qhull →
2020.2-6 →
armhf → 2023-09-18 21:37:54
sbuild (Debian sbuild) 0.72.0 (25 Oct 2016) on mb-lxc-02
+==============================================================================+
| qhull 2020.2-6 (armhf) Mon, 18 Sep 2023 21:28:06 +0000 |
+==============================================================================+
Package: qhull
Version: 2020.2-6
Source Version: 2020.2-6
Distribution: trixie-staging
Machine Architecture: armhf
Host Architecture: armhf
Build Architecture: armhf
I: NOTICE: Log filtering will replace 'var/lib/schroot/mount/trixie-staging-armhf-sbuild-78f03bcb-ffcd-4aaf-844d-f44bb84a9688' with '<<CHROOT>>'
+------------------------------------------------------------------------------+
| Update chroot |
+------------------------------------------------------------------------------+
Get:1 http://172.17.4.1/private trixie-staging InRelease [11.3 kB]
Get:2 http://172.17.4.1/private trixie-staging/main Sources [14.1 MB]
Get:3 http://172.17.4.1/private trixie-staging/main armhf Packages [14.7 MB]
Fetched 28.7 MB in 10s (2749 kB/s)
Reading package lists...
W: No sandbox user '_apt' on the system, can not drop privileges
W: http://172.17.4.1/private/dists/trixie-staging/InRelease: Key is stored in legacy trusted.gpg keyring (/etc/apt/trusted.gpg), see the DEPRECATION section in apt-key(8) for details.
+------------------------------------------------------------------------------+
| Fetch source files |
+------------------------------------------------------------------------------+
Check APT
---------
Checking available source versions...
Download source files with APT
------------------------------
Reading package lists...
NOTICE: 'qhull' packaging is maintained in the 'Git' version control system at:
https://salsa.debian.org/science-team/qhull.git
Please use:
git clone https://salsa.debian.org/science-team/qhull.git
to retrieve the latest (possibly unreleased) updates to the package.
Need to get 1320 kB of source archives.
Get:1 http://172.17.4.1/private trixie-staging/main qhull 2020.2-6 (dsc) [2199 B]
Get:2 http://172.17.4.1/private trixie-staging/main qhull 2020.2-6 (tar) [1299 kB]
Get:3 http://172.17.4.1/private trixie-staging/main qhull 2020.2-6 (diff) [18.6 kB]
Fetched 1320 kB in 0s (3325 kB/s)
Download complete and in download only mode
I: NOTICE: Log filtering will replace 'build/qhull-zYkfkZ/qhull-2020.2' with '<<PKGBUILDDIR>>'
I: NOTICE: Log filtering will replace 'build/qhull-zYkfkZ' with '<<BUILDDIR>>'
+------------------------------------------------------------------------------+
| Install build-essential |
+------------------------------------------------------------------------------+
Setup apt archive
-----------------
Merged Build-Depends: build-essential, fakeroot
Filtered Build-Depends: build-essential, fakeroot
dpkg-deb: building package 'sbuild-build-depends-core-dummy' in '/<<BUILDDIR>>/resolver-ORGqSm/apt_archive/sbuild-build-depends-core-dummy.deb'.
dpkg-scanpackages: warning: Packages in archive but missing from override file:
dpkg-scanpackages: warning: sbuild-build-depends-core-dummy
dpkg-scanpackages: info: Wrote 1 entries to output Packages file.
gpg: keybox '/<<BUILDDIR>>/resolver-ORGqSm/gpg/pubring.kbx' created
gpg: /<<BUILDDIR>>/resolver-ORGqSm/gpg/trustdb.gpg: trustdb created
gpg: key 37145E60F90AF620: public key "Sbuild Signer (Sbuild Build Dependency Archive Key) <buildd-tools-devel@lists.alioth.debian.org>" imported
gpg: Total number processed: 1
gpg: imported: 1
gpg: key 37145E60F90AF620: "Sbuild Signer (Sbuild Build Dependency Archive Key) <buildd-tools-devel@lists.alioth.debian.org>" not changed
gpg: key 37145E60F90AF620: secret key imported
gpg: Total number processed: 1
gpg: unchanged: 1
gpg: secret keys read: 1
gpg: secret keys imported: 1
gpg: using "Sbuild Signer" as default secret key for signing
Ign:1 copy:/<<BUILDDIR>>/resolver-ORGqSm/apt_archive ./ InRelease
Get:2 copy:/<<BUILDDIR>>/resolver-ORGqSm/apt_archive ./ Release [957 B]
Get:3 copy:/<<BUILDDIR>>/resolver-ORGqSm/apt_archive ./ Release.gpg [370 B]
Get:4 copy:/<<BUILDDIR>>/resolver-ORGqSm/apt_archive ./ Sources [349 B]
Get:5 copy:/<<BUILDDIR>>/resolver-ORGqSm/apt_archive ./ Packages [432 B]
Fetched 2108 B in 0s (9767 B/s)
Reading package lists...
W: No sandbox user '_apt' on the system, can not drop privileges
Reading package lists...
Install core build dependencies (apt-based resolver)
----------------------------------------------------
Installing build dependencies
Reading package lists...
Building dependency tree...
Reading state information...
The following packages were automatically installed and are no longer required:
krb5-locales libpam-cap netbase sensible-utils sgml-base
Use 'apt autoremove' to remove them.
The following NEW packages will be installed:
sbuild-build-depends-core-dummy
0 upgraded, 1 newly installed, 0 to remove and 44 not upgraded.
Need to get 852 B of archives.
After this operation, 0 B of additional disk space will be used.
Get:1 copy:/<<BUILDDIR>>/resolver-ORGqSm/apt_archive ./ sbuild-build-depends-core-dummy 0.invalid.0 [852 B]
debconf: delaying package configuration, since apt-utils is not installed
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Selecting previously unselected package sbuild-build-depends-core-dummy.
(Reading database ... 11771 files and directories currently installed.)
Preparing to unpack .../sbuild-build-depends-core-dummy_0.invalid.0_armhf.deb ...
Unpacking sbuild-build-depends-core-dummy (0.invalid.0) ...
Setting up sbuild-build-depends-core-dummy (0.invalid.0) ...
W: No sandbox user '_apt' on the system, can not drop privileges
+------------------------------------------------------------------------------+
| Check architectures |
+------------------------------------------------------------------------------+
Arch check ok (armhf included in any all)
+------------------------------------------------------------------------------+
| Install package build dependencies |
+------------------------------------------------------------------------------+
Setup apt archive
-----------------
Merged Build-Depends: debhelper-compat (= 13), cmake, pkg-kde-tools
Filtered Build-Depends: debhelper-compat (= 13), cmake, pkg-kde-tools
dpkg-deb: building package 'sbuild-build-depends-qhull-dummy' in '/<<BUILDDIR>>/resolver-ORGqSm/apt_archive/sbuild-build-depends-qhull-dummy.deb'.
dpkg-scanpackages: warning: Packages in archive but missing from override file:
dpkg-scanpackages: warning: sbuild-build-depends-core-dummy sbuild-build-depends-qhull-dummy
dpkg-scanpackages: info: Wrote 2 entries to output Packages file.
gpg: using "Sbuild Signer" as default secret key for signing
Ign:1 copy:/<<BUILDDIR>>/resolver-ORGqSm/apt_archive ./ InRelease
Get:2 copy:/<<BUILDDIR>>/resolver-ORGqSm/apt_archive ./ Release [963 B]
Get:3 copy:/<<BUILDDIR>>/resolver-ORGqSm/apt_archive ./ Release.gpg [370 B]
Get:4 copy:/<<BUILDDIR>>/resolver-ORGqSm/apt_archive ./ Sources [504 B]
Get:5 copy:/<<BUILDDIR>>/resolver-ORGqSm/apt_archive ./ Packages [583 B]
Fetched 2420 B in 0s (11.9 kB/s)
Reading package lists...
W: No sandbox user '_apt' on the system, can not drop privileges
Reading package lists...
Install qhull build dependencies (apt-based resolver)
-----------------------------------------------------
Installing build dependencies
Reading package lists...
Building dependency tree...
Reading state information...
The following packages were automatically installed and are no longer required:
krb5-locales libpam-cap netbase sgml-base util-linux-extra
Use 'apt autoremove' to remove them.
The following additional packages will be installed:
autoconf automake autopoint autotools-dev bsdextrautils bsdutils cmake
cmake-data debhelper dh-autoreconf dh-strip-nondeterminism dwz file gettext
gettext-base groff-base intltool-debian libarchive-zip-perl libarchive13
libblkid1 libbrotli1 libcurl4 libdebhelper-perl libelf1 libexpat1
libfile-stripnondeterminism-perl libicu72 libjsoncpp25 libmagic-mgc
libmagic1 libmount1 libnghttp2-14 libpipeline1 libproc2-0 libpsl5
libpython3-stdlib libpython3.11-minimal libpython3.11-stdlib librhash0
librtmp1 libsmartcols1 libssh2-1 libsub-override-perl libtool libuchardet0
libuuid1 libuv1 libxml2 m4 man-db media-types mount pkg-kde-tools po-debconf
procps python3 python3-minimal python3.11 python3.11-minimal util-linux
util-linux-extra
Suggested packages:
autoconf-archive gnu-standards autoconf-doc cmake-doc cmake-format
elpa-cmake-mode ninja-build dh-make gettext-doc libasprintf-dev
libgettextpo-dev groff lrzip cryptsetup-bin libtool-doc gfortran
| fortran95-compiler gcj-jdk m4-doc apparmor less www-browser nfs-common
cdbs libmail-box-perl python3-doc python3-tk python3-venv python3.11-venv
python3.11-doc binfmt-support dosfstools kbd util-linux-locales
Recommended packages:
curl | wget | lynx ca-certificates libarchive-cpio-perl publicsuffix
libltdl-dev uuid-runtime libwww-perl libmail-sendmail-perl psmisc
The following NEW packages will be installed:
autoconf automake autopoint autotools-dev bsdextrautils cmake cmake-data
debhelper dh-autoreconf dh-strip-nondeterminism dwz file gettext
gettext-base groff-base intltool-debian libarchive-zip-perl libarchive13
libbrotli1 libcurl4 libdebhelper-perl libelf1 libexpat1
libfile-stripnondeterminism-perl libicu72 libjsoncpp25 libmagic-mgc
libmagic1 libnghttp2-14 libpipeline1 libproc2-0 libpsl5 libpython3-stdlib
libpython3.11-minimal libpython3.11-stdlib librhash0 librtmp1 libssh2-1
libsub-override-perl libtool libuchardet0 libuv1 libxml2 m4 man-db
media-types pkg-kde-tools po-debconf procps python3 python3-minimal
python3.11 python3.11-minimal sbuild-build-depends-qhull-dummy
The following packages will be upgraded:
bsdutils libblkid1 libmount1 libsmartcols1 libuuid1 mount util-linux
util-linux-extra
8 upgraded, 54 newly installed, 0 to remove and 36 not upgraded.
Need to get 37.0 MB of archives.
After this operation, 137 MB of additional disk space will be used.
Get:1 copy:/<<BUILDDIR>>/resolver-ORGqSm/apt_archive ./ sbuild-build-depends-qhull-dummy 0.invalid.0 [868 B]
Get:2 http://172.17.4.1/private trixie-staging/main armhf bsdutils armhf 1:2.39.2-1 [85.9 kB]
Get:3 http://172.17.4.1/private trixie-staging/main armhf libblkid1 armhf 2.39.2-1 [143 kB]
Get:4 http://172.17.4.1/private trixie-staging/main armhf libmount1 armhf 2.39.2-1 [166 kB]
Get:5 http://172.17.4.1/private trixie-staging/main armhf libsmartcols1 armhf 2.39.2-1 [101 kB]
Get:6 http://172.17.4.1/private trixie-staging/main armhf util-linux-extra armhf 2.39.2-1 [136 kB]
Get:7 http://172.17.4.1/private trixie-staging/main armhf util-linux armhf 2.39.2-1 [1107 kB]
Get:8 http://172.17.4.1/private trixie-staging/main armhf mount armhf 2.39.2-1 [132 kB]
Get:9 http://172.17.4.1/private trixie-staging/main armhf libpython3.11-minimal armhf 3.11.5-3 [800 kB]
Get:10 http://172.17.4.1/private trixie-staging/main armhf libexpat1 armhf 2.5.0-1 [77.2 kB]
Get:11 http://172.17.4.1/private trixie-staging/main armhf python3.11-minimal armhf 3.11.5-3 [1676 kB]
Get:12 http://172.17.4.1/private trixie-staging/main armhf python3-minimal armhf 3.11.4-5 [26.2 kB]
Get:13 http://172.17.4.1/private trixie-staging/main armhf media-types all 10.1.0 [26.9 kB]
Get:14 http://172.17.4.1/private trixie-staging/main armhf libuuid1 armhf 2.39.2-1 [27.7 kB]
Get:15 http://172.17.4.1/private trixie-staging/main armhf libpython3.11-stdlib armhf 3.11.5-3 [1675 kB]
Get:16 http://172.17.4.1/private trixie-staging/main armhf python3.11 armhf 3.11.5-3 [582 kB]
Get:17 http://172.17.4.1/private trixie-staging/main armhf libpython3-stdlib armhf 3.11.4-5 [9200 B]
Get:18 http://172.17.4.1/private trixie-staging/main armhf python3 armhf 3.11.4-5 [26.2 kB]
Get:19 http://172.17.4.1/private trixie-staging/main armhf libuchardet0 armhf 0.0.7-1 [65.0 kB]
Get:20 http://172.17.4.1/private trixie-staging/main armhf groff-base armhf 1.22.4-10 [774 kB]
Get:21 http://172.17.4.1/private trixie-staging/main armhf bsdextrautils armhf 2.39.2-1 [80.5 kB]
Get:22 http://172.17.4.1/private trixie-staging/main armhf libpipeline1 armhf 1.5.7-1 [33.4 kB]
Get:23 http://172.17.4.1/private trixie-staging/main armhf man-db armhf 2.11.2-3 [1342 kB]
Get:24 http://172.17.4.1/private trixie-staging/main armhf libproc2-0 armhf 2:4.0.3-1 [54.2 kB]
Get:25 http://172.17.4.1/private trixie-staging/main armhf procps armhf 2:4.0.3-1 [731 kB]
Get:26 http://172.17.4.1/private trixie-staging/main armhf libmagic-mgc armhf 1:5.44-3 [305 kB]
Get:27 http://172.17.4.1/private trixie-staging/main armhf libmagic1 armhf 1:5.44-3 [95.3 kB]
Get:28 http://172.17.4.1/private trixie-staging/main armhf file armhf 1:5.44-3 [41.5 kB]
Get:29 http://172.17.4.1/private trixie-staging/main armhf gettext-base armhf 0.21-12 [156 kB]
Get:30 http://172.17.4.1/private trixie-staging/main armhf m4 armhf 1.4.19-3 [256 kB]
Get:31 http://172.17.4.1/private trixie-staging/main armhf autoconf all 2.71-3 [332 kB]
Get:32 http://172.17.4.1/private trixie-staging/main armhf autotools-dev all 20220109.1 [51.6 kB]
Get:33 http://172.17.4.1/private trixie-staging/main armhf automake all 1:1.16.5-1.3 [823 kB]
Get:34 http://172.17.4.1/private trixie-staging/main armhf autopoint all 0.21-13 [496 kB]
Get:35 http://172.17.4.1/private trixie-staging/main armhf libicu72 armhf 72.1-3 [9009 kB]
Get:36 http://172.17.4.1/private trixie-staging/main armhf libxml2 armhf 2.9.14+dfsg-1.3 [571 kB]
Get:37 http://172.17.4.1/private trixie-staging/main armhf libarchive13 armhf 3.6.2-1 [293 kB]
Get:38 http://172.17.4.1/private trixie-staging/main armhf libbrotli1 armhf 1.0.9-2+b3 [258 kB]
Get:39 http://172.17.4.1/private trixie-staging/main armhf libnghttp2-14 armhf 1.52.0-1 [60.6 kB]
Get:40 http://172.17.4.1/private trixie-staging/main armhf libpsl5 armhf 0.21.2-1 [57.5 kB]
Get:41 http://172.17.4.1/private trixie-staging/main armhf librtmp1 armhf 2.4+20151223.gitfa8646d.1-2+b2 [54.2 kB]
Get:42 http://172.17.4.1/private trixie-staging/main armhf libssh2-1 armhf 1.11.0-2 [195 kB]
Get:43 http://172.17.4.1/private trixie-staging/main armhf libcurl4 armhf 7.88.1-10+rpi1 [343 kB]
Get:44 http://172.17.4.1/private trixie-staging/main armhf libjsoncpp25 armhf 1.9.5-6 [64.7 kB]
Get:45 http://172.17.4.1/private trixie-staging/main armhf librhash0 armhf 1.4.3-3 [142 kB]
Get:46 http://172.17.4.1/private trixie-staging/main armhf libuv1 armhf 1.44.2-1+rpi1 [125 kB]
Get:47 http://172.17.4.1/private trixie-staging/main armhf cmake-data all 3.27.4-1 [2103 kB]
Get:48 http://172.17.4.1/private trixie-staging/main armhf cmake armhf 3.27.4-1 [7752 kB]
Get:49 http://172.17.4.1/private trixie-staging/main armhf libdebhelper-perl all 13.11.6 [81.9 kB]
Get:50 http://172.17.4.1/private trixie-staging/main armhf libtool all 2.4.7-7 [517 kB]
Get:51 http://172.17.4.1/private trixie-staging/main armhf dh-autoreconf all 20 [17.1 kB]
Get:52 http://172.17.4.1/private trixie-staging/main armhf libarchive-zip-perl all 1.68-1 [104 kB]
Get:53 http://172.17.4.1/private trixie-staging/main armhf libsub-override-perl all 0.09-4 [9304 B]
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Get:56 http://172.17.4.1/private trixie-staging/main armhf libelf1 armhf 0.188-2.1+rpi1 [171 kB]
Get:57 http://172.17.4.1/private trixie-staging/main armhf dwz armhf 0.15-1 [92.4 kB]
Get:58 http://172.17.4.1/private trixie-staging/main armhf gettext armhf 0.21-12 [1201 kB]
Get:59 http://172.17.4.1/private trixie-staging/main armhf intltool-debian all 0.35.0+20060710.6 [22.9 kB]
Get:60 http://172.17.4.1/private trixie-staging/main armhf po-debconf all 1.0.21+nmu1 [248 kB]
Get:61 http://172.17.4.1/private trixie-staging/main armhf debhelper all 13.11.6 [952 kB]
Get:62 http://172.17.4.1/private trixie-staging/main armhf pkg-kde-tools all 0.15.38 [97.8 kB]
debconf: delaying package configuration, since apt-utils is not installed
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Setting up librtmp1:armhf (2.4+20151223.gitfa8646d.1-2+b2) ...
Setting up libproc2-0:armhf (2:4.0.3-1) ...
Setting up autopoint (0.21-13) ...
Setting up libjsoncpp25:armhf (1.9.5-6) ...
Setting up autoconf (2.71-3) ...
Setting up mount (2.39.2-1) ...
Setting up librhash0:armhf (1.4.3-3) ...
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Setting up libxml2:armhf (2.9.14+dfsg-1.3) ...
Setting up libpython3-stdlib:armhf (3.11.4-5) ...
Setting up automake (1:1.16.5-1.3) ...
update-alternatives: using /usr/bin/automake-1.16 to provide /usr/bin/automake (automake) in auto mode
Setting up libfile-stripnondeterminism-perl (1.13.1-1) ...
Setting up python3.11 (3.11.5-3) ...
Setting up gettext (0.21-12) ...
Setting up libtool (2.4.7-7) ...
Setting up libarchive13:armhf (3.6.2-1) ...
Setting up python3 (3.11.4-5) ...
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Setting up dh-autoreconf (20) ...
Setting up pkg-kde-tools (0.15.38) ...
Setting up dh-strip-nondeterminism (1.13.1-1) ...
Setting up dwz (0.15-1) ...
Setting up groff-base (1.22.4-10) ...
Setting up libcurl4:armhf (7.88.1-10+rpi1) ...
Setting up po-debconf (1.0.21+nmu1) ...
Setting up man-db (2.11.2-3) ...
Not building database; man-db/auto-update is not 'true'.
Setting up cmake (3.27.4-1) ...
Setting up debhelper (13.11.6) ...
Setting up sbuild-build-depends-qhull-dummy (0.invalid.0) ...
Processing triggers for libc-bin (2.36-9+rpi1+deb12u1) ...
W: No sandbox user '_apt' on the system, can not drop privileges
+------------------------------------------------------------------------------+
| Build environment |
+------------------------------------------------------------------------------+
Kernel: Linux 4.15.0-187-generic armhf (armv8l)
Toolchain package versions: binutils_2.40-2+rpi2 dpkg-dev_1.21.22+rpi1 g++-12_12.2.0-14+rpi1 gcc-12_12.2.0-14+rpi1 libc6-dev_2.36-9+rpi1+deb12u1 libstdc++-12-dev_12.2.0-14+rpi1 libstdc++6_12.2.0-14+rpi1 linux-libc-dev_6.1.38-1+rpi1
Package versions: adduser_3.137 apt_2.6.1 autoconf_2.71-3 automake_1:1.16.5-1.3 autopoint_0.21-13 autotools-dev_20220109.1 base-files_12.4+rpi1+deb12u1 base-passwd_3.6.1 bash_5.2.15-2 binutils_2.40-2+rpi2 binutils-arm-linux-gnueabihf_2.40-2+rpi2 binutils-common_2.40-2+rpi2 bsdextrautils_2.39.2-1 bsdutils_1:2.39.2-1 build-essential_12.9 bzip2_1.0.8-5+b2 cmake_3.27.4-1 cmake-data_3.27.4-1 coreutils_9.1-1 cpp_4:12.2.0-3+rpi1 cpp-12_12.2.0-14+rpi1 dash_0.5.12-2 debconf_1.5.82 debhelper_13.11.6 debianutils_5.7-0.4 dh-autoreconf_20 dh-strip-nondeterminism_1.13.1-1 diffutils_1:3.8-4 dirmngr_2.2.40-1.1 dpkg_1.21.22+rpi1 dpkg-dev_1.21.22+rpi1 dwz_0.15-1 e2fsprogs_1.47.0-2 fakeroot_1.31-1.2 file_1:5.44-3 findutils_4.9.0-4 g++_4:12.2.0-3+rpi1 g++-12_12.2.0-14+rpi1 gcc_4:12.2.0-3+rpi1 gcc-12_12.2.0-14+rpi1 gcc-12-base_12.2.0-14+rpi1 gcc-7-base_7.5.0-6+rpi1+b2 gcc-8-base_8.4.0-7+rpi1 gcc-9-base_9.4.0-2+rpi1 gettext_0.21-12 gettext-base_0.21-12 gnupg_2.2.40-1.1 gnupg-l10n_2.2.40-1.1 gnupg-utils_2.2.40-1.1 gpg_2.2.40-1.1 gpg-agent_2.2.40-1.1 gpg-wks-client_2.2.40-1.1 gpg-wks-server_2.2.40-1.1 gpgconf_2.2.40-1.1 gpgsm_2.2.40-1.1 gpgv_2.2.40-1.1 grep_3.8-5 groff-base_1.22.4-10 gzip_1.12-1 hostname_3.23+nmu1 init-system-helpers_1.65.2 intltool-debian_0.35.0+20060710.6 iputils-ping_3:20221126-1 krb5-locales_1.20.1-3 libacl1_2.3.1-3 libapt-pkg6.0_2.6.1 libarchive-zip-perl_1.68-1 libarchive13_3.6.2-1 libasan8_12.2.0-14+rpi1 libassuan0_2.5.5-5 libatomic1_12.2.0-14+rpi1 libattr1_1:2.5.1-4 libaudit-common_1:3.1.1-1 libaudit1_1:3.0.9-1 libbinutils_2.40-2+rpi2 libblkid1_2.39.2-1 libbrotli1_1.0.9-2+b3 libbz2-1.0_1.0.8-5+b2 libc-bin_2.36-9+rpi1+deb12u1 libc-dev-bin_2.36-9+rpi1+deb12u1 libc6_2.36-9+rpi1+deb12u1 libc6-dev_2.36-9+rpi1+deb12u1 libcap-ng0_0.8.3-1+b1 libcap2_1:2.66-4 libcap2-bin_1:2.66-4 libcc1-0_12.2.0-14+rpi1 libcom-err2_1.47.0-2 libcrypt-dev_1:4.4.33-2 libcrypt1_1:4.4.33-2 libctf-nobfd0_2.40-2+rpi2 libctf0_2.40-2+rpi2 libcurl4_7.88.1-10+rpi1 libdb5.3_5.3.28+dfsg2-1 libdebconfclient0_0.270 libdebhelper-perl_13.11.6 libdpkg-perl_1.21.22+rpi1 libelf1_0.188-2.1+rpi1 libexpat1_2.5.0-1 libext2fs2_1.47.0-2 libfakeroot_1.31-1.2 libffi8_3.4.4-1 libfile-find-rule-perl_0.34-3 libfile-stripnondeterminism-perl_1.13.1-1 libgcc-12-dev_12.2.0-14+rpi1 libgcc-s1_12.2.0-14+rpi1 libgcrypt20_1.10.1-3 libgdbm-compat4_1.23-3 libgdbm6_1.23-3 libgmp10_2:6.2.1+dfsg1-1.1 libgnutls30_3.7.9-2 libgomp1_12.2.0-14+rpi1 libgpg-error0_1.46-1 libgssapi-krb5-2_1.20.1-2 libhogweed6_3.8.1-2 libicu72_72.1-3 libidn2-0_2.3.3-1+b2 libisl23_0.25-1 libjansson4_2.14-2 libjsoncpp25_1.9.5-6 libk5crypto3_1.20.1-2 libkeyutils1_1.6.3-2 libkrb5-3_1.20.1-2 libkrb5support0_1.20.1-2 libksba8_1.6.3-2 libldap-2.5-0_2.5.13+dfsg-5+rpi1 liblz4-1_1.9.4-1+rpi1+b1 liblzma5_5.4.1-0.2 libmagic-mgc_1:5.44-3 libmagic1_1:5.44-3 libmd0_1.0.4-2 libmount1_2.39.2-1 libmpc3_1.3.1-1 libmpfr6_4.2.0-1 libncursesw6_6.4-4 libnettle8_3.8.1-2 libnghttp2-14_1.52.0-1 libnpth0_1.6-3 libnsl-dev_1.3.0-2 libnsl2_1.3.0-2 libnumber-compare-perl_0.03-3 libp11-kit0_0.24.1-2 libpam-cap_1:2.66-4 libpam-modules_1.5.2-6 libpam-modules-bin_1.5.2-6 libpam-runtime_1.5.2-7 libpam0g_1.5.2-6 libpcre2-8-0_10.42-1 libpcre3_2:8.39-15 libperl5.36_5.36.0-7 libpipeline1_1.5.7-1 libproc2-0_2:4.0.3-1 libpsl5_0.21.2-1 libpython3-stdlib_3.11.4-5 libpython3.11-minimal_3.11.5-3 libpython3.11-stdlib_3.11.5-3 libreadline8_8.2-1.3 librhash0_1.4.3-3 librtmp1_2.4+20151223.gitfa8646d.1-2+b2 libsasl2-2_2.1.28+dfsg-10 libsasl2-modules-db_2.1.28+dfsg-10 libseccomp2_2.5.4-1+rpi1+b1 libselinux1_3.4-1+b2 libsemanage-common_3.5-1 libsemanage2_3.4-1+b2 libsepol1_3.1-1 libsepol2_3.4-2.1 libsmartcols1_2.39.2-1 libsqlite3-0_3.40.1-2 libss2_1.47.0-2 libssh2-1_1.11.0-2 libssl1.1_1.1.1o-1 libssl3_3.0.9-1 libstdc++-12-dev_12.2.0-14+rpi1 libstdc++6_12.2.0-14+rpi1 libsub-override-perl_0.09-4 libsystemd0_252.12-1~deb12u1+rpi1 libtasn1-6_4.19.0-2 libtext-glob-perl_0.11-3 libtinfo6_6.4-4 libtirpc-common_1.3.3+ds-1 libtirpc-dev_1.3.3+ds-1 libtirpc3_1.3.3+ds-1 libtool_2.4.7-7 libubsan1_12.2.0-14+rpi1 libuchardet0_0.0.7-1 libudev1_252.12-1~deb12u1+rpi1 libunistring2_1.0-2 libuuid1_2.39.2-1 libuv1_1.44.2-1+rpi1 libxml2_2.9.14+dfsg-1.3 libxxhash0_0.8.1-1 libzstd1_1.5.4+dfsg2-5 linux-libc-dev_6.1.38-1+rpi1 login_1:4.13+dfsg1-1 logsave_1.47.0-2 lsb-base_11.6+rpi1 m4_1.4.19-3 make_4.3-4.1 man-db_2.11.2-3 mawk_1.3.4.20200120-3.1 media-types_10.1.0 mount_2.39.2-1 nano_7.2-1 ncurses-base_6.4+20230625-2 ncurses-bin_6.4-4 netbase_6.4 passwd_1:4.13+dfsg1-1 patch_2.7.6-7 perl_5.36.0-7 perl-base_5.36.0-7 perl-modules-5.36_5.36.0-7 pinentry-curses_1.2.1-1 pkg-kde-tools_0.15.38 po-debconf_1.0.21+nmu1 procps_2:4.0.3-1 python3_3.11.4-5 python3-minimal_3.11.4-5 python3.11_3.11.5-3 python3.11-minimal_3.11.5-3 raspbian-archive-keyring_20120528.2 readline-common_8.2-1.3 rpcsvc-proto_1.4.3-1 sbuild-build-depends-core-dummy_0.invalid.0 sbuild-build-depends-qhull-dummy_0.invalid.0 sed_4.9-1 sensible-utils_0.0.20 sgml-base_1.31 sysvinit-utils_3.06-4 tar_1.34+dfsg-1.2 tzdata_2023c-10 usrmerge_37 util-linux_2.39.2-1 util-linux-extra_2.39.2-1 xz-utils_5.4.1-0.2 zlib1g_1:1.2.13.dfsg-1
+------------------------------------------------------------------------------+
| Build |
+------------------------------------------------------------------------------+
Unpack source
-------------
gpgv: Signature made Sun Jul 9 21:45:56 2023 UTC
gpgv: using RSA key 26FB43829C6392308856D6A6F82F07FB8EBA2D59
gpgv: issuer "roehling@debian.org"
gpgv: Can't check signature: No public key
dpkg-source: warning: cannot verify inline signature for ./qhull_2020.2-6.dsc: no acceptable signature found
dpkg-source: info: extracting qhull in /<<PKGBUILDDIR>>
dpkg-source: info: unpacking qhull_2020.2.orig.tar.gz
dpkg-source: info: unpacking qhull_2020.2-6.debian.tar.xz
dpkg-source: info: using patch list from debian/patches/series
dpkg-source: info: applying 0001-debianize-test-failure-msg.patch
dpkg-source: info: applying 0002-Fix-privacy-breach.patch
dpkg-source: info: applying 0003-Use-local-version-of-function-index.patch
dpkg-source: info: applying 0004-Build-qhullcpp-as-shared-library.patch
dpkg-source: info: applying 0005-Fix-CMake-target-export.patch
dpkg-source: info: applying 0006-Build-deprecated-libqhull-for-now.patch
Check disk space
----------------
Sufficient free space for build
User Environment
----------------
APT_CONFIG=/var/lib/sbuild/apt.conf
DEB_BUILD_OPTIONS=parallel=4
HOME=/sbuild-nonexistent
LC_ALL=POSIX
LOGNAME=buildd
PATH=/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin:/usr/games
SCHROOT_ALIAS_NAME=trixie-staging-armhf-sbuild
SCHROOT_CHROOT_NAME=trixie-staging-armhf-sbuild
SCHROOT_COMMAND=env
SCHROOT_GID=112
SCHROOT_GROUP=buildd
SCHROOT_SESSION_ID=trixie-staging-armhf-sbuild-78f03bcb-ffcd-4aaf-844d-f44bb84a9688
SCHROOT_UID=107
SCHROOT_USER=buildd
SHELL=/bin/sh
USER=buildd
dpkg-buildpackage
-----------------
dpkg-buildpackage: info: source package qhull
dpkg-buildpackage: info: source version 2020.2-6
dpkg-buildpackage: info: source distribution unstable
dpkg-source --before-build .
dpkg-buildpackage: info: host architecture armhf
debian/rules clean
dh clean --buildsystem=cmake --with pkgkde_symbolshelper
dh_auto_clean -O--buildsystem=cmake
dh_autoreconf_clean -O--buildsystem=cmake
dh_clean -O--buildsystem=cmake
debian/rules binary-arch
dh binary-arch --buildsystem=cmake --with pkgkde_symbolshelper
dh_update_autotools_config -a -O--buildsystem=cmake
dh_autoreconf -a -O--buildsystem=cmake
debian/rules override_dh_auto_configure
make[1]: Entering directory '/<<PKGBUILDDIR>>'
dh_auto_configure \
--buildsystem=cmake \
--builddir=/<<PKGBUILDDIR>>/obj-arm-linux-gnueabihf \
-- \
-DCMAKE_SKIP_RPATH=ON \
-DINCLUDE_INSTALL_DIR=include \
-DLINK_APPS_SHARED=ON \
-DLIB_INSTALL_DIR=lib/arm-linux-gnueabihf \
-DBIN_INSTALL_DIR=bin \
-DMAN_INSTALL_DIR=share/man/man1 \
-DDOC_INSTALL_DIR=share/doc/libqhull-dev/qhull
cd obj-arm-linux-gnueabihf && DEB_PYTHON_INSTALL_LAYOUT=deb cmake -DCMAKE_INSTALL_PREFIX=/usr -DCMAKE_BUILD_TYPE=None -DCMAKE_INSTALL_SYSCONFDIR=/etc -DCMAKE_INSTALL_LOCALSTATEDIR=/var -DCMAKE_EXPORT_NO_PACKAGE_REGISTRY=ON -DCMAKE_FIND_USE_PACKAGE_REGISTRY=OFF -DCMAKE_FIND_PACKAGE_NO_PACKAGE_REGISTRY=ON -DFETCHCONTENT_FULLY_DISCONNECTED=ON -DCMAKE_INSTALL_RUNSTATEDIR=/run -DCMAKE_SKIP_INSTALL_ALL_DEPENDENCY=ON "-GUnix Makefiles" -DCMAKE_VERBOSE_MAKEFILE=ON -DCMAKE_INSTALL_LIBDIR=lib/arm-linux-gnueabihf -DCMAKE_SKIP_RPATH=ON -DINCLUDE_INSTALL_DIR=include -DLINK_APPS_SHARED=ON -DLIB_INSTALL_DIR=lib/arm-linux-gnueabihf -DBIN_INSTALL_DIR=bin -DMAN_INSTALL_DIR=share/man/man1 -DDOC_INSTALL_DIR=share/doc/libqhull-dev/qhull ..
CMake Warning (dev) at CMakeLists.txt:70 (project):
cmake_minimum_required() should be called prior to this top-level project()
call. Please see the cmake-commands(7) manual for usage documentation of
both commands.
This warning is for project developers. Use -Wno-dev to suppress it.
-- The C compiler identification is GNU 12.2.0
-- The CXX compiler identification is GNU 12.2.0
-- Detecting C compiler ABI info
-- Detecting C compiler ABI info - done
-- Check for working C compiler: /usr/bin/cc - skipped
-- Detecting C compile features
-- Detecting C compile features - done
-- Detecting CXX compiler ABI info
-- Detecting CXX compiler ABI info - done
-- Check for working CXX compiler: /usr/bin/c++ - skipped
-- Detecting CXX compile features
-- Detecting CXX compile features - done
CMake Deprecation Warning at CMakeLists.txt:71 (cmake_minimum_required):
Compatibility with CMake < 3.5 will be removed from a future version of
CMake.
Update the VERSION argument <min> value or use a ...<max> suffix to tell
CMake that the project does not need compatibility with older versions.
-- Looking for sys/types.h
-- Looking for sys/types.h - found
-- Looking for inttypes.h
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--
-- ========== qhull Build Information ==========
-- Build Version: 8.0.2
-- Install Prefix (CMAKE_INSTALL_PREFIX): /usr
-- Binary Directory (BIN_INSTALL_DIR): bin
-- Library Directory (LIB_INSTALL_DIR): lib/arm-linux-gnueabihf
-- Include Directory (INCLUDE_INSTALL_DIR): include
-- Documentation Directory (DOC_INSTALL_DIR): share/doc/libqhull-dev/qhull
-- Man Pages Directory (MAN_INSTALL_DIR): share/man/man1
-- Build Type (CMAKE_BUILD_TYPE): None
-- Build static libraries: ON
-- Build shared library: ON
-- Use shared library for linking apps: ON
-- To override these options, add -D{OPTION_NAME}=... to the cmake command
-- Build the debug targets -DCMAKE_BUILD_TYPE=Debug
--
-- To build and install qhull, enter "make" and "make install"
-- To smoketest qhull, enter "ctest"
--
-- Configuring done (7.3s)
-- Generating done (0.2s)
CMake Warning:
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[ 74%] Building CXX object CMakeFiles/qhullcpp_static.dir/src/libqhullcpp/QhullPoint.cpp.o
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[ 82%] Building CXX object CMakeFiles/qhullcpp_static.dir/src/libqhullcpp/QhullStat.cpp.o
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[ 83%] Building CXX object CMakeFiles/qhullcpp_static.dir/src/libqhullcpp/QhullUser.cpp.o
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[ 83%] Building CXX object CMakeFiles/qhullcpp.dir/src/libqhullcpp/QhullRidge.cpp.o
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[ 87%] Building CXX object CMakeFiles/qhullcpp_static.dir/src/libqhullcpp/QhullVertex.cpp.o
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[ 87%] Building CXX object CMakeFiles/qhullcpp_static.dir/src/libqhullcpp/QhullVertexSet.cpp.o
/usr/bin/c++ -I/<<PKGBUILDDIR>>/src -g -O2 -ffile-prefix-map=/<<PKGBUILDDIR>>=. -flto=auto -ffat-lto-objects -fstack-protector-strong -Wformat -Werror=format-security -D_LARGEFILE_SOURCE -D_FILE_OFFSET_BITS=64 -Wdate-time -D_FORTIFY_SOURCE=2 -MD -MT CMakeFiles/qhullcpp_static.dir/src/libqhullcpp/QhullVertexSet.cpp.o -MF CMakeFiles/qhullcpp_static.dir/src/libqhullcpp/QhullVertexSet.cpp.o.d -o CMakeFiles/qhullcpp_static.dir/src/libqhullcpp/QhullVertexSet.cpp.o -c /<<PKGBUILDDIR>>/src/libqhullcpp/QhullVertexSet.cpp
[ 87%] Building CXX object CMakeFiles/qhullcpp.dir/src/libqhullcpp/QhullUser.cpp.o
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[ 88%] Building CXX object CMakeFiles/qhullcpp.dir/src/libqhullcpp/QhullVertex.cpp.o
/usr/bin/c++ -Dqhullcpp_EXPORTS -I/<<PKGBUILDDIR>>/src -g -O2 -ffile-prefix-map=/<<PKGBUILDDIR>>=. -flto=auto -ffat-lto-objects -fstack-protector-strong -Wformat -Werror=format-security -D_LARGEFILE_SOURCE -D_FILE_OFFSET_BITS=64 -Wdate-time -D_FORTIFY_SOURCE=2 -fPIC -MD -MT CMakeFiles/qhullcpp.dir/src/libqhullcpp/QhullVertex.cpp.o -MF CMakeFiles/qhullcpp.dir/src/libqhullcpp/QhullVertex.cpp.o.d -o CMakeFiles/qhullcpp.dir/src/libqhullcpp/QhullVertex.cpp.o -c /<<PKGBUILDDIR>>/src/libqhullcpp/QhullVertex.cpp
[ 88%] Building CXX object CMakeFiles/qhullcpp.dir/src/libqhullcpp/QhullVertexSet.cpp.o
/usr/bin/c++ -Dqhullcpp_EXPORTS -I/<<PKGBUILDDIR>>/src -g -O2 -ffile-prefix-map=/<<PKGBUILDDIR>>=. -flto=auto -ffat-lto-objects -fstack-protector-strong -Wformat -Werror=format-security -D_LARGEFILE_SOURCE -D_FILE_OFFSET_BITS=64 -Wdate-time -D_FORTIFY_SOURCE=2 -fPIC -MD -MT CMakeFiles/qhullcpp.dir/src/libqhullcpp/QhullVertexSet.cpp.o -MF CMakeFiles/qhullcpp.dir/src/libqhullcpp/QhullVertexSet.cpp.o.d -o CMakeFiles/qhullcpp.dir/src/libqhullcpp/QhullVertexSet.cpp.o -c /<<PKGBUILDDIR>>/src/libqhullcpp/QhullVertexSet.cpp
[ 89%] Building CXX object CMakeFiles/qhullcpp_static.dir/src/libqhullcpp/RboxPoints.cpp.o
/usr/bin/c++ -I/<<PKGBUILDDIR>>/src -g -O2 -ffile-prefix-map=/<<PKGBUILDDIR>>=. -flto=auto -ffat-lto-objects -fstack-protector-strong -Wformat -Werror=format-security -D_LARGEFILE_SOURCE -D_FILE_OFFSET_BITS=64 -Wdate-time -D_FORTIFY_SOURCE=2 -MD -MT CMakeFiles/qhullcpp_static.dir/src/libqhullcpp/RboxPoints.cpp.o -MF CMakeFiles/qhullcpp_static.dir/src/libqhullcpp/RboxPoints.cpp.o.d -o CMakeFiles/qhullcpp_static.dir/src/libqhullcpp/RboxPoints.cpp.o -c /<<PKGBUILDDIR>>/src/libqhullcpp/RboxPoints.cpp
[ 89%] Building CXX object CMakeFiles/qhullcpp_static.dir/src/libqhullcpp/RoadError.cpp.o
/usr/bin/c++ -I/<<PKGBUILDDIR>>/src -g -O2 -ffile-prefix-map=/<<PKGBUILDDIR>>=. -flto=auto -ffat-lto-objects -fstack-protector-strong -Wformat -Werror=format-security -D_LARGEFILE_SOURCE -D_FILE_OFFSET_BITS=64 -Wdate-time -D_FORTIFY_SOURCE=2 -MD -MT CMakeFiles/qhullcpp_static.dir/src/libqhullcpp/RoadError.cpp.o -MF CMakeFiles/qhullcpp_static.dir/src/libqhullcpp/RoadError.cpp.o.d -o CMakeFiles/qhullcpp_static.dir/src/libqhullcpp/RoadError.cpp.o -c /<<PKGBUILDDIR>>/src/libqhullcpp/RoadError.cpp
[ 90%] Building CXX object CMakeFiles/qhullcpp_static.dir/src/libqhullcpp/RoadLogEvent.cpp.o
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make -f CMakeFiles/qvoronoi.dir/build.make CMakeFiles/qvoronoi.dir/depend
make[3]: Entering directory '/<<PKGBUILDDIR>>/obj-arm-linux-gnueabihf'
cd /<<PKGBUILDDIR>>/obj-arm-linux-gnueabihf && /usr/bin/cmake -E cmake_depends "Unix Makefiles" /<<PKGBUILDDIR>> /<<PKGBUILDDIR>> /<<PKGBUILDDIR>>/obj-arm-linux-gnueabihf /<<PKGBUILDDIR>>/obj-arm-linux-gnueabihf /<<PKGBUILDDIR>>/obj-arm-linux-gnueabihf/CMakeFiles/qvoronoi.dir/DependInfo.cmake "--color="
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[ 91%] Building C object CMakeFiles/qvoronoi.dir/src/qvoronoi/qvoronoi_r.c.o
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[ 92%] Linking C executable qvoronoi
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[ 94%] Building CXX object CMakeFiles/qhullcpp.dir/src/libqhullcpp/RoadError.cpp.o
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make -f CMakeFiles/user_eg3.dir/build.make CMakeFiles/user_eg3.dir/depend
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/usr/bin/c++ -I/<<PKGBUILDDIR>>/src -g -O2 -ffile-prefix-map=/<<PKGBUILDDIR>>=. -flto=auto -ffat-lto-objects -fstack-protector-strong -Wformat -Werror=format-security -D_LARGEFILE_SOURCE -D_FILE_OFFSET_BITS=64 -Wdate-time -D_FORTIFY_SOURCE=2 -MD -MT CMakeFiles/user_eg3.dir/src/user_eg3/user_eg3_r.cpp.o -MF CMakeFiles/user_eg3.dir/src/user_eg3/user_eg3_r.cpp.o.d -o CMakeFiles/user_eg3.dir/src/user_eg3/user_eg3_r.cpp.o -c /<<PKGBUILDDIR>>/src/user_eg3/user_eg3_r.cpp
/usr/bin/cc -g -O2 -ffile-prefix-map=/<<PKGBUILDDIR>>=. -flto=auto -ffat-lto-objects -fstack-protector-strong -Wformat -Werror=format-security -D_LARGEFILE_SOURCE -D_FILE_OFFSET_BITS=64 -Wdate-time -D_FORTIFY_SOURCE=2 -flto=auto -ffat-lto-objects -Wl,-z,relro -Wl,-z,now -rdynamic CMakeFiles/user_eg.dir/src/user_eg/user_eg_r.c.o -o user_eg libqhull_r.so.8.0.2 -lm
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debian/rules execute_after_dh_auto_build
make[1]: Entering directory '/<<PKGBUILDDIR>>'
Building man pages
cd debian && \
for info in \
"qconvex:compute the convex hull:qconvex" \
"qdelaunay:compute the Delaunay triangulation:qdelaun" \
"qhalf:halfspace intersection about a point:qhalf" \
"qvoronoi:compute the Voronoi diagram:qvoronoi"; \
do \
comm=$(echo $info | cut -d: -f1) && \
purp=$(echo $info | cut -d: -f2) && \
doc=$(echo $info | cut -d: -f3) && \
COMM=$(echo $comm | tr [:lower:] [:upper:]) && \
echo -n Building man page for $comm... && \
sed -e "s/#command#/$comm/g" -e "s/#purpose#/$purp/g" \
-e "s/#COMMAND#/$COMM/g" -e "s/#doc#/$doc/g" \
manpage.in > $comm.1 && \
echo " done"; \
done
Building man page for qconvex... done
Building man page for qdelaunay... done
Building man page for qhalf... done
Building man page for qvoronoi... done
make[1]: Leaving directory '/<<PKGBUILDDIR>>'
debian/rules override_dh_auto_test
make[1]: Entering directory '/<<PKGBUILDDIR>>'
env LD_LIBRARY_PATH=/<<PKGBUILDDIR>>/obj-arm-linux-gnueabihf \
PATH=/<<PKGBUILDDIR>>/obj-arm-linux-gnueabihf:$PATH \
eg/q_test
Convex hull of 8 points in 3-d:
Number of vertices: 8
Number of facets: 6
Number of non-simplicial facets: 6
Statistics for: | qhull s Tcv
Number of points processed: 8
Number of hyperplanes created: 11
Number of distance tests for qhull: 34
Number of distance tests for merging: 96
Number of distance tests for checking: 100
Number of merged facets: 6
CPU seconds to compute hull (after input): 0.000274
Output completed. Verifying that all points are below outer planes of
all facets. Will make 48 distance computations.
