 0.5
+5
+0
+0
+0
+0
+5 2 4 5 9 1
+2
+5
+0.003004576780837543 -5.902852123112957e-019
+ -0.5 0.22390379870674
+-0.4344308308180709 -0.25154259940753
+-0.4431538257684129 0.47544639811427
+-0.005718418169504413 0.5
+
+Output completed. Verifying that all points are below outer planes of
+all facets. Will make 50 distance computations.
+rbox 4 z h s D2 | qhull Fd s n FD Tcv
+rbox 4 z h s D2 | qhull Fd s n FD Tcv
+begin
+ 4 3 real
+107643.7343385944 -0.2650304141580589 -0.9642400528764649
+797791.7732245287 -0.6912673062074456 0.7225991360143614
+874890.2679778723 0.9916265954087946 0.1291382796771071
+864878.4439653738 0.3984446264475182 0.9171923896626584
+end
+
+Convex hull of 4 points in 2-d:
+
+ Number of vertices: 4
+ Number of facets: 4
+
+Statistics for: rbox 4 z h s D2 | qhull Fd s n FD Tcv
+
+ Number of points processed: 4
+ Number of hyperplanes created: 6
+ Number of distance tests for qhull: 5
+ CPU seconds to compute hull (after input): 0
+
+
+Output completed. Verifying that all points are below 2.6e-009 of
+all facets. Will make 16 distance computations.
+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
+Vertices and facets:
+- p1(v2): -0.3 0.39 -0.092
+- p5(v1): 0.4 -0.22 -0.2
+- p4(v0): -0.46 -0.19 -0.018
+- p2(v3): 0.25 0.28 -0.33
+- f1
+ - flags: top simplicial
+ - area: 0.26
+ - normal: 0.2054 0.06987 0.9762
+ - offset: 0.125398
+ - center: -0.1205015151724569 -0.008790385787885111 -0.1024776532548504
+ - vertices: p1(v2) p5(v1) p4(v0)
+ - neighboring facets: f2 f3 f4
+- f2
+ - flags: bottom simplicial
+ - area: 0.23
+ - normal: -0.2032 -0.3001 -0.932
+ - offset: -0.1680571
+ - center: 0.0643014421937075 -0.04270356053094848 -0.1805812707066012
+ - maxoutside: 0.1132672
+ - coplanar set(furthest p3):
+ p0: 0.07025 -0.4742 -0.142
+ p3: 0.2976 -0.2965 -0.2712
+ furthest distance= 0.11
+ - vertices: p2(v3) p5(v1) p4(v0)
+ - neighboring facets: f1 f3 f4
+- f3
+ - flags: top simplicial
+ - area: 0.18
+ - normal: -0.3912 -0.01238 -0.9202
+ - offset: -0.1989549
+ - center: -0.1715856748140029 0.1590825675964337 -0.1454013928109105
+ - vertices: p2(v3) p1(v2) p4(v0)
+ - neighboring facets: f1 f2 f4
+- f4
+ - flags: bottom simplicial
+ - area: 0.16
+ - normal: 0.4184 0.3424 0.8413
+ - offset: 0.07254957
+ - center: 0.116549362001881 0.1503252206347391 -0.2053893818610149
+ - vertices: p2(v3) p1(v2) p5(v1)
+ - neighboring facets: f1 f2 f3
+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
+4
+4
+0.2053603787708732 0.06987429109559472 0.976188864039624 0.1253980026939646
+-0.2031613339148239 -0.3001304507855298 -0.9320124381751694 -0.1680570625036092
+-0.3911895500493897 -0.01238286325891918 -0.9202268202077502 -0.1989548866041478
+0.4183781509471983 0.3424157187037643 0.8412557271095323 0.07254956874669738
+4
+4
+0.2053603787708732 0.06987429109559472 0.976188864039624 0.125398002693964
+-0.2031613339148239 -0.3001304507855298 -0.9320124381751694 -0.1680570625036099
+-0.3911895500493897 -0.01238286325891918 -0.9202268202077502 -0.1989548866041485
+0.4183781509471983 0.3424157187037643 0.8412557271095323 0.07254956874669671
+4
+4
+0.2053603787708732 0.06987429109559472 0.976188864039624 0.1253980026939627
+-0.2031613339148239 -0.3001304507855298 -0.9320124381751694 -0.2813242952138535
+-0.3911895500493897 -0.01238286325891918 -0.9202268202077502 -0.1989548866041498
+0.4183781509471983 0.3424157187037643 0.8412557271095323 0.0725495687466954
+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
+4
+1
+2
+3
+4
+4
+0
+0
+0
+0
+4
+3 1 2 3
+3 0 2 3
+3 0 1 3
+3 0 1 2
+6
+1 1
+3 3 0 2
+3 3 1 2
+1 1
+3 2 0 1
+3 3 0 1
+Options selected for Qhull 2010.0.3 2010/01/05:
+ run-id 769043788 Centrum-premerge- 0.1 Qcoplanar-keep FFacets-xridge
+ summary FQhull Finner normals Fouter FQhull FIDs Fmerges Fneighbors
+ FNeighbors-vertex FOptions FQhull Fsummary FSize FVertex-average
+ Tcheck-frequently Tverify Fvertices _max-width 0.86
+ Error-roundoff 6.6e-016 _one-merge 0.3 _near-inside 1.5
+ Visible-distance 0.1 U-coplanar-distance 0.1 Width-outside 0.2
+ _wide-facet 0.6
+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
+10 3 6 4 4 4 4 2 0 0 0
+2 0.1132672327102436 -1.315898280434284e-015
+0
+2 0.8296676646636062 0.01051107893821416
+3 1
+-0.02780909644771783 0.06447846047808481 -0.1584624246583442
+4
+3 1 5 4
+3 2 5 4
+3 2 1 4
+3 2 1 5
+Options selected for Qhull 2010.0.3 2010/01/05:
+ run-id 769043788 Centrum-premerge- 0.1 Qcoplanar-keep FFacets-xridge
+ summary FQhull Finner normals Fouter FQhull FIDs Fmerges Fneighbors
+ FNeighbors-vertex FOptions FQhull Fsummary FSize FVertex-average
+ Tcheck-frequently Tverify Fvertices _max-width 0.86
+ Error-roundoff 6.6e-016 _one-merge 0.3 _near-inside 1.5
+ Visible-distance 0.1 U-coplanar-distance 0.1 Width-outside 0.2
+ _wide-facet 0.6
+
+Convex hull of 6 points in 3-d:
+
+ Number of vertices: 4
+ Number of coplanar points: 2
+ Number of facets: 4
+
+Statistics for: 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
+
+ Number of points processed: 4
+ Number of hyperplanes created: 5
+ Number of distance tests for qhull: 24
+ CPU seconds to compute hull (after input): 0
+ Total facet area: 0.82966766
+ Total volume: 0.010511079
+ Maximum distance of point above facet: 0.11 (0.4x)
+
+
+Output completed. Verifying that all points are below outer planes of
+all facets. Will make 24 distance computations.
+rbox P0.5,0.5 P0.5,0.5 W0 5 D2 | qhull d FN Qc
+7
+5 3 0 2 -7 -8
+1 0
+5 -10 1 -6 -7 -8
+4 -6 1 0 2
+3 -7 2 -6
+3 -10 -8 3
+4 -10 1 0 3
+rbox 10 D3 | qhull Fa PA5
+5
+0.2844546842397038
+0.1170134053930415
+0.1758021655943633
+0.07490600482805046
+0.2087585943133527
+rbox 10 D3 | qhull Fa PF0.4
+0
+QH7055 qhull warning: no facets printed
+
+echo === test Qt ${d:-`date`}
+date
+=== test Qt Wed Jan 6 20:33:04 EST 2010
+rbox c | qhull Qt s o Tcv
+3
+8 12 18
+ -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
+3 6 2 0
+3 4 6 0
+3 5 4 0
+3 1 5 0
+3 5 6 4
+3 6 5 7
+3 2 3 0
+3 3 1 0
+3 6 3 2
+3 3 6 7
+3 3 5 1
+3 5 3 7
+
+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 | qhull Qt s o Tcv
+
+ Number of points processed: 8
+ Number of hyperplanes created: 11
+ Number of distance tests for qhull: 35
+ Number of distance tests for merging: 166
+ 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 96 distance computations.
+rbox c | qhull Qt f i
+Vertices and facets:
+- p6(v6): 0.5 0.5 -0.5
+ neighbors: f17 f18 f25 f27 f33 f34
+- p2(v2): -0.5 0.5 -0.5
+ neighbors: f17 f29 f33
+- p0(v0): -0.5 -0.5 -0.5
+ neighbors: f17 f18 f21 f22 f29 f30
+- p4(v1): 0.5 -0.5 -0.5
+ neighbors: f18 f21 f25
+- p5(v7): 0.5 -0.5 0.5
+ neighbors: f21 f22 f25 f27 f37 f38
+- p1(v3): -0.5 -0.5 0.5
+ neighbors: f22 f30 f37
+- p7(v5): 0.5 0.5 0.5
+ neighbors: f27 f34 f38
+- p3(v8): -0.5 0.5 0.5
+ neighbors: f29 f30 f33 f34 f37 f38
+- f17
+ - flags: top simplicial tricoplanar seen keepcentrum
+ - owner of normal & centrum is facet f17
+ - normal: 0 0 -1
+ - offset: -0.5
+ - center: 0 0 -0.5
+ - vertices: p6(v6) p2(v2) p0(v0)
+ - neighboring facets: f29 f18 f33
+- f18
+ - flags: bottom simplicial tricoplanar seen
+ - owner of normal & centrum is facet f17
+ - normal: 0 0 -1
+ - offset: -0.5
+ - center: 0 0 -0.5
+ - vertices: p6(v6) p4(v1) p0(v0)
+ - neighboring facets: f21 f17 f25
+- f21
+ - flags: top simplicial tricoplanar keepcentrum
+ - owner of normal & centrum is facet f21
+ - normal: 0 -1 0
+ - offset: -0.5
+ - center: 0 -0.5 0
+ - vertices: p5(v7) p4(v1) p0(v0)
+ - neighboring facets: f18 f22 f25
+- f22
+ - flags: bottom simplicial tricoplanar seen
+ - owner of normal & centrum is facet f21
+ - normal: 0 -1 0
+ - offset: -0.5
+ - center: 0 -0.5 0
+ - vertices: p5(v7) p1(v3) p0(v0)
+ - neighboring facets: f30 f21 f37
+- f25
+ - flags: top simplicial tricoplanar keepcentrum
+ - owner of normal & centrum is facet f25
+ - normal: 1 0 0
+ - offset: -0.5
+ - center: 0.5 0 0
+ - vertices: p5(v7) p6(v6) p4(v1)
+ - neighboring facets: f18 f21 f27
+- f27
+ - flags: bottom simplicial tricoplanar seen
+ - owner of normal & centrum is facet f25
+ - normal: 1 0 0
+ - offset: -0.5
+ - center: 0.5 0 0
+ - vertices: p5(v7) p6(v6) p7(v5)
+ - neighboring facets: f34 f38 f25
+- f29
+ - flags: bottom simplicial tricoplanar keepcentrum
+ - owner of normal & centrum is facet f29
+ - normal: -1 0 0
+ - offset: -0.5
+ - center: -0.5 0 0
+ - vertices: p3(v8) p2(v2) p0(v0)
+ - neighboring facets: f17 f30 f33
+- f30
+ - flags: top simplicial tricoplanar
+ - owner of normal & centrum is facet f29
+ - normal: -1 0 0
+ - offset: -0.5
+ - center: -0.5 0 0
+ - vertices: p3(v8) p1(v3) p0(v0)
+ - neighboring facets: f22 f29 f37
+- f33
+ - flags: bottom simplicial tricoplanar keepcentrum
+ - owner of normal & centrum is facet f33
+ - normal: 0 1 0
+ - offset: -0.5
+ - center: 0 0.5 0
+ - vertices: p3(v8) p6(v6) p2(v2)
+ - neighboring facets: f17 f29 f34
+- f34
+ - flags: top simplicial tricoplanar
+ - owner of normal & centrum is facet f33
+ - normal: 0 1 0
+ - offset: -0.5
+ - center: 0 0.5 0
+ - vertices: p3(v8) p6(v6) p7(v5)
+ - neighboring facets: f27 f38 f33
+- f37
+ - flags: top simplicial tricoplanar keepcentrum
+ - owner of normal & centrum is facet f37
+ - normal: 0 0 1
+ - offset: -0.5
+ - center: 0 0 0.5
+ - vertices: p3(v8) p5(v7) p1(v3)
+ - neighboring facets: f22 f30 f38
+- f38
+ - flags: bottom simplicial tricoplanar
+ - owner of normal & centrum is facet f37
+ - normal: 0 0 1
+ - offset: -0.5
+ - center: 0 0 0.5
+ - vertices: p3(v8) p5(v7) p7(v5)
+ - neighboring facets: f27 f34 f37
+12
+6 2 0
+4 6 0
+5 4 0
+1 5 0
+5 6 4
+6 5 7
+2 3 0
+3 1 0
+6 3 2
+3 6 7
+3 5 1
+5 3 7
+rbox c | qhull Qt m FM n
+{
+Polygon[{{ 0.50000000, 0.50000000, -0.50000000},
+{ -0.50000000, 0.50000000, -0.50000000},
+{ -0.50000000, -0.50000000, -0.50000000}}],
+Polygon[{{ 0.50000000, -0.50000000, -0.50000000},
+{ 0.50000000, 0.50000000, -0.50000000},
+{ -0.50000000, -0.50000000, -0.50000000}}],
+Polygon[{{ 0.50000000, -0.50000000, 0.50000000},
+{ 0.50000000, -0.50000000, -0.50000000},
+{ -0.50000000, -0.50000000, -0.50000000}}],
+Polygon[{{ -0.50000000, -0.50000000, 0.50000000},
+{ 0.50000000, -0.50000000, 0.50000000},
+{ -0.50000000, -0.50000000, -0.50000000}}],
+Polygon[{{ 0.50000000, -0.50000000, 0.50000000},
+{ 0.50000000, 0.50000000, -0.50000000},
+{ 0.50000000, -0.50000000, -0.50000000}}],
+Polygon[{{ 0.50000000, 0.50000000, -0.50000000},
+{ 0.50000000, -0.50000000, 0.50000000},
+{ 0.50000000, 0.50000000, 0.50000000}}],
+Polygon[{{ -0.50000000, 0.50000000, -0.50000000},
+{ -0.50000000, 0.50000000, 0.50000000},
+{ -0.50000000, -0.50000000, -0.50000000}}],
+Polygon[{{ -0.50000000, 0.50000000, 0.50000000},
+{ -0.50000000, -0.50000000, 0.50000000},
+{ -0.50000000, -0.50000000, -0.50000000}}],
+Polygon[{{ 0.50000000, 0.50000000, -0.50000000},
+{ -0.50000000, 0.50000000, 0.50000000},
+{ -0.50000000, 0.50000000, -0.50000000}}],
+Polygon[{{ -0.50000000, 0.50000000, 0.50000000},
+{ 0.50000000, 0.50000000, -0.50000000},
+{ 0.50000000, 0.50000000, 0.50000000}}],
+Polygon[{{ -0.50000000, 0.50000000, 0.50000000},
+{ 0.50000000, -0.50000000, 0.50000000},
+{ -0.50000000, -0.50000000, 0.50000000}}],
+Polygon[{{ 0.50000000, -0.50000000, 0.50000000},
+{ -0.50000000, 0.50000000, 0.50000000},
+{ 0.50000000, 0.50000000, 0.50000000}}]}
+PLOT3D(POLYGONS(
+[[ 0.50000000, 0.50000000, -0.50000000],
+[ -0.50000000, 0.50000000, -0.50000000],
+[ -0.50000000, -0.50000000, -0.50000000]],
+[[ 0.50000000, -0.50000000, -0.50000000],
+[ 0.50000000, 0.50000000, -0.50000000],
+[ -0.50000000, -0.50000000, -0.50000000]],
+[[ 0.50000000, -0.50000000, 0.50000000],
+[ 0.50000000, -0.50000000, -0.50000000],
+[ -0.50000000, -0.50000000, -0.50000000]],
+[[ -0.50000000, -0.50000000, 0.50000000],
+[ 0.50000000, -0.50000000, 0.50000000],
+[ -0.50000000, -0.50000000, -0.50000000]],
+[[ 0.50000000, -0.50000000, 0.50000000],
+[ 0.50000000, 0.50000000, -0.50000000],
+[ 0.50000000, -0.50000000, -0.50000000]],
+[[ 0.50000000, 0.50000000, -0.50000000],
+[ 0.50000000, -0.50000000, 0.50000000],
+[ 0.50000000, 0.50000000, 0.50000000]],
+[[ -0.50000000, 0.50000000, -0.50000000],
+[ -0.50000000, 0.50000000, 0.50000000],
+[ -0.50000000, -0.50000000, -0.50000000]],
+[[ -0.50000000, 0.50000000, 0.50000000],
+[ -0.50000000, -0.50000000, 0.50000000],
+[ -0.50000000, -0.50000000, -0.50000000]],
+[[ 0.50000000, 0.50000000, -0.50000000],
+[ -0.50000000, 0.50000000, 0.50000000],
+[ -0.50000000, 0.50000000, -0.50000000]],
+[[ -0.50000000, 0.50000000, 0.50000000],
+[ 0.50000000, 0.50000000, -0.50000000],
+[ 0.50000000, 0.50000000, 0.50000000]],
+[[ -0.50000000, 0.50000000, 0.50000000],
+[ 0.50000000, -0.50000000, 0.50000000],
+[ -0.50000000, -0.50000000, 0.50000000]],
+[[ 0.50000000, -0.50000000, 0.50000000],
+[ -0.50000000, 0.50000000, 0.50000000],
+[ 0.50000000, 0.50000000, 0.50000000]]));
+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
+rbox c | qhull Qt p o
+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
+3
+8 12 18
+ -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
+3 6 2 0
+3 4 6 0
+3 5 4 0
+3 1 5 0
+3 5 6 4
+3 6 5 7
+3 2 3 0
+3 3 1 0
+3 6 3 2
+3 3 6 7
+3 3 5 1
+3 5 3 7
+rbox c | qhull Qt Fx
+8
+0
+1
+2
+3
+4
+5
+6
+7
+rbox c | qhull Qt FA s Fa
+12
+ 0.5
+ 0.5
+ 0.5
+ 0.5
+ 0.5
+ 0.5
+ 0.5
+ 0.5
+ 0.5
+ 0.5
+ 0.5
+ 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 | qhull Qt FA s Fa
+
+ 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
+ Approximate facet area: 6
+ Approximate volume: 1
+
+rbox 6 r s c G0.1 D2 | qhull Qt d FA Tcv
+
+Delaunay triangulation by the convex hull of 10 points in 3-d:
+
+ Number of input sites: 10
+ Number of Delaunay regions: 12
+ Number of triangulated facets: 3
+
+Statistics for: rbox 6 r s c G0.1 D2 | qhull Qt d FA Tcv
+
+ Number of points processed: 10
+ Number of hyperplanes created: 20
+ Number of facets in hull: 16
+ Number of distance tests for qhull: 51
+ Number of distance tests for merging: 257
+ Number of distance tests for checking: 100
+ Number of merged facets: 7
+ CPU seconds to compute hull (after input): 0
+ Approximate facet area: 0.64951905
+
+
+Output completed. Verifying that all points are below outer planes of
+all facets. Will make 120 distance computations.
+rbox 6 r s c G0.1 D2 | qhull d FA Tcv
+
+Delaunay triangulation by the convex hull of 10 points in 3-d:
+
+ Number of input sites: 10
+ Number of Delaunay regions: 9
+ Number of non-simplicial Delaunay regions: 3
+
+Statistics for: rbox 6 r s c G0.1 D2 | qhull d FA Tcv
+
+ Number of points processed: 10
+ Number of hyperplanes created: 20
+ Number of facets in hull: 10
+ Number of distance tests for qhull: 51
+ Number of distance tests for merging: 239
+ Number of distance tests for checking: 100
+ Number of merged facets: 7
+ CPU seconds to compute hull (after input): 0
+ Approximate facet area: 0.64951905
+
+
+Output completed. Verifying that all points are below outer planes of
+all facets. Will make 90 distance computations.
+rbox 6 r s c G0.1 D2 | qhull Qt v p Tcv
+2
+12
+-0.3359969878447703 -0.1939879513790815
+-0.3359969878447704 0.1939879513790817
+-0.2875 -5.224499218664525e-018
+0.3359969878447702 -0.1939879513790819
+0.3359969878447707 0.1939879513790815
+0.2875 -5.224499218664525e-018
+-2.27113250081401e-016 -0.3453321730569307
+-2.27113250081401e-016 -0.3453321730569307
+1.057503693988049e-016 0.3453321730569308
+1.057503693988049e-016 0.3453321730569308
+5.224499218664525e-018 -5.224499218664525e-018
+5.224499218664525e-018 -5.224499218664525e-018
+
+Output completed. Verifying that all points are below outer planes of
+all facets. Will make 120 distance computations.
