I: pbuilder: network access will be disabled during build I: Current time: Sun Feb 12 20:49:56 +14 2023 I: pbuilder-time-stamp: 1676184596 I: Building the build Environment I: extracting base tarball [/var/cache/pbuilder/bullseye-reproducible-base.tgz] I: copying local configuration I: mounting /proc filesystem I: mounting /sys filesystem I: creating /{dev,run}/shm I: mounting /dev/pts filesystem I: redirecting /dev/ptmx to /dev/pts/ptmx I: policy-rc.d already exists I: Copying source file I: copying [qhull_2020.2-3.dsc] I: copying [./qhull_2020.2.orig.tar.gz] I: copying [./qhull_2020.2-3.debian.tar.xz] I: Extracting source gpgv: unknown type of key resource 'trustedkeys.kbx' gpgv: keyblock resource '/tmp/dpkg-verify-sig.NhtNMmD9/trustedkeys.kbx': General error gpgv: Signature made Wed Dec 2 05:01:35 2020 +14 gpgv: using RSA key 26FB43829C6392308856D6A6F82F07FB8EBA2D59 gpgv: Can't check signature: No public key dpkg-source: warning: failed to verify signature on ./qhull_2020.2-3.dsc dpkg-source: info: extracting qhull in qhull-2020.2 dpkg-source: info: unpacking qhull_2020.2.orig.tar.gz dpkg-source: info: unpacking qhull_2020.2-3.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 I: Not using root during the build. I: Installing the build-deps I: user script /srv/workspace/pbuilder/2609468/tmp/hooks/D01_modify_environment starting debug: Running on ionos15-amd64. I: Changing host+domainname to test build reproducibility I: Adding a custom variable just for the fun of it... I: Changing /bin/sh to bash Removing 'diversion of /bin/sh to /bin/sh.distrib by dash' Adding 'diversion of /bin/sh to /bin/sh.distrib by bash' Removing 'diversion of /usr/share/man/man1/sh.1.gz to /usr/share/man/man1/sh.distrib.1.gz by dash' Adding 'diversion of /usr/share/man/man1/sh.1.gz to /usr/share/man/man1/sh.distrib.1.gz by bash' I: Setting pbuilder2's login shell to /bin/bash I: Setting pbuilder2's GECOS to second user,second room,second work-phone,second home-phone,second other I: user script /srv/workspace/pbuilder/2609468/tmp/hooks/D01_modify_environment finished I: user script /srv/workspace/pbuilder/2609468/tmp/hooks/D02_print_environment starting I: set BASH=/bin/sh BASHOPTS=checkwinsize:cmdhist:complete_fullquote:extquote:force_fignore:globasciiranges:hostcomplete:interactive_comments:progcomp:promptvars:sourcepath BASH_ALIASES=() BASH_ARGC=() BASH_ARGV=() BASH_CMDS=() BASH_LINENO=([0]="12" [1]="0") BASH_SOURCE=([0]="/tmp/hooks/D02_print_environment" [1]="/tmp/hooks/D02_print_environment") BASH_VERSINFO=([0]="5" [1]="1" [2]="4" [3]="1" [4]="release" [5]="x86_64-pc-linux-gnu") BASH_VERSION='5.1.4(1)-release' BUILDDIR=/build BUILDUSERGECOS='second user,second room,second work-phone,second home-phone,second other' BUILDUSERNAME=pbuilder2 BUILD_ARCH=amd64 DEBIAN_FRONTEND=noninteractive DEB_BUILD_OPTIONS='buildinfo=+all reproducible=+all,-fixfilepath parallel=16' DIRSTACK=() DISTRIBUTION= EUID=0 FUNCNAME=([0]="Echo" [1]="main") GROUPS=() HOME=/root HOSTNAME=i-capture-the-hostname HOSTTYPE=x86_64 HOST_ARCH=amd64 IFS=' ' INVOCATION_ID=db014523024844328e04da78d546b225 LANG=C LANGUAGE=et_EE:et LC_ALL=C MACHTYPE=x86_64-pc-linux-gnu MAIL=/var/mail/root OPTERR=1 OPTIND=1 OSTYPE=linux-gnu PATH=/usr/sbin:/usr/bin:/sbin:/bin:/usr/games:/i/capture/the/path PBCURRENTCOMMANDLINEOPERATION=build PBUILDER_OPERATION=build PBUILDER_PKGDATADIR=/usr/share/pbuilder PBUILDER_PKGLIBDIR=/usr/lib/pbuilder PBUILDER_SYSCONFDIR=/etc PIPESTATUS=([0]="0") POSIXLY_CORRECT=y PPID=2609468 PS4='+ ' PWD=/ SHELL=/bin/bash SHELLOPTS=braceexpand:errexit:hashall:interactive-comments:posix SHLVL=3 SUDO_COMMAND='/usr/bin/timeout -k 24.1h 24h /usr/bin/ionice -c 3 /usr/bin/nice -n 11 /usr/bin/unshare --uts -- /usr/sbin/pbuilder --build --configfile /srv/reproducible-results/rbuild-debian/tmp.e83eohmotG/pbuilderrc_WXmN --hookdir /etc/pbuilder/rebuild-hooks --debbuildopts -b --basetgz /var/cache/pbuilder/bullseye-reproducible-base.tgz --buildresult /srv/reproducible-results/rbuild-debian/tmp.e83eohmotG/b2 --logfile b2/build.log qhull_2020.2-3.dsc' SUDO_GID=111 SUDO_UID=106 SUDO_USER=jenkins TERM=unknown TZ=/usr/share/zoneinfo/Etc/GMT-14 UID=0 USER=root _='I: set' http_proxy=http://85.184.249.68:3128 I: uname -a Linux i-capture-the-hostname 5.14.0-0.bpo.2-amd64 #1 SMP Debian 5.14.9-2~bpo11+1 (2021-10-10) x86_64 GNU/Linux I: ls -l /bin total 5476 -rwxr-xr-x 1 root root 1234376 Aug 5 2021 bash -rwxr-xr-x 3 root root 38984 Jul 21 2020 bunzip2 -rwxr-xr-x 3 root root 38984 Jul 21 2020 bzcat lrwxrwxrwx 1 root root 6 Jul 21 2020 bzcmp -> bzdiff -rwxr-xr-x 1 root root 2225 Jul 21 2020 bzdiff lrwxrwxrwx 1 root root 6 Jul 21 2020 bzegrep -> bzgrep -rwxr-xr-x 1 root root 4877 Sep 5 2019 bzexe lrwxrwxrwx 1 root root 6 Jul 21 2020 bzfgrep -> bzgrep -rwxr-xr-x 1 root root 3775 Jul 21 2020 bzgrep -rwxr-xr-x 3 root root 38984 Jul 21 2020 bzip2 -rwxr-xr-x 1 root root 18424 Jul 21 2020 bzip2recover lrwxrwxrwx 1 root root 6 Jul 21 2020 bzless -> bzmore -rwxr-xr-x 1 root root 1297 Jul 21 2020 bzmore -rwxr-xr-x 1 root root 43936 Sep 24 2020 cat -rwxr-xr-x 1 root root 72672 Sep 24 2020 chgrp -rwxr-xr-x 1 root root 64448 Sep 24 2020 chmod -rwxr-xr-x 1 root root 72672 Sep 24 2020 chown -rwxr-xr-x 1 root root 151168 Sep 24 2020 cp -rwxr-xr-x 1 root root 125560 Dec 11 2020 dash -rwxr-xr-x 1 root root 113664 Sep 24 2020 date -rwxr-xr-x 1 root root 80968 Sep 24 2020 dd -rwxr-xr-x 1 root root 93936 Sep 24 2020 df -rwxr-xr-x 1 root root 147176 Sep 24 2020 dir -rwxr-xr-x 1 root root 84440 Jul 29 2021 dmesg lrwxrwxrwx 1 root root 8 Nov 8 2019 dnsdomainname -> hostname lrwxrwxrwx 1 root root 8 Nov 8 2019 domainname -> hostname -rwxr-xr-x 1 root root 39712 Sep 24 2020 echo -rwxr-xr-x 1 root root 28 Nov 10 2020 egrep -rwxr-xr-x 1 root root 39680 Sep 24 2020 false -rwxr-xr-x 1 root root 28 Nov 10 2020 fgrep -rwxr-xr-x 1 root root 69032 Jul 29 2021 findmnt -rwsr-xr-x 1 root root 34896 Feb 27 2021 fusermount -rwxr-xr-x 1 root root 203072 Nov 10 2020 grep -rwxr-xr-x 2 root root 2346 Mar 3 2021 gunzip -rwxr-xr-x 1 root root 6376 Mar 3 2021 gzexe -rwxr-xr-x 1 root root 98048 Mar 3 2021 gzip -rwxr-xr-x 1 root root 22600 Nov 8 2019 hostname -rwxr-xr-x 1 root root 72840 Sep 24 2020 ln -rwxr-xr-x 1 root root 56952 Feb 8 2020 login -rwxr-xr-x 1 root root 147176 Sep 24 2020 ls -rwxr-xr-x 1 root root 149736 Jul 29 2021 lsblk -rwxr-xr-x 1 root root 85184 Sep 24 2020 mkdir -rwxr-xr-x 1 root root 76896 Sep 24 2020 mknod -rwxr-xr-x 1 root root 48064 Sep 24 2020 mktemp -rwxr-xr-x 1 root root 59632 Jul 29 2021 more -rwsr-xr-x 1 root root 55528 Jul 29 2021 mount -rwxr-xr-x 1 root root 18664 Jul 29 2021 mountpoint -rwxr-xr-x 1 root root 147080 Sep 24 2020 mv lrwxrwxrwx 1 root root 8 Nov 8 2019 nisdomainname -> hostname lrwxrwxrwx 1 root root 14 Apr 19 2021 pidof -> /sbin/killall5 -rwxr-xr-x 1 root root 43872 Sep 24 2020 pwd lrwxrwxrwx 1 root root 4 Aug 5 2021 rbash -> bash -rwxr-xr-x 1 root root 52032 Sep 24 2020 readlink -rwxr-xr-x 1 root root 72704 Sep 24 2020 rm -rwxr-xr-x 1 root root 52032 Sep 24 2020 rmdir -rwxr-xr-x 1 root root 27472 Sep 28 2020 run-parts -rwxr-xr-x 1 root root 122224 Dec 23 2018 sed lrwxrwxrwx 1 root root 4 Feb 12 20:50 sh -> bash lrwxrwxrwx 1 root root 4 Feb 10 05:47 sh.distrib -> dash -rwxr-xr-x 1 root root 43808 Sep 24 2020 sleep -rwxr-xr-x 1 root root 84928 Sep 24 2020 stty -rwsr-xr-x 1 root root 71912 Jul 29 2021 su -rwxr-xr-x 1 root root 39744 Sep 24 2020 sync -rwxr-xr-x 1 root root 531928 Feb 17 2021 tar -rwxr-xr-x 1 root root 14456 Sep 28 2020 tempfile -rwxr-xr-x 1 root root 101408 Sep 24 2020 touch -rwxr-xr-x 1 root root 39680 Sep 24 2020 true -rwxr-xr-x 1 root root 14328 Feb 27 2021 ulockmgr_server -rwsr-xr-x 1 root root 35040 Jul 29 2021 umount -rwxr-xr-x 1 root root 39744 Sep 24 2020 uname -rwxr-xr-x 2 root root 2346 Mar 3 2021 uncompress -rwxr-xr-x 1 root root 147176 Sep 24 2020 vdir -rwxr-xr-x 1 root root 63744 Jul 29 2021 wdctl lrwxrwxrwx 1 root root 8 Nov 8 2019 ypdomainname -> hostname -rwxr-xr-x 1 root root 1984 Mar 3 2021 zcat -rwxr-xr-x 1 root root 1678 Mar 3 2021 zcmp -rwxr-xr-x 1 root root 5880 Mar 3 2021 zdiff -rwxr-xr-x 1 root root 29 Mar 3 2021 zegrep -rwxr-xr-x 1 root root 29 Mar 3 2021 zfgrep -rwxr-xr-x 1 root root 2081 Mar 3 2021 zforce -rwxr-xr-x 1 root root 7585 Mar 3 2021 zgrep -rwxr-xr-x 1 root root 2206 Mar 3 2021 zless -rwxr-xr-x 1 root root 1842 Mar 3 2021 zmore -rwxr-xr-x 1 root root 4553 Mar 3 2021 znew I: user script /srv/workspace/pbuilder/2609468/tmp/hooks/D02_print_environment finished -> Attempting to satisfy build-dependencies -> Creating pbuilder-satisfydepends-dummy package Package: pbuilder-satisfydepends-dummy Version: 0.invalid.0 Architecture: amd64 Maintainer: Debian Pbuilder Team Description: Dummy package to satisfy dependencies with aptitude - created by pbuilder This package was created automatically by pbuilder to satisfy the build-dependencies of the package being currently built. Depends: debhelper-compat (= 13), cmake, pkg-kde-tools dpkg-deb: building package 'pbuilder-satisfydepends-dummy' in '/tmp/satisfydepends-aptitude/pbuilder-satisfydepends-dummy.deb'. Selecting previously unselected package pbuilder-satisfydepends-dummy. (Reading database ... 19655 files and directories currently installed.) Preparing to unpack .../pbuilder-satisfydepends-dummy.deb ... Unpacking pbuilder-satisfydepends-dummy (0.invalid.0) ... dpkg: pbuilder-satisfydepends-dummy: dependency problems, but configuring anyway as you requested: pbuilder-satisfydepends-dummy depends on debhelper-compat (= 13); however: Package debhelper-compat is not installed. pbuilder-satisfydepends-dummy depends on cmake; however: Package cmake is not installed. pbuilder-satisfydepends-dummy depends on pkg-kde-tools; however: Package pkg-kde-tools is not installed. Setting up pbuilder-satisfydepends-dummy (0.invalid.0) ... Reading package lists... Building dependency tree... Reading state information... Initializing package states... Writing extended state information... Building tag database... pbuilder-satisfydepends-dummy is already installed at the requested version (0.invalid.0) pbuilder-satisfydepends-dummy is already installed at the requested version (0.invalid.0) The following NEW packages will be installed: autoconf{a} automake{a} autopoint{a} autotools-dev{a} bsdextrautils{a} cmake{a} cmake-data{a} debhelper{a} dh-autoreconf{a} dh-strip-nondeterminism{a} dwz{a} file{a} gettext{a} gettext-base{a} groff-base{a} intltool-debian{a} libarchive-zip-perl{a} libarchive13{a} libbrotli1{a} libcurl4{a} libdebhelper-perl{a} libelf1{a} libexpat1{a} libfile-stripnondeterminism-perl{a} libicu67{a} libjsoncpp24{a} libldap-2.4-2{a} libmagic-mgc{a} libmagic1{a} libmpdec3{a} libncurses6{a} libnghttp2-14{a} libpipeline1{a} libprocps8{a} libpsl5{a} libpython3-stdlib{a} libpython3.9-minimal{a} libpython3.9-stdlib{a} libreadline8{a} librhash0{a} librtmp1{a} libsasl2-2{a} libsasl2-modules-db{a} libsigsegv2{a} libssh2-1{a} libsub-override-perl{a} libtool{a} libuchardet0{a} libuv1{a} libxml2{a} m4{a} man-db{a} media-types{a} pkg-kde-tools{a} po-debconf{a} procps{a} python3{a} python3-minimal{a} python3.9{a} python3.9-minimal{a} readline-common{a} sensible-utils{a} The following packages are RECOMMENDED but will NOT be installed: ca-certificates curl libarchive-cpio-perl libgpm2 libldap-common libltdl-dev libmail-sendmail-perl libsasl2-modules libwww-perl lynx psmisc publicsuffix wget 0 packages upgraded, 62 newly installed, 0 to remove and 0 not upgraded. Need to get 33.9 MB of archives. After unpacking 129 MB will be used. Writing extended state information... Get: 1 http://deb.debian.org/debian bullseye/main amd64 bsdextrautils amd64 2.36.1-8 [145 kB] Get: 2 http://deb.debian.org/debian bullseye/main amd64 libuchardet0 amd64 0.0.7-1 [67.8 kB] Get: 3 http://deb.debian.org/debian bullseye/main amd64 groff-base amd64 1.22.4-6 [936 kB] Get: 4 http://deb.debian.org/debian bullseye/main amd64 libpipeline1 amd64 1.5.3-1 [34.3 kB] Get: 5 http://deb.debian.org/debian bullseye/main amd64 man-db amd64 2.9.4-2 [1354 kB] Get: 6 http://deb.debian.org/debian bullseye/main amd64 libpython3.9-minimal amd64 3.9.2-1 [801 kB] Get: 7 http://deb.debian.org/debian bullseye/main amd64 libexpat1 amd64 2.2.10-2 [96.9 kB] Get: 8 http://deb.debian.org/debian bullseye/main amd64 python3.9-minimal amd64 3.9.2-1 [1955 kB] Get: 9 http://deb.debian.org/debian bullseye/main amd64 python3-minimal amd64 3.9.2-3 [38.2 kB] Get: 10 http://deb.debian.org/debian bullseye/main amd64 media-types all 4.0.0 [30.3 kB] Get: 11 http://deb.debian.org/debian bullseye/main amd64 libmpdec3 amd64 2.5.1-1 [87.7 kB] Get: 12 http://deb.debian.org/debian bullseye/main amd64 readline-common all 8.1-1 [73.7 kB] Get: 13 http://deb.debian.org/debian bullseye/main amd64 libreadline8 amd64 8.1-1 [169 kB] Get: 14 http://deb.debian.org/debian bullseye/main amd64 libpython3.9-stdlib amd64 3.9.2-1 [1684 kB] Get: 15 http://deb.debian.org/debian bullseye/main amd64 python3.9 amd64 3.9.2-1 [466 kB] Get: 16 http://deb.debian.org/debian bullseye/main amd64 libpython3-stdlib amd64 3.9.2-3 [21.4 kB] Get: 17 http://deb.debian.org/debian bullseye/main amd64 python3 amd64 3.9.2-3 [37.9 kB] Get: 18 http://deb.debian.org/debian bullseye/main amd64 libncurses6 amd64 6.2+20201114-2 [102 kB] Get: 19 http://deb.debian.org/debian bullseye/main amd64 libprocps8 amd64 2:3.3.17-5 [63.9 kB] Get: 20 http://deb.debian.org/debian bullseye/main amd64 procps amd64 2:3.3.17-5 [502 kB] Get: 21 http://deb.debian.org/debian bullseye/main amd64 sensible-utils all 0.0.14 [14.8 kB] Get: 22 http://deb.debian.org/debian bullseye/main amd64 libmagic-mgc amd64 1:5.39-3 [273 kB] Get: 23 http://deb.debian.org/debian bullseye/main amd64 libmagic1 amd64 1:5.39-3 [126 kB] Get: 24 http://deb.debian.org/debian bullseye/main amd64 file amd64 1:5.39-3 [69.1 kB] Get: 25 http://deb.debian.org/debian bullseye/main amd64 gettext-base amd64 0.21-4 [175 kB] Get: 26 http://deb.debian.org/debian bullseye/main amd64 libsigsegv2 amd64 2.13-1 [34.8 kB] Get: 27 http://deb.debian.org/debian bullseye/main amd64 m4 amd64 1.4.18-5 [204 kB] Get: 28 http://deb.debian.org/debian bullseye/main amd64 autoconf all 2.69-14 [313 kB] Get: 29 http://deb.debian.org/debian bullseye/main amd64 autotools-dev all 20180224.1+nmu1 [77.1 kB] Get: 30 http://deb.debian.org/debian bullseye/main amd64 automake all 1:1.16.3-2 [814 kB] Get: 31 http://deb.debian.org/debian bullseye/main amd64 autopoint all 0.21-4 [510 kB] Get: 32 http://deb.debian.org/debian bullseye/main amd64 cmake-data all 3.18.4-2+deb11u1 [1725 kB] Get: 33 http://deb.debian.org/debian bullseye/main amd64 libicu67 amd64 67.1-7 [8622 kB] Get: 34 http://deb.debian.org/debian bullseye/main amd64 libxml2 amd64 2.9.10+dfsg-6.7 [693 kB] Get: 35 http://deb.debian.org/debian bullseye/main amd64 libarchive13 amd64 3.4.3-2+b1 [343 kB] Get: 36 http://deb.debian.org/debian bullseye/main amd64 libbrotli1 amd64 1.0.9-2+b2 [279 kB] Get: 37 http://deb.debian.org/debian bullseye/main amd64 libsasl2-modules-db amd64 2.1.27+dfsg-2.1 [69.1 kB] Get: 38 http://deb.debian.org/debian bullseye/main amd64 libsasl2-2 amd64 2.1.27+dfsg-2.1 [106 kB] Get: 39 http://deb.debian.org/debian bullseye/main amd64 libldap-2.4-2 amd64 2.4.57+dfsg-3 [232 kB] Get: 40 http://deb.debian.org/debian bullseye/main amd64 libnghttp2-14 amd64 1.43.0-1 [77.1 kB] Get: 41 http://deb.debian.org/debian bullseye/main amd64 libpsl5 amd64 0.21.0-1.2 [57.3 kB] Get: 42 http://deb.debian.org/debian bullseye/main amd64 librtmp1 amd64 2.4+20151223.gitfa8646d.1-2+b2 [60.8 kB] Get: 43 http://deb.debian.org/debian bullseye/main amd64 libssh2-1 amd64 1.9.0-2 [156 kB] Get: 44 http://deb.debian.org/debian bullseye/main amd64 libcurl4 amd64 7.74.0-1.3+deb11u1 [341 kB] Get: 45 http://deb.debian.org/debian bullseye/main amd64 libjsoncpp24 amd64 1.9.4-4 [78.9 kB] Get: 46 http://deb.debian.org/debian bullseye/main amd64 librhash0 amd64 1.4.1-2 [129 kB] Get: 47 http://deb.debian.org/debian bullseye/main amd64 libuv1 amd64 1.40.0-2 [132 kB] Get: 48 http://deb.debian.org/debian bullseye/main amd64 cmake amd64 3.18.4-2+deb11u1 [5593 kB] Get: 49 http://deb.debian.org/debian bullseye/main amd64 libdebhelper-perl all 13.3.4 [189 kB] Get: 50 http://deb.debian.org/debian bullseye/main amd64 libtool all 2.4.6-15 [513 kB] Get: 51 http://deb.debian.org/debian bullseye/main amd64 dh-autoreconf all 20 [17.1 kB] Get: 52 http://deb.debian.org/debian bullseye/main amd64 libarchive-zip-perl all 1.68-1 [104 kB] Get: 53 http://deb.debian.org/debian bullseye/main amd64 libsub-override-perl all 0.09-2 [10.2 kB] Get: 54 http://deb.debian.org/debian bullseye/main amd64 libfile-stripnondeterminism-perl all 1.12.0-1 [26.3 kB] Get: 55 http://deb.debian.org/debian bullseye/main amd64 dh-strip-nondeterminism all 1.12.0-1 [15.4 kB] Get: 56 http://deb.debian.org/debian bullseye/main amd64 libelf1 amd64 0.183-1 [165 kB] Get: 57 http://deb.debian.org/debian bullseye/main amd64 dwz amd64 0.13+20210201-1 [175 kB] Get: 58 http://deb.debian.org/debian bullseye/main amd64 gettext amd64 0.21-4 [1311 kB] Get: 59 http://deb.debian.org/debian bullseye/main amd64 intltool-debian all 0.35.0+20060710.5 [26.8 kB] Get: 60 http://deb.debian.org/debian bullseye/main amd64 po-debconf all 1.0.21+nmu1 [248 kB] Get: 61 http://deb.debian.org/debian bullseye/main amd64 debhelper all 13.3.4 [1049 kB] Get: 62 http://deb.debian.org/debian bullseye/main amd64 pkg-kde-tools all 0.15.32 [96.7 kB] Fetched 33.9 MB in 0s (95.2 MB/s) debconf: delaying package configuration, since apt-utils is not installed Selecting previously unselected package bsdextrautils. (Reading database ... (Reading database ... 5% (Reading database ... 10% (Reading database ... 15% (Reading database ... 20% (Reading database ... 25% (Reading database ... 30% (Reading database ... 35% (Reading database ... 40% (Reading database ... 45% (Reading database ... 50% (Reading database ... 55% (Reading database ... 60% (Reading database ... 65% (Reading database ... 70% (Reading database ... 75% (Reading database ... 80% (Reading database ... 85% (Reading database ... 90% (Reading database ... 95% (Reading database ... 100% (Reading database ... 19655 files and directories currently installed.) Preparing to unpack .../0-bsdextrautils_2.36.1-8_amd64.deb ... Unpacking bsdextrautils (2.36.1-8) ... Selecting previously unselected package libuchardet0:amd64. Preparing to unpack .../1-libuchardet0_0.0.7-1_amd64.deb ... Unpacking libuchardet0:amd64 (0.0.7-1) ... Selecting previously unselected package groff-base. Preparing to unpack .../2-groff-base_1.22.4-6_amd64.deb ... Unpacking groff-base (1.22.4-6) ... Selecting previously unselected package libpipeline1:amd64. Preparing to unpack .../3-libpipeline1_1.5.3-1_amd64.deb ... Unpacking libpipeline1:amd64 (1.5.3-1) ... Selecting previously unselected package man-db. Preparing to unpack .../4-man-db_2.9.4-2_amd64.deb ... Unpacking man-db (2.9.4-2) ... Selecting previously unselected package libpython3.9-minimal:amd64. Preparing to unpack .../5-libpython3.9-minimal_3.9.2-1_amd64.deb ... Unpacking libpython3.9-minimal:amd64 (3.9.2-1) ... Selecting previously unselected package libexpat1:amd64. Preparing to unpack .../6-libexpat1_2.2.10-2_amd64.deb ... Unpacking libexpat1:amd64 (2.2.10-2) ... Selecting previously unselected package python3.9-minimal. Preparing to unpack .../7-python3.9-minimal_3.9.2-1_amd64.deb ... Unpacking python3.9-minimal (3.9.2-1) ... Setting up libpython3.9-minimal:amd64 (3.9.2-1) ... Setting up libexpat1:amd64 (2.2.10-2) ... Setting up python3.9-minimal (3.9.2-1) ... Selecting previously unselected package python3-minimal. (Reading database ... (Reading database ... 5% (Reading database ... 10% (Reading database ... 15% (Reading database ... 20% (Reading database ... 25% (Reading database ... 30% (Reading database ... 35% (Reading database ... 40% (Reading database ... 45% (Reading database ... 50% (Reading database ... 55% (Reading database ... 60% (Reading database ... 65% (Reading database ... 70% (Reading database ... 75% (Reading database ... 80% (Reading database ... 85% (Reading database ... 90% (Reading database ... 95% (Reading database ... 100% (Reading database ... 20522 files and directories currently installed.) Preparing to unpack .../0-python3-minimal_3.9.2-3_amd64.deb ... Unpacking python3-minimal (3.9.2-3) ... Selecting previously unselected package media-types. Preparing to unpack .../1-media-types_4.0.0_all.deb ... Unpacking media-types (4.0.0) ... Selecting previously unselected package libmpdec3:amd64. 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Setting up intltool-debian (0.35.0+20060710.5) ... Setting up autoconf (2.69-14) ... Setting up dh-strip-nondeterminism (1.12.0-1) ... Setting up dwz (0.13+20210201-1) ... Setting up groff-base (1.22.4-6) ... Setting up procps (2:3.3.17-5) ... Setting up libcurl4:amd64 (7.74.0-1.3+deb11u1) ... Setting up libpython3.9-stdlib:amd64 (3.9.2-1) ... Setting up libpython3-stdlib:amd64 (3.9.2-3) ... Setting up automake (1:1.16.3-2) ... update-alternatives: using /usr/bin/automake-1.16 to provide /usr/bin/automake (automake) in auto mode Setting up po-debconf (1.0.21+nmu1) ... Setting up man-db (2.9.4-2) ... Not building database; man-db/auto-update is not 'true'. Setting up dh-autoreconf (20) ... Setting up cmake (3.18.4-2+deb11u1) ... Setting up python3.9 (3.9.2-1) ... Setting up debhelper (13.3.4) ... Setting up python3 (3.9.2-3) ... Setting up pkg-kde-tools (0.15.32) ... Processing triggers for libc-bin (2.31-13+deb11u2) ... Reading package lists... Building dependency tree... Reading state information... Reading extended state information... Initializing package states... Writing extended state information... Building tag database... -> Finished parsing the build-deps I: Building the package hostname: Name or service not known I: Running cd /build/qhull-2020.2/ && env PATH="/usr/sbin:/usr/bin:/sbin:/bin:/usr/games:/i/capture/the/path" HOME="/nonexistent/second-build" dpkg-buildpackage -us -uc -b && env PATH="/usr/sbin:/usr/bin:/sbin:/bin:/usr/games:/i/capture/the/path" HOME="/nonexistent/second-build" dpkg-genchanges -S > ../qhull_2020.2-3_source.changes dpkg-buildpackage: info: source package qhull dpkg-buildpackage: info: source version 2020.2-3 dpkg-buildpackage: info: source distribution unstable dpkg-buildpackage: info: source changed by Timo Röhling dpkg-source --before-build . dpkg-buildpackage: info: host architecture amd64 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 dh binary --buildsystem=cmake --with pkgkde_symbolshelper dh_update_autotools_config -O--buildsystem=cmake dh_autoreconf -O--buildsystem=cmake debian/rules override_dh_auto_configure make[1]: Entering directory '/build/qhull-2020.2' dh_auto_configure \ --buildsystem=cmake \ --builddir=/build/qhull-2020.2/obj-x86_64-linux-gnu \ -- \ -DCMAKE_SKIP_RPATH=ON \ -DINCLUDE_INSTALL_DIR=include \ -DLINK_APPS_SHARED=ON \ -DLIB_INSTALL_DIR=lib/x86_64-linux-gnu \ -DBIN_INSTALL_DIR=bin \ -DMAN_INSTALL_DIR=share/man/man1 \ -DDOC_INSTALL_DIR=share/doc/libqhull-dev/qhull cd obj-x86_64-linux-gnu && 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_PACKAGE_NO_PACKAGE_REGISTRY=ON -DCMAKE_INSTALL_RUNSTATEDIR=/run -DCMAKE_SKIP_INSTALL_ALL_DEPENDENCY=ON "-GUnix Makefiles" -DCMAKE_VERBOSE_MAKEFILE=ON -DCMAKE_INSTALL_LIBDIR=lib/x86_64-linux-gnu -DCMAKE_SKIP_RPATH=ON -DINCLUDE_INSTALL_DIR=include -DLINK_APPS_SHARED=ON -DLIB_INSTALL_DIR=lib/x86_64-linux-gnu -DBIN_INSTALL_DIR=bin -DMAN_INSTALL_DIR=share/man/man1 -DDOC_INSTALL_DIR=share/doc/libqhull-dev/qhull .. -- The C compiler identification is GNU 10.2.1 -- The CXX compiler identification is GNU 10.2.1 -- 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 -- Looking for sys/types.h -- Looking for sys/types.h - found -- Looking for inttypes.h -- Looking for inttypes.h - found -- Looking for stddef.h -- Looking for stddef.h - found -- Looking for stdint.h -- Looking for stdint.h - found -- Check size of off_t -- Check size of off_t - done -- Looking for fseeko -- Looking for fseeko - found -- Looking for ftello -- Looking for ftello - found -- Looking for PRIdMAX -- Looking for PRIdMAX - found -- -- ========== 