Delaunay triangulation by the convex hull of 8 points in 4-d:
Number of input sites: 8
Number of Delaunay regions: 11
Statistics for: | qhull s d Tcv
Number of points processed: 8
Number of hyperplanes created: 25
Number of facets in hull: 16
Number of distance tests for qhull: 33
CPU seconds to compute hull (after input): 0.000124
Output completed. Verifying that all points are below 1.3e-14 of
all facets. Will make 88 distance computations.
Delaunay triangulation by the convex hull of 8 points in 4-d:
Number of input sites: 8
Number of Delaunay regions: 11
Statistics for: | qhull s d Tcv
Number of points processed: 8
Number of hyperplanes created: 27
Number of facets in hull: 18
Number of distance tests for qhull: 27
CPU seconds to compute hull (after input): 0.000119
Output completed. Verifying that all points are below 1e-14 of
all facets. Will make 88 distance computations.
Halfspace intersection by the convex hull of 8 points in 3-d:
Number of halfspaces: 8
Number of non-redundant halfspaces: 8
Number of intersection points: 6
Number of non-simplicial intersection points: 6
Statistics for: | qhull H0 s Tcv Fp
Number of points processed: 8
Number of hyperplanes created: 11
Number of distance tests for qhull: 34
Number of distance tests for merging: 96
Number of distance tests for checking: 100
Number of merged facets: 6
CPU seconds to compute hull (after input): 0.000155
Output completed. Verifying that all points are below outer planes of
all facets. Will make 48 distance computations.
==============================
========= eg/q_test ==========
== Check qhull programs ======
==============================
qhull => qhull_r 8.0.2 (2020.2.r 2020/08/31)
qconvex => qhull_r 8.0.2 (2020.2.r 2020/08/31)
qvoronoi => qhull_r 8.0.2 (2020.2.r 2020/08/31)
qdelaunay => qhull_r 8.0.2 (2020.2.r 2020/08/31)
qhalf => qhull_r 8.0.2 (2020.2.r 2020/08/31)
-rwxr-xr-x 1 buildd buildd 44404 Sep 18 21:36 /<<PKGBUILDDIR>>/obj-arm-linux-gnueabihf/qconvex
-rwxr-xr-x 1 buildd buildd 44124 Sep 18 21:36 /<<PKGBUILDDIR>>/obj-arm-linux-gnueabihf/qdelaunay
-rwxr-xr-x 1 buildd buildd 44420 Sep 18 21:36 /<<PKGBUILDDIR>>/obj-arm-linux-gnueabihf/qhalf
-rwxr-xr-x 1 buildd buildd 47896 Sep 18 21:36 /<<PKGBUILDDIR>>/obj-arm-linux-gnueabihf/qhull
-rwxr-xr-x 1 buildd buildd 43536 Sep 18 21:36 /<<PKGBUILDDIR>>/obj-arm-linux-gnueabihf/qvoronoi
-rwxr-xr-x 1 buildd buildd 39968 Sep 18 21:36 /<<PKGBUILDDIR>>/obj-arm-linux-gnueabihf/user_eg
-rwxr-xr-x 1 buildd buildd 1332184 Sep 18 21:36 /<<PKGBUILDDIR>>/obj-arm-linux-gnueabihf/user_eg2
-rwxr-xr-x 1 buildd buildd 4060564 Sep 18 21:37 /<<PKGBUILDDIR>>/obj-arm-linux-gnueabihf/user_eg3
==============================
== check user_eg, user_eg2, and user_eg3
== errors if user_eg and user_eg2 not found
==============================
user_eg
========
user_eg 'cube qhull options' 'Delaunay options' 'halfspace options'
This is the output from user_eg_r.c. It shows how qhull() may be called from
an application, via Qhull's shared, reentrant library. user_eg is not part of
Qhull itself. If user_eg fails immediately, user_eg_r.c was incorrectly linked
to Qhull's non-reentrant library, libqhull.
Try -- user_eg 'T1' 'T1' 'T1'
========
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
Convex hull of 8 points in 3-d:
Number of vertices: 8
Number of facets: 6
Number of non-simplicial facets: 6
Statistics for: | qhull s Tcv
Number of points processed: 8
Number of hyperplanes created: 11
Number of distance tests for qhull: 34
Number of distance tests for merging: 96
Number of distance tests for checking: 100
Number of merged facets: 6
CPU seconds to compute hull (after input): 0.000231
Output completed. Verifying that all points are below outer planes of
all facets. Will make 48 distance computations.
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
========
compute 3-d Delaunay triangulation
seed: 1695073037
input
-0.465 -0.944 -0.467
-0.92 -0.731 0.896
-0.0376 -0.332 0.329
0.569 -0.627 -0.463
0.753 -0.225 -0.844
-0.168 0.497 0.761
0.117 0.101 0.258
-0.461 0.459 0.708
Delaunay triangulation by the convex hull of 8 points in 4-d:
Number of input sites: 8
Number of Delaunay regions: 11
Statistics for: | qhull s d Tcv
Number of points processed: 8
Number of hyperplanes created: 25
Number of facets in hull: 16
Number of distance tests for qhull: 33
CPU seconds to compute hull (after input): 0.000131
Output completed. Verifying that all points are below 1.3e-14 of
all facets. Will make 88 distance computations.
8 vertices and 16 facets with normals:
0.77 -0.095 0.57 0.29
0.88 0.062 0.47 -0.015
0.42 -0.75 -0.06 0.5
-0.21 -0.05 -0.77 -0.6
0.087 0.7 -0.058 0.7
-0.49 0.56 -0.52 0.42
-0.066 0.86 -0.47 -0.16
-0.5 0.5 -0.67 -0.2
0.2 -0.9 0.33 -0.19
-0.18 -0.25 -0.66 -0.68
-0.9 -0.099 -0.021 -0.42
-0.83 0.11 -0.29 -0.47
0.68 -0.28 0.67 0.053
0.76 -0.18 0.62 -0.032
-0.23 -0.19 0.87 -0.39
-0.28 0.04 0.74 -0.61
find 3-d Delaunay triangle or adjacent triangle closest to [0.5, 0.5, ...]
0.57 -0.63 -0.46
0.12 0.10 0.26
-0.17 0.50 0.76
0.75 -0.23 -0.84
========
Compute a new triangulation as a separate instance of Qhull
seed: 1695073038
input
-0.465 -0.681 -0.956
-0.00284 0.334 -0.666
0.0565 -0.974 -0.312
0.439 0.14 0.576
0.415 -0.156 -0.737
0.892 -0.161 0.776
0.884 0.235 -0.907
0.913 -0.363 0.569
Delaunay triangulation by the convex hull of 8 points in 4-d:
Number of input sites: 8
Number of Delaunay regions: 11
Statistics for: | qhull s d Tcv
Number of points processed: 8
Number of hyperplanes created: 27
Number of facets in hull: 18
Number of distance tests for qhull: 27
CPU seconds to compute hull (after input): 0.000128
Output completed. Verifying that all points are below 1e-14 of
all facets. Will make 88 distance computations.
8 vertices and 18 facets with normals:
0.42 -0.66 -0.12 0.61
0.3 -0.5 -0.0058 0.81
-0.49 0.67 0.23 0.5
0.063 -0.68 0.22 0.69
0.0015 0.065 -0.98 -0.21
-0.28 -0.41 -0.54 -0.68
0.42 -0.58 -0.69 -0.096
0.75 -0.56 -0.29 -0.2
0.88 0.31 0.019 -0.35
-0.33 0.82 0.25 0.39
0.86 0.081 -0.11 -0.49
0.69 0.41 -0.19 -0.56
-0.24 -0.6 0.72 -0.24
0.54 -0.49 0.0004 -0.68
-0.029 -0.37 -0.055 -0.93
-0.85 -0.12 0.28 -0.42
-0.57 0.62 0.3 0.44
-0.73 -0.19 0.64 0.16
========
Free memory allocated by the new instance of Qhull, and redisplay the old results.
8 vertices and 16 facets with normals:
0.77 -0.095 0.57 0.29
0.88 0.062 0.47 -0.015
0.42 -0.75 -0.06 0.5
-0.21 -0.05 -0.77 -0.6
0.087 0.7 -0.058 0.7
-0.49 0.56 -0.52 0.42
-0.066 0.86 -0.47 -0.16
-0.5 0.5 -0.67 -0.2
0.2 -0.9 0.33 -0.19
-0.18 -0.25 -0.66 -0.68
-0.9 -0.099 -0.021 -0.42
-0.83 0.11 -0.29 -0.47
0.68 -0.28 0.67 0.053
0.76 -0.18 0.62 -0.032
-0.23 -0.19 0.87 -0.39
-0.28 0.04 0.74 -0.61
========
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
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: 34
Number of distance tests for merging: 96
Number of distance tests for checking: 100
Number of merged facets: 6
CPU seconds to compute hull (after input): 0.000166
3
6
0 0 -1
0 -1 0
1 0 0
-1 0 0
0 1 0
0 0 1
Output completed. Verifying that all points are below outer planes of
all facets. Will make 48 distance computations.
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
user_eg 'QR1 p n Qt' 'v p' 'Fp'
========
user_eg 'cube qhull options' 'Delaunay options' 'halfspace options'
This is the output from user_eg_r.c. It shows how qhull() may be called from
an application, via Qhull's shared, reentrant library. user_eg is not part of
Qhull itself. If user_eg fails immediately, user_eg_r.c was incorrectly linked
to Qhull's non-reentrant library, libqhull.
Try -- user_eg 'T1' 'T1' 'T1'
========
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
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: 12
Number of distance tests for qhull: 22
Number of distance tests for merging: 100
Number of distance tests for checking: 100
Number of merged facets: 6
CPU seconds to compute hull (after input): 0.000193
3
8
0.9124763375291641 1.390833937612012 -0.4826674750136243
-0.5764091147442416 0.565375258822974 -1.532352227508615
-0.1847368907548403 1.250953879569599 1.183632828365285
-1.673622343028246 0.4254952007805605 0.1339480758702939
1.673622343028246 -0.4254952007805605 -0.1339480758702939
0.1847368907548403 -1.250953879569599 -1.183632828365285
0.5764091147442416 -0.565375258822974 1.532352227508615
-0.9124763375291641 -1.390833937612012 0.4826674750136243
4
12
-0.744442726136703 -0.4127293393945193 -0.5248423762474955 -1
-0.744442726136703 -0.4127293393945193 -0.5248423762474955 -1
0.380573002749541 -0.9081645691962865 0.1743596995716653 -1
0.380573002749541 -0.9081645691962865 0.1743596995716653 -1
-0.5486066141420022 -0.06994002902120684 0.8331501516894545 -1
-0.5486066141420022 -0.06994002902120684 0.8331501516894545 -1
0.5486066141420022 0.06994002902120672 -0.8331501516894545 -1
0.5486066141420022 0.06994002902120672 -0.8331501516894545 -1
0.7444427261367031 0.4127293393945192 0.5248423762474955 -1
0.7444427261367031 0.4127293393945192 0.5248423762474955 -1
-0.380573002749541 0.9081645691962864 -0.1743596995716652 -1
-0.380573002749541 0.9081645691962864 -0.1743596995716652 -1
Output completed. Verifying that all points are below outer planes of
all facets. Will make 96 distance computations.
8 vertices and 12 facets with normals:
-0.74 -0.41 -0.52
-0.74 -0.41 -0.52
0.38 -0.91 0.17
0.38 -0.91 0.17
-0.55 -0.07 0.83
-0.55 -0.07 0.83
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
========
compute 3-d Delaunay triangulation
seed: 1695073037
input
-0.465 -0.944 -0.467
-0.92 -0.731 0.896
-0.0376 -0.332 0.329
0.569 -0.627 -0.463
0.753 -0.225 -0.844
-0.168 0.497 0.761
0.117 0.101 0.258
-0.461 0.459 0.708
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: 25
Number of facets in hull: 16
Number of distance tests for qhull: 33
CPU seconds to compute hull (after input): 0.000109
3
11
29.23586129890066 2.062655206833063 15.69483687734982
-0.17469933825846 -0.04184525066066491 -0.6507310854331888
-0.2042867688086867 2.689824242321387 -1.476508759624757
-1.232979401530706 1.233464223873567 -1.638865856142494
0.549554917358175 -2.427824867526679 0.8772134624777563
-0.1326205982623336 -0.1815885843559381 -0.4831771028467554
-1.075977963942971 -0.118544870096726 -0.02535539029804718
-0.8880521812470107 0.1170420679015901 -0.3072873035284642
11.80217312119491 -2.779901717521974 9.636349409231038
-0.2885861193498161 -0.2421539458850049 1.112864607875388
-0.2323836642186387 0.03241317726493681 0.602299639243478
Output completed. Verifying that all points are below 1.3e-14 of
all facets. Will make 88 distance computations.
8 vertices and 16 facets with normals:
0.77 -0.095 0.57 0.29
0.88 0.062 0.47 -0.015
0.42 -0.75 -0.06 0.5
-0.21 -0.05 -0.77 -0.6
0.087 0.7 -0.058 0.7
-0.49 0.56 -0.52 0.42
-0.066 0.86 -0.47 -0.16
-0.5 0.5 -0.67 -0.2
0.2 -0.9 0.33 -0.19
-0.18 -0.25 -0.66 -0.68
-0.9 -0.099 -0.021 -0.42
-0.83 0.11 -0.29 -0.47
0.68 -0.28 0.67 0.053
0.76 -0.18 0.62 -0.032
-0.23 -0.19 0.87 -0.39
-0.28 0.04 0.74 -0.61
find 3-d Delaunay triangle or adjacent triangle closest to [0.5, 0.5, ...]
0.57 -0.63 -0.46
0.12 0.10 0.26
-0.17 0.50 0.76
0.75 -0.23 -0.84
========
Compute a new triangulation as a separate instance of Qhull
seed: 1695073038
input
-0.465 -0.681 -0.956
-0.00284 0.334 -0.666
0.0565 -0.974 -0.312
0.439 0.14 0.576
0.415 -0.156 -0.737
0.892 -0.161 0.776
0.884 0.235 -0.907
0.913 -0.363 0.569
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: 27
Number of facets in hull: 18
Number of distance tests for qhull: 27
CPU seconds to compute hull (after input): 0.000111
3
11
0.003498824873227557 0.1555768096548976 -2.33924269592378
-0.2045681650525845 -0.3052196589468695 -0.395775916212154
2.195320571620022 -3.007954789043852 -3.571340976390813
1.873196660693272 -1.386394106439585 -0.7239807459459744
1.247860829179387 0.4352523825988515 0.02647129808522386
0.8710077256918028 0.0824762259082705 -0.1090328645160392
0.6174399072850505 0.3613455795941069 -0.1673101966023752
-0.5009769725807176 -1.233309149872873 1.47806101625366
0.3988528516945116 -0.3637328674943854 0.000290899301478742
-0.01550590493223436 -0.1976832015349974 -0.02958662391091837
-1.015597899880501 -0.1446520457610623 0.3343774568653801
Output completed. Verifying that all points are below 1e-14 of
all facets. Will make 88 distance computations.
8 vertices and 18 facets with normals:
0.42 -0.66 -0.12 0.61
0.3 -0.5 -0.0058 0.81
-0.49 0.67 0.23 0.5
0.063 -0.68 0.22 0.69
0.0015 0.065 -0.98 -0.21
-0.28 -0.41 -0.54 -0.68
0.42 -0.58 -0.69 -0.096
0.75 -0.56 -0.29 -0.2
0.88 0.31 0.019 -0.35
-0.33 0.82 0.25 0.39
0.86 0.081 -0.11 -0.49
0.69 0.41 -0.19 -0.56
-0.24 -0.6 0.72 -0.24
0.54 -0.49 0.0004 -0.68
-0.029 -0.37 -0.055 -0.93
-0.85 -0.12 0.28 -0.42
-0.57 0.62 0.3 0.44
-0.73 -0.19 0.64 0.16
========
Free memory allocated by the new instance of Qhull, and redisplay the old results.
8 vertices and 16 facets with normals:
0.77 -0.095 0.57 0.29
0.88 0.062 0.47 -0.015
0.42 -0.75 -0.06 0.5
-0.21 -0.05 -0.77 -0.6
0.087 0.7 -0.058 0.7
-0.49 0.56 -0.52 0.42
-0.066 0.86 -0.47 -0.16
-0.5 0.5 -0.67 -0.2
0.2 -0.9 0.33 -0.19
-0.18 -0.25 -0.66 -0.68
-0.9 -0.099 -0.021 -0.42
-0.83 0.11 -0.29 -0.47
0.68 -0.28 0.67 0.053
0.76 -0.18 0.62 -0.032
-0.23 -0.19 0.87 -0.39
-0.28 0.04 0.74 -0.61
========
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
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: 34
Number of distance tests for merging: 96
Number of distance tests for checking: 100
Number of merged facets: 6
CPU seconds to compute hull (after input): 0.000172
3
6
0 0 -1
0 -1 0
1 0 0
-1 0 0
0 1 0
0 0 1
Output completed. Verifying that all points are below outer planes of
all facets. Will make 48 distance computations.
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
user_eg2
========
user_eg2 'cube qhull options' 'Delaunay options' 'halfspace options'
This is the output from user_eg2_r.c. It shows how qhull() may be called from
an application, via Qhull's static, reentrant library. user_eg2 is not part
of Qhull itself. If user_eg2 fails immediately, user_eg2_r.c was incorrectly
linked to Qhull's non-reentrant library, libqhullstatic.
Try -- user_eg2 'T1' 'T1' 'T1'
========
compute triangulated convex hull of cube after rotating input
Output completed. Verifying that all points are below outer planes of
all facets. Will make 96 distance computations.
8 vertices and 12 facets with normals:
-0 -0 -1
-0 -0 -1
0 -1 0
0 -1 0
1 -0 -0
1 -0 -0
-1 -0 -0
-1 -0 -0
0 1 -0
0 1 -0
-0 -0 1
-0 -0 1
add points in a diamond
9 vertices and 14 facets
10 vertices and 16 facets
11 vertices and 16 facets
12 vertices and 16 facets
13 vertices and 14 facets
14 vertices and 12 facets
14 vertices and 12 facets with normals:
0.71 -0.71 -0
-0.71 -0.71 0
-0.71 0.71 -0
0.71 0.71 -0
-0.71 -0 -0.71
-0 0.71 -0.71
0 -0.71 -0.71
0.71 0 -0.71
-0 -0.71 0.71
-0.71 0 0.71
0.71 0 0.71
-0 0.71 0.71
Convex hull of 14 points in 3-d:
Number of vertices: 14
Number of facets: 12
Number of non-simplicial facets: 12
Statistics for: user_eg2 cube example | qhull s Tcv Q11
Number of points processed: 14
Number of hyperplanes created: 23
Number of distance tests for qhull: 64
Number of distance tests for merging: 276
Number of distance tests for checking: 324
Number of merged facets: 18
CPU seconds to compute hull (after input): 0.000233
Output completed. Verifying that all points are below outer planes of
all facets. Will make 168 distance computations.
========
compute 2-d Delaunay triangulation
seed: 1695073037
8 vertices and 12 facets with normals:
-0.85 -0.18 0.49
0.4 -0.057 0.91
-0.49 0.47 -0.74
0.65 0.48 0.59
-0.83 -0.51 -0.22
-0.79 -0.55 -0.27
0.53 0.086 -0.84
-0.34 -0.72 -0.6
-0.49 0.46 -0.74
-0.63 -0.11 -0.77
0.35 -0.86 -0.37
0.099 -0.87 -0.49
Delaunay triangulation by the convex hull of 8 points in 3-d:
Number of input sites: 8
Number of Delaunay regions: 9
Statistics for: user_eg2 Delaunay example | qhull s d Tcv
Number of points processed: 8
Number of hyperplanes created: 21
Number of facets in hull: 12
Number of distance tests for qhull: 29
CPU seconds to compute hull (after input): 9.4e-05
Output completed. Verifying that all points are below 5.6e-15 of
all facets. Will make 72 distance computations.
========
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
find Delaunay triangle or adjacent triangle closest to [0.5, 0.5, ...]
0.36 0.87
0.33 0.57
0.75 -0.23
Delaunay triangulation by the convex hull of 14 points in 3-d:
Number of input sites: 14
Number of Delaunay regions: 20
Statistics for: user_eg2 Delaunay example | qhull s d Tcv
Number of points processed: 14
Number of hyperplanes created: 52
Number of facets in hull: 24
Number of distance tests for qhull: 73
CPU seconds to compute hull (after input): 9.4e-05
Output completed. Verifying that all points are below 5.6e-15 of
all facets. Will make 280 distance computations.
========
compute halfspace intersection about the origin for a diamond
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_eg2 halfspace example | qhull H0 s Tcv
Number of points processed: 8
Number of hyperplanes created: 11
Number of distance tests for qhull: 34
Number of distance tests for merging: 96
Number of distance tests for checking: 100
Number of merged facets: 6
CPU seconds to compute hull (after input): 0.000147
Output completed. Verifying that all points are below outer planes of
all facets. Will make 48 distance computations.
========
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
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_eg2 halfspace example | qhull H0 s Tcv
Number of points processed: 14
Number of hyperplanes created: 35
Number of distance tests for qhull: 58
Number of distance tests for merging: 248
Number of distance tests for checking: 256
Number of merged facets: 6
CPU seconds to compute hull (after input): 0.000147
Output completed. Verifying that all points are below outer planes of
all facets. Will make 192 distance computations.
user_eg2 'QR1 p' 'v p' 'Fp'
========
user_eg2 'cube qhull options' 'Delaunay options' 'halfspace options'
This is the output from user_eg2_r.c. It shows how qhull() may be called from
an application, via Qhull's static, reentrant library. user_eg2 is not part
of Qhull itself. If user_eg2 fails immediately, user_eg2_r.c was incorrectly
linked to Qhull's non-reentrant library, libqhullstatic.
Try -- user_eg2 'T1' 'T1' 'T1'
========
compute triangulated convex hull of cube after rotating input
Output completed. Verifying that all points are below outer planes of
all facets. Will make 96 distance computations.
8 vertices and 12 facets with normals:
-0.74 -0.41 -0.52
-0.74 -0.41 -0.52
0.38 -0.91 0.17
0.38 -0.91 0.17
-0.55 -0.07 0.83
-0.55 -0.07 0.83
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
add points in a diamond
9 vertices and 14 facets
10 vertices and 16 facets
11 vertices and 18 facets
12 vertices and 20 facets
13 vertices and 22 facets
14 vertices and 24 facets
14 vertices and 24 facets with normals:
-0.67 0.63 -0.39
0.67 -0.63 0.39
-0.1 -0.71 0.7
-0.65 -0.65 -0.41
-0.62 -0.62 -0.49
0.63 -0.7 -0.34
0.65 -0.66 0.37
-0.65 0.66 -0.37
0.1 0.71 -0.7
-0.63 0.7 0.34
0.62 0.62 0.49
0.65 0.65 0.41
-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
0.62 0.49 0.62
0.7 0.13 0.7
-0.11 -0.7 0.71
-0.68 -0.29 0.68
Convex hull of 14 points in 3-d:
Number of vertices: 14
Number of facets: 24
Statistics for: user_eg2 cube example | qhull s Tcv Q11 QR1 p QR1
Number of points processed: 14
Number of hyperplanes created: 46
Number of distance tests for qhull: 68
Number of distance tests for merging: 284
Number of distance tests for checking: 244
Number of merged facets: 6
CPU seconds to compute hull (after input): 0.000173
3
14
0.9124763375291641 1.390833937612012 -0.4826674750136243
-0.5764091147442416 0.565375258822974 -1.532352227508615
-0.1847368907548403 1.250953879569599 1.183632828365285
-1.673622343028246 0.4254952007805605 0.1339480758702939
1.673622343028246 -0.4254952007805605 -0.1339480758702939
0.1847368907548403 -1.250953879569599 -1.183632828365285
0.5764091147442416 -0.565375258822974 1.532352227508615
-0.9124763375291641 -1.390833937612012 0.4826674750136243
-2 0 0
2 0 0
0 -2 0
0 2 0
0 0 -2
0 0 2
Output completed. Verifying that all points are below outer planes of
all facets. Will make 192 distance computations.
========
compute 2-d Delaunay triangulation
seed: 1695073037
8 vertices and 12 facets with normals:
-0.85 -0.18 0.49
0.4 -0.057 0.91
-0.49 0.47 -0.74
0.65 0.48 0.59
-0.83 -0.51 -0.22
-0.79 -0.55 -0.27
0.53 0.086 -0.84
-0.34 -0.72 -0.6
-0.49 0.46 -0.74
-0.63 -0.11 -0.77
0.35 -0.86 -0.37
0.099 -0.87 -0.49
Voronoi diagram by the convex hull of 8 points in 3-d:
Number of Voronoi regions: 8
Number of Voronoi vertices: 9
Statistics for: user_eg2 Delaunay example | qhull s d Tcv v p
Number of points processed: 8
Number of hyperplanes created: 21
Number of facets in hull: 12
Number of distance tests for qhull: 29
CPU seconds to compute hull (after input): 8.3e-05
2
9
-0.3296063455478165 0.3157325606635629
-1.863034012446285 -1.14626920700135
-1.484731474144922 -1.018993963408553
0.3133503719932864 0.05067040439939535
-0.2871330271518474 -0.6005316120957428
-0.3268276642002595 0.3113096932553294
-0.4045918836075039 -0.07116304727736916
0.4740522760134831 -1.144242790603506
0.1007059361463855 -0.8835589156851529
Output completed. Verifying that all points are below 5.6e-15 of
all facets. Will make 72 distance computations.
========
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
find Delaunay triangle or adjacent triangle closest to [0.5, 0.5, ...]
0.36 0.87
0.33 0.57
0.75 -0.23
Voronoi diagram by the convex hull of 14 points in 3-d:
Number of Voronoi regions: 14
Number of Voronoi vertices: 20
Statistics for: user_eg2 Delaunay example | qhull s d Tcv v p
Number of points processed: 14
Number of hyperplanes created: 52
Number of facets in hull: 24
Number of distance tests for qhull: 73
CPU seconds to compute hull (after input): 8.3e-05
2
20
-0.9217901496494878 -0.4524212615220601
-0.7782189660382164 -0.9586405526516882
-0.7053525356369595 -0.7466650003987922
0.9548499056920796 0.3925036729734206
-0.293707689465833 -0.6028289168876003
-0.2909217271287554 -0.5834565380670735
-0.09378645239278252 -0.9001733122880422
2.258276253644213 -4.169082861085273
0.4460574652582531 -0.4689886364069825
0.2895510129684313 -0.3234862771176134
-2.307031570363123 -0.07322871829025257
1.378719542308818 0.6183693762554688
-0.1891199684849373 0.7715016998959698
-0.5100474908734441 -0.1489007721463812
-0.3614334012478865 -0.2656715292757013
-0.6032760148894851 0.1269106229638288
0.1710871532719355 0.1738951424971319
0.1427082169396754 0.0001161779700602425
-0.2392890689003836 0.6087419491610073
-0.4264820695494952 0.4999696352252979
Output completed. Verifying that all points are below 5.6e-15 of
all facets. Will make 280 distance computations.
========
compute halfspace intersection about the origin for a diamond
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_eg2 halfspace example | qhull H0 s Tcv Fp
Number of points processed: 8
Number of hyperplanes created: 11
Number of distance tests for qhull: 34
Number of distance tests for merging: 96
Number of distance tests for checking: 100
Number of merged facets: 6
CPU seconds to compute hull (after input): 0.000134
3
6
0 0 -1
0 -1 0
1 0 0
-1 0 0
0 1 0
0 0 1
Output completed. Verifying that all points are below outer planes of
all facets. Will make 48 distance computations.
========
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
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_eg2 halfspace example | qhull H0 s Tcv Fp
Number of points processed: 14
Number of hyperplanes created: 35
Number of distance tests for qhull: 58
Number of distance tests for merging: 248
Number of distance tests for checking: 256
Number of merged facets: 6
CPU seconds to compute hull (after input): 0.000134
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 0.4226497308103742
-0.5773502691896257 0.4226497308103742 0
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 -0.5773502691896257 0.4226497308103742
0.4226497308103742 -0.5773502691896257 0
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 0.4226497308103742 -0.5773502691896257
0.4226497308103742 0 -0.5773502691896257
Output completed. Verifying that all points are below outer planes of
all facets. Will make 192 distance computations.
user_eg3
========
user_eg3 commands... -- demonstrate calling rbox and qhull from C++.
user_eg3 is statically linked to qhullcpp and reentrant qhull. If user_eg3
fails immediately, it is probably linked to the non-reentrant qhull library.
Commands:
eg-100 Run the example in qh-code.htm
eg-convex 'rbox d | qconvex o' with std::vector and C++ classes
eg-delaunay 'rbox y c | qdelaunay o' with std::vector and C++ classes
eg-voronoi 'rbox y c | qvoronoi o' with std::vector and C++ classes
eg-fifo 'rbox y c | qvoronoi FN Fi Fo' with QhullUser and qh_fprintf
Rbox and Qhull commands:
rbox "200 D4" ... Generate points from rbox
qhull "d p" ... Run qhull with options and produce output
qhull-cout "o" ... Run qhull with options and produce output to cout
qhull "T1" ... Run qhull with level-1 trace to cerr
qhull-cout "T1z" ... Run qhull with level-1 trace to cout
facets Print qhull's facets when done
For example
user_eg3 rbox qhull
user_eg3 rbox qhull T1
user_eg3 rbox qhull d
user_eg3 rbox D2 10 2 "s r 5" qhull "s p" facets
user_eg3 eg-convex
user_eg3 rbox 10 eg-delaunay qhull "d o"
user_eg3 rbox D5 c P2 qhull d eg-delaunay
user_eg3 rbox "D5 c P2" qhull v eg-voronoi o
user_eg3 rbox D2 10 qhull "v" eg-fifo p Fi Fo
user_eg3 eg-100
- f24
- flags: bottom simplicial
- normal: -0.721696 -0.658796 -0.212466
- offset: -0.549277
- vertices: p40(v10) p27(v7) p0(v1)
- neighboring facets: f34 f47 f54
- f32
- flags: top simplicial
- normal: 0.389612 -0.428663 0.815138
- offset: -0.449315
- vertices: p22(v12) p13(v6) p82(v2)
- neighboring facets: f61 f72 f77
- f34
- flags: top simplicial
- normal: -0.452613 -0.760661 0.465335
- offset: -0.62552
- vertices: p22(v12) p27(v7) p0(v1)
- neighboring facets: f24 f80 f73
- f38
- flags: top simplicial
- normal: 0.998285 0.058513 -0.00174787
- offset: -0.477764
- vertices: p90(v13) p48(v8) p82(v2)
- neighboring facets: f100 f97 f57
- f46
- flags: bottom simplicial
- normal: -0.406035 0.904011 0.133791
- offset: -0.547585
- vertices: p73(v15) p76(v9) p97(v5)
- neighboring facets: f51 f87 f82
- f47
- flags: bottom simplicial
- normal: -0.992416 -0.0122817 -0.122308
- offset: -0.469463
- vertices: p73(v15) p40(v10) p0(v1)
- neighboring facets: f24 f81 f88
- f49
- flags: top simplicial
- normal: -0.107843 0.991034 0.0788761
- offset: -0.50132
- vertices: p21(v16) p97(v5) p29(v3)
- neighboring facets: f116 f66 f51
- f51
- flags: top simplicial
- normal: -0.177935 0.975873 0.126537
- offset: -0.506339
- vertices: p21(v16) p76(v9) p97(v5)
- neighboring facets: f46 f49 f67
- f52
- flags: top simplicial
- normal: -0.378163 -0.891276 -0.250241
- offset: -0.526009
- vertices: p98(v17) p27(v7) p83(v4)
- neighboring facets: f75 f53 f54
- f53
- flags: bottom simplicial
- normal: -0.430163 -0.821913 -0.373389
- offset: -0.546784
- vertices: p98(v17) p40(v10) p83(v4)
- neighboring facets: f108 f52 f54
- f54
- flags: top simplicial
- normal: -0.548096 -0.791241 -0.271162
- offset: -0.537299
- vertices: p98(v17) p40(v10) p27(v7)
- neighboring facets: f24 f52 f53
- f57
- flags: bottom simplicial
- normal: 0.974428 0.137974 -0.177349
- offset: -0.521881
- vertices: p19(v18) p90(v13) p48(v8)
- neighboring facets: f38 f60 f113
- f59
- flags: bottom simplicial
- normal: 0.239508 -0.0103785 -0.970839
- offset: -0.517616
- vertices: p19(v18) p4(v14) p83(v4)
- neighboring facets: f76 f110 f60
- f60
- flags: top simplicial
- normal: 0.567061 -0.0365561 -0.822865
- offset: -0.572132
- vertices: p19(v18) p4(v14) p48(v8)
- neighboring facets: f85 f57 f59
- f61
- flags: bottom simplicial
- normal: 0.433241 -0.284128 0.855321
- offset: -0.426268
- vertices: p37(v19) p13(v6) p82(v2)
- neighboring facets: f32 f69 f95
- f65
- flags: top simplicial
- normal: -0.198254 0.211674 0.957021
- offset: -0.497913
- vertices: p67(v20) p12(v11) p76(v9)
- neighboring facets: f79 f67 f68
- f66
- flags: top simplicial
- normal: -0.155514 0.97946 0.128347
- offset: -0.504016
- vertices: p67(v20) p21(v16) p29(v3)
- neighboring facets: f49 f71 f67
- f67
- flags: bottom simplicial
- normal: -0.16055 0.978089 0.132539
- offset: -0.504235
- vertices: p67(v20) p21(v16) p76(v9)
- neighboring facets: f51 f65 f66
- f68
- flags: top simplicial
- normal: 0.598999 -0.0537935 0.798941
- offset: -0.457967
- vertices: p67(v20) p37(v19) p12(v11)
- neighboring facets: f96 f65 f69
- f69
- flags: bottom simplicial
- normal: 0.69477 -0.0317528 0.718531
- offset: -0.45153
- vertices: p67(v20) p37(v19) p82(v2)
- neighboring facets: f61 f98 f68
- f71
- flags: bottom simplicial
- normal: 0.877687 0.308225 0.366966
- offset: -0.494379
- vertices: p67(v20) p90(v13) p29(v3)
- neighboring facets: f115 f66 f99
- f72
- flags: top simplicial
- normal: 0.245263 -0.887198 0.390801
- offset: -0.480731
- vertices: p41(v21) p22(v12) p82(v2)
- neighboring facets: f32 f74 f73
- f73
- flags: bottom simplicial
- normal: 0.0168085 -0.963019 0.268908
- offset: -0.510609
- vertices: p41(v21) p22(v12) p27(v7)
- neighboring facets: f34 f75 f72
- f74
- flags: bottom simplicial
- normal: 0.227082 -0.964773 0.132845
- offset: -0.464868
- vertices: p41(v21) p4(v14) p82(v2)
- neighboring facets: f84 f72 f76
- f75
- flags: bottom simplicial
- normal: 0.0345717 -0.998303 0.0468616
- offset: -0.47919
- vertices: p41(v21) p27(v7) p83(v4)
- neighboring facets: f52 f76 f73
- f76
- flags: top simplicial
- normal: 0.137757 -0.987556 0.0758723
- offset: -0.471349
- vertices: p41(v21) p4(v14) p83(v4)
- neighboring facets: f59 f75 f74
- f77
- flags: bottom simplicial
- normal: -0.323398 -0.00535492 0.946248
- offset: -0.501516
- vertices: p15(v22) p22(v12) p13(v6)
- neighboring facets: f32 f78 f80
- f78
- flags: top simplicial
- normal: -0.20543 0.0915675 0.974379
- offset: -0.474687
- vertices: p15(v22) p12(v11) p13(v6)
- neighboring facets: f94 f77 f79
- f79
- flags: bottom simplicial
- normal: -0.218614 0.160888 0.962457
- offset: -0.484859
- vertices: p15(v22) p12(v11) p76(v9)
- neighboring facets: f65 f82 f78
- f80
- flags: top simplicial
- normal: -0.593167 -0.119334 0.796186
- offset: -0.544059
- vertices: p15(v22) p22(v12) p0(v1)
- neighboring facets: f34 f81 f77
- f81
- flags: bottom simplicial
- normal: -0.974282 0.088044 0.20742
- offset: -0.50771
- vertices: p15(v22) p73(v15) p0(v1)
- neighboring facets: f47 f80 f82
- f82
- flags: top simplicial
- normal: -0.826328 0.394399 0.402034
- offset: -0.559684
- vertices: p15(v22) p73(v15) p76(v9)
- neighboring facets: f46 f79 f81
- f84
- flags: top simplicial
- normal: 0.82988 -0.542609 -0.129903
- offset: -0.585213
- vertices: p57(v23) p4(v14) p82(v2)
- neighboring facets: f74 f101 f85
- f85
- flags: bottom simplicial
- normal: 0.906692 -0.29884 -0.297664
- offset: -0.57209
- vertices: p57(v23) p4(v14) p48(v8)
- neighboring facets: f60 f102 f84
- f86
- flags: top simplicial
- normal: -0.85363 0.243861 -0.460269
- offset: -0.522928
- vertices: p11(v24) p40(v10) p97(v5)
- neighboring facets: f89 f87 f88
- f87
- flags: bottom simplicial
- normal: -0.890339 0.291001 -0.350165
- offset: -0.531756
- vertices: p11(v24) p73(v15) p97(v5)
- neighboring facets: f46 f86 f88
- f88
- flags: top simplicial
- normal: -0.987894 0.0156004 -0.154345
- offset: -0.477251
- vertices: p11(v24) p73(v15) p40(v10)
- neighboring facets: f47 f86 f87
- f89
- flags: bottom simplicial
- normal: -0.492188 0.332666 -0.804416
- offset: -0.526118
- vertices: p25(v25) p40(v10) p97(v5)
- neighboring facets: f86 f114 f109
- f94
- flags: bottom simplicial
- normal: 0.368779 -0.208614 0.905805
- offset: -0.440207
- vertices: p7(v26) p12(v11) p13(v6)
- neighboring facets: f78 f95 f96
- f95
- flags: top simplicial
- normal: 0.417114 -0.259346 0.871066
- offset: -0.429768
- vertices: p7(v26) p37(v19) p13(v6)
- neighboring facets: f61 f94 f96
- f96
- flags: bottom simplicial
- normal: 0.469304 -0.162419 0.867971
- offset: -0.446808
- vertices: p7(v26) p37(v19) p12(v11)
- neighboring facets: f68 f94 f95
- f97
- flags: top simplicial
- normal: 0.911891 0.1675 0.374697
- offset: -0.446013
- vertices: p28(v27) p90(v13) p82(v2)
- neighboring facets: f38 f98 f99
- f98
- flags: bottom simplicial
- normal: 0.888791 0.148029 0.433749
- offset: -0.448933
- vertices: p28(v27) p67(v20) p82(v2)
- neighboring facets: f69 f97 f99
- f99
- flags: top simplicial
- normal: 0.903592 0.183305 0.387197
- offset: -0.447956
- vertices: p28(v27) p67(v20) p90(v13)
- neighboring facets: f71 f97 f98
- f100
- flags: bottom simplicial
- normal: 0.93763 -0.294784 -0.184262
- offset: -0.546054
- vertices: p42(v28) p48(v8) p82(v2)
- neighboring facets: f38 f101 f102
- f101
- flags: top simplicial
- normal: 0.933493 -0.306605 -0.185968
- offset: -0.547862
- vertices: p42(v28) p57(v23) p82(v2)
- neighboring facets: f84 f100 f102
- f102
- flags: bottom simplicial
- normal: 0.928146 -0.300441 -0.219729
- offset: -0.55469
- vertices: p42(v28) p57(v23) p48(v8)
- neighboring facets: f85 f100 f101
- f108
- flags: top simplicial
- normal: 0.00135876 0.0103445 -0.999946
- offset: -0.494086
- vertices: p5(v30) p40(v10) p83(v4)
- neighboring facets: f53 f110 f109
- f109
- flags: top simplicial
- normal: -0.106214 0.129184 -0.985916
- offset: -0.504323
- vertices: p5(v30) p25(v25) p40(v10)
- neighboring facets: f89 f108 f111
- f110
- flags: bottom simplicial
- normal: 0.125474 0.0262996 -0.991748
- offset: -0.496467
- vertices: p5(v30) p19(v18) p83(v4)
- neighboring facets: f59 f108 f111
- f111
- flags: bottom simplicial
- normal: 0.0358445 0.163534 -0.985886
- offset: -0.514407
- vertices: p5(v30) p25(v25) p19(v18)
- neighboring facets: f112 f110 f109
- f112
- flags: top simplicial
- normal: 0.0769357 0.958704 -0.273801
- offset: -0.543222
- vertices: p78(v31) p25(v25) p19(v18)
- neighboring facets: f111 f113 f114
- f113
- flags: top simplicial
- normal: 0.129005 0.982313 -0.135717
- offset: -0.512909
- vertices: p78(v31) p19(v18) p90(v13)
- neighboring facets: f57 f115 f112
- f114
- flags: bottom simplicial
- normal: -0.0450665 0.957786 -0.283929
- offset: -0.551711
- vertices: p78(v31) p25(v25) p97(v5)
- neighboring facets: f89 f116 f112
- f115
- flags: top simplicial
- normal: 0.102483 0.993113 -0.0567803
- offset: -0.497056
- vertices: p78(v31) p90(v13) p29(v3)
- neighboring facets: f71 f116 f113
- f116
- flags: bottom simplicial
- normal: -0.00662022 0.999903 -0.0122926
- offset: -0.49314
- vertices: p78(v31) p97(v5) p29(v3)
- neighboring facets: f49 f115 f114
user_eg3 eg-convex
A 3-d diamond (rbox d)
3 rbox "d"
6
0 0 -0.5
0 0 0.5
0 -0.5 0
0 0.5 0
-0.5 0 0
0.5 0 0
Input points and facetlist of its convex hull (qhull o)
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 2 0 4
3 0 2 5
3 1 2 4
3 2 1 5
3 3 0 5
3 0 3 4
3 1 3 5
3 3 1 4
Input points and facetlist using std::vector and C++ classes
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 2 0 4
3 0 2 5
3 1 2 4
3 2 1 5
3 3 0 5
3 0 3 4
3 1 3 5
3 3 1 4
Its outward pointing normals as vector plus offset (qhull n)
4
8
-0.5773502691896258 -0.5773502691896258 -0.5773502691896258 -0.2886751345948129
0.5773502691896258 -0.5773502691896258 -0.5773502691896258 -0.2886751345948129
-0.5773502691896258 -0.5773502691896258 0.5773502691896258 -0.2886751345948129
0.5773502691896258 -0.5773502691896258 0.5773502691896258 -0.2886751345948129
0.5773502691896258 0.5773502691896258 -0.5773502691896258 -0.2886751345948129
-0.5773502691896258 0.5773502691896258 -0.5773502691896258 -0.2886751345948129
0.5773502691896258 0.5773502691896258 0.5773502691896258 -0.2886751345948129
-0.5773502691896258 0.5773502691896258 0.5773502691896258 -0.2886751345948129
user_eg3 eg-delaunay
A 2-d triangle in a square (rbox y c D2)
2 rbox "y c D2"
7
0.0795233 -0.451105
0.279706 0.0133225
-0.0888864 0.0861965
-0.5 -0.5
-0.5 0.5
0.5 -0.5
0.5 0.5
The 2-d input sites are lifted to a 3-d paraboloid.
A Delaunay region is a facet of the paraboloid's convex hull.
The Delaunay triangulation as input sites and Delaunay regions (qhull d o)
3
7 8 12
0.07952334739223432 -0.4511049142583319 0.209819606448483
0.2797056779076398 0.01332249167684696 0.07841275503825199
-0.08888640449278651 0.08619647248293871 0.01533062477215727
-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 2 4 3
3 2 6 4
3 5 0 3
3 0 2 3
3 6 1 5
3 1 6 2
3 1 0 5
3 0 1 2
The same results using std::vector and C++ classes
3
7 8 12
0.0795233 -0.451105 0.20982
0.279706 0.0133225 0.0784128
-0.0888864 0.0861965 0.0153306
-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 2 4 3
3 2 6 4
3 5 0 3
3 0 2 3
3 6 1 5
3 1 6 2
3 1 0 5
3 0 1 2
user_eg3 eg-voronoi
A 2-d triangle in a square (rbox y c D2)
2 rbox "y c D2"
7
0.0795233 -0.451105
0.279706 0.0133225
-0.0888864 0.0861965
-0.5 -0.5
-0.5 0.5
0.5 -0.5
0.5 0.5
Its Voronoi diagram as vertices and regions (qhull v o)
The Voronoi diagram is the dual of the Delaunay triangulation
Voronoi vertices are Delaunay regions, and Voronoi regions are Delaunay input sites
The Voronoi vertex at infinity is represented as '-10.101 -10.101'
2
9 7 1
-10.101 -10.101
-0.5894591914795221 -2.775557561562891e-17
0 0.5856274089010268
-1.387778780781446e-17 -2.967377898513707
-0.2290343684408742 -0.2527745420948135
0.9568726986640038 2.081668171172169e-17
0.1571419516493774 0.3619977084558904
0.3129256373384354 -0.2763523586794005
0.05307821633938364 -0.1643502208872393
4 8 4 3 7
4 8 6 5 7
5 8 4 1 2 6
4 4 1 0 3
3 2 0 1
4 7 3 0 5
4 6 2 0 5
The same results using std::vector and C++ classes
Qhull::prepareVoronoi assigns facetT.visit_id and vertexT.neighbors
The Voronoi regions are rotated by one Voronoi vertex (prepareVoronoi occurs twice)
2
9 7 1
-10.101 -10.101
-0.589459 -2.77556e-17
0 0.585627
-1.38778e-17 -2.96738
-0.229034 -0.252775
0.956873 2.08167e-17
0.157142 0.361998
0.312926 -0.276352
0.0530782 -0.16435
4 7 8 4 3
4 7 8 6 5
5 6 8 4 1 2
4 3 4 1 0
3 1 2 0
4 5 7 3 0
4 5 6 2 0
user_eg3 eg-fifo
A 2-d triangle in a square (rbox y c D2)
2 rbox "y c D2"
7
0.0795233 -0.451105
0.279706 0.0133225
-0.0888864 0.0861965
-0.5 -0.5
-0.5 0.5
0.5 -0.5
0.5 0.5
Its Voronoi vertices (qhull v p)
This is the first part of eg-voronoi, but without infinity
2
8
-0.5894591914795221 -2.775557561562891e-17
0 0.5856274089010268
-1.387778780781446e-17 -2.967377898513707
-0.2290343684408742 -0.2527745420948135
0.9568726986640038 2.081668171172169e-17
0.1571419516493774 0.3619977084558904
0.3129256373384354 -0.2763523586794005
0.05307821633938364 -0.1643502208872393
Its Voronoi regions (qhull v FN)
This is the second part of eg-voronoi, with ids one less
Regions are ordered by the corresponding input site.