+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
+Vertices and facets:
+- p6(v6): 0.5 0.5 -0.5
+ neighbors: f17 f18 f25 f27 f33 f34
+- p2(v2): -0.5 0.5 -0.5
+ neighbors: f17 f29 f33
+- p0(v0): -0.5 -0.5 -0.5
+ neighbors: f17 f18 f21 f22 f29 f30
+- p4(v1): 0.5 -0.5 -0.5
+ neighbors: f18 f21 f25
+- p5(v7): 0.5 -0.5 0.5
+ neighbors: f21 f22 f25 f27 f37 f38
+- p1(v3): -0.5 -0.5 0.5
+ neighbors: f22 f30 f37
+- p7(v5): 0.5 0.5 0.5
+ neighbors: f27 f34 f38
+- p3(v8): -0.5 0.5 0.5
+ neighbors: f29 f30 f33 f34 f37 f38
+- f17
+ - flags: top simplicial tricoplanar keepcentrum
+ - area: 0.5
+ - normal: 0 0 -1
+ - offset: -0.5
+ - center: 0 0 -0.5
+ - vertices: p6(v6) p2(v2) p0(v0)
+ - neighboring facets: f29 f18 f33
+- f18
+ - flags: bottom simplicial tricoplanar
+ - area: 0.5
+ - normal: 0 0 -1
+ - offset: -0.5
+ - center: 0 0 -0.5
+ - vertices: p6(v6) p4(v1) p0(v0)
+ - neighboring facets: f21 f17 f25
+- f21
+ - flags: top simplicial tricoplanar keepcentrum
+ - area: 0.5
+ - normal: 0 -1 0
+ - offset: -0.5
+ - center: 0 -0.5 0
+ - vertices: p5(v7) p4(v1) p0(v0)
+ - neighboring facets: f18 f22 f25
+- f22
+ - flags: bottom simplicial tricoplanar
+ - area: 0.5
+ - normal: 0 -1 0
+ - offset: -0.5
+ - center: 0 -0.5 0
+ - vertices: p5(v7) p1(v3) p0(v0)
+ - neighboring facets: f30 f21 f37
+- f25
+ - flags: top simplicial tricoplanar keepcentrum
+ - area: 0.5
+ - normal: 1 0 0
+ - offset: -0.5
+ - center: 0.5 0 0
+ - vertices: p5(v7) p6(v6) p4(v1)
+ - neighboring facets: f18 f21 f27
+- f27
+ - flags: bottom simplicial tricoplanar
+ - area: 0.5
+ - normal: 1 0 0
+ - offset: -0.5
+ - center: 0.5 0 0
+ - vertices: p5(v7) p6(v6) p7(v5)
+ - neighboring facets: f34 f38 f25
+- f29
+ - flags: bottom simplicial tricoplanar keepcentrum
+ - area: 0.5
+ - normal: -1 0 0
+ - offset: -0.5
+ - center: -0.5 0 0
+ - vertices: p3(v8) p2(v2) p0(v0)
+ - neighboring facets: f17 f30 f33
+- f30
+ - flags: top simplicial tricoplanar
+ - area: 0.5
+ - normal: -1 0 0
+ - offset: -0.5
+ - center: -0.5 0 0
+ - vertices: p3(v8) p1(v3) p0(v0)
+ - neighboring facets: f22 f29 f37
+- f33
+ - flags: bottom simplicial tricoplanar keepcentrum
+ - area: 0.5
+ - normal: 0 1 0
+ - offset: -0.5
+ - center: 0 0.5 0
+ - vertices: p3(v8) p6(v6) p2(v2)
+ - neighboring facets: f17 f29 f34
+- f34
+ - flags: top simplicial tricoplanar
+ - area: 0.5
+ - normal: 0 1 0
+ - offset: -0.5
+ - center: 0 0.5 0
+ - vertices: p3(v8) p6(v6) p7(v5)
+ - neighboring facets: f27 f38 f33
+- f37
+ - flags: top simplicial tricoplanar keepcentrum
+ - area: 0.5
+ - normal: 0 0 1
+ - offset: -0.5
+ - center: 0 0 0.5
+ - vertices: p3(v8) p5(v7) p1(v3)
+ - neighboring facets: f22 f30 f38
+- f38
+ - flags: bottom simplicial tricoplanar
+ - area: 0.5
+ - normal: 0 0 1
+ - offset: -0.5
+ - center: 0 0 0.5
+ - vertices: p3(v8) p5(v7) p7(v5)
+ - neighboring facets: f27 f34 f37
+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
+4
+12
+ 0 0 -1 -0.4999999999999993
+ 0 0 -1 -0.4999999999999993
+ 0 -1 0 -0.4999999999999993
+ 0 -1 0 -0.4999999999999993
+ 1 0 0 -0.4999999999999993
+ 1 0 0 -0.4999999999999993
+ -1 0 0 -0.4999999999999993
+ -1 0 0 -0.4999999999999993
+ 0 1 0 -0.4999999999999993
+ 0 1 0 -0.4999999999999993
+ 0 0 1 -0.4999999999999993
+ 0 0 1 -0.4999999999999993
+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
+4
+12
+ 0 0 -1 -0.5000000000000013
+ 0 0 -1 -0.5000000000000013
+ 0 -1 0 -0.5000000000000013
+ 0 -1 0 -0.5000000000000013
+ 1 0 0 -0.5000000000000013
+ 1 0 0 -0.5000000000000013
+ -1 0 0 -0.5000000000000013
+ -1 0 0 -0.5000000000000013
+ 0 1 0 -0.5000000000000013
+ 0 1 0 -0.5000000000000013
+ 0 0 1 -0.5000000000000013
+ 0 0 1 -0.5000000000000013
+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
+12
+17
+18
+21
+22
+25
+27
+29
+30
+33
+34
+37
+38
+12
+0
+0
+0
+0
+0
+0
+0
+0
+0
+0
+0
+0
+12
+3 6 1 8
+3 2 0 4
+3 1 3 4
+3 7 2 10
+3 1 2 5
+3 9 11 4
+3 0 7 8
+3 3 6 10
+3 0 6 9
+3 5 11 8
+3 3 7 11
+3 5 9 10
+8
+6 7 3 2 1 0 6
+3 10 3 7
+3 8 0 6
+6 11 9 8 6 7 10
+3 4 1 2
+6 11 5 4 2 3 10
+6 9 5 4 1 0 8
+3 11 5 9
+Options selected for Qhull 2010.0.3 2010/01/05:
+ run-id 769043788 Qtriangulate Centrum-premerge- 0.1 Qcoplanar-keep
+ FFacets-xridge summary FQhull Finner normals Fouter FQhull FIDs
+ Fmerges Fneighbors FNeighbors-vertex FOptions FQhull Fsummary FSize
+ FVertex-average Tcheck-frequently Tverify Fvertices _max-width 1
+ Error-roundoff 6.9e-016 _one-merge 0.3 _near-inside 1.5
+ Visible-distance 0.1 U-coplanar-distance 0.1 Width-outside 0.2
+ _wide-facet 0.6
+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
+10 3 8 8 12 8 12 0 0 0 6
+2 1.387359992873471e-015 -6.936799964367356e-016
+0
+2 6 1
+3 1
+ 0 0 0
+12
+3 6 2 0
+3 6 4 0
+3 5 4 0
+3 5 1 0
+3 5 6 4
+3 5 6 7
+3 3 2 0
+3 3 1 0
+3 3 6 2
+3 3 6 7
+3 3 5 1
+3 3 5 7
+Options selected for Qhull 2010.0.3 2010/01/05:
+ run-id 769043788 Qtriangulate Centrum-premerge- 0.1 Qcoplanar-keep
+ FFacets-xridge summary FQhull Finner normals Fouter FQhull FIDs
+ Fmerges Fneighbors FNeighbors-vertex FOptions FQhull Fsummary FSize
+ FVertex-average Tcheck-frequently Tverify Fvertices _max-width 1
+ Error-roundoff 6.9e-016 _one-merge 0.3 _near-inside 1.5
+ Visible-distance 0.1 U-coplanar-distance 0.1 Width-outside 0.2
+ _wide-facet 0.6
+
+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 | 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
+
+ Number of points processed: 8
+ Number of hyperplanes created: 11
+ Number of distance tests for qhull: 35
+ Number of distance tests for merging: 198
+ Number of distance tests for checking: 56
+ Number of merged facets: 6
+ CPU seconds to compute hull (after input): 0
+ Approximate facet area: 6
+ Approximate volume: 1
+
+
+Output completed. Verifying that all points are below outer planes of
+all facets. Will make 96 distance computations.
+rbox 6 r s c G0.1 D2 P0.1,0.1 | qhull s FP d FO Qt
+1
+0 10 16 0
+Options selected for Qhull 2010.0.3 2010/01/05:
+ run-id 769043788 summary FPoint-nearest delaunay Qtriangulate _pre-merge
+ _zero-centrum Pgood Qcoplanar _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
+
+Delaunay triangulation by the convex hull of 11 points in 3-d:
+
+ Number of input sites: 10
+ Number of nearly incident points: 1
+ Number of Delaunay regions: 12
+ Number of triangulated facets: 3
+
+Statistics for: rbox 6 r s c G0.1 D2 P0.1,0.1 | qhull s FP d FO Qt
+
+ Number of points processed: 10
+ Number of hyperplanes created: 20
+ Number of facets in hull: 16
+ Number of distance tests for qhull: 107
+ Number of distance tests for merging: 166
+ Number of distance tests for checking: 111
+ Number of merged facets: 6
+ CPU seconds to compute hull (after input): 0
+
+rbox 100 W0 | qhull Tv Q11
+
+Convex hull of 100 points in 3-d:
+
+ Number of vertices: 45
+ Number of facets: 86
+ Number of triangulated facets: 33
+
+Statistics for: rbox 100 W0 | qhull Tv Q11
+
+ Number of points processed: 52
+ Number of hyperplanes created: 172
+ Number of distance tests for qhull: 1576
+ Number of distance tests for merging: 1498
+ Number of distance tests for checking: 2172
+ Number of merged facets: 41
+ CPU seconds to compute hull (after input): 0
+
+
+Output completed. Verifying that all points are below outer planes of
+all facets. Will make 8600 distance computations.
+
+echo === test unbounded intersection ${d:-`date`}
+date
+=== test unbounded intersection Wed Jan 6 20:33:04 EST 2010
+rbox c | qhull PD0:0.5 n | qhull H0 Fp Tcv
+3
+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
+-10.101 -10.101 -10.101
+
+Output completed. Verifying that all points are below outer planes of
+all facets. Will make 25 distance computations.
+rbox 1000 W1e-3 D3 | qhull PA8 Fa FS s n Tcv
+8
+0.1446087232094602
+0.1622198334884075
+0.2057158590759609
+0.1567143851824352
+0.188985866819172
+0.1580674614313253
+0.1616733826473111
+0.1767351337533958
+0
+2 5.881743214947514 0.9968516315221347
+4
+8
+1.009144997325421e-005 0.9999999999463923 2.319049754624652e-006 -0.4999875785488853
+-1.229609861584452e-005 8.587946880918046e-005 0.9999999962367614 -0.5000048595493551
+-1.383340239672454e-005 -0.9999999998842695 6.332306547224586e-006 -0.4999917156571328
+1.802476239613105e-005 -1.901476191096464e-005 0.9999999996567733 -0.4999909156385879
+0.9999999996788913 1.780140020603311e-005 -1.803683546259361e-005 -0.4999971349013697
+3.470111681088062e-006 -3.668365732095583e-005 -0.9999999993211338 -0.4999893476858697
+-1.633273154317779e-005 -0.9999999998072314 1.08985791646657e-005 -0.4999921708899001
+-0.9999999997878146 -2.055073083002867e-005 -1.427680287414111e-006 -0.4999990322171606
+
+Convex hull of 1000 points in 3-d:
+
+ Number of vertices: 156
+ Number of facets: 308
+ Number of 'good' facets: 8
+
+Statistics for: rbox 1000 W1e-3 D3 | qhull PA8 Fa FS s n Tcv
+
+ Number of points processed: 203
+ Number of hyperplanes created: 1043
+ Number of distance tests for qhull: 21470
+ CPU seconds to compute hull (after input): 1.5e-005
+ Total facet area: 5.8817432
+ Total volume: 0.99685163
+
+
+Output completed. Verifying that all points are below outer planes of
+all facets. Will make 8000 distance computations.
+rbox 1000 W1e-3 D3 | qhull C-0.01 PM10 Fm n Tcv Qc
+10
+1
+1
+8
+0
+6
+7
+10
+0
+11
+6
+4
+10
+0.6345454980886085 0.2737427089707437 0.722784158750618 -0.7458921924784654
+-0.002537335608348058 0.6666534140166979 0.7453635270845306 -0.6767722083805113
+-0.0004022623770974538 0.9999997831336712 0.0005214571799133834 -0.5000167453415887
+-0.5357402012449896 -0.5359428531021374 -0.6524934443952053 -0.8112630402464979
+-0.005480509661076107 -0.9999701072857251 0.005454223027194169 -0.4992904789191578
+0.001196850675493192 0.0003334814784797861 0.9999992281689842 -0.4989807987213126
+0.9999992961453315 0.00118637926097064 1.459763172590211e-005 -0.4998611663332402
+-0.9129791746952518 0.146254515877973 -0.3808919048208779 -0.6797481567213486
+-0.999601787347817 0.02140818392627282 0.01838359029211947 -0.4985486000821886
+-0.003237401631533091 0.002761552371517554 -0.9999909464886048 -0.4969398742962436
+
+Output completed. Verifying that all points are below outer planes of
+all facets. Will make 10000 distance computations.
+rbox 1000 W1e-3 D3 | qhull C-0.01 PA8 PG n Tcv Qc
+4
+11
+0.6345454980886085 0.2737427089707437 0.722784158750618 -0.7458921924784654
+0.827830634881055 -0.3414688798813032 -0.4450791435520626 -0.76654742257561
+0.7383776593319755 -0.4655216164679664 0.4879426777814017 -0.7788991125303445
+0.2008161614085188 -0.8823413491644905 0.4256132198037725 -0.6982307124493007
+-0.4745617604911468 -0.2935495843214608 0.8298311738084084 -0.7523676152838531
+-0.8259135249806852 -0.5592200082473171 0.07169261907511673 -0.6812000445406895
+0.4193230672566199 0.6721295192910489 -0.610254106552413 -0.7755692997856909
+-0.5357402012449896 -0.5359428531021374 -0.6524934443952053 -0.8112630402464979
+-0.3304054030140147 0.436402674763686 -0.836890061548258 -0.7495022949733236
+0.6755431502353134 -0.2163920762108179 0.704851701795009 -0.7475007704997937
+-0.9129791746952518 0.146254515877973 -0.3808919048208779 -0.6797481567213486
+
+Output completed. Verifying that all points are below outer planes of
+all facets. Will make 8000 distance computations.
+rbox 10 | qhull FO Tz TO q_test.log.1
+cat q_test.log.1
+Options selected for Qhull 2010.0.3 2010/01/05:
+ run-id 769043788 Tz-stdout TOutput-file q_test.log.1 _pre-merge
+ _zero-centrum _max-width 0.92 Error-roundoff 6.8e-016 _one-merge 4.8e-015
+ _near-inside 2.4e-014 Visible-distance 1.4e-015
+ U-coplanar-distance 1.4e-015 Width-outside 2.7e-015 _wide-facet 8.2e-015
+
+Convex hull of 10 points in 3-d:
+
+ Number of vertices: 10
+ Number of facets: 16
+
+Statistics for: rbox 10 | qhull FO Tz TO q_test.log.1
+
+ Number of points processed: 10
+ Number of hyperplanes created: 27
+ Number of distance tests for qhull: 44
+ CPU seconds to compute hull (after input): 0
+
+
+echo === check Delaunay/Voronoi ${d:-`date`}
+date
+=== check Delaunay/Voronoi Wed Jan 6 20:33:04 EST 2010
+rbox 10 D2 | qhull d Tcv
+
+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 D2 | qhull d Tcv
+
+ Number of points processed: 10
+ Number of hyperplanes created: 28
+ Number of facets in hull: 16
+ Number of distance tests for qhull: 48
+ CPU seconds to compute hull (after input): 0
+
+
+Output completed. Verifying that all points are below 2.1e-015 of
+all facets. Will make 140 distance computations.
+rbox 10 D2 | qhull d Tcv Qz
+
+Delaunay triangulation by the convex hull of 11 points in 3-d:
+
+ Number of input sites and at-infinity: 11
+ Number of Delaunay regions: 14
+
+Statistics for: rbox 10 D2 | qhull d Tcv Qz
+
+ Number of points processed: 11
+ Number of hyperplanes created: 31
+ Number of facets in hull: 18
+ Number of distance tests for qhull: 56
+ CPU seconds to compute hull (after input): 0
+
+
+Output completed. Verifying that all points are below 2.1e-015 of
+all facets. Will make 154 distance computations.
+rbox 10 D3 | qhull 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 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 c | qhull d Qz Ft Tcv
+3
+10 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 0 0
+ 0 0 0
+4 9 1 2 0
+4 9 2 4 0
+4 9 4 1 0
+4 9 5 7 1
+4 9 7 6 2
+4 9 2 6 4
+4 9 6 7 4
+4 9 5 1 4
+4 9 7 5 4
+4 9 1 3 2
+4 9 3 7 2
+4 9 7 3 1
+
+Output completed. Verifying that all points are below outer planes of
+all facets. Will make 9 distance computations.
+rbox 10 s D2 c | qhull d Tcv
+
+Delaunay triangulation by the convex hull of 14 points in 3-d:
+
+ Number of input sites: 14
+ Number of Delaunay regions: 15
+ Number of non-simplicial Delaunay regions: 1
+
+Statistics for: rbox 10 s D2 c | qhull d Tcv
+
+ Number of points processed: 14
+ Number of hyperplanes created: 32
+ Number of facets in hull: 16
+ Number of distance tests for qhull: 110
+ Number of distance tests for merging: 388
+ Number of distance tests for checking: 182
+ Number of merged facets: 8
+ CPU seconds to compute hull (after input): 0
+ Maximum distance of point above facet: 1.4e-015 (0.3x)
+
+
+Output completed. Verifying that all points are below outer planes of
+all facets. Will make 210 distance computations.
+rbox 10 s D2 | qhull d Tcv Q8 Qz
+
+Delaunay triangulation by the convex hull of 11 points in 3-d:
+
+ Number of input sites and at-infinity: 11
+ Number of Delaunay regions: 1
+ Number of non-simplicial Delaunay regions: 1
+
+Statistics for: rbox 10 s D2 | qhull d Tcv Q8 Qz
+
+ Number of points processed: 11
+ Number of hyperplanes created: 19
+ Number of facets in hull: 11
+ Number of distance tests for qhull: 55
+ Number of distance tests for merging: 278
+ Number of distance tests for checking: 132
+ Number of merged facets: 7
+ 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 outer planes of
+all facets. Will make 11 distance computations.
+rbox 10 D2 | qhull d Tcv p
+3
+10
+-0.02222276248244826 -0.4979727817680433 0.2484707425541546
+-0.4285431913366012 0.4745826469497594 0.4088779556267987
+0.3105396575392593 0.2400179190933871 0.1540434803905201
+-0.01883958887200764 0.3630260628303756 0.1321428524029901
+0.3790312361708202 0.3779794437605696 0.2865331378987296
+-0.2994955874043476 0.3776609263174803 0.2323253821416525
+0.3471817493878135 0.08365533089605656 0.1275333814953112
+-0.004858197648877462 0.3482682405489201 0.121314369459436
+0.3443122672329771 -0.1437312230875075 0.1392096018573439
+0.3093307803471859 -0.07758103877080701 0.1017043492469564
+
+Output completed. Verifying that all points are below 2.1e-015 of
+all facets. Will make 140 distance computations.
+rbox 10 D2 | qhull d Tcv i
+14
+9 7 0
+8 9 0
+3 4 1
+3 7 4
+7 2 4
+0 5 1
+7 5 0
+5 3 1
+3 5 7
+6 7 9
+6 2 7
+8 6 9
+6 8 4
+2 6 4
+
+Output completed. Verifying that all points are below 2.1e-015 of
+all facets. Will make 140 distance computations.