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/x86_64-linux-gnu -- 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 -- Generating done CMake Warning: Manually-specified variables were not used by the project: CMAKE_EXPORT_NO_PACKAGE_REGISTRY CMAKE_FIND_PACKAGE_NO_PACKAGE_REGISTRY CMAKE_INSTALL_LIBDIR CMAKE_INSTALL_LOCALSTATEDIR CMAKE_INSTALL_RUNSTATEDIR CMAKE_INSTALL_SYSCONFDIR -- Build files have been written to: /build/qhull-2020.2/obj-x86_64-linux-gnu make[1]: Leaving directory '/build/qhull-2020.2' dh_auto_build -O--buildsystem=cmake cd obj-x86_64-linux-gnu && make -j16 "INSTALL=install --strip-program=true" VERBOSE=1 make[1]: Entering directory '/build/qhull-2020.2/obj-x86_64-linux-gnu' /usr/bin/cmake -S/build/qhull-2020.2 -B/build/qhull-2020.2/obj-x86_64-linux-gnu --check-build-system CMakeFiles/Makefile.cmake 0 /usr/bin/cmake -E cmake_progress_start /build/qhull-2020.2/obj-x86_64-linux-gnu/CMakeFiles /build/qhull-2020.2/obj-x86_64-linux-gnu//CMakeFiles/progress.marks make -f CMakeFiles/Makefile2 all make[2]: Entering directory '/build/qhull-2020.2/obj-x86_64-linux-gnu' make -f CMakeFiles/qhullstatic_r.dir/build.make CMakeFiles/qhullstatic_r.dir/depend make -f 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Scanning dependencies of target testqset make[3]: Leaving directory '/build/qhull-2020.2/obj-x86_64-linux-gnu' make -f CMakeFiles/testqset.dir/build.make CMakeFiles/testqset.dir/build make[3]: Entering directory '/build/qhull-2020.2/obj-x86_64-linux-gnu' Scanning dependencies of target testqset_r make[3]: Leaving directory '/build/qhull-2020.2/obj-x86_64-linux-gnu' make -f CMakeFiles/testqset_r.dir/build.make CMakeFiles/testqset_r.dir/build make[3]: Entering directory '/build/qhull-2020.2/obj-x86_64-linux-gnu' Scanning dependencies of target qhullstatic make[3]: Leaving directory '/build/qhull-2020.2/obj-x86_64-linux-gnu' make -f CMakeFiles/qhullstatic.dir/build.make CMakeFiles/qhullstatic.dir/build Scanning dependencies of target libqhull make[3]: Leaving directory '/build/qhull-2020.2/obj-x86_64-linux-gnu' make[3]: Entering directory '/build/qhull-2020.2/obj-x86_64-linux-gnu' make -f CMakeFiles/libqhull.dir/build.make CMakeFiles/libqhull.dir/build [ 1%] Building C object 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Scanning dependencies of target qhullcpp make[3]: Leaving directory '/build/qhull-2020.2/obj-x86_64-linux-gnu' make -f CMakeFiles/qhullcpp.dir/build.make CMakeFiles/qhullcpp.dir/build make[3]: Entering directory '/build/qhull-2020.2/obj-x86_64-linux-gnu' make[3]: Leaving directory '/build/qhull-2020.2/obj-x86_64-linux-gnu' [ 70%] Building CXX object CMakeFiles/qhullcpp.dir/src/libqhullcpp/Coordinates.cpp.o /usr/bin/c++ -Dqhullcpp_EXPORTS -I/build/qhull-2020.2/src -g -O2 -ffile-prefix-map=/build/qhull-2020.2=. -fstack-protector-strong -Wformat -Werror=format-security -Wdate-time -D_FORTIFY_SOURCE=2 -fPIC -o CMakeFiles/qhullcpp.dir/src/libqhullcpp/Coordinates.cpp.o -c /build/qhull-2020.2/src/libqhullcpp/Coordinates.cpp [ 70%] Built target user_eg make -f CMakeFiles/qconvex.dir/build.make CMakeFiles/qconvex.dir/depend make[3]: Entering directory '/build/qhull-2020.2/obj-x86_64-linux-gnu' cd /build/qhull-2020.2/obj-x86_64-linux-gnu && /usr/bin/cmake -E cmake_depends "Unix Makefiles" /build/qhull-2020.2 /build/qhull-2020.2 /build/qhull-2020.2/obj-x86_64-linux-gnu /build/qhull-2020.2/obj-x86_64-linux-gnu /build/qhull-2020.2/obj-x86_64-linux-gnu/CMakeFiles/qconvex.dir/DependInfo.cmake --color= Dependee "/build/qhull-2020.2/obj-x86_64-linux-gnu/CMakeFiles/qconvex.dir/DependInfo.cmake" is newer than depender "/build/qhull-2020.2/obj-x86_64-linux-gnu/CMakeFiles/qconvex.dir/depend.internal". 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Scanning dependencies of target rbox make[3]: Leaving directory '/build/qhull-2020.2/obj-x86_64-linux-gnu' make -f CMakeFiles/rbox.dir/build.make CMakeFiles/rbox.dir/build make[3]: Entering directory '/build/qhull-2020.2/obj-x86_64-linux-gnu' [ 75%] Building CXX object CMakeFiles/qhullcpp.dir/src/libqhullcpp/PointCoordinates.cpp.o /usr/bin/c++ -Dqhullcpp_EXPORTS -I/build/qhull-2020.2/src -g -O2 -ffile-prefix-map=/build/qhull-2020.2=. -fstack-protector-strong -Wformat -Werror=format-security -Wdate-time -D_FORTIFY_SOURCE=2 -fPIC -o CMakeFiles/qhullcpp.dir/src/libqhullcpp/PointCoordinates.cpp.o -c /build/qhull-2020.2/src/libqhullcpp/PointCoordinates.cpp [ 75%] Building C object CMakeFiles/rbox.dir/src/rbox/rbox_r.c.o /usr/bin/cc -I/build/qhull-2020.2/src -g -O2 -ffile-prefix-map=/build/qhull-2020.2=. -fstack-protector-strong -Wformat -Werror=format-security -Wdate-time -D_FORTIFY_SOURCE=2 -o CMakeFiles/rbox.dir/src/rbox/rbox_r.c.o -c /build/qhull-2020.2/src/rbox/rbox_r.c [ 76%] Building CXX object CMakeFiles/qhullcpp_static.dir/src/libqhullcpp/RboxPoints.cpp.o /usr/bin/c++ -I/build/qhull-2020.2/src -g -O2 -ffile-prefix-map=/build/qhull-2020.2=. -fstack-protector-strong -Wformat -Werror=format-security -Wdate-time -D_FORTIFY_SOURCE=2 -o CMakeFiles/qhullcpp_static.dir/src/libqhullcpp/RboxPoints.cpp.o -c /build/qhull-2020.2/src/libqhullcpp/RboxPoints.cpp [ 77%] Linking C executable rbox /usr/bin/cmake -E cmake_link_script CMakeFiles/rbox.dir/link.txt --verbose=1 /usr/bin/cc -g -O2 -ffile-prefix-map=/build/qhull-2020.2=. -fstack-protector-strong -Wformat -Werror=format-security -Wdate-time -D_FORTIFY_SOURCE=2 -Wl,-z,relro -Wl,-z,now -rdynamic CMakeFiles/rbox.dir/src/rbox/rbox_r.c.o -o rbox libqhull_r.so.8.0.2 -lm [ 77%] Building CXX object CMakeFiles/qhullcpp_static.dir/src/libqhullcpp/RoadError.cpp.o /usr/bin/c++ -I/build/qhull-2020.2/src -g -O2 -ffile-prefix-map=/build/qhull-2020.2=. -fstack-protector-strong -Wformat -Werror=format-security -Wdate-time -D_FORTIFY_SOURCE=2 -o CMakeFiles/qhullcpp_static.dir/src/libqhullcpp/RoadError.cpp.o -c /build/qhull-2020.2/src/libqhullcpp/RoadError.cpp [ 78%] Building CXX object CMakeFiles/qhullcpp_static.dir/src/libqhullcpp/RoadLogEvent.cpp.o /usr/bin/c++ -I/build/qhull-2020.2/src -g -O2 -ffile-prefix-map=/build/qhull-2020.2=. -fstack-protector-strong -Wformat -Werror=format-security -Wdate-time -D_FORTIFY_SOURCE=2 -o CMakeFiles/qhullcpp_static.dir/src/libqhullcpp/RoadLogEvent.cpp.o -c /build/qhull-2020.2/src/libqhullcpp/RoadLogEvent.cpp make[3]: Leaving directory '/build/qhull-2020.2/obj-x86_64-linux-gnu' make -f CMakeFiles/qdelaunay.dir/build.make CMakeFiles/qdelaunay.dir/depend make[3]: Entering directory '/build/qhull-2020.2/obj-x86_64-linux-gnu' cd /build/qhull-2020.2/obj-x86_64-linux-gnu && /usr/bin/cmake -E cmake_depends "Unix Makefiles" /build/qhull-2020.2 /build/qhull-2020.2 /build/qhull-2020.2/obj-x86_64-linux-gnu /build/qhull-2020.2/obj-x86_64-linux-gnu /build/qhull-2020.2/obj-x86_64-linux-gnu/CMakeFiles/qdelaunay.dir/DependInfo.cmake --color= [ 78%] Built target rbox make -f CMakeFiles/qhull.dir/build.make CMakeFiles/qhull.dir/depend make[3]: Entering directory '/build/qhull-2020.2/obj-x86_64-linux-gnu' cd /build/qhull-2020.2/obj-x86_64-linux-gnu && /usr/bin/cmake -E cmake_depends "Unix Makefiles" /build/qhull-2020.2 /build/qhull-2020.2 /build/qhull-2020.2/obj-x86_64-linux-gnu /build/qhull-2020.2/obj-x86_64-linux-gnu /build/qhull-2020.2/obj-x86_64-linux-gnu/CMakeFiles/qhull.dir/DependInfo.cmake --color= Dependee "/build/qhull-2020.2/obj-x86_64-linux-gnu/CMakeFiles/qdelaunay.dir/DependInfo.cmake" is newer than depender "/build/qhull-2020.2/obj-x86_64-linux-gnu/CMakeFiles/qdelaunay.dir/depend.internal". 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Scanning dependencies of target qhull make[3]: Leaving directory '/build/qhull-2020.2/obj-x86_64-linux-gnu' make -f CMakeFiles/qhull.dir/build.make CMakeFiles/qhull.dir/build make[3]: Entering directory '/build/qhull-2020.2/obj-x86_64-linux-gnu' [ 78%] Building C object CMakeFiles/qdelaunay.dir/src/qdelaunay/qdelaun_r.c.o /usr/bin/cc -I/build/qhull-2020.2/src -g -O2 -ffile-prefix-map=/build/qhull-2020.2=. -fstack-protector-strong -Wformat -Werror=format-security -Wdate-time -D_FORTIFY_SOURCE=2 -o CMakeFiles/qdelaunay.dir/src/qdelaunay/qdelaun_r.c.o -c /build/qhull-2020.2/src/qdelaunay/qdelaun_r.c [ 80%] Building C object CMakeFiles/qhull.dir/src/qhull/unix_r.c.o /usr/bin/cc -I/build/qhull-2020.2/src -g -O2 -ffile-prefix-map=/build/qhull-2020.2=. -fstack-protector-strong -Wformat -Werror=format-security -Wdate-time -D_FORTIFY_SOURCE=2 -o CMakeFiles/qhull.dir/src/qhull/unix_r.c.o -c /build/qhull-2020.2/src/qhull/unix_r.c [ 81%] Building CXX object CMakeFiles/qhullcpp.dir/src/libqhullcpp/Qhull.cpp.o /usr/bin/c++ -Dqhullcpp_EXPORTS -I/build/qhull-2020.2/src -g -O2 -ffile-prefix-map=/build/qhull-2020.2=. -fstack-protector-strong -Wformat -Werror=format-security -Wdate-time -D_FORTIFY_SOURCE=2 -fPIC -o CMakeFiles/qhullcpp.dir/src/libqhullcpp/Qhull.cpp.o -c /build/qhull-2020.2/src/libqhullcpp/Qhull.cpp [ 81%] Linking C executable qhull /usr/bin/cmake -E cmake_link_script CMakeFiles/qhull.dir/link.txt --verbose=1 [ 82%] Linking C executable qdelaunay make -f CMakeFiles/qhalf.dir/build.make CMakeFiles/qhalf.dir/depend /usr/bin/cmake -E cmake_link_script CMakeFiles/qdelaunay.dir/link.txt --verbose=1 make[3]: Entering directory '/build/qhull-2020.2/obj-x86_64-linux-gnu' cd /build/qhull-2020.2/obj-x86_64-linux-gnu && /usr/bin/cmake -E cmake_depends "Unix Makefiles" /build/qhull-2020.2 /build/qhull-2020.2 /build/qhull-2020.2/obj-x86_64-linux-gnu /build/qhull-2020.2/obj-x86_64-linux-gnu /build/qhull-2020.2/obj-x86_64-linux-gnu/CMakeFiles/qhalf.dir/DependInfo.cmake --color= /usr/bin/cc -g -O2 -ffile-prefix-map=/build/qhull-2020.2=. -fstack-protector-strong -Wformat -Werror=format-security -Wdate-time -D_FORTIFY_SOURCE=2 -Wl,-z,relro -Wl,-z,now -rdynamic CMakeFiles/qhull.dir/src/qhull/unix_r.c.o -o qhull libqhull_r.so.8.0.2 -lm make -f CMakeFiles/qvoronoi.dir/build.make CMakeFiles/qvoronoi.dir/depend make[3]: Entering directory '/build/qhull-2020.2/obj-x86_64-linux-gnu' cd /build/qhull-2020.2/obj-x86_64-linux-gnu && /usr/bin/cmake -E cmake_depends "Unix Makefiles" /build/qhull-2020.2 /build/qhull-2020.2 /build/qhull-2020.2/obj-x86_64-linux-gnu /build/qhull-2020.2/obj-x86_64-linux-gnu /build/qhull-2020.2/obj-x86_64-linux-gnu/CMakeFiles/qvoronoi.dir/DependInfo.cmake --color= Dependee "/build/qhull-2020.2/obj-x86_64-linux-gnu/CMakeFiles/qhalf.dir/DependInfo.cmake" is newer than depender "/build/qhull-2020.2/obj-x86_64-linux-gnu/CMakeFiles/qhalf.dir/depend.internal". 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[100%] Built target qhullcpp [100%] Linking CXX executable user_eg3 /usr/bin/cmake -E cmake_link_script CMakeFiles/user_eg3.dir/link.txt --verbose=1 /usr/bin/c++ -g -O2 -ffile-prefix-map=/build/qhull-2020.2=. -fstack-protector-strong -Wformat -Werror=format-security -Wdate-time -D_FORTIFY_SOURCE=2 -Wl,-z,relro -Wl,-z,now -rdynamic CMakeFiles/user_eg3.dir/src/user_eg3/user_eg3_r.cpp.o -o user_eg3 libqhullcpp.a libqhullstatic_r.a -lm make[3]: Leaving directory '/build/qhull-2020.2/obj-x86_64-linux-gnu' [100%] Built target user_eg3 make[2]: Leaving directory '/build/qhull-2020.2/obj-x86_64-linux-gnu' /usr/bin/cmake -E cmake_progress_start /build/qhull-2020.2/obj-x86_64-linux-gnu/CMakeFiles 0 make[1]: Leaving directory '/build/qhull-2020.2/obj-x86_64-linux-gnu' debian/rules execute_after_dh_auto_build make[1]: Entering directory '/build/qhull-2020.2' 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 > $comm.1 && \ echo " done"; \ done Building man page for qconvex... done Building man page for qdelaunay... done Building man page for qhalf... done Building man page for qvoronoi... done make[1]: Leaving directory '/build/qhull-2020.2' debian/rules override_dh_auto_test make[1]: Entering directory '/build/qhull-2020.2' env LD_LIBRARY_PATH=/build/qhull-2020.2/obj-x86_64-linux-gnu \ PATH=/build/qhull-2020.2/obj-x86_64-linux-gnu:$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): 0.000123 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: 9 Statistics for: | qhull s d Tcv Number of points processed: 8 Number of hyperplanes created: 26 Number of facets in hull: 16 Number of distance tests for qhull: 26 CPU seconds to compute hull (after input): 5.8e-05 Output completed. Verifying that all points are below 9.9e-15 of all facets. Will make 72 distance computations. Delaunay triangulation by the convex hull of 8 points in 4-d: Number of input sites: 8 Number of Delaunay regions: 14 Statistics for: | qhull s d Tcv Number of points processed: 8 Number of hyperplanes created: 30 Number of facets in hull: 18 Number of distance tests for qhull: 34 CPU seconds to compute hull (after input): 5.6e-05 Output completed. Verifying that all points are below 8.1e-15 of all facets. Will make 112 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): 7.5e-05 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 pbuilder2 pbuilder2 47888 Feb 12 20:50 /build/qhull-2020.2/obj-x86_64-linux-gnu/qconvex -rwxr-xr-x 1 pbuilder2 pbuilder2 47584 Feb 12 20:50 /build/qhull-2020.2/obj-x86_64-linux-gnu/qdelaunay -rwxr-xr-x 1 pbuilder2 pbuilder2 47920 Feb 12 20:50 /build/qhull-2020.2/obj-x86_64-linux-gnu/qhalf -rwxr-xr-x 1 pbuilder2 pbuilder2 51400 Feb 12 20:50 /build/qhull-2020.2/obj-x86_64-linux-gnu/qhull -rwxr-xr-x 1 pbuilder2 pbuilder2 47024 Feb 12 20:50 /build/qhull-2020.2/obj-x86_64-linux-gnu/qvoronoi -rwxr-xr-x 1 pbuilder2 pbuilder2 46624 Feb 12 20:50 /build/qhull-2020.2/obj-x86_64-linux-gnu/user_eg -rwxr-xr-x 1 pbuilder2 pbuilder2 1551536 Feb 12 20:50 /build/qhull-2020.2/obj-x86_64-linux-gnu/user_eg2 -rwxr-xr-x 1 pbuilder2 pbuilder2 4998000 Feb 12 20:50 /build/qhull-2020.2/obj-x86_64-linux-gnu/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): 0.000118 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: 1676184629 input -0.12 0.236 0.308 -0.562 -0.63 0.00298 0.152 0.17 0.997 -0.977 -0.0439 0.823 -0.23 -0.484 0.806 -0.907 -0.294 -0.203 -0.373 -0.807 -0.581 -0.849 0.193 0.447 Delaunay triangulation by the convex hull of 8 points in 4-d: Number of input sites: 8 Number of Delaunay regions: 9 Statistics for: | qhull s d Tcv Number of points processed: 8 Number of hyperplanes created: 26 Number of facets in hull: 16 Number of distance tests for qhull: 26 CPU seconds to compute hull (after input): 5.7e-05 Output completed. Verifying that all points are below 9.9e-15 of all facets. Will make 72 distance computations. 8 vertices and 16 facets with normals: 0.45 -0.44 0.16 0.76 -0.36 -0.88 0.26 0.16 0.85 -0.44 -0.024 -0.28 0.59 -0.63 0.014 -0.51 0.22 0.67 -0.46 0.54 0.27 0.72 -0.52 0.38 -0.39 0.078 0.78 -0.48 -0.38 0.078 0.78 -0.49 -0.65 -0.33 0.47 -0.5 -0.58 -0.26 0.46 -0.62 -0.28 -0.12 -0.59 -0.75 0.19 0.73 -0.57 0.32 -0.7 -0.13 0.17 -0.68 -0.68 -0.72 0.066 0.095 0.095 0.66 -0.51 0.54 -0.79 -0.31 0.31 -0.43 find 3-d Delaunay triangle or adjacent triangle closest to [0.5, 0.5, ...] -0.23 -0.48 0.81 -0.12 0.24 0.31 -0.37 -0.81 -0.58 0.15 0.17 1.00 ======== Compute a new triangulation as a separate instance of Qhull seed: 1676184630 input -0.12 0.5 -0.181 0.355 0.436 0.441 0.246 -0.472 0.355 0.892 0.723 -0.139 -0.568 -0.414 0.913 0.153 -0.952 -0.188 0.394 -0.673 0.253 0.524 -0.629 0.308 Delaunay triangulation by the convex hull of 8 points in 4-d: Number of input sites: 8 Number of Delaunay regions: 14 Statistics for: | qhull s d Tcv Number of points processed: 8 Number of hyperplanes created: 30 Number of facets in hull: 18 Number of distance tests for qhull: 34 CPU seconds to compute hull (after input): 5.5e-05 Output completed. Verifying that all points are below 8.1e-15 of all facets. Will make 112 distance computations. 8 vertices and 18 facets with normals: -0.56 0.14 -0.61 0.54 -0.41 0.83 0.33 0.21 0.45 -0.38 0.22 0.78 0.55 0.033 0.81 0.19 0.097 -0.87 0.49 -0.0073 0.6 -0.13 -0.59 -0.53 0.64 -0.16 -0.57 -0.49 0.64 -0.084 -0.48 -0.59 0.65 -0.081 -0.46 -0.6 0.69 0.019 -0.3 -0.66 0.66 -0.07 -0.45 -0.6 0.76 -0.0046 -0.19 -0.62 -0.41 0.075 0.57 -0.71 0.37 -0.11 0.9 -0.21 0.12 -0.64 0.71 -0.28 -0.72 -0.39 -0.099 -0.56 -0.2 -0.82 0.39 -0.36 0.48 -0.2 -0.56 -0.64 ======== Free memory allocated by the new instance of Qhull, and redisplay the old results. 8 vertices and 16 facets with normals: 0.45 -0.44 0.16 0.76 -0.36 -0.88 0.26 0.16 0.85 -0.44 -0.024 -0.28 0.59 -0.63 0.014 -0.51 0.22 0.67 -0.46 0.54 0.27 0.72 -0.52 0.38 -0.39 0.078 0.78 -0.48 -0.38 0.078 0.78 -0.49 -0.65 -0.33 0.47 -0.5 -0.58 -0.26 0.46 -0.62 -0.28 -0.12 -0.59 -0.75 0.19 0.73 -0.57 0.32 -0.7 -0.13 0.17 -0.68 -0.68 -0.72 0.066 0.095 0.095 0.66 -0.51 0.54 -0.79 -0.31 0.31 -0.43 ======== 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): 7.6e-05 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): 0.000108 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: 1676184629 input -0.12 0.236 0.308 -0.562 -0.63 0.00298 0.152 0.17 0.997 -0.977 -0.0439 0.823 -0.23 -0.484 0.806 -0.907 -0.294 -0.203 -0.373 -0.807 -0.581 -0.849 0.193 0.447 Voronoi diagram by the convex hull of 8 points in 4-d: Number of Voronoi regions: 8 Number of Voronoi vertices: 9 Statistics for: | qhull s d Tcv v p Number of points processed: 8 Number of hyperplanes created: 26 Number of facets in hull: 16 Number of distance tests for qhull: 26 CPU seconds to compute hull (after input): 5.7e-05 3 9 1.5299429190198 -0.7965092479172975 -0.04228223159957589 0.5702102064849931 -0.6118758003118683 0.01407546117800651 -0.4008445615597139 0.0804519966117578 0.8122853254475784 -0.3957166881542433 0.08019022515206027 0.8029345508546432 -0.6501573322892544 -0.3301765067144654 0.4684092114812283 -0.4613692125624394 -0.2103464193911246 0.3683426786985567 -0.1888322101249769 -0.08188619056832322 -0.3918171099389033 -0.5143562370289055 -0.09783326704194584 0.1253934744699682 -0.9126328562275244 -0.3626446155773843 0.3587754945788876 Output completed. Verifying that all points are below 9.9e-15 of all facets. Will make 72 distance computations. 8 vertices and 16 facets with normals: 0.45 -0.44 0.16 0.76 -0.36 -0.88 0.26 0.16 0.85 -0.44 -0.024 -0.28 0.59 -0.63 0.014 -0.51 0.22 0.67 -0.46 0.54 0.27 0.72 -0.52 0.38 -0.39 0.078 0.78 -0.48 -0.38 0.078 0.78 -0.49 -0.65 -0.33 0.47 -0.5 -0.58 -0.26 0.46 -0.62 -0.28 -0.12 -0.59 -0.75 0.19 0.73 -0.57 0.32 -0.7 -0.13 0.17 -0.68 -0.68 -0.72 0.066 0.095 0.095 0.66 -0.51 0.54 -0.79 -0.31 0.31 -0.43 find 3-d Delaunay triangle or adjacent triangle closest to [0.5, 0.5, ...] -0.23 -0.48 0.81 -0.12 0.24 0.31 -0.37 -0.81 -0.58 0.15 0.17 1.00 ======== Compute a new triangulation as a separate instance of Qhull seed: 1676184630 input -0.12 0.5 -0.181 0.355 0.436 0.441 0.246 -0.472 0.355 0.892 0.723 -0.139 -0.568 -0.414 0.913 0.153 -0.952 -0.188 0.394 -0.673 0.253 0.524 -0.629 0.308 Voronoi diagram by the convex hull of 8 points in 4-d: Number of Voronoi regions: 8 Number of Voronoi vertices: 14 Statistics for: | qhull s d Tcv v p Number of points processed: 8 Number of hyperplanes created: 30 Number of facets in hull: 18 Number of distance tests for qhull: 34 CPU seconds to compute hull (after input): 5.7e-05 3 14 6.64613358614621 -59.4422008176645 33.52405510479295 0.5645614393735819 -0.120960958765298 -0.5620319999967386 0.6510723991584557 -0.1584724640382938 -0.5855561200980223 0.5470504383298986 -0.07105841569632365 -0.4066265404139621 0.5356105840160003 -0.06707339291602238 -0.3823396315695506 0.5206327708099633 0.01419031502995555 -0.2248371871012425 0.5426762008381918 -0.05803050792400344 -0.3707780134130131 0.6109033249032858 -0.003733375531606298 -0.1500413641607106 -0.2878974743236399 0.05266748839154589 0.3971943368569609 0.8581552445474341 -0.2461137999106289 2.100684785236743 0.216605711769082 -1.129177712428297 1.255664706725901 -0.6495076739778275 -0.3517741233358174 -0.08874712204346968 -0.2788159667882325 -1.127403154710855 0.53243940179476 0.375838434925821 -0.1570922099604204 -0.4363382876470204 Output completed. Verifying that all points are below 8.1e-15 of all facets. Will make 112 distance computations. 8 vertices and 18 facets with normals: -0.56 0.14 -0.61 0.54 -0.41 0.83 0.33 0.21 0.45 -0.38 0.22 0.78 0.55 0.033 0.81 0.19 0.097 -0.87 0.49 -0.0073 0.6 -0.13 -0.59 -0.53 0.64 -0.16 -0.57 -0.49 0.64 -0.084 -0.48 -0.59 0.65 -0.081 -0.46 -0.6 0.69 0.019 -0.3 -0.66 0.66 -0.07 -0.45 -0.6 0.76 -0.0046 -0.19 -0.62 -0.41 0.075 0.57 -0.71 0.37 -0.11 0.9 -0.21 0.12 -0.64 0.71 -0.28 -0.72 -0.39 -0.099 -0.56 -0.2 -0.82 0.39 -0.36 0.48 -0.2 -0.56 -0.64 ======== Free memory allocated by the new instance of Qhull, and redisplay the old results. 8 vertices and 16 facets with normals: 0.45 -0.44 0.16 0.76 -0.36 -0.88 0.26 0.16 0.85 -0.44 -0.024 -0.28 0.59 -0.63 0.014 -0.51 0.22 0.67 -0.46 0.54 0.27 0.72 -0.52 0.38 -0.39 0.078 0.78 -0.48 -0.38 0.078 0.78 -0.49 -0.65 -0.33 0.47 -0.5 -0.58 -0.26 0.46 -0.62 -0.28 -0.12 -0.59 -0.75 0.19 0.73 -0.57 0.32 -0.7 -0.13 0.17 -0.68 -0.68 -0.72 0.066 0.095 0.095 0.66 -0.51 0.54 -0.79 -0.31 0.31 -0.43 ======== 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): 7.5e-05 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): 0.000125 Output completed. Verifying that all points are below outer planes of all facets. Will make 168 distance computations. ======== compute 2-d Delaunay triangulation seed: 1676184629 8 vertices and 12 facets with normals: -0.62 0.18 0.76 0.9 0.41 -0.15 -0.69 -0.64 0.32 -0.61 0.61 -0.51 0.12 0.71 -0.7 -0.47 -0.19 -0.86 -0.13 -0.27 -0.95 0.15 -0.41 -0.9 0.93 0.092 -0.36 0.9 -0.018 -0.43 -0.4 -0.91 0.027 -0.077 -0.96 -0.28 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: 18 Number of facets in hull: 12 Number of distance tests for qhull: 28 CPU seconds to compute hull (after input): 4.4e-05 Output completed. Verifying that all points are below 8.1e-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 0.51 -0.08 0.15 0.17 Delaunay triangulation by the convex hull of 14 points in 3-d: Number of input sites: 14 Number of Delaunay regions: 21 Statistics for: user_eg2 Delaunay example | qhull s d Tcv Number of points processed: 14 Number of hyperplanes created: 50 Number of facets in hull: 24 Number of distance tests for qhull: 73 CPU seconds to compute hull (after input): 4.4e-05 Output completed. Verifying that all points are below 8.1e-15 of all facets. Will make 294 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): 7.2e-05 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): 7.2e-05 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): 0.000106 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: 1676184629 8 vertices and 12 facets with normals: -0.62 0.18 0.76 0.9 0.41 -0.15 -0.69 -0.64 0.32 -0.61 0.61 -0.51 0.12 0.71 -0.7 -0.47 -0.19 -0.86 -0.13 -0.27 -0.95 0.15 -0.41 -0.9 0.93 0.092 -0.36 0.9 -0.018 -0.43 -0.4 -0.91 0.027 -0.077 -0.96 -0.28 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: 18 Number of facets in hull: 12 Number of distance tests for qhull: 28 CPU seconds to compute hull (after input): 4.2e-05 2 9 2.994349354353532 1.378608171651515 -0.5933826012743619 0.5961695417295512 0.08970887182385739 0.5070794257879989 -0.2702343143076831 -0.1090820857678249 -0.06774741037965545 -0.1398147789221125 0.08235125621072154 -0.2273842975842811 1.295863236886815 0.1279932218092973 1.049922691547202 -0.02134525464627679 -0.1389914868883175 -1.740246783120977 Output completed. Verifying that all points are below 8.1e-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 0.51 -0.08 0.15 0.17 Voronoi diagram by the convex hull of 14 points in 3-d: Number of Voronoi regions: 14 Number of Voronoi vertices: 21 Statistics for: user_eg2 Delaunay example | qhull s d Tcv v p Number of points processed: 14 Number of hyperplanes created: 50 Number of facets in hull: 24 Number of distance tests for qhull: 73 CPU seconds to compute hull (after input): 4.2e-05 2 21 0.08970887182385739 0.5070794257879989 -0.6711297563549512 -0.4388992935480627 -0.4531899286594102 -4.611892025589178 1.128052872928036 -0.3267681794774294 0.7436308298565699 -0.4641741474030159 0.1586832309171535 -0.2018199127931168 0.1868159441816132 -0.2279745926373064 0.1863748537454596 -1.269840499493709 -0.3331425861364105 -1.46662143525626 -0.2215906776678997 -2.1464358776046 -0.498800790875891 0.3897504505398521 -0.4694346908013824 0.5800040146374524 -1.214419600916174 -0.1671268199403232 0.1932242686745267 0.5381389130248695 