7
4 7 3 2 6
4 7 5 4 6
5 7 3 0 1 5
4 3 0 -1 2
3 1 -1 0
4 6 2 -1 4
4 5 1 -1 4
The same results as 'qhull v p FN' using std::vector and C++ classes
Qhull::prepareVoronoi assigns facet.visit_id and vertex.neighbors
prepareVoronoi is also called by q.outputQhull("FN"), hence the rotated vertices
2
8
-0.589459 -2.77556e-17
0 0.585627
-1.38778e-17 -2.96738
-0.229034 -0.252775
0.956873 2.08167e-17
0.157142 0.361998
0.312926 -0.276352
0.0530782 -0.16435
7
4 6 7 3 2
4 6 7 5 4
5 5 7 3 0 1
4 2 3 0 -1
3 0 1 -1
4 4 6 2 -1
4 4 5 1 -1
Hyperplanes for bounded facets between Voronoi regions (qhull v Fi)
Each hyperplane is the perpendicular bisector of 2 input sites.
10
5 0 1 0.3958261856523667 0.9183254492563615 0.1299172425168069
5 0 5 0.9933067158065388 -0.1155065726858348 -0.3427516509210134
5 0 2 -0.2990888272252211 0.954225273941663 0.1727022360246516
5 0 3 -0.9964596398753636 -0.08407250501478321 -0.2494748932535505
5 1 5 0.3943714145865591 -0.9189511343684148 -0.3773632397513814
5 1 2 -0.9810105005095815 0.1939546284313432 0.08394677360204827
5 1 6 0.4123709353479589 0.9110160326142727 -0.3945864897570009
5 2 6 0.8181972788475073 0.5749375730342683 -0.3366992011759034
5 2 3 -0.574189571650573 -0.8187223801800775 -0.3384613206611199
5 2 4 -0.7047972640762143 0.7094087795838752 -0.4154492254393445
Hyperplanes for unbounded rays of unbounded facets (qhull v Fo)
Each ray goes through the midpoint of 2 input sites, oriented outwards
4
5 3 5 1 -5.624508437144599e-18 -2.812254218572297e-18
5 3 4 -3.10259629632159e-16 1 -1.551298148160795e-16
5 4 6 1 -0 -0
5 5 6 -4.55634179336919e-17 1 2.278170896684595e-17
The same result as 'qhull v Fi' using QhullUser and its custom qh_fprintf
qh_fprintf captures the output from qh_eachvoronoi in io_r.c (qhull v Fi Fo Ta)
10
5 0 1 0.395826 0.918325 0.129917
5 0 5 0.993307 -0.115507 -0.342752
5 0 2 -0.299089 0.954225 0.172702
5 0 3 -0.99646 -0.0840725 -0.249475
5 1 5 0.394371 -0.918951 -0.377363
5 1 2 -0.981011 0.193955 0.0839468
5 1 6 0.412371 0.911016 -0.394586
5 2 6 0.818197 0.574938 -0.336699
5 2 3 -0.57419 -0.818722 -0.338461
5 2 4 -0.704797 0.709409 -0.415449
The same result as 'qhull v Fo' using QhullUser and its custom qh_fprintf
4
5 3 5 1 -5.62451e-18 -2.81225e-18
5 3 4 -3.1026e-16 1 -1.5513e-16
5 4 6 1 -0 -0
5 5 6 -4.55634e-17 1 2.27817e-17
Message codes captured by qh_fprintf in QhullUser.cpp (qhull v Fo Ta):
9231 9271 9272 9272 9273 9274 9271 9272 9272 9273 9274 9271 9272 9272 9273 9274 9271 9272 9272 9273 9274
user_eg3 rbox qhull
Results of qhull
Convex hull of 10 points in 2-d:
Number of vertices: 4
Number of facets: 4
Statistics for: rbox "10 D2" | qhull
Number of points processed: 4
Number of hyperplanes created: 5
Number of distance tests for qhull: 51
CPU seconds to compute hull (after input): 7.1e-05
user_eg3 rbox qhull T1
Results of T1
[QH0013]qh_initqhull_globals: for rbox "10 D2" | qhull T1
qh_meminitbuffers: memory initialized with alignment 8
qh_maxmin: dim min max width nearzero min-point max-point
0 -4.28543191e-01 3.79031236e-01 8.07574428e-01 7.6125e-15 p1 p4
1 -4.97972782e-01 4.74582647e-01 9.72555429e-01 1.6458e-14 p0 p1
qh_maxmin: found the max and min points (by dim): p1 p4 p0 p1
[QH1002]qh_maxsimplex: selected point p0 for 3`th initial vertex, det=0.7462, targetdet=0.7854, mindet=0.007854
[QH1028]qh_createsimplex: created simplex
qh_initialhull: qh.interior_point p-2: -0.02391 0.1182
[QH1027]qh_checkpolygon: check all facets from f1, qh.NEWtentative? 0
[QH1064]qh_checkconvex: check that facets are not-flipped and for qh.ZEROcentrum that simplicial vertices are below their neighbor (dist<0.0)
qh_initialhull: simplex constructed
[QH1042]qh_partitionall: partition all points into outside sets
Trace level T0, IStracing 1, point TP-3, merge TM0, dist TW1.8e+308, qh.tracefacet_id -1, traceridge_id -1, tracevertex_id -1, last qh.RERUN 0, rbox "10 D2" | qhull T1
Options selected for Qhull 2020.2.r 2020/08/31:
run-id 574471757 _pre-merge _zero-centrum _max-width 0.97
Error-roundoff 4.3e-16 _one-merge 2.1e-15 _near-inside 1.1e-14
Visible-distance 8.5e-16 U-max-coplanar 8.5e-16 Width-outside 1.7e-15
_wide-facet 5.1e-15
[QH1029]qh_furthestnext: made f3 next facet(dist 0.19)
[QH1030]qh_initbuild: initial hull created and points partitioned
[QH1037]qh_buildhull: start build hull
[QH1049]qh_addpoint: add p8(v4) 0.19 above f3 to hull of 3 facets, 0 merges, 3 outside at 0.000118 CPU secs. Previous p-1(v3) delta 0.000118 CPU, 3 facets, 0 merges, 3 hyperplanes, 61 distplanes, 0 retries
[QH1040]qh_findhorizon: find horizon for point p8 facet f3
[QH1041]qh_findhorizon: 2 horizon facets(good 2), 1 visible(good 1), 0 coplanar
[QH1032]qh_makenewfacets: created 2 new facets f4..f5 from point p8 to horizon
[QH1019]qh_matchnewfacets: match neighbors for new facets.
[QH1043]qh_partitionvisible: partitioned 2 points from outsidesets, 0 points from coplanarsets, and 0 deleted vertices
[QH1018]qh_deletevisible: delete 1 visible facets and 0 vertices
[QH1039]qh_buildhull: completed the hull construction
[QH1036]Qhull: algorithm completed
[QH1027]qh_checkpolygon: check all facets from f1, qh.NEWtentative? 0
[QH1064]qh_checkconvex: check that facets are not-flipped and for qh.ZEROcentrum that simplicial vertices are below their neighbor (dist<0.0)
Convex hull of 10 points in 2-d:
Number of vertices: 4
Number of facets: 4
Statistics for: rbox "10 D2" | qhull T1
Number of points processed: 4
Number of hyperplanes created: 5
Number of distance tests for qhull: 51
CPU seconds to compute hull (after input): 0.000158
user_eg3 rbox qhull d
Results of d
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
Number of points processed: 10
Number of hyperplanes created: 28
Number of facets in hull: 16
Number of distance tests for qhull: 47
CPU seconds to compute hull (after input): 0.000106
user_eg3 rbox y c
rbox y
rbox c
3 rbox "y" "c"
12
-0.306292 0.149266 -0.289011
-0.409906 -0.282924 -0.0983473
0.0770774 0.440163 -0.185531
-0.212802 0.438723 -0.375664
-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
user_eg3 rbox D2 10 2 "s r 5" qhull 's p' facets
rbox D2
rbox 10
rbox 2
rbox s r 5
Results of s p
Convex hull of 17 points in 2-d:
Number of vertices: 7
Number of facets: 7
Statistics for: rbox "10 D2" "2 D2" "s r 5 D2" | qhull s p
Number of points processed: 7
Number of hyperplanes created: 11
Number of distance tests for qhull: 78
CPU seconds to compute hull (after input): 8.6e-05
2
7
-0.02222276248244826 -0.4979727817680433
-0.4285431913366012 0.4745826469497594
0.3790312361708201 0.3779794437605696
0.1545084971874737 0.4755282581475768
-0.4045084971874738 -0.2938926261462365
0.1545084971874736 -0.4755282581475768
0.5 -1.224646799147353e-16
Facets created by Qhull::runQhull()
- f5
- flags: bottom simplicial
- normal: 0.952413 0.304811
- offset: -0.476206
- vertices: p4(v4) p16(v2)
- neighboring facets: f8 f11
- f6
- flags: bottom simplicial
- normal: -0.999511 -0.0312605
- offset: -0.413498
- vertices: p14(v5) p1(v1)
- neighboring facets: f10 f7
- f7
- flags: top simplicial
- normal: -0.470938 -0.882167
- offset: -0.44976
- vertices: p14(v5) p0(v3)
- neighboring facets: f9 f6
- f8
- flags: top simplicial
- normal: 0.809017 -0.587785
- offset: -0.404508
- vertices: p15(v6) p16(v2)
- neighboring facets: f5 f9
- f9
- flags: bottom simplicial
- normal: 0.125986 -0.992032
- offset: -0.491205
- vertices: p15(v6) p0(v3)
- neighboring facets: f7 f8
- f10
- flags: top simplicial
- normal: -0.00162183 0.999999
- offset: -0.475277
- vertices: p12(v7) p1(v1)
- neighboring facets: f6 f11
- f11
- flags: bottom simplicial
- normal: 0.398486 0.917174
- offset: -0.497712
- vertices: p12(v7) p4(v4)
- neighboring facets: f5 f10
user_eg3 rbox "10 D2" eg-convex
rbox 10 D2
Input points and facetlist for convex hull of rbox "10 D2" via C++ classes
2
10 4 4
-0.0222228 -0.497973
-0.428543 0.474583
0.31054 0.240018
-0.0188396 0.363026
0.379031 0.377979
-0.299496 0.377661
0.347182 0.0836553
-0.0048582 0.348268
0.344312 -0.143731
0.309331 -0.077581
2 4 1
2 1 0
2 8 4
2 0 8
user_eg3 rbox '10 D2' qhull s eg-convex
rbox 10 D2
Results of s
Convex hull of 10 points in 2-d:
Number of vertices: 4
Number of facets: 4
Statistics for: rbox "10 D2" | qhull s
Number of points processed: 4
Number of hyperplanes created: 5
Number of distance tests for qhull: 51
CPU seconds to compute hull (after input): 7.3e-05
Input points and facetlist for 'qhull s' via C++ classes
2
10 4 4
-0.0222228 -0.497973
-0.428543 0.474583
0.31054 0.240018
-0.0188396 0.363026
0.379031 0.377979
-0.299496 0.377661
0.347182 0.0836553
-0.0048582 0.348268
0.344312 -0.143731
0.309331 -0.077581
2 4 1
2 1 0
2 8 4
2 0 8
user_eg3 rbox 10 eg-delaunay qhull 'd o'
rbox 10
Delaunay triangulation of 10 points as 4-d paraboloid via C++ classes
4
10 15 30
-0.374949 0.224726 -0.0378235 0.192519
0.300492 0.369454 0.421096 0.404114
0.364148 0.233952 0.0348979 0.188555
-0.470713 -0.281065 0.135495 0.318928
0.264275 -0.326571 0.317506 0.2773
0.318323 0.0506033 0.489822 0.343815
0.433436 -0.248039 0.203767 0.290911
-0.285595 -0.00222701 -0.42931 0.265876
-0.40759 -0.362593 -0.0978938 0.307186
-0.301385 -0.378685 0.434172 0.422741
4 5 2 1 6
4 5 4 2 6
4 2 4 7 6
4 4 0 5 2
4 0 5 2 1
4 0 4 9 3
4 4 0 9 5
4 0 9 5 1
4 4 8 7 6
4 4 8 9 3
4 8 0 7 3
4 0 8 4 3
4 4 8 2 7
4 8 0 2 7
4 8 0 4 2
Results of d o
4
10 15 30
-0.374949442106252 0.2247255418679914 -0.03782349642163468 0.1925192701852094
0.3004920247946792 0.3694544596313075 0.4210962191420572 0.4041140804824029
0.3641479121187217 0.2339522165562512 0.03489791698278666 0.1885552061417448
-0.4707134565997063 -0.2810653003687648 0.1354949890035158 0.3189277533404903
0.2642752088273644 -0.3265712199048802 0.3175057017407433 0.2773000183087906
0.3183227589524563 0.05060330969337679 0.4898217078203537 0.3438153792710754
0.4334355904100794 -0.2480392830893763 0.2037671452423252 0.2909109464698327
-0.2855954200826543 -0.002227006947833121 -0.4293096679535784 0.2658764945305452
-0.4075898489985521 -0.3625928418362446 -0.09789381697577781 0.3071862533596335
-0.3013850588364387 -0.3786854184034145 0.4341719447953365 0.4227408774485775
4 5 2 1 6
4 5 4 2 6
4 2 4 7 6
4 4 0 5 2
4 0 5 2 1
4 0 4 9 3
4 4 0 9 5
4 0 9 5 1
4 4 8 7 6
4 4 8 9 3
4 8 0 7 3
4 0 8 4 3
4 4 8 2 7
4 8 0 2 7
4 8 0 4 2
user_eg3 rbox D5 c P2 qhull d eg-delaunay
rbox D5
rbox c
rbox P2
Results of d
Delaunay triangulation by the convex hull of 33 points in 6-d:
Number of input sites: 33
Number of Delaunay regions: 2
Number of non-simplicial Delaunay regions: 2
Statistics for: rbox "c D5" "P2 D5" | qhull d
Number of points processed: 33
Number of hyperplanes created: 87
Number of facets in hull: 11
Number of distance tests for qhull: 826
Number of distance tests for merging: 3868
Number of distance tests for checking: 363
Number of merged facets: 296
CPU seconds to compute hull (after input): 0.002088
Vertices and Delaunay regions of paraboloid from 'qhull d' via C++ classes
6
33 2 6
-0.5 -0.5 -0.5 -0.5 -0.5 1.25
-0.5 -0.5 -0.5 -0.5 0.5 1.25
-0.5 -0.5 -0.5 0.5 -0.5 1.25
-0.5 -0.5 -0.5 0.5 0.5 1.25
-0.5 -0.5 0.5 -0.5 -0.5 1.25
-0.5 -0.5 0.5 -0.5 0.5 1.25
-0.5 -0.5 0.5 0.5 -0.5 1.25
-0.5 -0.5 0.5 0.5 0.5 1.25
-0.5 0.5 -0.5 -0.5 -0.5 1.25
-0.5 0.5 -0.5 -0.5 0.5 1.25
-0.5 0.5 -0.5 0.5 -0.5 1.25
-0.5 0.5 -0.5 0.5 0.5 1.25
-0.5 0.5 0.5 -0.5 -0.5 1.25
-0.5 0.5 0.5 -0.5 0.5 1.25
-0.5 0.5 0.5 0.5 -0.5 1.25
-0.5 0.5 0.5 0.5 0.5 1.25
0.5 -0.5 -0.5 -0.5 -0.5 1.25
0.5 -0.5 -0.5 -0.5 0.5 1.25
0.5 -0.5 -0.5 0.5 -0.5 1.25
0.5 -0.5 -0.5 0.5 0.5 1.25
0.5 -0.5 0.5 -0.5 -0.5 1.25
0.5 -0.5 0.5 -0.5 0.5 1.25
0.5 -0.5 0.5 0.5 -0.5 1.25
0.5 -0.5 0.5 0.5 0.5 1.25
0.5 0.5 -0.5 -0.5 -0.5 1.25
0.5 0.5 -0.5 -0.5 0.5 1.25
0.5 0.5 -0.5 0.5 -0.5 1.25
0.5 0.5 -0.5 0.5 0.5 1.25
0.5 0.5 0.5 -0.5 -0.5 1.25
0.5 0.5 0.5 -0.5 0.5 1.25
0.5 0.5 0.5 0.5 -0.5 1.25
0.5 0.5 0.5 0.5 0.5 1.25
2 0 0 0 0 4
32 17 18 3 20 5 6 24 9 10 12 19 21 22 7 25 26 11 28 13 14 23 27 29 30 15 31 16 1 2 4 8 0
17 17 18 20 24 19 21 22 25 26 28 23 27 29 30 31 16 32
user_eg3 rbox '10 D2' eg-voronoi
rbox 10 D2
Voronoi vertices and regions for rbox "10 D2" via C++ classes
2
15 10 1
-10.101 -10.101
-0.129438 -0.0724741
0.0826769 -0.239764
0.129526 1.71603
0.174036 0.531752
0.185142 0.388255
-0.906594 -0.296296
-0.195481 -0.0711189
-0.140758 0.723386
-0.16763 0.208062
0.0586831 0.0663207
0.0880634 0.105408
0.476159 -0.0316837
3.09421 -0.0647219
0.541052 0.211562
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
user_eg3 rbox "D5 c P2" qhull v eg-voronoi o
rbox D5 c P2
Results of v
Voronoi diagram by the convex hull of 33 points in 6-d:
Number of Voronoi regions: 33
Number of Voronoi vertices: 2
Number of non-simplicial Voronoi vertices: 2
Statistics for: rbox "D5 c P2" | qhull v
Number of points processed: 33
Number of hyperplanes created: 87
Number of facets in hull: 11
Number of distance tests for qhull: 826
Number of distance tests for merging: 3868
Number of distance tests for checking: 363
Number of merged facets: 296
CPU seconds to compute hull (after input): 0.002223
Voronoi vertices and regions for 'qhull v' via C++ classes
5
3 33 1
-10.101 -10.101 -10.101 -10.101 -10.101
0 0 0 0 0
0.916667 0 0 0 0
2 0 2
2 0 1
2 0 1
2 0 1
2 0 1
2 0 1
2 0 1
2 0 1
2 0 1
2 0 1
2 0 1
2 0 1
2 0 1
2 0 1
2 0 1
2 0 1
2 0 1
3 0 1 2
3 0 1 2
3 0 1 2
3 0 1 2
3 0 1 2
3 0 1 2
3 0 1 2
3 0 1 2
3 0 1 2
3 0 1 2
3 0 1 2
3 0 1 2
3 0 1 2
3 0 1 2
3 0 1 2
3 0 1 2
Results of o
5
3 33 1
-10.101 -10.101 -10.101 -10.101 -10.101
0 0 0 0 0
0.9166666666666667 0 0 0 0
2 0 2
2 0 1
2 0 1
2 0 1
2 0 1
2 0 1
2 0 1
2 0 1
2 0 1
2 0 1
2 0 1
2 0 1
2 0 1
2 0 1
2 0 1
2 0 1
2 0 1
3 0 1 2
3 0 1 2
3 0 1 2
3 0 1 2
3 0 1 2
3 0 1 2
3 0 1 2
3 0 1 2
3 0 1 2
3 0 1 2
3 0 1 2
3 0 1 2
3 0 1 2
3 0 1 2
3 0 1 2
3 0 1 2
user_eg3 rbox '10 D2' eg-fifo
rbox 10 D2
Voronoi vertices for rbox "10 D2" via QhullUser and qh_fprintf
2
14
-0.129438 -0.0724741
0.0826769 -0.239764
0.129526 1.71603
0.174036 0.531752
0.185142 0.388255
-0.906594 -0.296296
-0.195481 -0.0711189
-0.140758 0.723386
-0.16763 0.208062
0.0586831 0.0663207
0.0880634 0.105408
0.476159 -0.0316837
3.09421 -0.0647219
0.541052 0.211562
10
5 6 0 1 -1 5
4 7 2 -1 5
3 13 4 10
4 8 3 2 7
6 13 4 3 2 -1 12
4 8 6 5 7
5 13 10 9 11 12
7 10 4 3 8 6 0 9
4 12 -1 1 11
4 11 1 0 9
Hyperplanes for bounded facets between Voronoi regions via QhullUser and qh_fprintf
19
5 0 5 -0.301881 0.953346 0.00878913
5 0 7 0.0205153 0.99979 0.0751143
5 0 9 0.619259 0.785187 0.137061
5 1 5 0.799595 -0.600539 0.546971
5 1 3 0.964872 -0.262721 0.325862
5 2 6 0.22816 -0.973624 0.0825353
5 2 4 0.444671 0.895694 -0.430084
5 2 7 -0.945841 0.32463 0.0490754
5 3 5 -0.998643 0.0520745 -0.178237
5 3 7 0.687752 -0.725945 0.26633
5 3 4 0.999294 0.037557 -0.193884
5 4 6 -0.107584 -0.994196 0.268542
5 4 7 -0.997018 -0.0771644 0.214549
5 5 7 0.995061 -0.0992661 0.187455
5 6 7 -0.799364 0.600847 0.00706064
5 6 9 -0.228542 -0.973534 0.077977
5 6 8 -0.0126184 -0.99992 -0.0256728
5 7 9 0.593695 -0.80469 0.0185277
5 8 9 -0.467479 0.884004 0.250603
Hyperplanes for unbounded facets between Voronoi regions via QhullUser and qh_fprintf
4
5 0 8 0.719063 0.694945 0.107173
5 0 1 -0.385496 0.92271 -0.076093
5 1 4 0.992921 -0.118775 0.0752121
5 4 8 -0.0664014 -0.997793 0.140881
Message codes captured by qh_fprintf in QhullUser.cpp (qhull v Fo Ta):
9231 9271 9272 9272 9273 9274 9271 9272 9272 9273 9274 9271 9272 9272 9273 9274 9271 9272 9272 9273 9274
user_eg3 rbox D2 10 qhull v eg-fifo p Fi Fo
rbox D2
rbox 10
Results of v
Voronoi diagram by the convex hull of 10 points in 3-d:
Number of Voronoi regions: 10
Number of Voronoi vertices: 14
Statistics for: rbox "10 D2" | qhull v
Number of points processed: 10
Number of hyperplanes created: 28
Number of facets in hull: 16
Number of distance tests for qhull: 47
CPU seconds to compute hull (after input): 0.000107
Voronoi vertices for 'qhull v' via C++ classes
2
14
-0.129438 -0.0724741
0.0826769 -0.239764
0.129526 1.71603
0.174036 0.531752
0.185142 0.388255
-0.906594 -0.296296
-0.195481 -0.0711189
-0.140758 0.723386
-0.16763 0.208062
0.0586831 0.0663207
0.0880634 0.105408
0.476159 -0.0316837
3.09421 -0.0647219
0.541052 0.211562
10
5 6 0 1 -1 5
4 7 2 -1 5
3 13 4 10
4 8 3 2 7
6 13 4 3 2 -1 12
4 8 6 5 7
5 13 10 9 11 12
7 10 4 3 8 6 0 9
4 12 -1 1 11
4 11 1 0 9
Hyperplanes for bounded facets between Voronoi regions via QhullUser and qh_fprintf
19
5 0 5 -0.301881 0.953346 0.00878913
5 0 7 0.0205153 0.99979 0.0751143
5 0 9 0.619259 0.785187 0.137061
5 1 5 0.799595 -0.600539 0.546971
5 1 3 0.964872 -0.262721 0.325862
5 2 6 0.22816 -0.973624 0.0825353
5 2 4 0.444671 0.895694 -0.430084
5 2 7 -0.945841 0.32463 0.0490754
5 3 5 -0.998643 0.0520745 -0.178237
5 3 7 0.687752 -0.725945 0.26633
5 3 4 0.999294 0.037557 -0.193884
5 4 6 -0.107584 -0.994196 0.268542
5 4 7 -0.997018 -0.0771644 0.214549
5 5 7 0.995061 -0.0992661 0.187455
5 6 7 -0.799364 0.600847 0.00706064
5 6 9 -0.228542 -0.973534 0.077977
5 6 8 -0.0126184 -0.99992 -0.0256728
5 7 9 0.593695 -0.80469 0.0185277
5 8 9 -0.467479 0.884004 0.250603
Hyperplanes for unbounded facets between Voronoi regions via QhullUser and qh_fprintf
4
5 0 8 0.719063 0.694945 0.107173
5 0 1 -0.385496 0.92271 -0.076093
5 1 4 0.992921 -0.118775 0.0752121
5 4 8 -0.0664014 -0.997793 0.140881
Message codes captured by qh_fprintf in QhullUser.cpp (qhull v Fo Ta):
9231 9271 9272 9272 9273 9274 9271 9272 9272 9273 9274 9271 9272 9272 9273 9274 9271 9272 9272 9273 9274
Results of p
2
14
-0.1294381801544404 -0.07247409101984709
0.08267689532419764 -0.2397644955865706
0.1295260566906467 1.716033573116839
0.1740355150742391 0.5317519038435656
0.1851415205797576 0.3882545794457364
-0.9065939866848106 -0.2962957610652136
-0.1954805620516264 -0.07111892482963184
-0.1407581310832469 0.7233857048236081
-0.1676297826663961 0.2080621273999384
0.05868313821742954 0.06632066014880161
0.08806341399736983 0.1054080604689984
0.4761588899009251 -0.03168366595227294
3.094213357897476 -0.064721945677682
0.5410515627308723 0.211561543495592
Results of Fi
19
5 0 5 -0.301880639203215 0.9533457293522944 0.008789126238507639
5 0 7 0.02051532578114256 0.9997895385570373 0.0751143044524602
5 0 9 0.619259133056969 0.7851866823409139 0.1370614663104577
5 1 5 0.7995952824356682 -0.6005392446015695 0.5469710423089691
5 1 3 0.9648718030091262 -0.2627211520946076 0.3258622775065155
5 2 6 0.2281595097543264 -0.9736237661995856 0.0825352874566877
5 2 4 0.4446710312325422 0.895693962234081 -0.4300843534994401
5 2 7 -0.9458410914974846 0.324629988810102 0.04907537812572163
5 3 5 -0.9986432053419565 0.05207445078292225 -0.1782370644858235
5 3 7 0.6877523324625964 -0.7259454037269318 0.2663295190946446
5 3 4 0.99929448732669 0.03755699133966526 -0.1938837324602515
5 4 6 -0.1075842248297359 -0.9941959739245502 0.2685422477498993
5 4 7 -0.9970183790688238 -0.07716444646969949 0.2145489484590234
5 5 7 0.995060920624513 -0.09926612839179721 0.1874553677160639
5 6 7 -0.7993641842155071 0.6008468199079334 0.007060641163779156
5 6 9 -0.2285415587894344 -0.9735341575446109 0.07797696388863322
5 6 8 -0.01261839651625044 -0.9999203848653946 -0.02567278177543585
5 7 9 0.5936952885926361 -0.8046899429612046 0.01852766555277021
5 8 9 -0.4674785097727935 0.8840044360186254 0.2506025495170938
Results of Fo
4
5 0 8 0.7190625207842074 0.6949453872092838 0.1071733734620183
5 0 1 -0.3854955578888163 0.922709691532494 -0.07609298438083834
5 1 4 0.9929212365203528 -0.1187746524595787 0.0752121188850394
5 4 8 -0.06640144810487485 -0.9977929883946747 0.1408811441173877
set +v
=== check front ends and examples Mon Sep 18 21:37:17 UTC 2023 ==================
qconvex -
qconvex -- compute the convex hull
http://www.qhull.org 2020.2.r 2020/08/31
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:
Qc - keep coplanar points with nearest facet
Qi - keep interior points with nearest facet
QJ - joggled input instead of merged facets
Qt - triangulated output
Qhull control options:
Qa - allow input with fewer or more points than coordinates
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
Qhull extra options:
QGn - good facet if visible from point n, -n for not visible
QVn - good facet if it includes point n, -n if not
Qw - allow option warnings
Q12 - allow wide facets and wide dupridge
Q14 - merge pinched vertices that create a dupridge
T options:
TFn - report summary when n or more facets created
TI file - input file, may be enclosed in single quotes
TO file - output file, may be enclosed in single quotes
Ts - statistics
Tv - verify result: structure, convexity, and in-circle test
Tz - send all output to stdout
Trace options:
T4 - trace at level n, 4=all, 5=mem/gauss, -1= events
Ta - annotate output with message codes
TAn - stop qhull after adding n vertices
TCn - stop qhull after building cone for point n
TVn - stop qhull after adding point n, -n for before
Tc - check frequently during execution
Tf - flush each qh_fprintf for debugging segfaults
TPn - turn on tracing when point n added to hull
TMn - turn on tracing at merge n
TWn - trace merge facets when width > n
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)
p - point coordinates
s - summary (stderr)
More formats:
Fa - area for each facet
FA - compute total area and volume for option 's'
Fc - count plus coplanar points for each facet
use 'Qc' (default) for coplanar and 'Qi' for interior
FC - centrum for each facet
Fd - use cdd format for input (homogeneous with offset first)
FD - use cdd format for numeric output (offset first)
FF - facet dump without ridges
Fi - inner plane for each facet
FI - ID for each facet
Fm - merge count for each facet (511 max)
FM - Maple output (2-d and 3-d)
Fn - count plus neighboring facets for each facet
FN - count plus neighboring facets for each point
Fo - outer plane (or max_outside) for each facet
FO - options and precision constants
FP - nearest vertex for each coplanar point
FQ - command used for qconvex
Fs - summary: #int (8), dimension, #points, tot vertices, tot facets,
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
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
Gc - centrums
GDn - drop dimension n in 3-d and 4-d output
Gh - hyperplane intersections
Gi - inner planes only
Gn - no planes
Go - outer planes only
Gr - 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
PFn - keep facets whose area is at least n
Pg - print good facets (needs 'QGn' or 'QVn')
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
-? - help with examples
-V - version
qconvex .
Qhull 2020.2.r 2020/08/31
Except for 'F.' and 'PG', upper-case options take an argument.
facet-dump Geomview incidences mathematica normals
off-format points summary
Farea FArea-total Fcoplanars FCentrums Fd-cdd-in
FD-cdd-out FFacets-xridge Finner FIDs Fmerges
FMaple Fneighbors FNeigh-vertex Fouter FOptions
FPoint-near FQhull Fsummary FSize Ftriangles
Fvertices FVertex-ave Fxtremes
Gall-points Gcentrums GDrop-dim Ghyperplanes Ginner
Gno-planes Gouter Gpoints Gridges Gvertices
PArea-keep Pdrop-d0:0D0 PFacet-area-keep Pgood PGood-neighbors
PMerge-keep Poutput-forced Pprecision-not
Qallow-short QbBound-0:0.5 QbB-scale-box Qcoplanar QGood-point
Qinterior QJoggle QRotate Qsearch-all Qtriangulate
QVertex-good Qwarn-allow Q12-allow-wide Q14-merge-pinched
TFacet-log TInput-file TOutput-file Tstatistics Tverify
Tz-stdout
T4-trace Tannotate TAdd-stop Tcheck-often TCone-stop
Tflush TMerge-trace TPoint-trace TVertex-stop TWide-trace
Angle-max Centrum-size Random-dist Ucoplanar-max Wide-outside
qconvex -? # [mar'19] isatty does not work for Git for Windows
qconvex -- compute the convex hull. Qhull 2020.2.r 2020/08/31
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 each option
-? - this message
-V - version
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)
FA - report total area and volume
FS - total area and volume
Fx - extreme points (convex hull vertices)
G - Geomview output (2-d, 3-d, and 4-d)
m - Mathematica output (2-d and 3-d)
o - OFF format (dim, n, points, facets)
QVn - print facets that include point n, -n if not
TI file - input file, may be enclosed in single quotes
TO file - output 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 Qc 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
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: 34
Number of distance tests for merging: 90
Number of distance tests for checking: 48
Number of merged facets: 6
CPU seconds to compute hull (after input): 0.000178
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 D2 | qconvex s i
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: 5
CPU seconds to compute hull (after input): 6.7e-05
4
0 2
1 0
2 3
3 1
rbox c D2 | qconvex s n
Convex hull of 4 points in 2-d:
Number of vertices: 4
Number of facets: 4
Statistics for: rbox c D2 | qconvex s n
Number of points processed: 4
Number of hyperplanes created: 6
Number of distance tests for qhull: 5
CPU seconds to compute hull (after input): 6.8e-05
3
4
-0 -1 -0.5
-1 0 -0.5
1 -0 -0.5
0 1 -0.5
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: 5544
Number of distance tests for qhull: 25487
CPU seconds to compute hull (after input): 0.01152
Total facet area: 3.1201951
Total volume: 0.51650274
qhull output completed. Verifying that 1000 points are
below 2.1e-15 of the nearest facet.
rbox c d D2 | qconvex s Qc Fx
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: 35
CPU seconds to compute hull (after input): 7.7e-05
4
0
2
3
1
rbox y 1000 W0 | qconvex Qc s n
Convex hull of 1004 points in 3-d:
Number of vertices: 4
Number of coplanar points: 1000
Number of facets: 4
Statistics for: rbox y 1000 W0 | qconvex Qc s n
Number of points processed: 4
Number of hyperplanes created: 4
Number of distance tests for qhull: 11000
CPU seconds to compute hull (after input): 0.000873
4
4
0.2135848119563837 0.1168704340428168 0.9699086708284446 -0.09806074564261894
0.08553875579270347 -0.8316435307282575 -0.5486822022403076 -0.1234144150397865
-0.749541668500822 -0.02779445272382575 -0.6613733859014791 -0.2159556159595279
0.3120013537900506 0.9498158823230658 -0.02247097950761911 -0.02453689035981485
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: 180
Number of distance tests for qhull: 6420
CPU seconds to compute hull (after input): 0.000786
Input joggled by: 2.1e-11
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 QR1695073037
Number of points processed: 24
Number of hyperplanes created: 4108
Number of distance tests for qhull: 4215
Number of distance tests for merging: 121143
Number of distance tests for checking: 98304
Number of merged facets: 2036
CPU seconds to compute hull (after input): 0.0941
Approximate facet area: 0.00035546337
Approximate volume: 8.5511197e-06
rbox c D6 | qconvex s FA TF500
At 21:37:17 & 0.002832 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 21:37:17 & 0.005627 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 21:37:17 & 0.008338 CPU secs, qhull has created 1567 facets and merged 1216.
The current hull contains 37 facets and 48 vertices. There are 16
outside points. Next is point p9(v49), 0.45 above f1061.
At 21:37:17 & 0.010005 CPU secs, qhull has created 1819 facets and merged 1462.
The current hull contains 12 facets and 64 vertices. Last point was p11
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 s FA TF500
Number of points processed: 64
Number of hyperplanes created: 358
Number of distance tests for qhull: 2515
Number of distance tests for merging: 14300
Number of distance tests for checking: 0
Number of merged facets: 1462
First post-merge with 'C3.5e-15' and 'A1.8e+308'
At 21:37:17 & 0.010438 CPU secs, qhull has created 1819 facets and merged 1462.
The current hull contains 12 facets and 64 vertices. Last point was p11
Testing all coplanar points.
computing area of each facet and volume of the convex hull
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 s FA TF500
Number of points processed: 64
Number of hyperplanes created: 358
Number of distance tests for qhull: 2515
Number of distance tests for merging: 14420
Number of distance tests for checking: 768
Number of merged facets: 1462
CPU seconds to compute hull (after input): 0.01057
Approximate facet area: 12
Approximate volume: 1
rbox c D7 | qconvex s FA TF1000
At 21:37:17 & 0.006323 CPU secs, qhull has created 1048 facets and merged 469.
The current hull contains 230 facets and 24 vertices. There are 104
outside points. Next is point p79(v25), 0.66 above f145.
At 21:37:17 & 0.014802 CPU secs, qhull has created 2146 facets and merged 1272.
The current hull contains 273 facets and 31 vertices. There are 97
outside points. Next is point p120(v32), 0.54 above f437.
At 21:37:18 & 0.024424 CPU secs, qhull has created 3310 facets and merged 2244.
The current hull contains 243 facets and 36 vertices. There are 92
outside points. Next is point p60(v37), 0.54 above f1338.
At 21:37:18 & 0.033085 CPU secs, qhull has created 4322 facets and merged 3099.
The current hull contains 249 facets and 42 vertices. There are 86
outside points. Next is point p30(v43), 0.54 above f2005.
At 21:37:18 & 0.043223 CPU secs, qhull has created 5491 facets and merged 4196.
The current hull contains 186 facets and 48 vertices. There are 80
outside points. Next is point p21(v49), 0.5 above f2995.
At 21:37:18 & 0.053576 CPU secs, qhull has created 6589 facets and merged 5175.
The current hull contains 194 facets and 53 vertices. There are 75
outside points. Next is point p56(v54), 0.28 above f3731.
At 21:37:18 & 0.065874 CPU secs, qhull has created 7867 facets and merged 6337.
The current hull contains 203 facets and 60 vertices. There are 68
outside points. Next is point p76(v61), 0.29 above f5879.
At 21:37:18 & 0.077638 CPU secs, qhull has created 8971 facets and merged 7362.
The current hull contains 179 facets and 67 vertices. There are 61
outside points. Next is point p80(v68), 0.23 above f7175.
At 21:37:18 & 0.089846 CPU secs, qhull has created 9984 facets and merged 8352.
The current hull contains 104 facets and 77 vertices. There are 51
outside points. Next is point p96(v78), 0.41 above f6748.
At 21:37:18 & 0.10371 CPU secs, qhull has created 10990 facets and merged 9326.
The current hull contains 54 facets and 90 vertices. There are 38
outside points. Next is point p18(v91), 0.41 above f10178.
At 21:37:18 & 0.11635 CPU secs, qhull has created 11996 facets and merged 10295.
The current hull contains 34 facets and 114 vertices. There are 14
outside points. Next is point p19(v115), 0.38 above f11792.
At 21:37:18 & 0.12535 CPU secs, qhull has created 12860 facets and merged 11072.
The current hull contains 14 facets and 128 vertices. Last point was p77
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 | qconvex s FA TF1000
Number of points processed: 128
Number of hyperplanes created: 1789
Number of distance tests for qhull: 10122
Number of distance tests for merging: 87203
Number of distance tests for checking: 0
Number of merged facets: 11072
First post-merge with 'C4.4e-15' and 'A1.8e+308'
At 21:37:18 & 0.12717 CPU secs, qhull has created 12860 facets and merged 11072.
The current hull contains 14 facets and 128 vertices. Last point was p77
Testing all coplanar points.
computing area of each facet and volume of the convex hull
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 | qconvex s FA TF1000
Number of points processed: 128
Number of hyperplanes created: 1789
Number of distance tests for qhull: 10122
Number of distance tests for merging: 87371
Number of distance tests for checking: 1792
Number of merged facets: 11072
CPU seconds to compute hull (after input): 0.1275
Approximate facet area: 14
Approximate volume: 1
rbox d G1 D12 | qconvex QR0 FA Pp
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 Pp QR1695073038
Number of points processed: 24
Number of hyperplanes created: 4108
Number of distance tests for qhull: 4215
Number of distance tests for merging: 121143
Number of distance tests for checking: 98304
Number of merged facets: 2036
CPU seconds to compute hull (after input): 0.09367
Approximate facet area: 0.00035546337
Approximate volume: 8.5511197e-06
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 2 0
2 3 2
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
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: 35
CPU seconds to compute hull (after input): 8e-05
2
0 2
1 0
rbox c | qconvex Q0
QH6029 qhull option error: option 'Q0' is not used with this program.
It may be used with qhull.
While executing: | qconvex Q0
Options selected for Qhull 2020.2.r 2020/08/31:
run-id 574488564 _maxoutside 0
qvoronoi -
qvoronoi -- compute the Voronoi diagram
http://www.qhull.org 2020.2.r 2020/08/31
input (stdin):
first lines: dimension and number of points (or vice-versa).
other lines: point coordinates, best if one point per line
comments: start with a non-numeric character
options:
Qu - compute furthest-site Voronoi diagram
Qhull control options:
Qa - allow input with fewer or more points than coordinates
QRn - random rotation (n=seed, n=0 time, n=-1 time/no rotate)
Qs - search all points for the initial simplex
Qz - add point-at-infinity to Voronoi diagram
Qhull extra options:
QGn - Voronoi vertices if visible from point n, -n if not
QVn - Voronoi vertices for input point n, -n if not
Qw - allow option warnings
Q12 - allow wide facets and wide dupridge
Q14 - merge pinched vertices that create a dupridge
T options:
TFn - report summary when n or more facets created
TI file - input file, may be enclosed in single quotes
TO file - output file, may be enclosed in single quotes
Ts - statistics
Tv - verify result: structure, convexity, and in-circle test
Tz - send all output to stdout
Trace options:
T4 - trace at level n, 4=all, 5=mem/gauss, -1= events
Ta - annotate output with message codes
TAn - stop qhull after adding n vertices
TCn - stop qhull after building cone for point n
TVn - stop qhull after adding point n, -n for before
Tc - check frequently during execution
Tf - flush each qh_fprintf for debugging segfaults
TPn - turn on tracing when point n added to hull
TMn - turn on tracing at merge n
TWn - trace merge facets when width > n
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, summary to stdout):
p - Voronoi vertices
s - summary to stderr
f - facet dump
i - Delaunay regions (use 'Pp' to avoid warning)
o - OFF format (dim, Voronoi vertices, and Voronoi regions)
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 output (2-d only)
Ga - all points as dots
Gp - coplanar points and vertices as radii
Gv - vertices as spheres
Gc - centrums
GDn - drop dimension n in 3-d and 4-d output
Gh - hyperplane intersections
Gi - inner planes only
Gn - no planes
Go - outer planes only
Gr - ridges
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
PFn - keep Voronoi vertices whose 'area' is at least n
Pg - print good Voronoi vertices (needs 'QGn' or 'QVn')
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
-? - help with examples
-V - version
qvoronoi .
Qhull 2020.2.r 2020/08/31
Except for 'F.' and 'PG', upper-case options take an argument.
facet-dump Geomview i-delaunay off-format p-vertices
summary
Fcoincident Fd-cdd-in FD-cdd-out FF-dump-xridge Fi-bounded
FIDs Fmerges Fneighbors FNeigh-region Fo-unbounded
FOptions FPoint-near FQvoronoi Fsummary Fvoronoi
Fxtremes
Gall-points Gcentrums GDrop-dim Ghyperplanes Ginner
Gno-planes Gouter Gpoints Gridges Gvertices
PArea-keep Pdrop-d0:0D0 PFacet-area-keep Pgood PGood-neighbors
PMerge-keep Poutput-forced Pprecision-not
Qallow-short QG-vertex-good QRotate Qsearch-all Qupper-voronoi
QV-point-good Qwarn-allow Qzinfinite Q12-allow-wide Q14-merge-pinched
TFacet-log TInput-file TOutput-file Tstatistics Tverify
Tz-stdout
T4-trace Tannotate TAdd-stop Tcheck-often TCone-stop
Tflush TMerge-trace TPoint-trace TVertex-stop TWide-trace
Angle-max Centrum-size Random-dist Wide-outside
qvoronoi -? # [mar'19] isatty does not work for Git for Windows
qvoronoi -- compute the Voronoi diagram. Qhull 2020.2.r 2020/08/31
input (stdin): dimension, number of points, point coordinates
comments start with a non-numeric character
options (qvoronoi.htm):
Qu - compute furthest-site Voronoi diagram
Tv - verify result: structure, convexity, and in-circle test
. - concise list of all options
- - one-line description of all options
-? - this message
-V - version
output options (subset):
Fi - separating hyperplanes for bounded regions, 'Fo' for unbounded
FN - count and Voronoi vertices for each Voronoi region
Fv - Voronoi diagram as Voronoi vertices between adjacent input sites
G - Geomview output (2-d only)
o - OFF file format (dim, Voronoi vertices, and Voronoi regions)
p - Voronoi vertices
QVn - Voronoi vertices for input point n, -n if not
s - summary of results (default)
TI file - input file, may be enclosed in single quotes
TO file - output file, may be enclosed in single quotes
examples:
rbox c P0 D2 | qvoronoi s o rbox c P0 D2 | qvoronoi Fi
rbox c P0 D2 | qvoronoi Fo rbox c P0 D2 | qvoronoi Fv
rbox c P0 D2 | qvoronoi s Qu Fv rbox c P0 D2 | qvoronoi Qu Fo
rbox c G1 d D2 | qvoronoi s p rbox c P0 D2 | qvoronoi s Fv QV0
rbox c P0 D2 | qvoronoi s o
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: 6
Number of facets in hull: 5
Number of distance tests for qhull: 7
Number of distance tests for merging: 34
Number of distance tests for checking: 25
Number of merged facets: 1
CPU seconds to compute hull (after input): 0.000102
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
rbox c P0 D2 | qvoronoi Fi Tv
4
5 0 3 0.7071067811865475 -0.7071067811865475 -0.3535533905932737
5 0 1 -0.7071067811865475 -0.7071067811865475 -0.3535533905932737
5 0 2 -0.7071067811865475 0.7071067811865475 -0.3535533905932737
5 0 4 0.7071067811865475 0.7071067811865475 -0.3535533905932737
Voronoi ridge statistics
4 bounded ridges
0 max. distance of midpoint to ridge
4 bounded ridges with ok normal
2.2e-16 ave. angle to ridge
2.2e-16 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 Tv
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
Output completed. Verifying that all points are below outer planes of
all facets. Will make 20 distance computations.