+rbox 10 D2 | qhull d Tcv o
+3
+10 14 21
+-0.02222276248244826 -0.4979727817680433 0.2484707425541546
+-0.4285431913366012 0.4745826469497594 0.4088779556267987
+0.3105396575392593 0.2400179190933871 0.1540434803905201
+-0.01883958887200764 0.3630260628303756 0.1321428524029901
+0.3790312361708202 0.3779794437605696 0.2865331378987296
+-0.2994955874043476 0.3776609263174803 0.2323253821416525
+0.3471817493878135 0.08365533089605656 0.1275333814953112
+-0.004858197648877462 0.3482682405489201 0.121314369459436
+0.3443122672329771 -0.1437312230875075 0.1392096018573439
+0.3093307803471859 -0.07758103877080701 0.1017043492469564
+3 9 7 0
+3 8 9 0
+3 3 4 1
+3 3 7 4
+3 7 2 4
+3 0 5 1
+3 7 5 0
+3 5 3 1
+3 3 5 7
+3 6 7 9
+3 6 2 7
+3 8 6 9
+3 6 8 4
+3 2 6 4
+
+Output completed. Verifying that all points are below 2.1e-015 of
+all facets. Will make 140 distance computations.
+rbox 10 D2 | qhull v Tcv o
+2
+15 10 1
+-10.101 -10.101
+-0.1294381801544405 -0.07247409101984713
+0.08267689532419757 -0.2397644955865707
+0.1295260566906469 1.71603357311684
+0.1740355150742393 0.5317519038435643
+0.1851415205797575 0.3882545794457365
+-0.906593986684811 -0.2962957610652137
+-0.1954805620516266 -0.07111892482963184
+-0.140758131083247 0.723385704823608
+-0.1676297826663961 0.2080621273999393
+0.05868313821742954 0.06632066014880164
+0.0880634139973699 0.1054080604689985
+0.4761588899009251 -0.03168366595227296
+3.094213357897465 -0.06472194567768184
+0.5410515627308723 0.2115615434955919
+5 7 1 2 0 6
+4 8 3 0 6
+3 14 5 11
+4 9 4 3 8
+6 14 5 4 3 0 13
+4 9 7 6 8
+5 14 11 10 12 13
+7 11 5 4 9 7 1 10
+4 13 0 2 12
+4 12 2 1 10
+
+Output completed. Verifying that all points are below 2.1e-015 of
+all facets. Will make 140 distance computations.
+rbox 10 D2 | qhull v Tcv p
+2
+14
+-0.1294381801544405 -0.07247409101984713
+0.08267689532419757 -0.2397644955865707
+0.1295260566906469 1.71603357311684
+0.1740355150742393 0.5317519038435643
+0.1851415205797575 0.3882545794457365
+-0.906593986684811 -0.2962957610652137
+-0.1954805620516266 -0.07111892482963184
+-0.140758131083247 0.723385704823608
+-0.1676297826663961 0.2080621273999393
+0.05868313821742954 0.06632066014880164
+0.0880634139973699 0.1054080604689985
+0.4761588899009251 -0.03168366595227296
+3.094213357897465 -0.06472194567768184
+0.5410515627308723 0.2115615434955919
+
+Output completed. Verifying that all points are below 2.1e-015 of
+all facets. Will make 140 distance computations.
+rbox 10 D2 | qhull v Tcv G
+{appearance {linewidth 3} LIST # rbox 10 D2 | qhull v Tcv G
+{appearance {+edge -face} OFF 15 10 1 # Voronoi centers and cells
+ 0 0 0 # infinity not used
+# 1 f8
+-0.1294381801544405 -0.07247409101984713 0
+# 2 f11
+0.08267689532419757 -0.2397644955865707 0
+# 3 f12
+0.1295260566906469 1.71603357311684 0
+# 4 f14
+0.1740355150742393 0.5317519038435643 0
+# 5 f15
+0.1851415205797575 0.3882545794457365 0
+# 6 f19
+-0.906593986684811 -0.2962957610652137 0
+# 7 f20
+-0.1954805620516266 -0.07111892482963184 0
+# 8 f21
+-0.140758131083247 0.723385704823608 0
+# 9 f22
+-0.1676297826663961 0.2080621273999393 0
+# 10 f23
+0.05868313821742954 0.06632066014880164 0
+# 11 f24
+0.0880634139973699 0.1054080604689985 0
+# 12 f25
+0.4761588899009251 -0.03168366595227296 0
+# 13 f26
+3.094213357897465 -0.06472194567768184 0
+# 14 f27
+0.5410515627308723 0.2115615434955919 0
+4 7 1 2 6 # p0(v2)
+3 8 3 6 # p1(v0)
+3 14 5 11 # p2(v8)
+4 9 4 3 8 # p3(v7)
+5 14 5 4 3 13 # p4(v1)
+4 9 7 6 8 # p5(v9)
+5 14 11 10 12 13 # p6(v10)
+7 11 5 4 9 7 1 10 # p7(v5)
+3 13 2 12 # p8(v6)
+4 12 2 1 10 # p9(v3)
+}
+}
+
+Output completed. Verifying that all points are below 2.1e-015 of
+all facets. Will make 140 distance computations.
+rbox 10 D2 | qhull v Tcv Fv
+23
+4 0 1 0 6
+4 0 7 1 7
+4 0 9 1 2
+4 0 8 0 2
+4 0 5 6 7
+4 1 4 0 3
+4 1 3 3 8
+4 1 5 6 8
+4 2 7 5 11
+4 2 4 5 14
+4 2 6 11 14
+4 3 4 3 4
+4 3 7 4 9
+4 3 5 8 9
+4 4 8 0 13
+4 4 7 4 5
+4 4 6 13 14
+4 5 7 7 9
+4 6 7 10 11
+4 6 9 10 12
+4 6 8 12 13
+4 7 9 1 10
+4 8 9 2 12
+
+Output completed. Verifying that all points are below 2.1e-015 of
+all facets. Will make 140 distance computations.
+rbox 10 D2 | qhull v Tcv Fi
+19
+5 0 7 0.02051532578114318 0.9997895385570373 0.07511430445246034
+5 0 9 0.6192591330569687 0.785186682340914 0.1370614663104578
+5 0 5 -0.3018806392032151 0.9533457293522945 0.008789126238507562
+5 1 3 0.9648718030091262 -0.2627211520946075 0.3258622775065154
+5 1 5 0.7995952824356682 -0.6005392446015697 0.5469710423089692
+5 2 7 -0.9458410914974847 0.3246299888101017 0.04907537812572171
+5 2 4 0.4446710312325427 0.8956939622340808 -0.4300843534994402
+5 2 6 0.228159509754326 -0.9736237661995858 0.08253528745668785
+5 3 4 0.99929448732669 0.03755699133966514 -0.1938837324602516
+5 3 7 0.6877523324625938 -0.7259454037269345 0.2663295190946454
+5 3 5 -0.9986432053419565 0.0520744507829223 -0.1782370644858236
+5 4 7 -0.9970183790688239 -0.0771644464696991 0.2145489484590232
+5 4 6 -0.1075842248297362 -0.9941959739245502 0.2685422477498993
+5 5 7 0.9950609206245129 -0.09926612839179749 0.187455367716064
+5 6 7 -0.799364184215507 0.6008468199079338 0.00706064116377911
+5 6 9 -0.2285415587894346 -0.9735341575446109 0.07797696388863325
+5 6 8 -0.01261839651625043 -0.9999203848653945 -0.02567278177543587
+5 7 9 0.593695288592636 -0.8046899429612046 0.01852766555277025
+5 8 9 -0.4674785097727936 0.8840044360186256 0.2506025495170938
+
+Voronoi ridge statistics
+ 19 bounded ridges
+3.8e-017 ave. distance of midpoint to ridge
+1.1e-016 max. distance of midpoint to ridge
+ 19 bounded ridges with ok normal
+2.3e-017 ave. angle to ridge
+8.4e-017 max. angle to ridge
+
+Output completed. Verifying that all points are below 2.1e-015 of
+all facets. Will make 140 distance computations.
+rbox 10 D2 | qhull v Tcv Fo
+4
+5 0 1 -0.3854955578888162 0.9227096915324941 -0.07609298438083832
+5 0 8 0.719062520784207 0.6949453872092842 0.1071733734620185
+5 1 4 0.9929212365203528 -0.1187746524595787 0.07521211888503934
+5 4 8 -0.06640144810487507 -0.9977929883946748 0.1408811441173878
+
+Output completed. Verifying that all points are below 2.1e-015 of
+all facets. Will make 140 distance computations.
+rbox 10 D2 | qhull v Qu o Fv Fi Fo Tcv
+2
+3 10 1
+-10.101 -10.101
+-0.06934933486244871 0.05349366577784779
+-0.3051278694340226 0.1614985055810222
+3 0 2 1
+2 0 1
+0
+0
+3 0 1 2
+0
+0
+0
+2 0 2
+0
+5
+4 0 8 0 2
+4 0 4 1 2
+4 0 1 0 1
+4 1 4 0 1
+4 4 8 0 2
+1
+5 0 4 0.4164624817835533 0.9091529031283372 -0.01975252543405322
+4
+5 0 8 0.7190625207842071 0.6949453872092841 0.1071733734620185
+5 0 1 -0.385495557888816 0.9227096915324942 -0.07609298438083825
+5 1 4 0.9929212365203528 -0.1187746524595787 0.07521211888503931
+5 4 8 -0.06640144810487507 -0.9977929883946748 0.1408811441173878
+
+Voronoi ridge statistics
+ 1 bounded ridges
+3.3e-018 ave. distance of midpoint to ridge
+3.3e-018 max. distance of midpoint to ridge
+ 1 bounded ridges with ok normal
+ 0 max. angle to ridge
+
+Output completed. Verifying that all points are below 2.1e-015 of
+all facets. Will make 20 distance computations.
+rbox 10 D3 | qhull v Fv Tcv
+32
+6 0 1 0 17 15 3
+7 0 9 0 7 12 11 2
+6 0 6 0 7 18 17
+5 0 7 0 2 3
+6 0 2 2 3 15 11
+5 0 8 7 18 12
+7 0 5 11 12 18 17 15
+5 1 7 0 5 3
+6 1 2 3 5 0 15
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+6 2 3 1 4 13 9
+6 2 9 1 2 11 9
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+6 2 4 4 5 0 13
+7 2 5 9 11 15 0 13
+7 3 9 0 6 10 9 1
+5 3 7 0 4 1
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+7 3 4 0 8 14 13 4
+6 3 8 6 8 14 10
+6 3 5 9 10 14 13
+5 4 7 0 5 4
+5 4 6 0 16 8
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+6 4 5 13 0 16 14
+6 5 9 9 11 12 10
+7 5 8 10 12 18 16 14
+6 5 6 0 17 18 16
+5 6 9 0 6 7
+7 6 8 6 7 18 16 8
+5 7 9 0 1 2
+6 8 9 6 7 12 10
+
+Output completed. Verifying that all points are below 2.9e-015 of
+all facets. Will make 180 distance computations.
+rbox 10 D3 | qhull v Fi Tcv
+13
+6 0 2 0.1026012494065407 0.8309156055795222 -0.5468566905731636 0.2399036185798246
+6 0 8 -0.1644981128676534 0.5492243080463516 -0.8193247404503217 0.1220237399030442
+6 0 5 -0.1640386761614814 0.6276090456203117 -0.7610507201092119 0.1709974344854014
+6 2 3 0.8628264983391888 0.1277424492346302 -0.4890933453107615 -0.1660057988150948
+6 2 9 0.5146151495466439 -0.7556910962035635 -0.4050953159143437 -0.3000434746332832
+6 2 7 0.9862472983740704 0.008356748990702056 0.1650649302430827 -0.2195655184060845
+6 3 8 -0.9471370887617876 -0.1545163381156412 -0.2811690529684561 0.04372902199764636
+6 3 5 -0.9850113492204077 -0.1553182373520525 -0.07502590921037614 0.09265233510028274
+6 4 8 -0.717713539929897 -0.2457215366779668 -0.6515429387338295 -0.02974683605231285
+6 5 9 0.7110332662678564 -0.693517783370965 -0.1160378317993187 -0.2706062861955821
+6 5 8 -0.1310037283001485 -0.04490613421135386 -0.9903643078593113 -0.2004293237314498
+6 6 8 0.563653077615962 0.07101685912338848 0.8229531054770395 0.4221671959133707
+6 8 9 0.7278413449934528 -0.6852671087526036 0.0256118367160405 -0.2412830130907242
+
+Voronoi ridge statistics
+ 15 non-simplicial Voronoi vertices for all ridges
+2.5e-017 ave. distance to ridge
+7.2e-017 max. distance to ridge
+ 13 bounded ridges
+4.1e-017 ave. distance of midpoint to ridge
+1.2e-016 max. distance of midpoint to ridge
+ 13 bounded ridges with ok normal
+7.9e-018 ave. angle to ridge
+ 5e-017 max. angle to ridge
+
+Output completed. Verifying that all points are below 2.9e-015 of
+all facets. Will make 180 distance computations.
+rbox 10 D3 | qhull v Fo Tcv
+19
+6 0 1 -0.1769702595802888 0.8331351847724078 0.5239916899325132 0.004105600879712603
+6 0 9 0.5856843296472444 -0.1558732679166011 -0.7954102025713886 -0.1264594278193164
+6 0 6 -0.3055017680243689 0.3812318858994053 -0.8725427891556766 -0.04822326899809229
+6 0 7 0.6633910639781656 0.667288353076621 -0.3385831509130483 0.06175731395259088
+6 1 7 0.7533877382120362 0.3349392388487628 -0.5658821628141002 0.06152842458597945
+6 1 2 0.2077539373736713 0.4344067294949112 -0.8764297432625571 0.2556318087147513
+6 1 5 -0.08886729274769883 0.2768317827550713 -0.9568002760954576 0.1656561460661369
+6 2 4 0.8896724708236495 0.4529391082738921 -0.05769799697211233 -0.1249699490416031
+6 2 5 -0.6080629223625024 -0.1069684332549475 -0.7866493734408967 -0.05602222006342435
+6 3 9 0.115764860415124 -0.9728190902550374 -0.2005530222370838 -0.2615067759720445
+6 3 7 0.313105673132462 -0.1651787990807289 0.9352437125084114 -0.1060546443225209
+6 3 6 -0.8429664438017094 -0.1288333013498811 -0.5223117412882754 -0.1470675860428305
+6 3 4 -0.6546392846048734 0.1665291828386521 0.7373706247980797 0.1638426312062791
+6 4 7 0.8997625993863545 -0.3161631359012115 0.3007792151107231 -0.2534488584590283
+6 4 6 -0.6610636619910347 -0.1756381951302929 -0.7294834194184102 -0.1931488689248214
+6 4 5 -0.8177140658972858 -0.2799433900977096 -0.5029666040348315 0.01966883326066588
+6 5 6 -0.4656867325018189 -0.06587339986788439 -0.8824945112359766 -0.374728122564582
+6 6 9 0.7885740013077053 -0.5314391513195502 0.3093921022041632 -0.04784058563315538
+6 7 9 -0.01257265438745097 -0.8388634914110146 -0.5441966291143086 -0.20188365801714
+
+Voronoi ridge statistics
+ 14 non-simplicial Voronoi vertices for all ridges
+ 2e-017 ave. distance to ridge
+4.6e-017 max. distance to ridge
+
+Output completed. Verifying that all points are below 2.9e-015 of
+all facets. Will make 180 distance computations.
+rbox 10 D3 | qhull v Qu o Fv Fi Fo Tcv
+3
+10 10 1
+-10.101 -10.101 -10.101
+-0.04510412048603353 -0.1962229636993575 -0.06746145990413341
+-0.203283876182382 -0.3188041900902703 0.1251484339163773
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+6 7 9 0 2 1 4
+3
+6 1 9 0.5123553720802023 -0.363812082853534 -0.7779027838170596 -0.100757404152973
+6 2 6 -0.5221667006142687 -0.08192192666458392 -0.8488997200501195 -0.2535440955968327
+6 6 7 0.7522136453226688 0.06033708575303692 0.6561509489997046 0.09003235761431798
+15
+6 0 1 -0.1769702595802887 0.8331351847724077 0.5239916899325134 0.004105600879712502
+6 0 9 0.5856843296472445 -0.1558732679166013 -0.7954102025713885 -0.1264594278193165
+6 1 6 -0.2436653478720985 0.1478836806870481 -0.9585184480399011 -0.04663519095132838
+6 1 2 0.207753937373669 0.4344067294949101 -0.8764297432625582 0.2556318087147513
+6 1 4 0.4442200788473618 0.4986447037065234 -0.7443265284902031 0.1737545932855555
+6 1 7 0.7533877382120362 0.3349392388487629 -0.5658821628141002 0.06152842458597949
+6 2 5 -0.6080629223625018 -0.1069684332549471 -0.7866493734408971 -0.05602222006342417
+6 2 4 0.8896724708236495 0.4529391082738921 -0.05769799697211298 -0.1249699490416032
+6 3 6 -0.8429664438017093 -0.1288333013498812 -0.5223117412882754 -0.1470675860428305
+6 3 7 0.3131056731324615 -0.1651787990807287 0.9352437125084115 -0.1060546443225208
+6 4 6 -0.6610636619910348 -0.1756381951302929 -0.7294834194184101 -0.1931488689248214
+6 4 7 0.8997625993863544 -0.3161631359012116 0.3007792151107231 -0.2534488584590283
+6 5 6 -0.4656867325018182 -0.06587339986788397 -0.882494511235977 -0.3747281225645819
+6 6 9 0.7885740013077053 -0.5314391513195504 0.309392102204163 -0.04784058563315548
+6 7 9 -0.01257265438745048 -0.838863491411015 -0.544196629114308 -0.2018836580171402
+
+Voronoi ridge statistics
+ 9 non-simplicial Voronoi vertices for all ridges
+2.7e-017 ave. distance to ridge
+ 7e-017 max. distance to ridge
+ 3 bounded ridges
+7.2e-017 ave. distance of midpoint to ridge
+9.7e-017 max. distance of midpoint to ridge
+ 3 bounded ridges with ok normal
+1.5e-017 ave. angle to ridge
+4.6e-017 max. angle to ridge
+
+Output completed. Verifying that all points are below 2.9e-015 of
+all facets. Will make 90 distance computations.
+rbox 5 D2 | qhull v f FnN o
+Vertices and facets:
+- p3(v5): 0.43 -0.11 0.19
+ neighbors: f5 f6 f7 f8
+- p2(v1): 0.47 -0.11 0.24
+ neighbors: f1 f5 f7
+- p4(v0): -0.39 0.45 0.36
+ neighbors: f1 f3 f5 f6
+- p0(v3): -0.34 0.23 0.17
+ neighbors: f3 f6 f8
+- p1(v2): 0.32 -0.23 0.16
+ neighbors: f1 f3 f7 f8
+- f5
+ - flags: top simplicial
+ - normal: 0.437 0.773 -0.4599
+ - offset: -0.01170704
+ - center: 0.4751017705052503 0.8404705693422866
+ - vertices: p3(v5) p2(v1) p4(v0)
+ - neighboring facets: f1 f6 f7
+- f6
+ - flags: bottom simplicial
+ - normal: 0.3235 0.6691 -0.669
+ - offset: 0.0657
+ - center: 0.2417735613471299 0.5000766029034821
+ - vertices: p3(v5) p0(v3) p4(v0)
+ - neighboring facets: f3 f5 f8
+- f7
+ - flags: top simplicial
+ - normal: 0.6288 -0.3317 -0.7033
+ - offset: -0.1682885
+ - center: 0.447029359505762 -0.2357835939937328
+ - vertices: p3(v5) p1(v2) p2(v1)
+ - neighboring facets: f1 f5 f8
+- f8
+ - flags: top simplicial
+ - normal: 0.1177 0.1841 -0.9758
+ - offset: 0.15929
+ - center: 0.06029550723695779 0.09433023738340308
+ - vertices: p3(v5) p0(v3) p1(v2)
+ - neighboring facets: f3 f7 f6
+4
+3 -1 1 2
+3 -3 0 3
+3 -1 0 3
+3 -3 2 1
+5
+3 3 -3 1
+4 3 -3 -1 2
+3 2 -1 0
+4 3 1 0 2
+4 1 -3 -1 0
+2
+5 5 1
+-10.101 -10.101
+0.4751017705052503 0.8404705693422866
+0.2417735613471299 0.5000766029034821
+0.447029359505762 -0.2357835939937328
+0.06029550723695779 0.09433023738340308
+3 2 4 0
+3 3 4 0
+3 1 3 0
+4 3 4 2 1
+3 1 2 0
+
+echo === check Halfspace ${d:-`date`}
+date
+=== check Halfspace Wed Jan 6 20:33:05 EST 2010
+rbox 100 s D4 | qhull FA FV n s Tcv | qhull H Fp Tcv | qhull FA Tcv
+
+Convex hull of 100 points in 4-d:
+
+ Number of vertices: 100
+ Number of facets: 584
+
+Statistics for: rbox 100 s D4 | qhull FA FV n s Tcv
+
+ Number of points processed: 100
+ Number of hyperplanes created: 1718
+ Number of distance tests for qhull: 4091
+ CPU seconds to compute hull (after input): 1.5e-005
+ Total facet area: 1.7919449
+ Total volume: 0.18640279
+
+
+Output completed. Verifying that all points are below 2.8e-015 of
+all facets. Will make 58400 distance computations.