0.5957180339017502 0.4191216321437531 3.301642080444855 0.8528770578062254 -0.4093458687182214 -0.2235293446624338 -0.4563813149926431 0.2971725053337521 -0.02171602142418425 0.04930081769513681 0.06005183001146641 -0.1901942308103824 -0.001676630105290011 -0.2208605250725637 Output completed. Verifying that all points are below 8.1e-15 of all facets. Will make 294 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): 7.7e-05 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): 7.7e-05 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): 4.8e-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 944578257 _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 7e-05 CPU secs. Previous p-1(v3) delta 7e-05 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): 9e-05 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): 6.9e-05 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): 5.4e-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): 4.2e-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): 0.001207 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): 0.001237 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): 6.8e-05 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 Sun Feb 12 20:50:29 +14 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): 0.000103 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): 6.5e-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): 3.7e-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): 0.005264 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): 5.2e-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): 0.000406 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): 0.000394 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 QR1676184629 Number of points processed: 24 Number of hyperplanes created: 4107 Number of distance tests for qhull: 4215 Number of distance tests for merging: 121142 Number of distance tests for checking: 98304 Number of merged facets: 2036 CPU seconds to compute hull (after input): 0.04386 Approximate facet area: 0.00035546337 Approximate volume: 8.5511197e-06 rbox c D6 | qconvex s FA TF500 At 20:50:29 & 0.001493 CPU secs, qhull has created 543 facets and merged 289. The current hull contains 91 facets and 23 vertices. There are 41 outside points. Next is point p27(v24), 0.64 above f107. At 20:50:29 & 0.002929 CPU secs, qhull has created 1061 facets and merged 737. The current hull contains 69 facets and 33 vertices. There are 31 outside points. Next is point p22(v34), 0.52 above f610. At 20:50:29 & 0.004381 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 20:50:29 & 0.005246 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 20:50:29 & 0.005415 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): 0.005463 Approximate facet area: 12 Approximate volume: 1 rbox c D7 | qconvex s FA TF1000 At 20:50:29 & 0.003398 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 20:50:29 & 0.007494 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 20:50:29 & 0.012057 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 20:50:29 & 0.016097 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 20:50:29 & 0.020698 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 20:50:29 & 0.025183 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 20:50:29 & 0.030502 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 20:50:29 & 0.03549 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 20:50:29 & 0.040571 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 20:50:29 & 0.045971 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 20:50:29 & 0.051268 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 20:50:29 & 0.055922 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 20:50:29 & 0.056355 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): 0.05648 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 QR1676184629 Number of points processed: 24 Number of hyperplanes created: 4107 Number of distance tests for qhull: 4215 Number of distance tests for merging: 121142 Number of distance tests for checking: 98304 Number of merged facets: 2036 CPU seconds to compute hull (after input): 0.04341 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): 4.2e-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 944578257 _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): 5.9e-05 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): 5.6e-05 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): 5.3e-05 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): 7.9e-05 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): 7.7e-05 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): 5.9e-05 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): 5.8e-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): 5.6e-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): 8e-05 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): 6.2e-05 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): 0.000942 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): 6.8e-05 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): 5.8e-05 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): 9.8e-05 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): 7e-05 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): 6.9e-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): 0.005254 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): 6.9e-05 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): 4.2e-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 QR1676184629 Number of points processed: 24 Number of hyperplanes created: 4107 Number of distance tests for qhull: 4215 Number of distance tests for merging: 121142 Number of distance tests for checking: 98304 Number of merged facets: 2036 CPU seconds to compute hull (after input): 0.04477 Approximate facet area: 1.735661e-07 Approximate volume: 2.0876757e-09 rbox c D7 | qhull FA TF1000 At 20:50:29 & 0.003346 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 20:50:29 & 0.007464 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 20:50:29 & 0.012012 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 20:50:29 & 0.016095 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 20:50:29 & 0.020673 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 20:50:29 & 0.025364 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 20:50:29 & 0.030708 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 20:50:29 & 0.035829 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 20:50:29 & 0.041051 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 20:50:29 & 0.046488 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 20:50:29 & 0.051569 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 20:50:29 & 0.055951 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 20:50:29 & 0.056375 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): 0.0565 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): 0.000407 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): 4.7e-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 944578257 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): 0.0001 [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 i-capture-the-hostname Sun Feb 12 20:50:29 +14 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): 0.002196 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): 0.001631 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): 0.01775 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): 0.03198 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): 0.002941 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): 0.03402 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: 309311 Number of distance tests for checking: 54701 Number of merged facets: 6165 CPU seconds to compute hull (after input): 0.05511 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): 0.07936 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): 0.003257 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): 0.02216 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): 0.06419 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. Sun Feb 12 20:50:30 +14 2023 qhull <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): 6e-05 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 Sun Feb 12 20:50:30 +14 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): 6.7e-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): 4.2e-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): 3.9e-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): 0.000105 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): 0.001331 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): 0.000102 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): 0.00107 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): 0.08718 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): 0.06133 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): 0.000474 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): 0.003571 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): 0.003563 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): 8.2e-05 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): 8e-05 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): 3.8e-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): 6.7e-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 944611871 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): 6.9e-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 944611871 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 Sun Feb 12 20:50:31 +14 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): 0.000114 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): 0.000105 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): 0.000177 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): 0.000139 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 944611871 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): 0.000136 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 944611871 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 944611871 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): 0.000129 1 0 10 36 0 rbox 100 W0 | qhull Tv Q11 FO Options selected for Qhull 2020.2.r 2020/08/31: run-id 944611871 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): 0.000476 Output completed. Verifying that all points are below outer planes of all facets. Will make 8600 distance computations. set +v === test unbounded intersection Sun Feb 12 20:50:31 +14 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): 0.008642 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 944611871 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): 7.1e-05 set +v === check Delaunay/Voronoi Sun Feb 12 20:50:31 +14 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): 8.6e-05 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): 8.5e-05 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): 0.000108 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): 0.000202 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): 0.000147 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 Sun Feb 12 20:50:31 +14 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): 0.001536 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): 0.001552 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): 0.01788 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): 0.008865 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): 0.5165 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): 0.008864 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): 8.7e-05 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): 0.000114 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): 5.1e-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): 4.7e-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 Sun Feb 12 20:50:31 +14 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): 9.2e-05 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-1676184631 Number of points processed: 10 Number of hyperplanes created: 29 Number of distance tests for qhull: 48 CPU seconds to compute hull (after input): 7.8e-05 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): 6.8e-05 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): 0.002003 qhull invoked by: rbox 1000 D3 | qhull Tcvs 2020.2.r 2020/08/31 with options: run-id 944611871 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 0.002 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 0.569 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) 31808 for facets and their normals, neighbor and vertex sets 3504 for vertices and their neighbor sets 32768 for input points, outside and coplanar sets, and qhT memory statistics: 1390 quick allocations 687 short allocations 119 long allocations 1421 short frees 119 long frees 36248 bytes of short memory in use 2088 bytes of short memory in freelists 92728 bytes of dropped short memory 520 bytes of unused short memory (estimated) 21640 bytes of long memory allocated (max, except for input) 0 bytes of long memory in use (in 0 pieces) 131064 bytes of short memory buffers (minus links) 65536 bytes per short memory buffer (initially 131072 bytes) 127 calls to qh_setlarger 11 average copy size freelists(bytes->count): 24->4 32->0 40->9 48->0 72->11 120->7 size in bytes: merge 72 ridge 32 vertex 48 facet 120 normal 24 ridge vertices 32 facet vertices or neighbors 40 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): 0.000133 [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): 0.000149 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): 0.001559 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): 0.001633 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): 0.001701 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 944611871 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 0.001695 CPU secs. Previous p56(v78) delta 0.001695 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): 0.001753 [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 20:50:31 & 0.000384 CPU secs, qhull has created 102 facets and merged 0. The current hull contains 46 facets and 25 vertices. There are 75 outside points. Next is point p55(v26), 0.035 above f44. At 20:50:31 & 0.000758 CPU secs, qhull has created 203 facets and merged 0. The current hull contains 86 facets and 45 vertices. There are 55 outside points. Next is point p82(v46), 0.067 above f117. At 20:50:31 & 0.001263 CPU secs, qhull has created 306 facets and merged 0. The current hull contains 122 facets and 63 vertices. There are 37 outside points. Next is point p50(v64), 0.042 above f218. At 20:50:31 & 0.001903 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): 0.002645 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): 0.002508 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): 0.00032 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): 0.000334 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): 0.01638 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): 0.000357 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 944611871 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): 0.000329 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 944611871 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): 0.06149 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): 9e-05 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): 8.6e-05 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): 0.00011 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): 4.8e-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 Sun Feb 12 20:50:32 +14 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 944628678 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 944628678 Tcheck-frequently Tverify Centrum-premerge- 0 _zero-centrum _max-width 0.99 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 t1676184632 | qhull FO Tcv C-0 Number of points processed: 200 Number of hyperplanes created: 397 Number of distance tests for qhull: 2066 CPU seconds to compute hull (after input): 0.003783 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 944628678 Tcheck-frequently Tverify Centrum-premerge- 0 _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 1000 points in 3-d: Number of vertices: 40 Number of facets: 76 Statistics for: rbox 1000 L20 t1676184632 | qhull FO Tcv C-0 Number of points processed: 53 Number of hyperplanes created: 214 Number of distance tests for qhull: 14295 CPU seconds to compute hull (after input): 0.001141 Output completed. Verifying that all points are below outer planes of all facets. Will make 76000 distance computations. rbox 200 L20 D4 t | qhull FO Tcv C-0 Options selected for Qhull 2020.2.r 2020/08/31: run-id 944628678 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: 59 Number of facets: 254 Statistics for: rbox 200 L20 D4 t1676184632 | qhull FO Tcv C-0 Number of points processed: 72 Number of hyperplanes created: 809 Number of distance tests for qhull: 7020 CPU seconds to compute hull (after input): 0.003562 Output completed. Verifying that all points are below outer planes of all facets. Will make 50800 distance computations. rbox 200 L20 D5 t | qhull FO Tcv Qx Options selected for Qhull 2020.2.r 2020/08/31: run-id 944628678 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 8.2e-15 U-max-coplanar 8.2e-15 Width-outside 1.6e-14 _wide-facet 4.9e-14 Convex hull of 200 points in 5-d: Number of vertices: 102 Number of facets: 1520 Statistics for: rbox 200 L20 D5 t1676184632 | qhull FO Tcv Qx Number of points processed: 113 Number of hyperplanes created: 5231 Number of distance tests for qhull: 17769 CPU seconds to compute hull (after input): 0.0198 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 304000 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 944628678 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: 264 Statistics for: rbox 1000 W1e-3 s D2 t1676184632 | qhull d FO Tcv Qu Q0 Number of points processed: 1000 Number of hyperplanes created: 4817 Number of facets in hull: 1996 Number of distance tests for qhull: 27858 CPU seconds to compute hull (after input): 0.05998 Output completed. Verifying that all points are below 2.1e-15 of all facets. Will make 264000 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 944628678 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: 264 Statistics for: rbox 1000 W1e-3 s D2 t1676184632 | qhull d FO Tcv Qu C-0 Number of points processed: 1000 Number of hyperplanes created: 4817 Number of facets in hull: 1996 Number of distance tests for qhull: 27858 CPU seconds to compute hull (after input): 0.06112 Output completed. Verifying that all points are below 2.1e-15 of all facets. Will make 264000 distance computations. set +v === check joggle and TRn Sun Feb 12 20:50:32 +14 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): 0.0134 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): 0.02507 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): 0.02864 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): 0.02914 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): 0.02908 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 944628678 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): 0.001372 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 Sun Feb 12 20:50:32 +14 2023 rbox 100 D3 s | qhull E0.01 Qx Tcv FO Options selected for Qhull 2020.2.r 2020/08/31: run-id 944628678 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): 0.001437 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): 0.000507 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): 0.000354 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): 0.000385 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): 0.000214 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): 0.000271 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): 0.000259 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): 0.01044 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): 0.06679 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): 0.01044 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): 0.007228 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): 0.009348 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 944628678 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): 0.01028 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 944628678 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): 0.0101 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 944628678 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): 0.01052 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 944628678 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): 0.01038 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 Sun Feb 12 20:50:32 +14 2023 rbox 1000 s D3 | qhull C-0.01 Q5 FO Tcv Options selected for Qhull 2020.2.r 2020/08/31: run-id 944628678 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): 0.00842 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 Sun Feb 12 20:50:32 +14 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 944628678 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): 0.008498 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 944628678 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): 0.009724 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): 0.009152 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 Sun Feb 12 20:50:32 +14 2023 rbox 100 s D3 t | qhull R1e-3 Tcv Qc Convex hull of 100 points in 3-d: Number of vertices: 96 Number of coplanar points: 4 Number of facets: 162 Number of non-simplicial facets: 22 Statistics for: rbox 100 s D3 t1676184632 | qhull R1e-3 Tcv Qc Number of points processed: 96 Number of hyperplanes created: 468 Number of distance tests for qhull: 1640 Number of distance tests for merging: 3206 Number of distance tests for checking: 1662 Number of merged facets: 47 CPU seconds to compute hull (after input): 0.003681 Maximum distance of point above facet: 0.003 (0.8x) Maximum distance of vertex below facet: -0.0044 (1.1x) Output completed. Verifying that all points are below outer planes of all facets. Will make 16200 distance computations. rbox 100 s D3 t | qhull R1e-2 Tcv Qc Convex hull of 100 points in 3-d: Number of vertices: 66 Number of coplanar points: 34 Number of facets: 75 Number of non-simplicial facets: 36 Statistics for: rbox 100 s D3 t1676184632 | qhull R1e-2 Tcv Qc Number of points processed: 67 Number of hyperplanes created: 290 Number of distance tests for qhull: 2754 Number of distance tests for merging: 3384 Number of distance tests for checking: 2610 Number of merged facets: 114 CPU seconds to compute hull (after input): 0.003151 Maximum distance of point above facet: 0.026 (0.7x) Maximum distance of vertex below facet: -0.05 (1.3x) Output completed. Verifying that all points are below outer planes of all facets. Will make 7500 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: 18 Number of coplanar points: 482 Number of facets: 18 Number of non-simplicial facets: 11 Statistics for: rbox 500 s D3 t1676184632 | qhull R0.05 A-1 Tcv Qc Number of points processed: 23 Number of hyperplanes created: 78 Number of distance tests for qhull: 20195 Number of distance tests for merging: 1151 Number of distance tests for checking: 7482 Number of merged facets: 45 CPU seconds to compute hull (after input): 0.002054 Maximum distance of point above facet: 0.15 (0.3x) Maximum distance of vertex below facet: -0.31 (0.5x) Output completed. Verifying that all points are below outer planes of all facets. Will make 9000 distance computations. rbox 100 W0 D3 t | qhull R1e-3 Tcv Qc Convex hull of 100 points in 3-d: Number of vertices: 41 Number of coplanar points: 59 Number of facets: 51 Number of non-simplicial facets: 9 Statistics for: rbox 100 W0 D3 t1676184632 | qhull R1e-3 Tcv Qc Number of points processed: 47 Number of hyperplanes created: 161 Number of distance tests for qhull: 1895 Number of distance tests for merging: 1452 Number of distance tests for checking: 1485 Number of merged facets: 45 CPU seconds to compute