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 Fv
Furthest-site Voronoi vertices by the convex hull of 5 points in 3-d:
Number of Voronoi regions: 5
Number of Voronoi vertices: 1
Number of non-simplicial Voronoi vertices: 1
Statistics for: rbox c P0 D2 | qvoronoi s Qu Fv
Number of points processed: 5
Number of hyperplanes created: 6
Number of facets in hull: 5
Number of distance tests for qhull: 7
Number of distance tests for merging: 34
Number of distance tests for checking: 25
Number of merged facets: 1
CPU seconds to compute hull (after input): 0.000104
4
4 1 2 0 1
4 1 3 0 1
4 2 4 0 1
4 3 4 0 1
rbox c P0 D2 | qvoronoi s Qu Qt Fv
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: 6
Number of facets in hull: 6
Number of distance tests for qhull: 7
Number of distance tests for merging: 34
Number of distance tests for checking: 25
Number of merged facets: 1
CPU seconds to compute hull (after input): 0.000112
4
4 1 3 0 2
4 1 2 0 1
4 2 4 0 1
4 3 4 0 2
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
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: 16
Number of facets in hull: 10
Number of distance tests for qhull: 41
Number of distance tests for merging: 108
Number of distance tests for checking: 72
Number of merged facets: 3
CPU seconds to compute hull (after input): 0.000158
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
rbox c G1 d D2 | qvoronoi QJ p
2
10
-2.57276422388486e-11 1.749999999802917
-2.05463598231932e-11 -1.750000000331276
0.5833333333083517 -0.5833333333052267
1.862254794815499e-11 -7.815052443180038e-11
1.750000000002628 3.498100747664324e-11
0.5833333333132078 0.5833333333796981
-0.5833333332888888 0.5833333333317835
-7.592293460589872e-11 -7.815050692933323e-11
-1.750000000049026 2.293196879294717e-11
-0.5833333333977307 -0.5833333333229861
rbox c P-0.1 P+0.1 P+0.1 D2 | qvoronoi s Fc FP FQ Fn FN
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: 7
Number of facets in hull: 5
Number of distance tests for qhull: 31
Number of distance tests for merging: 54
Number of distance tests for checking: 36
Number of merged facets: 3
CPU seconds to compute hull (after input): 0.000135
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 3 1
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
rbox P0 c D2 | qvoronoi s Fv QV0
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: 6
Number of facets in hull: 5
Number of distance tests for qhull: 7
Number of distance tests for merging: 34
Number of distance tests for checking: 25
Number of merged facets: 1
CPU seconds to compute hull (after input): 0.000103
4
4 0 3 1 3
4 0 1 1 2
4 0 2 2 4
4 0 4 3 4
qdelaunay -
qdelaunay -- compute the Delaunay triangulation
http://www.qhull.org 2020.2.r 2020/08/31
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:
QJ - joggled input instead of merged facets
Qt - triangulated output
Qu - compute furthest-site Delaunay triangulation
Qhull control options:
Qa - allow input with fewer or more points than coordinates
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
Qz - add point-at-infinity to Delaunay triangulation
Qhull extra options:
QGn - print Delaunay region if visible from point n, -n if not
QVn - print Delaunay regions that include point n, -n if not
Qw - allow option warnings
Q12 - allow wide facets and wide dupridge
Q14 - merge pinched vertices that create a dupridge
T options:
TFn - report summary when n or more facets created
TI file - input file, may be enclosed in single quotes
TO file - output file, may be enclosed in single quotes
Ts - statistics
Tv - verify result: structure, convexity, and in-circle test
Tz - send all output to stdout
Trace options:
T4 - trace at level n, 4=all, 5=mem/gauss, -1= events
Ta - annotate output with message codes
TAn - stop qhull after adding n vertices
TCn - stop qhull after building cone for point n
TVn - stop qhull after adding point n, -n for before
Tc - check frequently during execution
Tf - flush each qh_fprintf for debugging segfaults
TPn - turn on tracing when point n added to hull
TMn - turn on tracing at merge n
TWn - trace merge facets when width > n
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,
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 output (2-d and 3-d points lifted to a paraboloid)
Ga - all points as dots
Gp - coplanar points and vertices as radii
Gv - vertices as spheres
Gc - centrums
GDn - drop dimension n in 3-d and 4-d output
Gh - hyperplane intersections
Gi - inner planes only
Gn - no planes
Go - outer planes only
Gr - ridges
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
PFn - keep Delaunay regions whose area is at least n
Pg - print good Delaunay regions (needs 'QGn' or 'QVn')
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
-? - help with examples
-V - version
qdelaunay .
Qhull 2020.2.r 2020/08/31
Except for 'F.' and 'PG', upper-case options take an argument.
facet-dump Geomview incidences mathematica off-format
points-lifted summary
Farea FArea-total Fcoincident Fd-cdd-in FD-cdd-out
FF-dump-xridge FIDs Fmerges FMaple Fneighbors
FNeigh-vertex FOptions FPoint-near FQdelaun Fsummary
FSize Fvertices Fxtremes
Gall-points Gcentrums GDrop-dim Ghyperplanes Ginner
Gno-planes Gouter Gpoints Gridges Gtransparent
Gvertices
PArea-keep Pdrop-d0:0D0 PFacet-area-keep Pgood PGood-neighbors
PMerge-keep Poutput-forced Pprecision-not
Qallow-short QGood-point QJoggle Qrotate Qsearch-all
Qtriangulate QupperDelaunay QVertex-good Qwarn-allow Qzinfinite
Q12-allow-wide Q14-merge-pinched
TFacet-log TInput-file TOutput-file Tstatistics Tverify
Tz-stdout
T4-trace Tannotate TAdd-stop Tcheck-often TCone-stop
Tflush TMerge-trace TPoint-trace TVertex-stop TWide-trace
Angle-max Centrum-size Random-dist Wide-outside
qdelaunay -? # [mar'19] isatty does not work for Git for Windows
qdelaunay -- compute the Delaunay triangulation. Qhull 2020.2.r 2020/08/31
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 each option
-? - this message
-V - version
output options (subset):
s - summary of results (default)
i - vertices incident to each Delaunay region
Fx - extreme points (vertices of the convex hull)
G - Geomview output (2-d and 3-d points lifted to a paraboloid)
m - Mathematica output (2-d inputs lifted to a paraboloid)
o - OFF format (shows the points lifted to a paraboloid)
QVn - print Delaunay regions that include point n, -n if not
TI file - input file, may be enclosed in single quotes
TO file - output 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
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: 6
Number of facets in hull: 5
Number of distance tests for qhull: 7
Number of distance tests for merging: 34
Number of distance tests for checking: 25
Number of merged facets: 1
CPU seconds to compute hull (after input): 9.7e-05
3
5 4 6
0 0 0
-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 3 0 1
3 0 2 1
3 4 0 3
3 0 4 2
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
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: 6
Number of facets in hull: 6
Number of distance tests for qhull: 7
Number of distance tests for merging: 34
Number of distance tests for checking: 25
Number of merged facets: 1
CPU seconds to compute hull (after input): 9.8e-05
2
3 4 2 1
3 4 3 1
rbox c G1 d D2 | qdelaunay s i
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: 16
Number of facets in hull: 10
Number of distance tests for qhull: 41
Number of distance tests for merging: 108
Number of distance tests for checking: 72
Number of merged facets: 3
CPU seconds to compute hull (after input): 0.00015
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
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 7 5
3 8 4 7
rbox c G1 d D2 | qhull d Qbb QJ s Ft
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: 19
Number of facets in hull: 12
Number of distance tests for qhull: 31
CPU seconds to compute hull (after input): 0.000106
Input joggled by: 8.3e-11
2
8 10 15
-1.000000000061343 -0.999999999957446
-0.9999999999945448 0.9999999999532114
1.000000000029778 -0.9999999999701502
0.9999999999806051 1.000000000003233
-7.748592400792811e-11 -0.5000000000743411
2.849349704487493e-11 0.49999999991804
-0.5000000000721135 -1.37371989142159e-11
0.5000000000148132 7.166044474310069e-11
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
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: 251
Number of facets in hull: 86
Number of distance tests for qhull: 1650
Number of distance tests for merging: 2765
Number of distance tests for checking: 1248
Number of merged facets: 155
CPU seconds to compute hull (after input): 0.001749
rbox c P-0.1 P+0.1 P+0.1 D2 | qdelaunay s Fx Fa Fc FP FQ Fn FN
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: 7
Number of facets in hull: 5
Number of distance tests for qhull: 31
Number of distance tests for merging: 54
Number of distance tests for checking: 35
Number of merged facets: 3
CPU seconds to compute hull (after input): 0.000128
Approximate facet area: 1
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 3 1
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
rbox P0 P0 c D2 | qdelaunay s FP QV0
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: 6
Number of facets in hull: 5
Number of distance tests for qhull: 18
Number of distance tests for merging: 34
Number of distance tests for checking: 30
Number of merged facets: 1
CPU seconds to compute hull (after input): 0.00011
1
0 1 2 0
qhalf -
qhalf -- compute the intersection of halfspaces about a point
http://www.qhull.org 2020.2.r 2020/08/31
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
Qc - keep coplanar halfspaces
Qi - keep other redundant halfspaces
QJ - joggled input instead of merged facets
Qt - triangulated output
Qhull control options:
Qa - allow input with fewer or more points than coordinates
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 halfspaces for the initial simplex
Qhull extra options:
QGn - print intersection if visible to halfspace n, -n for not
QVn - print intersections for halfspace n, -n if not
Qw - allow option warnings
Q12 - allow wide facets and wide dupridge
Q14 - merge pinched vertices that create a dupridge
T options:
TFn - report summary when n or more facets created
TI file - input file, may be enclosed in single quotes
TO file - output file, may be enclosed in single quotes
Ts - statistics
Tv - verify result: structure, convexity, and in-circle test
Tz - send all output to stdout
Trace options:
T4 - trace at level n, 4=all, 5=mem/gauss, -1= events
Ta - annotate output with message codes
TAn - stop qhull after adding n vertices
TCn - stop qhull after building cone for point n
TVn - stop qhull after adding point n, -n for before
Tc - check frequently during execution
Tf - flush each qh_fprintf for debugging segfaults
TPn - turn on tracing when point n added to hull
TMn - turn on tracing at merge n
TWn - trace merge facets when width > n
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 2-d or 3-d convex hull)
Fn - count plus neighboring intersections for each intersection
FN - count plus intersections for each 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
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
Gc - centrums
GDn - drop dimension n in 3-d and 4-d output
Gh - hyperplane intersections
Gi - inner planes (i.e., halfspace intersections) only
Gn - no planes
Go - outer planes only
Gr - ridges
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
PFn - keep facets whose area is at least n
Pg - print good facets (needs 'QGn' or 'QVn')
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
-? - help with examples
-V - version
qhalf .
Qhull 2020.2.r 2020/08/31
Except for 'F.' and 'PG', upper_case options take an argument.
facet-dump Geomview H0,0-interior incidences mathematica
off-format point-dual summary
Fc-redundant Fd-cdd-in FF-dump-xridge FIDs Fmerges
FMaple Fneighbors FN-intersect FOptions Fp-coordinates
FP-nearest FQhalf Fsummary Fv-halfspace Fx-non-redundant
Gall-points Gcentrums GDrop-dim Ghyperplanes Ginner
Gno-planes Gouter Gpoints Gridges Gvertices
PArea-keep Pdrop-d0:0D0 PFacet-area-keep Pgood PGood-neighbors
PMerge-keep Poutput-forced Pprecision-not
Qallow-short Qbk:0Bk:0-drop Qcoplanar QG-half-good Qi-redundant
QJoggle QRotate Qsearch-all Qtriangulate QVertex-good
Qwarn-allow Q12-allow-wide Q14-merge-pinched
TFacet-log TInput-file TOutput-file Tstatistics Tverify
Tz-stdout
T4-trace Tannotate TAdd-stop Tcheck-often TCone-stop
Tflush TMerge-trace TPoint-trace TVertex-stop TWide-trace
Angle-max Centrum-size Random-dist Ucoplanar-max Wide-outside
qhalf -? # [mar'19] isatty does not work for Git for Windows
qhalf -- halfspace intersection about a point. Qhull 2020.2.r 2020/08/31
input (stdin): [dimension, 1, interior point]
dimension+1, number of halfspaces, 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 each option
-? - this message
-V - version
output options (subset):
s - summary of results (default)
Fp - intersection coordinates
Fv - non-redundant halfspaces incident to each intersection
Fx - non-redundant halfspaces
G - Geomview output (dual convex hull)
m - Mathematica output (dual convex hull)
o - OFF file format (dual convex hull)
QVn - print intersections for halfspace n, -n if not
TI file - input file, may be enclosed in single quotes
TO file - output 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
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: 32
Number of distance tests for merging: 101
Number of distance tests for checking: 48
Number of merged facets: 7
CPU seconds to compute hull (after input): 0.000175
3
12
0 0 -0.5
0 0 -0.5
0 -0.5 0
0 -0.5 0
-0.5 0 0
-0.5 0 0
0.5 0 0
0.5 0 0
0 0.5 0
0 0.5 0
0 0 0.5
0 0 0.5
rbox c | qhull FQ FV n | qhalf s i
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: 10
Number of distance tests for merging: 51
Number of distance tests for checking: 48
Number of merged facets: 1
CPU seconds to compute hull (after input): 0.000114
8
1 0 3
0 1 2
5 1 3
1 5 2
4 0 2
0 4 3
5 4 2
4 5 3
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 1 0 3
3 0 1 2
3 5 1 3
3 1 5 2
3 4 0 2
3 0 4 3
3 5 4 2
3 4 5 3
rbox d D2 | qhull FQ n | qhalf s H0 Fc FP Fn FN FQ Fv Fx
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: 5
CPU seconds to compute hull (after input): 6.8e-05
4
0
0
0
0
0
4
2 1 2
2 0 3
2 0 3
2 1 2
4
2 0 1
2 2 0
2 1 3
2 3 2
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
0
1
3
2
# qhull - printed at end
qhull .
Qhull 2020.2.r 2020/08/31
Except for 'F.' and 'PG', upper-case options take an argument.
delaunay facet-dump Geomview H0,0-interior Halfspace
incidences mathematica normals off-format points
summary voronoi
Farea FArea-total Fcoplanars FCentrums Fd-cdd-in
FD-cdd-out FFacets-xridge Finner FIDs Fmerges
FMaple Fneighbors FNeigh-vertex Fouter FOptions
Fpoint-intersect FPoint-near FQhull Fsummary FSize
Ftriangles Fvertices Fvoronoi FVertex-ave Fxtremes
Gall-points Gcentrums GDrop-dim Ghyperplanes Ginner
Gno-planes Gouter Gpoints Gridges Gtransparent
Gvertices
PArea-keep Pdrop-d0:0D0 PFacet-area-keep Pgood PGood-neighbors
PMerge-keep Poutput-forced Pprecision-not
Qallow-short QbBound-0:0.5 QbB-scale-box Qbb-scale-last Qbk:0Bk:0-drop
Qcoplanar Qinterior QJoggle QRotate Qsearch-all
Qtriangulate QupperDelaunay Qwarn-allow Qxact-merge Qzinfinite
Qfurthest Qgood-only QGood-point Qmax-outside Qrandom
Qvneighbors QVertex-good
Q0-no-premerge Q1-angle-merge 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
Q12-allow-wide Q14-merge-pinched Q15-duplicates
TFacet-log TInput-file TOutput-file Tstatistics Tverify
Tz-stdout
T4-trace Tannotate TAdd-stop Tcheck-often TCone-stop
Tflush TMerge-trace TPoint-trace TRerun TVertex-stop
TWide-trace
Angle-max Centrum-size Error-round Random-dist Ucoplanar-max
Visible-min Wide-outside
qhull -? # [mar'19] isatty does not work for Git for Windows
qhull -- compute convex hulls and related structures. Qhull 2020.2.r 2020/08/31
input (stdin): dimension, number of points, 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
-? - this message
-V - version
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
FA - report total area and volume
Fp - halfspace intersections
FS - total area and volume
Fx - extreme points (convex hull vertices)
G - Geomview output (2-d, 3-d and 4-d)
m - Mathematica output (2-d and 3-d)
o - OFF format (if 'v', outputs Voronoi regions)
QVn - print facets that include point n, -n if not
TI file - input file, may be enclosed in single quotes
TO file - output file, may be enclosed in single quotes
examples:
rbox D4 | qhull Tv 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 d D2 | qhull Qc s f Fx | more 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 Qc rbox c | qhull n
rbox 1000 s | qhull Tv s FA
Convex hull of 1000 points in 3-d:
Number of vertices: 1000
Number of facets: 1996
Statistics for: rbox 1000 s | qhull Tv s FA
Number of points processed: 1000
Number of hyperplanes created: 5544
Number of distance tests for qhull: 25487
CPU seconds to compute hull (after input): 0.01164
Total facet area: 3.1201951
Total volume: 0.51650274
qhull output completed. Verifying that 1000 points are
below 2.1e-15 of the nearest facet.
rbox 10 D2 | qhull d QJ s i TO q_test.log.1
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 QJ s i TO q_test.log.1
Number of points processed: 10
Number of hyperplanes created: 28
Number of facets in hull: 16
Number of distance tests for qhull: 47
CPU seconds to compute hull (after input): 0.000126
Input joggled by: 4e-11
cat q_test.log.1
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
rbox 10 D2 | qhull v Qbb Qt p
2
14
-0.1294381801544404 -0.07247409101984714
0.08267689532419747 -0.2397644955865706
0.1295260566906465 1.716033573116837
0.1740355150742391 0.5317519038435655
0.1851415205797575 0.3882545794457364
-0.9065939866848107 -0.2962957610652135
-0.1954805620516266 -0.07111892482963184
-0.1407581310832468 0.7233857048236082
-0.1676297826663962 0.2080621273999375
0.05868313821742954 0.06632066014880154
0.08806341399736994 0.1054080604689985
0.4761588899009253 -0.03168366595227294
3.094213357897477 -0.064721945677682
0.5410515627308725 0.2115615434955919
rbox 10 D2 | qhull d Qu QJ m
{
Polygon[{{ 0.37903124, 0.37797944, 0.29963416},
{ -0.02222276, -0.49797278, 0.23792952},
{ -0.42854319, 0.47458265, 0.49797278}}],
Polygon[{{ 0.34431227, -0.14373122, 0.06080143},
{ -0.02222276, -0.49797278, 0.23792952},
{ 0.37903124, 0.37797944, 0.29963416}}]}
rbox 10 D2 | qhull v Qu QJ o
2
3 10 1
-10.101 -10.101
-0.06934933488573394 0.05349366577046777
-0.3051278692468022 0.16149850548211
3 0 2 1
2 0 1
0
0
3 0 1 2
0
0
0
2 0 2
0
rbox c d D2 | qhull Qc s f Fx
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 | qhull Qc s f Fx
Number of points processed: 4
Number of hyperplanes created: 6
Number of distance tests for qhull: 35
CPU seconds to compute hull (after input): 7.7e-05
Vertices and facets:
- p2(v2): 0.5 -0.5
- p0(v1): -0.5 -0.5
- p1(v3): -0.5 0.5
- p3(v4): 0.5 0.5
- f1
- flags: bottom simplicial
- normal: -0 -1
- offset: -0.5
- coplanar set(furthest p4):
p4: 0 -0.5
furthest distance= 0
- vertices: p2(v2) p0(v1)
- neighboring facets: f2 f4
- f2
- flags: top simplicial
- normal: -1 0
- offset: -0.5
- coplanar set(furthest p6):
p6: -0.5 0
furthest distance= 0
- vertices: p1(v3) p0(v1)
- neighboring facets: f1 f5
- f4
- flags: bottom simplicial
- normal: 1 -0
- offset: -0.5
- coplanar set(furthest p7):
p7: 0.5 0
furthest distance= 0
- vertices: p3(v4) p2(v2)
- neighboring facets: f1 f5
- f5
- flags: top simplicial
- normal: 0 1
- offset: -0.5
- coplanar set(furthest p5):
p5: 0 0.5
furthest distance= 0
- vertices: p3(v4) p1(v3)
- neighboring facets: f2 f4
4
0
2
3
1
rbox c | qhull FV n | qhull H Fp
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
rbox d D12 | qhull QR0 FA
Convex hull of 24 points in 12-d:
Number of vertices: 24
Number of facets: 4096
Statistics for: rbox d D12 | qhull QR0 FA QR1695073038
Number of points processed: 24
Number of hyperplanes created: 4108
Number of distance tests for qhull: 4215
Number of distance tests for merging: 121143
Number of distance tests for checking: 98304
Number of merged facets: 2036
CPU seconds to compute hull (after input): 0.09463
Approximate facet area: 1.735661e-07
Approximate volume: 2.0876757e-09
rbox c D7 | qhull FA TF1000
At 21:37:18 & 0.006415 CPU secs, qhull has created 1048 facets and merged 469.
The current hull contains 230 facets and 24 vertices. There are 104
outside points. Next is point p79(v25), 0.66 above f145.
At 21:37:18 & 0.015089 CPU secs, qhull has created 2146 facets and merged 1272.
The current hull contains 273 facets and 31 vertices. There are 97
outside points. Next is point p120(v32), 0.54 above f437.
At 21:37:18 & 0.024802 CPU secs, qhull has created 3310 facets and merged 2244.
The current hull contains 243 facets and 36 vertices. There are 92
outside points. Next is point p60(v37), 0.54 above f1338.
At 21:37:18 & 0.033486 CPU secs, qhull has created 4322 facets and merged 3099.
The current hull contains 249 facets and 42 vertices. There are 86
outside points. Next is point p30(v43), 0.54 above f2005.
At 21:37:18 & 0.043619 CPU secs, qhull has created 5491 facets and merged 4196.
The current hull contains 186 facets and 48 vertices. There are 80
outside points. Next is point p21(v49), 0.5 above f2995.
At 21:37:18 & 0.054173 CPU secs, qhull has created 6589 facets and merged 5175.
The current hull contains 194 facets and 53 vertices. There are 75
outside points. Next is point p56(v54), 0.28 above f3731.
At 21:37:18 & 0.06664 CPU secs, qhull has created 7867 facets and merged 6337.
The current hull contains 203 facets and 60 vertices. There are 68
outside points. Next is point p76(v61), 0.29 above f5879.
At 21:37:18 & 0.07872 CPU secs, qhull has created 8971 facets and merged 7362.
The current hull contains 179 facets and 67 vertices. There are 61
outside points. Next is point p80(v68), 0.23 above f7175.
At 21:37:18 & 0.09102 CPU secs, qhull has created 9984 facets and merged 8352.
The current hull contains 104 facets and 77 vertices. There are 51
outside points. Next is point p96(v78), 0.41 above f6748.
At 21:37:18 & 0.10502 CPU secs, qhull has created 10990 facets and merged 9326.
The current hull contains 54 facets and 90 vertices. There are 38
outside points. Next is point p18(v91), 0.41 above f10178.
At 21:37:18 & 0.11777 CPU secs, qhull has created 11996 facets and merged 10295.
The current hull contains 34 facets and 114 vertices. There are 14
outside points. Next is point p19(v115), 0.38 above f11792.
At 21:37:18 & 0.12662 CPU secs, qhull has created 12860 facets and merged 11072.
The current hull contains 14 facets and 128 vertices. Last point was p77
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 FA TF1000
Number of points processed: 128
Number of hyperplanes created: 1789
Number of distance tests for qhull: 10122
Number of distance tests for merging: 87203
Number of distance tests for checking: 0
Number of merged facets: 11072
First post-merge with 'C4.4e-15' and 'A1.8e+308'
At 21:37:18 & 0.12834 CPU secs, qhull has created 12860 facets and merged 11072.
The current hull contains 14 facets and 128 vertices. Last point was p77
Testing all coplanar points.
computing area of each facet and volume of the convex hull
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 FA TF1000
Number of points processed: 128
Number of hyperplanes created: 1789
Number of distance tests for qhull: 10122
Number of distance tests for merging: 87371
Number of distance tests for checking: 1792
Number of merged facets: 11072
CPU seconds to compute hull (after input): 0.1286
Approximate facet area: 14
Approximate volume: 1
rbox y 1000 W0 | qhull Qc
Convex hull of 1004 points in 3-d:
Number of vertices: 4
Number of coplanar points: 1000
Number of facets: 4
Statistics for: rbox y 1000 W0 | qhull Qc
Number of points processed: 4
Number of hyperplanes created: 4
Number of distance tests for qhull: 11000
CPU seconds to compute hull (after input): 0.000893
rbox c | qhull n
4
6
-0 -0 -1 -0.5
0 -1 0 -0.5
1 -0 -0 -0.5
-1 -0 -0 -0.5
0 1 -0 -0.5
-0 -0 1 -0.5
rbox c | qhull TA1
Early exit due to 'TAn', 'TVn', 'TCn', 'TRn', or precision error with 'QJn'.
Convex hull of 8 points in 3-d:
Number of vertices: 5
Number of facets: 6
Statistics for: rbox c | qhull TA1
Number of points processed: 5
Number of hyperplanes created: 8
Number of distance tests for qhull: 25
CPU seconds to compute hull (after input): 7.4e-05
rbox 10 s | qhull C1e-5 T1P-1f
[QH1008]qh_readpoints: read in 10 3-dimensional points
[QH0013]qh_initqhull_globals: for rbox 10 s | qhull C1e-5 T1P-1f
Trace level T1, IStracing 0, point TP-1, merge TM0, dist TW1.8e+308, qh.tracefacet_id -1, traceridge_id -1, tracevertex_id -1, last qh.RERUN 0, rbox 10 s | qhull C1e-5 T1P-1f
Options selected for Qhull 2020.2.r 2020/08/31:
run-id 574488564 Centrum-postmerge 1e-05 Trace-point -1 Tflush _pre-merge
_max-width 0.88 Error-roundoff 6.7e-16 _one-merge 3e-05
_near-inside 0.00015 Visible-distance 1.3e-15 U-max-coplanar 1.3e-15
Width-outside 2.7e-15 _wide-facet 8e-15
[QH2112]qh_qhull: finished qh_buildhull and qh_postmerge, start tracing (TP-1)
[QH1022]qh_check_maxout: check and update qh.min_vertex -6.7e-16 and qh.max_outside 1.1e-16
[QH1055]qh_check_maxout: determine actual maxoutside
[QH1024]qh_check_maxout: p7(v6) is qh.min_vertex -6.7e-16 below facet f4. Point p2 for f4 is qh.max_outside 1.1e-16 above f4. 0 points are outside of not-good facets
[QH1036]Qhull: algorithm completed
[QH1027]qh_checkpolygon: check all facets from f4, qh.NEWtentative? 0
[QH1062]qh_checkconvex: check that facets are not-flipped and that their centrums are convex by qh.DISTround ('En', 'Rn')
Convex hull of 10 points in 3-d:
Number of vertices: 10
Number of facets: 16
Statistics for: rbox 10 s | qhull C1e-5 T1P-1f
Number of points processed: 10
Number of hyperplanes created: 27
Number of distance tests for qhull: 51
CPU seconds to compute hull (after input): 0.000252
[QH1006]qh_freeqhull: free global memory
[QH1005]qh_freebuild: free memory from qh_inithull and qh_buildhull
[QH1061]qh_freeqhull: clear qhT except for qh.qhmem and qh.qhstat
set +v
=== check quality of Qhull for mb-lxc-02 Mon Sep 18 21:37:18 UTC 2023
rbox 1000 W0 | qhull QR2 QJ s Fs Tv
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: 33543
CPU seconds to compute hull (after input): 0.00452
After 1 retries, input joggled by: 2.9e-11
10 3 1000 144 284 144 284 0 0 33 0
2 5.045982607091333e-11 -5.045982607091333e-11
Output completed. Verifying that all points are below 2.9e-15 of
all facets. Will make 284000 distance computations.
rbox 1000 W0 | qhull QR2 s Fs Tv
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: 18050
Number of distance tests for merging: 3163
Number of distance tests for checking: 15481
Number of merged facets: 92
CPU seconds to compute hull (after input): 0.003241
10 3 1000 84 98 84 98 0 6 13 0
2 1.942124858599573e-15 -1.241679291552168e-15
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: 110
Number of coplanar points: 890
Number of facets: 57
Number of non-simplicial facets: 57
Statistics for: rbox 1000 s | qhull C0.02 Qc Tv
Number of points processed: 1000
Number of hyperplanes created: 5544
Number of distance tests for qhull: 81537
Number of distance tests for merging: 80706
Number of distance tests for checking: 8256
Number of merged facets: 1939
CPU seconds to compute hull (after input): 0.03904
Maximum distance of vertex below facet: -0.079 (1.3x)
Output completed. Verifying that all points are below outer planes of
all facets. Will make 57000 distance computations.
rbox 500 s D4 | qhull C0.01 Qc Tv
Convex hull of 500 points in 4-d:
Number of vertices: 462
Number of coplanar points: 38
Number of facets: 345
Number of non-simplicial facets: 332
Statistics for: rbox 500 s D4 | qhull C0.01 Qc Tv
Number of points processed: 500
Number of hyperplanes created: 11283
Number of distance tests for qhull: 42789
Number of distance tests for merging: 217359
Number of distance tests for checking: 12552
Number of merged facets: 2821
CPU seconds to compute hull (after input): 0.06943
Maximum distance of vertex below facet: -0.08 (2.0x)
Output completed. Verifying that all points are below outer planes of
all facets. Will make 172500 distance computations.
rbox 1000 s | qhull C-0.02 Qc Tv
Convex hull of 1000 points in 3-d:
Number of vertices: 52
Number of coplanar points: 948
Number of facets: 47
Number of non-simplicial facets: 38
Statistics for: rbox 1000 s | qhull C-0.02 Qc Tv
Number of points processed: 53
Number of hyperplanes created: 214
Number of distance tests for qhull: 47445
Number of distance tests for merging: 2943
Number of distance tests for checking: 19555
Number of merged facets: 107
CPU seconds to compute hull (after input): 0.005866
Maximum distance of point above facet: 0.039 (0.7x)
Maximum distance of vertex below facet: -0.057 (0.9x)
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: 126
Number of coplanar points: 874
Number of facets: 206
Number of non-simplicial facets: 148
Statistics for: rbox 1000 s D4 | qhull C-0.01 Qc Tv
Number of points processed: 126
Number of hyperplanes created: 1371
Number of distance tests for qhull: 414344
Number of distance tests for merging: 73447
Number of distance tests for checking: 124140
Number of merged facets: 1331
CPU seconds to compute hull (after input): 0.05813
Maximum distance of point above facet: 0.068 (1.7x)
Maximum distance of vertex below facet: -0.1 (2.6x)
Output completed. Verifying that all points are below outer planes of
all facets. Will make 206000 distance computations.
rbox 200 s D5 | qhull C-0.01 Qx Qc Tv
Convex hull of 200 points in 5-d:
Number of vertices: 161
Number of coplanar points: 39
Number of facets: 416
Number of non-simplicial facets: 365
Statistics for: rbox 200 s D5 | qhull C-0.01 Qx Qc Tv
Number of points processed: 161
Number of hyperplanes created: 4552
Number of distance tests for qhull: 229096
Number of distance tests for merging: 309307
Number of distance tests for checking: 54701
Number of merged facets: 6165
CPU seconds to compute hull (after input): 0.1112
Maximum distance of point above facet: 0.059 (1.2x)
Maximum distance of vertex below facet: -0.1 (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 83200 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: 4454
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: 19805
Number of distance tests for qhull: 33228
Number of distance tests for merging: 330047
Number of distance tests for checking: 88758
Number of merged facets: 3862
CPU seconds to compute hull (after input): 0.168
Maximum distance of point above facet: 0.003 (0.5x)
Maximum distance of vertex below facet: -0.014 (2.3x)
QH7076 qhull input warning: exact merge ('Qx'). Verify may report that a point is outside of a facet. See qh-optq.htm#Qx
Output completed. Verifying that all points are below outer planes of
all facets. Will make 445400 distance computations.
rbox 1000 W1e-4 | qhull C-1e-6 Qc Tv
Convex hull of 1000 points in 3-d:
Number of vertices: 145
Number of coplanar points: 87
Number of facets: 243
Number of non-simplicial facets: 29
Statistics for: rbox 1000 W1e-4 | qhull C-1e-6 Qc Tv
Number of points processed: 185
Number of hyperplanes created: 940
Number of distance tests for qhull: 40788
Number of distance tests for merging: 7744
Number of distance tests for checking: 6136
Number of merged facets: 143
CPU seconds to compute hull (after input): 0.006587
Maximum distance of point above facet: 8.3e-07 (0.3x)
Maximum distance of vertex below facet: -3.9e-06 (1.3x)
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: 291
Number of coplanar points: 645
Number of facets: 1270
Number of non-simplicial facets: 150
Statistics for: rbox 1000 W5e-4 D4 | qhull C-1e-5 Qc Tv
Number of points processed: 365
Number of hyperplanes created: 6253
Number of distance tests for qhull: 173452
Number of distance tests for merging: 91161
Number of distance tests for checking: 56354
Number of merged facets: 1354
CPU seconds to compute hull (after input): 0.04644
Maximum distance of point above facet: 0.00013 (3.3x)
Maximum distance of vertex below facet: -0.00021 (5.4x)
Output completed. Verifying that all points are below outer planes of
all facets. Will make 1270000 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: 306
Number of coplanar points: 33
Number of facets: 5557
Number of non-simplicial facets: 287
Statistics for: rbox 400 W1e-3 D5 | qhull C-1e-5 Qx Qc Tv
Number of points processed: 338
Number of hyperplanes created: 24498
Number of distance tests for qhull: 262194
Number of distance tests for merging: 271068
Number of distance tests for checking: 90075
Number of merged facets: 1472
CPU seconds to compute hull (after input): 0.153
Maximum distance of point above facet: 5.5e-05 (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 2222800 distance computations.
set +v
=== check input format etc. Mon Sep 18 21:37:19 UTC 2023
qhull <<EOF
2 4 input comment
1 0 1 1 1 2 0 0
EOF
Convex hull of 4 points in 2-d:
Number of vertices: 3
Number of facets: 3
Statistics for: input comment | qhull
Number of points processed: 3
Number of hyperplanes created: 4
Number of distance tests for qhull: 8
CPU seconds to compute hull (after input): 8e-05
qhull <<EOF
2 4 input comment
1 0 1 1 1 2 0 0 0
EOF
QH6410 qhull error: instead of 4 points in 2-d, input contains 4 points and 1 extra coordinates.
Line 1 is the first comment.
Line 2 is the first point.
Line 2 is the first long line.
Override with option 'Qa' (allow-short)
While executing: input comment | qhull
Options selected for Qhull 2020.2.r 2020/08/31:
run-id 574505371 _maxoutside 0
qhull Qa <<EOF
2 4 input comment
1 0 1 1 1 2 0 0 0
EOF
QH7073 qhull warning: instead of 4 points in 2-d, input contains 4 points and 1 extra coordinates.
Line 1 is the first comment.
Line 2 is the first point.
Line 2 is the first long line.
Continuing with 4 points.
Convex hull of 4 points in 2-d:
Number of vertices: 3
Number of facets: 3
Statistics for: input comment | qhull Qa
Number of points processed: 3
Number of hyperplanes created: 4
Number of distance tests for qhull: 8
CPU seconds to compute hull (after input): 6.2e-05
qhull <<EOF
2 4 input comment
1 0 1 1 1 2 0
EOF
QH6410 qhull error: instead of 4 points in 2-d, input contains 3 points and 1 extra coordinates.
Line 1 is the first comment.
Line 2 is the first point.
Line 2 is the first long line.
Override with option 'Qa' (allow-short)
While executing: input comment | qhull
Options selected for Qhull 2020.2.r 2020/08/31:
run-id 574505371 _maxoutside 0
qhull Qa <<EOF
2 4 input comment
1 0 1 1 1 2 0
EOF
QH7073 qhull warning: instead of 4 points in 2-d, input contains 3 points and 1 extra coordinates.
Line 1 is the first comment.
Line 2 is the first point.
Line 2 is the first long line.
Continuing with 3 points.
QH6013 qhull input error: input is less than 2-dimensional since all points have the same x coordinate 1
While executing: input comment | qhull Qa
Options selected for Qhull 2020.2.r 2020/08/31:
run-id 574505371 Qallow-short _pre-merge _zero-centrum _max-width 2
Error-roundoff 1.7e-15 _one-merge 8.6e-15 _near-inside 4.3e-14
Visible-distance 3.4e-15 U-max-coplanar 3.4e-15 Width-outside 6.9e-15
_wide-facet 2.1e-14 _maxoutside 1e-14
qhull <<EOF
2
4 input comment
1 #another comment
0 1 1 1 2 0
EOF
QH6410 qhull error: instead of 4 points in 2-d, input contains 3 points and 1 extra coordinates.
Line 2 is the first comment.
Line 3 is the first point.
Line 3 is the first short line.
Line 4 is the first long line.
Override with option 'Qa' (allow-short)
While executing: input comment | qhull
Options selected for Qhull 2020.2.r 2020/08/31:
run-id 574505371 _maxoutside 0
qhull <<EOF
2 4 1 0 1 1 1 2 0 0
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: 8
CPU seconds to compute hull (after input): 6.8e-05
qhull d Qz <<EOF
2 5 1 0 1 1 0 1 0 0 0
EOF
QH6410 qhull error: instead of 5 points in 2-d, input contains 4 points and 1 extra coordinates.
Line 1 is the first point.
Line 1 is the first long line.
Override with option 'Qa' (allow-short)
While executing: | qhull d Qz
Options selected for Qhull 2020.2.r 2020/08/31:
run-id 574505371 delaunay Qz-infinity-point _maxoutside 0
qhull d Q8 Qz <<EOF
2 5 1 0 1 1 0 1 0 0 0
EOF
QH6410 qhull error: instead of 5 points in 2-d, input contains 4 points and 1 extra coordinates.
Line 1 is the first point.
Line 1 is the first long line.
Override with option 'Qa' (allow-short)
While executing: | qhull d Q8 Qz
Options selected for Qhull 2020.2.r 2020/08/31:
run-id 574505371 delaunay Q8-no-near-inside Qz-infinity-point
_maxoutside 0
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 -0.5
0 -0.5 0
-0.5 0 0
0.5 0 0
0 0.5 0
0 0 0.5
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-15 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: 45
CPU seconds to compute hull (after input): 0.000166
Output completed. Verifying that all points are below 2.5e-15 of
all facets. Will make 99 distance computations.
set +v
=== check rbox Mon Sep 18 21:37:19 UTC 2023
rbox 3 n D2
2
3
0.2234321234034673 0.2236923805658635
-0.4021654933711192 -0.1954478539484067
0.1079163058734651 -0.2506519423338137
rbox 3 D2
2 rbox 3 D2
3
-0.3570490315156514 0.07692619792830779
-0.1013959339832849 -0.1614655765345931
0.2480525339469802 0.01893219260399437
rbox 3 h D2
rbox 3 h D2
begin
3 3 real
1 0.16093073846859 -0.2370837309743126
1 0.3337314574362071 0.02459860548805315
1 0.4287583324394733 0.141286041719174
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
6.07777520648928 9.167769643634342
2.704250554278727 -9.661033665445665
7.007182209759188 9.71126632738045
rbox 3 B10 D2 C2,1E-13,1
2 rbox 3 B10 D2 C2,1E-13,1
5
-9.999843472614739 -7.369244235911633
-9.999843472614687 -7.369244235911641
-9.999843472614732 -7.369244235911689
-9.05910767527214 3.577294343688799
3.585928123058684 8.693857927521558
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 r D2
2 rbox 8 L2 r D2
14
0.5 0
0.365341024366395 0.06484834485976565
0.365341024366395 -0.06484834485976565
0.2225209339563144 0.108902508397385
0.2225209339563144 -0.108902508397385
0.07473009358642427 0.1311783933967415
0.07473009358642427 -0.1311783933967415
-0.07473009358642424 0.1311783933967415
-0.07473009358642424 -0.1311783933967415
-0.2225209339563144 0.108902508397385
-0.2225209339563144 -0.108902508397385
-0.365341024366395 0.06484834485976565
-0.365341024366395 -0.06484834485976565
-0.5 0
rbox 8 L2 D2 C1,1E-13,2
2 rbox 8 L2 D2 C1,1E-13,2
10
-0.4014722424908947 -0.04984578721860422
-0.4014722424908402 -0.04984578721870322
-0.3537770307209493 0.06930438433003638
-0.353777030720961 0.06930438433002231
-0.4536521880095642 -0.02515341795345205
0.09926382627500697 0.1290357464938974
0.4803069842605469 -0.01107504705944207
-0.4407884497398482 0.03158561585376829
-0.43365738760839 -0.03505243423659854
0.1399579896503841 -0.1241320388139711
rbox 4 L4 r D3
3 rbox 4 L4 r D3
12
0.5 0 0
0.25 0 0.04782181019473453
0.25 0 -0.04782181019473453
3.061616997868383e-17 0.5 0
1.530808498934192e-17 0.25 0.04782181019473453
1.530808498934192e-17 0.25 -0.04782181019473453
-0.5 6.123233995736766e-17 0
-0.25 3.061616997868383e-17 0.04782181019473453
-0.25 3.061616997868383e-17 -0.04782181019473453
-9.184850993605148e-17 -0.5 0
-4.592425496802574e-17 -0.25 0.04782181019473453
-4.592425496802574e-17 -0.25 -0.04782181019473453
rbox 4 L4 s D5 W1e-3
5 rbox 4 L4 s D5 W1e-3
4
-0.1779876601833928 -0.1311655069863711 0.09099061083332423 -0.0147197628642461 0.0491007664448838
0.08530477699633816 0.08551065958609008 0.2073152333839907 -0.05556059038062115 0.04824638578429845
-0.2043906348252541 0.01359444539903207 0.07833891569611255 -0.2253375927975145 0.03863248544102459
0.07678497944972421 0.03657959246981071 0.1769587053753909 0.1423142450665639 -0.04874898497507386
rbox 4 L4 s D5 W1e-3 C1,1E-12
5 rbox 4 L4 s D5 W1e-3 C1,1E-12
8
0.0002946652970602764 0.01409557808797486 -0.004433138692070485 0.02830701320254122 0.06321803825410263
0.0002946652976213024 0.01409557808713995 -0.004433138692549452 0.02830701320252706 0.0632180382541969
0.0395007958298621 0.08424796754402081 0.05096384542027204 -0.09702947578293189 -0.05829868829611209
0.03950079583077567 0.08424796754434548 0.05096384542100907 -0.0970294757837081 -0.05829868829594329
-0.04232294908783042 0.03923635869829208 -0.002523757174853624 -0.007690531229328437 -0.06262981797685649
-0.04232294908753993 0.0392363586986717 -0.00252375717458491 -0.007690531229051642 -0.06262981797676299
-0.1462855747417375 0.02301178389047249 0.1483804611920676 -0.1253035217565061 -0.04852571310121132
-0.1462855747427029 0.0230117838896562 0.1483804611927586 -0.1253035217563368 -0.04852571310078617
rbox y
3 rbox y
4
-0.3062920647731908 0.1492658412542808 -0.2890111205997049
-0.4099055704752966 -0.2829236833219637 -0.09834729097629646
0.07707741817187275 0.4401626986825491 -0.1855306003107974
-0.2128018845923262 0.4387234094913336 -0.3756640258949846
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 M3,4 C1,1E-14
3 rbox 10 M3,4 C1,1E-14
20
0 0 0
2.814732056869875e-15 7.201579527185838e-15 -3.053021210295168e-15
3 4 0
3.000000000000008 3.999999999999992 4.994823238807566e-15
6 8 0
6.000000000000008 7.999999999999996 1.743024766205834e-15
-4 3 0
-4.000000000000005 2.999999999999993 -4.748389036160324e-15
-1 7 0
-1.000000000000006 7.000000000000004 -1.260957588684708e-16
2 11 0
2.000000000000001 11.00000000000001 2.063112521602872e-16
-8 6 0
-7.999999999999993 6.000000000000001 6.666691421220716e-16
-5 10 0
-4.999999999999996 9.999999999999991 4.071436025268804e-15
-2 14 0
-1.999999999999991 14 -7.015196799314765e-15
0 0 5
-4.412629440811118e-15 -3.063055438048258e-15 4.999999999999999
rbox 27 M1,0,1
3 rbox 27 M1,0,1
27
0 0 0
1 0 0
2 0 0
0 1 0
1 1 0
2 1 0
0 2 0
1 2 0
2 2 0
0 0 1
1 0 1
2 0 1
0 1 1
1 1 1
2 1 1
0 2 1
1 2 1
2 2 1
0 0 2
1 0 2
2 0 2
0 1 2
1 1 2
2 1 2
0 2 2
1 2 2
2 2 2
rbox 10 L4 r D3 | qhull Tcv
Convex hull of 30 points in 3-d:
Number of vertices: 30
Number of facets: 22
Number of non-simplicial facets: 22
Statistics for: rbox 10 L4 r D3 | qhull Tcv
Number of points processed: 30
Number of hyperplanes created: 62
Number of distance tests for qhull: 307
Number of distance tests for merging: 765
Number of distance tests for checking: 730
Number of merged facets: 43
CPU seconds to compute hull (after input): 0.001327
Output completed. Verifying that all points are below outer planes of
all facets. Will make 660 distance computations.
rbox 10 L4 s D5 W1e-3 | qhull Tcv
Convex hull of 10 points in 5-d:
Number of vertices: 10
Number of facets: 40
Statistics for: rbox 10 L4 s D5 W1e-3 | qhull Tcv
Number of points processed: 10
Number of hyperplanes created: 64
Number of distance tests for qhull: 69
CPU seconds to compute hull (after input): 0.000291
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 2.2e-15 of
all facets. Will make 400 distance computations.