+
+Output completed. Verifying that all points are below outer planes of
+all facets. Will make 58400 distance computations.
+
+Convex hull of 100 points in 4-d:
+
+ Number of vertices: 100
+ Number of facets: 584
+
+Statistics for: | qhull FA Tcv
+
+ Number of points processed: 100
+ Number of hyperplanes created: 1718
+ Number of distance tests for qhull: 4091
+ CPU seconds to compute hull (after input): 0
+ Total facet area: 1.7919449
+ Total volume: 0.18640279
+
+
+Output completed. Verifying that all points are below 2.8e-015 of
+all facets. Will make 58400 distance computations.
+rbox d D3 | qhull FQ n s FD Tcv | qhull Fd H0.1,0.1 Fp FQ Tcv
+
+Convex hull of 6 points in 3-d:
+
+ Number of vertices: 6
+ Number of facets: 8
+
+Statistics for: rbox d D3 | qhull FQ n s FD Tcv
+
+ 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.
+3
+6
+-8.870129023647033e-018 -8.870129023647033e-018 0.5000000000000001
+-1.046932722806315e-017 0.5000000000000001 0
+-0.5000000000000001 -3.834687558809669e-017 0
+0.5000000000000001 -1.046932722806315e-017 0
+-3.834687558809669e-017 -0.5000000000000001 0
+-5.983440739404378e-018 -4.925665994873207e-017 -0.5000000000000002
+rbox d D3 | qhull FQ n s FD Tcv | qhull Fd H0.1,0.1 Fp FQ Tcv
+
+Output completed. Verifying that all points are below outer planes of
+all facets. Will make 48 distance computations.
+rbox 5 r D2 | qhull s n Tcv | qhull H0 Fp Tcv
+
+Convex hull of 5 points in 2-d:
+
+ Number of vertices: 5
+ Number of facets: 5
+
+Statistics for: rbox 5 r D2 | qhull s n Tcv
+
+ Number of points processed: 5
+ Number of hyperplanes created: 8
+ Number of distance tests for qhull: 8
+ CPU seconds to compute hull (after input): 0
+
+
+Output completed. Verifying that all points are below 1.3e-015 of
+all facets. Will make 25 distance computations.
+2
+5
+-0.4045084971874738 -0.2938926261462365
+ 0.5 -1.146068174088666e-016
+0.1545084971874737 -0.4755282581475768
+-0.4045084971874737 0.2938926261462367
+0.1545084971874737 0.4755282581475768
+
+Output completed. Verifying that all points are below 6.4e-015 of
+all facets. Will make 25 distance computations.
+
+echo === check qhull ${d:-`date`}
+date
+=== check qhull Wed Jan 6 20:33:05 EST 2010
+rbox 10 s D3 | qhull Tcv
+
+Convex hull of 10 points in 3-d:
+
+ Number of vertices: 10
+ Number of facets: 16
+
+Statistics for: rbox 10 s D3 | qhull Tcv
+
+ Number of points processed: 10
+ Number of hyperplanes created: 29
+ Number of distance tests for qhull: 49
+ CPU seconds to compute hull (after input): 0
+
+
+Output completed. Verifying that all points are below 2e-015 of
+all facets. Will make 160 distance computations.
+rbox 10 s D3 | qhull f Pd0:0.5 Pd2 Tcv
+Vertices and facets:
+- p7(v8): 0.2 0.093 0.45
+- p9(v5): 0.29 -0.16 0.38
+- p3(v1): 0.48 -0.13 0.022
+- p8(v10): 0.32 0.025 -0.38
+- f16
+ - flags: bottom simplicial
+ - normal: 0.858 0.1759 0.4826
+ - offset: -0.4016457
+ - vertices: p7(v8) p9(v5) p3(v1)
+ - neighboring facets: f7 f27 f23
+- f27
+ - flags: bottom simplicial
+ - normal: 0.646 0.7625 0.03668
+ - offset: -0.2138755
+ - vertices: p8(v10) p7(v8) p3(v1)
+ - neighboring facets: f16 f26 f28
+
+Output completed. Verifying that all points are below 2e-015 of
+all facets. Will make 20 distance computations.
+rbox 10 s D3 | qhull f Tcv PD2:-0.5
+Vertices and facets:
+- p4(v7): 0.23 -0.32 -0.31
+- p1(v3): -0.072 0.057 -0.49
+- p6(v2): -0.13 -0.47 -0.09
+- p0(v9): -0.37 -0.27 0.19
+- p8(v10): 0.32 0.025 -0.38
+- p5(v6): 0.028 0.16 -0.47
+- f12
+ - flags: top simplicial
+ - normal: -0.2354 -0.5691 -0.7879
+ - offset: -0.3715833
+ - vertices: p4(v7) p1(v3) p6(v2)
+ - neighboring facets: f21 f11 f25
+- f21
+ - flags: bottom simplicial
+ - normal: -0.8148 -0.2922 -0.5006
+ - offset: -0.2881945
+ - vertices: p0(v9) p1(v3) p6(v2)
+ - neighboring facets: f12 f19 f20
+- f24
+ - flags: top simplicial
+ - normal: 0.2636 -0.06941 -0.9621
+ - offset: -0.4497787
+ - vertices: p8(v10) p5(v6) p1(v3)
+ - neighboring facets: f9 f25 f28
+- f25
+ - flags: bottom simplicial
+ - normal: 0.2402 -0.2624 -0.9346
+ - offset: -0.4268812
+ - vertices: p8(v10) p4(v7) p1(v3)
+ - neighboring facets: f12 f24 f26
+
+Output completed. Verifying that all points are below 2e-015 of
+all facets. Will make 40 distance computations.
+rbox 10 s D3 | qhull QR-1
+
+Convex hull of 10 points in 3-d:
+
+ Number of vertices: 10
+ Number of facets: 16
+
+Statistics for: rbox 10 s D3 | qhull QR-1 QR-1262827985
+
+ Number of points processed: 10
+ Number of hyperplanes created: 29
+ Number of distance tests for qhull: 49
+ CPU seconds to compute hull (after input): 0
+
+rbox 10 s D3 | qhull QR-40
+
+Convex hull of 10 points in 3-d:
+
+ Number of vertices: 10
+ Number of facets: 16
+
+Statistics for: rbox 10 s D3 | qhull QR-40 QR-40
+
+ Number of points processed: 10
+ Number of hyperplanes created: 29
+ Number of distance tests for qhull: 49
+ CPU seconds to compute hull (after input): 0
+
+rbox 1000 D3 | qhull Tcvs
+
+
+ qhull invoked by: rbox 1000 D3 | qhull Tcvs
+2010.0.3 2010/01/05 with options:
+ run-id 769060595 Tcheck-frequently Tverify Tstatistics _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
+
+precision constants:
+ 0.5 max. abs. coordinate in the (transformed) input('Qbd:n')
+ 6.9e-016 max. roundoff error for distance computation('En')
+ 6.7e-016 max. roundoff error for angle computations
+ 2.8e-015 min. distance for outside points ('Wn')
+ 1.4e-015 min. distance for visible facets ('Vn')
+ 1.4e-015 max. distance for coplanar facets ('Un')
+ 8.3e-015 max. facet width for recomputing centrum and area
+ 2.4e-014 max. distance for near-inside points
+ 1.4e-015 radius of pre-merge centrum
+ 4.9e-015 max. distance for merging two simplicial facets
+ 2.2e-016 max. roundoff error for arithmetic operations
+ 1.1e-308 min. denominator for divisions
+ zero diagonal for Gauss: 8.88e-015 1.78e-014 2.66e-014
+
+
+precision statistics
+2.4e-017 ave. distance of a new vertex to a facet(!0s)
+ 9e-017 max. distance of a new vertex to a facet
+5.9e-017 max. distance of an output vertex to a facet
+-5.4e-017 min. distance of an output vertex to a facet
+ 0.0026 min. denominator in hyperplane computation
+
+summary information
+ 73 number of vertices in output
+ 142 number of facets in output
+ 3 average number of neighbors per facet
+ 3 maximum number of neighbors
+ 3 average number of vertices per facet
+ 3 maximum number of vertices
+ 82 vertices created altogether
+ 368 facets created altogether
+ 0 maximum merges for a facet(at most 511)
+ 0.93 average angle(cosine) of facet normals for all ridges
+ 1 maximum angle(cosine) of facet normals across a ridge
+ 0.21 minimum angle(cosine) of facet normals across a ridge
+
+build hull statistics
+ 81 points processed
+ 73 max. vertices at any one time
+ 2.78 ave. visible facets per iteration
+ 0.21 ave. visible facets without an horizon neighbor
+ 2.78 ave. facets deleted per iteration
+ 8 maximum
+ 5.43 ave. visible vertices per iteration
+ 11 maximum
+ 4.38 ave. horizon facets per iteration
+ 4.48 ave. new or merged facets per iteration
+ 10 maximum(includes initial simplex)
+ -0.77 average new facet balance
+ 1.5 standard deviation
+ 77 number of trials
+ 7 determinants computed(area & initial hull)
+ 504 distance tests for facet visibility
+ 73 points checked for facets' outer planes
+ 12.4 ave. distance tests per check
+ 1629 max visit_id/2
+ 619 max vertex_visit/2
+
+partitioning statistics(see previous for outer planes)
+ 8 total vertices deleted
+ 1 maximum vertices deleted per iteration
+ 135 calls to findbest
+ 2.59 ave. facets tested
+ 7 max. facets tested
+ 2045 calls to findbestnew
+ 4.47 ave. facets tested
+ 13 max. facets tested
+ 36 calls due to qh_sharpnewfacets
+ 927 calls to findhorizon
+ 3.02 ave. facets tested
+ 6 max. facets tested
+ 5 horizon facets better than bestfacet
+ 919 inside points
+ 8 inside points that were coplanar with a facet
+-3.1e-017 difference in max_outside at final check
+ 3747 distance tests for initial partition
+ 3132 partitions of a point
+ 8558 distance tests for partitioning
+ 513 distance tests for checking flipped facets
+ 1162 distance tests for statistics
+ 16990 total number of distance tests
+ 8 partitions of coplanar points or deleted vertices
+ 75 distance tests for these partitions
+
+statistics for matching ridges
+ 726 total lookups for matching ridges of new facets
+ 0.563 average number of tests to match a ridge
+
+statistics for determining merges
+ 1089 distance tests for checking simplicial convexity
+
+statistics for merging
+ 9e-017 max distance of vertex or coplanar point above facet(w/roundoff)
+-6.9e-016 max distance of merged vertex below facet(or roundoff)
+
+memory usage statistics(in bytes)
+ 21584 for facets a
+Convex hull of 1000 points in 3-d:
+
+ Number of vertices: 73
+ Number of facets: 142
+
+Statistics for: rbox 1000 D3 | qhull Tcvs
+
+ 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
+
+nd their normals, neighbor and vertex sets
+ 1752 for vertices and their neighbor sets
+ 30368 for input points and outside and coplanar sets
+
+memory statistics:
+ 1166 quick allocations
+ 673 short allocations
+ 69 long allocations
+ 1184 short frees
+ 68 long frees
+ 25312 bytes of short memory in use
+ 680 bytes of short memory in freelists
+ 105072 bytes of dropped short memory
+ 3100 bytes of unused short memory (estimated)
+ 10916 bytes of long memory allocated (max, except for input)
+ 96 bytes of long memory in use (in 1 pieces)
+ 131064 bytes of short memory buffers (minus links)
+ 65536 bytes per short memory buffer (initially 131072 bytes)
+ 73 calls to qh_setlarger
+ 15 average copy size
+ freelists(bytes->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 -10 q_test.log.1
+qh_mem 004B0170 n 1022 free short: 88 bytes (tot 8984 cnt 228)
+qh_mem 004B01C8 n 1023 free short: 88 bytes (tot 8896 cnt 227)
+qh_mem 004B0220 n 1024 free short: 88 bytes (tot 8808 cnt 226)
+qh_mem 004B0278 n 1025 free short: 88 bytes (tot 8720 cnt 225)
+qh_mem 003E72E8 n 30 free long: 96 bytes (tot 0 cnt 0)
+qh_mem 004B02D0 n 1026 free short: 16 bytes (tot 8704 cnt 224)
+qh_mem 004B0050 n 1027 free short: 88 bytes (tot 8616 cnt 223)
+qh_mem 004B00A8 n 1028 free short: 88 bytes (tot 8528 cnt 222)
+qh_mem 004B0100 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): 1.5e-005
+
+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 2010.0.3 2010/01/05:
+ run-id 769060595 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 5e-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 7e-017
+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 7e-017
+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 7e-017
+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 7e-017
+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 7e-017
+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 7e-017
+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 7e-017
+qh_addpoint: add p2(v79) to hull of 152 facets(0.014 above f288) and 22 outside at 1.5e-005 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 20:33:05 & 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 20:33:05 & 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 20:33:05 & 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 20:33:05 & 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 2010.0.3 2010/01/05:
+ run-id 769077402 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): 1.5e-005
+
+Options selected for Qhull 2010.0.3 2010/01/05:
+ run-id 769077402 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
+-0.08928142660407064 -0.3194671263098746 0.3605569202297553
+-0.1534778158747163 0.03516440701453923 0.5
+-0.01663016790622813 0.3709299907861696 0.07648632831350027
+0.3932651765570925 0.4421392241401818 -0.09396622763110282
+0.1994247283046842 0.5 0.06620718432588453
+-0.2331094527352669 0.3262436269787957 -0.128966098672764
+ -0.5 0.2819439085196089 -0.5
+ 0.5 0.3760666748352666 0.1399187075693636
+0.4888102268053205 -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
+-0.02221493611318519 -0.366434993563625 0.5972263834933854
+-0.06676722137887703 -0.1566931052661437 0.6939998615477233
+0.02820502736438534 0.04189077954915425 0.4000814320337246
+0.3126723396709862 0.08400649026409396 0.2817873818077145
+0.1781470954214662 0.1182274414396169 0.3929477075294902
+-0.1220315663349177 0.01546165115708639 0.2574974761506135
+-0.3072535691850386 -0.01073880122111999 2.710505431213761e-020
+0.3867462923626847 0.04492879989084676 0.4441034944549364
+0.3789805913148267 -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
+-5.73397038057534 -0.366434993563625 17.14322461142018
+-6.40076198881529 -0.1566931052661437 20
+-4.979360188660042 0.04189077954915425 11.32346018178494
+-0.7218812392989215 0.08400649026409396 7.831392539952951
+-2.735252796494544 0.1182274414396169 11.11287098934976
+-7.227875597731385 0.01546165115708639 7.114348923589702
+ -10 -0.01073880122111999 -0.4870359524963758
+0.3867462923626843 0.04492879989084676 12.62300161615219
+0.2705209571204674 -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
+-0.08928142660407071 -0.3194671263098746 0.3605569202297554
+-0.1534778158747163 0.03516440701453923 0.4999999999999999
+-0.01663016790622816 0.3709299907861696 0.07648632831350057
+0.3932651765570925 0.4421392241401818 -0.09396622763110278
+0.1994247283046842 0.5 0.06620718432588439
+-0.2331094527352669 0.3262436269787957 -0.1289660986727639
+ -0.5 0.2819439085196089 -0.4999999999999999
+ 0.5 0.3760666748352666 0.1399187075693635
+0.4888102268053205 -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 Wed Jan 6 20:33:06 EST 2010 ==
+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 2010.0.3 2010/01/05:
+ run-id 769077402 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 t1262827986 | qhull FO Tcv C-0
+
+ Number of points processed: 200
+ Number of hyperplanes created: 398
+ Number of distance tests for qhull: 2106
+ CPU seconds to compute hull (after input): 0
+
+Options selected for Qhull 2010.0.3 2010/01/05:
+ run-id 769077402 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: 57
+ Number of facets: 110
+
+Statistics for: rbox 1000 L20 t1262827986 | qhull FO Tcv C-0
+
+ Number of points processed: 77
+ Number of hyperplanes created: 330
+ Number of distance tests for qhull: 15606
+ CPU seconds to compute hull (after input): 0
+
+Options selected for Qhull 2010.0.3 2010/01/05:
+ run-id 769077402 Tcheck-frequently Tverify Centrum-premerge- 0
+ _zero-centrum _max-width 1 Error-roundoff 6.9e-016 _one-merge 4.8e-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 110000 distance computations.
+rbox 200 L20 D4 t | qhull FO Tcv C-0
+
+Convex hull of 200 points in 4-d:
+
+ Number of vertices: 61
+ Number of facets: 299
+
+Statistics for: rbox 200 L20 D4 t1262827986 | qhull FO Tcv C-0
+
+ Number of points processed: 71
+ Number of hyperplanes created: 900
+ Number of distance tests for qhull: 6283
+ CPU seconds to compute hull (after input): 0
+
+Options selected for Qhull 2010.0.3 2010/01/05:
+ run-id 769077402 Tcheck-frequently Tverify Centrum-premerge- 0
+ _zero-centrum _max-width 0.99 Error-roundoff 1e-015 _one-merge 9e-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 59800 distance computations.
+rbox 200 L20 D5 t | qhull FO Tcv Qx
+
+Convex hull of 200 points in 5-d:
+
+ Number of vertices: 104
+ Number of facets: 1438
+
+Statistics for: rbox 200 L20 D5 t1262827986 | qhull FO Tcv Qx
+
+ Number of points processed: 117
+ Number of hyperplanes created: 5328
+ Number of distance tests for qhull: 19776
+ CPU seconds to compute hull (after input): 1.5e-005
+
+Options selected for Qhull 2010.0.3 2010/01/05:
+ run-id 769077402 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 287600 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: 267
+
+Statistics for: rbox 1000 W1e-3 s D2 t1262827986 | qhull d FO Tcv Qu Q0
+
+ Number of points processed: 1000
+ Number of hyperplanes created: 4606
+ Number of facets in hull: 1996
+ Number of distance tests for qhull: 27314
+ CPU seconds to compute hull (after input): 0
+
+Options selected for Qhull 2010.0.3 2010/01/05:
+ run-id 769077402 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 267000 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: 267
+
+Statistics for: rbox 1000 W1e-3 s D2 t1262827986 | qhull d FO Tcv Qu C-0
+
+ Number of points processed: 1000
+ Number of hyperplanes created: 4606
+ Number of facets in hull: 1996
+ Number of distance tests for qhull: 27314
+ CPU seconds to compute hull (after input): 0
+
+Options selected for Qhull 2010.0.3 2010/01/05:
+ run-id 769077402 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 267000 distance computations.
+
+echo === check joggle and TRn ${d:-`date`}
+date
+=== check joggle and TRn Wed Jan 6 20:33:06 EST 2010
+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: 11249
+ Number of distance tests for qhull: 120401
+ CPU seconds to compute hull (after input): 3.1e-005
+ Percentage of runs with precision errors: 100.0
+
+
+precision problems (corrected unless 'Q0' or an error)
+ 100 coplanar horizon facets for new vertices
+ 397 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: 24818
+ Number of distance tests for qhull: 197992
+ CPU seconds to compute hull (after input): 3.1e-005
+ Percentage of runs with precision errors: 62.0
+
+
+precision problems (corrected unless 'Q0' or an error)
+ 7 coplanar half ridges in output
+ 55 coplanar horizon facets for new vertices
+ 120 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: 29128
+ Number of distance tests for qhull: 216985
+ CPU seconds to compute hull (after input): 4.6e-005
+ Percentage of runs with precision errors: 8.0
+
+
+precision problems (corrected unless 'Q0' or an error)
+ 1 coplanar half ridges in output
+ 7 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: 219095
+ CPU seconds to compute hull (after input): 4.6e-005
+ 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): 4.6e-005
+ 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
+ Input joggled by: 6.7e+003
+
+Options selected for Qhull 2010.0.3 2010/01/05:
+ run-id 769077402 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 Wed Jan 6 20:33:06 EST 2010
+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 2010.0.3 2010/01/05:
+ run-id 769094209 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: 64528
+ 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): 1.5e-005
+ 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: 172072
+ 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): 1.6e-005
+ 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
+ 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): 1.5e-005
+ 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: 64357
+ 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): 1.5e-005
+ 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 2010.0.3 2010/01/05:
+ run-id 769094209 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: 64911
+ 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
+ Maximum distance of point above facet: 0.02 (0.7x)
+ Maximum distance of vertex below facet: -0.049 (1.6x)
+
+Options selected for Qhull 2010.0.3 2010/01/05:
+ run-id 769094209 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): 1.5e-005
+ Maximum distance of point above facet: 0.02 (0.7x)
+ Maximum distance of vertex below facet: -0.035 (1.2x)
+
+Options selected for Qhull 2010.0.3 2010/01/05:
+ run-id 769094209 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: 64528
+ 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): 1.5e-005
+ Maximum distance of point above facet: 0.02 (0.7x)
+ Maximum distance of vertex below facet: -0.035 (1.2x)
+
+Options selected for Qhull 2010.0.3 2010/01/05:
+ run-id 769094209 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 Wed Jan 6 20:33:07 EST 2010
+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): 1.5e-005
+ Maximum distance of point above facet: 0.022 (0.7x)
+ Maximum distance of vertex below facet: -0.035 (1.2x)
+
+Options selected for Qhull 2010.0.3 2010/01/05:
+ run-id 769094209 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 Wed Jan 6 20:33:07 EST 2010
+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): 1.5e-005
+ Maximum distance of point above facet: 0.02 (0.7x)
+ Maximum distance of vertex below facet: -0.009 (0.3x)
+
+Options selected for Qhull 2010.0.3 2010/01/05:
+ run-id 769094209 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): 1.5e-005
+ Maximum distance of point above facet: 0.02 (0.7x)
+ Maximum distance of vertex below facet: -0.042 (1.4x)
+
+Options selected for Qhull 2010.0.3 2010/01/05:
+ run-id 769094209 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
+ 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.