hull (after input): 0.001445 Maximum distance of point above facet: 0.0021 (0.5x) 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 5100 distance computations. rbox 100 W0 D3 t | qhull R1e-3 Qx Tcv Qc Convex hull of 100 points in 3-d: Number of vertices: 41 Number of coplanar points: 59 Number of facets: 51 Number of non-simplicial facets: 9 Statistics for: rbox 100 W0 D3 t1676184632 | qhull R1e-3 Qx Tcv Qc Number of points processed: 49 Number of hyperplanes created: 161 Number of distance tests for qhull: 2512 Number of distance tests for merging: 1585 Number of distance tests for checking: 1179 Number of merged facets: 47 CPU seconds to compute hull (after input): 0.00141 Maximum distance of point above facet: 0.002 (0.5x) Maximum distance of vertex below facet: -0.0046 (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 5100 distance computations. rbox 100 W0 D3 t | qhull R1e-2 Tcv Qc Convex hull of 100 points in 3-d: Number of vertices: 28 Number of coplanar points: 72 Number of facets: 23 Number of non-simplicial facets: 11 Statistics for: rbox 100 W0 D3 t1676184632 | qhull R1e-2 Tcv Qc Number of points processed: 34 Number of hyperplanes created: 111 Number of distance tests for qhull: 2797 Number of distance tests for merging: 1555 Number of distance tests for checking: 1710 Number of merged facets: 58 CPU seconds to compute hull (after input): 0.001158 Maximum distance of point above facet: 0.029 (0.7x) Maximum distance of vertex below facet: -0.058 (1.4x) Output completed. Verifying that all points are below outer planes of all facets. Will make 2300 distance computations. rbox 100 W0 D3 t | qhull R1e-2 Qx Tcv Qc Convex hull of 100 points in 3-d: Number of vertices: 30 Number of coplanar points: 70 Number of facets: 26 Number of non-simplicial facets: 13 Statistics for: rbox 100 W0 D3 t1676184632 | qhull R1e-2 Qx Tcv Qc Number of points processed: 34 Number of hyperplanes created: 107 Number of distance tests for qhull: 3179 Number of distance tests for merging: 1356 Number of distance tests for checking: 1186 Number of merged facets: 46 CPU seconds to compute hull (after input): 0.001052 Maximum distance of point above facet: 0.026 (0.7x) Maximum distance of vertex below facet: -0.039 (1.0x) QH7076 qhull input warning: exact merge ('Qx'). Verify may report that a point is outside of a facet. See qh-optq.htm#Qx Output completed. Verifying that all points are below outer planes of all facets. Will make 2600 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 t1676184632 | qhull R0.05 A-1 Tcv Qc Number of points processed: 12 Number of hyperplanes created: 27 Number of distance tests for qhull: 11324 Number of distance tests for merging: 310 Number of distance tests for checking: 3485 Number of merged facets: 15 CPU seconds to compute hull (after input): 0.000933 Maximum distance of point above facet: 0.11 (0.2x) Maximum distance of vertex below facet: -0.22 (0.4x) Output completed. Verifying that all points are below outer planes of all facets. Will make 3000 distance computations. rbox 500 W0 D3 t | qhull R0.05 Qx Tcv Qc Convex hull of 500 points in 3-d: Number of vertices: 9 Number of coplanar points: 491 Number of facets: 7 Number of non-simplicial facets: 6 Statistics for: rbox 500 W0 D3 t1676184632 | qhull R0.05 Qx Tcv Qc Number of points processed: 13 Number of hyperplanes created: 26 Number of distance tests for qhull: 12633 Number of distance tests for merging: 290 Number of distance tests for checking: 3800 Number of merged facets: 15 CPU seconds to compute hull (after input): 0.00106 Maximum distance of point above facet: 0.13 (0.7x) Maximum distance of vertex below facet: -0.15 (0.7x) QH7076 qhull input warning: exact merge ('Qx'). Verify may report that a point is outside of a facet. See qh-optq.htm#Qx Output completed. Verifying that all points are below outer planes of all facets. Will make 3500 distance computations. rbox 1000 W1e-20 t | qhull Tcv Qc Convex hull of 1000 points in 3-d: Number of vertices: 78 Number of coplanar points: 922 Number of facets: 92 Number of non-simplicial facets: 6 Statistics for: rbox 1000 W1e-20 t1676184632 | qhull Tcv Qc Number of points processed: 92 Number of hyperplanes created: 284 Number of distance tests for qhull: 17765 Number of distance tests for merging: 2805 Number of distance tests for checking: 15984 Number of merged facets: 88 CPU seconds to compute hull (after input): 0.003996 Output completed. Verifying that all points are below outer planes of all facets. Will make 92000 distance computations. rbox 1000 W1e-20 D4 t | qhull Tcv Qc Convex hull of 1000 points in 4-d: Number of vertices: 269 Number of coplanar points: 731 Number of facets: 1014 Number of non-simplicial facets: 8 Statistics for: rbox 1000 W1e-20 D4 t1676184632 | qhull Tcv Qc Number of points processed: 360 Number of hyperplanes created: 4935 Number of distance tests for qhull: 88157 Number of distance tests for merging: 57815 Number of distance tests for checking: 85160 Number of merged facets: 1167 CPU seconds to compute hull (after input): 0.1589 Output completed. Verifying that all points are below outer planes of all facets. Will make 1014000 distance computations. rbox 500 W1e-20 D5 t | qhull Tv Qc Convex hull of 500 points in 5-d: Number of vertices: 342 Number of coplanar points: 158 Number of facets: 5370 Number of non-simplicial facets: 10 Statistics for: rbox 500 W1e-20 D5 t1676184632 | qhull Tv Qc Number of points processed: 406 Number of hyperplanes created: 26563 Number of distance tests for qhull: 122635 Number of distance tests for merging: 295365 Number of distance tests for checking: 118774 Number of merged facets: 3476 CPU seconds to compute hull (after input): 0.07027 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 2685000 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: 5986 Number of non-simplicial facets: 10 Statistics for: rbox 100 W1e-20 D6 t1676184633 | qhull Tv Qc Number of points processed: 100 Number of hyperplanes created: 20029 Number of distance tests for qhull: 31337 Number of distance tests for merging: 159820 Number of distance tests for checking: 62120 Number of merged facets: 135 CPU seconds to compute hull (after input): 0.04341 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 598600 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: 2083 Number of non-simplicial facets: 1 Statistics for: rbox 50 W1e-20 D6 t1676184633 | qhull Qv Tv Qc Number of points processed: 50 Number of hyperplanes created: 6156 Number of distance tests for qhull: 8969 Number of distance tests for merging: 3441368 Number of distance tests for checking: 21278 Number of merged facets: 4 CPU seconds to compute hull (after input): 0.1071 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 104150 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: 8504 Number of facets: 8 Number of non-simplicial facets: 8 Statistics for: rbox 10000 D4 t1676184633 | qhull QR0 Qc C-0.01 A0.3 Tv QR1676184633 Number of points processed: 57 Number of hyperplanes created: 425 Number of distance tests for qhull: 1813591 Number of distance tests for merging: 32546 Number of distance tests for checking: 89688 Number of merged facets: 460 CPU seconds to compute hull (after input): 0.06256 Maximum distance of point above facet: 0.058 Maximum distance of vertex below facet: -0.18 (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 t1676184633 | qhull d QR0 Qc C-1e-8 Qu Tv QR1676184633 Number of points processed: 1000 Number of hyperplanes created: 5481 Number of facets in hull: 1996 Number of distance tests for qhull: 29389 Number of distance tests for merging: 34885 Number of distance tests for checking: 17931 Number of merged facets: 1 CPU seconds to compute hull (after input): 0.007213 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: 167 Number of coplanar points: 29 Number of facets: 1844 Number of non-simplicial facets: 450 Statistics for: rbox 300 D5 t1676184633 | qhull A-0.999 Qx Qc Tcv Number of points processed: 197 Number of hyperplanes created: 11560 Number of distance tests for qhull: 157395 Number of distance tests for merging: 119234 Number of distance tests for checking: 32298 Number of merged facets: 1189 CPU seconds to compute hull (after input): 0.04759 Maximum distance of vertex below facet: -0.021 (0.2x) QH7076 qhull input warning: exact merge ('Qx'). Verify may report that a point is outside of a facet. See qh-optq.htm#Qx Output completed. Verifying that all points are below outer planes of all facets. Will make 553200 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: 2 Number of facets: 3703 Number of non-simplicial facets: 251 Statistics for: rbox 100 D6 t1676184633 | qhull A-0.9999 Qx Qc Tcv Number of points processed: 93 Number of hyperplanes created: 15710 Number of distance tests for qhull: 33919 Number of distance tests for merging: 66524 Number of distance tests for checking: 63799 Number of merged facets: 689 CPU seconds to compute hull (after input): 0.04625 Maximum distance of vertex below facet: -0.008 (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 370300 distance computations. rbox 50 D7 t |qhull A-0.99999 Qx Qc Tcv W0.1 Convex hull of 50 points in 7-d: Number of vertices: 47 Number of coplanar points: 3 Number of facets: 4814 Number of non-simplicial facets: 83 Statistics for: rbox 50 D7 t1676184633 | qhull A-0.99999 Qx Qc Tcv W0.1 Number of points processed: 47 Number of hyperplanes created: 14389 Number of distance tests for qhull: 21809 Number of distance tests for merging: 64345 Number of distance tests for checking: 142458 Number of merged facets: 232 CPU seconds to compute hull (after input): 0.04998 Maximum distance of point above facet: 0.08 Maximum distance of vertex below facet: -0.0022 (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 240700 distance computations. set +v ======================================================= === The following commands may cause errors Sun Feb 12 20:50:33 +14 2023 ======================================================= === check bad cases for Qhull Sun Feb 12 20:50:33 +14 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: 992 Number of facets: 1507 Number of non-simplicial facets: 6 Statistics for: rbox 1000 L100000 s G1e-6 t1676184633 | qhull Tv Number of points processed: 994 Number of hyperplanes created: 3392 Number of distance tests for qhull: 29900 Number of distance tests for merging: 133573 Number of distance tests for checking: 123156 Number of merged facets: 475 CPU seconds to compute hull (after input): 0.01668 Maximum distance of vertex below facet: -4e-15 (0.7x) Output completed. Verifying that all points are below outer planes of all facets. Will make 1507000 distance computations. rbox 1000 L100000 s G1e-6 t | qhull Tv Q10 Convex hull of 1000 points in 3-d: Number of vertices: 992 Number of facets: 1507 Number of non-simplicial facets: 6 Statistics for: rbox 1000 L100000 s G1e-6 t1676184633 | qhull Tv Q10 Number of points processed: 994 Number of hyperplanes created: 3392 Number of distance tests for qhull: 29896 Number of distance tests for merging: 133573 Number of distance tests for checking: 123156 Number of merged facets: 475 CPU seconds to compute hull (after input): 0.01673 Maximum distance of vertex below facet: -4e-15 (0.7x) Output completed. Verifying that all points are below outer planes of all facets. Will make 1507000 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: 1111 Number of non-simplicial facets: 50 Statistics for: rbox 1000 s Z1 G1e-13 t1676184633 | qhull Tv Number of points processed: 1001 Number of hyperplanes created: 12238 Number of distance tests for qhull: 35101 Number of distance tests for merging: 674249 Number of distance tests for checking: 675784 Number of merged facets: 9913 CPU seconds to compute hull (after input): 0.08313 Maximum distance of point above facet: 3.6e-14 (6.5x) Maximum distance of vertex below facet: -2.4e-14 (4.3x) Output completed. Verifying that all points are below outer planes of all facets. Will make 1112111 distance computations. rbox 1000 s W1e-13 P0 t | qhull d Qbb Qc Q12 Tv QH6417 qhull precision error (qh_merge_twisted): twisted facet f74662 does not contain pinched vertices. Too wide to merge into neighbor. mindist -1.7e-11 maxdist 2.1e-14 vertexdist 0.0011 maxpinched 1.8e-13 neighbor f75017 mindist -2.3e-13 maxdist 0 ERRONEOUS FACET: - f74662 - flags: top upperDelaunay tested keepcentrum - merges: 511max - normal: 2.175e-13 3.043e-15 1.879e-13 1 - offset: -0.4998369 - center: 0.2984373683816343 0.09502905186938548 0.3597477871812085 0.499836868087778 - maxoutside: 1.754152e-14 - vertices: p392(v773) p297(v772) p671(v769) p638(v767) p646(v764) p896(v762) p977(v756) p729(v753) p356(v752) p2(v751) p881(v750) p779(v749) p923(v748) p285(v745) p897(v744) p260(v743) p34(v742) p948(v739) p87(v738) p804(v737) p688(v735) p139(v733) p514(v730) p491(v725) p226(v723) p59(v722) p873(v721) p268(v720) p701(v719) p197(v718) p4(v717) p691(v716) p784(v715) p230(v714) p317(v713) p331(v712) p271(v711) p840(v710) p194(v709) p137(v708) p170(v707) p512(v706) p817(v705) p189(v704) p373(v703) p540(v702) p447(v701) p158(v700) p165(v699) p850(v698) p276(v697) p853(v696) p366(v695) 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p411(v404) p695(v403) p428(v400) p104(v399) p145(v398) p413(v397) p205(v396) p35(v394) p906(v393) p830(v391) p8(v390) p419(v388) p725(v387) p525(v386) p335(v385) p64(v380) p841(v379) p103(v378) p708(v376) p136(v375) p302(v374) p998(v373) p574(v372) p875(v371) p658(v370) p845(v369) p524(v368) p346(v367) p224(v366) p299(v365) p939(v364) p950(v363) p759(v362) p584(v361) p502(v360) p446(v359) p961(v358) p807(v357) p860(v356) p450(v355) p914(v354) p485(v353) p492(v352) p833(v351) p480(v350) p201(v349) p451(v348) p589(v347) p441(v346) p99(v345) p862(v344) p200(v343) p462(v342) p624(v341) p9(v340) p768(v339) p314(v338) p868(v337) p42(v336) p513(v335) p903(v334) p174(v333) p521(v332) p666(v331) p386(v330) p395(v329) p597(v328) p89(v327) p435(v326) p715(v325) p568(v324) p872(v321) p861(v317) p157(v316) p265(v315) p870(v314) p444(v313) p802(v312) p489(v311) p30(v310) p609(v309) p746(v308) p184(v307) p509(v306) p689(v305) p155(v304) p144(v303) p142(v302) p758(v301) p341(v300) p572(v299) 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p384(v2) p712(v1) - neighboring facets: f64991 f74552 f64992 f65022 f64998 f65021 f29368 f58440 f29390 f31007 f14875 f14377 f29395 f31006 f74562 f29389 f58427 f74664 f58423 f58408 f64986 f58406 f58441 f58410 f64984 f64988 f13868 f58414 f74560 f64989 f29374 f14378 f31005 f45474 f22240 f65013 f65011 f65038 f19417 f65014 f58436 f65005 f19416 f65023 f65024 f62222 f65006 f38437 f62220 f7660 f65008 f65009 f58425 f65018 f58421 f65019 f62247 f62289 f39966 f62235 f62244 f41042 f40999 f62243 f41034 f63623 f64902 f22080 f41033 f65224 f40937 f64901 f65219 f65225 f65220 f65222 f47997 f65233 f37860 f65232 f63648 f47996 f22116 f65217 f56394 f64895 f41073 f41074 f65227 f46343 f65205 f65230 f64860 f47036 f65229 f13784 f65213 f65203 f65216 f63689 f65208 f65206 f64857 f7787 f64863 f40984 f40895 f65211 f64856 f45535 f63692 f63693 f28981 f45534 f22359 f65210 f63690 f63691 f7923 f45537 f7922 f63591 f28980 f45532 f22356 f7799 f3450 f12534 f40974 f40979 f20156 f7925 f45536 f63535 f63630 f62100 f63639 f63636 f20764 f63632 f63633 f62197 f19242 f40925 f63638 f37877 f63635 f63618 f63625 f40916 f40924 f40917 f63617 f40948 f40947 f63622 f63628 f40940 f19247 f39965 f62237 f37878 f37875 f6588 f19248 f37849 f37090 f19215 f74900 f62101 f6284 f62121 f74969 f62098 f37871 f74942 f36428 f63561 f74841 f62103 f74939 f74937 f62107 f62095 f62082 f20136 f58285 f62104 f74898 f19435 f62081 f62089 f62094 f74905 f39988 f74211 f62240 f62257 f19434 f39987 f62258 f37080 f39986 f62097 f39983 f37850 f37874 f62239 f39984 f19262 f64911 f41054 f65143 f41056 f74733 f41081 f65139 f62249 f66555 f65140 f41092 f41084 f41091 f64904 f41083 f41037 f63532 f64871 f74993 f63533 f40991 f64862 f63536 f63595 f63599 f63598 f63589 f63549 f63584 f74940 f74987 f62291 f74952 f24399 f45529 f20729 f28978 f20947 f45530 f20756 f20948 f40968 f20757 f22345 f40902 f40976 f20728 f40977 f20945 f40973 f64865 f64869 f74838 f63547 f40867 f63546 f62290 f63592 f63566 f22430 f63562 f63564 f63540 f20936 f63538 f40908 f20946 f63688 f64874 f21525 f63687 f64859 f64868 f63660 f65135 f22160 f65200 f65144 f22134 f65201 f65198 f41067 f41059 f41068 f64893 f65146 f64889 f64920 f64890 f64918 f65142 f65145 f69531 f32420 f59610 f59607 f58509 f32417 f65196 f8524 f59612 f58510 f32434 f32418 f58506 f74736 f59616 f69573 f60755 f74723 f59606 f32487 f32486 f14887 f74720 f5898 f63602 f69574 f45522 f7741 f59614 f45521 f15382 f74717 f59617 f59609 f45527 f22333 f45526 f74713 f15380 f74714 f32431 f7739 f31600 f64961 f22334 f31598 f46335 f7740 f14886 f64959 f24371 f32468 f32438 f59634 f74121 f32437 f59619 f41134 f32466 f64964 f7743 f15904 f22353 f64943 f41133 f64941 f64946 f7742 f7784 f12532 f7785 f3436 f22358 f28977 f22352 f64944 f64947 f59629 f22355 f7545 f22361 f74697 f46336 f64936 f32455 f74114 f31601 f16404 f59635 f74690 f64934 f74702 f74701 f32457 f49989 f59630 f69534 f74710 f24361 f66596 f49984 f24334 f63601 f69571 f24372 f73470 f23635 f12550 f12541 f73393 f49618 f23634 f11854 f66565 f58184 f66586 f66584 f66594 f22490 f49617 f22433 f66599 f57504 f66604 f22470 f48642 f57506 f63611 f57501 f22493 f22436 f22495 f63604 f49990 f22494 f22474 f50008 f24370 f22471 f63614 f63615 f11856 f40907 f63609 f50006 f66605 f63607 f22435 f63612 f57507 f57503 f63606 f63569 f63568 f64921 f64899 f64912 f64896 f64916 f64898 f47029 f47030 f65214 f48618 f62265 f62262 f62264 f22409 f62260 f22418 f37865 f37864 f45513 f40885 f63581 f40884 f63579 f63576 f63587 f63577 f63582 f63586 f63571 f63574 f28973 f13783 f28974 f3445 f3437 f12531 f68974 f60881 f66725 f62228 f74974 f74979 f74977 f68978 f19307 f50174 f66742 f74891 f66546 f74904 f66738 f66734 f74956 f50163 f66741 f23622 f66637 f40812 f50175 f50166 f50160 f66640 f66638 f66543 f66641 f49963 f66733 f66531 f66731 f54330 f52391 f66736 f66726 f66729 f52394 f49648 f66532 f73922 f66728 f66547 f66558 f66544 f22859 f49977 f68976 f66564 f49970 f49969 f66587 f66561 f66581 f66567 f22482 f73406 f66573 f66572 f22483 f66569 f49976 f22473 f66534 f22480 f66529 f22478 f66570 f50172 f55278 f55277 f58183 f50014 f22159 f65137 f64892 f63643 f63654 f63641 f63656 f40933 f63653 f63646 f63644 f63647 f74888 f66810 f55246 f66816 f60876 f66813 f40811 f66696 f66806 f66818 f66817 f66815 f74921 f8955 f66808 f62202 f66822 f55260 f22778 f22827 f66712 f22772 f72495 f51060 f68225 f68218 f66795 f66697 f66664 f68217 f68972 f68973 f54327 f66693 f66794 f54326 f68224 f68220 f51095 f55272 f66709 f51094 f51080 f55259 f9175 f66662 f52149 f54322 f55235 f66665 f66659 f55255 f66714 f68222 f68223 f66660 f66792 f66789 f66790 f66711 f66694 f66700 f66715 f51085 f51078 f51074 f66803 f22612 f51083 f51073 f51088 f36663 f51076 f36664 f66804 f55238 f51107 f66704 f52142 f64971 f5969 f28906 f45511 f64970 f64950 f64978 f45507 f45514 f28922 f64973 f3503 f64976 f64979 f65119 f64931 f45515 f64925 f45495 f65122 f65133 f65120 f65130 f65125 f65117 f64967 f64951 f64966 f64956 f22777 f50169 f66767 f55285 f22856 f53470 f28910 f22854 f27250 f50170 f53458 f66779 f66749 f22872 f53462 f66768 f54329 f58213 f66782 f22909 f66625 f28915 f66617 f66623 f66626 f73963 f39916 f66628 f50142 f66758 f53457 f66629 f25747 f66627 f66610 f26160 f66776 f27251 f9627 f53469 f66618 f28904 f66620 f66621 f66611 f66607 f74958 f66775 f74753 f60868 f60852 f60771 f74738 f60867 f74866 f33296 f74741 f28919 f17554 f74718 f74156 f60781 f66754 f74145 f60768 f74160 f74146 f74132 f14888 f32470 f74725 f74743 f66705 f52401 f17555 f74154 f69532 f66676 f74926 f66667 f58454 f29367 f66677 f66671 f13926 f29397 f74528 f58453 f29392 f58457 f13925 f60849 f8118 f14878 f22611 f74208 f26161 f66668 f66674 f74887 f59636 f60858 f30198 f14882 f13933 f74856 f30199 f30197 f74879 f74873 f74857 f74870 f74814 f60853 f74832 f74829 f74867 f14877 f58485 f28971 f60844 f54332 f74730 f32488 f74875 f74731 f30196 f69570 f74722 f7560 f51087 f12899 f28916 f51091 f51090 f51063 f66644 f51062 f66765 f54345 f66651 f50176 f58415 f66643 f10984 f55300 f66653 f10510 f66656 f66654 f66764 f66757 f66762 f66751 f66760 f10074 f66747 f54348 f54346 f54349 f54341 f66657 f52144 f52141 f66707 f22953 f74886 f54343 f22960 f54340 f54338 f66648 f66686 f66689 f66685 f8117 f22610 f66650 f66688 f66647 f48625 f22927 f52400 f66752 f74175 f28968 f69536 f58362 f28970 f55295 f58387 f74172 f69535 f28945 f28966 f28946 f28923 f28965 f58383 f28920 f66681 f58434 f66682 f39143 f66679 f38387 f51065 f66702 f68977 f66699 f58364 f69518 f58250 f72762 f66755 f22873 f58249 f73948 f58212 f60789 f73955 f66778 f74187 f73951 f58391 f62122 f73973 f64975 f74764 f73929 f74539 f58154 f74959 f58433 f28940 f28938 f58312 f74737 f58384 f74734 f74141 f57508 f60310 f60309 f60826 f60871 f60827 f17070 f41098 f17077 f22165 f32467 f8116 f41163 f64883 f32454 f12906 f22208 f59637 f41106 f22173 f62214 f64927 f64930 f41114 f41116 f41021 f19454 f41108 f41117 f64887 f41101 f64933 f41104 f62217 f64928 f64923 f41103 f64957 f12890 f22183 f32453 f64952 f64953 f64938 f41109 f64886 f60870 f74835 f74774 f74837 f74834 f74854 f74128 f74727 f74756 f58466 f58465 f58470 f74167 f10964 f13908 f74538 f66673 f29396 f60834 f74842 f74847 f22170 f18796 f22171 f41097 f41099 f60819 f74844 f60832 f60865 f27399 f58137 f69698 f73920 f28903 f58136 f73924 f69699 f69581 f69702 f58140 f69700 f58142 f71083 f71082 f71092 f58159 f71080 f71093 f73383 f71091 f69701 f25681 f71090 f25682 f58160 f71081 f58167 f69683 f73885 f69684 f55303 f58361 f56396 f56388 f11434 f55302 f55301 f56389 f55298 f56395 f58169 f56390 f55293 f55297 f36429 f35588 f62198 f36419 f48630 f62061 f62174 f74948 f35586 f6593 f36409 f62110 f19109 f35585 f36406 f19263 f62048 f62109 f74963 f62200 f75015 f74996 f74955 f74883 f74951 f74945 f36998 f38427 f62192 f74715 f62190 f38428 f74884 f74893 f62147 f63552 f74999 f64875 f62137 f62203 f63551 f19106 f75017 f66823 f66824 f74917 f62047 f36405 f74944 f74947 f62069 f38417 f62064 f62066 f62077 f8954 f64872 f62078 f62076 f62075 f48631 f62068 f74881 f62175 f62124 f38425 f62227 f65132 f65123 f74031 f74840 f74793 f28941 f58139 f74754 f74148 f74055 f74108 f74749 f45476 f12901 f74060 f74143 f74163 f74162 f74153 f74168 f62250 f58447 f69517 f63658 f20132 f62225 f41046 f66720 f63659 f22423 f68226 f62234 f62246 f58400 f64906 f64908 f48627 f39915 f74214 f65114 f41161 f41039 f19420 f62285 f65046 f36426 f19564 f64909 f40818 f74212 f55263 f73966 f65112 f62230 f39142 f41057 f22166 f74215 f65116 f41002 f73967 f58448 f22424 f55232 f66800 f60875 f55233 f68975 f22993 f54352 f66723 f22967 f66717 f22994 f22992 f66719 f52386 f23613 f54351 f66722 f66798 f66797 f55245 f66801 f60878 f69421 f52387 f65060 f62213 f65061 f62252 f65055 f65045 f62286 f65056 f62283 f62288 f64880 f62211 f19570 f62275 f62276 f38436 f62279 f62270 f64881 f62273 f64878 f62268 f64877 f62272 f62267 f62278 f62232 f40827 f65036 f65064 f65066 f65068 f74199 f65104 f65035 f44983 f74204 f65027 f65063 f65069 f65044 f74213 f65101 f65097 f65100 f65092 f65096 f65089 f48603 f65050 f65099 f65053 f65105 f45477 f48613 f48617 f74206 f48599 f65094 f65080 f48600 f65030 f65087 f65033 f65037 f58412 f65077 f65091 f45487 f48614 f65052 f22389 f22385 f65081 f65075 f65082 f65237 f45480 f65244 f48605 f65238 f45473 f45438 f45439 f65074 f74209 f65235 f45486 f65071 f48635 f48606 f65252 f48633 f65249 f48639 f65247 f65253 f65250 f48638 f48636 f48623 f65245 f45475 f45440 f58399 f74203 f29347 f74201 f74531 f74190 f74529 f74527 f74195 f74194 f74193 f58405 f74688 f74704 f74706 f74707 f74698 f74711 f74709 - ridges: - r170595 tested simplicialtop simplicialbot vertices: p773(v660) p990(v489) p602(v194) between f74662 and f64991 - r170632 tested simplicialbot vertices: p563(v582) p207(v488) p651(v80) between f74662 and f74552 - r170592 tested simplicialtop vertices: p773(v660) p990(v489) p568(v324) between f64992 and f74662 - r170609 tested simplicialbot vertices: p536(v663) p990(v489) p568(v324) between f74662 and f65022 - r170578 tested simplicialbot vertices: p773(v660) p637(v493) p568(v324) between f74662 and f64998 - r170611 tested simplicialbot vertices: p536(v663) p568(v324) p177(v106) between f74662 and f65021 - r170623 tested simplicialtop vertices: p628(v405) p507(v256) p565(v46) between f29368 and f74662 - r170472 tested simplicialbot vertices: p176(v577) p507(v256) p409(v147) between f74662 and f58440 - r170479 tested simplicialtop vertices: p213(v407) p190(v263) p417(v151) between f29390 and f74662 - r170620 tested simplicialbot vertices: p522(v411) p190(v263) p417(v151) between f74662 and f31007 - r170626 tested simplicialtop vertices: p837(v264) p417(v151) p651(v80) between f14875 and f74662 - r170550 tested simplicialbot vertices: p190(v263) p507(v256) p565(v46) between f74662 and f14377 - r170589 tested simplicialbot vertices: p213(v407) p837(v264) p417(v151) between f74662 and f29395 - r170628 tested simplicialbot vertices: p522(v411) p417(v151) p651(v80) between f74662 and f31006 - r170618 tested simplicialtop vertices: p923(v748) p522(v411) p409(v147) between f74562 and f74662 - r170483 tested simplicialbot vertices: p213(v407) p190(v263) p565(v46) between f74662 and f29389 - r170431 tested simplicialbot vertices: p757(v576) p453(v254) p910(v193) between f74662 and f58427 - r170433 tested vertices: p757(v576) p910(v193) p382(v85) between f74662 and f74664 - r170461 tested vertices: p28(v659) p910(v193) p382(v85) between f74664 and f74662 - r170496 tested vertices: p28(v659) p207(v488) p382(v85) between f74662 and f74664 - r170566 tested vertices: p178(v622) p728(v104) p382(v85) between f74662 and f74664 - r170437 tested vertices: p563(v582) p207(v488) p382(v85) between f74664 and f74662 - r170562 tested vertices: p971(v192) p728(v104) p382(v85) between f74664 and f74662 - r170558 tested vertices: p757(v576) p971(v192) p382(v85) between f74664 and f74662 - r170353 tested vertices: p18(v484) p361(v189) p382(v85) between f74662 and f74664 - r170357 tested vertices: p563(v582) p751(v262) p382(v85) between f74662 and f74664 - r170351 tested vertices: p18(v484) p275(v187) p382(v85) between f74664 and f74662 - r170362 tested vertices: p751(v262) p225(v148) p382(v85) between f74662 and f74664 - r170348 tested vertices: p275(v187) p580(v158) p382(v85) between f74664 and f74662 - r170355 tested vertices: p178(v622) p361(v189) p382(v85) between f74664 and f74662 - r170429 tested simplicialbot vertices: p757(v576) p411(v404) p453(v254) between f74662 and f58423 - r170396 tested simplicialtop vertices: p678(v575) p411(v404) p453(v254) between f58408 and f74662 - r170630 tested simplicialtop vertices: p28(v659) p207(v488) p409(v147) between f64986 and f74662 - r170400 tested simplicialbot vertices: p678(v575) p411(v404) p177(v106) between f74662 and f58406 - r170583 tested simplicialtop vertices: p176(v577) p579(v406) p409(v147) between f58441 and f74662 - r170520 tested simplicialtop vertices: p678(v575) p453(v254) p876(v19) between f58410 and f74662 - r170458 tested simplicialbot vertices: p28(v659) p910(v193) p876(v19) between f74662 and f64984 - r170537 tested simplicialtop vertices: p28(v659) p792(v257) p876(v19) between f64988 and f74662 - r170462 tested simplicialtop vertices: p453(v254) p910(v193) p876(v19) between f13868 and f74662 - r170540 tested simplicialbot vertices: p678(v575) p792(v257) p876(v19) between f74662 and f58414 - r170629 tested simplicialbot vertices: p923(v748) p522(v411) p651(v80) between f74662 and f74560 - r170569 tested simplicialbot vertices: p28(v659) p792(v257) p409(v147) between f74662 and f64989 - r170585 tested simplicialtop vertices: p579(v406) p792(v257) p409(v147) between f29374 and f74662 - r170476 tested simplicialtop vertices: p190(v263) p507(v256) p409(v147) between f14378 and f74662 - r170617 tested simplicialtop vertices: p522(v411) p190(v263) p409(v147) between f31005 and f74662 - r170394 tested simplicialbot vertices: p242(v492) p623(v255) p177(v106) between f74662 and f45474 - r170524 tested simplicialbot vertices: p872(v321) p971(v192) p965(v57) between f74662 and f22240 - r170415 tested simplicialtop vertices: p162(v662) p218(v661) p965(v57) between f65013 and f74662 - r170419 tested simplicialbot vertices: p162(v662) p872(v321) p965(v57) between f74662 and f65011 - r170374 tested simplicialtop vertices: p809(v664) p773(v660) p637(v493) between f65038 and f74662 - r170561 tested simplicialbot vertices: p216(v288) p971(v192) p728(v104) between f74662 and f19417 - r170532 tested simplicialbot vertices: p162(v662) p218(v661) p990(v489) between f74662 and f65014 - r170625 tested simplicialbot vertices: p176(v577) p628(v405) p507(v256) between f74662 and f58436 - r170519 tested simplicialtop vertices: p218(v661) p216(v288) p965(v57) between f65005 and f74662 - r170515 tested simplicialtop vertices: p216(v288) p971(v192) p965(v57) between f19416 and f74662 - r170575 tested simplicialtop vertices: p536(v663) p162(v662) p872(v321) between f65023 and f74662 - r170572 tested simplicialbot vertices: p536(v663) p162(v662) p990(v489) between f74662 and f65024 - r170606 tested simplicialbot vertices: p178(v622) p216(v288) p728(v104) between f74662 and f62222 - r170405 tested simplicialbot vertices: p218(v661) p216(v288) p898(v169) between f74662 and f65006 - r170402 tested simplicialtop vertices: p564(v442) p216(v288) p898(v169) between f38437 and f74662 - r170522 tested simplicialbot vertices: p178(v622) p564(v442) p216(v288) between f74662 and f62220 - r170381 tested simplicialbot vertices: p602(v194) p898(v169) p808(v91) between f74662 and f7660 - r170535 tested simplicialtop vertices: p218(v661) p602(v194) p898(v169) between f65008 and f74662 - r170612 tested simplicialtop vertices: p218(v661) p990(v489) p602(v194) between f65009 and f74662 - r170599 tested simplicialtop vertices: p757(v576) p872(v321) p971(v192) between f58425 and f74662 - r170511 tested simplicialtop vertices: p536(v663) p411(v404) p177(v106) between f65018 and f74662 - r170426 tested simplicialtop vertices: p757(v576) p411(v404) p872(v321) between f58421 and f74662 - r170422 tested simplicialbot vertices: p536(v663) p411(v404) p872(v321) between f74662 and f65019 - r169781 tested simplicialbot vertices: p601(v624) p562(v449) p327(v170) between f74662 and f62247 - r170276 tested simplicialbot vertices: p166(v629) p171(v294) p468(v172) between f74662 and f62289 - r169949 tested simplicialtop vertices: p493(v444) p864(v290) p327(v170) between f39966 and f74662 - r170161 tested simplicialbot vertices: p412(v623) p404(v467) p13(v171) between f74662 and f62235 - r169777 tested simplicialtop vertices: p601(v624) p562(v449) p473(v448) between f62244 and f74662 - r169954 tested simplicialtop vertices: p370(v470) p963(v181) p102(v17) between f41042 and f74662 - r169834 tested simplicialbot vertices: p175(v466) p963(v181) p102(v17) between f74662 and f40999 - r170212 tested simplicialtop vertices: p601(v624) p473(v448) p238(v291) between f62243 and f74662 - r168405 tested simplicialbot vertices: p345(v469) p941(v459) p527(v182) between f74662 and f41034 - r169020 tested simplicialtop vertices: p286(v639) p944(v461) p144(v303) between f63623 and f74662 - r168865 tested simplicialbot vertices: p849(v651) p211(v475) p527(v182) between f74662 and f64902 - r166024 tested simplicialbot vertices: p155(v304) p924(v297) p100(v53) between f74662 and f22080 - r168401 tested simplicialtop vertices: p345(v469) p941(v459) p665(v30) between f41033 and f74662 - r168818 tested simplicialtop vertices: p98(v678) p345(v469) p665(v30) between f65224 and f74662 - r168820 tested simplicialtop vertices: p941(v459) p144(v303) p665(v30) between f40937 and f74662 - r167200 tested simplicialtop vertices: p849(v651) p746(v308) p527(v182) between f64901 and f74662 - r168823 tested simplicialbot vertices: p98(v678) p144(v303) p665(v30) between f74662 and f65219 - r168238 tested simplicialbot vertices: p98(v678) p345(v469) p184(v307) between f74662 and f65225 - r166250 tested simplicialbot vertices: p98(v678) p112(v505) p144(v303) between f74662 and f65220 - r166254 tested simplicialtop vertices: p98(v678) p112(v505) p184(v307) between f65222 and f74662 - r169022 tested simplicialtop vertices: p112(v505) p513(v335) p23(v201) between f47997 and f74662 - r167496 tested simplicialtop vertices: p541(v679) p112(v505) p144(v303) between f65233 and f74662 - r168793 tested simplicialbot vertices: p405(v435) p365(v281) p510(v28) between f74662 and f37860 - r168942 tested simplicialbot vertices: p541(v679) p944(v461) p144(v303) between f74662 and f65232 - r167140 tested simplicialtop vertices: p722(v641) p286(v639) p144(v303) between f63648 and f74662 - r165769 tested simplicialbot vertices: p112(v505) p184(v307) p23(v201) between f74662 and f47996 - r165766 tested simplicialtop vertices: p184(v307) p23(v201) p993(v99) between f22116 and f74662 - r165675 tested simplicialtop vertices: p76(v677) p811(v504) p513(v335) between f65217 and f74662 - r167895 tested simplicialtop vertices: p851(v551) p136(v375) p484(v232) between f56394 and f74662 - r168706 tested simplicialbot vertices: p727(v650) p571(v473) p993(v99) between f74662 and f64895 - r168975 tested simplicialtop vertices: p279(v474) p184(v307) p993(v99) between f41073 and f74662 - r168977 tested simplicialtop vertices: p279(v474) p489(v311) p184(v307) between f41074 and f74662 - r167636 tested simplicialbot vertices: p541(v679) p112(v505) p710(v179) between f74662 and f65227 - r166770 tested simplicialtop vertices: p855(v503) p513(v335) p710(v179) between f46343 and f74662 - r168863 tested simplicialbot vertices: p125(v676) p70(v643) p710(v179) between f74662 and f65205 - r165943 tested simplicialbot vertices: p541(v679) p70(v643) p944(v461) between f74662 and f65230 - r168423 tested simplicialtop vertices: p126(v645) p883(v464) p339(v180) between f64860 and f74662 - r168190 tested simplicialbot vertices: p112(v505) p513(v335) p710(v179) between f74662 and f47036 - r165939 tested simplicialtop vertices: p541(v679) p70(v643) p710(v179) between f65229 and f74662 - r167638 tested simplicialbot vertices: p26(v251) p575(v131) p829(v33) between f74662 and f13784 - r167894 tested simplicialtop vertices: p76(v677) p855(v503) p978(v60) between f65213 and f74662 - r167360 tested simplicialtop vertices: p125(v676) p855(v503) p710(v179) between f65203 and f74662 - r166767 tested simplicialbot vertices: p76(v677) p855(v503) p513(v335) between f74662 and f65216 - r166064 tested simplicialtop vertices: p70(v643) p883(v464) p734(v462) between f63689 and f74662 - r167984 tested simplicialtop vertices: p125(v676) p734(v462) p219(v199) between f65208 and f74662 - r166060 tested simplicialtop vertices: p125(v676) p70(v643) p734(v462) between f65206 and f74662 - r168995 tested simplicialbot vertices: p555(v644) p734(v462) p219(v199) between f74662 and f64857 - r166934 tested simplicialtop vertices: p219(v199) p995(v109) p978(v60) between f7787 and f74662 - r166156 tested simplicialtop vertices: p126(v645) p494(v636) p883(v464) between f64863 and f74662 - r168710 tested simplicialbot vertices: p883(v464) p734(v462) p155(v304) between f74662 and f40984 - r166020 tested simplicialtop vertices: p181(v455) p924(v297) p100(v53) between f40895 and f74662 - r167363 tested simplicialbot vertices: p125(v676) p855(v503) p978(v60) between f74662 and f65211 - r166376 tested simplicialtop vertices: p555(v644) p521(v332) p219(v199) between f64856 and f74662 - r166372 tested simplicialbot vertices: p185(v500) p521(v332) p219(v199) between f74662 and f45535 - r169044 tested simplicialtop vertices: p555(v644) p734(v462) p155(v304) between f63692 and f74662 - r166515 tested simplicialbot vertices: p555(v644) p303(v463) p155(v304) between f74662 and f63693 - r167299 tested simplicialbot vertices: p428(v400) p708(v376) p575(v131) between f74662 and f28981 - r169050 tested simplicialbot vertices: p185(v500) p219(v199) p995(v109) between f74662 and f45534 - r167405 tested simplicialtop vertices: p174(v333) p893(v200) p829(v33) between f22359 and f74662 - r166938 tested simplicialtop vertices: p125(v676) p219(v199) p978(v60) between f65210 and f74662 - r166519 tested simplicialtop vertices: p555(v644) p303(v463) p105(v18) between f63690 and f74662 - r169132 tested simplicialbot vertices: p555(v644) p521(v332) p105(v18) between f74662 and f63691 - r168960 tested simplicialtop vertices: p893(v200) p559(v110) p978(v60) between f7923 and f74662 - r168999 tested simplicialbot vertices: p358(v501) p903(v334) p559(v110) between f74662 and f45537 - r168958 tested simplicialbot vertices: p893(v200) p995(v109) p978(v60) between f74662 and f7922 - r166883 tested simplicialtop vertices: p494(v636) p300(v95) p915(v8) between f63591 and f74662 - r167875 tested simplicialtop vertices: p428(v400) p26(v251) p575(v131) between f28980 and f74662 - r167581 tested simplicialtop vertices: p185(v500) p575(v131) p995(v109) between f45532 and f74662 - r167401 tested simplicialbot vertices: p174(v333) p893(v200) p559(v110) between f74662 and f22356 - r166841 tested simplicialtop vertices: p893(v200) p995(v109) p829(v33) between f7799 and f74662 - r166837 tested simplicialbot vertices: p575(v131) p995(v109) p829(v33) between f74662 and f3450 - r166432 tested simplicialtop vertices: p352(v234) p871(v233) p391(v132) between f12534 and f74662 - r169116 tested simplicialtop vertices: p303(v463) p155(v304) p924(v297) between f40974 and f74662 - r168813 tested simplicialbot vertices: p883(v464) p155(v304) p100(v53) between f74662 and f40979 - r169193 tested simplicialbot vertices: p924(v297) p172(v176) p915(v8) between f74662 and f20156 - r168853 tested simplicialbot vertices: p23(v201) p559(v110) p978(v60) between f74662 and f7925 - r168849 tested simplicialtop vertices: p358(v501) p23(v201) p559(v110) between f45536 and f74662 - r166887 tested simplicialbot vertices: p364(v631) p300(v95) p915(v8) between f74662 and f63535 - r166395 tested simplicialbot vertices: p248(v640) p206(v164) p954(v87) between f74662 and f63630 - r168790 tested simplicialtop vertices: p594(v611) p365(v281) p510(v28) between f62100 and f74662 - r169031 tested simplicialtop vertices: p248(v640) p289(v282) p954(v87) between f63639 and f74662 - r168901 tested simplicialtop vertices: p248(v640) p39(v460) p610(v178) between f63636 and f74662 - r167169 tested simplicialtop vertices: p341(v300) p552(v177) p407(v62) between f20764 and f74662 - r166392 tested simplicialtop vertices: p248(v640) p206(v164) p822(v88) between f63632 and f74662 - r167087 tested simplicialbot vertices: p248(v640) p142(v302) p822(v88) between f74662 and f63633 - r167084 tested simplicialtop vertices: p775(v621) p142(v302) p822(v88) between f62197 and f74662 - r167989 tested simplicialbot vertices: p289(v282) p258(v163) p220(v3) between f74662 and f19242 - r168315 tested simplicialbot vertices: p325(v458) p699(v457) p758(v301) between f74662 and f40925 - r167233 tested simplicialbot vertices: p248(v640) p289(v282) p220(v3) between f74662 and f63638 - r166564 tested simplicialtop vertices: p128(v436) p289(v282) p258(v163) between f37877 and f74662 - r165763 tested simplicialbot vertices: p248(v640) p325(v458) p610(v178) between f74662 and f63635 - r168903 tested simplicialbot vertices: p286(v639) p325(v458) p758(v301) between f74662 and f63618 - r165759 tested simplicialtop vertices: p248(v640) p325(v458) p220(v3) between f63625 and f74662 - r165998 tested simplicialtop vertices: p699(v457) p258(v163) p220(v3) between f40916 and f74662 - r165995 tested simplicialtop vertices: p325(v458) p699(v457) p220(v3) between f40924 and f74662 - r167711 tested simplicialbot vertices: p699(v457) p258(v163) p433(v54) between f74662 and f40917 - r167608 tested simplicialtop vertices: p286(v639) p325(v458) p610(v178) between f63617 and f74662 - r168665 tested simplicialbot vertices: p944(v461) p39(v460) p610(v178) between f74662 and f40948 - r169064 tested simplicialtop vertices: p944(v461) p39(v460) p933(v97) between f40947 and f74662 - r167611 tested simplicialbot vertices: p286(v639) p944(v461) p610(v178) between f74662 and f63622 - r169093 tested simplicialbot vertices: p248(v640) p39(v460) p142(v302) between f74662 and f63628 - r169066 tested simplicialtop vertices: p39(v460) p142(v302) p933(v97) between f40940 and f74662 - r167641 tested simplicialbot vertices: p349(v283) p886(v98) p433(v54) between f74662 and f19247 - r168060 tested simplicialbot vertices: p493(v444) p864(v290) p539(v51) between f74662 and f39965 - r169036 tested simplicialbot vertices: p601(v624) p493(v444) p539(v51) between f74662 and f62237 - r165950 tested simplicialbot vertices: p128(v436) p349(v283) p258(v163) between f74662 and f37878 - r166561 tested simplicialbot vertices: p128(v436) p289(v282) p954(v87) between f74662 and f37875 - r168991 tested simplicialtop vertices: p206(v164) p954(v87) p936(v50) between f6588 and f74662 - r165946 tested simplicialtop vertices: p349(v283) p258(v163) p433(v54) between f19248 and f74662 - r166801 tested simplicialtop vertices: p895(v434) p187(v161) p954(v87) between f37849 and f74662 - r166798 tested simplicialbot vertices: p895(v434) p187(v161) p510(v28) between f74662 and f37090 - r169000 tested simplicialtop vertices: p130(v279) p187(v161) p510(v28) between f19215 and f74662 - r170792 tested simplicialtop vertices: p671(v769) p122(v606) p84(v605) between f74900 and f74662 - r166494 tested simplicialbot vertices: p594(v611) p895(v434) p510(v28) between f74662 and f62101 - r167327 tested simplicialbot vertices: p187(v161) p954(v87) p936(v50) between f74662 and f6284 - r168917 tested simplicialbot vertices: p416(v614) p187(v161) p936(v50) between f74662 and f62121 - r165897 tested vertices: p919(v617) p642(v438) p945(v90) between f74969 and f74662 - r170799 tested simplicialtop vertices: p671(v769) p919(v617) p945(v90) between f74969 and f74662 - r170800 tested vertices: p671(v769) p919(v617) p84(v605) between f74662 and f74969 - r166498 tested simplicialtop vertices: p594(v611) p895(v434) p32(v162) between f62098 and f74662 - r169180 tested simplicialtop vertices: p128(v436) p349(v283) p539(v51) between f37871 and f74662 - r170825 tested simplicialtop vertices: p297(v772) p621(v610) p997(v433) between f74942 and f74662 - r168320 tested simplicialtop vertices: p554(v430) p613(v295) p198(v174) between f36428 and f74662 - r166548 tested simplicialtop vertices: p281(v633) p735(v207) p523(v115) between f63561 and f74662 - r170758 tested simplicialtop vertices: p896(v762) p135(v602) p824(v423) between f74841 and f74662 - r167649 tested simplicialtop vertices: p86(v612) p997(v433) p510(v28) between f62103 and f74662 - r170828 tested simplicialtop vertices: p297(v772) p768(v339) p61(v94) between f74939 and f74662 - r170822 tested simplicialbot vertices: p297(v772) p621(v610) p61(v94) between f74662 and f74937 - r167724 tested simplicialtop vertices: p86(v612) p405(v435) p312(v173) between f62107 and f74662 - r168066 tested simplicialbot vertices: p621(v610) p613(v295) p61(v94) between f74662 and f62095 - r168486 tested simplicialbot vertices: p43(v609) p997(v433) p510(v28) between f74662 and f62082 - r168062 tested simplicialbot vertices: p613(v295) p198(v174) p61(v94) between f74662 and f20136 - r169160 tested simplicialtop vertices: p929(v567) p560(v212) p550(v118) between f58285 and f74662 - r167652 tested simplicialbot vertices: p86(v612) p405(v435) p510(v28) between f74662 and f62104 - r170788 tested simplicialbot vertices: p671(v769) p343(v441) p654(v287) between f74662 and f74898 - r169183 tested simplicialtop vertices: p864(v290) p349(v283) p886(v98) between f19435 and f74662 - r168642 tested simplicialtop vertices: p43(v609) p130(v279) p510(v28) between f62081 and f74662 - r166276 tested simplicialbot vertices: p621(v610) p704(v89) p22(v35) between f74662 and f62089 - r168926 tested simplicialtop vertices: p621(v610) p613(v295) p22(v35) between f62094 and f74662 - r170798 tested simplicialtop vertices: p671(v769) p791(v616) p654(v287) between f74905 and f74662 - r166927 tested simplicialbot vertices: p41(v446) p682(v445) p238(v291) between f74662 and f39988 - r169656 tested simplicialtop vertices: p897(v744) p176(v577) p611(v79) between f74211 and f74662 - r166923 tested simplicialbot vertices: p601(v624) p41(v446) p238(v291) between f74662 and f62240 - r168788 tested simplicialtop vertices: p11(v626) p365(v281) p32(v162) between f62257 and f74662 - r168056 tested simplicialbot vertices: p864(v290) p349(v283) p539(v51) between f74662 and f19434 - r165728 tested simplicialtop vertices: p41(v446) p682(v445) p32(v162) between f39987 and f74662 - r165724 tested simplicialbot vertices: p11(v626) p682(v445) p32(v162) between f74662 and f62258 - r167304 tested simplicialtop vertices: p895(v434) p793(v280) p32(v162) between f37080 and f74662 - r167307 tested simplicialbot vertices: p41(v446) p793(v280) p32(v162) between f74662 and f39986 - r169070 tested simplicialbot vertices: p594(v611) p365(v281) p32(v162) between f74662 and f62097 - r168551 tested simplicialtop vertices: p41(v446) p128(v436) p539(v51) between f39983 and f74662 - r169130 tested simplicialbot vertices: p895(v434) p793(v280) p954(v87) between f74662 and f37850 - r166429 tested simplicialtop vertices: p128(v436) p793(v280) p954(v87) between f37874 and f74662 - r169080 tested simplicialtop vertices: p601(v624) p41(v446) p539(v51) between f62239 and f74662 - r166425 tested simplicialbot vertices: p41(v446) p128(v436) p793(v280) between f74662 and f39984 - r169184 tested simplicialtop vertices: p714(v284) p704(v89) p22(v35) between f19262 and f74662 - r167507 tested simplicialtop vertices: p196(v652) p395(v329) p138(v55) between f64911 and f74662 - r165904 tested simplicialbot vertices: p818(v471) p395(v329) p138(v55) between f74662 and f41054 - r167242 tested simplicialbot vertices: p505(v674) p196(v652) p395(v329) between f74662 and f65143 - r165908 tested simplicialtop vertices: p818(v471) p395(v329) p543(v196) between f41056 and f74662 - r170670 tested simplicialbot vertices: p729(v753) p948(v739) p37(v552) between f74662 and f74733 - r167592 tested simplicialbot vertices: p211(v475) p818(v471) p138(v55) between f74662 and f41081 - r166900 tested simplicialbot vertices: p505(v674) p395(v329) p543(v196) between f74662 and f65139 - r169171 tested simplicialbot vertices: p319(v625) p682(v445) p124(v93) between f74662 and f62249 - r168794 tested simplicialtop vertices: p17(v684) p27(v519) p403(v515) between f66555 and f74662 - r166896 tested simplicialtop vertices: p505(v674) p776(v498) p543(v196) between f65140 and f74662 - r167415 tested simplicialtop vertices: p992(v476) p211(v475) p489(v311) between f41092 and f74662 - r166153 tested simplicialtop vertices: p211(v475) p345(v469) p489(v311) between f41084 and f74662 - r167563 tested simplicialbot vertices: p992(v476) p211(v475) p138(v55) between f74662 and f41091 - r167588 tested simplicialtop vertices: p849(v651) p211(v475) p818(v471) between f64904 and f74662 - r166149 tested simplicialbot vertices: p211(v475) p345(v469) p527(v182) between f74662 and f41083 - r167023 tested simplicialbot vertices: p345(v469) p489(v311) p184(v307) between f74662 and f41037 - r166632 tested simplicialbot vertices: p600(v630) p689(v305) p300(v95) between f74662 and f63532 - r169196 tested simplicialtop vertices: p581(v646) p294(v618) p439(v29) between f64871 and f74662 - r166876 tested simplicialtop vertices: p600(v630) p457(v452) p311(v451) between f74993 and f74662 - r166629 tested simplicialbot vertices: p600(v630) p347(v465) p689(v305) between f74662 and f63533 - r169185 tested simplicialbot vertices: p347(v465) p679(v175) p439(v29) between f74662 and f40991 - r169024 tested simplicialbot vertices: p126(v645) p494(v636) p689(v305) between f74662 and f64862 - r168987 tested simplicialbot vertices: p364(v631) p311(v451) p300(v95) between f74662 and f63536 - r167722 tested simplicialtop vertices: p494(v636) p689(v305) p300(v95) between f63595 and f74662 - r166160 tested simplicialbot vertices: p494(v636) p883(v464) p100(v53) between f74662 and f63599 - r167570 tested simplicialtop vertices: p494(v636) p181(v455) p100(v53) between f63598 and f74662 - r169188 tested simplicialbot vertices: p494(v636) p181(v455) p924(v297) between f74662 and f63589 - r168936 tested simplicialbot vertices: p656(v632) p457(v452) p553(v166) between