rbox 10 L4 s D5 W1e-3 C1,1E-12 | qhull Tcv
Convex hull of 20 points in 5-d:
Number of vertices: 19
Number of facets: 144
Number of non-simplicial facets: 2
Statistics for: rbox 10 L4 s D5 W1e-3 C1,1E-12 | qhull Tcv
Number of points processed: 19
Number of hyperplanes created: 269
Number of distance tests for qhull: 413
Number of distance tests for merging: 2659
Number of distance tests for checking: 1264
Number of merged facets: 6
CPU seconds to compute hull (after input): 0.001733
Maximum distance of point above facet: 3.9e-15 (0.4x)
Maximum distance of vertex below facet: -3.2e-15 (0.3x)
QH7076 qhull input warning: exact merge ('Qx'). Verify may report that a point is outside of a facet. See qh-optq.htm#Qx
Output completed. Verifying that all points are below outer planes of
all facets. Will make 2880 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: 28
Number of distance tests for qhull: 47
CPU seconds to compute hull (after input): 0.000161
Output completed. Verifying that all points are below 1.7e-15 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: 52
CPU seconds to compute hull (after input): 0.000198
Output completed. Verifying that all points are below 2.4e-15 of
all facets. Will make 260 distance computations.
rbox y r 100 W0 O0.5 | qhull s p Tcv
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: 1100
CPU seconds to compute hull (after input): 0.000154
3
4
1 0.5 0.5
0.5 1 0.5
0.5 0.5 1
0 0 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: 76
Number of distance tests for qhull: 1284
Number of distance tests for merging: 606
Number of distance tests for checking: 1052
Number of merged facets: 15
CPU seconds to compute hull (after input): 0.001033
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: 84
CPU seconds to compute hull (after input): 0.000809
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-15 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: 88
Number of distance tests for qhull: 46
CPU seconds to compute hull (after input): 0.000664
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-15 of
all facets. Will make 840 distance computations.
rbox 1000 D4 | qhull s i A-0.97 C0.2 A0.7 Tcv
Convex hull of 1000 points in 4-d:
Number of vertices: 16
Number of facets: 8
Number of non-simplicial facets: 8
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: 2352
Number of distance tests for qhull: 505738
Number of distance tests for merging: 119874
Number of distance tests for checking: 13386
Number of merged facets: 1929
CPU seconds to compute hull (after input): 0.09231
Maximum distance of point above facet: 0.04
Maximum distance of vertex below facet: -0.76 (0.5x)
96
117 465 771 856
117 670 120 465
117 771 120 299
117 456 771 299
117 771 456 856
117 675 465 856
117 675 456 299
117 120 771 465
117 456 675 856
117 675 670 465
117 120 670 675
117 120 675 299
118 530 456 299
118 914 530 299
118 675 456 856
118 675 856 380
118 380 856 837
118 530 914 380
118 530 380 837
118 675 914 299
118 856 530 837
118 456 530 856
118 456 675 299
118 914 675 380
119 380 530 837
119 639 380 837
119 111 639 638
119 111 638 837
119 530 750 111
119 638 639 837
119 530 111 837
119 914 530 380
119 750 914 639
119 914 750 530
119 111 750 639
119 639 914 380
120 750 530 111
120 771 750 111
120 530 771 111
120 914 750 299
120 771 456 299
120 771 530 456
120 530 914 299
120 750 914 530
120 456 530 299
120 750 120 299
120 120 771 299
120 771 120 750
121 670 675 465
121 856 380 837
121 638 856 837
121 639 670 638
121 670 465 638
121 380 639 837
121 639 638 837
121 465 856 638
121 856 675 380
121 675 639 380
121 465 675 856
121 675 670 639
122 120 670 465
122 750 111 639
122 111 771 638
122 771 465 638
122 465 670 638
122 771 120 465
122 670 639 638
122 120 750 639
122 750 771 111
122 670 120 639
122 639 111 638
122 120 771 750
123 856 465 638
123 771 465 856
123 465 771 638
123 530 856 837
123 111 530 837
123 856 638 837
123 456 771 856
123 530 456 856
123 771 530 111
123 638 111 837
123 771 111 638
123 530 771 456
124 914 675 299
124 750 120 639
124 750 914 299
124 914 639 380
124 675 120 299
124 639 675 380
124 670 675 639
124 675 914 380
124 120 670 639
124 914 750 639
124 120 750 299
124 670 120 675
Output completed. Verifying that all points are below outer planes of
all facets. Will make 8000 distance computations.
rbox 3 D2 | qhull Qb0B1:-2 p
2
3
-0.5 -2
-0.1839506649197531 -0.1614655765345934
0.2480525339469802 -1.552736350137872
rbox 100 r D2 | qhull Pd0:0.7 PD0:0.8 Pg n Tcv
3
6
0.7501110696304588 0.6613118653236527 -0.4997532801828658
0.7071067811865485 0.7071067811865467 -0.4997532801828658
0.7501110696304543 -0.6613118653236579 -0.4997532801828658
0.7901550123756914 0.6129070536529753 -0.4997532801828658
0.7901550123756885 -0.6129070536529789 -0.4997532801828659
0.707106781186544 -0.7071067811865511 -0.4997532801828658
Output completed. Verifying that all points are below 1.3e-15 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: 36
Number of facets: 20
Number of non-simplicial facets: 20
Statistics for: rbox 1000 s | qhull C0.05 Tcv
Number of points processed: 1000
Number of hyperplanes created: 5544
Number of distance tests for qhull: 50001
Number of distance tests for merging: 82277
Number of distance tests for checking: 23318
Number of merged facets: 1976
CPU seconds to compute hull (after input): 0.1522
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 20000 distance computations.
rbox 1000 s t | qhull Qm C0.05 Tcv
Convex hull of 1000 points in 3-d:
Number of vertices: 46
Number of facets: 25
Number of non-simplicial facets: 25
Statistics for: rbox 1000 s t1695073040 | qhull Qm C0.05 Tcv
Number of points processed: 1000
Number of hyperplanes created: 5446
Number of distance tests for qhull: 55434
Number of distance tests for merging: 81210
Number of distance tests for checking: 23242
Number of merged facets: 1971
CPU seconds to compute hull (after input): 0.1588
Maximum distance of vertex below facet: -0.19 (1.3x)
Output completed. Verifying that all points are below outer planes of
all facets. Will make 25000 distance computations.
rbox 500 D2 | qhull n A-0.95 C0.1 Tcv
3
4
0.004814116480453948 0.9999884120741163 -0.4852084337990873
-0.9999815737204624 -0.006070602898184517 -0.4913197370926178
-0.006423098021811921 -0.9999793716931376 -0.4958250456626817
0.9999972817907392 0.002331611273993484 -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: 226
Number of hyperplanes created: 1612
Number of distance tests for qhull: 9967
CPU seconds to compute hull (after input): 0.0235
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, 0.00000000, 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}}]}
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, 0.00000000, 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]]));
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: 5
CPU seconds to compute hull (after input): 7.5e-05
Output completed. Verifying that all points are below 1.3e-15 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: 5
Number of distance tests for qhull: 3
CPU seconds to compute hull (after input): 7.4e-05
Output completed. Verifying that all points are below 1.3e-15 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: 34
CPU seconds to compute hull (after input): 0.000109
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-15 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: 10
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): 0.000136
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: 61
Number of distance tests for qhull: 162
CPU seconds to compute hull (after input): 0.000328
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-15 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: 23
Number of distance tests for merging: 146
Number of distance tests for checking: 154
Number of merged facets: 4
CPU seconds to compute hull (after input): 0.000245
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: 296
Number of distance tests for qhull: 787
CPU seconds to compute hull (after input): 0.002472
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-15 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: 36
Number of distance tests for qhull: 46
Number of distance tests for merging: 517
Number of distance tests for checking: 320
Number of merged facets: 11
CPU seconds to compute hull (after input): 0.000429
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: 4843
CPU seconds to compute hull (after input): 0.01484
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-15 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: 69
Number of distance tests for qhull: 87
Number of distance tests for merging: 1184
Number of distance tests for checking: 768
Number of merged facets: 26
CPU seconds to compute hull (after input): 0.00089
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: 162
Number of distance tests for merging: 2645
Number of distance tests for checking: 1792
Number of merged facets: 57
CPU seconds to compute hull (after input): 0.001856
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: 5
CPU seconds to compute hull (after input): 7e-05
Output completed. Verifying that all points are below 1.3e-15 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: 34
Number of distance tests for merging: 96
Number of distance tests for checking: 100
Number of merged facets: 6
CPU seconds to compute hull (after input): 0.000191
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: 25
Number of distance tests for qhull: 167
Number of distance tests for merging: 510
Number of distance tests for checking: 412
Number of merged facets: 36
CPU seconds to compute hull (after input): 0.000802
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: 86
Number of distance tests for qhull: 721
Number of distance tests for merging: 2647
Number of distance tests for checking: 1810
Number of merged facets: 210
CPU seconds to compute hull (after input): 0.005896
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: 357
Number of distance tests for qhull: 2570
Number of distance tests for merging: 14388
Number of distance tests for checking: 8642
Number of merged facets: 1488
CPU seconds to compute hull (after input): 0.0642
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: 1826
Number of distance tests for qhull: 9654
Number of distance tests for merging: 89631
Number of distance tests for checking: 1960
Number of merged facets: 11535
CPU seconds to compute hull (after input): 0.1258
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: 62
Number of distance tests for qhull: 138
CPU seconds to compute hull (after input): 0.000318
Output completed. Verifying that all points are below 2.1e-15 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: 897
CPU seconds to compute hull (after input): 0.001894
Output completed. Verifying that all points are below 1.3e-15 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: 1690
CPU seconds to compute hull (after input): 0.004756
Output completed. Verifying that all points are below 2e-15 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: 1717
Number of distance tests for qhull: 4090
CPU seconds to compute hull (after input): 0.01465
Output completed. Verifying that all points are below 2.8e-15 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: 25
Number of distance tests for qhull: 2025
Number of distance tests for merging: 510
Number of distance tests for checking: 412
Number of merged facets: 36
CPU seconds to compute hull (after input): 0.000923
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: 1487
Number of distance tests for merging: 146
Number of distance tests for checking: 154
Number of merged facets: 4
CPU seconds to compute hull (after input): 0.0003
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: 1581
CPU seconds to compute hull (after input): 0.004699
Output completed. Verifying that all points are below 2.1e-15 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: 116
Number of distance tests for qhull: 1210
CPU seconds to compute hull (after input): 0.000736
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: 297
Number of distance tests for qhull: 1748
CPU seconds to compute hull (after input): 0.002218
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: 854
CPU seconds to compute hull (after input): 0.00193
Output completed. Verifying that all points are below 1.3e-15 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: 298
Number of distance tests for qhull: 1459
Number of distance tests for merging: 11679
Number of distance tests for checking: 6438
Number of merged facets: 97
CPU seconds to compute hull (after input): 0.0169
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: 1003
Number of distance tests for qhull: 6999
Number of distance tests for merging: 26735
Number of distance tests for checking: 22944
Number of merged facets: 330
CPU seconds to compute hull (after input): 0.05115
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: 1621
CPU seconds to compute hull (after input): 0.00474
Output completed. Verifying that all points are below 2.1e-15 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: 1847
Number of distance tests for merging: 2078
Number of distance tests for checking: 1209
Number of merged facets: 3
CPU seconds to compute hull (after input): 0.005326
Maximum distance of vertex below facet: -1.1e-15 (0.3x)
set +v
=== check qhull option errors Mon Sep 18 21:37:20 UTC 2023
rbox 10 | qhull d H0
QH6037 qhull option error (qh_readpoints): can not use Delaunay('d') or Voronoi('v') with halfspace intersection('H')
While executing: rbox 10
| qhull d H0
Options selected for Qhull 2020.2.r 2020/08/31:
run-id 574522178 delaunay Halfspace-about 0 _maxoutside 0
rbox 10 | qhull Zza
QH7094 qhull option warning: unknown option 'Z'(5a)
QH7036 qhull option warning: missing space after option 'Z'(5a), reserved for sub-options, ignoring 'Z' options to next space
QH6035 qhull option error: see previous warnings, use 'Qw' to override: 'qhull Zza' (last offset 6)
While executing: | qhull Zza
Options selected for Qhull 2020.2.r 2020/08/31:
run-id 574522178 _maxoutside 0
rbox 10 | qhull Zza Qw
QH7094 qhull option warning: unknown option 'Z'(5a)
QH7036 qhull option warning: missing space after option 'Z'(5a), reserved for sub-options, ignoring 'Z' options to next space
Convex hull of 10 points in 3-d:
Number of vertices: 10
Number of facets: 16
Statistics for: rbox 10 | qhull Zza Qw
Number of points processed: 10
Number of hyperplanes created: 26
Number of distance tests for qhull: 43
CPU seconds to compute hull (after input): 0.000118
rbox 10 | qhull Q999
Convex hull of 10 points in 3-d:
Number of vertices: 10
Number of facets: 16
Statistics for: rbox 10 | qhull Q999
Number of points processed: 10
Number of hyperplanes created: 26
Number of distance tests for qhull: 43
CPU seconds to compute hull (after input): 0.000116
rbox 10 | qhull Q999 Qw
Convex hull of 10 points in 3-d:
Number of vertices: 10
Number of facets: 16
Statistics for: rbox 10 | qhull Q999 Qw
Number of points processed: 10
Number of hyperplanes created: 26
Number of distance tests for qhull: 43
CPU seconds to compute hull (after input): 0.000114
qhull TIxyzlkajdfhwh
QH6041 qhull option error: cannot open 'TI' file "xyzlkajdfhwh"
While executing: | qhull TIxyzlkajdfhwh
Options selected for Qhull 2020.2.r 2020/08/31:
run-id 574522178 _maxoutside 0
rbox 10 >r.x
qhull TIr.x
Convex hull of 10 points in 3-d:
Number of vertices: 10
Number of facets: 16
Statistics for: rbox 10 | qhull TIr.x
Number of points processed: 10
Number of hyperplanes created: 26
Number of distance tests for qhull: 43
CPU seconds to compute hull (after input): 0.000112
qhull p TI r.x TO x.x
cat x.x
3
10
-0.374949442106252 0.2247255418679914 -0.03782349642163468
0.3004920247946792 0.3694544596313075 0.4210962191420572
0.3641479121187217 0.2339522165562512 0.03489791698278666
-0.4707134565997063 -0.2810653003687648 0.1354949890035158
0.2642752088273644 -0.3265712199048802 0.3175057017407433
0.3183227589524563 0.05060330969337679 0.4898217078203537
0.4334355904100794 -0.2480392830893763 0.2037671452423252
-0.2855954200826543 -0.002227006947833121 -0.4293096679535784
-0.4075898489985521 -0.3625928418362446 -0.09789381697577781
-0.3013850588364387 -0.3786854184034145 0.4341719447953365
set +v
=== check qhull output formats Mon Sep 18 21:37:20 UTC 2023
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: 7
CPU seconds to compute hull (after input): 7.6e-05
Output completed. Verifying that all points are below 1.3e-15 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: 7
CPU seconds to compute hull (after input): 7.6e-05
rbox 5 r s D2 | qhull s o
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: 7
CPU seconds to compute hull (after input): 7.2e-05
2
5 5 5
0.1545084971874737 0.4755282581475768
-0.4045084971874737 0.2938926261462366
-0.4045084971874738 -0.2938926261462365
0.1545084971874736 -0.4755282581475768
0.5 -1.224646799147353e-16
2 4 0
2 2 3
2 3 4
2 1 2
2 0 1
rbox 5 r s D2 | qhull f
Vertices and facets:
- p0(v3): 0.15 0.48
- p4(v2): 0.5 -1.2e-16
- p3(v4): 0.15 -0.48
- p2(v1): -0.4 -0.29
- p1(v5): -0.4 0.29
- f3
- flags: bottom simplicial
- normal: 0.809 0.5878
- offset: -0.4045085
- vertices: p0(v3) p4(v2)
- neighboring facets: f5 f7
- f4
- flags: bottom simplicial
- normal: -0.309 -0.9511
- offset: -0.4045085
- vertices: p3(v4) p2(v1)
- neighboring facets: f6 f5
- f5
- flags: top simplicial
- normal: 0.809 -0.5878
- offset: -0.4045085
- vertices: p3(v4) p4(v2)
- neighboring facets: f3 f4
- f6
- flags: top simplicial
- normal: -1 9.444e-17
- offset: -0.4045085
- vertices: p1(v5) p2(v1)
- neighboring facets: f4 f7
- f7
- flags: bottom simplicial
- normal: -0.309 0.9511
- offset: -0.4045085
- vertices: p1(v5) p0(v3)
- 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 -0.9510565162951536 -0.4045084971874738
0.8090169943749472 -0.5877852522924732 -0.4045084971874737
-1 9.444121133484361e-17 -0.4045084971874738
-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 -1.224646799147353e-16
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 -1.224646799147353e-16
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 -1.224646799147353e-16
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 -1.224646799147353e-16
3
5
0.8090169943749476 0.587785252292473 -0.4045084971874737
-0.3090169943749476 -0.9510565162951536 -0.4045084971874738
0.8090169943749472 -0.5877852522924732 -0.4045084971874737
-1 9.444121133484361e-17 -0.4045084971874738
-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(v3): 0.38 -0.47 -0.22
- p6(v1): -0.31 -0.011 -0.49
- p1(v4): -0.067 -0.16 0.46
- p7(v2): 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(v3) p6(v1)
- neighboring facets: f9 f6 f7
- f6
- flags: bottom simplicial
- normal: -0.9301 -0.3157 0.1877
- offset: -0.1977325
- vertices: p0(v5) p1(v4) p6(v1)
- neighboring facets: f17 f5 f8
- f7
- flags: bottom simplicial
- normal: 0.7008 -0.3956 0.5936
- offset: -0.323519
- vertices: p0(v5) p9(v3) p7(v2)
- neighboring facets: f10 f8 f5
- f8
- flags: top simplicial
- normal: 0.6544 -0.298 0.6949
- offset: -0.3219447
- vertices: p0(v5) p1(v4) p7(v2)
- neighboring facets: f13 f7 f6
- f9
- flags: bottom simplicial
- normal: 0.4866 0.2316 -0.8424
- offset: -0.2582907
- vertices: p3(v6) p9(v3) p6(v1)
- neighboring facets: f5 f16 f10
- f10
- flags: top simplicial
- normal: 0.943 0.1711 -0.2855
- offset: -0.3386013
- vertices: p3(v6) p9(v3) p7(v2)
- neighboring facets: f7 f14 f9
- f13
- flags: bottom simplicial
- normal: 0.08536 0.8035 0.5892
- offset: -0.1388354
- vertices: p4(v7) p1(v4) p7(v2)
- 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(v2)
- 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(v1)
- neighboring facets: f9 f18 f14
- f17
- flags: top simplicial
- normal: -0.6179 0.7381 0.2709
- offset: -0.04995414
- vertices: p5(v8) p1(v4) p6(v1)
- 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(v1)
- 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(v4)
- 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(v4)
- 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-15 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
-0.0222149361131852 -0.366434993563625 0.3270621312102882
-0.06676722137887703 -0.1566931052661437 0.4589771055234383
0.02820502736438535 0.04189077954915421 0.05832764185809314
0.3126723396709863 0.08400649026409401 -0.1029227018383543
0.1781470954214661 0.1182274414396169 0.04860343742054274
-0.1220315663349177 0.01546165115708642 -0.1360330368727753
-0.3072535691850387 -0.01073880122111998 -0.4870359524963758
0.3867462923626847 0.04492879989084675 0.118335500935405
0.3789805913148268 -0.4732086509216658 -0.2177962499836425
rbox 10 D3 | qhull o
3
10 14 21
-0.0222149361131852 -0.366434993563625 0.3270621312102882
-0.06676722137887703 -0.1566931052661437 0.4589771055234383
0.02820502736438535 0.04189077954915421 0.05832764185809314
0.3126723396709863 0.08400649026409401 -0.1029227018383543
0.1781470954214661 0.1182274414396169 0.04860343742054274
-0.1220315663349177 0.01546165115708642 -0.1360330368727753
-0.3072535691850387 -0.01073880122111998 -0.4870359524963758
0.3867462923626847 0.04492879989084675 0.118335500935405
-0.1352406177997967 0.01093378431250691 -0.2358910583293913
0.3789805913148268 -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: 297
Number of distance tests for merging: 90
Number of distance tests for checking: 168
Number of merged facets: 6
CPU seconds to compute hull (after input): 0.000179
rbox 50 D3 s | qhull C0.1 Qc Pd0d1d2 Pg s p Tcv
Convex hull of 50 points in 3-d:
Number of vertices: 17
Number of coplanar points: 33
Number of facets: 11
Number of 'good' facets: 1
Statistics for: rbox 50 D3 s | qhull C0.1 Qc Pd0d1d2 Pg s p Tcv
Number of points processed: 50
Number of hyperplanes created: 236
Number of distance tests for qhull: 1191
Number of distance tests for merging: 3250
Number of distance tests for checking: 1146
Number of merged facets: 85
CPU seconds to compute hull (after input): 0.002581
Maximum distance of vertex below facet: -0.24 (0.8x)
3
4
0.4995640899182717 0.005583735684776723 0.02011322848106416
0.3642936952899509 -0.2163723184172344 -0.2654677445467591
0.39379735093457 0.04855022442420501 -0.3042474685273066
0.397166795352245 -0.07497301400429786 -0.2943426300092109
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
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: 107
CPU seconds to compute hull (after input): 0.000185
1
0 1 12 1e-15
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
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: 404
Number of distance tests for qhull: 1996
Number of distance tests for merging: 3783
Number of distance tests for checking: 1381
Number of merged facets: 105
CPU seconds to compute hull (after input): 0.002031
Maximum distance of point above facet: 0.0057 (0.6x)
Maximum distance of vertex below facet: -0.0087 (1.0x)
10
29 92 222 0.05221620842441997
49 2 292 0.03790045221711884
99 9 336 0.02993864679572162
54 84 340 0.06479664045626413
54 72 226 0.03827167959574595
96 6 368 0.02282529175708784
19 1 372 0.01048228658130246
69 26 409 0.04998878658421259
19 66 371 0.008281093788857875
19 45 371 0.04608027722786196
rbox 100 s D2 | qhull C0.1 i Fx Tcv
6
4 28
77 70
6 68
70 6
68 4
28 77
6
4
28
77
70
6
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 # v3
0 0.009951 0 0
0 0 0.009951 0
-0.04234 -0.2077 -0.4529 # p3
1
0.009951 0 0 0 # v2
0 0.009951 0 0
0 0 0.009951 0
0.004313 -0.4976 0.04904 # p2
1
0.009951 0 0 0 # v1
0 0.009951 0 0
0 0 0.009951 0
-0.4876 0.03313 -0.1055 # p0
1
0.009951 0 0 0 # v4
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-15 of
all facets. Will make 16 distance computations.
rbox 6 D4 | qhull f Tcv
Vertices and facets:
- p3(v5): 0.1 -0.13 -0.17 -0.42
- p0(v4): -0.33 -0.43 -0.46 0.15
- p2(v3): 0.11 0.4 -0.063 -0.18
- p1(v1): -0.35 -0.24 0.14 -0.18
- p4(v2): 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(v5) p0(v4) p2(v3) p1(v1)
- neighboring facets: f6 f8 f10 f5
- f5
- flags: top simplicial
- normal: 0.6142 0.09488 -0.7743 0.1197
- offset: -0.1313181
- vertices: p3(v5) p0(v4) p2(v3) p4(v2)
- 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(v4) p2(v3) p1(v1)
- 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(v4) p2(v3) p4(v2)
- 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(v5) p2(v3) p1(v1)
- 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(v5) p2(v3) p4(v2)
- 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(v5) p0(v4) p1(v1)
- 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(v5) p0(v4) p4(v2)
- neighboring facets: f5 f7 f9 f10
Output completed. Verifying that all points are below 3e-15 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 -0.2391184267952278 0.1365988111464296 -0.1837860440684352
0.1079548672847029 0.397449696341017 -0.062960620096848 -0.1791453880063681
0.1034612661259819 -0.1265049433582509 -0.1685859450777862 -0.4239815160855479
0.1426585555473888 -0.3376619446442108 -0.08430490557505277 0.08744874697872318
-0.2489141260729303 -0.4997188728300099 0.224904344160952 -0.03269336003129686
rbox 6 D4 | qhull o
4
6 8 16
-0.3257826863096865 -0.4296101703584289 -0.4581337649916613 0.1458114577883961
-0.3468340047139991 -0.2391184267952278 0.1365988111464296 -0.1837860440684352
0.1079548672847029 0.397449696341017 -0.062960620096848 -0.1791453880063681
0.1034612661259819 -0.1265049433582509 -0.1685859450777862 -0.4239815160855479
0.1426585555473888 -0.3376619446442108 -0.08430490557505277 0.08744874697872318
-0.2489141260729303 -0.4997188728300099 0.224904344160952 -0.03269336003129686
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: 1997
Number of distance tests for qhull: 13977
CPU seconds to compute hull (after input): 0.1506
Total facet area: 3.1415592
Total volume: 0.7853647
qhull output completed. Verifying that 1000 points are
below 1.3e-15 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: 5544
Number of distance tests for qhull: 25487
CPU seconds to compute hull (after input): 0.1161
Total facet area: 3.1201951
Total volume: 0.51650274
qhull output completed. Verifying that 1000 points are
below 2.1e-15 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: 25
Number of distance tests for qhull: 167
Number of distance tests for merging: 510
Number of distance tests for checking: 412
Number of merged facets: 36
CPU seconds to compute hull (after input): 0.000827
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: 86
Number of distance tests for qhull: 721
Number of distance tests for merging: 2702
Number of distance tests for checking: 400
Number of merged facets: 210
CPU seconds to compute hull (after input): 0.005701
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: 86
Number of distance tests for qhull: 721
Number of distance tests for merging: 2702
Number of distance tests for checking: 400
Number of merged facets: 210
CPU seconds to compute hull (after input): 0.005765
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: 47
CPU seconds to compute hull (after input): 0.000154
Total facet area: 0.46254269
Output completed. Verifying that all points are below 2.1e-15 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: 47
CPU seconds to compute hull (after input): 0.00015
Total facet area: 0.46254269
Output completed. Verifying that all points are below 2.1e-15 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: 5
Number of distance tests for qhull: 51
CPU seconds to compute hull (after input): 7.5e-05
Total facet area: 2.8999576
Total volume: 0.46254269
Output completed. Verifying that all points are below 1.3e-15 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-15 of
all facets. Will make 56 distance computations.
rbox 1000 s | qhull FS Tcv
0
2 3.120195135077461 0.516502736886338
qhull output completed. Verifying that 1000 points are
below 2.1e-15 of the nearest facet.
rbox 10 W0 D2 | qhull p Qc FcC Tcv
2
10
-0.3863076515368257 0.5
-0.05259535978789942 0.5
0.2626424396993987 0.5
0.3748708151978168 0.5
-0.01474997775140219 0.5
0.1582814042067914 0.5
-0.5 0.4508927962285399
-0.5 -0.003085198815060031
-0.3688616616361418 -0.5
-0.2798755283280048 0.5
5
0
0
0
0
5 2 4 5 9 1
2
5
0.003004576780837498 -8.023127287351645e-18
-0.5 0.2239037987067399
-0.4344308308180709 -0.25154259940753
-0.4431538257684129 0.4754463981142699
-0.005718418169504469 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
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: 5
Number of distance tests for qhull: 4
CPU seconds to compute hull (after input): 7e-05
rbox 4 z h s D2 | qhull Fd s n FD Tcv
begin
4 3 real
107643.7343385944 -0.2650304141580589 -0.964240052876465
797791.7732245289 -0.6912673062074456 0.7225991360143615
874890.2679778723 0.9916265954087946 0.1291382796771071
864878.4439653738 0.3984446264475182 0.9171923896626583
end
Output completed. Verifying that all points are below 2.6e-09 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
Options selected for Qhull 2020.2.r 2020/08/31:
run-id 574538985 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-16 _one-merge 0.3 _near-inside 1.5
Visible-distance 0.1 U-max-coplanar 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: 4
Number of distance tests for qhull: 22
CPU seconds to compute hull (after input): 9.9e-05
Total facet area: 0.82966766
Total volume: 0.010511079
Maximum distance of point above facet: 0.11 (0.4x)
Vertices and facets:
- p1(v3): -0.3 0.39 -0.092
- p5(v2): 0.4 -0.22 -0.2
- p4(v1): -0.46 -0.19 -0.018
- p2(v4): 0.25 0.28 -0.33
- f1
- flags: top simplicial isarea
- area: 0.26
- normal: 0.2054 0.06987 0.9762
- offset: 0.125398
- center: -0.1205015151724569 -0.008790385787885074 -0.1024776532548504
- vertices: p1(v3) p5(v2) p4(v1)
- neighboring facets: f2 f3 f4
- f2
- flags: bottom simplicial isarea
- area: 0.23
- normal: -0.2032 -0.3001 -0.932
- offset: -0.1680571
- center: 0.06430144219370747 -0.04270356053094847 -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(v4) p5(v2) p4(v1)
- neighboring facets: f1 f3 f4
- f3
- flags: top simplicial isarea
- area: 0.18
- normal: -0.3912 -0.01238 -0.9202
- offset: -0.1989549
- center: -0.1715856748140029 0.1590825675964338 -0.1454013928109104
- vertices: p2(v4) p1(v3) p4(v1)
- neighboring facets: f1 f2 f4
- f4
- flags: bottom simplicial isarea
- area: 0.16
- normal: 0.4184 0.3424 0.8413
- offset: 0.07254957
- center: 0.116549362001881 0.1503252206347392 -0.2053893818610149
- vertices: p2(v4) p1(v3) p5(v2)
- 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
0.205360378770873 0.06987429109559466 0.976188864039624 0.1253980026939646
-0.2031613339148238 -0.3001304507855299 -0.9320124381751694 -0.1680570625036091
-0.3911895500493898 -0.01238286325891905 -0.9202268202077502 -0.1989548866041478
0.4183781509471984 0.3424157187037644 0.8412557271095321 0.07254956874669725
4
4
0.205360378770873 0.06987429109559466 0.976188864039624 0.125398002693964
-0.2031613339148238 -0.3001304507855299 -0.9320124381751694 -0.1680570625036098
-0.3911895500493898 -0.01238286325891905 -0.9202268202077502 -0.1989548866041485
0.4183781509471984 0.3424157187037644 0.8412557271095321 0.0725495687466966
4
4
0.205360378770873 0.06987429109559466 0.976188864039624 0.1253980026939626
-0.2031613339148238 -0.3001304507855299 -0.9320124381751694 -0.2813242952138535
-0.3911895500493898 -0.01238286325891905 -0.9202268202077502 -0.1989548866041498
0.4183781509471984 0.3424157187037644 0.8412557271095321 0.07254956874669528
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 2020.2.r 2020/08/31:
run-id 574538985 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-16 _one-merge 0.3 _near-inside 1.5
Visible-distance 0.1 U-max-coplanar 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 0.1132672327102437 -1.315898280434284e-15
0
2 0.8296676646636063 0.01051107893821417
3 1
-0.02780909644771785 0.06447846047808484 -0.1584624246583442
4
3 1 5 4
3 2 5 4
3 2 1 4
3 2 1 5
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 1 0 -4 -8
1 1
5 -10 2 -3 -4 -8
4 2 -3 0 1
3 -4 0 -3
3 -10 -8 3
4 -10 2 1 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
QH7055 qhull warning: no facets printed
0
set +v
=== test Qt Mon Sep 18 21:37:21 UTC 2023
rbox c | qhull Qt s o Tcv
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: 34
Number of distance tests for merging: 96
Number of distance tests for checking: 100
Number of merged facets: 6
CPU seconds to compute hull (after input): 0.000201
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
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(v3): -0.5 0.5 -0.5
neighbors: f17 f29 f33
- p0(v1): -0.5 -0.5 -0.5
neighbors: f17 f18 f21 f22 f29 f30
- p4(v2): 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(v4): -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
- owner of normal & centrum is facet f17
- normal: -0 -0 -1
- offset: -0.5
- center: 0 0 -0.5
- vertices: p6(v6) p2(v3) p0(v1)
- neighboring facets: f29 f18 f33
- f18
- flags: bottom simplicial tricoplanar
- owner of normal & centrum is facet f17
- normal: -0 -0 -1
- offset: -0.5
- center: 0 0 -0.5
- vertices: p6(v6) p4(v2) p0(v1)
- 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(v2) p0(v1)
- neighboring facets: f18 f22 f25
- f22
- flags: bottom simplicial tricoplanar
- owner of normal & centrum is facet f21
- normal: 0 -1 0
- offset: -0.5
- center: 0 -0.5 0
- vertices: p5(v7) p1(v4) p0(v1)
- 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(v2)
- neighboring facets: f18 f21 f27
- f27
- flags: bottom simplicial tricoplanar
- 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(v3) p0(v1)
- 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(v4) p0(v1)
- 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(v3)
- 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(v4)
- 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
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: 34
Number of distance tests for merging: 90
Number of distance tests for checking: 48
Number of merged facets: 6
CPU seconds to compute hull (after input): 0.000141
Approximate facet area: 6
Approximate volume: 1
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
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: 19
Number of facets in hull: 16
Number of distance tests for qhull: 48
Number of distance tests for merging: 170
Number of distance tests for checking: 164
Number of merged facets: 7
CPU seconds to compute hull (after input): 0.000277
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: 19
Number of facets in hull: 10
Number of distance tests for qhull: 48
Number of distance tests for merging: 170
Number of distance tests for checking: 164
Number of merged facets: 7
CPU seconds to compute hull (after input): 0.000281
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 -0.1939879513790814
-0.3359969878447704 0.1939879513790817
-0.2875 0
0.3359969878447702 -0.1939879513790819
0.3359969878447707 0.1939879513790815
0.2875 0
-2.220446049250313e-16 -0.3453321730569308
-2.220446049250313e-16 -0.3453321730569308
1.110223024625157e-16 0.3453321730569308
1.110223024625157e-16 0.3453321730569308
0 0
0 0
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
Options selected for Qhull 2020.2.r 2020/08/31:
run-id 574538985 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-16 _one-merge 0.3 _near-inside 1.5
Visible-distance 0.1 U-max-coplanar 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: 34
Number of distance tests for merging: 102
Number of distance tests for checking: 126
Number of merged facets: 6
CPU seconds to compute hull (after input): 0.000231
Approximate facet area: 6
Approximate volume: 1
Vertices and facets:
- p6(v6): 0.5 0.5 -0.5
neighbors: f17 f18 f25 f27 f33 f34
- p2(v3): -0.5 0.5 -0.5
neighbors: f17 f29 f33
- p0(v1): -0.5 -0.5 -0.5
neighbors: f17 f18 f21 f22 f29 f30
- p4(v2): 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(v4): -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 isarea keepcentrum
- area: 0.5
- normal: -0 -0 -1
- offset: -0.5
- center: 0 0 -0.5
- vertices: p6(v6) p2(v3) p0(v1)
- neighboring facets: f29 f18 f33
- f18
- flags: bottom simplicial tricoplanar isarea
- area: 0.5
- normal: -0 -0 -1
- offset: -0.5
- center: 0 0 -0.5
- vertices: p6(v6) p4(v2) p0(v1)
- neighboring facets: f21 f17 f25
- f21
- flags: top simplicial tricoplanar isarea keepcentrum
- area: 0.5
- normal: 0 -1 0
- offset: -0.5
- center: 0 -0.5 0
- vertices: p5(v7) p4(v2) p0(v1)
- neighboring facets: f18 f22 f25
- f22
- flags: bottom simplicial tricoplanar isarea
- area: 0.5
- normal: 0 -1 0
- offset: -0.5
- center: 0 -0.5 0
- vertices: p5(v7) p1(v4) p0(v1)
- neighboring facets: f30 f21 f37
- f25
- flags: top simplicial tricoplanar isarea keepcentrum
- area: 0.5
- normal: 1 -0 -0
- offset: -0.5
- center: 0.5 0 0
- vertices: p5(v7) p6(v6) p4(v2)
- neighboring facets: f18 f21 f27
- f27
- flags: bottom simplicial tricoplanar isarea
- 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 isarea keepcentrum
- area: 0.5
- normal: -1 -0 -0
- offset: -0.5
- center: -0.5 0 0
- vertices: p3(v8) p2(v3) p0(v1)
- neighboring facets: f17 f30 f33
- f30
- flags: top simplicial tricoplanar isarea
- area: 0.5
- normal: -1 -0 -0
- offset: -0.5
- center: -0.5 0 0
- vertices: p3(v8) p1(v4) p0(v1)
- neighboring facets: f22 f29 f37
- f33
- flags: bottom simplicial tricoplanar isarea keepcentrum
- area: 0.5
- normal: 0 1 -0
- offset: -0.5
- center: 0 0.5 0
- vertices: p3(v8) p6(v6) p2(v3)
- neighboring facets: f17 f29 f34
- f34
- flags: top simplicial tricoplanar isarea
- 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 isarea keepcentrum
- area: 0.5
- normal: -0 -0 1
- offset: -0.5
- center: 0 0 0.5
- vertices: p3(v8) p5(v7) p1(v4)
- neighboring facets: f22 f30 f38
- f38
- flags: bottom simplicial tricoplanar isarea
- 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 2020.2.r 2020/08/31:
run-id 574538985 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-16 _one-merge 0.3 _near-inside 1.5
Visible-distance 0.1 U-max-coplanar 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-15 -6.936799964367356e-16
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
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
Options selected for Qhull 2020.2.r 2020/08/31:
run-id 574538985 summary FPoint-nearest delaunay Qtriangulate _pre-merge
_zero-centrum Pgood Qcoplanar _max-width 1 Error-roundoff 6.9e-16
_one-merge 4.9e-15 _near-inside 2.4e-14 Visible-distance 1.4e-15
U-max-coplanar 1.4e-15 Width-outside 2.8e-15 _wide-facet 8.3e-15
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: 19
Number of facets in hull: 16
Number of distance tests for qhull: 79
Number of distance tests for merging: 153
Number of distance tests for checking: 100
Number of merged facets: 6
CPU seconds to compute hull (after input): 0.000211
1
0 10 36 0
rbox 100 W0 | qhull Tv Q11 FO
Options selected for Qhull 2020.2.r 2020/08/31:
run-id 574538985 Tverify Q11-trinormals Qtriangulate _pre-merge
_zero-centrum _max-width 1 Error-roundoff 6.9e-16 _one-merge 4.9e-15
_near-inside 2.4e-14 Visible-distance 1.4e-15 U-max-coplanar 1.4e-15
Width-outside 2.8e-15 _wide-facet 8.3e-15
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 FO
Number of points processed: 52
Number of hyperplanes created: 171
Number of distance tests for qhull: 1575
Number of distance tests for merging: 1368
Number of distance tests for checking: 1131
Number of merged facets: 41
CPU seconds to compute hull (after input): 0.000925
Output completed. Verifying that all points are below outer planes of
all facets. Will make 8600 distance computations.
set +v
=== test unbounded intersection Mon Sep 18 21:37:21 UTC 2023
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
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: 21452
CPU seconds to compute hull (after input): 0.01657
Total facet area: 5.8817432
Total volume: 0.99685163
8
0.1446087232094601
0.1622198334884075
0.2057158590759608
0.1567143851824352
0.188985866819172
0.1580674614313252
0.1616733826473111
0.1767351337533958
0
2 5.881743214947513 0.9968516315221345
4
8
1.009144997325421e-05 0.9999999999463923 2.319049754624652e-06 -0.4999875785488853
-1.229609861584452e-05 8.587946880918045e-05 0.9999999962367613 -0.500004859549355
-1.383340239672454e-05 -0.9999999998842694 6.332306547224586e-06 -0.4999917156571327
1.802476239613105e-05 -1.901476191096464e-05 0.9999999996567733 -0.4999909156385879
0.9999999996788914 1.780140020603311e-05 -1.803683546259361e-05 -0.4999971349013697
3.470111681088057e-06 -3.668365732095583e-05 -0.9999999993211337 -0.4999893476858696
-1.633273154317779e-05 -0.9999999998072314 1.08985791646657e-05 -0.4999921708899001
-0.9999999997878146 -2.055073082985623e-05 -1.427680287303445e-06 -0.4999990322171605
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
5
8
6
6
2
0
7
10
4
10
0.6345454980886096 0.2737427089707436 0.7227841587506171 -0.7458921924784656
-0.00253733560834815 0.666653414016696 0.7453635270845322 -0.6767722083805112
-0.003237401631533091 0.002761552371517554 -0.9999909464886048 -0.4969398742962436
-0.0004022623770974538 0.9999997831336711 0.0005214571799133833 -0.5000167453415887
-0.999601787347817 0.0214081839262726 0.01838359029211947 -0.4985486000821885
-0.005480509661076107 -0.9999701072857251 0.005454223027194169 -0.4992904789191579
-0.9987007292177809 -0.05077399000218431 -0.004342280406757339 -0.5182179901342427
0.6755431502353132 -0.2163920762108173 0.7048517017950092 -0.7475007704997935
0.001196850675493193 0.0003334814784797861 0.9999992281689842 -0.4989807987213126
0.9999992961453315 0.00118637926097064 1.459763172590229e-05 -0.4998611663332402
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
12
0.6345454980886096 0.2737427089707436 0.7227841587506171 -0.7458921924784656
-0.00253733560834815 0.666653414016696 0.7453635270845322 -0.6767722083805112
-0.9785529186794025 -0.009694358843403266 -0.2057673558916428 -0.5832522471275383
0.8278306348810541 -0.3414688798813042 -0.4450791435520636 -0.7665474225756105
0.7383776593319754 -0.4655216164679661 0.4879426777814019 -0.7788991125303445
0.2008161614085187 -0.8823413491644904 0.4256132198037728 -0.6982307124493007
0.41932306725662 0.6721295192910486 -0.6102541065524131 -0.7755692997856908
-0.3210285130221472 0.4863414284958994 -0.8126578054478755 -0.7591490151594069
-0.4745617604911457 -0.2935495843214587 0.8298311738084099 -0.7523676152838523
-0.8238864443814345 -0.556605789918439 0.1067760337987315 -0.695666244857558
-0.5357402012449896 -0.5359428531021374 -0.6524934443952053 -0.811263040246498
0.6755431502353132 -0.2163920762108173 0.7048517017950092 -0.7475007704997935
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 2020.2.r 2020/08/31:
run-id 574538985 Tz-stdout TOutput-file q_test.log.1 _pre-merge
_zero-centrum _max-width 0.92 Error-roundoff 6.8e-16 _one-merge 4.8e-15
_near-inside 2.4e-14 Visible-distance 1.4e-15 U-max-coplanar 1.4e-15
Width-outside 2.7e-15 _wide-facet 8.2e-15
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: 26
Number of distance tests for qhull: 43
CPU seconds to compute hull (after input): 0.000136
set +v
=== check Delaunay/Voronoi Mon Sep 18 21:37:21 UTC 2023
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: 47
CPU seconds to compute hull (after input): 0.000151
Output completed. Verifying that all points are below 2.1e-15 of
all facets. Will make 140 distance computations.
rbox 10 D2 | qhull d Qz Tcv
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 Qz Tcv
Number of points processed: 11
Number of hyperplanes created: 30
Number of facets in hull: 18
Number of distance tests for qhull: 55
CPU seconds to compute hull (after input): 0.000164
Output completed. Verifying that all points are below 2.1e-15 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: 43
Number of facets in hull: 27
Number of distance tests for qhull: 66
CPU seconds to compute hull (after input): 0.000199
Output completed. Verifying that all points are below 2.9e-15 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 7 5 4
4 9 6 7 4
4 9 7 6 2
4 9 2 6 4
4 9 5 7 1
4 9 5 1 4
4 9 7 3 1
4 9 1 3 2
4 9 3 7 2
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: 115
Number of distance tests for merging: 296
Number of distance tests for checking: 272
Number of merged facets: 8
CPU seconds to compute hull (after input): 0.000385
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 Qz Q8
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 Qz Q8
Number of points processed: 11
Number of hyperplanes created: 19
Number of facets in hull: 11
Number of distance tests for qhull: 54
Number of distance tests for merging: 201
Number of distance tests for checking: 204
Number of merged facets: 7
CPU seconds to compute hull (after input): 0.000306
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
-0.01883958887200765 0.3630260628303755 0.13214285240299
0.3790312361708201 0.3779794437605696 0.2865331378987296
-0.2994955874043476 0.3776609263174803 0.2323253821416525
0.3471817493878135 0.08365533089605659 0.1275333814953112
-0.00485819764887746 0.3482682405489201 0.121314369459436
0.3443122672329771 -0.1437312230875075 0.1392096018573439
0.309330780347186 -0.07758103877080702 0.1017043492469565
Output completed. Verifying that all points are below 2.1e-15 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-15 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
-0.01883958887200765 0.3630260628303755 0.13214285240299
0.3790312361708201 0.3779794437605696 0.2865331378987296
-0.2994955874043476 0.3776609263174803 0.2323253821416525
0.3471817493878135 0.08365533089605659 0.1275333814953112
-0.00485819764887746 0.3482682405489201 0.121314369459436
0.3443122672329771 -0.1437312230875075 0.1392096018573439
0.309330780347186 -0.07758103877080702 0.1017043492469565
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-15 of
all facets. Will make 140 distance computations.
rbox 10 D2 | qhull v Tcv o
2
15 10 1
-10.101 -10.101
-0.1294381801544404 -0.07247409101984714
0.08267689532419747 -0.2397644955865706
0.1295260566906465 1.716033573116837
0.1740355150742391 0.5317519038435655
0.1851415205797575 0.3882545794457364
-0.9065939866848107 -0.2962957610652135
-0.1954805620516266 -0.07111892482963184
-0.1407581310832468 0.7233857048236082
-0.1676297826663962 0.2080621273999375
0.05868313821742954 0.06632066014880154
0.08806341399736994 0.1054080604689985
0.4761588899009253 -0.03168366595227294
3.094213357897477 -0.064721945677682
0.5410515627308725 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-15 of
all facets. Will make 140 distance computations.