+rbox 100 s D3 t | qhull R1e-3 Tcv Qc
+
+Convex hull of 100 points in 3-d:
+
+ Number of vertices: 96
+ Number of coplanar points: 4
+ Number of facets: 151
+ Number of non-simplicial facets: 33
+
+Statistics for: rbox 100 s D3 t1262827987 | qhull R1e-3 Tcv Qc
+
+ Number of points processed: 96
+ Number of hyperplanes created: 437
+ Number of distance tests for qhull: 1665
+ Number of distance tests for merging: 3856
+ Number of distance tests for checking: 1447
+ Number of merged facets: 63
+ CPU seconds to compute hull (after input): 1.5e-005
+ Maximum distance of point above facet: 0.0026 (0.7x)
+ Maximum distance of vertex below facet: -0.0047 (1.2x)
+
+
+Output completed. Verifying that all points are below outer planes of
+all facets. Will make 15100 distance computations.
+rbox 100 s D3 t | qhull R1e-2 Tcv Qc
+
+Convex hull of 100 points in 3-d:
+
+ Number of vertices: 58
+ Number of coplanar points: 42
+ Number of facets: 60
+ Number of non-simplicial facets: 35
+
+Statistics for: rbox 100 s D3 t1262827987 | qhull R1e-2 Tcv Qc
+
+ Number of points processed: 61
+ Number of hyperplanes created: 254
+ Number of distance tests for qhull: 3136
+ Number of distance tests for merging: 3872
+ Number of distance tests for checking: 1852
+ Number of merged facets: 111
+ CPU seconds to compute hull (after input): 0
+ Maximum distance of point above facet: 0.03 (0.7x)
+ Maximum distance of vertex below facet: -0.061 (1.5x)
+
+
+Output completed. Verifying that all points are below outer planes of
+all facets. Will make 6000 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: 20
+ Number of coplanar points: 480
+ Number of facets: 15
+ Number of non-simplicial facets: 13
+
+Statistics for: rbox 500 s D3 t1262827987 | qhull R0.05 A-1 Tcv Qc
+
+ Number of points processed: 26
+ Number of hyperplanes created: 86
+ Number of distance tests for qhull: 27123
+ Number of distance tests for merging: 1723
+ Number of distance tests for checking: 8454
+ Number of merged facets: 56
+ CPU seconds to compute hull (after input): 0
+ Maximum distance of point above facet: 0.15 (0.2x)
+ Maximum distance of vertex below facet: -0.24 (0.4x)
+
+
+Output completed. Verifying that all points are below outer planes of
+all facets. Will make 7500 distance computations.
+rbox 100 W0 D3 t | qhull R1e-3 Tcv Qc
+
+Convex hull of 100 points in 3-d:
+
+ Number of vertices: 39
+ Number of coplanar points: 61
+ Number of facets: 50
+ Number of non-simplicial facets: 6
+
+Statistics for: rbox 100 W0 D3 t1262827987 | qhull R1e-3 Tcv Qc
+
+ Number of points processed: 43
+ Number of hyperplanes created: 143
+ Number of distance tests for qhull: 1835
+ Number of distance tests for merging: 1474
+ Number of distance tests for checking: 1104
+ Number of merged facets: 32
+ CPU seconds to compute hull (after input): 0
+ Maximum distance of point above facet: 0.0022 (0.5x)
+ Maximum distance of vertex below facet: -0.0036 (0.9x)
+
+
+Output completed. Verifying that all points are below outer planes of
+all facets. Will make 5000 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: 49
+ Number of non-simplicial facets: 6
+
+Statistics for: rbox 100 W0 D3 t1262827987 | qhull R1e-3 Qx Tcv Qc
+
+ Number of points processed: 42
+ Number of hyperplanes created: 148
+ Number of distance tests for qhull: 2360
+ Number of distance tests for merging: 1359
+ Number of distance tests for checking: 1081
+ Number of merged facets: 31
+ CPU seconds to compute hull (after input): 0
+ Maximum distance of point above facet: 0.0021 (0.5x)
+ Maximum distance of vertex below facet: -0.004 (1.0x)
+
+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 4900 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: 9
+
+Statistics for: rbox 100 W0 D3 t1262827987 | qhull R1e-2 Tcv Qc
+
+ Number of points processed: 31
+ Number of hyperplanes created: 105
+ Number of distance tests for qhull: 2384
+ Number of distance tests for merging: 1465
+ Number of distance tests for checking: 1125
+ Number of merged facets: 40
+ CPU seconds to compute hull (after input): 0
+ Maximum distance of point above facet: 0.025 (0.6x)
+ Maximum distance of vertex below facet: -0.046 (1.1x)
+
+
+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: 28
+ Number of coplanar points: 72
+ Number of facets: 29
+ Number of non-simplicial facets: 11
+
+Statistics for: rbox 100 W0 D3 t1262827987 | qhull R1e-2 Qx Tcv Qc
+
+ Number of points processed: 32
+ Number of hyperplanes created: 106
+ Number of distance tests for qhull: 3494
+ Number of distance tests for merging: 1349
+ Number of distance tests for checking: 1141
+ Number of merged facets: 38
+ CPU seconds to compute hull (after input): 1.5e-005
+ Maximum distance of point above facet: 0.026 (0.6x)
+ Maximum distance of vertex below facet: -0.038 (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 2900 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 t1262827987 | qhull R0.05 A-1 Tcv Qc
+
+ Number of points processed: 14
+ Number of hyperplanes created: 34
+ Number of distance tests for qhull: 13190
+ Number of distance tests for merging: 579
+ Number of distance tests for checking: 3900
+ Number of merged facets: 21
+ CPU seconds to compute hull (after input): 0
+ Maximum distance of point above facet: 0.13 (0.2x)
+ Maximum distance of vertex below facet: -0.2 (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: 8
+ Number of coplanar points: 492
+ Number of facets: 6
+ Number of non-simplicial facets: 6
+
+Statistics for: rbox 500 W0 D3 t1262827987 | qhull R0.05 Qx Tcv Qc
+
+ Number of points processed: 16
+ Number of hyperplanes created: 39
+ Number of distance tests for qhull: 18602
+ Number of distance tests for merging: 512
+ Number of distance tests for checking: 3794
+ Number of merged facets: 25
+ CPU seconds to compute hull (after input): 0
+ Maximum distance of point above facet: 0.11 (0.5x)
+ Maximum distance of vertex below facet: -0.17 (0.8x)
+
+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 1000 W1e-20 t | qhull Tcv Qc
+
+Convex hull of 1000 points in 3-d:
+
+ Number of vertices: 85
+ Number of coplanar points: 915
+ Number of facets: 99
+ Number of non-simplicial facets: 6
+
+Statistics for: rbox 1000 W1e-20 t1262827987 | qhull Tcv Qc
+
+ Number of points processed: 103
+ Number of hyperplanes created: 314
+ Number of distance tests for qhull: 17474
+ Number of distance tests for merging: 4494
+ Number of distance tests for checking: 31961
+ Number of merged facets: 103
+ CPU seconds to compute hull (after input): 0
+
+
+Output completed. Verifying that all points are below outer planes of
+all facets. Will make 99000 distance computations.
+rbox 1000 W1e-20 D4 t | qhull Tcv Qc
+
+Convex hull of 1000 points in 4-d:
+
+ Number of vertices: 291
+ Number of coplanar points: 709
+ Number of facets: 1098
+ Number of non-simplicial facets: 8
+
+Statistics for: rbox 1000 W1e-20 D4 t1262827987 | qhull Tcv Qc
+
+ Number of points processed: 363
+ Number of hyperplanes created: 4944
+ Number of distance tests for qhull: 77136
+ Number of distance tests for merging: 75790
+ Number of distance tests for checking: 153113
+ Number of merged facets: 1148
+ CPU seconds to compute hull (after input): 0.000109
+
+
+Output completed. Verifying that all points are below outer planes of
+all facets. Will make 1098000 distance computations.
+rbox 500 W1e-20 D5 t | qhull Tv Qc
+
+Convex hull of 500 points in 5-d:
+
+ Number of vertices: 357
+ Number of coplanar points: 143
+ Number of facets: 5624
+ Number of non-simplicial facets: 10
+
+Statistics for: rbox 500 W1e-20 D5 t1262827988 | qhull Tv Qc
+
+ Number of points processed: 407
+ Number of hyperplanes created: 26660
+ Number of distance tests for qhull: 124300
+ Number of distance tests for merging: 299911
+ Number of distance tests for checking: 241343
+ Number of merged facets: 3392
+ CPU seconds to compute hull (after input): 0.000109
+
+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 2812000 distance computations.
+rbox 100 W1e-20 D6 t | qhull Tv Qc
+
+Convex hull of 100 points in 6-d:
+
+ Number of vertices: 99
+ Number of coplanar points: 1
+ Number of facets: 5987
+ Number of non-simplicial facets: 8
+
+Statistics for: rbox 100 W1e-20 D6 t1262827988 | qhull Tv Qc
+
+ Number of points processed: 100
+ Number of hyperplanes created: 20805
+ Number of distance tests for qhull: 33169
+ Number of distance tests for merging: 205663
+ Number of distance tests for checking: 124429
+ Number of merged facets: 213
+ CPU seconds to compute hull (after input): 7.8e-005
+
+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 598700 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: 2049
+ Number of non-simplicial facets: 1
+
+Statistics for: rbox 50 W1e-20 D6 t1262827988 | qhull Qv Tv Qc
+
+ Number of points processed: 50
+ Number of hyperplanes created: 6722
+ Number of distance tests for qhull: 9793
+ Number of distance tests for merging: 3409430
+ Number of distance tests for checking: 41868
+ Number of merged facets: 2
+ CPU seconds to compute hull (after input): 0.00014
+
+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 102450 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: 7557
+ Number of facets: 8
+ Number of non-simplicial facets: 8
+
+Statistics for: rbox 10000 D4 t1262827988 | qhull QR0 Qc C-0.01 A0.3 Tv QR1262827988
+
+ Number of points processed: 42
+ Number of hyperplanes created: 280
+ Number of distance tests for qhull: 1195764
+ Number of distance tests for merging: 9453
+ Number of distance tests for checking: 99514
+ Number of merged facets: 283
+ CPU seconds to compute hull (after input): 6.2e-005
+ Maximum distance of point above facet: 0.081
+ Maximum distance of vertex below facet: -0.13
+
+
+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: 18
+
+Statistics for: rbox 1000 D2 t1262827988 | qhull d QR0 Qc C-1e-8 Qu Tv QR1262827988
+
+ Number of points processed: 1000
+ Number of hyperplanes created: 5554
+ Number of facets in hull: 1996
+ Number of distance tests for qhull: 30518
+ CPU seconds to compute hull (after input): 1.5e-005
+
+
+Output completed. Verifying that all points are below outer planes of
+all facets. Will make 18000 distance computations.
+rbox 300 D5 t |qhull A-0.999 Qx Qc Tcv
+
+Convex hull of 300 points in 5-d:
+
+ Number of vertices: 156
+ Number of coplanar points: 33
+ Number of facets: 1721
+ Number of non-simplicial facets: 427
+
+Statistics for: rbox 300 D5 t1262827988 | qhull A-0.999 Qx Qc Tcv
+
+ Number of points processed: 201
+ Number of hyperplanes created: 12171
+ Number of distance tests for qhull: 179621
+ Number of distance tests for merging: 56968
+ Number of distance tests for checking: 20698
+ Number of merged facets: 1137
+ CPU seconds to compute hull (after input): 4.6e-005
+ Maximum distance of vertex below facet: -0.021 (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 516300 distance computations.
+rbox 100 D6 t |qhull A-0.9999 Qx Qc Tcv
+
+Convex hull of 100 points in 6-d:
+
+ Number of vertices: 90
+ Number of coplanar points: 1
+ Number of facets: 3862
+ Number of non-simplicial facets: 245
+
+Statistics for: rbox 100 D6 t1262827988 | qhull A-0.9999 Qx Qc Tcv
+
+ Number of points processed: 94
+ Number of hyperplanes created: 13686
+ Number of distance tests for qhull: 27172
+ Number of distance tests for merging: 81053
+ Number of distance tests for checking: 83121
+ Number of merged facets: 602
+ CPU seconds to compute hull (after input): 6.2e-005
+ Maximum distance of vertex below facet: -0.0071 (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 386200 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: 47
+ Number of coplanar points: 2
+ Number of facets: 4864
+ Number of non-simplicial facets: 91
+
+Statistics for: rbox 50 D7 t1262827988 | qhull A-0.99999 Qx Qc Tcv W0.1
+
+ Number of points processed: 47
+ Number of hyperplanes created: 13336
+ Number of distance tests for qhull: 20540
+ Number of distance tests for merging: 97428
+ Number of distance tests for checking: 113814
+ Number of merged facets: 254
+ CPU seconds to compute hull (after input): 6.2e-005
+ Maximum distance of point above facet: 0.086
+ Maximum distance of vertex below facet: -0.0018 (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 243200 distance computations.
+
+echo === check bad cases for Qhull. May cause errors ${d:-`date`}
+date
+=== check bad cases for Qhull. May cause errors Wed Jan 6 20:33:09 EST 2010
+rbox 1000 L100000 s G1e-6 t | qhull Tv
+QH6154 qhull precision error: initial facet 1 is coplanar with the interior point
+ERRONEOUS FACET:
+- f1
+ - flags: bottom simplicial flipped
+ - normal: 0 0 1
+ - offset: 0
+ - vertices: p961(v2) p777(v1) p485(v0)
+ - neighboring facets: f2 f3 f4
+
+While executing: rbox 1000 L100000 s G1e-6 t1262827989 | qhull Tv
+Options selected for Qhull 2010.0.3 2010/01/05:
+ run-id 769127823 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
+
+precision problems (corrected unless 'Q0' or an error)
+ 2 flipped facets
+
+The input to qhull appears to be less than 3 dimensional, or a
+computation has overflowed.
+
+Qhull could not construct a clearly convex simplex from points:
+- p441(v3): 0.00028 -0.5 0
+- p961(v2): -4.7e-005 0.5 0
+- p777(v1): 0.5 0.0017 0
+- p485(v0): -0.5 -0.0036 0
+
+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 6.9e-016. The center point, facets and distances
+to the center point are as follows:
+
+center point 5.99e-005 -0.0004625 0
+
+facet p961 p777 p485 distance= 0
+facet p441 p777 p485 distance= 0
+facet p441 p961 p485 distance= 0
+facet p441 p961 p777 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: -0.5 0.5 difference= 1
+ 1: -0.5 0.5 difference= 1
+ 2: 0 0 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 6.9e-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 1000 L100000 s G1e-6 t | qhull Tv Q10
+QH6154 qhull precision error: initial facet 1 is coplanar with the interior point
+ERRONEOUS FACET:
+- f1
+ - flags: bottom simplicial flipped
+ - normal: 0 0 1
+ - offset: 0
+ - vertices: p961(v2) p777(v1) p485(v0)
+ - neighboring facets: f2 f3 f4
+
+While executing: rbox 1000 L100000 s G1e-6 t1262827989 | qhull Tv Q10
+Options selected for Qhull 2010.0.3 2010/01/05:
+ run-id 769127823 Tverify Q10-no-narrow _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
+
+precision problems (corrected unless 'Q0' or an error)
+ 2 flipped facets
+
+The input to qhull appears to be less than 3 dimensional, or a
+computation has overflowed.
+
+Qhull could not construct a clearly convex simplex from points:
+- p441(v3): 0.00028 -0.5 0
+- p961(v2): -4.7e-005 0.5 0
+- p777(v1): 0.5 0.0017 0
+- p485(v0): -0.5 -0.0036 0
+
+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 6.9e-016. The center point, facets and distances
+to the center point are as follows:
+
+center point 5.99e-005 -0.0004625 0
+
+facet p961 p777 p485 distance= 0
+facet p441 p777 p485 distance= 0
+facet p441 p961 p485 distance= 0
+facet p441 p961 p777 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: -0.5 0.5 difference= 1
+ 1: -0.5 0.5 difference= 1
+ 2: 0 0 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 6.9e-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 1000 s Z1 G1e-13 t | qhull Tv
+
+Convex hull of 1001 points in 3-d:
+
+ Number of vertices: 1001
+ Number of facets: 1410
+ Number of non-simplicial facets: 146
+
+Statistics for: rbox 1000 s Z1 G1e-13 t1262827989 | qhull Tv
+
+ Number of points processed: 1001
+ Number of hyperplanes created: 4938
+ Number of distance tests for qhull: 28876
+ Number of distance tests for merging: 148847
+ Number of distance tests for checking: 308338
+ Number of merged facets: 2258
+ CPU seconds to compute hull (after input): 3.1e-005
+ Maximum distance of point above facet: 1.4e-014 (2.4x)
+ Maximum distance of vertex below facet: -1.7e-014 (3.1x)
+
+
+Output completed. Verifying that all points are below outer planes of
+all facets. Will make 1411410 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 t1262827989 | qhull d Qbb Qc Tv
+
+ Number of points processed: 1001
+ Number of hyperplanes created: 13876
+ Number of facets in hull: 3726
+ Number of distance tests for qhull: 56917
+ Number of distance tests for merging: 190963
+ Number of distance tests for checking: 289581
+ Number of merged facets: 4391
+ CPU seconds to compute hull (after input): 6.3e-005
+ Maximum distance of point above facet: 4.3e-014 (2.1x)
+ Maximum distance of vertex below facet: -4.8e-014 (2.4x)
+
+
+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: 884
+ Total number of deleted points due to merging: 71
+ Total number of nearly incident points: 45
+ Number of Delaunay regions: 1064
+ Number of non-simplicial Delaunay regions: 359
+
+Statistics for: rbox 1000 s W1e-13 t1262827989 | qhull d Tv
+
+ Number of points processed: 955
+ Number of hyperplanes created: 10496
+ Number of facets in hull: 2106
+ Number of distance tests for qhull: 4768700
+ Number of distance tests for merging: 284649
+ Number of distance tests for checking: 2107000
+ Number of merged facets: 7387
+ CPU seconds to compute hull (after input): 0.000625
+ Maximum distance of point above facet: 3.2e-011 (3138.6x)
+ Maximum distance of vertex below facet: -4.9e-014 (4.8x)
+
+qhull precision warning:
+The initial hull is narrow (cosine of min. angle is 1.0000000000000000).
+A coplanar point may lead to 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 1064000 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: 708
+ Total number of deleted points due to merging: 207
+ Total number of nearly incident points: 85
+ Number of Delaunay regions: 522
+ Number of non-simplicial Delaunay regions: 101
+
+Statistics for: rbox 1000 s W1e-13 D2 t1262827990 | qhull d Tv
+
+ Number of points processed: 915
+ Number of hyperplanes created: 4471
+ Number of facets in hull: 979
+ Number of distance tests for qhull: 726533
+ Number of distance tests for merging: 106688
+ Number of distance tests for checking: 305010
+ Number of merged facets: 1998
+ CPU seconds to compute hull (after input): 4.7e-005
+ Maximum distance of point above facet: 3e-013 (54.5x)
+ Maximum distance of vertex below facet: -4.7e-014 (8.5x)
+
+qhull precision warning:
+The initial hull is narrow (cosine of min. angle is 1.0000000000000000).
+A coplanar point may lead to 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 522000 distance computations.
+
+echo =======================================================
+=======================================================
+echo =======================================================
+=======================================================
+echo === The following commands may cause errors ${d:-`date`}
+date
+=== The following commands may cause errors Wed Jan 6 20:33:10 EST 2010
+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): 3.1e-005
+
+
+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
+
+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 2010.0.3 2010/01/05:
+ run-id 769144630 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 2010.0.3 2010/01/05:
+ run-id 769144630 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 2010.0.3 2010/01/05
+ 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 2010.0.3 2010/01/05.
+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 2010.0.3 2010/01/05
+
+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: <http://www.qhull.org>
+ - CVS: <http://savannah.nongnu.org/projects/qhull/>
+ - mirror: <http://www6.uniovi.es/ftp/pub/mirrors/geom.umn.edu/software/ghindex.html>
+ - news: <http://www.qhull.org/news>
+ - Geomview: <http://www.geomview.org>
+ - news group: <news:comp.graphics.algorithms>
+ - FAQ: <http://exaflop.org/docs/cgafaq/cga6.html>
+ - 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= <<
+ <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]]".