f74662 and f63549 - r168888 tested simplicialbot vertices: p834(v635) p566(v453) p735(v207) between f74662 and f63584 - r170829 tested simplicialbot vertices: p297(v772) p768(v339) p312(v173) between f74662 and f74940 - r168462 tested vertices: p294(v618) p117(v439) p679(v175) between f74987 and f74662 - r169194 tested vertices: p294(v618) p679(v175) p439(v29) between f74987 and f74662 - r167156 tested simplicialbot vertices: p656(v632) p117(v439) p679(v175) between f74662 and f74987 - r165988 tested vertices: p656(v632) p600(v630) p679(v175) between f74987 and f74662 - r165992 tested vertices: p656(v632) p600(v630) p457(v452) between f74662 and f74987 - r167859 tested simplicialtop vertices: p600(v630) p347(v465) p679(v175) between f62291 and f74662 - r170838 tested simplicialbot vertices: p392(v773) p671(v769) p122(v606) between f74662 and f74952 - r166946 tested simplicialtop vertices: p708(v376) p575(v131) p974(v63) between f24399 and f74662 - r166942 tested simplicialbot vertices: p185(v500) p575(v131) p974(v63) between f74662 and f45529 - r166006 tested simplicialbot vertices: p885(v298) p172(v176) p836(v96) between f74662 and f20729 - r167296 tested simplicialtop vertices: p428(v400) p708(v376) p871(v233) between f28978 and f74662 - r168169 tested simplicialbot vertices: p341(v300) p885(v298) p836(v96) between f74662 and f20947 - r168887 tested simplicialtop vertices: p185(v500) p521(v332) p974(v63) between f45530 and f74662 - r166197 tested simplicialtop vertices: p572(v299) p974(v63) p105(v18) between f20756 and f74662 - r168381 tested simplicialtop vertices: p341(v300) p572(v299) p836(v96) between f20948 and f74662 - r167484 tested simplicialtop vertices: p303(v463) p172(v176) p836(v96) between f40968 and f74662 - r166193 tested simplicialbot vertices: p572(v299) p974(v63) p815(v36) between f74662 and f20757 - r167926 tested simplicialbot vertices: p521(v332) p974(v63) p105(v18) between f74662 and f22345 - r167173 tested simplicialtop vertices: p408(v456) p341(v300) p407(v62) between f40902 and f74662 - r168150 tested simplicialtop vertices: p303(v463) p572(v299) p105(v18) between f40976 and f74662 - r166010 tested simplicialtop vertices: p885(v298) p172(v176) p915(v8) between f20728 and f74662 - r167487 tested simplicialbot vertices: p303(v463) p572(v299) p836(v96) between f74662 and f40977 - r168488 tested simplicialbot vertices: p341(v300) p572(v299) p815(v36) between f74662 and f20945 - r169191 tested simplicialtop vertices: p303(v463) p924(v297) p172(v176) between f40973 and f74662 - r166599 tested simplicialbot vertices: p581(v646) p347(v465) p439(v29) between f74662 and f64865 - r166595 tested simplicialtop vertices: p581(v646) p347(v465) p689(v305) between f64869 and f74662 - r170754 tested simplicialtop vertices: p896(v762) p688(v735) p92(v425) between f74838 and f74662 - r168628 tested simplicialbot vertices: p364(v631) p566(v453) p449(v296) between f74662 and f63547 - r168362 tested simplicialbot vertices: p457(v452) p311(v451) p449(v296) between f74662 and f40867 - r168358 tested simplicialtop vertices: p364(v631) p311(v451) p449(v296) between f63546 and f74662 - r166873 tested simplicialtop vertices: p600(v630) p311(v451) p300(v95) between f62290 and f74662 - r169096 tested simplicialbot vertices: p494(v636) p924(v297) p915(v8) between f74662 and f63592 - r165929 tested simplicialbot vertices: p281(v633) p364(v631) p552(v177) between f74662 and f63566 - r167908 tested simplicialbot vertices: p624(v341) p576(v205) p815(v36) between f74662 and f22430 - r166552 tested simplicialtop vertices: p281(v633) p566(v453) p735(v207) between f63562 and f74662 - r166737 tested simplicialtop vertices: p281(v633) p364(v631) p566(v453) between f63564 and f74662 - r165925 tested simplicialbot vertices: p364(v631) p885(v298) p552(v177) between f74662 and f63540 - r167910 tested simplicialtop vertices: p341(v300) p576(v205) p815(v36) between f20936 and f74662 - r168862 tested simplicialtop vertices: p364(v631) p885(v298) p915(v8) between f63538 and f74662 - r168986 tested simplicialbot vertices: p408(v456) p341(v300) p576(v205) between f74662 and f40908 - r168806 tested simplicialtop vertices: p341(v300) p885(v298) p552(v177) between f20946 and f74662 - r167435 tested simplicialbot vertices: p70(v643) p883(v464) p339(v180) between f74662 and f63688 - r168251 tested simplicialbot vertices: p581(v646) p142(v302) p339(v180) between f74662 and f64874 - r168255 tested simplicialtop vertices: p142(v302) p339(v180) p933(v97) between f21525 and f74662 - r167431 tested simplicialbot vertices: p70(v643) p339(v180) p933(v97) between f74662 and f63687 - r168954 tested simplicialbot vertices: p126(v645) p689(v305) p339(v180) between f74662 and f64859 - r168957 tested simplicialtop vertices: p581(v646) p689(v305) p339(v180) between f64868 and f74662 - r167741 tested simplicialtop vertices: p70(v643) p944(v461) p933(v97) between f63660 and f74662 - r169211 tested simplicialbot vertices: p505(v674) p776(v498) p848(v100) between f74662 and f65135 - r168183 tested simplicialbot vertices: p802(v312) p30(v310) p585(v184) between f74662 and f22160 - r165686 tested simplicialtop vertices: p69(v675) p609(v309) p23(v201) between f65200 and f74662 - r166555 tested simplicialbot vertices: p69(v675) p288(v472) p414(v10) between f74662 and f65144 - r165682 tested simplicialbot vertices: p609(v309) p23(v201) p993(v99) between f74662 and f22134 - r168859 tested simplicialbot vertices: p69(v675) p358(v501) p23(v201) between f74662 and f65201 - r167320 tested simplicialtop vertices: p69(v675) p358(v501) p903(v334) between f65198 and f74662 - r169162 tested simplicialbot vertices: p571(v473) p609(v309) p993(v99) between f74662 and f41067 - r167224 tested simplicialbot vertices: p288(v472) p609(v309) p585(v184) between f74662 and f41059 - r167220 tested simplicialtop vertices: p571(v473) p609(v309) p585(v184) between f41068 and f74662 - r167301 tested simplicialbot vertices: p856(v649) p288(v472) p585(v184) between f74662 and f64893 - r166559 tested simplicialtop vertices: p69(v675) p288(v472) p609(v309) between f65146 and f74662 - r167089 tested simplicialbot vertices: p856(v649) p30(v310) p414(v10) between f74662 and f64889 - r167942 tested simplicialtop vertices: p196(v652) p571(v473) p585(v184) between f64920 and f74662 - r167303 tested simplicialtop vertices: p856(v649) p288(v472) p414(v10) between f64890 and f74662 - r168922 tested simplicialbot vertices: p196(v652) p802(v312) p585(v184) between f74662 and f64918 - r168944 tested simplicialtop vertices: p505(v674) p196(v652) p802(v312) between f65142 and f74662 - r167561 tested simplicialtop vertices: p69(v675) p980(v502) p414(v10) between f65145 and f74662 - r165918 tested simplicialtop vertices: p197(v718) p851(v551) p926(v129) between f69531 and f74662 - r168700 tested simplicialbot vertices: p551(v413) p626(v265) p692(v152) between f74662 and f32420 - r167541 tested simplicialbot vertices: p44(v586) p991(v414) p551(v413) between f74662 and f59610 - r168696 tested simplicialbot vertices: p109(v585) p551(v413) p692(v152) between f74662 and f59607 - r166334 tested simplicialbot vertices: p120(v584) p476(v269) p771(v154) between f74662 and f58509 - r168894 tested simplicialtop vertices: p551(v413) p626(v265) p874(v48) between f32417 and f74662 - r167324 tested simplicialbot vertices: p69(v675) p980(v502) p903(v334) between f74662 and f65196 - r169118 tested simplicialbot vertices: p31(v208) p523(v115) p407(v62) between f74662 and f8524 - r168744 tested simplicialtop vertices: p44(v586) p109(v585) p551(v413) between f59612 and f74662 - r166338 tested simplicialbot vertices: p120(v584) p551(v413) p476(v269) between f74662 and f58510 - r167538 tested simplicialtop vertices: p991(v414) p551(v413) p476(v269) between f32434 and f74662 - r165818 tested simplicialbot vertices: p551(v413) p310(v268) p874(v48) between f74662 and f32418 - r165814 tested simplicialtop vertices: p120(v584) p551(v413) p310(v268) between f58506 and f74662 - r170673 tested simplicialtop vertices: p729(v753) p701(v719) p37(v552) between f74736 and f74662 - r169017 tested simplicialbot vertices: p44(v586) p357(v197) p440(v82) between f74662 and f59616 - r166773 tested simplicialbot vertices: p701(v719) p136(v375) p371(v231) between f74662 and f69573 - r167052 tested simplicialtop vertices: p448(v590) p826(v419) p133(v71) between f60755 and f74662 - r170657 tested simplicialtop vertices: p356(v752) p701(v719) p448(v590) between f74723 and f74662 - r168911 tested simplicialtop vertices: p109(v585) p719(v266) p692(v152) between f59606 and f74662 - r169123 tested simplicialtop vertices: p826(v419) p681(v418) p434(v14) between f32487 and f74662 - r168185 tested simplicialbot vertices: p826(v419) p133(v71) p434(v14) between f74662 and f32486 - r166200 tested simplicialbot vertices: p626(v265) p368(v155) p434(v14) between f74662 and f14887 - r170658 tested simplicialtop vertices: p356(v752) p669(v499) p371(v231) between f74720 and f74662 - r168335 tested simplicialtop vertices: p692(v152) p133(v71) p434(v14) between f5898 and f74662 - r169187 tested simplicialtop vertices: p249(v637) p408(v456) p407(v62) between f63602 and f74662 - r169009 tested simplicialbot vertices: p701(v719) p37(v552) p136(v375) between f74662 and f69574 - r167239 tested simplicialbot vertices: p669(v499) p666(v331) p357(v197) between f74662 and f45522 - r168734 tested simplicialtop vertices: p357(v197) p5(v153) p423(v24) between f7741 and f74662 - r168889 tested simplicialbot vertices: p44(v586) p109(v585) p719(v266) between f74662 and f59614 - r166512 tested simplicialbot vertices: p669(v499) p357(v197) p133(v71) between f74662 and f45521 - r166508 tested simplicialtop vertices: p719(v266) p357(v197) p133(v71) between f15382 and f74662 - r170660 tested simplicialbot vertices: p356(v752) p669(v499) p133(v71) between f74662 and f74717 - r168801 tested simplicialbot vertices: p44(v586) p719(v266) p357(v197) between f74662 and f59617 - r169019 tested simplicialtop vertices: p44(v586) p991(v414) p440(v82) between f59609 and f74662 - r167524 tested simplicialbot vertices: p669(v499) p136(v375) p666(v331) between f74662 and f45527 - r169144 tested simplicialtop vertices: p666(v331) p332(v108) p71(v42) between f22333 and f74662 - r165862 tested simplicialtop vertices: p669(v499) p136(v375) p371(v231) between f45526 and f74662 - r170652 tested simplicialtop vertices: p2(v751) p120(v584) p310(v268) between f74713 and f74662 - r168909 tested simplicialbot vertices: p719(v266) p692(v152) p133(v71) between f74662 and f15380 - r170653 tested simplicialbot vertices: p2(v751) p988(v588) p310(v268) between f74662 and f74714 - r168946 tested simplicialtop vertices: p991(v414) p5(v153) p440(v82) between f32431 and f74662 - r168898 tested simplicialbot vertices: p357(v197) p5(v153) p440(v82) between f74662 and f7739 - r168670 tested simplicialtop vertices: p431(v412) p332(v108) p423(v24) between f31600 and f74662 - r168693 tested simplicialtop vertices: p777(v657) p30(v310) p414(v10) between f64961 and f74662 - r168139 tested simplicialtop vertices: p666(v331) p357(v197) p332(v108) between f22334 and f74662 - r168732 tested simplicialbot vertices: p431(v412) p5(v153) p423(v24) between f74662 and f31598 - r168570 tested simplicialtop vertices: p980(v502) p306(v185) p414(v10) between f46335 and f74662 - r168135 tested simplicialbot vertices: p357(v197) p332(v108) p423(v24) between f74662 and f7740 - r166204 tested simplicialtop vertices: p626(v265) p692(v152) p434(v14) between f14886 and f74662 - r168573 tested simplicialbot vertices: p777(v657) p306(v185) p414(v10) between f74662 and f64959 - r169146 tested simplicialtop vertices: p136(v375) p666(v331) p71(v42) between f24371 and f74662 - r169126 tested simplicialtop vertices: p681(v418) p368(v155) p434(v14) between f32468 and f74662 - r168117 tested simplicialbot vertices: p991(v414) p431(v412) p548(v267) between f74662 and f32438 - r166912 tested simplicialtop vertices: p988(v588) p614(v417) p771(v154) between f59634 and f74662 - r170637 tested simplicialtop vertices: p688(v735) p139(v733) p828(v144) between f74121 and f74662 - r168113 tested simplicialtop vertices: p991(v414) p431(v412) p5(v153) between f32437 and f74662 - r169177 tested simplicialtop vertices: p590(v587) p476(v269) p771(v154) between f59619 and f74662 - r166669 tested simplicialtop vertices: p806(v481) p306(v185) p461(v59) between f41134 and f74662 - r166908 tested simplicialtop vertices: p614(v417) p736(v416) p771(v154) between f32466 and f74662 - r166665 tested simplicialbot vertices: p777(v657) p806(v481) p306(v185) between f74662 and f64964 - r167669 tested simplicialtop vertices: p398(v198) p332(v108) p222(v101) between f7743 and f74662 - r167665 tested simplicialbot vertices: p548(v267) p332(v108) p222(v101) between f74662 and f15904 - r166013 tested simplicialbot vertices: p174(v333) p398(v198) p75(v130) between f74662 and f22353 - r168397 tested simplicialbot vertices: p921(v655) p548(v267) p222(v101) between f74662 and f64943 - r167811 tested simplicialbot vertices: p806(v481) p222(v101) p461(v59) between f74662 and f41133 - r167808 tested simplicialtop vertices: p921(v655) p806(v481) p222(v101) between f64941 and f74662 - r167776 tested simplicialbot vertices: p921(v655) p922(v482) p329(v480) between f74662 and f64946 - r168435 tested simplicialtop vertices: p398(v198) p222(v101) p461(v59) between f7742 and f74662 - r166675 tested simplicialbot vertices: p398(v198) p332(v108) p71(v42) between f74662 and f7784 - r168215 tested simplicialtop vertices: p352(v234) p391(v132) p712(v1) between f12532 and f74662 - r166672 tested simplicialtop vertices: p398(v198) p75(v130) p71(v42) between f7785 and f74662 - r168068 tested simplicialbot vertices: p75(v130) p71(v42) p712(v1) between f74662 and f3436 - r166017 tested simplicialbot vertices: p174(v333) p75(v130) p829(v33) between f74662 and f22358 - r166436 tested simplicialbot vertices: p428(v400) p352(v234) p871(v233) between f74662 and f28977 - r168809 tested simplicialtop vertices: p174(v333) p398(v198) p461(v59) between f22352 and f74662 - r168886 tested simplicialbot vertices: p921(v655) p329(v480) p548(v267) between f74662 and f64944 - r167780 tested simplicialtop vertices: p921(v655) p922(v482) p806(v481) between f64947 and f74662 - r167998 tested simplicialtop vertices: p988(v588) p310(v268) p996(v102) between f59629 and f74662 - r168979 tested simplicialbot vertices: p174(v333) p559(v110) p461(v59) between f74662 and f22355 - r168379 tested simplicialtop vertices: p306(v185) p559(v110) p461(v59) between f7545 and f74662 - r168375 tested simplicialbot vertices: p903(v334) p306(v185) p559(v110) between f74662 and f22361 - r170647 tested simplicialbot vertices: p779(v749) p266(v415) p771(v154) between f74662 and f74697 - r168768 tested simplicialtop vertices: p980(v502) p903(v334) p306(v185) between f46336 and f74662 - r168623 tested simplicialtop vertices: p377(v654) p922(v482) p329(v480) between f64936 and f74662 - r168704 tested simplicialbot vertices: p736(v416) p266(v415) p350(v56) between f74662 and f32455 - r170636 tested simplicialbot vertices: p688(v735) p92(v425) p828(v144) between f74662 and f74114 - r169113 tested simplicialtop vertices: p431(v412) p548(v267) p332(v108) between f31601 and f74662 - r168291 tested simplicialbot vertices: p310(v268) p996(v102) p874(v48) between f74662 and f16404 - r167758 tested simplicialbot vertices: p988(v588) p120(v584) p771(v154) between f74662 and f59635 - r170633 tested simplicialtop vertices: p923(v748) p207(v488) p651(v80) between f74690 and f74662 - r167020 tested simplicialtop vertices: p377(v654) p329(v480) p350(v56) between f64934 and f74662 - r170642 tested simplicialbot vertices: p779(v749) p329(v480) p350(v56) between f74662 and f74702 - r170641 tested simplicialtop vertices: p779(v749) p266(v415) p350(v56) between f74701 and f74662 - r168081 tested simplicialtop vertices: p736(v416) p266(v415) p771(v154) between f32457 and f74662 - r167005 tested simplicialtop vertices: p753(v516) p31(v208) p523(v115) between f49989 and f74662 - r167743 tested simplicialbot vertices: p988(v588) p614(v417) p996(v102) between f74662 and f59630 - r165922 tested simplicialbot vertices: p197(v718) p851(v551) p136(v375) between f74662 and f69534 - r170650 tested simplicialbot vertices: p881(v750) p590(v587) p476(v269) between f74662 and f74710 - r167255 tested simplicialbot vertices: p302(v374) p716(v236) p905(v73) between f74662 and f24361 - r165807 tested simplicialbot vertices: p68(v689) p589(v347) p953(v133) between f74662 and f66596 - r168891 tested simplicialbot vertices: p403(v515) p560(v212) p550(v118) between f74662 and f49984 - r167251 tested simplicialtop vertices: p302(v374) p871(v233) p905(v73) between f24334 and f74662 - r169120 tested simplicialbot vertices: p249(v637) p31(v208) p407(v62) between f74662 and f63601 - r167159 tested simplicialtop vertices: p197(v718) p37(v552) p136(v375) between f69571 and f74662 - r168876 tested simplicialbot vertices: p708(v376) p871(v233) p905(v73) between f74662 and f24372 - r167646 tested vertices: p805(v690) p780(v211) p607(v21) between f73470 and f74662 - r167556 tested vertices: p209(v512) p56(v235) p607(v21) between f74662 and f73470 - r167552 tested vertices: p209(v512) p462(v342) p607(v21) between f73470 and f74662 - r167872 tested vertices: p56(v235) p780(v211) p607(v21) between f74662 and f73470 - r168881 tested simplicialbot vertices: p302(v374) p871(v233) p391(v132) between f74662 and f23635 - r166906 tested simplicialbot vertices: p716(v236) p953(v133) p905(v73) between f74662 and f12550 - r166902 tested simplicialtop vertices: p56(v235) p953(v133) p905(v73) between f12541 and f74662 - r167273 tested simplicialtop vertices: p491(v725) p865(v688) p106(v117) between f73393 and f74662 - r165813 tested vertices: p491(v725) p68(v689) p519(v517) between f73393 and f74662 - r166711 tested vertices: p491(v725) p716(v236) p953(v133) between f73393 and f74662 - r167040 tested simplicialbot vertices: p491(v725) p865(v688) p519(v517) between f74662 and f73393 - r165809 tested vertices: p491(v725) p68(v689) p953(v133) between f74662 and f73393 - r169151 tested simplicialtop vertices: p209(v512) p56(v235) p905(v73) between f49618 and f74662 - r169152 tested simplicialtop vertices: p302(v374) p484(v232) p391(v132) between f23634 and f74662 - r169147 tested simplicialbot vertices: p484(v232) p391(v132) p712(v1) between f74662 and f11854 - r166184 tested simplicialtop vertices: p315(v685) p589(v347) p56(v235) between f66565 and f74662 - r167504 tested simplicialtop vertices: p569(v560) p403(v515) p560(v212) between f58184 and f74662 - r166180 tested simplicialbot vertices: p865(v688) p315(v685) p589(v347) between f74662 and f66586 - r167039 tested simplicialtop vertices: p865(v688) p519(v517) p589(v347) between f66584 and f74662 - r165811 tested simplicialbot vertices: p68(v689) p519(v517) p589(v347) between f74662 and f66594 - r166941 tested simplicialbot vertices: p589(v347) p56(v235) p953(v133) between f74662 and f22490 - r167692 tested simplicialbot vertices: p209(v512) p576(v205) p905(v73) between f74662 and f49617 - r167689 tested simplicialtop vertices: p624(v341) p576(v205) p905(v73) between f22433 and f74662 - r169033 tested simplicialbot vertices: p805(v690) p254(v518) p607(v21) between f74662 and f66599 - r167544 tested simplicialbot vertices: p38(v553) p624(v341) p815(v36) between f74662 and f57504 - r167644 tested simplicialtop vertices: p805(v690) p451(v348) p780(v211) between f66604 and f74662 - r168656 tested simplicialbot vertices: p99(v345) p735(v207) p523(v115) between f74662 and f22470 - r168050 tested simplicialbot vertices: p209(v512) p462(v342) p576(v205) between f74662 and f48642 - r167548 tested simplicialtop vertices: p38(v553) p624(v341) p905(v73) between f57506 and f74662 - r167761 tested simplicialtop vertices: p264(v638) p254(v518) p577(v113) between f63611 and f74662 - r167804 tested simplicialtop vertices: p38(v553) p708(v376) p974(v63) between f57501 and f74662 - r167648 tested simplicialbot vertices: p451(v348) p780(v211) p673(v116) between f74662 and f22493 - r168716 tested simplicialtop vertices: p462(v342) p576(v205) p577(v113) between f22436 and f74662 - r166415 tested simplicialbot vertices: p451(v348) p441(v346) p798(v210) between f74662 and f22495 - r167002 tested simplicialbot vertices: p249(v637) p753(v516) p31(v208) between f74662 and f63604 - r169158 tested simplicialbot vertices: p753(v516) p99(v345) p523(v115) between f74662 and f49990 - r166412 tested simplicialtop vertices: p451(v348) p441(v346) p673(v116) between f22494 and f74662 - r167475 tested simplicialtop vertices: p441(v346) p798(v210) p735(v207) between f22474 and f74662 - r167764 tested simplicialbot vertices: p254(v518) p577(v113) p607(v21) between f74662 and f50008 - r168786 tested simplicialbot vertices: p136(v375) p484(v232) p71(v42) between f74662 and f24370 - r166612 tested simplicialbot vertices: p99(v345) p798(v210) p735(v207) between f74662 and f22471 - r166608 tested simplicialtop vertices: p264(v638) p99(v345) p798(v210) between f63614 and f74662 - r168214 tested simplicialtop vertices: p264(v638) p408(v456) p99(v345) between f63615 and f74662 - r168783 tested simplicialtop vertices: p484(v232) p71(v42) p712(v1) between f11856 and f74662 - r166979 tested simplicialbot vertices: p408(v456) p576(v205) p577(v113) between f74662 and f40907 - r166975 tested simplicialbot vertices: p264(v638) p408(v456) p577(v113) between f74662 and f63609 - r168446 tested simplicialbot vertices: p254(v518) p451(v348) p798(v210) between f74662 and f50006 - r168443 tested simplicialtop vertices: p805(v690) p254(v518) p451(v348) between f66605 and f74662 - r166115 tested simplicialtop vertices: p249(v637) p753(v516) p99(v345) between f63607 and f74662 - r169032 tested simplicialtop vertices: p462(v342) p577(v113) p607(v21) between f22435 and f74662 - r168165 tested simplicialbot vertices: p264(v638) p254(v518) p798(v210) between f74662 and f63612 - r169092 tested simplicialbot vertices: p38(v553) p708(v376) p905(v73) between f74662 and f57507 - r167807 tested simplicialtop vertices: p38(v553) p974(v63) p815(v36) between f57503 and f74662 - r166119 tested simplicialbot vertices: p249(v637) p408(v456) p99(v345) between f74662 and f63606 - r167212 tested simplicialbot vertices: p281(v633) p552(v177) p407(v62) between f74662 and f63569 - r167209 tested simplicialtop vertices: p281(v633) p523(v115) p407(v62) between f63568 and f74662 - r167166 tested simplicialbot vertices: p196(v652) p571(v473) p489(v311) between f74662 and f64921 - r168724 tested simplicialbot vertices: p727(v650) p279(v474) p489(v311) between f74662 and f64899 - r169047 tested simplicialbot vertices: p196(v652) p992(v476) p138(v55) between f74662 and f64912 - r168721 tested simplicialtop vertices: p727(v650) p279(v474) p993(v99) between f64896 and f74662 - r167162 tested simplicialtop vertices: p196(v652) p992(v476) p489(v311) between f64916 and f74662 - r168637 tested simplicialtop vertices: p727(v650) p571(v473) p489(v311) between f64898 and f74662 - r166004 tested simplicialbot vertices: p811(v504) p23(v201) p978(v60) between f74662 and f47029 - r165679 tested simplicialbot vertices: p811(v504) p513(v335) p23(v201) between f74662 and f47030 - r166001 tested simplicialbot vertices: p76(v677) p811(v504) p978(v60) between f74662 and f65214 - r168952 tested simplicialtop vertices: p94(v509) p768(v339) p93(v52) between f48618 and f74662 - r166221 tested simplicialtop vertices: p11(v626) p682(v445) p124(v93) between f62265 and f74662 - r167680 tested simplicialtop vertices: p11(v626) p868(v337) p93(v52) between f62262 and f74662 - r166224 tested simplicialbot vertices: p11(v626) p868(v337) p124(v93) between f74662 and f62264 - r168477 tested simplicialtop vertices: p768(v339) p312(v173) p93(v52) between f22409 and f74662 - r167976 tested simplicialbot vertices: p11(v626) p365(v281) p93(v52) between f74662 and f62260 - r169181 tested simplicialtop vertices: p768(v339) p198(v174) p61(v94) between f22418 and f74662 - r165852 tested simplicialtop vertices: p405(v435) p365(v281) p93(v52) between