rbox 10 D2 | qhull v Tcv p
2
14
-0.1294381801544404 -0.07247409101984714
0.08267689532419747 -0.2397644955865706
0.1295260566906465 1.716033573116837
0.1740355150742391 0.5317519038435655
0.1851415205797575 0.3882545794457364
-0.9065939866848107 -0.2962957610652135
-0.1954805620516266 -0.07111892482963184
-0.1407581310832468 0.7233857048236082
-0.1676297826663962 0.2080621273999375
0.05868313821742954 0.06632066014880154
0.08806341399736994 0.1054080604689985
0.4761588899009253 -0.03168366595227294
3.094213357897477 -0.064721945677682
0.5410515627308725 0.2115615434955919
Output completed. Verifying that all points are below 2.1e-15 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
-0.1294381801544404 -0.07247409101984714 0
# 2 f11
0.08267689532419747 -0.2397644955865706 0
# 3 f12
0.1295260566906465 1.716033573116837 0
# 4 f14
0.1740355150742391 0.5317519038435655 0
# 5 f15
0.1851415205797575 0.3882545794457364 0
# 6 f19
-0.9065939866848107 -0.2962957610652135 0
# 7 f20
-0.1954805620516266 -0.07111892482963184 0
# 8 f21
-0.1407581310832468 0.7233857048236082 0
# 9 f22
-0.1676297826663962 0.2080621273999375 0
# 10 f23
0.05868313821742954 0.06632066014880154 0
# 11 f24
0.08806341399736994 0.1054080604689985 0
# 12 f25
0.4761588899009253 -0.03168366595227294 0
# 13 f26
3.094213357897477 -0.064721945677682 0
# 14 f27
0.5410515627308725 0.2115615434955919 0
4 7 1 2 6 # p0(v3)
3 8 3 6 # p1(v1)
3 14 5 11 # p2(v8)
4 9 4 3 8 # p3(v7)
5 14 5 4 3 13 # p4(v2)
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(v4)
}
}
Output completed. Verifying that all points are below 2.1e-15 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-15 of
all facets. Will make 140 distance computations.
rbox 10 D2 | qhull v Tcv Fi
19
5 0 7 0.02051532578114336 0.9997895385570373 0.07511430445246037
5 0 9 0.619259133056969 0.7851866823409139 0.1370614663104577
5 0 5 -0.301880639203215 0.9533457293522944 0.008789126238507583
5 1 3 0.9648718030091262 -0.2627211520946079 0.3258622775065156
5 1 5 0.7995952824356682 -0.6005392446015695 0.5469710423089692
5 2 7 -0.9458410914974847 0.3246299888101017 0.04907537812572171
5 2 4 0.444671031232542 0.8956939622340812 -0.4300843534994401
5 2 6 0.2281595097543261 -0.9736237661995858 0.08253528745668784
5 3 4 0.9992944873266901 0.03755699133966539 -0.1938837324602516
5 3 7 0.6877523324625971 -0.7259454037269313 0.2663295190946441
5 3 5 -0.9986432053419565 0.05207445078292259 -0.1782370644858237
5 4 7 -0.9970183790688238 -0.07716444646969993 0.2145489484590235
5 4 6 -0.1075842248297359 -0.9941959739245502 0.2685422477498993
5 5 7 0.9950609206245129 -0.09926612839179765 0.187455367716064
5 6 7 -0.7993641842155074 0.6008468199079334 0.007060641163779212
5 6 9 -0.2285415587894342 -0.973534157544611 0.07797696388863314
5 6 8 -0.01261839651625044 -0.9999203848653946 -0.02567278177543585
5 7 9 0.5936952885926361 -0.8046899429612046 0.01852766555277016
5 8 9 -0.4674785097727932 0.8840044360186256 0.2506025495170936
Voronoi ridge statistics
19 bounded ridges
4.2e-17 ave. distance of midpoint to ridge
1.7e-16 max. distance of midpoint to ridge
19 bounded ridges with ok normal
5.8e-17 ave. angle to ridge
2.2e-16 max. angle to ridge
Output completed. Verifying that all points are below 2.1e-15 of
all facets. Will make 140 distance computations.
rbox 10 D2 | qhull v Tcv Fo
4
5 0 1 -0.3854955578888161 0.922709691532494 -0.07609298438083822
5 0 8 0.719062520784207 0.6949453872092842 0.1071733734620186
5 1 4 0.9929212365203526 -0.1187746524595787 0.07521211888503937
5 4 8 -0.06640144810487483 -0.9977929883946747 0.1408811441173877
Output completed. Verifying that all points are below 2.1e-15 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
-0.06934933486244874 0.05349366577784781
-0.3051278694340224 0.161498505581022
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 0.4164624817835529 0.9091529031283372 -0.01975252543405325
4
5 0 8 0.7190625207842071 0.6949453872092841 0.1071733734620185
5 0 1 -0.3854955578888162 0.922709691532494 -0.07609298438083828
5 1 4 0.9929212365203528 -0.1187746524595786 0.07521211888503934
5 4 8 -0.06640144810487485 -0.9977929883946747 0.1408811441173877
Voronoi ridge statistics
1 bounded ridges
1.2e-16 ave. distance of midpoint to ridge
1.2e-16 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-15 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
5 1 5 15 0 17
6 2 3 1 4 13 9
6 2 9 1 2 11 9
7 2 7 1 2 3 5 4
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
5 3 6 0 8 6
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
5 4 8 8 16 14
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-15 of
all facets. Will make 180 distance computations.
rbox 10 D3 | qhull v Fi Tcv
13
6 0 2 0.1026012494065408 0.8309156055795224 -0.5468566905731632 0.2399036185798246
6 0 8 -0.1644981128676535 0.549224308046351 -0.8193247404503221 0.1220237399030437
6 0 5 -0.1640386761614813 0.6276090456203122 -0.7610507201092116 0.1709974344854015
6 2 3 0.8628264983391892 0.127742449234631 -0.4890933453107607 -0.1660057988150948
6 2 9 0.5146151495466437 -0.7556910962035636 -0.4050953159143434 -0.3000434746332832
6 2 7 0.9862472983740704 0.008356748990702902 0.1650649302430821 -0.2195655184060844
6 3 8 -0.9471370887617877 -0.1545163381156413 -0.2811690529684558 0.04372902199764667
6 3 5 -0.9850113492204077 -0.1553182373520528 -0.07502590921037623 0.09265233510028284
6 4 8 -0.7177135399298967 -0.245721536677967 -0.65154293873383 -0.02974683605231299
6 5 9 0.7110332662678562 -0.693517783370965 -0.116037831799318 -0.2706062861955821
6 5 8 -0.1310037283001485 -0.04490613421135446 -0.9903643078593113 -0.2004293237314498
6 6 8 0.563653077615962 0.07101685912338832 0.8229531054770393 0.4221671959133705
6 8 9 0.7278413449934529 -0.6852671087526033 0.02561183671604023 -0.2412830130907243
Voronoi ridge statistics
15 non-simplicial Voronoi vertices for all ridges
6.9e-17 ave. distance to ridge
1.9e-16 max. distance to ridge
13 bounded ridges
7.8e-17 ave. distance of midpoint to ridge
3e-16 max. distance of midpoint to ridge
13 bounded ridges with ok normal
8.5e-17 ave. angle to ridge
2.2e-16 max. angle to ridge
Output completed. Verifying that all points are below 2.9e-15 of
all facets. Will make 180 distance computations.
rbox 10 D3 | qhull v Fo Tcv
19
6 0 1 -0.1769702595802885 0.8331351847724077 0.5239916899325134 0.004105600879712498
6 0 9 0.5856843296472444 -0.1558732679166009 -0.7954102025713885 -0.1264594278193164
6 0 6 -0.305501768024369 0.3812318858994052 -0.8725427891556765 -0.04822326899809234
6 0 7 0.6633910639781613 0.6672883530766242 -0.3385831509130507 0.06175731395259272
6 1 7 0.7533877382120365 0.334939238848763 -0.5658821628140998 0.06152842458597928
6 1 2 0.2077539373736714 0.4344067294949102 -0.8764297432625574 0.2556318087147513
6 1 5 -0.08886729274769822 0.2768317827550689 -0.9568002760954583 0.1656561460661369
6 2 4 0.8896724708236493 0.4529391082738924 -0.05769799697211265 -0.124969949041603
6 2 5 -0.6080629223625026 -0.1069684332549473 -0.7866493734408965 -0.05602222006342437
6 3 9 0.1157648604151236 -0.9728190902550374 -0.2005530222370839 -0.2615067759720444
6 3 7 0.3131056731324619 -0.1651787990807294 0.9352437125084113 -0.1060546443225209
6 3 6 -0.8429664438017094 -0.1288333013498811 -0.5223117412882753 -0.1470675860428305
6 3 4 -0.6546392846048742 0.1665291828386516 0.7373706247980789 0.1638426312062793
6 4 7 0.8997625993863546 -0.3161631359012113 0.3007792151107228 -0.2534488584590283
6 4 6 -0.6610636619910346 -0.1756381951302929 -0.7294834194184102 -0.1931488689248214
6 4 5 -0.8177140658972858 -0.2799433900977097 -0.5029666040348314 0.01966883326066583
6 5 6 -0.4656867325018191 -0.06587339986788447 -0.8824945112359766 -0.374728122564582
6 6 9 0.7885740013077054 -0.5314391513195501 0.309392102204163 -0.04784058563315544
6 7 9 -0.0125726543874506 -0.8388634914110149 -0.5441966291143082 -0.2018836580171401
Voronoi ridge statistics
14 non-simplicial Voronoi vertices for all ridges
4.3e-17 ave. distance to ridge
9.7e-17 max. distance to ridge
Output completed. Verifying that all points are below 2.9e-15 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
-0.04510412048603351 -0.1962229636993575 -0.06746145990413344
-0.2032838761823815 -0.3188041900902701 0.1251484339163768
0.1359785067833994 0.06954805978697726 -0.07249043373758879
-0.9550934192592715 0.3815223390696589 -0.9370156532984113
-0.01637948561987637 -0.8836250780525146 -0.03718065630611937
0.09499885792019704 -0.7038538868165176 -0.181396220925921
2.128743389186444 -4.06034590041635 -1.2162468947864
2.789531685277133 -5.393666229616701 -1.494034092231969
2.640156785601998 -4.796303906482405 -1.459799746992412
3 0 3 4
7 0 1 3 4 6 7 9
4 0 7 8 9
3 0 2 5
5 0 5 6 7 8
3 0 8 9
9 0 1 2 3 5 6 7 8 9
6 0 1 2 4 5 6
0
5 0 1 2 3 4
18
5 0 1 0 3 4
5 0 9 0 3 4
8 1 6 0 3 1 6 7 9
5 1 2 0 7 9
5 1 4 0 6 7
6 1 7 0 4 1 6
5 1 9 1 3 4
5 2 5 0 9 8
5 2 4 0 7 8
5 2 6 7 9 8
5 3 6 0 5 2
5 3 7 0 2 5
7 4 6 0 5 6 7 8
5 4 7 0 6 5
5 5 6 0 9 8
6 6 9 0 3 1 2
6 6 7 1 2 5 6
6 7 9 0 2 1 4
3
6 1 9 0.5123553720802024 -0.363812082853534 -0.7779027838170592 -0.100757404152973
6 2 6 -0.5221667006142685 -0.08192192666458321 -0.8488997200501196 -0.2535440955968309
6 6 7 0.752213645322669 0.06033708575303686 0.6561509489997043 0.09003235761431796
15
6 0 1 -0.1769702595802886 0.8331351847724078 0.5239916899325134 0.004105600879712498
6 0 9 0.5856843296472447 -0.1558732679166012 -0.7954102025713884 -0.1264594278193166
6 1 6 -0.2436653478720986 0.147883680687048 -0.9585184480399009 -0.04663519095132841
6 1 2 0.2077539373736637 0.4344067294949081 -0.8764297432625605 0.255631808714752
6 1 4 0.444220078847362 0.4986447037065236 -0.744326528490203 0.1737545932855555
6 1 7 0.7533877382120362 0.3349392388487629 -0.5658821628141001 0.06152842458597942
6 2 5 -0.6080629223625006 -0.1069684332549458 -0.7866493734408982 -0.05602222006342417
6 2 4 0.8896724708236509 0.4529391082738904 -0.0576979969721034 -0.1249699490416035
6 3 6 -0.8429664438017096 -0.1288333013498811 -0.5223117412882751 -0.1470675860428304
6 3 7 0.3131056731324613 -0.1651787990807291 0.9352437125084115 -0.1060546443225207
6 4 6 -0.6610636619910349 -0.1756381951302929 -0.7294834194184099 -0.1931488689248214
6 4 7 0.8997625993863546 -0.3161631359012115 0.3007792151107228 -0.2534488584590282
6 5 6 -0.4656867325018176 -0.06587339986788343 -0.8824945112359772 -0.374728122564582
6 6 9 0.7885740013077054 -0.5314391513195503 0.3093921022041629 -0.04784058563315553
6 7 9 -0.01257265438745033 -0.8388634914110151 -0.5441966291143079 -0.2018836580171402
Voronoi ridge statistics
9 non-simplicial Voronoi vertices for all ridges
1.5e-16 ave. distance to ridge
4.4e-16 max. distance to ridge
3 bounded ridges
6.4e-16 ave. distance of midpoint to ridge
1.7e-15 max. distance of midpoint to ridge
3 bounded ridges with ok normal
7.4e-17 ave. angle to ridge
2.2e-16 max. angle to ridge
Output completed. Verifying that all points are below 2.9e-15 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(v2): 0.47 -0.11 0.24
neighbors: f1 f5 f7
- p4(v1): -0.39 0.45 0.36
neighbors: f1 f3 f5 f6
- p0(v4): -0.34 0.23 0.17
neighbors: f3 f6 f8
- p1(v3): 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: 0.4751017705052502 0.8404705693422864
- vertices: p3(v5) p2(v2) p4(v1)
- neighboring facets: f1 f6 f7
- f6
- flags: bottom simplicial
- normal: 0.3235 0.6691 -0.669
- offset: 0.0657
- center: 0.24177356134713 0.5000766029034823
- vertices: p3(v5) p0(v4) p4(v1)
- neighboring facets: f3 f5 f8
- f7
- flags: top simplicial
- normal: 0.6288 -0.3317 -0.7033
- offset: -0.1682885
- center: 0.4470293595057619 -0.2357835939937328
- vertices: p3(v5) p1(v3) p2(v2)
- neighboring facets: f1 f5 f8
- f8
- flags: top simplicial
- normal: 0.1177 0.1841 -0.9758
- offset: 0.15929
- center: 0.06029550723695781 0.09433023738340306
- vertices: p3(v5) p0(v4) p1(v3)
- 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
0.4751017705052502 0.8404705693422864
0.24177356134713 0.5000766029034823
0.4470293595057619 -0.2357835939937328
0.06029550723695781 0.09433023738340306
3 2 4 0
3 3 4 0
3 1 3 0
4 3 4 2 1
3 1 2 0
set +v
=== check Halfspace and Qhull identity pipeline, showing the input Mon Sep 18 21:37:21 UTC 2023
=== the Qhull pipeline recreates 100 4-D cospherical points with the same area and volume
rbox 100 s D4 | qhull FA FV s n | head
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 s n
Number of points processed: 100
Number of hyperplanes created: 1717
Number of distance tests for qhull: 4090
CPU seconds to compute hull (after input): 0.003138
Total facet area: 1.7919449
Total volume: 0.18640279
4 1
-0.006240661006237819 -0.006198497499885543 -0.0019864189252863 0.03528712962677102
5
584
-0.4728063044129454 -0.06576180062326932 0.3296766529322419 -0.8145200357250598 -0.4001269961794449
0.9350657178932537 -0.116181174817606 -0.009048199757790566 0.3347718147035652 -0.3733488931324643
0.5670388949132408 -0.5323662756300656 -0.3876606744394214 0.4947446227302695 -0.4846392631626165
0.8393609616706702 -0.1089654738688994 -0.05104156673138016 0.530089105710936 -0.4115455431603698
0.6753770108964836 -0.1536990905729236 -0.0485198359900459 0.7196445707605155 -0.4414725485817289
0.20025580309926 0.08170320261530004 0.2334845247641378 0.9480016754748583 -0.4466269780920115
rbox 100 s D4 | qhull FQ FA FV n s | qhull s H Fp | head
Convex hull of 100 points in 4-d:
Number of vertices: 100
Number of facets: 584
Statistics for: rbox 100 s D4 | qhull FQ FA FV n s
Number of points processed: 100
Number of hyperplanes created: 1717
Number of distance tests for qhull: 4090
CPU seconds to compute hull (after input): 0.003085
Total facet area: 1.7919449
Total volume: 0.18640279
Halfspace intersection by the convex hull of 584 points in 4-d:
Number of halfspaces: 584
Number of non-redundant halfspaces: 584
Number of intersection points: 100
Number of non-simplicial intersection points: 100
Statistics for: rbox 100 s D4 | qhull FQ FA FV n s | qhull s H Fp
Number of points processed: 584
Number of hyperplanes created: 4013
Number of distance tests for qhull: 29717
Number of distance tests for merging: 76931
Number of distance tests for checking: 18265
Number of merged facets: 3444
CPU seconds to compute hull (after input): 0.03639
Maximum distance of point above facet: 2.4e-14 (0.4x)
Maximum distance of vertex below facet: -1.7e-14 (0.3x)
4
100
-0.1497820974007844 0.4220759056868791 -0.1730594919621551 0.1395265758865447
-0.1656824599698354 0.2695081565763442 0.2399815540443042 -0.3038478726528215
-0.1287028906527846 0.3274268489457611 0.1066154632455187 -0.3389105597705839
0.2152206390581626 0.2489384546335302 -0.342896351704003 0.1553441801811403
-0.3478218321497436 0.1609400522171699 0.2504669650899252 -0.2009591303498609
-0.2026608048181584 0.132737676060139 -0.4340855448243784 0.05365675464591807
-0.1243914612976075 -0.06208848857682957 -0.4348180038806073 -0.2039732517850684
0.318659177699236 0.2994118752602876 -0.2407753518255607 -0.02891517550426
rbox 100 s D4 | qhull FQ FA FV n s Tcv | qhull FQ s 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 FQ FA FV n s Tcv
Number of points processed: 100
Number of hyperplanes created: 1717
Number of distance tests for qhull: 4090
CPU seconds to compute hull (after input): 0.01469
Total facet area: 1.7919449
Total volume: 0.18640279
Output completed. Verifying that all points are below 2.8e-15 of
all facets. Will make 58400 distance computations.
Halfspace intersection by the convex hull of 584 points in 4-d:
Number of halfspaces: 584
Number of non-redundant halfspaces: 584
Number of intersection points: 100
Number of non-simplicial intersection points: 100
Statistics for: rbox 100 s D4 | qhull FQ FA FV n s Tcv | qhull FQ s H Fp Tcv
Number of points processed: 584
Number of hyperplanes created: 4013
Number of distance tests for qhull: 29717
Number of distance tests for merging: 77031
Number of distance tests for checking: 51837
Number of merged facets: 3444
CPU seconds to compute hull (after input): 0.8582
Maximum distance of point above facet: 2.4e-14 (0.4x)
Maximum distance of vertex below facet: -1.7e-14 (0.3x)
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: rbox 100 s D4 | qhull FQ FA FV n s Tcv | qhull FQ s H Fp Tcv | qhull FA Tcv
Number of points processed: 100
Number of hyperplanes created: 1717
Number of distance tests for qhull: 4090
CPU seconds to compute hull (after input): 0.01475
Total facet area: 1.7919449
Total volume: 0.18640279
Output completed. Verifying that all points are below 2.8e-15 of
all facets. Will make 58400 distance computations.
echo === the Qhull pipeline recreates a 3-D tetrahedron
=== the Qhull pipeline recreates a 3-D tetrahedron
rbox d D3 | qhull n FD
rbox d D3 | qhull n FD
begin
8 4 real
0.2886751345948129 0.5773502691896258 0.5773502691896258 0.5773502691896258
0.2886751345948129 -0.5773502691896258 0.5773502691896258 0.5773502691896258
0.2886751345948129 0.5773502691896258 0.5773502691896258 -0.5773502691896258
0.2886751345948129 -0.5773502691896258 0.5773502691896258 -0.5773502691896258
0.2886751345948129 -0.5773502691896258 -0.5773502691896258 0.5773502691896258
0.2886751345948129 0.5773502691896258 -0.5773502691896258 0.5773502691896258
0.2886751345948129 -0.5773502691896258 -0.5773502691896258 -0.5773502691896258
0.2886751345948129 0.5773502691896258 -0.5773502691896258 -0.5773502691896258
end
rbox d D3 | qhull s n FD Tcv | qhull s Fd H0.1,0.1 Fp Tcv
Convex hull of 6 points in 3-d:
Number of vertices: 6
Number of facets: 8
Statistics for: rbox d D3 | qhull s n FD Tcv
Number of points processed: 6
Number of hyperplanes created: 11
Number of distance tests for qhull: 10
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): 0.000132
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 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: rbox d D3 | qhull s n FD Tcv | qhull s Fd H0.1,0.1 Fp Tcv
Number of points processed: 8
Number of hyperplanes created: 10
Number of distance tests for qhull: 30
Number of distance tests for merging: 95
Number of distance tests for checking: 100
Number of merged facets: 6
CPU seconds to compute hull (after input): 0.000203
3
6
-1.387778780781446e-17 -1.387778780781446e-17 -0.5
-2.775557561562891e-17 0.5 0
-0.5 0 0
0.5 -2.775557561562891e-17 0
0 -0.5 0
-1.387778780781446e-17 1.387778780781446e-17 0.4999999999999999
Output completed. Verifying that all points are below outer planes of
all facets. Will make 48 distance computations.
echo === the Qhull pipeline recreates a regular 2-D pentagon
=== the Qhull pipeline recreates a regular 2-D pentagon
rbox 5 r D2 | qhull FQ n
rbox 5 r D2 | qhull FQ n
3
5
0.8090169943749476 0.587785252292473 -0.4045084971874737
-0.3090169943749476 -0.9510565162951536 -0.4045084971874738
0.8090169943749472 -0.5877852522924732 -0.4045084971874737
-1 9.444121133484361e-17 -0.4045084971874738
-0.3090169943749474 0.9510565162951536 -0.4045084971874738
rbox 5 r D2 | qhull s FQ n Tcv | qhull s 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 FQ n Tcv
Number of points processed: 5
Number of hyperplanes created: 8
Number of distance tests for qhull: 7
CPU seconds to compute hull (after input): 7.6e-05
Output completed. Verifying that all points are below 1.3e-15 of
all facets. Will make 25 distance computations.
Halfspace intersection by the convex hull of 5 points in 2-d:
Number of halfspaces: 5
Number of non-redundant halfspaces: 5
Number of intersection points: 5
Statistics for: rbox 5 r D2 | qhull s FQ n Tcv | qhull s H0 Fp Tcv
Number of points processed: 5
Number of hyperplanes created: 7
Number of distance tests for qhull: 8
CPU seconds to compute hull (after input): 8.4e-05
2
5
-0.4045084971874738 -0.2938926261462365
0.5 -1.528090898784888e-16
0.1545084971874736 -0.4755282581475768
-0.4045084971874737 0.2938926261462366
0.1545084971874737 0.4755282581475768
Output completed. Verifying that all points are below 6.4e-15 of
all facets. Will make 25 distance computations.
set +v
=== check qhull Mon Sep 18 21:37:22 UTC 2023
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: 48
CPU seconds to compute hull (after input): 0.000152
Output completed. Verifying that all points are below 2e-15 of
all facets. Will make 160 distance computations.
rbox 10 s D3 | qhull f Pd0:0.5 Pd2 Pg Tcv
Vertices and facets:
- p7(v8): 0.2 0.093 0.45
- p9(v5): 0.29 -0.16 0.38
- p3(v2): 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(v2)
- 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(v2)
- neighboring facets: f16 f26 f28
Output completed. Verifying that all points are below 2e-15 of
all facets. Will make 20 distance computations.
rbox 10 s D3 | qhull f Tcv PD2:-0.5 Pg
Vertices and facets:
- p4(v7): 0.23 -0.32 -0.31
- p1(v4): -0.072 0.057 -0.49
- p6(v3): -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(v4) p6(v3)
- neighboring facets: f21 f11 f25
- f21
- flags: bottom simplicial
- normal: -0.8148 -0.2922 -0.5006
- offset: -0.2881945
- vertices: p0(v9) p1(v4) p6(v3)
- 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(v4)
- 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(v4)
- neighboring facets: f12 f24 f26
Output completed. Verifying that all points are below 2e-15 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-1695073042
Number of points processed: 10
Number of hyperplanes created: 29
Number of distance tests for qhull: 48
CPU seconds to compute hull (after input): 0.000114
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: 48
CPU seconds to compute hull (after input): 0.00012
rbox 1000 D3 | qhull Tcvs
qhull 2020.2.r 2020/08/31 Statistics: rbox 1000 D3 | qhull Tcvs
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: 367
Number of distance tests for qhull: 12879
CPU seconds to compute hull (after input): 0.0039
qhull invoked by: rbox 1000 D3 | qhull Tcvs
2020.2.r 2020/08/31 with options:
run-id 574555792 Tcheck-frequently Tverify Tstatistics _pre-merge
_zero-centrum _max-width 1 Error-roundoff 6.9e-16 _one-merge 4.9e-15
_near-inside 2.4e-14 Visible-distance 1.4e-15 U-max-coplanar 1.4e-15
Width-outside 2.8e-15 _wide-facet 8.3e-15
precision constants:
0.5 max. abs. coordinate in the (transformed) input ('Qbd:n')
6.9e-16 max. roundoff error for distance computation ('En')
6.7e-16 max. roundoff error for angle computations
2.8e-15 min. distance for outside points ('Wn')
1.4e-15 min. distance for visible facets ('Vn')
1.4e-15 max. distance for coplanar facets ('Un')
8.3e-15 max. facet width for recomputing centrum and area
2.4e-14 max. distance for near-inside points
1.4e-15 radius of pre-merge centrum
4.9e-15 max. distance for merging two simplicial facets
2.2e-16 max. roundoff error for arithmetic operations
1.1e-308 min. denominator for division
zero diagonal for Gauss: 8.88e-15 1.78e-14 2.66e-14
precision statistics
3.8e-17 ave. distance of a new vertex to a facet
1.7e-16 max. distance of a new vertex to a facet
1.4e-16 max. distance of an output vertex to a facet
-1.7e-16 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
0.0039 cpu seconds for qhull after input
82 vertices created altogether
367 facets created altogether
0 maximum merges for a facet (at most 511)
0.93 average cosine (angle) of facet normals for all ridges
1 maximum cosine of facet normals (flatest) across a ridge
0.21 minimum cosine of facet normals (sharpest) 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 count
7 determinants for initial hull or voronoi vertices
503 distance tests for facet visibility
73 points checked for facets' outer planes
11.4 ave. distance tests per check
1668 max visit_id/2
3125 max vertex_visit/2
partitioning statistics (see previous for outer planes)
8 total vertices deleted
1 maximum vertices deleted per iteration
132 calls to findbest
2.53 ave. facets tested
6 max. facets tested
2048 calls to findbestnew
4.47 ave. facets tested
13 max. facets tested
36 calls due to qh_sharpnewfacets
927 calls to findhorizon
3.01 ave. facets tested
5 max. facets tested
0.00539 ave. clearly better
5 new bestfacets during qh_findbesthorizon
919 inside points
8 inside points that were coplanar with a facet
-2.8e-17 difference in max_outside at final check
3747 distance tests for initial partition
3132 partitions of a point
8553 distance tests for partitioning
518 distance tests for checking flipped facets
1160 distance tests for statistics
16915 total number of distance tests
8 partitions of coplanar points or deleted vertices
76 distance tests for these partitions
statistics for matching ridges
726 total lookups for matching ridges of new facets
0.583 average number of tests to match a ridge
statistics for determining merges
1089 distance tests for checking simplicial convexity
statistics for merging
1.7e-16 max distance of vertex or coplanar point above facet (w/roundoff)
-6.9e-16 max distance of vertex below facet (or roundoff)
memory usage statistics (in bytes)
21584 for facets and their normals, neighbor and vertex sets
2044 for vertices and their neighbor sets
32104 for input points, outside and coplanar sets, and qhT
memory statistics:
1413 quick allocations
687 short allocations
69 long allocations
1445 short frees
68 long frees
25680 bytes of short memory in use
1472 bytes of short memory in freelists
103912 bytes of dropped short memory
1364 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)
100 calls to qh_setlarger
14 average copy size
freelists(bytes->count): 16->1 24->13 32->0 48->11 88->7
size in bytes: merge 48 ridge 20 vertex 28 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.
# Test tracing 'Tn', combine stderr/stdout 'Tz', flush fprintf 'Tf'
rbox 100 D3 | qhull T1 Tz Tf TA1 TO q_test.log.1
tail -n -10 q_test.log.1
Statistics for: rbox 100 D3 | qhull T1 Tz Tf TA1 TO q_test.log.1
Number of points processed: 5
Number of hyperplanes created: 8
Number of distance tests for qhull: 456
CPU seconds to compute hull (after input): 0.000666
[QH1006]qh_freeqhull: free global memory
[QH1005]qh_freebuild: free memory from qh_inithull and qh_buildhull
[QH1061]qh_freeqhull: clear qhT except for qh.qhmem and qh.qhstat
rm q_test.log.1
rbox 100 s D3 | qhull TcvA10
Early exit due to 'TAn', 'TVn', 'TCn', 'TRn', or precision error with 'QJn'.
Convex hull of 100 points in 3-d:
Number of vertices: 14
Number of facets: 24
Statistics for: rbox 100 s D3 | qhull TcvA10
Number of points processed: 14
Number of hyperplanes created: 48
Number of distance tests for qhull: 599
CPU seconds to compute hull (after input): 0.00028
rbox 100 s D3 | qhull TcvV-2
Early exit due to 'TAn', '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: 1488
CPU seconds to compute hull (after input): 0.003126
rbox 100 s D3 | qhull TcvC2
Early exit due to 'TAn', '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: 1495
CPU seconds to compute hull (after input): 0.003055
rbox 100 s D3 | qhull TcvV2
Early exit due to 'TAn', '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: 1495
CPU seconds to compute hull (after input): 0.003123
rbox 100 s D3 | qhull T1cvV2P2
[QH1008]qh_readpoints: read in 100 3-dimensional points
[QH0013]qh_initqhull_globals: for rbox 100 s D3 | qhull T1cvV2P2
Trace level T1, IStracing 0, point TP2, merge TM0, dist TW1.8e+308, qh.tracefacet_id -1, traceridge_id -1, tracevertex_id -1, last qh.RERUN 0, rbox 100 s D3 | qhull T1cvV2P2
Options selected for Qhull 2020.2.r 2020/08/31:
run-id 574555792 Tcheck-frequently Tverify TV-stop-after-point 2
Trace-point 2 _pre-merge _zero-centrum _max-width 0.94
Error-roundoff 6.7e-16 _one-merge 4.7e-15 _near-inside 2.3e-14
Visible-distance 1.3e-15 U-max-coplanar 1.3e-15 Width-outside 2.7e-15
_wide-facet 8.1e-15
qh_findbest: point p2 starting at f7 isnewfacets? 1, unless 0 exit if > 2.7e-15, testhorizon? 1, noupper? 0, Last qh_addpoint p41, Last merge #0, max_outside 4e-17
qh_findbest: point p2 starting at f15 isnewfacets? 1, unless 0 exit if > 2.7e-15, testhorizon? 1, noupper? 0, Last qh_addpoint p52, Last merge #0, max_outside 1.1e-16
qh_findbest: point p2 starting at f37 isnewfacets? 1, unless 0 exit if > 2.7e-15, testhorizon? 1, noupper? 0, Last qh_addpoint p73, Last merge #0, max_outside 1.1e-16
qh_findbest: point p2 starting at f52 isnewfacets? 1, unless 0 exit if > 2.7e-15, testhorizon? 1, noupper? 0, Last qh_addpoint p87, Last merge #0, max_outside 1.1e-16
qh_findbest: point p2 starting at f72 isnewfacets? 1, unless 0 exit if > 2.7e-15, testhorizon? 1, noupper? 0, Last qh_addpoint p76, Last merge #0, max_outside 1.1e-16
qh_findbest: point p2 starting at f120 isnewfacets? 1, unless 0 exit if > 2.7e-15, testhorizon? 1, noupper? 0, Last qh_addpoint p84, Last merge #0, max_outside 1.1e-16
qh_findbest: point p2 starting at f211 isnewfacets? 1, unless 0 exit if > 2.7e-15, testhorizon? 1, noupper? 0, Last qh_addpoint p10, Last merge #0, max_outside 1.1e-16
qh_findbest: point p2 starting at f289 isnewfacets? 1, unless 0 exit if > 2.7e-15, testhorizon? 1, noupper? 0, Last qh_addpoint p6, Last merge #0, max_outside 1.1e-16
[QH1049]qh_addpoint: add p2(v79) 0.014 above f288 to hull of 152 facets, 0 merges, 22 outside at 0.003451 CPU secs. Previous p56(v78) delta 0.003451 CPU, 152 facets, 0 merges, 390 hyperplanes, 3835 distplanes, 0 retries
[QH1040]qh_findhorizon: find horizon for point p2 facet f288
[QH1041]qh_findhorizon: 5 horizon facets(good 5), 3 visible(good 3), 0 coplanar
[QH1032]qh_makenewfacets: created 5 new facets f390..f394 from point p2 to horizon
[QH1019]qh_matchnewfacets: match neighbors for new facets.
[QH1043]qh_partitionvisible: partitioned 0 points from outsidesets, 0 points from coplanarsets, and 0 deleted vertices
[QH1018]qh_deletevisible: delete 3 visible facets and 0 vertices
[QH1027]qh_checkpolygon: check all facets from f62, qh.NEWtentative? 0
[QH1039]qh_buildhull: completed the hull construction
[QH1036]Qhull: algorithm completed
[QH1027]qh_checkpolygon: check all facets from f62, qh.NEWtentative? 0
[QH1064]qh_checkconvex: check that facets are not-flipped and for qh.ZEROcentrum that simplicial vertices are below their neighbor (dist<0.0)
Early exit due to 'TAn', '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: 1495
CPU seconds to compute hull (after input): 0.003631
[QH1006]qh_freeqhull: free global memory
[QH1005]qh_freebuild: free memory from qh_inithull and qh_buildhull
[QH1061]qh_freeqhull: clear qhT except for qh.qhmem and qh.qhstat
rbox 100 s D3 | qhull TcvF100
At 21:37:22 & 0.000666 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 21:37:22 & 0.001434 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 21:37:22 & 0.002362 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 21:37:22 & 0.003567 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.
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: 1690
CPU seconds to compute hull (after input): 0.00497
Output completed. Verifying that all points are below 2e-15 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: 506
Number of distance tests for qhull: 4421
CPU seconds to compute hull (after input): 0.004823
Output completed. Verifying that all points are below 2e-15 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: 109
Number of distance tests for qhull: 1163
CPU seconds to compute hull (after input): 0.000654
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: 1172
CPU seconds to compute hull (after input): 0.00066
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: 4014
Number of distance tests for qhull: 9050
CPU seconds to compute hull (after input): 0.02881
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: 293
Number of distance tests for qhull: 2135
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: 109
Number of distance tests for qhull: 1163
CPU seconds to compute hull (after input): 0.000704
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 Pg Tcv
Vertices and facets:
- p11(v14): -0.31 0.47 0.07
- p59(v8): 0.44 0.42 -0.11
- p33(v3): -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(v3)
- 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(v3): -0.5 0.5 -0.5
neighbors: f1 f3 f10
- p4(v2): 0.5 -0.5 -0.5
neighbors: f1 f2 f9
- p0(v1): -0.5 -0.5 -0.5
neighbors: f1 f2 f3
- p5(v7): 0.5 -0.5 0.5
neighbors: f2 f9 f13
- p1(v4): -0.5 -0.5 0.5
neighbors: f2 f3 f13
- p7(v5): 0.5 0.5 0.5
neighbors: f10 f13 f9
- p3(v8): -0.5 0.5 0.5
neighbors: f3 f10 f13
- f1
- flags: bottom tested
- 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(v3) p4(v2) p0(v1)
- neighboring facets: f2 f3 f10 f9
- ridges:
- r4 tested simplicialtop simplicialbot
vertices: p2(v3) p0(v1)
between f1 and f3
- r3 tested simplicialtop simplicialbot
vertices: p4(v2) p0(v1)
between f2 and f1
- r1 tested simplicialtop
vertices: p6(v6) p4(v2)
between f9 and f1
- r2 tested simplicialbot
vertices: p6(v6) p2(v3)
between f1 and f10
- f2
- flags: top tested
- 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(v4) p4(v2) p0(v1)
- neighboring facets: f1 f3 f13 f9
- ridges:
- r3 tested simplicialtop simplicialbot
vertices: p4(v2) p0(v1)
between f2 and f1
- r8 tested simplicialtop simplicialbot
vertices: p1(v4) p0(v1)
between f3 and f2
- r7 tested simplicialtop
vertices: p5(v7) p1(v4)
between f13 and f2
- r6 tested
vertices: p5(v7) p4(v2)
between f2 and f9
- f9
- flags: bottom tested
- 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(v2)
- neighboring facets: f2 f1 f10 f13
- ridges:
- r1 tested simplicialtop
vertices: p6(v6) p4(v2)
between f9 and f1
- r6 tested
vertices: p5(v7) p4(v2)
between f2 and f9
- r10 tested simplicialbot
vertices: p5(v7) p7(v5)
between f9 and f13
- r11 tested simplicialtop simplicialbot
vertices: p6(v6) p7(v5)
between f10 and f9
- f3
- flags: bottom tested
- 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(v4) p2(v3) p0(v1)
- neighboring facets: f1 f2 f13 f10
- ridges:
- r4 tested simplicialtop simplicialbot
vertices: p2(v3) p0(v1)
between f1 and f3
- r13 tested
vertices: p3(v8) p2(v3)
between f10 and f3
- r14 tested
vertices: p3(v8) p1(v4)
between f3 and f13
- r8 tested simplicialtop simplicialbot
vertices: p1(v4) p0(v1)
between f3 and f2
- f10
- flags: top tested
- 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(v3)
- neighboring facets: f3 f1 f9 f13
- ridges:
- r2 tested simplicialbot
vertices: p6(v6) p2(v3)
between f1 and f10
- r11 tested simplicialtop simplicialbot
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(v3)
between f10 and f3
- f13
- flags: bottom tested
- 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(v4)
- neighboring facets: f10 f2 f9 f3
- ridges:
- r7 tested simplicialtop
vertices: p5(v7) p1(v4)
between f13 and f2
- r14 tested
vertices: p3(v8) p1(v4)
between f3 and f13
- r16 tested
vertices: p3(v8) p7(v5)
between f13 and f10
- r10 tested simplicialbot
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
Options selected for Qhull 2020.2.r 2020/08/31:
run-id 574555792 QbBound-unit-box 0.5 Tcheck-frequently Tverify
_pre-merge _zero-centrum _max-width 1 Error-roundoff 6.9e-16
_one-merge 4.9e-15 _near-inside 2.4e-14 Visible-distance 1.4e-15
U-max-coplanar 1.4e-15 Width-outside 2.8e-15 _wide-facet 8.3e-15
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: 109
Number of distance tests for qhull: 1163
CPU seconds to compute hull (after input): 0.000708
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
Options selected for Qhull 2020.2.r 2020/08/31:
run-id 574555792 delaunay Qbbound-last Tcheck-frequently Tverify
_pre-merge _zero-centrum Pgood _max-width 2e+06 Error-roundoff 1.4e-09
_one-merge 9.7e-09 _near-inside 4.9e-08 Visible-distance 2.8e-09
U-max-coplanar 2.8e-09 Width-outside 5.5e-09 _wide-facet 1.7e-08
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: 5457
Number of facets in hull: 1996
Number of distance tests for qhull: 27959
CPU seconds to compute hull (after input): 0.1151
qhull output completed. Verifying that 1000 points are
below 4.2e-09 of the nearest facet.
rbox 10 D3 | qhull QbB p Tcv
3
9
-0.08928142660407055 -0.3194671263098747 0.3605569202297553
-0.1534778158747162 0.03516440701453921 0.5
-0.01663016790622804 0.3709299907861695 0.0764863283135003
0.3932651765570926 0.4421392241401818 -0.09396622763110282
0.199424728304684 0.5 0.06620718432588452
-0.2331094527352667 0.3262436269787957 -0.128966098672764
-0.5 0.2819439085196089 -0.5
0.4999999999999999 0.3760666748352666 0.1399187075693636
0.4888102268053206 -0.5 -0.2153953634886358
Output completed. Verifying that all points are below 2.1e-15 of
all facets. Will make 140 distance computations.
rbox 10 D3 | qhull Qbb p Tcv
QH7040 qhull option warning: option 'Qbb' (scale-last-coordinate) is normally used with 'd' or 'v'
3
9
-0.0222149361131852 -0.366434993563625 0.4072229792632261
-0.06676722137887703 -0.1566931052661437 0.4732086509216659
0.02820502736438535 0.04189077954915421 0.272798317696016
0.3126723396709863 0.08400649026409401 0.1921386936513206
0.1781470954214661 0.1182274414396169 0.2679341378370068
-0.1220315663349177 0.01546165115708642 0.1755764518932639
-0.3072535691850387 -0.01073880122111998 0
0.3867462923626847 0.04492879989084675 0.3028150683084346
0.3789805913148268 -0.4732086509216658 0.1346773760895938
Output completed. Verifying that all points are below 2e-15 of
all facets. Will make 140 distance computations.
rbox 10 D3 | qhull Qb0:-10B2:20 p Tcv
3
9
-5.733970380575339 -0.366434993563625 17.14322461142018
-6.400761988815288 -0.1566931052661437 20
-4.97936018866004 0.04189077954915421 11.32346018178493
-0.7218812392989191 0.08400649026409401 7.831392539952951
-2.735252796494545 0.1182274414396169 11.11287098934976
-7.227875597731384 0.01546165115708642 7.114348923589702
-10 -0.01073880122111998 -0.4870359524963758
0.3867462923626847 0.04492879989084675 12.62300161615219
0.2705209571204694 -0.4732086509216658 5.343669467959105
Output completed. Verifying that all points are below 7.5e-14 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-14 of
all facets. Will make 140 distance computations.
3
9
-0.08928142660407051 -0.3194671263098747 0.3605569202297555
-0.153477815874716 0.03516440701453921 0.5
-0.01663016790622796 0.3709299907861695 0.07648632831350011
0.3932651765570927 0.4421392241401818 -0.09396622763110274
0.1994247283046841 0.5 0.06620718432588446
-0.2331094527352668 0.3262436269787957 -0.1289660986727639
-0.5 0.2819439085196089 -0.4999999999999999
0.5 0.3760666748352666 0.1399187075693635
0.4888102268053207 -0.5 -0.2153953634886357
Output completed. Verifying that all points are below 2.1e-15 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: 31
Number of facets in hull: 16
Number of distance tests for qhull: 61
CPU seconds to compute hull (after input): 0.000157
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-15 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: 31
Number of facets in hull: 16
Number of distance tests for qhull: 61
CPU seconds to compute hull (after input): 0.000157
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-15 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: 43
Number of facets in hull: 27
Number of distance tests for qhull: 66
CPU seconds to compute hull (after input): 0.0002
Output completed. Verifying that all points are below 2.9e-15 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: 48
CPU seconds to compute hull (after input): 7.3e-05
Output completed. Verifying that all points are below 1.3e-15 of
all facets. Will make 40 distance computations.
echo "== next command will error ${d:-`date`} =="
== next command will error Mon Sep 18 21:37:22 UTC 2023 ==
rbox 10 D2 | qhull Qb1:1B1:1 Tcv
QH6154 Qhull precision error: Initial simplex is flat (facet 1 is coplanar with the interior point)
While executing: rbox 10 D2 | qhull Qb1:1B1:1 Tcv
Options selected for Qhull 2020.2.r 2020/08/31:
run-id 574555792 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-16 _one-merge 4.3e-15 _near-inside 2.1e-14
Visible-distance 1.7e-15 U-max-coplanar 1.7e-15 Width-outside 3.4e-15
_wide-facet 1e-14 _maxoutside 5.1e-15
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(v3): -0.022 1
- p4(v2): 0.38 1
- p1(v1): -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-16. 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-16.