+
+ 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). 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.
+
+ 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
diff --git a/eg/qhulltest-ok.txt b/eg/qhulltest-ok.txt
new file mode 100644
index 0000000..63a05a6
--- /dev/null
+++ b/eg/qhulltest-ok.txt
@@ -0,0 +1,1059 @@
+********* Start testing of orgQhull::PointCoordinates_test *********
+Config: Using QTest library 4.6.0, Qt 4.6.0
+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::Coordinates_test *********
+Config: Using QTest library 4.6.0, Qt 4.6.0
+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 4.6.0, Qt 4.6.0
+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 4.6.0, Qt 4.6.0
+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
+..\..\cpp\qhulltest\QhullFacet_test.cpp(106) : failure location
+Hyperplane: 0.979144 -0.184925 0.0841393 -0.5
+
+InnerPlane: 0.979144 -0.184925 0.0841393 -0.5
+innerOffset+0.5 1.05471e-015
+OuterPlane: 0.979144 -0.184925 0.0841393 -0.5
+outerOffset+0.5 -2.22045e-015
+Center: p11479608: 0.489572 -0.0924626 0.0420696
+
+Hyperplane: 0.979144 -0.184925 0.0841393 -0.5
+
+InnerPlane: 0.979144 -0.184925 0.0841393 -0.5
+innerOffset+0.5 1.05471e-015
+OuterPlane: 0.979144 -0.184925 0.0841393 -0.5
+outerOffset+0.5 -2.22045e-015
+Center: p11479608: 0.489572 -0.0924626 0.0420696
+
+Hyperplane: -0.0631615 -0.670688 -0.739046 -0.5
+
+InnerPlane: -0.0631615 -0.670688 -0.739046 -0.5
+innerOffset+0.5 1.11022e-015
+OuterPlane: -0.0631615 -0.670688 -0.739046 -0.5
+outerOffset+0.5 -2.22045e-015
+Center: p11477808: -0.0315808 -0.335344 -0.369523
+
+Hyperplane: -0.0631615 -0.670688 -0.739046 -0.5
+
+InnerPlane: -0.0631615 -0.670688 -0.739046 -0.5
+innerOffset+0.5 1.11022e-015
+OuterPlane: -0.0631615 -0.670688 -0.739046 -0.5
+outerOffset+0.5 -2.22045e-015
+Center: p11477808: -0.0315808 -0.335344 -0.369523
+
+Hyperplane: 0.193099 0.718318 -0.66838 -0.5
+
+InnerPlane: 0.193099 0.718318 -0.66838 -0.5
+innerOffset+0.5 1.11022e-015
+OuterPlane: 0.193099 0.718318 -0.66838 -0.5
+outerOffset+0.5 -2.22045e-015
+Center: p11481432: 0.0965496 0.359159 -0.33419
+
+Hyperplane: 0.193099 0.718318 -0.66838 -0.5
+
+InnerPlane: 0.193099 0.718318 -0.66838 -0.5
+innerOffset+0.5 1.11022e-015
+OuterPlane: 0.193099 0.718318 -0.66838 -0.5
+outerOffset+0.5 -2.22045e-015
+Center: p11481432: 0.0965496 0.359159 -0.33419
+
+Hyperplane: -0.193099 -0.718318 0.66838 -0.5
+
+InnerPlane: -0.193099 -0.718318 0.66838 -0.5
+innerOffset+0.5 1.11022e-015
+OuterPlane: -0.193099 -0.718318 0.66838 -0.5
+outerOffset+0.5 -2.22045e-015
+Center: p11476960: -0.0965496 -0.359159 0.33419
+
+Hyperplane: -0.193099 -0.718318 0.66838 -0.5
+
+InnerPlane: -0.193099 -0.718318 0.66838 -0.5
+innerOffset+0.5 1.11022e-015
+OuterPlane: -0.193099 -0.718318 0.66838 -0.5
+outerOffset+0.5 -2.22045e-015
+Center: p11476960: -0.0965496 -0.359159 0.33419
+
+Hyperplane: -0.979144 0.184925 -0.0841393 -0.5
+
+InnerPlane: -0.979144 0.184925 -0.0841393 -0.5
+innerOffset+0.5 1.05471e-015
+OuterPlane: -0.979144 0.184925 -0.0841393 -0.5
+outerOffset+0.5 -2.22045e-015
+Center: p11481544: -0.489572 0.0924626 -0.0420696
+
+Hyperplane: -0.979144 0.184925 -0.0841393 -0.5
+
+InnerPlane: -0.979144 0.184925 -0.0841393 -0.5
+innerOffset+0.5 1.05471e-015
+OuterPlane: -0.979144 0.184925 -0.0841393 -0.5
+outerOffset+0.5 -2.22045e-015
+Center: p11481544: -0.489572 0.0924626 -0.0420696
+
+Hyperplane: 0.0631615 0.670688 0.739046 -0.5
+
+InnerPlane: 0.0631615 0.670688 0.739046 -0.5
+innerOffset+0.5 1.11022e-015
+OuterPlane: 0.0631615 0.670688 0.739046 -0.5
+outerOffset+0.5 -2.22045e-015
+Center: p11481272: 0.0315808 0.335344 0.369523
+
+Hyperplane: 0.0631615 0.670688 0.739046 -0.5
+
+InnerPlane: 0.0631615 0.670688 0.739046 -0.5
+innerOffset+0.5 1.11022e-015
+OuterPlane: 0.0631615 0.670688 0.739046 -0.5
+outerOffset+0.5 -2.22045e-015
+Center: p11481272: 0.0315808 0.335344 0.369523
+
+Voronoi vertex: -4.8518e-017 -1.79978e-017 -1.52764e-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 4.6.0, Qt 4.6.0
+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
+- p0 (v6): 0.554541 -0.0686476 -0.661643
+ neighborFacets: f8 f7 f3
+- p5 (v5): 0.424603 -0.116278 0.745783
+ neighborFacets: f6 f7 f14
+- p4 (v2): 0.361442 -0.786965 0.00673698
+ neighborFacets: f3 f6 f7
+- p1 (v1): 0.617702 0.60204 0.0774023
+ neighborFacets: f7 f8 f14
+- p2 (v3): -0.424603 0.116278 -0.745783
+ neighborFacets: f3 f8 f12
+- p6 (v0): -0.617702 -0.60204 -0.0774023
+ neighborFacets: f3 f6 f12
+- p3 (v7): -0.361442 0.786965 -0.00673698
+ neighborFacets: f8 f12 f14
+- f7
+ - flags: bottom tested seen
+ - merges: 1
+ - normal: 0.979144 -0.184925 0.0841393
+ - offset: -0.5
+ - center: 0.489572 -0.0924626 0.0420696
+ - vertices: p0(v6) p5(v5) p4(v2) p1(v1)
+ - neighboring facets: f6 f14 f8 f3
+ - ridges:
+ - r2 tested
+ vertices: p5(v5) p1(v1)
+ between f7 and f14
+ - r6 tested
+ vertices: p0(v6) p1(v1)
+ between f8 and f7
+ - r7 tested
+ vertices: p0(v6) p4(v2)
+ between f7 and f3
+ - r8 tested
+ vertices: p5(v5) p4(v2)
+ between f6 and f7
+- f3
+ - flags: bottom tested seen
+ - merges: 1
+ - normal: -0.0631615 -0.670688 -0.739046
+ - offset: -0.5
+ - center: -0.0315808 -0.335344 -0.369523
+ - vertices: p0(v6) p2(v3) p4(v2) p6(v0)
+ - neighboring facets: f6 f12 f7 f8
+ - ridges:
+ - r3 tested
+ vertices: p2(v3) p6(v0)
+ between f3 and f12
+ - r11 tested
+ vertices: p4(v2) p6(v0)
+ between f6 and f3
+ - r7 tested
+ vertices: p0(v6) p4(v2)
+ between f7 and f3
+ - r10 tested
+ vertices: p0(v6) p2(v3)
+ between f3 and f8
+- f8
+ - flags: bottom tested seen coplanar
+ - merges: 1
+ - normal: 0.193099 0.718318 -0.66838
+ - offset: -0.5
+ - center: 0.0965496 0.359159 -0.33419
+ - vertices: p3(v7) p0(v6) p2(v3) p1(v1)
+ - neighboring facets: f3 f7 f14 f12
+ - ridges:
+ - r10 tested
+ vertices: p0(v6) p2(v3)
+ between f3 and f8
+ - r6 tested
+ vertices: p0(v6) p1(v1)
+ between f8 and f7
+ - r13 tested
+ vertices: p3(v7) p1(v1)
+ between f14 and f8
+ - r14 tested
+ vertices: p3(v7) p2(v3)
+ between f8 and f12
+
+Facets only
+- f7
+ - flags: bottom tested seen
+ - merges: 1
+ - normal: 0.979144 -0.184925 0.0841393
+ - offset: -0.5
+ - center: 0.489572 -0.0924626 0.0420696
+ - vertices: p0(v6) p5(v5) p4(v2) p1(v1)
+ - neighboring facets: f6 f14 f8 f3
+ - ridges:
+ - r2 tested
+ vertices: p5(v5) p1(v1)
+ between f7 and f14
+ - r6 tested
+ vertices: p0(v6) p1(v1)
+ between f8 and f7
+ - r7 tested
+ vertices: p0(v6) p4(v2)
+ between f7 and f3
+ - r8 tested
+ vertices: p5(v5) p4(v2)
+ between f6 and f7
+- f3
+ - flags: bottom tested seen
+ - merges: 1
+ - normal: -0.0631615 -0.670688 -0.739046
+ - offset: -0.5
+ - center: -0.0315808 -0.335344 -0.369523
+ - vertices: p0(v6) p2(v3) p4(v2) p6(v0)
+ - neighboring facets: f6 f12 f7 f8
+ - ridges:
+ - r3 tested
+ vertices: p2(v3) p6(v0)
+ between f3 and f12
+ - r11 tested
+ vertices: p4(v2) p6(v0)
+ between f6 and f3
+ - r7 tested
+ vertices: p0(v6) p4(v2)
+ between f7 and f3
+ - r10 tested
+ vertices: p0(v6) p2(v3)
+ between f3 and f8
+- f8
+ - flags: bottom tested seen coplanar
+ - merges: 1
+ - normal: 0.193099 0.718318 -0.66838
+ - offset: -0.5
+ - center: 0.0965496 0.359159 -0.33419
+ - vertices: p3(v7) p0(v6) p2(v3) p1(v1)
+ - neighboring facets: f3 f7 f14 f12
+ - ridges:
+ - r10 tested
+ vertices: p0(v6) p2(v3)
+ between f3 and f8
+ - r6 tested
+ vertices: p0(v6) p1(v1)
+ between f8 and f7
+ - r13 tested
+ vertices: p3(v7) p1(v1)
+ between f14 and f8
+ - r14 tested
+ vertices: p3(v7) p2(v3)
+ between f8 and f12
+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 4.6.0, Qt 4.6.0
+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()
+- f8
+ - flags: bottom tested seen coplanar
+ - merges: 1
+ - normal: 0.193099 0.718318 -0.66838
+ - offset: -0.5
+ - center: 0.0965496 0.359159 -0.33419
+ - vertices: p3(v7) p0(v6) p2(v3) p1(v1)
+ - neighboring facets: f3 f7 f14 f12
+ - ridges:
+ - r10 tested
+ vertices: p0(v6) p2(v3)
+ between f3 and f8
+ - r6 tested
+ vertices: p0(v6) p1(v1)
+ between f8 and f7
+ - r13 tested
+ vertices: p3(v7) p1(v1)
+ between f14 and f8
+ - r14 tested
+ vertices: p3(v7) p2(v3)
+ between f8 and f12
+- f3
+ - flags: bottom tested seen
+ - merges: 1
+ - normal: -0.0631615 -0.670688 -0.739046
+ - offset: -0.5
+ - center: -0.0315808 -0.335344 -0.369523
+ - vertices: p0(v6) p2(v3) p4(v2) p6(v0)
+ - neighboring facets: f6 f12 f7 f8
+ - ridges:
+ - r3 tested
+ vertices: p2(v3) p6(v0)
+ between f3 and f12
+ - r11 tested
+ vertices: p4(v2) p6(v0)
+ between f6 and f3
+ - r7 tested
+ vertices: p0(v6) p4(v2)
+ between f7 and f3
+ - r10 tested
+ vertices: p0(v6) p2(v3)
+ between f3 and f8
+
+Facet identifiers: f8 f3
+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 4.6.0, Qt 4.6.0
+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 4.6.0, Qt 4.6.0
+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 (v6): 0.554541 -0.0686476 -0.661643
+ neighborFacets: f8 f7 f3
+- p7 (v8): -0.554541 0.0686476 0.661643
+ neighborFacets: f6 f12 f14
+- p5 (v5): 0.424603 -0.116278 0.745783
+ neighborFacets: f6 f7 f14
+- p6 (v0): -0.617702 -0.60204 -0.0774023
+ neighborFacets: f3 f6 f12
+- p3 (v7): -0.361442 0.786965 -0.00673698
+ neighborFacets: f8 f12 f14
+- p4 (v2): 0.361442 -0.786965 0.00673698
+ neighborFacets: f3 f6 f7
+- p2 (v3): -0.424603 0.116278 -0.745783
+ neighborFacets: f3 f8 f12
+- p1 (v1): 0.617702 0.60204 0.0774023
+ neighborFacets: f7 f8 f14
+
+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 4.6.0, Qt 4.6.0
+PASS : orgQhull::QhullPoint_test::initTestCase()
+PASS : orgQhull::QhullPoint_test::t_construct()
+PASS : orgQhull::QhullPoint_test::t_convert()
+p0
+p5
+p1
+p4
+p2
+p6
+p3
+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 4.6.0, Qt 4.6.0
+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[]
+p2289496: 0 1 2
+p2289520: 3 4 5
+
+QhullPoints
+p0: 0.554541 -0.0686476 -0.661643
+p1: 0.617702 0.60204 0.0774023
+p2: -0.424603 0.116278 -0.745783
+p3: -0.361442 0.786965 -0.00673698
+p4: 0.361442 -0.786965 0.00673698
+p5: 0.424603 -0.116278 0.745783
+p6: -0.617702 -0.60204 -0.0774023
+p7: -0.554541 0.0686476 0.661643
+RunId
+p0: 0.554541 -0.0686476 -0.661643
+p1: 0.617702 0.60204 0.0774023
+p2: -0.424603 0.116278 -0.745783
+p3: -0.361442 0.786965 -0.00673698
+p4: 0.361442 -0.786965 0.00673698
+p5: 0.424603 -0.116278 0.745783
+p6: -0.617702 -0.60204 -0.0774023
+p7: -0.554541 0.0686476 0.661643
+RunId w/ message
+ 0.554541 -0.0686476 -0.661643
+ 0.617702 0.60204 0.0774023
+ -0.424603 0.116278 -0.745783
+ -0.361442 0.786965 -0.00673698
+ 0.361442 -0.786965 0.00673698
+ 0.424603 -0.116278 0.745783
+ -0.617702 -0.60204 -0.0774023
+ -0.554541 0.0686476 0.661643
+RunId w/ identifiers
+p0: 0.554541 -0.0686476 -0.661643
+p1: 0.617702 0.60204 0.0774023
+p2: -0.424603 0.116278 -0.745783
+p3: -0.361442 0.786965 -0.00673698
+p4: 0.361442 -0.786965 0.00673698
+p5: 0.424603 -0.116278 0.745783
+p6: -0.617702 -0.60204 -0.0774023
+p7: -0.554541 0.0686476 0.661643
+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 4.6.0, Qt 4.6.0
+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 4.6.0, Qt 4.6.0
+PASS : orgQhull::QhullRidge_test::initTestCase()
+PASS : orgQhull::QhullRidge_test::t_construct()
+2
+8
+6
+7
+XFAIL : orgQhull::QhullRidge_test::t_getSet() SetIterator copy constructor not reset to BOT
+..\..\cpp\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 4.6.0, Qt 4.6.0
+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: - f6
+ - flags: top tested seen coplanar
+ - merges: 1
+ - normal: -0.193099 -0.718318 0.66838
+ - offset: -0.5
+ - center: -0.0965496 -0.359159 0.33419
+ - vertices: p7(v8) p5(v5) p4(v2) p6(v0)
+ - neighboring facets: f3 f7 f12 f14
+ - ridges:
+ - r11 tested
+ vertices: p4(v2) p6(v0)
+ between f6 and f3
+ - r16 tested
+ vertices: p7(v8) p6(v0)
+ between f12 and f6
+ - r17 tested
+ vertices: p7(v8) p5(v5)
+ between f6 and f14
+ - r8 tested
+ vertices: p5(v5) p4(v2)
+ between f6 and f7
+- f14
+ - flags: bottom tested coplanar
+ - merges: 1
+ - normal: 0.0631615 0.670688 0.739046
+ - offset: -0.5
+ - center: 0.0315808 0.335344 0.369523
+ - vertices: p7(v8) p3(v7) p5(v5) p1(v1)
+ - neighboring facets: f7 f8 f12 f6
+ - ridges:
+ - r2 tested
+ vertices: p5(v5) p1(v1)
+ between f7 and f14
+ - r17 tested
+ vertices: p7(v8) p5(v5)
+ between f6 and f14
+ - r19 tested
+ vertices: p7(v8) p3(v7)
+ between f14 and f12
+ - r13 tested
+ vertices: p3(v7) p1(v1)
+ between f14 and f8
+- f8
+ - flags: bottom tested seen coplanar
+ - merges: 1
+ - normal: 0.193099 0.718318 -0.66838
+ - offset: -0.5
+ - center: 0.0965496 0.359159 -0.33419
+ - vertices: p3(v7) p0(v6) p2(v3) p1(v1)
+ - neighboring facets: f3 f7 f14 f12
+ - ridges:
+ - r10 tested
+ vertices: p0(v6) p2(v3)
+ between f3 and f8
+ - r6 tested
+ vertices: p0(v6) p1(v1)
+ between f8 and f7
+ - r13 tested
+ vertices: p3(v7) p1(v1)
+ between f14 and f8
+ - r14 tested
+ vertices: p3(v7) p2(v3)
+ between f8 and f12
+- f3
+ - flags: bottom tested seen
+ - merges: 1
+ - normal: -0.0631615 -0.670688 -0.739046
+ - offset: -0.5
+ - center: -0.0315808 -0.335344 -0.369523
+ - vertices: p0(v6) p2(v3) p4(v2) p6(v0)
+ - neighboring facets: f6 f12 f7 f8
+ - ridges:
+ - r3 tested
+ vertices: p2(v3) p6(v0)
+ between f3 and f12
+ - r11 tested
+ vertices: p4(v2) p6(v0)
+ between f6 and f3
+ - r7 tested
+ vertices: p0(v6) p4(v2)
+ between f7 and f3
+ - r10 tested
+ vertices: p0(v6) p2(v3)
+ between f3 and f8
+
+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 4.6.0, Qt 4.6.0
+PASS : orgQhull::QhullVertex_test::initTestCase()
+PASS : orgQhull::QhullVertex_test::t_constructConvert()
+6
+5
+1
+2
+3
+0
+7
+8
+XFAIL : orgQhull::QhullVertex_test::t_getSet() ListIterator copy constructor not reset to BOT
+..\..\cpp\qhulltest\QhullVertex_test.cpp(107) : failure location
+Point 0:
+p0: 0.554541 -0.0686476 -0.661643
+
+Point 5:
+p5: 0.424603 -0.116278 0.745783
+
+Point 1:
+p1: 0.617702 0.60204 0.0774023
+
+Point 4:
+p4: 0.361442 -0.786965 0.00673698
+
+Point 2:
+p2: -0.424603 0.116278 -0.745783
+
+Point 6:
+p6: -0.617702 -0.60204 -0.0774023
+
+Point 3:
+p3: -0.361442 0.786965 -0.00673698
+
+Point 7:
+p7: -0.554541 0.0686476 0.661643
+
+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)
+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 4.6.0, Qt 4.6.0
+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 4.6.0, Qt 4.6.0
+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 0xb13fb0 pointsEnd 0xb140f0 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 925096783
+PASS : orgQhull::UsingLibQhull_test::t_UsingLibQhull()
+INFO : Caught QH1
+INFO : QH10054 Report previous NOthrow error
+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 4.6.0, Qt 4.6.0
+PASS : orgQhull::Qhull_test::initTestCase()
+INFO : Caught QH10023 Qhull error: checkIfQhullInitialized failed. Call runQhull() first.