f37865 and f74662 - r165848 tested simplicialbot vertices: p405(v435) p312(v173) p93(v52) between f74662 and f37864 - r169212 tested simplicialtop vertices: p776(v498) p597(v328) p543(v196) between f45513 and f74662 - r167193 tested simplicialbot vertices: p296(v454) p234(v285) p553(v166) between f74662 and f40885 - r168399 tested simplicialtop vertices: p834(v635) p535(v64) p787(v37) between f63581 and f74662 - r167189 tested simplicialtop vertices: p296(v454) p234(v285) p535(v64) between f40884 and f74662 - r168355 tested simplicialtop vertices: p834(v635) p296(v454) p535(v64) between f63579 and f74662 - r168984 tested simplicialtop vertices: p478(v634) p457(v452) p553(v166) between f63576 and f74662 - r168503 tested simplicialtop vertices: p834(v635) p478(v634) p296(v454) between f63587 and f74662 - r168500 tested simplicialbot vertices: p478(v634) p296(v454) p553(v166) between f74662 and f63577 - r168713 tested simplicialbot vertices: p834(v635) p735(v207) p787(v37) between f74662 and f63582 - r167773 tested simplicialbot vertices: p834(v635) p478(v634) p566(v453) between f74662 and f63586 - r167521 tested simplicialtop vertices: p478(v634) p566(v453) p449(v296) between f63571 and f74662 - r167517 tested simplicialbot vertices: p478(v634) p457(v452) p449(v296) between f74662 and f63574 - r165964 tested simplicialtop vertices: p428(v400) p352(v234) p639(v72) between f28973 and f74662 - r169039 tested simplicialtop vertices: p26(v251) p639(v72) p829(v33) between f13783 and f74662 - r165960 tested simplicialbot vertices: p428(v400) p26(v251) p639(v72) between f74662 and f28974 - r169213 tested simplicialbot vertices: p75(v130) p639(v72) p829(v33) between f74662 and f3445 - r166585 tested simplicialtop vertices: p75(v130) p639(v72) p712(v1) between f3437 and f74662 - r166582 tested simplicialbot vertices: p352(v234) p639(v72) p712(v1) between f74662 and f12531 - r158423 tested simplicialbot vertices: p691(v716) p470(v532) p446(v359) between f74662 and f68974 - r166755 tested simplicialtop vertices: p84(v605) p596(v428) p127(v168) between f60881 and f74662 - r169100 tested simplicialtop vertices: p189(v704) p584(v361) p469(v206) between f66725 and f74662 - r166074 tested simplicialtop vertices: p412(v623) p175(v466) p509(v306) between f62228 and f74662 - r167231 tested simplicialtop vertices: p919(v617) p84(v605) p127(v168) between f74974 and f74662 - r166542 tested simplicialbot vertices: p817(v705) p875(v371) p127(v168) between f74662 and f74979 - r166546 tested simplicialtop vertices: p817(v705) p919(v617) p127(v168) between f74977 and f74662 - r166226 tested simplicialtop vertices: p4(v717) p246(v546) p574(v372) between f68978 and f74662 - r167820 tested simplicialtop vertices: p234(v285) p504(v114) p535(v64) between f19307 and f74662 - r168281 tested simplicialtop vertices: p877(v522) p459(v521) p452(v123) between f50174 and f74662 - r168484 tested simplicialtop vertices: p817(v705) p875(v371) p867(v221) between f66742 and f74662 - r166759 tested simplicialbot vertices: p84(v605) p596(v428) p228(v277) between f74662 and f74891 - r167605 tested simplicialtop vertices: p17(v684) p480(v350) p820(v213) between f66546 and f74662 - r170797 tested simplicialbot vertices: p671(v769) p791(v616) p945(v90) between f74662 and f74904 - r165901 tested simplicialbot vertices: p817(v705) p919(v617) p642(v438) between f74662 and f66738 - r167389 tested simplicialtop vertices: p817(v705) p273(v615) p642(v438) between f66734 and f74662 - r170842 tested simplicialtop vertices: p392(v773) p416(v614) p379(v437) between f74956 and f74662 - r169053 tested simplicialtop vertices: p459(v521) p584(v361) p867(v221) between f50163 and f74662 - r169051 tested simplicialbot vertices: p817(v705) p584(v361) p867(v221) between f74662 and f66741 - r166731 tested simplicialbot vertices: p574(v372) p867(v221) p452(v123) between f74662 and f23622 - r168871 tested simplicialtop vertices: p180(v694) p480(v350) p262(v4) between f66637 and f74662 - r170110 tested simplicialbot vertices: p562(v449) p863(v293) p781(v92) between f74662 and f40812 - r166605 tested simplicialbot vertices: p877(v522) p459(v521) p480(v350) between f74662 and f50175 - r166602 tested simplicialbot vertices: p877(v522) p480(v350) p820(v213) between f74662 and f50166 - r166734 tested simplicialtop vertices: p459(v521) p867(v221) p452(v123) between f50160 and f74662 - r168873 tested simplicialbot vertices: p180(v694) p584(v361) p262(v4) between f74662 and f66640 - r167412 tested simplicialtop vertices: p180(v694) p459(v521) p480(v350) between f66638 and f74662 - r168869 tested simplicialbot vertices: p17(v684) p480(v350) p262(v4) between f74662 and f66543 - r167575 tested simplicialbot vertices: p180(v694) p459(v521) p584(v361) between f74662 and f66641 - r165731 tested simplicialtop vertices: p415(v513) p469(v206) p262(v4) between f49963 and f74662 - r169105 tested simplicialbot vertices: p817(v705) p273(v615) p234(v285) between f74662 and f66733 - r168086 tested simplicialbot vertices: p96(v683) p535(v64) p787(v37) between f74662 and f66531 - r168306 tested simplicialtop vertices: p817(v705) p631(v533) p234(v285) between f66731 and f74662 - r168194 tested simplicialtop vertices: p455(v538) p299(v365) p24(v69) between f54330 and f74662 - r168158 tested simplicialtop vertices: p631(v533) p415(v513) p504(v114) between f52391 and f74662 - r166484 tested simplicialbot vertices: p817(v705) p631(v533) p584(v361) between f74662 and f66736 - r166480 tested simplicialtop vertices: p189(v704) p631(v533) p584(v361) between f66726 and f74662 - r167861 tested simplicialbot vertices: p189(v704) p631(v533) p415(v513) between f74662 and f66729 - r168309 tested simplicialbot vertices: p631(v533) p234(v285) p504(v114) between f74662 and f52394 - r167823 tested simplicialbot vertices: p415(v513) p504(v114) p535(v64) between f74662 and f49648 - r168090 tested simplicialbot vertices: p96(v683) p415(v513) p535(v64) between f74662 and f66532 - r165756 tested vertices: p569(v560) p8(v390) p560(v212) between f74662 and f73922 - r165752 tested simplicialtop vertices: p569(v560) p8(v390) p586(v12) between f73922 and f74662 - r169042 tested simplicialbot vertices: p189(v704) p415(v513) p469(v206) between f74662 and f66728 - r168421 tested simplicialtop vertices: p17(v684) p96(v683) p415(v513) between f66547 and f74662 - r169106 tested simplicialbot vertices: p17(v684) p96(v683) p517(v209) between f74662 and f66558 - r165735 tested simplicialtop vertices: p17(v684) p415(v513) p262(v4) between f66544 and f74662 - r169102 tested simplicialbot vertices: p584(v361) p469(v206) p262(v4) between f74662 and f22859 - r166285 tested simplicialtop vertices: p63(v514) p862(v344) p330(v65) between f49977 and f74662 - r166229 tested simplicialbot vertices: p4(v717) p246(v546) p810(v222) between f74662 and f68976 - r167871 tested simplicialtop vertices: p315(v685) p56(v235) p780(v211) between f66564 and f74662 - r166282 tested simplicialbot vertices: p63(v514) p862(v344) p673(v116) between f74662 and f49970 - r166716 tested simplicialtop vertices: p63(v514) p780(v211) p673(v116) between f49969 and f74662 - r168861 tested simplicialtop vertices: p865(v688) p315(v685) p63(v514) between f66587 and f74662 - r166712 tested simplicialbot vertices: p315(v685) p63(v514) p780(v211) between f74662 and f66561 - r168841 tested simplicialtop vertices: p865(v688) p63(v514) p106(v117) between f66581 and f74662 - r166260 tested simplicialtop vertices: p967(v686) p862(v344) p517(v209) between f66567 and f74662 - r165953 tested simplicialtop vertices: p441(v346) p862(v344) p673(v116) between f22482 and f74662 - r167837 tested vertices: p491(v725) p106(v117) p330(v65) between f73406 and f74662 - r167841 tested vertices: p491(v725) p569(v560) p330(v65) between f74662 and f73406 - r165754 tested vertices: p491(v725) p569(v560) p586(v12) between f73406 and f74662 - r168342 tested vertices: p491(v725) p268(v720) p844(v555) between f74662 and f73406 - r166706 tested vertices: p491(v725) p844(v555) p586(v12) between f74662 and f73406 - r166504 tested vertices: p491(v725) p268(v720) p15(v557) between f73406 and f74662 - r168746 tested simplicialtop vertices: p967(v686) p403(v515) p330(v65) between f66573 and f74662 - r166256 tested simplicialbot vertices: p967(v686) p862(v344) p330(v65) between f74662 and f66572 - r165957 tested simplicialbot vertices: p441(v346) p862(v344) p517(v209) between f74662 and f22483 - r168989 tested simplicialbot vertices: p967(v686) p17(v684) p517(v209) between f74662 and f66569 - r168844 tested simplicialbot vertices: p63(v514) p106(v117) p330(v65) between f74662 and f49976 - r169176 tested simplicialtop vertices: p441(v346) p735(v207) p787(v37) between f22473 and f74662 - r168752 tested simplicialbot vertices: p96(v683) p200(v343) p517(v209) between f74662 and f66534 - r169087 tested simplicialtop vertices: p441(v346) p200(v343) p517(v209) between f22480 and f74662 - r168756 tested simplicialtop vertices: p96(v683) p200(v343) p787(v37) between f66529 and f74662 - r169128 tested simplicialbot vertices: p441(v346) p200(v343) p787(v37) between f74662 and f22478 - r168749 tested simplicialtop vertices: p967(v686) p17(v684) p403(v515) between f66570 and f74662 - r166917 tested simplicialbot vertices: p877(v522) p810(v222) p452(v123) between f74662 and f50172 - r165689 tested simplicialbot vertices: p246(v546) p574(v372) p452(v123) between f74662 and f55278 - r165693 tested simplicialtop vertices: p246(v546) p810(v222) p452(v123) between f55277 and f74662 - r169210 tested simplicialbot vertices: p569(v560) p403(v515) p330(v65) between f74662 and f58183 - r168796 tested simplicialbot vertices: p27(v519) p403(v515) p550(v118) between f74662 and f50014 - r167868 tested simplicialtop vertices: p802(v312) p30(v310) p848(v100) between f22159 and f74662 - r167864 tested simplicialtop vertices: p505(v674) p802(v312) p848(v100) between f65137 and f74662 - r167093 tested simplicialtop vertices: p856(v649) p30(v310) p585(v184) between f64892 and f74662 - r167982 tested simplicialbot vertices: p722(v641) p699(v457) p433(v54) between f74662 and f63643 - r169122 tested simplicialtop vertices: p655(v642) p941(v459) p527(v182) between f63654 and f74662 - r167978 tested simplicialtop vertices: p722(v641) p941(v459) p433(v54) between f63641 and f74662 - r168679 tested simplicialbot vertices: p655(v642) p941(v459) p886(v98) between f74662 and f63656 - r168480 tested simplicialtop vertices: p941(v459) p886(v98) p433(v54) between f40933 and f74662 - r167196 tested simplicialbot vertices: p655(v642) p746(v308) p527(v182) between f74662 and f63653 - r168868 tested simplicialbot vertices: p722(v641) p941(v459) p144(v303) between f74662 and f63646 - r168024 tested simplicialtop vertices: p722(v641) p699(v457) p758(v301) between f63644 and f74662 - r167136 tested simplicialbot vertices: p722(v641) p286(v639) p758(v301) between f74662 and f63647 - r166445 tested simplicialtop vertices: p911(v604) p596(v428) p228(v277) between f74888 and f74662 - r168300 tested simplicialtop vertices: p331(v712) p305(v543) p91(v278) between f66810 and f74662 - r166849 tested simplicialbot vertices: p305(v543) p283(v541) p644(v228) between f74662 and f55246 - r165793 tested simplicialbot vertices: p317(v713) p641(v544) p845(v369) between f74662 and f66816 - r166449 tested simplicialbot vertices: p911(v604) p305(v543) p228(v277) between f74662 and f60876 - r168884 tested simplicialbot vertices: p317(v713) p305(v543) p644(v228) between f74662 and f66813 - r170113 tested simplicialtop vertices: p562(v449) p327(v170) p781(v92) between f40811 and f74662 - r166463 tested simplicialbot vertices: p158(v700) p446(v359) p313(v68) between f74662 and f66696 - r168593 tested simplicialtop vertices: p331(v712) p506(v542) p845(v369) between f66806 and f74662 - r169133 tested simplicialbot vertices: p317(v713) p331(v712) p305(v543) between f74662 and f66818 - r169155 tested simplicialtop vertices: p317(v713) p331(v712) p845(v369) between f66817 and f74662 - r165797 tested simplicialtop vertices: p317(v713) p641(v544) p644(v228) between f66815 and f74662 - r167014 tested simplicialbot vertices: p230(v714) p305(v543) p91(v278) between f74662 and f74921 - r168003 tested simplicialtop vertices: p789(v214) p475(v119) p107(v66) between f8955 and f74662 - r168297 tested simplicialbot vertices: p331(v712) p255(v431) p91(v278) between f74662 and f66808 - r168348 tested simplicialtop vertices: p775(v621) p659(v620) p235(v167) between f62202 and f74662 - r167011 tested simplicialtop vertices: p230(v714) p305(v543) p228(v277) between f66822 and f74662 - r168597 tested simplicialbot vertices: p641(v544) p506(v542) p845(v369) between f74662 and f55260 - r167958 tested simplicialtop vertices: p807(v357) p269(v219) p233(v39) between f22778 and f74662 - r167955 tested simplicialbot vertices: p961(v358) p269(v219) p233(v39) between f74662 and f22827 - r166386 tested simplicialbot vertices: p540(v702) p890(v530) p807(v357) between f74662 and f66712 - r169170 tested simplicialtop vertices: p860(v356) p450(v355) p534(v218) between f22772 and f74662 - r165858 tested simplicialtop vertices: p491(v725) p718(v559) p716(v236) between f72495 and f74662 - r168545 tested simplicialbot vertices: p374(v524) p961(v358) p233(v39) between f74662 and f51060 - r165845 tested simplicialbot vertices: p691(v716) p705(v545) p648(v120) between f74662 and f68225 - r165841 tested simplicialtop vertices: p784(v715) p705(v545) p648(v120) between f68218 and f74662 - r168702 tested simplicialtop vertices: p840(v710) p158(v700) p892(v528) between f66795 and f74662 - r167283 tested simplicialbot vertices: p158(v700) p892(v528) p446(v359) between f74662 and f66697 - r168054 tested simplicialtop vertices: p276(v697) p483(v526) p994(v217) between f66664 and f74662 - r168920 tested simplicialbot vertices: p784(v715) p376(v531) p648(v120) between f74662 and f68217 - r166098 tested simplicialtop vertices: p691(v716) p892(v528) p446(v359) between f68972 and f74662 - r166095 tested simplicialtop vertices: p691(v716) p705(v545) p892(v528) between f68973 and f74662 - r167655 tested simplicialtop vertices: p985(v537) p892(v528) p191(v121) between f54327 and f74662 - r166459 tested simplicialtop vertices: p158(v700) p520(v529) p313(v68) between f66693 and f74662 - r168970 tested simplicialbot vertices: p840(v710) p158(v700) p450(v355) between f74662 and f66794 - r167454 tested simplicialbot vertices: p985(v537) p939(v364) p191(v121) between f74662 and f54326 - r168860 tested simplicialtop vertices: p691(v716) p641(v544) p648(v120) between f68224 and f74662 - r168893 tested simplicialbot vertices: p784(v715) p705(v545) p269(v219) between f74662 and f68220 - r167036 tested simplicialbot vertices: p892(v528) p807(v357) p269(v219) between f74662 and f51095 - r167033 tested simplicialbot vertices: p705(v545) p892(v528) p269(v219) between f74662 and f55272 - r167451 tested simplicialtop vertices: p540(v702) p939(v364) p191(v121) between f66709 and f74662 - r167657 tested simplicialtop vertices: p892(v528) p807(v357) p191(v121) between f51094 and f74662 - r166651 tested simplicialbot vertices: p483(v526) p983(v216) p648(v120) between f74662 and f51080 - r167145 tested simplicialtop vertices: p641(v544) p506(v542) p163(v22) between f55259 and f74662 - r166647 tested simplicialtop vertices: p983(v216) p648(v120) p163(v22) between f9175 and f74662 - r166088 tested simplicialbot vertices: p276(v697) p376(v531) p961(v358) between f74662 and f66662 - r167017 tested simplicialbot vertices: p376(v531) p483(v526) p648(v120) between f74662 and f52149 - r169021 tested simplicialtop vertices: p985(v537) p939(v364) p534(v218) between f54322 and f74662 - r167950 tested simplicialtop vertices: p506(v542) p983(v216) p163(v22) between f55235 and f74662 - r168919 tested simplicialtop vertices: p276(v697) p376(v531) p483(v526) between f66665 and f74662 - r168052 tested simplicialbot vertices: p276(v697) p374(v524) p994(v217) between f74662 and f66659 - r167149 tested simplicialbot vertices: p641(v544) p648(v120) p163(v22) between f74662 and f55255 - r166179 tested simplicialtop vertices: p540(v702) p700(v224) p534(v218) between f66714 and f74662 - r167770 tested simplicialtop vertices: p784(v715) p961(v358) p269(v219) between f68222 and f74662 - r167767 tested simplicialtop vertices: p784(v715) p376(v531) p961(v358) between f68223 and f74662 - r166092 tested simplicialtop vertices: p276(v697) p374(v524) p961(v358) between f66660 and f74662 - r167585 tested simplicialbot vertices: p840(v710) p985(v537) p892(v528) between f74662 and f66792 - r166860 tested simplicialbot vertices: p840(v710) p450(v355) p534(v218) between f74662 and f66789 - r166864 tested simplicialtop vertices: p840(v710) p985(v537) p534(v218) between f66790 and f74662 - r169103 tested simplicialbot vertices: p540(v702) p807(v357) p191(v121) between f74662 and f66711 - r168972 tested simplicialbot vertices: p158(v700) p520(v529) p450(v355) between f74662 and f66694 - r166847 tested simplicialtop vertices: p447(v701) p520(v529) p860(v356) between f66700 and f74662 - r166175 tested simplicialbot vertices: p540(v702) p939(v364) p534(v218) between f74662 and f66715 - r167952 tested simplicialtop vertices: p490(v527) p374(v524) p994(v217) between f51085 and f74662 - r168549 tested simplicialbot vertices: p483(v526) p914(v354) p983(v216) between f74662 and f51078 - r167082 tested simplicialtop vertices: p483(v526) p485(v353) p994(v217) between f51074 and f74662 - r169109 tested simplicialtop vertices: p331(v712) p255(v431) p914(v354) between f66803 and f74662 - r166972 tested simplicialbot vertices: p485(v353) p475(v119) p107(v66) between f74662 and f22612 - r166122 tested simplicialbot vertices: p490(v527) p485(v353) p994(v217) between f74662 and f51083 - r167079 tested simplicialbot vertices: p483(v526) p485(v353) p107(v66) between f74662 and f51073 - r166126 tested simplicialtop vertices: p490(v527) p485(v353) p475(v119) between f51088 and f74662 - r168000 tested simplicialtop vertices: p255(v431) p789(v214) p107(v66) between f36663 and f74662 - r168317 tested simplicialtop vertices: p483(v526) p914(v354) p107(v66) between f51076 and f74662 - r169107 tested simplicialbot vertices: p255(v431) p914(v354) p107(v66) between f74662 and f36664 - r169015 tested simplicialbot vertices: p331(v712) p506(v542) p914(v354) between f74662 and f66804 - r169013 tested simplicialtop vertices: p506(v542) p914(v354) p983(v216) between f55238 and f74662 - r168895 tested simplicialbot vertices: p520(v529) p860(v356) p450(v355) between f74662 and f51107 - r166844 tested simplicialbot vertices: p447(v701) p520(v529) p313(v68) between f74662 and f66704 - r166389 tested simplicialtop vertices: p890(v530) p807(v357) p233(v39) between f52142 and f74662 - r168192 tested simplicialbot vertices: p899(v658) p30(v310) p848(v100) between f74662 and f64971 - r168782 tested simplicialtop vertices: p966(v159) p159(v86) p241(v20) between f5969 and f74662 - r167406 tested simplicialtop vertices: p906(v393) p324(v246) p750(v135) between f28906 and f74662 - r166044 tested simplicialbot vertices: p776(v498) p723(v183) p848(v100) between f74662 and f45511 - r166041 tested simplicialtop vertices: p899(v658) p723(v183) p848(v100) between f64970 and f74662 - r168188 tested simplicialbot vertices: p916(v656) p740(v483) p402(v188) between f74662 and f64950 - r165936 tested simplicialbot vertices: p899(v658) p723(v183) p55(v31) between f74662 and f64978 - r165932 tested simplicialtop vertices: p141(v497) p723(v183) p55(v31) between f45507 and f74662 - r168948 tested simplicialbot vertices: p776(v498) p141(v497) p723(v183) between f74662 and f45514 - r169007 tested simplicialbot vertices: p35(v394) p981(v247) p427(v142) between f74662 and f28922 - r166235 tested simplicialtop vertices: p899(v658) p740(v483) p402(v188) between f64973 and f74662 - r166398 tested simplicialbot vertices: p801(v136) p750(v135) p277(v75) between f74662 and f3503 - r166231 tested simplicialtop vertices: p899(v658) p777(v657) p740(v483) between f64976 and f74662 - r167967 tested simplicialtop vertices: p899(v658) p402(v188) p55(v31) between f64979 and f74662 - r168968 tested simplicialtop vertices: p108(v673) p724(v107) p149(v58) between f65119 and f74662 - r167948 tested simplicialbot vertices: p336(v653) p141(v497) p597(v328) between f74662 and f64931 - r167944 tested simplicialtop vertices: p776(v498) p141(v497) p597(v328) between f45515 and f74662 - r168374 tested simplicialbot vertices: p336(v653) p597(v328) p724(v107) between f74662 and f64925 - r168370 tested simplicialtop vertices: p707(v496) p597(v328) p724(v107) between f45495 and f74662 - r169034 tested simplicialbot vertices: p108(v673) p812(v648) p149(v58) between f74662 and f65122 - r168878 tested simplicialbot vertices: p108(v673) p81(v672) p175(v466) between f74662 and f65133 - r168537 tested simplicialtop vertices: p108(v673) p707(v496) p724(v107) between f65120 and f74662 - r167248 tested simplicialtop vertices: p108(v673) p653(v468) p509(v306) between f65130 and f74662 - r168681 tested simplicialtop vertices: p108(v673) p81(v672) p707(v496) between f65125 and f74662 - r168684 tested simplicialbot vertices: p81(v672) p707(v496) p597(v328) between f74662 and f65117 - r169198 tested simplicialbot vertices: p777(v657) p740(v483) p157(v316) between f74662 and f64967 - r169203 tested simplicialtop vertices: p916(v656) p740(v483) p157(v316) between f64951 and f74662 - r169201 tested simplicialtop vertices: p777(v657) p806(v481) p157(v316) between f64966 and f74662 - r169209 tested simplicialbot vertices: p916(v656) p806(v481) p157(v316) between f74662 and f64956 - r169045 tested simplicialbot vertices: p860(v356) p810(v222) p301(v122) between f74662 and f22777 - r168951 tested simplicialtop vertices: p877(v522) p502(v360) p538(v220) between f50169 and f74662 - r167512 tested simplicialbot vertices: p137(v708) p950(v363) p301(v122) between f74662 and f66767 - r168418 tested simplicialtop vertices: p730(v547) p446(v359) p313(v68) between f55285 and f74662 - r167440 tested simplicialtop vertices: p502(v360) p810(v222) p301(v122) between f22856 and f74662 - r167437 tested simplicialtop vertices: p549(v536) p502(v360) p301(v122) between f53470 and f74662 - r168141 tested simplicialtop vertices: p906(v393) p750(v135) p277(v75) between f28910 and f74662 - r166418 tested simplicialbot vertices: p502(v360) p538(v220) p635(v41) between f74662 and f22854 - r168178 tested simplicialbot vertices: p725(v387) p635(v41) p121(v23) between f74662 and f27250 - r167713 tested simplicialbot vertices: p877(v522) p502(v360) p810(v222) between f74662 and f50170 - r165985 tested simplicialbot vertices: p496(v535) p950(v363) p53(v125) between f74662 and f53458 - r166878 tested simplicialbot vertices: p194(v709) p137(v708) p549(v536) between f74662 and f66779 - r166466 tested simplicialbot vertices: p512(v706) p759(v362) p53(v125) between f74662 and f66749 - r167260 tested simplicialtop vertices: p759(v362) p932(v223) p24(v69) between f22872 and f74662 - r165981 tested simplicialtop vertices: p496(v535) p950(v363) p860(v356) between f53462 and f74662 - r168914 tested simplicialtop vertices: p137(v708) p549(v536) p301(v122) between f66768 and f74662 - r167100 tested simplicialbot vertices: p455(v538) p545(v126) p24(v69) between f74662 and f54329 - r165745 tested simplicialbot vertices: p680(v563) p335(v385) p204(v242) between f74662 and f58213 - r166761 tested simplicialtop vertices: p194(v709) p137(v708) p950(v363) between f66782 and f74662 - r167515 tested simplicialbot vertices: p950(v363) p860(v356) p301(v122) between f74662 and f22909 - r166146 tested simplicialbot vertices: p687(v693) p877(v522) p820(v213) between f74662 and f66625 - r167111 tested simplicialtop vertices: p35(v394) p891(v141) p748(v77) between f28915 and f74662 - r168257 tested simplicialtop vertices: p229(v692) p17(v684) p820(v213) between f66617 and f74662 - r166867 tested simplicialbot vertices: p687(v693) p968(v520) p538(v220) between f74662 and f66623 - r166142 tested simplicialtop vertices: p687(v693) p877(v522) p538(v220) between f66626 and f74662 - r169085 tested