- 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
Options selected for Qhull 2020.2.r 2020/08/31:
run-id 574555792 Tcheck-frequently Tverify Centrum-premerge- 0
_zero-centrum _max-width 0.98 Error-roundoff 3.4e-16 _one-merge 1.7e-15
_near-inside 8.5e-15 Visible-distance 6.8e-16 U-max-coplanar 6.8e-16
Width-outside 1.4e-15 _wide-facet 4.1e-15
Convex hull of 200 points in 2-d:
Number of vertices: 200
Number of facets: 200
Statistics for: rbox 200 L20 D2 t1695073042 | qhull FO Tcv C-0
Number of points processed: 200
Number of hyperplanes created: 397
Number of distance tests for qhull: 2082
CPU seconds to compute hull (after input): 0.006349
Output completed. Verifying that all points are below 1e-15 of
all facets. Will make 40000 distance computations.
rbox 1000 L20 t | qhull FO Tcv C-0
Options selected for Qhull 2020.2.r 2020/08/31:
run-id 574555792 Tcheck-frequently Tverify Centrum-premerge- 0
_zero-centrum _max-width 1 Error-roundoff 6.9e-16 _one-merge 4.8e-15
_near-inside 2.4e-14 Visible-distance 1.4e-15 U-max-coplanar 1.4e-15
Width-outside 2.8e-15 _wide-facet 8.3e-15
Convex hull of 1000 points in 3-d:
Number of vertices: 43
Number of facets: 82
Statistics for: rbox 1000 L20 t1695073042 | qhull FO Tcv C-0
Number of points processed: 50
Number of hyperplanes created: 201
Number of distance tests for qhull: 10251
CPU seconds to compute hull (after input): 0.001987
Output completed. Verifying that all points are below outer planes of
all facets. Will make 82000 distance computations.
rbox 200 L20 D4 t | qhull FO Tcv C-0
Options selected for Qhull 2020.2.r 2020/08/31:
run-id 574555792 Tcheck-frequently Tverify Centrum-premerge- 0
_zero-centrum _max-width 0.99 Error-roundoff 1e-15 _one-merge 9.1e-15
_near-inside 4.5e-14 Visible-distance 6e-15 U-max-coplanar 6e-15
Width-outside 1.2e-14 _wide-facet 3.6e-14
Convex hull of 200 points in 4-d:
Number of vertices: 64
Number of facets: 301
Statistics for: rbox 200 L20 D4 t1695073042 | qhull FO Tcv C-0
Number of points processed: 67
Number of hyperplanes created: 723
Number of distance tests for qhull: 5206
CPU seconds to compute hull (after input): 0.006092
Output completed. Verifying that all points are below outer planes of
all facets. Will make 60200 distance computations.
rbox 200 L20 D5 t | qhull FO Tcv Qx
Options selected for Qhull 2020.2.r 2020/08/31:
run-id 574555792 Tcheck-frequently Tverify Qxact-merge _zero-centrum
_max-width 0.99 Error-roundoff 1.4e-15 _one-merge 1.5e-14
_near-inside 7.5e-14 Visible-distance 8.1e-15 U-max-coplanar 8.1e-15
Width-outside 1.6e-14 _wide-facet 4.9e-14
Convex hull of 200 points in 5-d:
Number of vertices: 97
Number of facets: 1472
Statistics for: rbox 200 L20 D5 t1695073042 | qhull FO Tcv Qx
Number of points processed: 113
Number of hyperplanes created: 5038
Number of distance tests for qhull: 19568
CPU seconds to compute hull (after input): 0.03562
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 294400 distance computations.
rbox 1000 W1e-3 s D2 t | qhull d FO Tcv Qu Q0
Options selected for Qhull 2020.2.r 2020/08/31:
run-id 574572599 delaunay Tcheck-frequently Tverify QupperDelaunay
Q0-no-premerge Pgood _max-width 1 Error-roundoff 6.9e-16
Visible-distance 6.9e-16 U-max-coplanar 6.9e-16 Width-outside 1.4e-15
_wide-facet 4.2e-15
Furthest-site Delaunay triangulation by the convex hull of 1000 points in 3-d:
Number of input sites: 1000
Number of Delaunay regions: 256
Statistics for: rbox 1000 W1e-3 s D2 t1695073043 | qhull d FO Tcv Qu Q0
Number of points processed: 1000
Number of hyperplanes created: 4628
Number of facets in hull: 1996
Number of distance tests for qhull: 27859
CPU seconds to compute hull (after input): 0.112
Output completed. Verifying that all points are below 2.1e-15 of
all facets. Will make 256000 distance computations.
rbox 1000 W1e-3 s D2 t | qhull d FO Tcv Qu C-0
Options selected for Qhull 2020.2.r 2020/08/31:
run-id 574572599 delaunay Tcheck-frequently Tverify QupperDelaunay
Centrum-premerge- 0 _zero-centrum Pgood _max-width 1
Error-roundoff 6.9e-16 _one-merge 4.9e-15 _near-inside 2.4e-14
Visible-distance 1.4e-15 U-max-coplanar 1.4e-15 Width-outside 2.8e-15
_wide-facet 8.3e-15
Furthest-site Delaunay triangulation by the convex hull of 1000 points in 3-d:
Number of input sites: 1000
Number of Delaunay regions: 256
Statistics for: rbox 1000 W1e-3 s D2 t1695073043 | qhull d FO Tcv Qu C-0
Number of points processed: 1000
Number of hyperplanes created: 4628
Number of facets in hull: 1996
Number of distance tests for qhull: 27859
CPU seconds to compute hull (after input): 0.1141
Output completed. Verifying that all points are below 2.1e-15 of
all facets. Will make 256000 distance computations.
set +v
=== check joggle and TRn Mon Sep 18 21:37:23 UTC 2023
rbox 100 W0 | qhull QJ1e-14 Qc TR100 Tv
Early exit due to 'TAn', '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: 11218
Number of distance tests for qhull: 119030
CPU seconds to compute hull (after input): 0.02886
Percentage of runs with precision errors: 100.0
precision problems (corrected unless 'Q0' or an error)
100 coplanar horizon facets for new vertices
400 coplanar points during partitioning
rbox 100 W0 | qhull QJ1e-13 Qc TR100 Tv
Early exit due to 'TAn', '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: 24747
Number of distance tests for qhull: 195826
CPU seconds to compute hull (after input): 0.05348
Percentage of runs with precision errors: 63.0
precision problems (corrected unless 'Q0' or an error)
10 coplanar half ridges in output
53 coplanar horizon facets for new vertices
119 coplanar points during partitioning
rbox 100 W0 | qhull QJ1e-12 Qc TR100 Tv
Early exit due to 'TAn', '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: 29152
Number of distance tests for qhull: 216487
CPU seconds to compute hull (after input): 0.06158
Percentage of runs with precision errors: 8.0
precision problems (corrected unless 'Q0' or an error)
2 coplanar half ridges in output
6 coplanar horizon facets for new vertices
17 coplanar points during partitioning
rbox 100 W0 | qhull QJ1e-11 Qc TR100 Tv
Convex hull of 100 points in 3-d:
Number of vertices: 66
Number of coplanar points: 34
Number of facets: 128
Statistics for: rbox 100 W0 | qhull QJ1e-11 Qc TR100 Tv
Number of points processed: 75
Number of hyperplanes created: 29577
Number of distance tests for qhull: 218409
CPU seconds to compute hull (after input): 0.06201
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-15 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: 29583
Number of distance tests for qhull: 218315
CPU seconds to compute hull (after input): 0.06177
Percentage of runs with precision errors: 0.0
Output completed. Verifying that all points are below 2.1e-15 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
Options selected for Qhull 2020.2.r 2020/08/31:
run-id 574572599 delaunay Qbound-dim-low 0 1e+04 QBound-dim-high 0 1e+05
Qbound-dim-low 1 1e+04 QBound-dim-high 1 1e+06 Qbound-dim-low 2 1e+05
QBound-dim-high 2 1e+07 Tverify Pgood _run 1 QJoggle 6.7e+03
_joggle-seed 16807 _max-width 1e+14 Error-roundoff 0.11
Visible-distance 0.11 U-max-coplanar 0.11 Width-outside 0.23
_wide-facet 0.68
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: 1477
Number of facets in hull: 560
Number of distance tests for qhull: 3418
CPU seconds to compute hull (after input): 0.002731
Input joggled by: 6.7e+03
Output completed. Verifying that all points are below 0.34 of
all facets. Will make 48800 distance computations.
set +v
=== check precision options Mon Sep 18 21:37:23 UTC 2023
rbox 100 D3 s | qhull E0.01 Qx Tcv FO
Options selected for Qhull 2020.2.r 2020/08/31:
run-id 574572599 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-max-coplanar 0.02 Width-outside 0.04
_wide-facet 0.12
Convex hull of 100 points in 3-d:
Number of vertices: 46
Number of facets: 41
Number of non-simplicial facets: 29
Statistics for: rbox 100 D3 s | qhull E0.01 Qx Tcv FO
Number of points processed: 46
Number of hyperplanes created: 162
Number of distance tests for qhull: 3834
Number of distance tests for merging: 1887
Number of distance tests for checking: 1989
Number of merged facets: 60
CPU seconds to compute hull (after input): 0.002633
Maximum distance of point above facet: 0.048 (0.6x)
Maximum distance of vertex below facet: -0.072 (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 4100 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: 169
Number of distance tests for qhull: 1565
CPU seconds to compute hull (after input): 0.000998
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: 127
Number of distance tests for qhull: 1691
CPU seconds to compute hull (after input): 0.000723
precision problems (corrected unless 'Q0' or an error)
23 coplanar points during partitioning
Output completed. Verifying that all points are below outer planes 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: 131
Number of distance tests for qhull: 1720
CPU seconds to compute hull (after input): 0.000785
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: 45
Number of distance tests for qhull: 2377
CPU seconds to compute hull (after input): 0.00042
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: 63
Number of facets in hull: 28
Number of distance tests for qhull: 141
Number of distance tests for merging: 474
Number of distance tests for checking: 236
Number of merged facets: 7
CPU seconds to compute hull (after input): 0.000485
Maximum distance of point above facet: 1.6e-15 (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: 123
Number of facets in hull: 60
Number of distance tests for qhull: 224
CPU seconds to compute hull (after input): 0.00049
Output completed. Verifying that all points are below 2.8e-15 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: 108
Number of coplanar points: 892
Number of facets: 95
Number of non-simplicial facets: 78
Statistics for: rbox 1000 s D3 | qhull C-0.01 Tcv Qc
Number of points processed: 112
Number of hyperplanes created: 464
Number of distance tests for qhull: 62162
Number of distance tests for merging: 6682
Number of distance tests for checking: 24376
Number of merged facets: 264
CPU seconds to compute hull (after input): 0.01896
Maximum distance of point above facet: 0.021 (0.7x)
Maximum distance of vertex below facet: -0.029 (1.0x)
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 V0 Qc Tcv
Convex hull of 1000 points in 3-d:
Number of vertices: 137
Number of coplanar points: 863
Number of facets: 87
Number of non-simplicial facets: 82
Statistics for: rbox 1000 s D3 | qhull C-0.01 V0 Qc Tcv
Number of points processed: 466
Number of hyperplanes created: 2572
Number of distance tests for qhull: 232428
Number of distance tests for merging: 47390
Number of distance tests for checking: 38513
Number of merged facets: 1818
CPU seconds to compute hull (after input): 0.1178
Maximum distance of point above facet: 0.026 (0.9x)
Maximum distance of vertex below facet: -0.075 (2.5x)
Output completed. Verifying that all points are below outer planes of
all facets. Will make 87000 distance computations.
rbox 1000 s D3 | qhull C-0.01 U0 Qc Tcv
Convex hull of 1000 points in 3-d:
Number of vertices: 108
Number of coplanar points: 892
Number of facets: 97
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: 505
Number of distance tests for qhull: 62212
Number of distance tests for merging: 7315
Number of distance tests for checking: 24575
Number of merged facets: 260
CPU seconds to compute hull (after input): 0.01895
Maximum distance of point above facet: 0.021 (0.7x)
Maximum distance of vertex below facet: -0.029 (1.0x)
Output completed. Verifying that all points are below outer planes of
all facets. Will make 97000 distance computations.
rbox 1000 s D3 | qhull C-0.01 V0 Qcm Tcv
Convex hull of 1000 points in 3-d:
Number of vertices: 87
Number of coplanar points: 913
Number of facets: 88
Number of non-simplicial facets: 56
Statistics for: rbox 1000 s D3 | qhull C-0.01 V0 Qcm Tcv
Number of points processed: 90
Number of hyperplanes created: 457
Number of distance tests for qhull: 46340
Number of distance tests for merging: 5761
Number of distance tests for checking: 21602
Number of merged facets: 192
CPU seconds to compute hull (after input): 0.01336
Maximum distance of point above facet: 0.032 (1.1x)
Maximum distance of vertex below facet: -0.041 (1.4x)
Output completed. Verifying that all points are below outer planes of
all facets. Will make 88000 distance computations.
rbox 1000 s D3 | qhull C-0.01 Qcm Tcv
Convex hull of 1000 points in 3-d:
Number of vertices: 101
Number of coplanar points: 899
Number of facets: 95
Number of non-simplicial facets: 69
Statistics for: rbox 1000 s D3 | qhull C-0.01 Qcm Tcv
Number of points processed: 104
Number of hyperplanes created: 433
Number of distance tests for qhull: 59136
Number of distance tests for merging: 6024
Number of distance tests for checking: 24116
Number of merged facets: 232
CPU seconds to compute hull (after input): 0.0172
Maximum distance of point above facet: 0.023 (0.8x)
Maximum distance of vertex below facet: -0.031 (1.0x)
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 Q1 FO Tcv Qc
Options selected for Qhull 2020.2.r 2020/08/31:
run-id 574589406 Centrum-premerge- 0.01 Q1-angle-merge Tcheck-frequently
Tverify Qcoplanar-keep _max-width 1 Error-roundoff 6.9e-16
_one-merge 0.03 _near-inside 0.15 Visible-distance 0.01
U-max-coplanar 0.01 Width-outside 0.02 _wide-facet 0.06
Convex hull of 1000 points in 3-d:
Number of vertices: 107
Number of coplanar points: 893
Number of facets: 97
Number of non-simplicial facets: 80
Statistics for: rbox 1000 s D3 | qhull C-0.01 Q1 FO Tcv Qc
Number of points processed: 111
Number of hyperplanes created: 450
Number of distance tests for qhull: 61776
Number of distance tests for merging: 6387
Number of distance tests for checking: 24594
Number of merged facets: 253
CPU seconds to compute hull (after input): 0.01871
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 97000 distance computations.
rbox 1000 s D3 | qhull C-0.01 Q2 FO Tcv Qc
Options selected for Qhull 2020.2.r 2020/08/31:
run-id 574589406 Centrum-premerge- 0.01 Q2-no-merge-independent
Tcheck-frequently Tverify Qcoplanar-keep _max-width 1
Error-roundoff 6.9e-16 _one-merge 0.03 _near-inside 0.15
Visible-distance 0.01 U-max-coplanar 0.01 Width-outside 0.02
_wide-facet 0.06
Convex hull of 1000 points in 3-d:
Number of vertices: 106
Number of coplanar points: 894
Number of facets: 92
Number of non-simplicial facets: 74
Statistics for: rbox 1000 s D3 | qhull C-0.01 Q2 FO Tcv Qc
Number of points processed: 110
Number of hyperplanes created: 451
Number of distance tests for qhull: 60312
Number of distance tests for merging: 6396
Number of distance tests for checking: 23893
Number of merged facets: 260
CPU seconds to compute hull (after input): 0.01844
Maximum distance of point above facet: 0.023 (0.8x)
Maximum distance of vertex below facet: -0.049 (1.6x)
Output completed. Verifying that all points are below outer planes of
all facets. Will make 92000 distance computations.
rbox 1000 s D3 | qhull C-0.01 Q3 FO Tcv Qc
Options selected for Qhull 2020.2.r 2020/08/31:
run-id 574589406 Centrum-premerge- 0.01 Q3-no-merge-vertices
Tcheck-frequently Tverify Qcoplanar-keep _max-width 1
Error-roundoff 6.9e-16 _one-merge 0.03 _near-inside 0.15
Visible-distance 0.01 U-max-coplanar 0.01 Width-outside 0.02
_wide-facet 0.06
Convex hull of 1000 points in 3-d:
Number of vertices: 112
Number of coplanar points: 888
Number of facets: 94
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: 468
Number of distance tests for qhull: 61911
Number of distance tests for merging: 6879
Number of distance tests for checking: 24243
Number of merged facets: 268
CPU seconds to compute hull (after input): 0.01905
Maximum distance of point above facet: 0.021 (0.7x)
Maximum distance of vertex below facet: -0.03 (1.0x)
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 Q4 FO Tcv Qc
Options selected for Qhull 2020.2.r 2020/08/31:
run-id 574589406 Centrum-premerge- 0.01 Q4-avoid-old-into-new
Tcheck-frequently Tverify Qcoplanar-keep _max-width 1
Error-roundoff 6.9e-16 _one-merge 0.03 _near-inside 0.15
Visible-distance 0.01 U-max-coplanar 0.01 Width-outside 0.02
_wide-facet 0.06
Convex hull of 1000 points in 3-d:
Number of vertices: 108
Number of coplanar points: 892
Number of facets: 95
Number of non-simplicial facets: 78
Statistics for: rbox 1000 s D3 | qhull C-0.01 Q4 FO Tcv Qc
Number of points processed: 112
Number of hyperplanes created: 464
Number of distance tests for qhull: 62162
Number of distance tests for merging: 6682
Number of distance tests for checking: 24376
Number of merged facets: 264
CPU seconds to compute hull (after input): 0.01921
Maximum distance of point above facet: 0.021 (0.7x)
Maximum distance of vertex below facet: -0.029 (1.0x)
Output completed. Verifying that all points are below outer planes of
all facets. Will make 95000 distance computations.
echo === this may generate an error ${d:-`date`}
=== this may generate an error Mon Sep 18 21:37:24 UTC 2023
rbox 1000 s D3 | qhull C-0.01 Q5 FO Tcv
Options selected for Qhull 2020.2.r 2020/08/31:
run-id 574589406 Centrum-premerge- 0.01 Q5-no-check-outer
Tcheck-frequently Tverify _max-width 1 Error-roundoff 6.9e-16
_one-merge 0.03 Visible-distance 0.01 U-max-coplanar 0.01
Width-outside 0.02 _wide-facet 0.06
Convex hull of 1000 points in 3-d:
Number of vertices: 108
Number of facets: 95
Number of non-simplicial facets: 78
Statistics for: rbox 1000 s D3 | qhull C-0.01 Q5 FO Tcv
Number of points processed: 112
Number of hyperplanes created: 464
Number of distance tests for qhull: 35756
Number of distance tests for merging: 6682
Number of distance tests for checking: 2036
Number of merged facets: 264
CPU seconds to compute hull (after input): 0.0152
Maximum distance of point above facet: 0.022 (0.7x)
Maximum distance of vertex below facet: -0.031 (1.0x)
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 95000 distance computations.
echo === this should generate an error ${d:-`date`}
=== this should generate an error Mon Sep 18 21:37:24 UTC 2023
rbox 1000 s D3 | qhull C-0.01 Q6 FO Po Tcv Qc
Options selected for Qhull 2020.2.r 2020/08/31:
run-id 574589406 Centrum-premerge- 0.01 Q6-no-concave-merge Poutput-forced
Tcheck-frequently Tverify Qcoplanar-keep _max-width 1
Error-roundoff 6.9e-16 _one-merge 0.03 _near-inside 0.15
Visible-distance 0.01 U-max-coplanar 0.01 Width-outside 0.02
_wide-facet 0.06
QH6117 qhull precision error: f328 is concave to f329. Centrum of f328 is 0.001027 above f329
QH6117 qhull precision error: f329 is concave to f328. Centrum of f329 is 0.004134 above f328
QH6117 qhull precision error: f482 is concave to f484. Centrum of f482 is 0.0001795 above f484
QH6117 qhull precision error: f484 is concave to f482. Centrum of f484 is 6.818e-05 above f482
Convex hull of 1000 points in 3-d:
Number of vertices: 115
Number of coplanar points: 885
Number of facets: 184
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: 115
Number of hyperplanes created: 455
Number of distance tests for qhull: 52081
Number of distance tests for merging: 1190
Number of distance tests for checking: 28981
Number of merged facets: 88
CPU seconds to compute hull (after input): 0.01574
Maximum distance of point above facet: 0.02 (0.7x)
Maximum distance of vertex below facet: -0.009 (0.3x)
rbox 1000 s D3 | qhull C-0.01 Q7 FO Tcv Qc
Options selected for Qhull 2020.2.r 2020/08/31:
run-id 574589406 Centrum-premerge- 0.01 Q7-no-breadth-first
Tcheck-frequently Tverify Qcoplanar-keep _max-width 1
Error-roundoff 6.9e-16 _one-merge 0.03 _near-inside 0.15
Visible-distance 0.01 U-max-coplanar 0.01 Width-outside 0.02
_wide-facet 0.06
Convex hull of 1000 points in 3-d:
Number of vertices: 108
Number of coplanar points: 892
Number of facets: 99
Number of non-simplicial facets: 77
Statistics for: rbox 1000 s D3 | qhull C-0.01 Q7 FO Tcv Qc
Number of points processed: 110
Number of hyperplanes created: 449
Number of distance tests for qhull: 55287
Number of distance tests for merging: 6050
Number of distance tests for checking: 22232
Number of merged facets: 242
CPU seconds to compute hull (after input): 0.01828
Maximum distance of point above facet: 0.021 (0.7x)
Maximum distance of vertex below facet: -0.031 (1.0x)
Output completed. Verifying that all points are below outer planes of
all facets. Will make 99000 distance computations.
rbox 1000 s D3 | qhull C-0.01 Qx Tcv Qc
Convex hull of 1000 points in 3-d:
Number of vertices: 115
Number of coplanar points: 885
Number of facets: 101
Number of non-simplicial facets: 76
Statistics for: rbox 1000 s D3 | qhull C-0.01 Qx Tcv Qc
Number of points processed: 115
Number of hyperplanes created: 455
Number of distance tests for qhull: 89505
Number of distance tests for merging: 5154
Number of distance tests for checking: 19846
Number of merged facets: 171
CPU seconds to compute hull (after input): 0.01697
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 101000 distance computations.
echo === this may generate an error e.g., t1263080158 ${d:-`date`}
=== this may generate an error e.g., t1263080158 Mon Sep 18 21:37:24 UTC 2023
rbox 100 s D3 t | qhull R1e-3 Tcv Qc
Convex hull of 100 points in 3-d:
Number of vertices: 100
Number of facets: 166
Number of non-simplicial facets: 24
Statistics for: rbox 100 s D3 t1695073044 | qhull R1e-3 Tcv Qc
Number of points processed: 100
Number of hyperplanes created: 474
Number of distance tests for qhull: 1613
Number of distance tests for merging: 3042
Number of distance tests for checking: 1610
Number of merged facets: 41
CPU seconds to compute hull (after input): 0.006959
Maximum distance of point above facet: 0.0018 (0.4x)
Maximum distance of vertex below facet: -0.0043 (1.1x)
Output completed. Verifying that all points are below outer planes of
all facets. Will make 16600 distance computations.
rbox 100 s D3 t | qhull R1e-2 Tcv Qc
Convex hull of 100 points in 3-d:
Number of vertices: 60
Number of coplanar points: 40
Number of facets: 59
Number of non-simplicial facets: 40
Statistics for: rbox 100 s D3 t1695073044 | qhull R1e-2 Tcv Qc
Number of points processed: 64
Number of hyperplanes created: 294
Number of distance tests for qhull: 3489
Number of distance tests for merging: 4018
Number of distance tests for checking: 2888
Number of merged facets: 145
CPU seconds to compute hull (after input): 0.005866
Maximum distance of point above facet: 0.04 (1.0x)
Maximum distance of vertex below facet: -0.063 (1.6x)
Output completed. Verifying that all points are below outer planes of
all facets. Will make 5900 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: 19
Number of coplanar points: 481
Number of facets: 15
Number of non-simplicial facets: 13
Statistics for: rbox 500 s D3 t1695073044 | qhull R0.05 A-1 Tcv Qc
Number of points processed: 22
Number of hyperplanes created: 75
Number of distance tests for qhull: 22441
Number of distance tests for merging: 1163
Number of distance tests for checking: 7072
Number of merged facets: 45
CPU seconds to compute hull (after input): 0.004551
Maximum distance of point above facet: 0.16 (0.3x)
Maximum distance of vertex below facet: -0.21 (0.3x)
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: 34
Number of coplanar points: 66
Number of facets: 45
Number of non-simplicial facets: 7
Statistics for: rbox 100 W0 D3 t1695073044 | qhull R1e-3 Tcv Qc
Number of points processed: 44
Number of hyperplanes created: 160
Number of distance tests for qhull: 1896
Number of distance tests for merging: 1376
Number of distance tests for checking: 1245
Number of merged facets: 41
CPU seconds to compute hull (after input): 0.002273
Maximum distance of point above facet: 0.003 (0.7x)
Maximum distance of vertex below facet: -0.0069 (1.7x)
Output completed. Verifying that all points are below outer planes of
all facets. Will make 4500 distance computations.
rbox 100 W0 D3 t | qhull R1e-3 Qx Tcv Qc
Convex hull of 100 points in 3-d:
Number of vertices: 36
Number of coplanar points: 64
Number of facets: 47
Number of non-simplicial facets: 7
Statistics for: rbox 100 W0 D3 t1695073044 | qhull R1e-3 Qx Tcv Qc
Number of points processed: 46
Number of hyperplanes created: 162
Number of distance tests for qhull: 2724
Number of distance tests for merging: 1367
Number of distance tests for checking: 1047
Number of merged facets: 41
CPU seconds to compute hull (after input): 0.002395
Maximum distance of point above facet: 0.002 (0.5x)
Maximum distance of vertex below facet: -0.0059 (1.5x)
QH7076 qhull input warning: exact merge ('Qx'). Verify may report that a point is outside of a facet. See qh-optq.htm#Qx
Output completed. Verifying that all points are below outer planes of
all facets. Will make 4700 distance computations.
rbox 100 W0 D3 t | qhull R1e-2 Tcv Qc
Convex hull of 100 points in 3-d:
Number of vertices: 22
Number of coplanar points: 78
Number of facets: 21
Number of non-simplicial facets: 10
Statistics for: rbox 100 W0 D3 t1695073044 | qhull R1e-2 Tcv Qc
Number of points processed: 26
Number of hyperplanes created: 94
Number of distance tests for qhull: 2652
Number of distance tests for merging: 1030
Number of distance tests for checking: 1240
Number of merged facets: 35
CPU seconds to compute hull (after input): 0.00153
Maximum distance of point above facet: 0.03 (0.7x)
Maximum distance of vertex below facet: -0.049 (1.2x)
Output completed. Verifying that all points are below outer planes of
all facets. Will make 2100 distance computations.
rbox 100 W0 D3 t | qhull R1e-2 Qx Tcv Qc
Convex hull of 100 points in 3-d:
Number of vertices: 21
Number of coplanar points: 79
Number of facets: 23
Number of non-simplicial facets: 7
Statistics for: rbox 100 W0 D3 t1695073044 | qhull R1e-2 Qx Tcv Qc
Number of points processed: 28
Number of hyperplanes created: 97
Number of distance tests for qhull: 3427
Number of distance tests for merging: 1086
Number of distance tests for checking: 1013
Number of merged facets: 30
CPU seconds to compute hull (after input): 0.001609
Maximum distance of point above facet: 0.025 (0.6x)
Maximum distance of vertex below facet: -0.045 (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 2300 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 t1695073044 | qhull R0.05 A-1 Tcv Qc
Number of points processed: 13
Number of hyperplanes created: 40
Number of distance tests for qhull: 14531
Number of distance tests for merging: 473
Number of distance tests for checking: 3607
Number of merged facets: 20
CPU seconds to compute hull (after input): 0.00252
Maximum distance of point above facet: 0.11 (0.2x)
Maximum distance of vertex below facet: -0.14 (0.2x)
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 t1695073044 | qhull R0.05 Qx Tcv Qc
Number of points processed: 19
Number of hyperplanes created: 50
Number of distance tests for qhull: 23151
Number of distance tests for merging: 547
Number of distance tests for checking: 3472
Number of merged facets: 34
CPU seconds to compute hull (after input): 0.003719
Maximum distance of point above facet: 0.099 (0.5x)
Maximum distance of vertex below facet: -0.18 (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 3000 distance computations.
rbox 1000 W1e-20 t | qhull Tcv Qc
Convex hull of 1000 points in 3-d:
Number of vertices: 80
Number of coplanar points: 920
Number of facets: 94
Number of non-simplicial facets: 6
Statistics for: rbox 1000 W1e-20 t1695073044 | qhull Tcv Qc
Number of points processed: 103
Number of hyperplanes created: 320
Number of distance tests for qhull: 21515
Number of distance tests for merging: 3262
Number of distance tests for checking: 16606
Number of merged facets: 108
CPU seconds to compute hull (after input): 0.008776
Output completed. Verifying that all points are below outer planes of
all facets. Will make 94000 distance computations.
rbox 1000 W1e-20 D4 t | qhull Tcv Qc
Convex hull of 1000 points in 4-d:
Number of vertices: 278
Number of coplanar points: 722
Number of facets: 1031
Number of non-simplicial facets: 8
Statistics for: rbox 1000 W1e-20 D4 t1695073044 | qhull Tcv Qc
Number of points processed: 360
Number of hyperplanes created: 4865
Number of distance tests for qhull: 72755
Number of distance tests for merging: 57425
Number of distance tests for checking: 87756
Number of merged facets: 1153
CPU seconds to compute hull (after input): 0.2728
Output completed. Verifying that all points are below outer planes of
all facets. Will make 1031000 distance computations.
rbox 500 W1e-20 D5 t | qhull Tv Qc
Convex hull of 500 points in 5-d:
Number of vertices: 354
Number of coplanar points: 146
Number of facets: 5686
Number of non-simplicial facets: 10
Statistics for: rbox 500 W1e-20 D5 t1695073044 | qhull Tv Qc
Number of points processed: 389
Number of hyperplanes created: 25151
Number of distance tests for qhull: 116270
Number of distance tests for merging: 287053
Number of distance tests for checking: 125022
Number of merged facets: 2990
CPU seconds to compute hull (after input): 0.149
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 2843000 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: 5809
Number of non-simplicial facets: 9
Statistics for: rbox 100 W1e-20 D6 t1695073045 | qhull Tv Qc
Number of points processed: 100
Number of hyperplanes created: 20266
Number of distance tests for qhull: 32101
Number of distance tests for merging: 200068
Number of distance tests for checking: 60434
Number of merged facets: 213
CPU seconds to compute hull (after input): 0.1075
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 580900 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: 1927
Number of non-simplicial facets: 2
Statistics for: rbox 50 W1e-20 D6 t1695073045 | qhull Qv Tv Qc
Number of points processed: 50
Number of hyperplanes created: 5158
Number of distance tests for qhull: 7474
Number of distance tests for merging: 3095363
Number of distance tests for checking: 19817
Number of merged facets: 9
CPU seconds to compute hull (after input): 0.2775
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 96350 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: 8808
Number of facets: 8
Number of non-simplicial facets: 8
Statistics for: rbox 10000 D4 t1695073045 | qhull QR0 Qc C-0.01 A0.3 Tv QR1695073045
Number of points processed: 45
Number of hyperplanes created: 253
Number of distance tests for qhull: 1187600
Number of distance tests for merging: 17376
Number of distance tests for checking: 89634
Number of merged facets: 282
CPU seconds to compute hull (after input): 0.08342
Maximum distance of point above facet: 0.044
Maximum distance of vertex below facet: -0.19 (0.1x)
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: 15
Statistics for: rbox 1000 D2 t1695073045 | qhull d QR0 Qc C-1e-8 Qu Tv QR1695073045
Number of points processed: 1000
Number of hyperplanes created: 5606
Number of facets in hull: 1996
Number of distance tests for qhull: 30765
CPU seconds to compute hull (after input): 0.01668
Output completed. Verifying that all points are below outer planes of
all facets. Will make 15000 distance computations.
rbox 300 D5 t |qhull A-0.999 Qx Qc Tcv
Convex hull of 300 points in 5-d:
Number of vertices: 161
Number of coplanar points: 32
Number of facets: 1656
Number of non-simplicial facets: 445
Statistics for: rbox 300 D5 t1695073045 | qhull A-0.999 Qx Qc Tcv
Number of points processed: 190
Number of hyperplanes created: 11240
Number of distance tests for qhull: 161391
Number of distance tests for merging: 58866
Number of distance tests for checking: 29754
Number of merged facets: 1164
CPU seconds to compute hull (after input): 0.0836
Maximum distance of vertex below facet: -0.024 (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 496800 distance computations.
rbox 100 D6 t |qhull A-0.9999 Qx Qc Tcv
Convex hull of 100 points in 6-d:
Number of vertices: 86
Number of coplanar points: 1
Number of facets: 4092
Number of non-simplicial facets: 283
Statistics for: rbox 100 D6 t1695073046 | qhull A-0.9999 Qx Qc Tcv
Number of points processed: 93
Number of hyperplanes created: 15740
Number of distance tests for qhull: 28752
Number of distance tests for merging: 68846
Number of distance tests for checking: 70224
Number of merged facets: 688
CPU seconds to compute hull (after input): 0.09337
Maximum distance of vertex below facet: -0.0064 (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 409200 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: 48
Number of coplanar points: 1
Number of facets: 4791
Number of non-simplicial facets: 75
Statistics for: rbox 50 D7 t1695073046 | qhull A-0.99999 Qx Qc Tcv W0.1
Number of points processed: 48
Number of hyperplanes created: 15291
Number of distance tests for qhull: 25528
Number of distance tests for merging: 64309
Number of distance tests for checking: 140777
Number of merged facets: 213
CPU seconds to compute hull (after input): 0.1105
Maximum distance of point above facet: 0.059
Maximum distance of vertex below facet: -0.0021 (0.2x)
QH7076 qhull input warning: exact merge ('Qx'). Verify may report that a point is outside of a facet. See qh-optq.htm#Qx
Output completed. Verifying that all points are below outer planes of
all facets. Will make 239550 distance computations.
set +v
=======================================================
=== The following commands may cause errors Mon Sep 18 21:37:26 UTC 2023
=======================================================
=== check bad cases for Qhull Mon Sep 18 21:37:26 UTC 2023
rbox 1000 L100000 s G1e-6 t | qhull Tv
QH7089 qhull precision warning: The initial hull is narrow. Is the input lower
dimensional (e.g., a square in 3-d instead of a cube)? Cosine of the minimum
angle is 1.0000000000000000. If so, Qhull may produce a wide facet.
Options 'Qs' (search all points), 'Qbb' (scale last coordinate), or
'QbB' (scale to unit box) may remove this warning.
See 'Limitations' in qh-impre.htm. Use 'Pp' to skip this warning.
Convex hull of 1000 points in 3-d:
Number of vertices: 995
Number of facets: 1523
Number of non-simplicial facets: 3
Statistics for: rbox 1000 L100000 s G1e-6 t1695073046 | qhull Tv
Number of points processed: 995
Number of hyperplanes created: 3634
Number of distance tests for qhull: 29879
Number of distance tests for merging: 130854
Number of distance tests for checking: 119051
Number of merged facets: 464
CPU seconds to compute hull (after input): 0.03233
Maximum distance of vertex below facet: -2.3e-15 (0.4x)
Output completed. Verifying that all points are below outer planes of
all facets. Will make 1523000 distance computations.
rbox 1000 L100000 s G1e-6 t | qhull Tv Q10
Convex hull of 1000 points in 3-d:
Number of vertices: 995
Number of facets: 1523
Number of non-simplicial facets: 3
Statistics for: rbox 1000 L100000 s G1e-6 t1695073046 | qhull Tv Q10
Number of points processed: 996
Number of hyperplanes created: 3666
Number of distance tests for qhull: 34412
Number of distance tests for merging: 131306
Number of distance tests for checking: 119674
Number of merged facets: 467
CPU seconds to compute hull (after input): 0.0327
Maximum distance of vertex below facet: -2.3e-15 (0.4x)
Output completed. Verifying that all points are below outer planes of
all facets. Will make 1523000 distance computations.
rbox 1000 s Z1 G1e-13 t | qhull Tv
Convex hull of 1001 points in 3-d:
Number of vertices: 1001
Number of facets: 1480
Number of non-simplicial facets: 149
Statistics for: rbox 1000 s Z1 G1e-13 t1695073046 | qhull Tv
Number of points processed: 1001
Number of hyperplanes created: 4349
Number of distance tests for qhull: 28300
Number of distance tests for merging: 86652
Number of distance tests for checking: 279624
Number of merged facets: 1494
CPU seconds to compute hull (after input): 0.04111
Maximum distance of point above facet: 7.6e-15 (1.4x)
Maximum distance of vertex below facet: -1.9e-14 (3.5x)
Output completed. Verifying that all points are below outer planes of
all facets. Will make 1481480 distance computations.
rbox 1000 s W1e-13 P0 t | qhull d Qbb Qc Q12 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 t1695073046 | qhull d Qbb Qc Q12 Tv
Number of points processed: 1001
Number of hyperplanes created: 95176
Number of facets in hull: 2008
Number of distance tests for qhull: 145880
Number of distance tests for merging: 9640473
Number of distance tests for checking: 2009924
Number of merged facets: 88433
CPU seconds to compute hull (after input): 2.898
Maximum distance of point above facet: 3.5e-13 (34.3x)
Maximum distance of vertex below facet: -2.7e-13 (27.0x)
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 Q12 Tv
QH7089 qhull precision warning: The initial hull is narrow. Is the input lower
dimensional (e.g., a square in 3-d instead of a cube)? Cosine of the minimum
angle is 1.0000000000000000. If so, Qhull may produce a wide facet.
Options 'Qs' (search all points), 'Qbb' (scale last coordinate), or
'QbB' (scale to unit box) may remove this warning.
See 'Limitations' in qh-impre.htm. Use 'Pp' to skip this warning.
Delaunay triangulation by the convex hull of 1000 points in 4-d:
Number of input sites: 877
Total number of deleted points due to merging: 89
Total number of nearly incident points: 34
Number of Delaunay regions: 969
Number of non-simplicial Delaunay regions: 328
Statistics for: rbox 1000 s W1e-13 t1695073049 | qhull d Q12 Tv
Number of points processed: 966
Number of hyperplanes created: 11306
Number of facets in hull: 1934
Number of distance tests for qhull: 1698124
Number of distance tests for merging: 2963289
Number of distance tests for checking: 1890350
Number of merged facets: 8477
CPU seconds to compute hull (after input): 0.7316
Maximum distance of point above facet: 3.2e-12 (319.0x)
Maximum distance of vertex below facet: -5.5e-14 (5.4x)
Output completed. Verifying that all points are below outer planes of
all facets. Will make 969000 distance computations.
rbox 1000 s W1e-13 t D2 | qhull d Tv
QH7089 qhull precision warning: The initial hull is narrow. Is the input lower
dimensional (e.g., a square in 3-d instead of a cube)? Cosine of the minimum
angle is 1.0000000000000000. If so, Qhull may produce a wide facet.
Options 'Qs' (search all points), 'Qbb' (scale last coordinate), or
'QbB' (scale to unit box) may remove this warning.
See 'Limitations' in qh-impre.htm. Use 'Pp' to skip this warning.
QH6347 qhull precision error (qh_mergefacet): wide merge for facet f855 into f592 for mergetype 6 (flip). maxdist 0 (0.0x) mindist -1.2e-11 (2181.4x) vertexdist 0.024 Allow with 'Q12' (allow-wide)
ERRONEOUS FACET:
- f855
- flags: top simplicial upperDelaunay newfacet flipped
- normal: 1.55e-13 -2.256e-13 1
- offset: -0.25
- vertices: p188(v167) p981(v53) p314(v7)
- neighboring facets: f592 f858 f862
ERRONEOUS OTHER FACET:
- f592
- flags: bottom simplicial upperDelaunay tested
- normal: -1.809e-10 1.459e-10 1
- offset: -0.25
- center: -0.3893721421594778 0.3135141143867444 0.2499999999999824
- outside set(furthest p737):
p370: -0.3895 0.3135 0.25
p247: -0.3931 0.3089 0.25
p737: -0.3889 0.3142 0.25
- furthest distance= 3.7e-14
- vertices: p422(v112) p981(v53) p314(v7)
- neighboring facets: f855 f591 f593
- ridges:
While executing: rbox 1000 s W1e-13 D2 t1695073050 | qhull d Tv
Options selected for Qhull 2020.2.r 2020/08/31:
run-id 574690248 delaunay Tverify _pre-merge _zero-centrum Pgood
_max-width 1 Error-roundoff 6.9e-16 _one-merge 4.9e-15
_near-inside 2.4e-14 Visible-distance 1.4e-15 U-max-coplanar 1.4e-15
Width-outside 2.8e-15 _wide-facet 8.3e-15 _narrow-hull 0
_maxoutside 7.7e-15
Last point added to hull was p188. Last merge was #261.
At error exit:
Delaunay triangulation by the convex hull of 1000 points in 3-d:
Number of input sites: 167
Total number of nearly incident points: 833
Number of Delaunay regions: 119
Number of non-simplicial Delaunay regions: 15
Statistics for: rbox 1000 s W1e-13 D2 t1695073050 | qhull d Tv
Number of points processed: 167
Number of hyperplanes created: 840
Number of facets in hull: 266
Number of distance tests for qhull: 32461
Number of distance tests for merging: 12671
Number of distance tests for checking: 0
Number of merged facets: 261
Maximum distance of point above facet: 8.4e-15 (1.5x)
Maximum distance of vertex below facet: -1.9e-14 (3.4x)
precision problems (corrected unless 'Q0' or an error)
24 flipped facets
52 coplanar horizon facets for new vertices
A wide merge error has occurred. Qhull has produced a wide facet due to facet merges and vertex merges.
This usually occurs when the input is nearly degenerate and substantial merging has occurred.
See http://www.qhull.org/html/qh-impre.htm#limit
set +v
=== check Qhull without merging Q0 Mon Sep 18 21:37:30 UTC 2023
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: 26353
CPU seconds to compute hull (after input): 0.05218
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-15 of the nearest facet.
rbox 100 s D3 | qhull Q0 E1e-3 Tc Po
QH6115 qhull precision error: f100 is concave to f247, since p44(v13) is 0.002232 above f247
QH6115 qhull precision error: f139 is concave to f274, since p90(v32) is 0.007128 above f274
QH6115 qhull precision error: f163 is concave to f232, since p5(v6) is 0.001226 above f232
QH6115 qhull precision error: f293 is concave to f389, since p11(v61) is 0.002161 above f389
QH6115 qhull precision error: f307 is concave to f459, since p75(v21) is 0.01537 above f459
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: 1727
CPU seconds to compute hull (after input): 0.004685
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
QH6115 qhull precision error: f123 is concave to f235, since p85(v8) is 0.06092 above f235
QH6115 qhull precision error: f177 is concave to f272, since p98(v20) is 0.03571 above f272
QH6115 qhull precision error: f246 is concave to f252, since p7(v57) is 0.02104 above f252
QH6115 qhull precision error: f261 is concave to f305, since p82(v60) is 0.01847 above f305
QH6115 qhull precision error: f266 is concave to f317, since p82(v60) is 0.02592 above f317
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: 1664
CPU seconds to compute hull (after input): 0.00256
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: 917
CPU seconds to compute hull (after input): 0.000196
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
QH6115 qhull precision error: f94 is concave to f270, since p44(v13) is 0.003303 above f270
QH6115 qhull precision error: f157 is concave to f255, since p5(v6) is 0.005886 above f255
QH6115 qhull precision error: f289 is concave to f386, since p30(v62) is 0.000726 above f386
QH6115 qhull precision error: f381 is concave to f293, since p56(v79) is 0.0006018 above f293
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: 498
Number of distance tests for qhull: 1643
CPU seconds to compute hull (after input): 0.004904
precision problems (corrected unless 'Q0' or an error)
10 coplanar half ridges in output
4 concave half ridges in output
10 coplanar horizon facets for new vertices
rbox 100 s D3 | qhull Q0 R1e-2 Tc Po
QH6115 qhull precision error: f78 is concave to f147, since p57(v1) is 0.01085 above f147
QH6115 qhull precision error: f89 is concave to f194, since p17(v2) is 0.0111 above f194
QH6115 qhull precision error: f106 is concave to f122, since p74(v27) is 0.01501 above f122
QH6115 qhull precision error: f122 is concave to f106, since p95(v30) is 0.00822 above f106
QH6115 qhull precision error: f126 is concave to f213, since p95(v30) is 0.007437 above f213
QH6115 qhull precision error: f141 is concave to f288, since p81(v34) is 0.007157 above f288
QH6115 qhull precision error: f147 is concave to f227, since p90(v19) is 0.1078 above f227
QH6115 qhull precision error: f161 is concave to f252, since p20(v24) is 0.008976 above f252
QH6115 qhull precision error: f176 is concave to f277, since p38(v22) is 0.008285 above f277
QH6115 qhull precision error: f181 is concave to f276, since p73(v12) is 0.02209 above f276
QH6115 qhull precision error: f186 is concave to f291, since p85(v8) is 0.04316 above f291
QH6115 qhull precision error: f194 is concave to f89, since p82(v45) is 0.009743 above f89
QH6115 qhull precision error: f198 is concave to f273, since p82(v45) is 0.01834 above f273
QH6115 qhull precision error: f213 is concave to f126, since p93(v48) is 0.01071 above f126
QH6115 qhull precision error: f227 is concave to f147, since p37(v51) is 0.007006 above f147
QH6115 qhull precision error: f273 is concave to f198, since p29(v60) is 0.006128 above f198
QH6115 qhull precision error: f288 is concave to f141, since p96(v63) is 0.005493 above f141
QH6115 qhull precision error: f291 is concave to f186, since p34(v64) is 0.008643 above f186
QH6115 qhull precision error: f300 is concave to f355, since p30(v66) is 0.006345 above f355
QH6115 qhull precision error: f324 is concave to f384, since p75(v20) is 0.02388 above f384
QH6115 qhull precision error: f361 is concave to f406, since p41(v5) is 0.009438 above f406
QH6115 qhull precision error: f368 is concave to f367, since p11(v69) is 0.007227 above f367
QH6115 qhull precision error: f390 is concave to f391, since p99(v73) is 0.007279 above f391
QH6115 qhull precision error: f391 is concave to f390, since p43(v74) is 0.01052 above f390
Convex hull of 100 points in 3-d:
Number of vertices: 88
Number of facets: 172
Statistics for: rbox 100 s D3 | qhull Q0 R1e-2 Tc Po
Number of points processed: 88
Number of hyperplanes created: 413
Number of distance tests for qhull: 1702
CPU seconds to compute hull (after input): 0.00385
precision problems (corrected unless 'Q0' or an error)
49 coplanar half ridges in output
24 concave half ridges in output
53 coplanar horizon facets for new vertices
12 coplanar points during partitioning
rbox 100 s D3 | qhull Q0 R0.05 Tc
QH6136 qhull precision error: facet f193 is flipped, distance= 0.391655882694
ERRONEOUS FACET:
- f193
- flags: top simplicial flipped
- normal: -0.2813 -0.9389 0.1981
- offset: 0.2910058
- vertices: p19(v46) p65(v35) p74(v28)
- neighboring facets: f183 f194 f195
A flipped facet occurs when its distance to the interior point is
greater than or equal to -0.024, the maximum roundoff error.
While executing: rbox 100 s D3 | qhull Q0 R0.05 Tc
Options selected for Qhull 2020.2.r 2020/08/31:
run-id 574690248 Q0-no-premerge Random-perturb 0.05 Tcheck-frequently
_max-width 0.94 Error-roundoff 0.024 Visible-distance 0.024
U-max-coplanar 0.024 Width-outside 0.048 _wide-facet 0.15 _maxoutside 0.19
Last point added to hull was p19.
Qhull has finished constructing the hull.