+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
+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 2010.1 2010/01/06:
+ run-id 925096783
+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 2010.1 2010/01/06:
+ run-id 925096783
+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 2010.1 2010/01/06:
+ run-id 925096783 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 2010.1 2010/01/06:
+ run-id 925096783
+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
+-0.5773502691896257 0.5773502691896257 0.5773502691896257 -0.2886751345948129
+0.5773502691896257 0.5773502691896257 0.5773502691896257 -0.2886751345948129
+-0.5773502691896257 0.5773502691896257 -0.5773502691896257 -0.2886751345948129
+0.5773502691896257 0.5773502691896257 -0.5773502691896257 -0.2886751345948129
+0.5773502691896257 -0.5773502691896257 0.5773502691896257 -0.2886751345948129
+-0.5773502691896257 -0.5773502691896257 0.5773502691896257 -0.2886751345948129
+-0.5773502691896257 -0.5773502691896257 -0.5773502691896257 -0.2886751345948129
+0.5773502691896257 -0.5773502691896257 -0.5773502691896257 -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 127 tests.
+
+Qhull output at end
+qhull: no message for error. Check cerr or error stream
+
+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
+
diff --git a/html/qh-code.htm b/html/qh-code.htm
index cec3135..6f5126f 100644
--- a/html/qh-code.htm
+++ b/html/qh-code.htm
@@ -212,8 +212,10 @@ C++ programs</a></h2>
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 an external
-command.
+Most users will find it easier to call Qhull as a program.
+
+<p><b>Note:</b> Please download the latest sources from
+git://gitorious.org/qhull/qhull.git
<p>
Qhull's C++ interface provides wrapper classes for Qhull and Rbox. It provides access to Qhull's data structures.
@@ -261,8 +263,7 @@ See RboxPoints.cpp for an example.
A more flexible approach extends Qhull's classes. For example,
to access the vertices of a <a href="#facet-cpp">QhullFacet</a>,
define a constructor of <a href="#vertexset-cpp">QhullVertexSet</a>
-that takes a QhullFacet as a parameter. Please send these extensions
-to bradb@shore.net for incorporation into Qhull.
+that takes a QhullFacet as a parameter.
</p>
<p>
With care, you may create multiple Qhull instances, but only one instance may be active at time.
diff --git a/html/qh-get.htm b/html/qh-get.htm
index 7bc03ee..c336561 100644
--- a/html/qh-get.htm
+++ b/html/qh-get.htm
@@ -34,12 +34,12 @@ width="100" height="100"></a> Qhull Downloads</h1>
</li>
<li><a
href="http://www.qhull.org/download/qhull-2010.1.zip">Download:
- Qhull 2010.1 for Windows</a> (1.2 Mbytes) <p>Type: console programs for
- Windows 95, 98, ME, 2000, NT, XP</p>
+ Qhull 2010.1 for Windows</a> (2.4 Mbytes) <p>Type: console programs for
+ Windows</p>
<p>Includes executables, documentation, sources files, and a cygwin Makefile. It runs in a
DOS window.</p>
</li>
- <li><a href="http://www.qhull.org/download/qhull-2010.1-src.tgz">Download: Qhull 2010.1 for Unix</a> (725K)
+ <li><a href="http://www.qhull.org/download/qhull-2010.1-src.tgz">Download: Qhull 2010.1 for Unix</a> (660K)
<p>Type: C source code for 32-bit and 64-bit architectures</p>
<p>Includes documentation, source files, a simple Makefile, DevStudio project files, and Qt project files.
Includes preliminary C++ support.
@@ -130,16 +130,6 @@ and upgraded it to 2002.1.
"bcc32 -WX -w- -O2-e -erbox -lc rbox.c". The
options for qhull are the same. [D. Zwick] </p>
</li>
- <li><a
- href="http://www.qhull.org/download/qhull-1.0.sit.hqx">Download:
- Qhull version 1.0 (Mac)</a> (180K) <p>Type: C source
- code, packaged for Macintosh w/68881 </p>
- <p>The Macintosh implementation of Qhull 1.0 reads input
- from a file and returns the results to a file. The code
- is compiled for a 68881 floating point coprocessor. The
- package includes Think C projects for Qhull and the rbox
- input generator. </p>
- </li>
</ul>
<!-- Navigation links -->
<hr>
diff --git a/html/trolltech2.rtf b/html/trolltech2.rtf
deleted file mode 100644
index c181751..0000000
--- a/html/trolltech2.rtf
+++ /dev/null
@@ -1,335 +0,0 @@
-{\rtf1\ansi\ansicpg1252\deff0\deflang1033\deflangfe1033{\fonttbl{\f0\fswiss\fprq2\fcharset0 Arial;}{\f1\fnil\fcharset0 Tahoma;}{\f2\fnil\fprq1\fcharset0 Courier New;}{\f3\fnil\fprq1\fcharset0 Lucida Console;}{\f4\fswiss Arial;}{\f5\fswiss\fcharset0 Arial;}{\f6\froman\fcharset0 Times New Roman;}}
-{\colortbl ;\red255\green0\blue0;\red0\green0\blue255;\red1\green0\blue1;\red0\green128\blue0;\red163\green21\blue21;\red0\green0\blue165;}
-{\*\generator Msftedit 5.41.15.1515;}\viewkind4\uc1\pard\nowidctlpar\f0\fs20 Problems with Qt 4.5.2. documentation Qt 4.4.3 and Thid\par
-Christrine and Joanna\par
-\par
-----\par
-Creator\par
-\par
-Integrate with QTestLib\par
-\par
--------\par
-/git/bin/ssh-keygen does not work under MSYS\par
-\par
-------\par
-Qt 4.6.0\par
-\par
-If QTDIR set in qtvars but not system environment, get\par
-\par
------\par
-Did not update qhulltest.vcproj after installing a new version.\par
-\par
-Depends reports\par
-\pard \cf1\b\f1\fs17 Error: The Side-by-Side configuration information for "c:\\qt\\4.6.0\\bin\\MOC.EXE" contains errors. This application has failed to start because the application configuration is incorrect. Reinstalling the application may fix this problem (14001).\par
-\pard\nowidctlpar\cf0\b0\f0\fs20\par
-\par
-\f2\fs16 Moc'ing RboxPoints_test.cpp...\par
-The system cannot execute the specified program.\par
-Project : error PRJ0019: A tool returned an error code from "Moc'ing RboxPoints_test.cpp..."\par
-\f0\fs20\par
-\f2\fs16 WARNING: Can't find the Qt version that's associated with this project. Defaulting to 4.6.0 instead.\par
-\f0\fs20\par
-qhulltest.vcproj\par
-\tab <Globals>\par
-\tab\tab <Global\par
-\tab\tab\tab Name="QtVersion"\par
-\tab\tab\tab Value="4.5.2"\par
-\tab\tab />\par
-\tab\tab <Global\par
-\tab\tab\tab Name="QtVersion Win32"\par
-\tab\tab\tab Value="4.5.3"\par
-\tab\tab />\par
-\tab </Globals>\par
---------------\par
-git\par
-\par
-exclude ConvexHull/* included the ConvexHull directory? Not tmp/* or cpp/unused/*\par
-\par
-What does D mean? Why not these files?\par
-ISPY-/local/qhull/html> git checkout next\par
-D File_id.diz\par
-D QHULL-GO.pif\par
-D eg/Qhull-go.bat\par
-D eg/q_eg\par
-D eg/q_egtest\par
-D eg/q_test\par
-D eg/q_test.bat\par
-D html/qh--4d.gif\par
-D html/qh--cone.gif\par
-D html/qh--dt.gif\par
-D html/qh--geom.gif\par
-D html/qh--half.gif\par
-D html/qh--rand.gif\par
-D html/rbox.htm\par
-D html/rbox.man\par
-D html/rbox.txt\par
-Switched to branch 'next'\par
-\par
---\par
-cd qhull3.0\par
-164 git init\par
-165 git add .\par
-166 git commit\par
-167 git config --global user.name bbarber\par
-168 git config --global user.email bradb@shore.net\par
-169 mv .git ../qhull3.1\par
-170 cd ../qhull3.1\par
-171 git add .\par
-172 git commit -a\par
-173 cd ../qhull2002.1\par
-174 mv ../qhull3.1/.git .\par
-175 git add .\par
-176 git commit -a\par
-177 mv .git ../qhull-2003.1/\par
-178 cd ../qhull-2003.1/\par
-179 git add .\par
-180 git commit -a\par
-git branch next\par
-191 git checkout next\par
-192 git status\par
-193 git add .\par
-194 git commit -a\par
-195 git add .\par
-196 git commit -a\par
-197 git log --stat --summary\par
-git remote add origin git@gitorious.org:qhull/qhull.git\par
-\par
-On CMD\par
-/qt/git/bin\par
-./sh\par
-PATH=/bin:$PATH\par
-ssh-agent \par
-SSH_AUTH_SOCK=/tmp/ssh-JeBcgds488/agent.488; export SSH_AUTH_SOCK;\par
-SSH_AGENT_PID=5252; export SSH_AGENT_PID;\par
-echo Agent pid 5252;\par
-ssh-add c:/bash/home/bbarber/.ssh/bradb@shore.net-091205\par
-\par
-On bash\par
-export SSH_AUTH_SOCK=c:/qt/git/tmp/ssh-JeBcgds488/agent.488;\par
-git push origin master\par
-git push origin next\par
-\par
-e .git/info/exclude\par
-html/trolltech.rtf\par
-ConvexHull\par
-ConvexHull/*\par
-cpp/unused/*\par
-news/*\par
-qtpro/*/Makefile*\par
-qtpro/*/object_script*\par
-tmp/*\par
-\par
-# Executables\par
-*.a\par
-*.dll\par
-*.exe\par
-\par
-# DevStudio files\par
-*.bsc\par
-*.ncb\par
-*.pdb\par
-*.suo\par
-\par
-# Data files\par
-*.off\par
-*.x\par
-\par
-\par
------\par
-\f3 ** Change to static link library before shipping, or define Qt for static linking.\par
-\f0\par
------\par
-\pard\f4 4) No complaints if qhull.pro has 'CONFIG += debug', but the command line adds 'release'.\f5 It should be debug_and_release\par
-\par
-\f4 Running build steps for project qhull...\par
-Starting: c:/qt/2009.05/qt/bin/qmake.exe C:/bash/local/qhull/qtpro/qhull/qhull.pro -spec win32-g++ -r CONFIG+=release \par
-Exited with code 0.\par
-Starting: C:/Qt/2009.05/mingw/bin/mingw32-make.exe -w \par
-mingw32-make: Entering directory `C:/bash/local/qhull/qtpro/qhull'\par
-C:/Qt/2009.05/mingw/bin/mingw32-make -f Makefile.Debug\par
-mingw32-make[1]: Entering directory `C:/bash/local/qhull/qtpro/qhull'\par
-mingw32-make[1]: Nothing to be done for `first'.\par
-mingw32-make[1]: Leaving directory `C:/bash/local/qhull/qtpro/qhull'\par
-mingw32-make: Leaving directory `C:/bash/local/qhull/qtpro/qhull'\par
-Exited with code 0.\par
-\par
-\f5 --------\par
-\f4 'Handling external libraries' has a bad URL to 'Declaring other Libraries\par
-\par
-Why does the make file call both gcc and g++. These appear to be the same in mingw, but is that necessarily so?\par
-\par
-gcc -c -g -Wall -DUNICODE -DQT_LARGEFILE_SUPPORT -DQT_DLL -DQT_CORE_LIB -DQT_THREAD_SUPPORT -I"c:\\Qt\\2009.05\\qt\\include\\QtCore" -I"c:\\Qt\\2009.05\\qt\\include" -I"c:\\Qt\\2009.05\\qt\\include\\ActiveQt" -I"..\\..\\tmp\\moc" -I"c:\\Qt\\2009.05\\qt\\mkspecs\\win32-g++" -o ..\\..\\tmp\\obj\\usermem.o ..\\..\\src\\usermem.c\par
-g++ -enable-stdcall-fixup -Wl,-enable-auto-import -Wl,-enable-runtime-pseudo-reloc -mthreads -Wl -shared -Wl,--out-implib,..\\..\\tmp\\lib\\..\\..\\\\libqhull.a -o ..\\..\\qhull.dll object_script.qhull.Debug -L"c:\\Qt\\2009.05\\qt\\lib" -lQtCored4\par
-Creating library file: ..\\..\\tmp\\lib\\..\\..\\\\libqhull.a\par
-\par
-\f5 ------\par
-Executable is not relative to $BUILDDIR in qtcreator 'Could not find the executable". It is relative to QTDIR/.. instead\f4\par
-\pard\nowidctlpar\f0\par
-\par
------\par
-Qhull users on 'const' and warn64\par
-\par
--------\par
-\f3 - Ask Jim and Andy about operator<<\par
- - Note to Jim Frost on coding conventions\par
-\f0\par
------\par
-\f3 Style &*r.Coordinates() -- Search Qt\par
-\par
-\f0 -----\par
-Find python program for counters. Change user.h to last code instead of next. When were error codes added? Put into changes.txt\par
-\par
-----\par
-Options->Text Editor->File Formats->XML -- Review formating options\par
-\par
----\par
-#def symbol for QT_VERSION\par
-\par
----\par
-\cf2\f3 How to\par
- using\cf0 \cf3 orgQhull\cf0 ::\cf3 QhullVertexSet::PrintVertexSet\cf0 ;\par
-\par
-\f2\fs16 ..\\cpp\\QhullVertex.cpp(46) : error C2885: 'orgQhull::QhullVertexSet::PrintVertexSet': not a valid using-declaration at non-class scope\par
-\f3\fs20\par
-\f0 ---\par
-Why does moving operator<< into orgQhull cause errors for RboxPoints_test?\par
-\par
-\pard\sb100\sa100\f6\fs24 ------\par
-C++, why does \f3\fs20 \cf4 //friend std::ostream & operator<<(std::ostream &os, Point &p);\par
-\cf0\f6\fs24 in point.h cause operator<< to fail for Points and QhullFacet? Is the friend in orgQhull hide the operator in global?\par
------\par
-Add documentation 'Initializing References' in 'Initializers[C++]' . Tricky rules\par
-----\par
-next, previous, peekPrevious, and peekNext returns an iterator [typedef'd as 'Item' in qiterator.h], but the documented signature is T&. How is the conversion done?\f2\fs16 \f6\fs24\par
-----\par
-What is role of operator=?\par
-----\par
-Need to count XPASSs per testcase. These need fixing in the test code. Otherwise hidden in log. (QEXPECTED_FAIL)\par
----\par
-Can you use ostream<<FacetList to write to a QString? \par
----\par
-QFIXUP(int, message) for messages into the test log. Need callback or count of each type\par
-Workaround\par
-\f3\fs20 \cf3 QEXPECT_FAIL\cf0 (0,\cf5 "toQList for QhullFacetList"\cf0 , \cf3 QTest\cf0 ::\cf3 Continue\cf0 );\par
- \cf3 QCOMPARE\cf0 (\cf3 fs2\cf0 .\cf3 count\cf0 (),6);\par
-\cf2 ----\par
-Can not conditional compile a member function e.g., QHullFacetSet.toStdVector. So a library needs to know all includes.\par
-toQList must be defined outside of class.\par
-toQLIst(QHullFacet)\par
-qhullcpp includes\par
-"..\\..\\4.3.0\\include\\QtCore","..\\..\\4.3.0\\include\\QtCore","..\\..\\4.3.0\\include\\QtGui","..\\..\\4.3.0\\include\\QtGui","..\\..\\4.3.0\\include","..\\..\\4.3.0\\include\\QtTest","..\\src","..\\..\\4.3.0\\include\\ActiveQt","moc","uic_h",".",..\\..\\4.3.0\\mkspecs\\win32-msvc2005\par
-Qhulltest includes\par
-.,..\\cpp,..\\..\\cpp,..\\src,..\\..\\src,..\\tmp,..\\..\\tmp,"\\qt\\4.3.0\\include\\QtCore","\\qt\\4.3.0\\include\\QtGui","\\qt\\4.3.0\\include","\\qt\\4.3.0\\include\\QtTest","\\qt\\4.3.0\\include\\ActiveQt",\\qt\\4.3.0\\mkspecs\\win32-msvc2005\par
-How does template instantiation know when to define a function and where. Is the same rule for globals as members?\par
-Can you specialize a templated base class or does the declaration need to be specialized as well? Can not specialize a templated base class. The specialization has to occur before declaring the derived class, but need the derived class to implement the specialization\par
-#\cf4 //Conversion \par
-#//ClassRefs before //Types\par
-\cf0 \cf3 std\cf0 ::\cf3 vector\cf0 <\cf3 QhullVertex\cf0 > \cf3 vertices_toStdVector\cf0 () \cf2 const\cf0 ;\par
-\cf4 How to use precompiled headers with Qt\par
-Need QSTOP or QBREAK to cancel a test\par
-'\cf6\f2\fs16 scalar deleting destructor' What does this mean in calling ~QhullQh from ~Qhull\cf4\f3\fs20\par
-copy assignment needed for vector<T> \par
-\cf2 #ifndef\cf0 \cf3 QT_NO_STL\par
-std\cf0 ::\cf3 vector\cf0 <\cf3 QhullFacet\cf0 > \cf3 QhullFacetSet\cf0 ::\par
-\cf3 toStdVector\cf0 () \cf2 const\par
-\cf0\{\par
- \cf3 QhullFacetSetIterator\cf0 \cf3 i\cf0 (*\cf2 this\cf0 );\par
- \cf3 std\cf0 ::\cf3 vector\cf0 <\cf3 QhullFacet\cf0 > \cf3 vs\cf0 ;\par
- \cf3 vs\cf0 .\cf3 reserve\cf0 (\cf3 i\cf0 .\cf3 countRemaining\cf0 ());\par
- \cf2 while\cf0 (\cf3 i\cf0 .\cf3 hasNext\cf0 ())\{\par
- \cf3 vs\cf0 .\cf3 push_back\cf0 (\cf3 i\cf0 .\cf3 next\cf0 ());\par
- \}\par
- \cf2 return\cf0 \cf3 vs\cf0 ;\par
-\}\cf4 //toStdVector\par
-\cf2 #endif\par
-\par
-\cf0\f6\fs24\par
----\par
-Highlights 'operator' as misspelled\par
-\f3\fs20 \cf2 using\cf0 \cf3 Point\cf0 ::\cf2 operator\cf0 [];\par
-\f6\fs24 ---------\par
-Gotcha\par
-\f3\fs20 \cf3 Point\cf0 \cf3 p2\cf0 ();\par
- \cf3 QVERIFY\cf0 (\cf3 p2\cf0 ==\cf3 p\cf0 );\par
-\f2\fs16 ..\\cpp\\qhulltest\\Point_test.cpp(62) : error C2679: binary '==' : no operator found which takes a right-hand operand of type 'orgQhull::Point' (or there is no acceptable conversion)\par
-\f6\fs24 ---\par
- <no include file>\par
- \cf3\f3\fs20 QHULL_DECLARE_SEQUENTIAL_ITERATOR\cf0 (\cf3 Point\cf0 , \cf3 coordT\cf0 )\par
-\f2\fs16 c:\\bash\\local\\qhull\\cpp\\Point.h(137) : error C4430: missing type specifier - int assumed.\par
-\pard\nowidctlpar\f0\fs20 ----\par
-Use an extra space '\f3 : ' in initializer lists\par
-\f0\par
-============================\par
-== Qt newsletter\par
-============================\par
-\par
-QLineEdit\par
-QToolBox\par
-http://www.froglogic.com/freeware/\par
-missed a Taste of Qt 4\par
-See http://doc.trolltech.com/ 3.3/activeqt-dotnet.html for details.\par
-For more information about using precompiled headers, see http://doc.trolltech.com/3.3/qmake-manual-7.html.\par
-add defrag for paging file\par
-\par
-mssing\par
-file://localhost/C:/download/Qt Quarterly/qq11-events.html\par
-\par
-============================\par
-== DevStudio notes\par
-============================\par
-\par
-\pard\keepn\sb100\sa100 DevStudio8/vc/include/vector -- change ++* to ++\par
-\pard\nowidctlpar\tab _Myt operator--(int)\par
-\tab\tab\{\tab // postdecrement\par
-\tab\tab _Myt _Tmp = *this;\par
-\tab\tab _SCL_SECURE_VALIDATE(this->_Mycont != NULL);\par
-\tab\tab _SCL_SECURE_VALIDATE_RANGE(_Myptr >= ((_Myvec *)(this->_Mycont))->_Myfirst);\par
-\tab\tab --_Myptr;\par
-\tab\tab return (_Tmp);\par
-\tab\tab\}\par
-\par
-\par
-\tab # Instead of\par
-\tab _Myt operator--(int)\par
-\tab\tab\{\tab // postdecrement\par
-\tab\tab _Myt _Tmp = *this;\par
-\tab\tab --*this;\par
-\tab\tab return (_Tmp);\par
-\tab\tab\}\par
-\par
-============================\par
-== Qt notes\par
-============================\par
-\par
------------------------\par
-Cust ID 43151\par
-Licence 1530522\par
-Brad Barber\par
-\par
----------------------------------------\par
-vcapp does not set "Configuration->C++->Output files->Program Database Filename" and "Configuation->C++->Browse Information->Browse file" By default, both are set to DESTDIR.\par
-\par
-ProgramDatabaseFile="thidd.pdb"\par
-\par
-------------------------------------------\par
-vcapp/vclib does not set "Configuration->C++->Browse Information->Enable Browse Information->Include all Browse Information (/FR)\par
-\par
-QRegExp is not precompiled\par
-\par
-QRegExp does not capture positive look-ahead #163710\par
-\par
-Xml Schema for .ui files #163702\par
-\par
-Use "docked=true" to position DockWidgets\par
-\par
- * [156793] Introduced PRECOMPILED_DIR for PCH output (defaults to\par
- OBJECTS_DIR).\par
- * [257985] Fixed qmake location detection bug.\par
- * Ensured that empty INCLUDEPATH definitions are stripped out.\par
- * Allow QMAKE_UUID to override qmake deteremined UUID in the vcproj\par
- generator.\par
-\par
-----\par
-EOF\par
-}
-�
\ No newline at end of file
diff --git a/index.htm b/index.htm
index cc70d89..64eeda7 100644
--- a/index.htm
+++ b/index.htm
@@ -51,13 +51,13 @@ and higher. </p>
<ul>
<li><a href="http://www.qhull.org/news">News</a> and
<a href="http://www.qhull.org/news/qhull-news.html#bugs">Bugs</a>
- about Qhull 2003.1 2003/12/30</li>
+ about Qhull 2010.1 2010/01/06</li>
<li><a href="http://www.qhull.org/download">Download</a>
Qhull</li>
<li><a
href="http://www.geom.uiuc.edu/graphics/pix/Special_Topics/Computational_Geometry/welcome.html">Examples
</a>of Qhull output </li>
- <li><a href=http://savannah.nongnu.org/projects/qhull/>Development</a> at Savannah
+ <li><a href=http://gitorious.org/qhull/>Development</a> at Gitorious
<li><input name=as_q size=10 value="">
<input type="submit" value="Search">
www.qhull.org
diff --git a/vcproj/libqhull.vcproj b/project/libqhull.vcproj
similarity index 100%
rename from vcproj/libqhull.vcproj
rename to project/libqhull.vcproj
diff --git a/qtpro/libqhull/libqhull.pro b/project/libqhull/libqhull.pro
similarity index 100%
rename from qtpro/libqhull/libqhull.pro
rename to project/libqhull/libqhull.pro
diff --git a/qtpro/libqhullcpp/libqhullcpp.pro b/project/libqhullcpp/libqhullcpp.pro
similarity index 96%
rename from qtpro/libqhullcpp/libqhullcpp.pro
rename to project/libqhullcpp/libqhullcpp.pro
index 38793b0..03791d9 100644
--- a/qtpro/libqhullcpp/libqhullcpp.pro
+++ b/project/libqhullcpp/libqhullcpp.pro
@@ -10,10 +10,12 @@ LIBS += -L../..
build_pass:CONFIG(debug, debug|release):{
TARGET = qhullcppd
LIBS += libqhulld
+ PRE_TARGETDEPS += ../../libqhulld.a
OBJECTS_DIR = ../../tmp/libqhullcpp/Debug
}else:build_pass:CONFIG(release, debug|release):{
TARGET = qhullcpp
LIBS += libqhull
+ PRE_TARGETDEPS += ../../libqhull.a
OBJECTS_DIR = ../../tmp/libqhullcpp/Release
}
QT -= gui
diff --git a/qtpro/qconvex/qconvex.pro b/project/qconvex/qconvex.pro
similarity index 90%
rename from qtpro/qconvex/qconvex.pro
rename to project/qconvex/qconvex.pro
index f00fb8e..c87868e 100644
--- a/qtpro/qconvex/qconvex.pro
+++ b/project/qconvex/qconvex.pro
@@ -12,9 +12,11 @@ QMAKE_CFLAGS += -Wall -Wextra -Wshadow -Wcast-qual -Wwrite-strings
QMAKE_CFLAGS += -Wno-sign-conversion # Many size_t vs. int errors
build_pass:CONFIG(debug, debug|release):{
LIBS += libqhulld
+ PRE_TARGETDEPS += ../../libqhulld.a
OBJECTS_DIR = ../../tmp/qconvex/Debug
}else:build_pass:CONFIG(release, debug|release):{
LIBS += libqhull
+ PRE_TARGETDEPS += ../../libqhull.a
OBJECTS_DIR = ../../tmp/qconvex/Release
}
QT -= gui
diff --git a/qtpro/qdelaunay/qdelaunay.pro b/project/qdelaunay/qdelaunay.pro
similarity index 90%
rename from qtpro/qdelaunay/qdelaunay.pro
rename to project/qdelaunay/qdelaunay.pro
index a10ae1e..0f96156 100644
--- a/qtpro/qdelaunay/qdelaunay.pro
+++ b/project/qdelaunay/qdelaunay.pro
@@ -12,9 +12,11 @@ QMAKE_CFLAGS += -Wall -Wextra -Wshadow -Wcast-qual -Wwrite-strings
QMAKE_CFLAGS += -Wno-sign-conversion # Many size_t vs. int errors
build_pass:CONFIG(debug, debug|release):{
LIBS += libqhulld
+ PRE_TARGETDEPS += ../../libqhulld.a
OBJECTS_DIR = ../../tmp/qdelaunay/Debug
}else:build_pass:CONFIG(release, debug|release):{
LIBS += libqhull
+ PRE_TARGETDEPS += ../../libqhull.a
OBJECTS_DIR = ../../tmp/qdelaunay/Release
}
QT -= gui
diff --git a/qtpro/qhalf/qhalf.pro b/project/qhalf/qhalf.pro
similarity index 90%
rename from qtpro/qhalf/qhalf.pro
rename to project/qhalf/qhalf.pro
index b2227f4..23aefc7 100644
--- a/qtpro/qhalf/qhalf.pro
+++ b/project/qhalf/qhalf.pro
@@ -12,9 +12,11 @@ QMAKE_CFLAGS += -Wall -Wextra -Wshadow -Wcast-qual -Wwrite-strings
QMAKE_CFLAGS += -Wno-sign-conversion # Many size_t vs. int errors
build_pass:CONFIG(debug, debug|release):{
LIBS += libqhulld
+ PRE_TARGETDEPS += ../../libqhulld.a
OBJECTS_DIR = ../../tmp/qconvex/Debug
}else:build_pass:CONFIG(release, debug|release):{
LIBS += libqhull
+ PRE_TARGETDEPS += ../../libqhull.a
OBJECTS_DIR = ../../tmp/qconvex/Release
}
QT -= gui
diff --git a/qtpro/qhull-all.pro b/project/qhull-all.pro
similarity index 100%
rename from qtpro/qhull-all.pro
rename to project/qhull-all.pro
diff --git a/vcproj/qhull.sln b/project/qhull.sln
similarity index 100%
rename from vcproj/qhull.sln
rename to project/qhull.sln
diff --git a/vcproj/qhull.vcproj b/project/qhull.vcproj
similarity index 100%
rename from vcproj/qhull.vcproj
rename to project/qhull.vcproj
diff --git a/qtpro/qhull/qhull.pro b/project/qhull/qhull.pro
similarity index 90%
rename from qtpro/qhull/qhull.pro
rename to project/qhull/qhull.pro
index ad799d2..4a6330a 100644
--- a/qtpro/qhull/qhull.pro
+++ b/project/qhull/qhull.pro
@@ -12,9 +12,11 @@ QMAKE_CFLAGS += -Wall -Wextra -Wshadow -Wcast-qual -Wwrite-strings
QMAKE_CFLAGS += -Wno-sign-conversion # Many size_t vs. int errors
build_pass:CONFIG(debug, debug|release):{
LIBS += libqhulld
+ PRE_TARGETDEPS += ../../libqhulld.a
OBJECTS_DIR = ../../tmp/qhull/Debug
}else:build_pass:CONFIG(release, debug|release):{
LIBS += libqhull
+ PRE_TARGETDEPS += ../../libqhull.a
OBJECTS_DIR = ../../tmp/qhull/Release
}
QT -= gui
diff --git a/vcproj/qhullcpp.vcproj b/project/qhullcpp.vcproj
similarity index 100%
rename from vcproj/qhullcpp.vcproj
rename to project/qhullcpp.vcproj
diff --git a/vcproj/qhulltest.vcproj b/project/qhulltest.vcproj
similarity index 100%
rename from vcproj/qhulltest.vcproj
rename to project/qhulltest.vcproj
diff --git a/qtpro/qhulltest/qhulltest.pro b/project/qhulltest/qhulltest.pro
similarity index 96%
rename from qtpro/qhulltest/qhulltest.pro
rename to project/qhulltest/qhulltest.pro
index acf2a40..06594d4 100644
--- a/qtpro/qhulltest/qhulltest.pro
+++ b/project/qhulltest/qhulltest.pro
@@ -10,10 +10,12 @@ CONFIG -= app_bundle
LIBS += -L../..
build_pass:CONFIG(debug, debug|release):{
LIBS += libqhullcppd
+ PRE_TARGETDEPS += ../../libqhullcppd.a
OBJECTS_DIR = ../../tmp/qhulltest/Debug
}else:build_pass:CONFIG(release, debug|release):{
LIBS += libqhullcpp
OBJECTS_DIR = ../../tmp/qhulltest/Release
+ PRE_TARGETDEPS += ../../libqhullcpp.a
}
QT -= gui
MOC_DIR = ../../tmp/moc
diff --git a/qtpro/qvoronoi/qvoronoi.pro b/project/qvoronoi/qvoronoi.pro
similarity index 90%
rename from qtpro/qvoronoi/qvoronoi.pro
rename to project/qvoronoi/qvoronoi.pro
index 884bffb..ce49023 100644
--- a/qtpro/qvoronoi/qvoronoi.pro
+++ b/project/qvoronoi/qvoronoi.pro
@@ -12,9 +12,11 @@ QMAKE_CFLAGS += -Wall -Wextra -Wshadow -Wcast-qual -Wwrite-strings
QMAKE_CFLAGS += -Wno-sign-conversion # Many size_t vs. int errors
build_pass:CONFIG(debug, debug|release):{
LIBS += libqhulld
+ PRE_TARGETDEPS += ../../libqhulld.a
OBJECTS_DIR = ../../tmp/qvoronoi/Debug
}else:build_pass:CONFIG(release, debug|release):{
LIBS += libqhull
+ PRE_TARGETDEPS += ../../libqhull.a
OBJECTS_DIR = ../../tmp/qvoronoi/Release
}
QT -= gui
diff --git a/vcproj/rbox.vcproj b/project/rbox.vcproj
similarity index 100%
rename from vcproj/rbox.vcproj
rename to project/rbox.vcproj
diff --git a/qtpro/rbox/rbox.pro b/project/rbox/rbox.pro
similarity index 90%
rename from qtpro/rbox/rbox.pro
rename to project/rbox/rbox.pro
index 674817c..ae18d90 100644
--- a/qtpro/rbox/rbox.pro
+++ b/project/rbox/rbox.pro
@@ -10,9 +10,11 @@ QMAKE_CFLAGS += -Wall -Wextra -Wshadow -Wcast-qual -Wwrite-strings
QMAKE_CFLAGS += -Wno-sign-conversion # Many size_t vs. int errors
build_pass:CONFIG(debug, debug|release):{
LIBS += libqhulld
+ PRE_TARGETDEPS += ../../libqhulld.a
OBJECTS_DIR = ../../tmp/rbox/Debug
}else:build_pass:CONFIG(release, debug|release):{
LIBS += libqhull
+ PRE_TARGETDEPS += ../../libqhull.a
OBJECTS_DIR = ../../tmp/rbox/Release
}
QT -= gui
diff --git a/qtpro/user_eg/user_eg.pro b/project/user_eg/user_eg.pro
similarity index 90%
rename from qtpro/user_eg/user_eg.pro
rename to project/user_eg/user_eg.pro
index 70a8521..23c89b2 100644
--- a/qtpro/user_eg/user_eg.pro
+++ b/project/user_eg/user_eg.pro
@@ -11,9 +11,11 @@ QMAKE_CFLAGS += -Wall -Wextra -Wshadow -Wcast-qual -Wwrite-strings
QMAKE_CFLAGS += -Wno-sign-conversion # Many size_t vs. int errors
build_pass:CONFIG(debug, debug|release):{
LIBS += libqhulld
+ PRE_TARGETDEPS += ../../libqhulld.a
OBJECTS_DIR = ../../tmp/user_eg/Debug
}else:build_pass:CONFIG(release, debug|release):{
LIBS += libqhull
+ PRE_TARGETDEPS += ../../libqhull.a
OBJECTS_DIR = ../../tmp/user_eg/Release
}
QT -= gui
diff --git a/qtpro/user_eg2/user_eg2.pro b/project/user_eg2/user_eg2.pro
similarity index 90%
rename from qtpro/user_eg2/user_eg2.pro
rename to project/user_eg2/user_eg2.pro
index 869bfd8..3ae3d25 100644
--- a/qtpro/user_eg2/user_eg2.pro
+++ b/project/user_eg2/user_eg2.pro
@@ -11,9 +11,11 @@ QMAKE_CFLAGS += -Wall -Wextra -Wshadow -Wcast-qual -Wwrite-strings
QMAKE_CFLAGS += -Wno-sign-conversion # Many size_t vs. int errors
build_pass:CONFIG(debug, debug|release):{
LIBS += libqhulld
+ PRE_TARGETDEPS += ../../libqhulld.a
OBJECTS_DIR = ../../tmp/user_eg2/Debug
}else:build_pass:CONFIG(release, debug|release):{
LIBS += libqhull
+ PRE_TARGETDEPS += ../../libqhull.a
OBJECTS_DIR = ../../tmp/user_eg2/Release
}
QT -= gui
diff --git a/vcproj/user_eg3.vcproj b/project/user_eg3.vcproj
similarity index 100%
rename from vcproj/user_eg3.vcproj
rename to project/user_eg3.vcproj
diff --git a/qtpro/user_eg3/user_eg3.pro b/project/user_eg3/user_eg3.pro
similarity index 94%
rename from qtpro/user_eg3/user_eg3.pro
rename to project/user_eg3/user_eg3.pro
index 4cd127f..4ec2412 100644
--- a/qtpro/user_eg3/user_eg3.pro
+++ b/project/user_eg3/user_eg3.pro
@@ -8,9 +8,11 @@ CONFIG += console warn_on
LIBS += -L../..
build_pass:CONFIG(debug, debug|release):{
LIBS += libqhullcppd
+ PRE_TARGETDEPS += ../../libqhullcppd.a
OBJECTS_DIR = ../../tmp/user_eg3/Debug
}else:build_pass:CONFIG(release, debug|release):{
LIBS += libqhullcpp
+ PRE_TARGETDEPS += ../../libqhullcpp.a
OBJECTS_DIR = ../../tmp/user_eg3/Release
}
QT -= gui
diff --git a/qhull.ilk b/qhull.ilk
deleted file mode 100644
index 6c31410ad03e6c994a7dd1a623eeb1155ae5da2e..0000000000000000000000000000000000000000
GIT binary patch
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diff --git a/src/Changes.txt b/src/Changes.txt
index c2dcd06..0a4d46c 100644
--- a/src/Changes.txt
+++ b/src/Changes.txt
@@ -73,31 +73,43 @@ Qhull cpp questions
To do
- ConvexHull is a submodule to git. How to get rid of?
- Review Warn64
- - SUBDIRS to sln -- qmake -tp vc
- review all #pragma
- review all FIXUP [^0-9]
- clean up warnings for libqhullcpp
-117.405 - Abandon savannah
- - Add config directory to Qhull
- - Fix README Visual C++ quickstart
+ - Abandon savannah
- Review changes with Kent Williams
Keep size of qh_set as int, set.h, global.c
Keep size of qh_mem as int, mem.h, global.c
- Why rename index in qh_initthresholds(), poly2.c, qhull.c -- Seems OK
- Measure performance of Qhull
- qhulltest --all added to output
- Number the FIXUPS
- - Review qh-code.htm#cpp
- Add test of user_eg3, etc.
- - Add vcproj for qconvex, etc.
- Review all ptr_intT
- Change tabs to spaces in src/*.c *.h
- Check for wraparound of 64-bit ints -- e.g., a large set
- Reconsider old_qhstat data type (amorilia)
libqhull.h: qhstatT *old_qhstat; /* for saving qh_qhstat in save_qhull() and UsingLibQhull. Free with qh_free() */
mem.h: setT *tempstack; /* stack of temporary memory, managed by users */
-
- - Add library dependencies to .pro files. For now, rebuild on changes.
+ - Add vcproj for qconvex, etc. Change qhullcpp to libqhull.dll
+ - Add config directory to Qhull
+ - 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
+ - Add output of qhulltest to source
+ - Make distribution -- remove tmp, news, .git, leftovers from project, change CRLF
+
+qhull 2010.1 2010/01/06
+
+- Fixed serious bug in qh_gethash [poly.c]
+- Documentation and build system are incomplete (see above)
+- First release of C++ interface [qh-code.htm]
+- Development moved to http://gitorious.org/qhull
+ git clone git@gitorious.org:qhull/qhull.git
+- Did not fix conformant tesselations for 'Qt'.
+ For details, see http://www.qhull.org/news#bugs of May 2007 and Dec 2006.
+- Use g++ builds for Windows distribution (10% faster than msvc2005)
+ Combined vcproj/ and qtproj/ into project/
+ vcproj will be replaced by qmake generated files
qhull 2010.0.3 2010/01/05
@@ -123,7 +135,7 @@ Code changes
- Makefile.txt corrected for libqhull build [amorilia]
- Renamed index to idx to avoid shadowing BSD strings.h [kwilliams]
-qhull 2010.0.1 2010/01/03
+qhull 2010.0.1 2010/01/03
New Features:
- Added option 'Ta' to annotate output with message codes
@@ -136,6 +148,7 @@ Preliminary C++ support:
Changes to qhull options and results
- Allow 'd' and 'v' as the filename for 'TO ..' and 'TI ...' in qdelaunay [M. Jambon]
+ - 'rbox tN' requires an integer (previously allowed floats)
- Allow quoted filenames for 'TO ...' and 'TI ...'
- Prefix error messages and warnings with a message code (e.g., QH6012)
- Fixed rbox ignoring flags that were not separated by spaces
@@ -147,7 +160,6 @@ Changes to qhull options and results
- Removed extra spaces at end of line
Breaking Code Changes:
- - 'rbox tN' takes an integer (previously allowed floats)
- Renamed qh.coplanarset to coplanarfacetset. Avoids conflict with facetT.coplanarset
- qh_restore_qhull() zeroes out qh.old_qhstat and qh.old_tempstack. Ownership moved.
- Rewrote save_qhull/restore_qhull
diff --git a/src/global.c b/src/global.c
index 6abb9fd..73ee5d5 100644
--- a/src/global.c
+++ b/src/global.c
@@ -12,8 +12,8 @@
see qhull_a.h for internal functions
copyright (c) 1993-2010 The Geometry Center.
- $Id: //product/qhull/main/rel/src/global.c#55 $$Change: 1152 $
- $DateTime: 2010/01/05 22:11:10 $$Author: bbarber $
+ $Id: //product/qhull/main/rel/src/global.c#56 $$Change: 1159 $
+ $DateTime: 2010/01/06 22:14:43 $$Author: bbarber $
*/
#include "qhull_a.h"
@@ -47,7 +47,7 @@ qhT qh_qh; /* all global variables.
recompile user_eg.c, rbox.c, libqhull.c, qconvex.c, qdelaun.c qvoronoi.c, qhalf.c
*/
-const char *qh_version = "2010.0.3 2010/01/05";
+const char *qh_version = "2010.1 2010/01/06";
/*-<a href="qh-globa.htm#TOC"
>-------------------------------</a><a name="appendprint">-</a>
diff --git a/src/poly2.c b/src/poly2.c
index 34c8a57..58a2c9a 100644
--- a/src/poly2.c
+++ b/src/poly2.c
@@ -9,8 +9,8 @@
frequently used code is in poly.c
copyright (c) 1993-2010 The Geometry Center.
- $Id: //product/qhull/main/rel/src/poly2.c#38 $$Change: 1150 $
- $DateTime: 2010/01/04 22:43:14 $$Author: bbarber $
+ $Id: //product/qhull/main/rel/src/poly2.c#39 $$Change: 1154 $
+ $DateTime: 2010/01/06 20:41:28 $$Author: bbarber $
*/
#include "qhull_a.h"
@@ -341,8 +341,7 @@ Verify may report that a point is outside of a facet.\n");
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, "\n\
-qhull input warning: no outer plane check ('Q5') or no processing of\n\
+ 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");
}
diff --git a/user_eg3.ilk b/user_eg3.ilk
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--
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