At error exit:
Convex hull of 100 points in 3-d:
Number of vertices: 46
Number of facets: 88
Statistics for: rbox 100 s D3 | qhull Q0 R0.05 Tc
Number of points processed: 46
Number of hyperplanes created: 196
Number of distance tests for qhull: 2023
CPU seconds to compute hull (after input): 0.001478
precision problems (corrected unless 'Q0' or an error)
1 flipped facets
34 coplanar horizon facets for new vertices
51 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
QH6136 qhull precision error: facet f193 is flipped, distance= 0.391655882694
QH6115 qhull precision error: f119 is concave to f134, since p31(v31) is 0.05178 above f134
QH6115 qhull precision error: f124 is concave to f131, since p5(v6) is 0.1065 above f131
QH6115 qhull precision error: f147 is concave to f91, since p69(v36) is 0.0354 above f91
QH6113 qhull precision error: f193 is flipped (interior point is outside)
Convex hull of 100 points in 3-d:
Number of vertices: 46
Number of facets: 88
Statistics for: rbox 100 s D3 | qhull Q0 R0.05 Tc Po
Number of points processed: 46
Number of hyperplanes created: 196
Number of distance tests for qhull: 2023
CPU seconds to compute hull (after input): 0.001425
precision problems (corrected unless 'Q0' or an error)
35 coplanar half ridges in output
3 concave half ridges in output
1 flipped facets
34 coplanar horizon facets for new vertices
51 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: 22590
CPU seconds to compute hull (after input): 0.01909
rbox 50 s | qhull Q0 V0.05 W0.01 Tc Po
QH7088 Qhull precision warning: in post-processing (qh_check_maxout) p0 for f36 is 0.061 above hidden facet f70 nearest vertices 0.15
QH7088 Qhull precision warning: in post-processing (qh_check_maxout) p8 for f38 is 0.26 above hidden facet f145 nearest vertices 0.14
QH6297 Qhull precision error (qh_check_maxout): large increase in qh.max_outside during post-processing dist 0.26 (46669910714866.6x). See warning QH0032/QH0033. Allow with 'Q12' (allow-wide) and 'Pp'
ERRONEOUS FACET:
- f145
- flags: top simplicial
- normal: -0.6276 0.1677 -0.7602
- offset: -0.2196772
- maxoutside: 0.2588526
- vertices: p2(v43) p0(v13) p24(v6)
- neighboring facets: f39 f146 f147
ERRONEOUS and NEIGHBORING FACETS to output
While executing: rbox 50 s | qhull Q0 V0.05 W0.01 Tc Po
Options selected for Qhull 2020.2.r 2020/08/31:
run-id 574690248 Q0-no-premerge Visible 0.05 W-outside 0.01
Tcheck-frequently Poutput-forced _max-width 0.98 Error-roundoff 6.9e-16
_near-inside 2.4e-14 U-max-coplanar 0.05 _wide-facet 0.3 _maxoutside 0.01
Last point added to hull was p10.
At error exit:
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: 538
precision problems (corrected unless 'Q0' or an error)
7 flipped facets
82 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 6.9e-16.
- 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 D5 | qhull Q0 R1e-2 Tc Po
QH6107 qhull topology error: facets f721, f756 and f722 meet at a ridge with more than 2 neighbors. Can not continue due to no qh.PREmerge and no 'Qx' (MERGEexact)
ERRONEOUS FACET:
- f721
- flags: bottom simplicial newfacet
- offset: 0
- vertices: p84(v29) p2(v19) p58(v12) p3(v7) p9(v2)
- neighboring facets: f362 f720 f728 f722 f740
ERRONEOUS OTHER FACET:
- f756
- flags: top simplicial newfacet
- offset: 0
- vertices: p84(v29) p40(v26) p2(v19) p58(v12) p9(v2)
- neighboring facets: f566
ERRONEOUS and NEIGHBORING FACETS to output
While executing: rbox 100 s D5 | qhull Q0 R1e-2 Tc Po
Options selected for Qhull 2020.2.r 2020/08/31:
run-id 574690248 Q0-no-premerge Random-perturb 0.01 Tcheck-frequently
Poutput-forced _max-width 0.88 Error-roundoff 0.0045
Visible-distance 0.0045 U-max-coplanar 0.0045 Width-outside 0.009
_wide-facet 0.027 _maxoutside 0.054
Last point added to hull was p84.
Convex hull of 100 points in 5-d:
Number of vertices: 29
Number of facets: 340
Statistics for: rbox 100 s D5 | qhull Q0 R1e-2 Tc Po
Number of points processed: 28
Number of hyperplanes created: 720
Number of distance tests for qhull: 2275
precision problems (corrected unless 'Q0' or an error)
1 flipped facets
24 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)
set +v
=== check nearly incident points Mon Sep 18 21:37:30 UTC 2023
rbox L100 2000 D4 s C1,1e-13 t2 | qhull
Convex hull of 4000 points in 4-d:
Number of vertices: 2096
Number of facets: 13614
Number of non-simplicial facets: 52
Statistics for: rbox L100 2000 D4 s C1,1e-13 t2 | qhull
Number of points processed: 2111
Number of hyperplanes created: 51581
Number of distance tests for qhull: 585497
Number of distance tests for merging: 267217
Number of distance tests for checking: 152193
Number of merged facets: 129
CPU seconds to compute hull (after input): 0.1983
Maximum distance of point above facet: 1.8e-14 (1.9x)
Maximum distance of vertex below facet: -8.9e-15 (0.9x)
rbox L100 2000 D4 s C1,1e-13 t2 | qhull Q12
Convex hull of 4000 points in 4-d:
Number of vertices: 2096
Number of facets: 13614
Number of non-simplicial facets: 52
Statistics for: rbox L100 2000 D4 s C1,1e-13 t2 | qhull Q12
Number of points processed: 2111
Number of hyperplanes created: 51581
Number of distance tests for qhull: 585497
Number of distance tests for merging: 267217
Number of distance tests for checking: 152193
Number of merged facets: 129
CPU seconds to compute hull (after input): 0.1937
Maximum distance of point above facet: 1.8e-14 (1.9x)
Maximum distance of vertex below facet: -8.9e-15 (0.9x)
rbox 50 C1,1E-13 t1447644703 | qhull d
QH6271 qhull topology error (qh_check_dupridge): wide merge (1125070907263.1x wider) due to dupridge between f1143 and f1169 (vertex dist 6.5e-14), merge dist 0.015, while processing p54
- Allow error with option 'Q12'
- Experimental option merge-pinched-vertices ('Q14') may avoid this error. It merges nearly adjacent vertices.
- A bounding box for the input sites may alleviate this error.
ERRONEOUS FACET:
- f1143
- flags: bottom upperDelaunay newfacet dupridge mergeridge2 flipped
- normal: 0.2935 0.3842 0.4668 0.7405
- offset: 0.05514914
- vertices: p54(v76) p45(v56) p76(v36) p44(v19)
- neighboring facets: f405 f1159 f1169 f1144
- ridges:
- r576 tested simplicialbot
vertices: p45(v56) p76(v36) p44(v19)
between f405 and f1143
- r1072 simplicialtop simplicialbot
vertices: p54(v76) p76(v36) p44(v19)
between f1143 and f1159
- r1073 simplicialbot
vertices: p54(v76) p45(v56) p44(v19)
between f1169 and f1143
- r1074 simplicialtop simplicialbot
vertices: p54(v76) p45(v56) p76(v36)
between f1143 and f1144
ERRONEOUS OTHER FACET:
- f1169
- flags: bottom upperDelaunay newfacet dupridge mergeridge1 flipped
- normal: -0.3214 0.1166 0.5495 0.7623
- offset: 0.114967
- vertices: p54(v76) p45(v56) p44(v19) p92(v11)
- neighboring facets: f405 f1159 f1170 f1143
- ridges:
- r561 tested simplicialbot
vertices: p45(v56) p44(v19) p92(v11)
between f405 and f1169
- r1070 simplicialtop simplicialbot
vertices: p54(v76) p44(v19) p92(v11)
between f1169 and f1159
- r1071 simplicialtop simplicialbot
vertices: p54(v76) p45(v56) p92(v11)
between f1170 and f1169
- r1073 simplicialbot
vertices: p54(v76) p45(v56) p44(v19)
between f1169 and f1143
While executing: rbox 50 C1,1E-13 t1447644703 | qhull d
Options selected for Qhull 2020.2.r 2020/08/31:
run-id 574707055 delaunay _pre-merge _zero-centrum Pgood _max-width 0.94
Error-roundoff 1e-15 _one-merge 9.2e-15 _near-inside 4.6e-14
Visible-distance 6.1e-15 U-max-coplanar 6.1e-15 Width-outside 1.2e-14
_wide-facet 3.7e-14 _maxoutside 1.2e-14
Last point added to hull was p54. Last merge was #247.
At error exit:
Delaunay triangulation by the convex hull of 100 points in 4-d:
Number of input sites: 76
Number of nearly incident points: 1
Number of Delaunay regions: 266
Number of non-simplicial Delaunay regions: 73
Statistics for: rbox 50 C1,1E-13 t1447644703 | qhull d
Number of points processed: 76
Number of hyperplanes created: 1087
Number of facets in hull: 303
Number of distance tests for qhull: 5296
Number of distance tests for merging: 10632
Number of distance tests for checking: 0
Number of merged facets: 249
Maximum distance of point above facet: 1.3e-14 (1.3x)
Maximum distance of vertex below facet: -1.3e-14 (1.3x)
precision problems (corrected unless 'Q0' or an error)
4 flipped facets
73 coplanar horizon facets for new vertices
1 coplanar points during partitioning
213 degenerate hyperplanes recomputed with gaussian elimination
17 nearly singular or axis-parallel hyperplanes
1 dupridges with multiple neighbors
A wide merge error has occurred. Qhull has produced a wide facet due to facet merges and vertex merges.
This usually occurs when the input is nearly degenerate and substantial merging has occurred.
See http://www.qhull.org/html/qh-impre.htm#limit
rbox 50 C1,1E-13 t1447644703 | qhull d Q12
QH6271 qhull topology error (qh_check_dupridge): wide merge (1125070907263.1x wider) due to dupridge between f1143 and f1169 (vertex dist 6.5e-14), merge dist 0.015, while processing p54
- Allow error with option 'Q12'
- Experimental option merge-pinched-vertices ('Q14') may avoid this error. It merges nearly adjacent vertices.
- A bounding box for the input sites may alleviate this error.
Delaunay triangulation by the convex hull of 100 points in 4-d:
Number of input sites: 99
Total number of nearly incident points: 1
Number of Delaunay regions: 307
Number of non-simplicial Delaunay regions: 133
Statistics for: rbox 50 C1,1E-13 t1447644703 | qhull d Q12
Number of points processed: 99
Number of hyperplanes created: 1504
Number of facets in hull: 345
Number of distance tests for qhull: 7670
Number of distance tests for merging: 18282
Number of distance tests for checking: 7318
Number of merged facets: 456
CPU seconds to compute hull (after input): 0.008487
Maximum distance of point above facet: 1.3e-14 (1.3x)
Maximum distance of vertex below facet: -0.0012 (119810840063.5x)
rbox 50 C1,1E-13 t1447644703 | qhull d Q14
Delaunay triangulation by the convex hull of 100 points in 4-d:
Number of input sites: 99
Total number of nearly incident points: 1
Number of Delaunay regions: 312
Number of non-simplicial Delaunay regions: 137
Statistics for: rbox 50 C1,1E-13 t1447644703 | qhull d Q14
Number of points processed: 99
Number of hyperplanes created: 1487
Number of facets in hull: 350
Number of distance tests for qhull: 5360
Number of distance tests for merging: 17768
Number of distance tests for checking: 4953
Number of merged facets: 513
CPU seconds to compute hull (after input): 0.008288
Maximum distance of point above facet: 1.3e-14 (1.3x)
Maximum distance of vertex below facet: -1.4e-14 (1.4x)
set +v
=======================================================
=== Testing done. Print documentation
=======================================================
qhull -
qhull -- compute convex hulls and related structures.
http://www.qhull.org 2020.2.r 2020/08/31
input (stdin):
first lines: dimension and number of points (or vice-versa).
other lines: point coordinates, best if one point per line
comments: start with a non-numeric character
halfspaces: use dim plus one and put offset after coefficients.
May be preceded by a single interior point ('H').
options:
d - Delaunay triangulation by lifting points to a paraboloid
d Qu - furthest-site Delaunay triangulation (upper convex hull)
Hn,n,... - halfspace intersection about point [n,n,0,...]
Qc - keep coplanar points with nearest facet
Qi - keep interior points with nearest facet
QJ - joggled input instead of merged facets
Qt - triangulated output
v - Voronoi diagram (dual of the Delaunay triangulation)
v Qu - furthest-site Voronoi diagram
Qhull control options:
Qa - allow input with fewer or more points than coordinates
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)
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
QVn - good facet if it includes point n, -n if not
Qx - exact pre-merges (skips coplanar and angle-coplanar facets)
Qz - add point-at-infinity to Delaunay triangulation
Qhull extra options:
Qf - partition point to furthest outside facet
Qg - only build good facets (needs 'QGn', 'QVn', or 'PdD')
QGn - good facet if visible from point n, -n for not visible
Qm - only process points that would increase max_outside
Qr - process random outside points instead of furthest ones
Qv - test vertex neighbors for convexity
Qw - allow option warnings
Q0 - turn off default premerge with 'C-0'/'Qx'
Q1 - merge by mergetype/angle instead of mergetype/distance
Q2 - merge all coplanar facets instead of merging 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
Q12 - allow wide facets and wide dupridge
Q14 - merge pinched vertices that create a dupridge
Q15 - check for duplicate ridges with the same vertices
T options:
TFn - report summary when n or more facets created
TI file - input file, may be enclosed in single quotes
TO file - output file, may be enclosed in single quotes
Ts - statistics
Tv - verify result: structure, convexity, and point inclusion
Tz - send all output to stdout
Trace options:
T4 - trace at level n, 4=all, 5=mem/gauss, -1= events
Ta - annotate output with message codes
TAn - stop qhull after adding n vertices
TCn - stop qhull after building cone for point n
TVn - stop qhull after adding point n, -n for before
Tc - check frequently during execution
Tf - flush each qh_fprintf for debugging segfaults
TPn - turn on tracing when point n added to hull
TP-1 turn on tracing after qh_buildhull and qh_postmerge
TMn - turn on tracing at merge n
TWn - trace merge facets when width > n
TRn - rerun qhull n times for statistics to adjust 'QJn'
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)
n - normals with offsets
o - OFF format (dim, points and facets; Voronoi regions)
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 output (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
Gc - centrums
GDn - drop dimension n in 3-d and 4-d output
Gh - hyperplane intersections
Gi - inner planes only
Gn - no planes
Go - outer planes only
Gr - ridges
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
PFn - keep facets whose area is at least n
Pg - print good facets (needs 'QGn' or 'QVn')
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
-? - help with examples
-V - version
rbox
rbox -- generate various point distributions. Default is random in cube.
args (any order, space separated): Version: 2019/11/10
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
Cn,r,m add n nearly adjacent points within radius r of m points
Pn,m,r add point [n,m,r] first, pads with 0, maybe repeated
Ln lens distribution of radius n. Also 's', 'r', 'G', 'W'.
Mn,m,r lattice(Mesh) rotated by [n,-m,0], [m,n,0], [0,0,r], ...
'27 M1,0,1' is {0,1,2} x {0,1,2} x {0,1,2}. Try 'M3,4 z'.
W0.1 random distribution within 0.1 of the cube's or sphere's surface
Z0.5 s random points in a 0.5 disk projected to a sphere
Z0.5 s G0.6 same as Z0.5 within a 0.6 gap
Bn bounding box coordinates, default 0.5
h output as homogeneous coordinates for cdd
n remove command line from the first line of output
On offset coordinates by n
t use time as the random number seed(default is command line)
tn use n as the random number seed
z print integer coordinates, default 'Bn' is 1e+06
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
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
-? - this message
-V - version
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
FA - report total area and volume
Fp - halfspace intersections
FS - total area and volume
Fx - extreme points (convex hull vertices)
G - Geomview output (2-d, 3-d and 4-d)
m - Mathematica output (2-d and 3-d)
o - OFF format (if 'v', outputs Voronoi regions)
QVn - print facets that include point n, -n if not
TI file - input file, may be enclosed in single quotes
TO file - output file, may be enclosed in single quotes
examples:
rbox D4 | qhull Tv 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 d D2 | qhull Qc s f Fx | more 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 Qc rbox c | qhull n
- html manual: html/index.htm
- installation: README.txt
- see also: COPYING.txt, REGISTER.txt, Changes.txt
- WWW: <http://www.qhull.org>
- GIT: <git@github.com:qhull/qhull.git>
- news: <http://www.qhull.org/news>
- Geomview: <http://www.geomview.org>
- news group: <news:comp.graphics.algorithms>
- FAQ: <http://www.faqs.org/faqs/graphics/algorithms-faq/>
- email: qhull@qhull.org
- bug reports: qhull_bug@qhull.org
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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
(html/index.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.
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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 -?'. 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: output formats ('F'),
Geomview output ('G'), printing ('P'), Qhull control ('Q'),
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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
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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 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'. To
print the centrum coordinates, use option 'Ft'. The
centrum indices for option 'i' are one more than
the centrum indices for option 'Ft'.
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
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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, 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
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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.
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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
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last float is the offset. The hyperplane is ori-
ented toward 'QVn' (if defined), or the first input
site of the pair. Use 'Tv' to verify that the
hyperplanes are perpendicular bisectors. Use
'Fo' for unbounded regions, and 'Fv' for the
corresponding Voronoi vertices.
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 'QVn' (if defined), or the first input
site of the pair. Use 'Tv' to verify that the
hyperplanes are perpendicular bisectors. Use
'Fi' for bounded regions, and 'Fv' for the
corresponding Voronoi vertices.
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
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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
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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
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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.
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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 'd', 'PAn',
'PFn', and 'PMn'
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
Qa Allow input with fewer or more points than coordinates
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.
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QBk:n Scale the k'th coordinate of the input points.
After scaling, the upper bound will be n. 'QBk'
scales to +0.5.
Qc Keep coplanar points with the nearest facet. Out-
put formats 'p', 'f', 'Gp', 'Fc', 'FN', and 'FP'
will print the points.
Qf Partition points to the furthest outside facet.
Qg Only build good facets. With the 'Qg' option,
Qhull will only build those facets that it needs to
determine the good facets in the output. See
'QGn', 'QVn', and 'PdD' for defining good facets,
and 'Pg' and 'PG' for printing good facets and
their neighbors.
QGn A facet is good (see 'Qg' and 'Pg') if it is visi-
ble from point n. If n < 0, a facet is good if it
is not visible from point n. Point n is not added
to the hull (unless 'TCn' or 'TPn'). With rbox,
use the 'Pn,m,r' option to define your point; it
will be point 0 (QG0).
Qi Keep interior points with the nearest facet. Out-
put formats 'p', 'f', 'Gp', 'FN', 'FP', and 'Fc'
will print the points.
QJn Joggle each input coordinate by adding a random
number in [-n,n]. If a precision error occurs,
then qhull increases n and tries again. It does
not increase n beyond a certain value, and it stops
after a certain number of attempts [see user.h].
Option 'QJ' selects a default value for n. The
output will be simplicial. For Delaunay triangula-
tions, 'QJn' sets 'Qbb' to scale the last coordi-
nate (not if 'Qbk:n' or 'QBk:n' is set). 'QJn' is
deprecated for Voronoi diagrams. See also 'Qt'.
Qm Only process points that would otherwise increase
max_outside. Other points are treated as coplanar
or interior points.
Qr Process random outside points instead of furthest
ones. This makes Qhull equivalent to the random-
ized incremental algorithms. CPU time is not
reported since the randomization is inefficient.
QRn Randomly rotate the input points. If n=0, use time
as the random number seed. If n>0, use n as the
random number seed. If n=-1, don't rotate but use
time as the random number seed. For Delaunay tri-
angulations ('d' and 'v'), rotate about the last
axis.
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qhull(1) qhull(1)
Qs Search all points for the initial simplex.
Qt Triangulated output. Triangulate non-simplicial
facets. 'Qt' is deprecated for Voronoi diagrams.
See also 'QJn'
Qv Test vertex neighbors for convexity after post-
merging. To use the 'Qv' option, you also need to
set a merge option (e.g., 'Qx' or 'C-0').
QVn A good facet (see 'Qg' and 'Pg') includes point n.
If n<0, then a good facet does not include point n.
The point is either in the initial simplex or it is
the first point added to the hull. Option 'QVn'
may not be used with merging.
Qw Allow option warnings. Otherwise Qhull returns an
error after most option warnings.
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 merges by mergetype/angle instead
of mergetype/distance.
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 2019/05/03 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.
Q12 With 'Q12', Qhull allows wide facets and wide dupridge
Q14 With 'Q14', Qhull merges pinched vertices that create a dupridge.
Q15 With 'Q15', Qhull checks for duplicate ridges with the same vertices.
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.
TAn Stop Qhull after adding n vertices.
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'.
Tf Flush output after each qh_fprintf. Use 'Tf' for
debugging segfaults. See 'Tz' for redirecting stderr.
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.
TMn Turn on tracing at n'th merge.
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.
TP-1 Turn on tracing after qh_buildhull and qh_postmerge.
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 2019/05/03 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'
TWn Trace merge facets when the width is greater than
n.
Tz Redirect stderr to stdout. See 'Tf' for flushing writes.
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 2019/05/03 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 2019/05/03 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 2019/05/03 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
Cn,r,m add n nearly coincident points within radius r of m points
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
make[1]: Leaving directory '/<<PKGBUILDDIR>>'
create-stamp debian/debhelper-build-stamp
dh_testroot -a -O--buildsystem=cmake
dh_prep -a -O--buildsystem=cmake
debian/rules override_dh_auto_install
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dh_auto_install --buildsystem=cmake
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make -f CMakeFiles/Makefile2 preinstall
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Install the project...
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-- Installing: /<<PKGBUILDDIR>>/debian/tmp/usr/share/doc/libqhull-dev/qhull/html/qh-code.htm
-- Installing: /<<PKGBUILDDIR>>/debian/tmp/usr/share/doc/libqhull-dev/qhull/html/qh-eg.htm
-- Installing: /<<PKGBUILDDIR>>/debian/tmp/usr/share/doc/libqhull-dev/qhull/html/qh-faq.htm
-- Installing: /<<PKGBUILDDIR>>/debian/tmp/usr/share/doc/libqhull-dev/qhull/html/qh-impre.htm
-- Installing: /<<PKGBUILDDIR>>/debian/tmp/usr/share/doc/libqhull-dev/qhull/html/qh-optc.htm
-- Installing: /<<PKGBUILDDIR>>/debian/tmp/usr/share/doc/libqhull-dev/qhull/html/qh-optf.htm
-- Installing: /<<PKGBUILDDIR>>/debian/tmp/usr/share/doc/libqhull-dev/qhull/html/qh-optg.htm
-- Installing: /<<PKGBUILDDIR>>/debian/tmp/usr/share/doc/libqhull-dev/qhull/html/qh-opto.htm
-- Installing: /<<PKGBUILDDIR>>/debian/tmp/usr/share/doc/libqhull-dev/qhull/html/qh-optp.htm
-- Installing: /<<PKGBUILDDIR>>/debian/tmp/usr/share/doc/libqhull-dev/qhull/html/qh-optq.htm
-- Installing: /<<PKGBUILDDIR>>/debian/tmp/usr/share/doc/libqhull-dev/qhull/html/qh-optt.htm
-- Installing: /<<PKGBUILDDIR>>/debian/tmp/usr/share/doc/libqhull-dev/qhull/html/qh-quick.htm
-- Installing: /<<PKGBUILDDIR>>/debian/tmp/usr/share/doc/libqhull-dev/qhull/html/qhalf.htm
-- Installing: /<<PKGBUILDDIR>>/debian/tmp/usr/share/doc/libqhull-dev/qhull/html/qhull-cpp.xml
-- Installing: /<<PKGBUILDDIR>>/debian/tmp/usr/share/doc/libqhull-dev/qhull/html/qhull.htm
-- Installing: /<<PKGBUILDDIR>>/debian/tmp/usr/share/doc/libqhull-dev/qhull/html/qhull.man
-- Installing: /<<PKGBUILDDIR>>/debian/tmp/usr/share/doc/libqhull-dev/qhull/html/qhull.txt
-- Installing: /<<PKGBUILDDIR>>/debian/tmp/usr/share/doc/libqhull-dev/qhull/html/qh_findbestfacet-drielsma.pdf
-- Installing: /<<PKGBUILDDIR>>/debian/tmp/usr/share/doc/libqhull-dev/qhull/html/qvoronoi.htm
-- Installing: /<<PKGBUILDDIR>>/debian/tmp/usr/share/doc/libqhull-dev/qhull/html/qvoron_f.htm
-- Installing: /<<PKGBUILDDIR>>/debian/tmp/usr/share/doc/libqhull-dev/qhull/html/rbox.htm
-- Installing: /<<PKGBUILDDIR>>/debian/tmp/usr/share/doc/libqhull-dev/qhull/html/rbox.man
-- Installing: /<<PKGBUILDDIR>>/debian/tmp/usr/share/doc/libqhull-dev/qhull/html/rbox.txt
-- Installing: /<<PKGBUILDDIR>>/debian/tmp/usr/share/doc/libqhull-dev/qhull/html/qh-get.htm
-- Installing: /<<PKGBUILDDIR>>/debian/tmp/usr/share/doc/libqhull-dev/qhull/src/Changes.txt
make[2]: Leaving directory '/<<PKGBUILDDIR>>/obj-arm-linux-gnueabihf'
make[1]: Leaving directory '/<<PKGBUILDDIR>>'
debian/rules execute_after_dh_auto_install
make[1]: Entering directory '/<<PKGBUILDDIR>>'
No need for extra copy of license
rm --verbose debian/tmp/usr/share/doc/libqhull-dev/qhull/COPYING.txt
removed 'debian/tmp/usr/share/doc/libqhull-dev/qhull/COPYING.txt'
No need for doc/ copies of man pages in ../../man/man1/ or for other formats.
removed 'debian/tmp/usr/share/doc/libqhull-dev/qhull/html/qhull.man'
removed 'debian/tmp/usr/share/doc/libqhull-dev/qhull/html/qhull.txt'
removed 'debian/tmp/usr/share/doc/libqhull-dev/qhull/html/rbox.man'
removed 'debian/tmp/usr/share/doc/libqhull-dev/qhull/html/rbox.txt'
rm --verbose debian/tmp/usr/share/doc/libqhull-dev/qhull/src/Changes.txt
removed 'debian/tmp/usr/share/doc/libqhull-dev/qhull/src/Changes.txt'
make[1]: Leaving directory '/<<PKGBUILDDIR>>'
dh_install -a -O--buildsystem=cmake
dh_installdocs -a -O--buildsystem=cmake
debian/rules override_dh_installchangelogs
make[1]: Entering directory '/<<PKGBUILDDIR>>'
dh_installchangelogs src/Changes.txt
make[1]: Leaving directory '/<<PKGBUILDDIR>>'
dh_installexamples -a -O--buildsystem=cmake
dh_installman -a -O--buildsystem=cmake
dh_installsystemduser -a -O--buildsystem=cmake
dh_perl -a -O--buildsystem=cmake
dh_link -a -O--buildsystem=cmake
dh_strip_nondeterminism -a -O--buildsystem=cmake
debian/rules override_dh_compress
make[1]: Entering directory '/<<PKGBUILDDIR>>'
dh_compress -X.c -X.h -X.txt
make[1]: Leaving directory '/<<PKGBUILDDIR>>'
dh_fixperms -a -O--buildsystem=cmake
dh_missing -a -O--buildsystem=cmake
dh_dwz -a -O--buildsystem=cmake
dh_strip -a -O--buildsystem=cmake
dh_makeshlibs -a -O--buildsystem=cmake
dpkg-gensymbols: warning: debian/libqhullcpp8.0/DEBIAN/symbols doesn't match completely debian/libqhullcpp8.0.symbols
--- debian/libqhullcpp8.0.symbols (libqhullcpp8.0_2020.2-6_armhf)
+++ dpkg-gensymbolsGgz5sO 2023-09-18 21:37:40.110870378 +0000
@@ -1,9 +1,9 @@
libqhullcpp.so.8.0 libqhullcpp8.0 #MINVER#
* Build-Depends-Package: libqhull-dev
- (optional=libstdc++|regex)"^_Z(Z|GTt|GV|TI|TS|TT|TV|Thn?\d+_|Tvn?\d+_n?\d+_)?N?r?V?K?[RO]?S[abdiost]" 0~unused
- (optional=non-lto)_ZN8orgQhull10QhullErrorD0Ev@Base 2020.1
- (optional=non-lto)_ZN8orgQhull10QhullErrorD1Ev@Base 2020.1
- (optional=non-lto)_ZN8orgQhull10QhullErrorD2Ev@Base 2020.1
+#MISSING: 2020.2-6# (optional=libstdc++|regex)"^_Z(Z|GTt|GV|TI|TS|TT|TV|Thn?\d+_|Tvn?\d+_n?\d+_)?N?r?V?K?[RO]?S[abdiost]" 0~unused
+#MISSING: 2020.2-6# (optional=non-lto)_ZN8orgQhull10QhullErrorD0Ev@Base 2020.1
+#MISSING: 2020.2-6# (optional=non-lto)_ZN8orgQhull10QhullErrorD1Ev@Base 2020.1
+#MISSING: 2020.2-6# (optional=non-lto)_ZN8orgQhull10QhullErrorD2Ev@Base 2020.1
_ZN8orgQhull10QhullFacet13s_empty_facetE@Base 2020.1
_ZN8orgQhull10QhullFacet13voronoiVertexEv@Base 2020.1
_ZN8orgQhull10QhullFacet9facetAreaEv@Base 2020.1
@@ -12,12 +12,12 @@
_ZN8orgQhull10QhullFacetC1ERKNS_5QhullEP6facetT@Base 2020.1
_ZN8orgQhull10QhullFacetC2ERKNS_5QhullE@Base 2020.1
_ZN8orgQhull10QhullFacetC2ERKNS_5QhullEP6facetT@Base 2020.1
- (optional=inline-ctor)_ZN8orgQhull10QhullPointC1EPNS_7QhullQhEPd@Base 2020.2
+#MISSING: 2020.2-6# (optional=inline-ctor)_ZN8orgQhull10QhullPointC1EPNS_7QhullQhEPd@Base 2020.2
_ZN8orgQhull10QhullPointC1ERKNS_5QhullE@Base 2020.1
_ZN8orgQhull10QhullPointC1ERKNS_5QhullEPd@Base 2020.1
_ZN8orgQhull10QhullPointC1ERKNS_5QhullERNS_11CoordinatesE@Base 2020.1
_ZN8orgQhull10QhullPointC1ERKNS_5QhullEiPd@Base 2020.1
- (optional=inline-ctor)_ZN8orgQhull10QhullPointC2EPNS_7QhullQhEPd@Base 2020.2
+#MISSING: 2020.2-6# (optional=inline-ctor)_ZN8orgQhull10QhullPointC2EPNS_7QhullQhEPd@Base 2020.2
_ZN8orgQhull10QhullPointC2ERKNS_5QhullE@Base 2020.1
_ZN8orgQhull10QhullPointC2ERKNS_5QhullEPd@Base 2020.1
_ZN8orgQhull10QhullPointC2ERKNS_5QhullERNS_11CoordinatesE@Base 2020.1
@@ -185,9 +185,9 @@
_ZN8orgQhull9RoadErrorC2EiPKciifx@Base 2020.1
_ZN8orgQhull9RoadErrorC2EiRKNSt7__cxx1112basic_stringIcSt11char_traitsIcESaIcEEE@Base 2020.1
_ZN8orgQhull9RoadErrorC2Ev@Base 2020.1
- (optional=non-lto)_ZN8orgQhull9RoadErrorD0Ev@Base 2020.1
- (optional=non-lto)_ZN8orgQhull9RoadErrorD1Ev@Base 2020.1
- (optional=non-lto)_ZN8orgQhull9RoadErrorD2Ev@Base 2020.1
+#MISSING: 2020.2-6# (optional=non-lto)_ZN8orgQhull9RoadErrorD0Ev@Base 2020.1
+#MISSING: 2020.2-6# (optional=non-lto)_ZN8orgQhull9RoadErrorD1Ev@Base 2020.1
+#MISSING: 2020.2-6# (optional=non-lto)_ZN8orgQhull9RoadErrorD2Ev@Base 2020.1
_ZN8orgQhull9RoadErroraSERKS0_@Base 2020.1
_ZNK8orgQhull10QhullFacet10innerplaneEv@Base 2020.1
_ZNK8orgQhull10QhullFacet10outerplaneEv@Base 2020.1
@@ -260,7 +260,7 @@
_ZTIN8orgQhull9RoadErrorE@Base 2020.1
_ZTSN8orgQhull10QhullErrorE@Base 2020.1
_ZTSN8orgQhull9RoadErrorE@Base 2020.1
- (optional=non-lto)_ZTVN8orgQhull10QhullErrorE@Base 2020.1
+#MISSING: 2020.2-6# (optional=non-lto)_ZTVN8orgQhull10QhullErrorE@Base 2020.1
_ZTVN8orgQhull9RoadErrorE@Base 2020.1
_ZlsRSoRKN8orgQhull10QhullFacet10PrintFacetE@Base 2020.1
_ZlsRSoRKN8orgQhull10QhullFacet10PrintFlagsE@Base 2020.1
dh_shlibdeps -a -O--buildsystem=cmake
dpkg-shlibdeps: warning: package could avoid a useless dependency if debian/qhull-bin/usr/bin/qdelaunay debian/qhull-bin/usr/bin/qvoronoi debian/qhull-bin/usr/bin/qconvex debian/qhull-bin/usr/bin/qhalf debian/qhull-bin/usr/bin/qhull debian/qhull-bin/usr/bin/rbox were not linked against ld-linux-armhf.so.3 (they use none of the library's symbols)
dpkg-shlibdeps: warning: symbol __aeabi_atexit@CXXABI_ARM_1.3.3 used by debian/libqhullcpp8.0/usr/lib/arm-linux-gnueabihf/libqhullcpp.so.8.0.2 found in none of the libraries
dh_installdeb -a -O--buildsystem=cmake
dh_gencontrol -a -O--buildsystem=cmake
dh_md5sums -a -O--buildsystem=cmake
dh_builddeb -a -O--buildsystem=cmake
dpkg-deb: building package 'libqhull-r8.0-dbgsym' in '../libqhull-r8.0-dbgsym_2020.2-6_armhf.deb'.
dpkg-deb: building package 'libqhull8.0' in '../libqhull8.0_2020.2-6_armhf.deb'.
dpkg-deb: building package 'libqhull-dev' in '../libqhull-dev_2020.2-6_armhf.deb'.
dpkg-deb: building package 'libqhullcpp8.0' in '../libqhullcpp8.0_2020.2-6_armhf.deb'.
dpkg-deb: building package 'libqhull8.0-dbgsym' in '../libqhull8.0-dbgsym_2020.2-6_armhf.deb'.
dpkg-deb: building package 'libqhullcpp8.0-dbgsym' in '../libqhullcpp8.0-dbgsym_2020.2-6_armhf.deb'.
dpkg-deb: building package 'libqhull-r8.0' in '../libqhull-r8.0_2020.2-6_armhf.deb'.
dpkg-deb: building package 'qhull-bin' in '../qhull-bin_2020.2-6_armhf.deb'.
dpkg-deb: building package 'qhull-bin-dbgsym' in '../qhull-bin-dbgsym_2020.2-6_armhf.deb'.
dpkg-genbuildinfo --build=any -O../qhull_2020.2-6_armhf.buildinfo
dpkg-genchanges --build=any -mRaspbian mythic lxc autobuilder 1 <root@raspbian.org> -O../qhull_2020.2-6_armhf.changes
dpkg-genchanges: info: binary-only arch-specific upload (source code and arch-indep packages not included)
dpkg-source --after-build .
dpkg-buildpackage: info: binary-only upload (no source included)
--------------------------------------------------------------------------------
Build finished at 2023-09-18T21:37:48Z
Finished
--------
I: Built successfully
+------------------------------------------------------------------------------+
| Post Build Chroot |
+------------------------------------------------------------------------------+
+------------------------------------------------------------------------------+
| Changes |
+------------------------------------------------------------------------------+
qhull_2020.2-6_armhf.changes:
-----------------------------
Format: 1.8
Date: Sun, 09 Jul 2023 23:44:21 +0200
Source: qhull
Binary: libqhull-dev libqhull-r8.0 libqhull-r8.0-dbgsym libqhull8.0 libqhull8.0-dbgsym libqhullcpp8.0 libqhullcpp8.0-dbgsym qhull-bin qhull-bin-dbgsym
Architecture: armhf
Version: 2020.2-6
Distribution: trixie-staging
Urgency: medium
Maintainer: Raspbian mythic lxc autobuilder 1 <root@raspbian.org>
Changed-By: Timo Röhling <roehling@debian.org>
Description:
libqhull-dev - calculate convex hulls and related structures (development files)
libqhull-r8.0 - calculate convex hulls and related structures (reentrant shared l
libqhull8.0 - calculate convex hulls and related structures (shared library)
libqhullcpp8.0 - calculate convex hulls and related structures (C++ shared library
qhull-bin - calculate convex hulls and related structures (utilities)
Closes: 1040724
Changes:
qhull (2020.2-6) unstable; urgency=medium
.
* Avoid deprecation warning with CMake 3.27 (Closes: #1040724)
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257fb7f942fe60be5a60914788f1162b 8176 math optional qhull_2020.2-6_armhf.buildinfo
+------------------------------------------------------------------------------+
| Package contents |
+------------------------------------------------------------------------------+
libqhull-dev_2020.2-6_armhf.deb
-------------------------------
new Debian package, version 2.0.
size 430232 bytes: control archive=2416 bytes.
823 bytes, 19 lines control
4632 bytes, 64 lines md5sums
Package: libqhull-dev
Source: qhull
Version: 2020.2-6
Architecture: armhf
Maintainer: Debian Science Maintainers <debian-science-maintainers@alioth-lists.debian.net>
Installed-Size: 1836
Depends: libqhull8.0 (= 2020.2-6), libqhull-r8.0 (= 2020.2-6), libqhullcpp8.0 (= 2020.2-6)
Section: libdevel
Priority: optional
Multi-Arch: same
Homepage: https://www.qhull.org
Description: calculate convex hulls and related structures (development files)
Qhull computes convex hulls, Delaunay triangulations, halfspace
intersections about a point, Voronoi diagrams, furthest-site
Delaunay triangulations, and furthest-site Voronoi diagrams. It
runs in 2-d, 3-d, 4-d, and higher dimensions.
.
This package contains the files necessary for development (headers and
libraries), as well as the library documentation in HTML format.
drwxr-xr-x root/root 0 2023-07-09 21:44 ./
drwxr-xr-x root/root 0 2023-07-09 21:44 ./usr/
drwxr-xr-x root/root 0 2023-07-09 21:44 ./usr/include/
drwxr-xr-x root/root 0 2023-07-09 21:44 ./usr/include/libqhull/
-rw-r--r-- root/root 1428 2020-05-24 19:59 ./usr/include/libqhull/DEPRECATED.txt
-rw-r--r-- root/root 7559 2020-05-22 02:00 ./usr/include/libqhull/geom.h
-rw-r--r-- root/root 7853 2020-05-22 02:00 ./usr/include/libqhull/io.h
-rw-r--r-- root/root 59922 2020-05-24 02:23 ./usr/include/libqhull/libqhull.h
-rw-r--r-- root/root 8772 2020-05-22 02:00 ./usr/include/libqhull/mem.h
-rw-r--r-- root/root 11362 2020-05-22 02:00 ./usr/include/libqhull/merge.h
-rw-r--r-- root/root 11602 2020-06-02 17:21 ./usr/include/libqhull/poly.h
-rw-r--r-- root/root 5064 2020-05-22 02:00 ./usr/include/libqhull/qhull_a.h
-rw-r--r-- root/root 15121 2020-05-22 02:00 ./usr/include/libqhull/qset.h
-rw-r--r-- root/root 944 2020-05-22 02:00 ./usr/include/libqhull/random.h
-rw-r--r-- root/root 13683 2020-05-22 02:00 ./usr/include/libqhull/stat.h
-rw-r--r-- root/root 38319 2020-05-24 02:32 ./usr/include/libqhull/user.h
drwxr-xr-x root/root 0 2023-07-09 21:44 ./usr/include/libqhull_r/
-rw-r--r-- root/root 8111 2020-05-22 02:00 ./usr/include/libqhull_r/geom_r.h
-rw-r--r-- root/root 8579 2020-05-22 02:00 ./usr/include/libqhull_r/io_r.h
-rw-r--r-- root/root 60736 2020-09-02 02:21 ./usr/include/libqhull_r/libqhull_r.h
-rw-r--r-- root/root 9142 2020-05-22 02:00 ./usr/include/libqhull_r/mem_r.h
-rw-r--r-- root/root 12155 2020-05-22 02:00 ./usr/include/libqhull_r/merge_r.h
-rw-r--r-- root/root 12315 2020-06-02 17:21 ./usr/include/libqhull_r/poly_r.h
-rw-r--r-- root/root 5471 2020-05-22 02:00 ./usr/include/libqhull_r/qhull_ra.h
-rw-r--r-- root/root 15675 2020-05-22 02:00 ./usr/include/libqhull_r/qset_r.h
-rw-r--r-- root/root 1074 2020-05-22 02:00 ./usr/include/libqhull_r/random_r.h
-rw-r--r-- root/root 13237 2020-05-22 02:00 ./usr/include/libqhull_r/stat_r.h
-rw-r--r-- root/root 36642 2020-05-20 01:14 ./usr/include/libqhull_r/user_r.h
drwxr-xr-x root/root 0 2023-07-09 21:44 ./usr/include/libqhullcpp/
-rw-r--r-- root/root 12862 2020-07-24 22:43 ./usr/include/libqhullcpp/Coordinates.h
-rw-r--r-- root/root 6989 2020-07-24 22:31 ./usr/include/libqhullcpp/PointCoordinates.h
-rw-r--r-- root/root 6690 2020-05-23 14:25 ./usr/include/libqhullcpp/Qhull.h
-rw-r--r-- root/root 2373 2020-05-22 02:00 ./usr/include/libqhullcpp/QhullError.h
-rw-r--r-- root/root 7623 2020-06-02 16:48 ./usr/include/libqhullcpp/QhullFacet.h
-rw-r--r-- root/root 4377 2020-07-24 01:39 ./usr/include/libqhullcpp/QhullFacetList.h
-rw-r--r-- root/root 4288 2020-07-24 02:47 ./usr/include/libqhullcpp/QhullFacetSet.h
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libqhull-r8.0-dbgsym_2020.2-6_armhf.deb
---------------------------------------
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libqhull-r8.0_2020.2-6_armhf.deb
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.
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libqhull8.0-dbgsym_2020.2-6_armhf.deb
-------------------------------------
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libqhull8.0_2020.2-6_armhf.deb
------------------------------
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Description: calculate convex hulls and related structures (shared library)
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.
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libqhullcpp8.0-dbgsym_2020.2-6_armhf.deb
----------------------------------------
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libqhullcpp8.0_2020.2-6_armhf.deb
---------------------------------
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Homepage: https://www.qhull.org
Description: calculate convex hulls and related structures (C++ shared library)
Qhull computes convex hulls, Delaunay triangulations, halfspace
intersections about a point, Voronoi diagrams, furthest-site
Delaunay triangulations, and furthest-site Voronoi diagrams. It
runs in 2-d, 3-d, 4-d, and higher dimensions.
.
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qhull-bin-dbgsym_2020.2-6_armhf.deb
-----------------------------------
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qhull-bin_2020.2-6_armhf.deb
----------------------------
new Debian package, version 2.0.
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Suggests: geomview
Section: math
Priority: optional
Homepage: https://www.qhull.org
Description: calculate convex hulls and related structures (utilities)
Qhull computes convex hulls, Delaunay triangulations, halfspace
intersections about a point, Voronoi diagrams, furthest-site
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runs in 2-d, 3-d, 4-d, and higher dimensions.
.
This package contains the qhull executable that gives a pipe interface to
some of the functionality of the library. Also included is rbox is a
useful tool in generating input for Qhull; it generates hypercubes,
diamonds, cones, circles, simplices, spirals, lattices, and random points.
.
Qhull produces graphical output for Geomview. This helps with
understanding the output (http://www.geomview.org).
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drwxr-xr-x root/root 0 2023-07-09 21:44 ./usr/share/doc/
drwxr-xr-x root/root 0 2023-07-09 21:44 ./usr/share/doc/qhull-bin/
-rw-r--r-- root/root 1599 2023-07-09 21:44 ./usr/share/doc/qhull-bin/changelog.Debian.gz
-rw-r--r-- root/root 56585 2020-09-04 02:07 ./usr/share/doc/qhull-bin/changelog.gz
-rw-r--r-- root/root 2350 2022-02-22 08:30 ./usr/share/doc/qhull-bin/copyright
drwxr-xr-x root/root 0 2023-07-09 21:44 ./usr/share/man/
drwxr-xr-x root/root 0 2023-07-09 21:44 ./usr/share/man/man1/
-rw-r--r-- root/root 637 2023-07-09 21:44 ./usr/share/man/man1/qconvex.1.gz
-rw-r--r-- root/root 645 2023-07-09 21:44 ./usr/share/man/man1/qdelaunay.1.gz
-rw-r--r-- root/root 641 2023-07-09 21:44 ./usr/share/man/man1/qhalf.1.gz
-rw-r--r-- root/root 12910 2023-07-09 21:44 ./usr/share/man/man1/qhull.1.gz
-rw-r--r-- root/root 641 2023-07-09 21:44 ./usr/share/man/man1/qvoronoi.1.gz
-rw-r--r-- root/root 1919 2023-07-09 21:44 ./usr/share/man/man1/rbox.1.gz
+------------------------------------------------------------------------------+
| Post Build |
+------------------------------------------------------------------------------+
+------------------------------------------------------------------------------+
| Cleanup |
+------------------------------------------------------------------------------+
Purging /<<BUILDDIR>>
Not cleaning session: cloned chroot in use
+------------------------------------------------------------------------------+
| Summary |
+------------------------------------------------------------------------------+
Build Architecture: armhf
Build-Space: 107664
Build-Time: 157
Distribution: trixie-staging
Host Architecture: armhf
Install-Time: 403
Job: qhull_2020.2-6
Machine Architecture: armhf
Package: qhull
Package-Time: 582
Source-Version: 2020.2-6
Space: 107664
Status: successful
Version: 2020.2-6
--------------------------------------------------------------------------------
Finished at 2023-09-18T21:37:48Z
Build needed 00:09:42, 107664k disk space