vertices: p173(v565) p725(v387) p121(v23) between f74662 and f73963 - r169166 tested vertices: p173(v565) p725(v387) p706(v243) between f73963 and f74662 - r168110 tested simplicialtop vertices: p173(v565) p968(v520) p121(v23) between f73963 and f74662 - r169239 tested simplicialbot vertices: p514(v730) p173(v565) p968(v520) between f74662 and f73963 - r167419 tested vertices: p173(v565) p419(v388) p706(v243) between f74662 and f73963 - r167422 tested vertices: p173(v565) p419(v388) p650(v140) between f73963 and f74662 - r169952 tested simplicialbot vertices: p389(v443) p864(v290) p327(v170) between f74662 and f39916 - r168148 tested simplicialtop vertices: p687(v693) p968(v520) p201(v349) between f66628 and f74662 - r166870 tested simplicialtop vertices: p968(v520) p538(v220) p121(v23) between f50142 and f74662 - r167473 tested simplicialbot vertices: p170(v707) p496(v535) p932(v223) between f74662 and f66758 - r167471 tested simplicialtop vertices: p496(v535) p932(v223) p53(v125) between f53457 and f74662 - r166834 tested simplicialbot vertices: p687(v693) p229(v692) p201(v349) between f74662 and f66629 - r165749 tested simplicialtop vertices: p335(v385) p204(v242) p85(v225) between f25747 and f74662 - r166831 tested simplicialtop vertices: p687(v693) p229(v692) p820(v213) between f66627 and f74662 - r168452 tested simplicialtop vertices: p385(v691) p173(v565) p550(v118) between f66610 and f74662 - r168817 tested simplicialtop vertices: p335(v385) p299(v365) p481(v47) between f26160 and f74662 - r166881 tested simplicialbot vertices: p194(v709) p549(v536) p635(v41) between f74662 and f66776 - r168760 tested simplicialbot vertices: p725(v387) p706(v243) p635(v41) between f74662 and f27251 - r168182 tested simplicialtop vertices: p538(v220) p635(v41) p121(v23) between f9627 and f74662 - r166422 tested simplicialbot vertices: p549(v536) p502(v360) p635(v41) between f74662 and f53469 - r166984 tested simplicialbot vertices: p229(v692) p17(v684) p27(v519) between f74662 and f66618 - r167409 tested simplicialbot vertices: p906(v393) p324(v246) p212(v44) between f74662 and f28904 - r168079 tested simplicialbot vertices: p229(v692) p385(v691) p201(v349) between f74662 and f66620 - r166324 tested simplicialtop vertices: p229(v692) p385(v691) p27(v519) between f66621 and f74662 - r168449 tested simplicialbot vertices: p385(v691) p173(v565) p201(v349) between f74662 and f66611 - r166320 tested simplicialbot vertices: p385(v691) p27(v519) p550(v118) between f74662 and f66607 - r170839 tested simplicialbot vertices: p392(v773) p416(v614) p343(v441) between f74662 and f74958 - r168763 tested simplicialtop vertices: p194(v709) p706(v243) p635(v41) between f66775 and f74662 - r170687 tested simplicialtop vertices: p977(v756) p245(v426) p900(v186) between f74753 and f74662 - r166238 tested simplicialbot vertices: p95(v603) p245(v426) p900(v186) between f74662 and f60868 - r169060 tested simplicialbot vertices: p593(v601) p616(v424) p824(v423) between f74662 and f60852 - r166915 tested simplicialbot vertices: p617(v592) p738(v420) p900(v186) between f74662 and f60771 - r168649 tested simplicialtop vertices: p46(v591) p738(v420) p647(v272) between f74738 and f74662 - r167443 tested simplicialbot vertices: p95(v603) p900(v186) p996(v102) between f74662 and f60867 - r168673 tested vertices: p593(v601) p683(v598) p824(v423) between f74866 and f74662 - r170683 tested simplicialbot vertices: p977(v756) p683(v598) p824(v423) between f74662 and f74866 - r168290 tested simplicialtop vertices: p738(v420) p900(v186) p874(v48) between f33296 and f74662 - r168287 tested simplicialbot vertices: p738(v420) p647(v272) p874(v48) between f74662 and f74741 - r166682 tested simplicialbot vertices: p35(v394) p151(v143) p748(v77) between f74662 and f28919 - r168934 tested simplicialtop vertices: p647(v272) p354(v271) p363(v83) between f17554 and f74662 - r170661 tested simplicialtop vertices: p356(v752) p448(v590) p133(v71) between f74718 and f74662 - r169533 tested simplicialtop vertices: p87(v738) p830(v391) p636(v156) between f74156 and f74662 - r169345 tested simplicialbot vertices: p986(v593) p830(v391) p636(v156) between f74662 and f60781 - r169054 tested simplicialtop vertices: p512(v706) p204(v242) p53(v125) between f66754 and f74662 - r169520 tested simplicialtop vertices: p804(v737) p830(v391) p744(v45) between f74145 and f74662 - r168932 tested simplicialtop vertices: p46(v591) p647(v272) p363(v83) between f60768 and f74662 - r169529 tested simplicialbot vertices: p87(v738) p354(v271) p363(v83) between f74662 and f74160 - r169521 tested simplicialbot vertices: p804(v737) p146(v569) p744(v45) between f74662 and f74146 - r169023 tested vertices: p146(v569) p145(v398) p236(v248) between f74132 and f74662 - r168602 tested simplicialtop vertices: p292(v571) p145(v398) p744(v45) between f74132 and f74662 - r167898 tested vertices: p145(v398) p236(v248) p151(v143) between f74662 and f74132 - r168040 tested vertices: p146(v569) p145(v398) p744(v45) between f74662 and f74132 - r169539 tested vertices: p948(v739) p292(v571) p145(v398) between f74662 and f74132 - r168498 tested simplicialtop vertices: p626(v265) p368(v155) p874(v48) between f14888 and f74662 - r169163 tested simplicialtop vertices: p681(v418) p354(v271) p368(v155) between f32470 and f74662 - r170667 tested simplicialbot vertices: p729(v753) p448(v590) p826(v419) between f74662 and f74725 - r167719 tested simplicialbot vertices: p647(v272) p368(v155) p874(v48) between f74662 and f74743 - r168416 tested simplicialtop vertices: p447(v701) p730(v547) p313(v68) between f66705 and f74662 - r168651 tested simplicialtop vertices: p630(v534) p299(v365) p85(v225) between f52401 and f74662 - r167715 tested simplicialbot vertices: p647(v272) p354(v271) p368(v155) between f74662 and f17555 - r169536 tested simplicialtop vertices: p87(v738) p292(v571) p744(v45) between f74154 and f74662 - r169139 tested simplicialbot vertices: p197(v718) p998(v373) p926(v129) between f74662 and f69532 - r167374 tested simplicialbot vertices: p850(v698) p213(v407) p565(v46) between f74662 and f66676 - r168640 tested vertices: p43(v609) p130(v279) p704(v89) between f74662 and f74926 - r168343 tested vertices: p43(v609) p997(v433) p704(v89) between f74926 and f74662 - r166280 tested vertices: p621(v610) p997(v433) p704(v89) between f74662 and f74926 - r166331 tested simplicialtop vertices: p379(v437) p130(v279) p704(v89) between f74926 and f74662 - r166327 tested vertices: p379(v437) p130(v279) p187(v161) between f74662 and f74926 - r168266 tested simplicialtop vertices: p850(v698) p67(v525) p565(v46) between f66667 and f74662 - r168302 tested simplicialtop vertices: p195(v579) p213(v407) p837(v264) between f58454 and f74662 - r165894 tested simplicialbot vertices: p628(v405) p797(v145) p565(v46) between f74662 and f29367 - r167371 tested simplicialtop vertices: p850(v698) p213(v407) p760(v258) between f66677 and f74662 - r166728 tested simplicialtop vertices: p850(v698) p760(v258) p825(v149) between f66671 and f74662 - r166724 tested simplicialbot vertices: p960(v260) p760(v258) p825(v149) between f74662 and f13926 - r168935 tested simplicialbot vertices: p282(v408) p960(v260) p825(v149) between f74662 and f29397 - r170305 tested simplicialtop vertices: p285(v745) p34(v742) p545(v126) between f74528 and f74662 - r167796 tested simplicialbot vertices: p195(v579) p213(v407) p858(v81) between f74662 and f58453 - r167794 tested simplicialbot vertices: p213(v407) p760(v258) p858(v81) between f74662 and f29392 - r167333 tested simplicialtop vertices: p195(v579) p960(v260) p858(v81) between f58457 and f74662 - r167330 tested simplicialtop vertices: p960(v260) p760(v258) p858(v81) between f13925 and f74662 - r168305 tested simplicialtop vertices: p88(v600) p195(v579) p837(v264) between f60849 and f74662 - r167069 tested simplicialtop vertices: p529(v204) p475(v119) p698(v38) between f8118 and f74662 - r168939 tested simplicialtop vertices: p837(v264) p751(v262) p774(v150) between f14878 and f74662 - r167143 tested simplicialtop vertices: p492(v352) p421(v259) p14(v67) between f22611 and f74662 - r170294 tested simplicialbot vertices: p260(v743) p742(v578) p579(v406) between f74662 and f74208 - r168654 tested simplicialbot vertices: p335(v385) p299(v365) p85(v225) between f74662 and f26161 - r166571 tested simplicialbot vertices: p850(v698) p67(v525) p492(v352) between f74662 and f66668 - r166575 tested simplicialbot vertices: p850(v698) p492(v352) p421(v259) between f74662 and f66674 - r170785 tested simplicialtop vertices: p638(v767) p88(v600) p837(v264) between f74887 and f74662 - r168095 tested simplicialtop vertices: p573(v589) p614(v417) p996(v102) between f59636 and f74662 - r168980 tested simplicialtop vertices: p135(v602) p616(v424) p824(v423) between f60858 and f74662 - r168766 tested simplicialbot vertices: p649(v409) p674(v261) p225(v148) between f74662 and f30198 - r167619 tested simplicialbot vertices: p837(v264) p674(v261) p774(v150) between f74662 and f14882 - r168764 tested simplicialtop vertices: p674(v261) p225(v148) p866(v15) between f13933 and f74662 - r170760 tested simplicialtop vertices: p646(v764) p92(v425) p828(v144) between f74856 and f74662 - r167468 tested simplicialtop vertices: p649(v409) p674(v261) p774(v150) between f30199 and f74662 - r167464 tested simplicialbot vertices: p649(v409) p751(v262) p774(v150) between f74662 and f30197 - r170781 tested simplicialtop vertices: p638(v767) p135(v602) p88(v600) between f74879 and f74662 - r170765 tested simplicialtop vertices: p646(v764) p88(v600) p854(v274) between f74873 and f74662 - r170759 tested simplicialbot vertices: p646(v764) p74(v253) p828(v144) between f74662 and f74857 - r165834 tested simplicialbot vertices: p135(v602) p88(v600) p854(v274) between f74662 and f74870 - r166929 tested simplicialtop vertices: p685(v597) p824(v423) p372(v273) between f74814 and f74662 - r168104 tested simplicialbot vertices: p593(v601) p683(v598) p603(v157) between f74662 and f60853 - r170756 tested simplicialbot vertices: p896(v762) p685(v597) p824(v423) between f74662 and f74832 - r170751 tested simplicialtop vertices: p896(v762) p685(v597) p684(v78) between f74829 and f74662 - r170680 tested simplicialbot vertices: p977(v756) p824(v423) p372(v273) between f74662 and f74867 - r166752 tested simplicialbot vertices: p837(v264) p751(v262) p651(v80) between f74662 and f14877 - r166750 tested simplicialtop vertices: p563(v582) p751(v262) p651(v80) between f58485 and f74662 - r168772 tested simplicialbot vertices: p104(v399) p324(v246) p801(v136) between f74662 and f28971 - r168209 tested simplicialbot vertices: p88(v600) p195(v579) p74(v253) between f74662 and f60844 - r168730 tested simplicialbot vertices: p455(v538) p299(v365) p481(v47) between f74662 and f54332 - r170663 tested simplicialtop vertices: p729(v753) p87(v738) p354(v271) between f74730 and f74662 - r169165 tested simplicialbot vertices: p826(v419) p681(v418) p354(v271) between f74662 and f32488 - r170764 tested simplicialbot vertices: p646(v764) p92(v425) p854(v274) between f74662 and f74875 - r170664 tested simplicialbot vertices: p729(v753) p87(v738) p292(v571) between f74662 and f74731 - r169094 tested simplicialtop vertices: p649(v409) p751(v262) p225(v148) between f30196 and f74662 - r168609 tested simplicialbot vertices: p197(v718) p37(v552) p465(v249) between f74662 and f69570 - r170656 tested simplicialbot vertices: p356(v752) p701(v719) p371(v231) between f74662 and f74722 - r167446 tested simplicialtop vertices: p900(v186) p996(v102) p874(v48) between f7560 and f74662 - r168366 tested simplicialbot vertices: p490(v527) p291(v215) p475(v119) between f74662 and f51087 - r169005 tested simplicialbot vertices: p981(v247) p324(v246) p427(v142) between f74662 and f12899 - r168454 tested simplicialtop vertices: p35(v394) p981(v247) p891(v141) between f28916 and f74662 - r168120 tested simplicialbot vertices: p490(v527) p374(v524) p833(v351) between f74662 and f51091 - r168123 tested simplicialbot vertices: p490(v527) p833(v351) p291(v215) between f74662 and f51090 - r168220 tested simplicialbot vertices: p374(v524) p474(v523) p833(v351) between f74662 and f51063 - r168264 tested simplicialtop vertices: p366(v695) p474(v523) p833(v351) between f66644 and f74662 - r168223 tested simplicialtop vertices: p374(v524) p474(v523) p233(v39) between f51062 and f74662 - r168918 tested simplicialtop vertices: p170(v707) p496(v535) p860(v356) between f66765 and f74662 - r169008 tested simplicialbot vertices: p140(v540) p932(v223) p24(v69) between f74662 and f54345 - r168866 tested simplicialtop vertices: p366(v695) p833(v351) p291(v215) between f66651 and f74662 - r167632 tested simplicialbot vertices: p474(v523) p143(v227) p785(v127) between f74662 and f50176 - r170065 tested simplicialbot vertices: p678(v575) p695(v403) p792(v257) between f74662 and f58415 - r167628 tested simplicialbot vertices: p366(v695) p474(v523) p785(v127) between f74662 and f66643 - r166248 tested simplicialtop vertices: p143(v227) p932(v223) p36(v124) between f10984 and f74662 - r168200 tested simplicialtop vertices: p251(v549) p716(v236) p518(v43) between f55300 and f74662 - r166244 tested simplicialtop vertices: p853(v696) p143(v227) p36(v124) between f66653 and f74662 - r165703 tested simplicialtop vertices: p700(v224) p36(v124) p223(v13) between f10510 and f74662 - r167703 tested simplicialtop vertices: p853(v696) p36(v124) p233(v39) between f66656 and f74662 - r168198 tested simplicialtop vertices: p853(v696) p474(v523) p143(v227) between f66654 and f74662 - r167986 tested simplicialtop vertices: p170(v707) p860(v356) p534(v218) between f66764 and f74662 - r166982 tested simplicialbot vertices: p170(v707) p932(v223) p223(v13) between f74662 and f66757 - r166132 tested simplicialbot vertices: p170(v707) p700(v224) p534(v218) between f74662 and f66762 - r167257 tested simplicialtop vertices: p512(v706) p759(v362) p24(v69) between f66751 and f74662 - r166129 tested simplicialtop vertices: p170(v707) p700(v224) p223(v13) between f66760 and f74662 - r165707 tested simplicialbot vertices: p932(v223) p36(v124) p223(v13) between f74662 and f10074 - r169003 tested simplicialtop vertices: p512(v706) p630(v534) p85(v225) between f66747 and f74662 - r166308 tested simplicialtop vertices: p140(v540) p143(v227) p785(v127) between f54348 and f74662 - r168857 tested simplicialbot vertices: p140(v540) p143(v227) p932(v223) between f74662 and f54346 - r166312 tested simplicialbot vertices: p140(v540) p346(v367) p785(v127) between f74662 and f54349 - r167490 tested simplicialtop vertices: p940(v539) p346(v367) p224(v366) between f54341 and f74662 - r169026 tested simplicialbot vertices: p853(v696) p474(v523) p233(v39) between f74662 and f66657 - r166167 tested simplicialbot vertices: p890(v530) p700(v224) p36(v124) between f74662 and f52144 - r167701 tested simplicialbot vertices: p890(v530) p36(v124) p233(v39) between f74662 and f52141 - r166163 tested simplicialtop vertices: p540(v702) p890(v530) p700(v224) between f66707 and f74662 - r167062 tested simplicialtop vertices: p346(v367) p545(v126) p24(v69) between f22953 and f74662 - r170784 tested simplicialtop vertices: p638(v767) p837(v264) p674(v261) between f74886 and f74662 - r167059 tested simplicialtop vertices: p140(v540) p346(v367) p24(v69) between f54343 and f74662 - r168167 tested simplicialbot vertices: p346(v367) p224(v366) p785(v127) between f74662 and f22960 - r168928 tested simplicialtop vertices: p940(v539) p224(v366) p531(v226) between f54340 and f74662 - r167494 tested simplicialbot vertices: p940(v539) p346(v367) p545(v126) between f74662 and f54338 - r169069 tested simplicialtop vertices: p366(v695) p224(v366) p785(v127) between f66648 and f74662 - r166696 tested simplicialtop vertices: p165(v699) p291(v215) p475(v119) between f66686 and f74662 - r168912 tested simplicialtop vertices: p165(v699) p67(v525) p492(v352) between f66689 and f74662 - r166692 tested simplicialtop vertices: p165(v699) p475(v119) p384(v2) between f66685 and f74662 - r169001 tested simplicialbot vertices: p529(v204) p475(v119) p384(v2) between f74662 and f8117 - r166051 tested simplicialbot vertices: p492(v352) p291(v215) p14(v67) between f74662 and f22610 - r166047 tested simplicialtop vertices: p366(v695) p291(v215) p14(v67) between f66650 and f74662 - r167342 tested simplicialtop vertices: p165(v699) p492(v352) p291(v215) between f66688 and f74662 - r167973 tested simplicialbot vertices: p366(v695) p224(v366) p14(v67) between f74662 and f66647 - r168664 tested simplicialtop vertices: p422(v510) p119(v112) p698(v38) between f48625 and f74662 - r168930 tested simplicialbot vertices: p224(v366) p531(v226) p14(v67) between f74662 and f22927 - r168172 tested simplicialbot vertices: p630(v534) p299(v365) p24(v69) between f74662 and f52400 - r167308 tested simplicialbot vertices: p512(v706) p630(v534) p24(v69) between f74662 and f66752 - r167922 tested simplicialtop vertices: p284(v570) p413(v397) p465(v249) between f74175 and f74662 - r168769 tested simplicialtop vertices: p104(v399) p324(v246) p427(v142) between f28968 and f74662 - r168271 tested simplicialbot vertices: p197(v718) p284(v570) p998(v373) between f74662 and f69536 - r167920 tested simplicialbot vertices: p284(v570) p413(v397) p322(v25) between f74662 and f58362 - r169095 tested simplicialbot vertices: p104(v399) p801(v136) p322(v25) between f74662 and f28970 - r168026 tested simplicialbot vertices: p328(v548) p998(v373) p667(v230) between f74662 and f55295 - r166071 tested simplicialtop vertices: p338(v572) p145(v398) p465(v249) between f58387 and f74662 - r166067 tested simplicialbot vertices: p338(v572) p413(v397) p465(v249) between f74662 and f74172 - r168274 tested simplicialtop vertices: p197(v718) p284(v570) p465(v249) between f69535 and f74662 - r166808 tested simplicialbot vertices: p413(v397) p182(v250) p322(v25) between f74662 and f28945 - r168349 tested simplicialbot vertices: p104(v399) p182(v250) p427(v142) between f74662 and f28966 - r166804 tested simplicialtop vertices: p413(v397) p182(v250) p151(v143) between f28946 and f74662 - r168827 tested simplicialtop vertices: p35(v394) p182(v250) p427(v142) between f28923 and f74662 - r168353 tested simplicialtop vertices: p104(v399) p182(v250) p322(v25) between f28965 and f74662 - r168994 tested simplicialtop vertices: p338(v572) p413(v397) p151(v143) between f58383 and f74662 - r168830 tested simplicialbot vertices: p35(v394) p182(v250) p151(v143) between f74662 and f28920 - r167740 tested simplicialbot vertices: p165(v699) p611(v79) p384(v2) between f74662 and f66681 - r165890 tested simplicialtop vertices: p176(v577) p628(v405) p797(v145) between f58434 and f74662 - r167737 tested simplicialbot vertices: p165(v699) p797(v145) p611(v79) between f74662 and f66682 - r169922 tested simplicialtop vertices: p389(v443) p864(v290) p886(v98) between f39143 and f74662 - r167851 tested simplicialbot vertices: p165(v699) p67(v525) p797(v145) between f74662 and f66679 - r169010 tested simplicialbot vertices: p379(v437) p714(v284) p704(v89) between f74662 and f38387 - r168904 tested simplicialtop vertices: p67(v525) p797(v145) p565(v46) between f51065 and f74662 - r165714 tested simplicialbot vertices: p447(v701) p730(v547) p810(v222) between f74662 and f66702 - r167726 tested simplicialtop vertices: p4(v717) p730(v547) p810(v222) between f68977 and f74662 - r165710 tested simplicialtop vertices: p447(v701) p860(v356) p810(v222) between f66699 and f74662 - r168029 tested simplicialtop vertices: p284(v570) p998(v373) p667(v230) between f58364 and f74662 - r167728 tested simplicialbot vertices: p4(v717) p730(v547) p446(v359) between f74662 and f69518 - r166540 tested simplicialbot vertices: p161(v564) p525(v386) p955(v139) between f74662 and f58250 - r169409 tested vertices: p139(v733) p901(v554) p731(v244) between f72762 and f74662 - r165833 tested vertices: p139(v733) p525(v386) p955(v139) between f72762 and f74662 - r168630 tested vertices: p139(v733) p525(v386) p650(v140) between f74662 and f72762 - r168541 tested vertices: p139(v733) p731(v244) p650(v140) between f72762 and f74662 - r166920 tested simplicialbot vertices: p512(v706) p204(v242) p85(v225) between f74662 and f66755 - r166470 tested simplicialbot vertices: p759(v362) p932(v223) p53(v125) between f74662 and f22873 - r166536 tested simplicialtop vertices: p161(v564) p204(v242) p955(v139) between f58249 and f74662 - r167557 tested simplicialbot vertices: p161(v564) p204(v242) p53(v125) between f74662 and f73948 - r168864 tested simplicialbot vertices: p680(v563) p204(v242) p955(v139) between f74662 and f58212 - r169356 tested simplicialtop vertices: p567(v594) p205(v396) p77(v245) between f60789 and f74662 - r166795 tested simplicialtop vertices: p194(v709) p161(v564) p419(v388) between f73955 and f74662 - r167417 tested vertices: p161(v564) p419(v388) p525(v386) between f74662 and f73955 - r168629 tested vertices: p419(v388) p525(v386) p650(v140) between f73955 and f74662 - r166791 tested simplicialtop vertices: p194(v709) p419(v388) p706(v243) between f66778 and f74662 - r170304 tested simplicialtop vertices: p34(v742) p97(v573) p545(v126) between f74187 and f74662 - r166765 tested vertices: p194(v709) p950(v363) p53(v125) between f73951 and f74662 - r167560 tested simplicialbot vertices: p194(v709) p161(v564) p53(v125) between f74662 and f73951 - r167096 tested simplicialtop vertices: p97(v573) p455(v538) p545(v126) between f58391 and f74662 - r168598 tested simplicialbot vertices: p416(v614) p379(v437) p187(v161) between f74662 and f62122 - r168540 tested simplicialbot vertices: p929(v567) p731(v244) p650(v140) between f74662 and f73973 - r168543 tested vertices: p929(v567) p173(v565) p650(v140) between f73973 and f74662 - r169189 tested vertices: p929(v567) p173(v565) p550(v118) between f74662 and f73973 - r167265 tested vertices: p929(v567) p8(v390) p731(v244) between f74662 and f73973 - r168695 tested simplicialbot vertices: p899(v658) p777(v657) p30(v310) between f74662 and f64975 - r169308 tested vertices: p46(v591) p738(v420) p636(v156) between f74662 and f74764 - r169348 tested simplicialtop vertices: p986(v593) p738(v420) p636(v156) between f74764 and f74662 - r167262 tested simplicialtop vertices: p929(v567) p8(v390) p560(v212) between f73929 and f74662 - r170315 tested simplicialbot vertices: p285(v745) p711(v580) p531(v226) between f74662 and f74539 - r166477 tested simplicialtop vertices: p15(v557) p841(v379) p675(v137) between f58154 and f74662 - r170840 tested simplicialtop vertices: p392(v773) p671(v769) p343(v441) between f74959 and f74662 - r167597 tested simplicialtop vertices: p176(v577) p797(v145) p611(v79) between f58433 and f74662 - r168913 tested simplicialbot vertices: p205(v396) p891(v141) p748(v77) between f74662 and f28940 - r168835 tested simplicialtop vertices: p205(v396) p236(v248) p748(v77) between f28938 and f74662 - r168838 tested simplicialbot vertices: p146(v569) p205(v396) p236(v248) between f74662 and f58312 - r170674 tested simplicialbot vertices: p729(v753) p701(v719) p448(v590) between f74662 and f74737 - r167901 tested simplicialbot vertices: p338(v572) p145(v398) p151(v143) between f74662 and f58384 - r170671 tested simplicialtop vertices: p729(v753) p948(v739) p292(v571) between f74734 and f74662 - r169524 tested simplicialtop vertices: p804(v737) p146(v569) p205(v396) between f74141 and f74662 - r169427 tested simplicialbot vertices: p901(v554) p731(v244) p274(v134) between f74662 and f57508 - r166211 tested simplicialtop vertices: p573(v589) p245(v426) p396(v27) between f60310 and f74662 - r168807 tested simplicialbot vertices: p573(v589) p360(v270) p396(v27) between f74662 and f60309 - r168461 tested simplicialtop vertices: p683(v598) p156(v275) p396(v27) between f60826 and f74662 - r166207 tested simplicialbot vertices: p95(v603) p573(v589) p245(v426) between f74662 and f60871 - r167046 tested simplicialbot vertices: p683(v598) p245(v426) p396(v27) between f74662 and f60827 - r168726 tested simplicialtop vertices: p360(v270) p275(v187) p703(v103) between f17070 and f74662 - r168736 tested simplicialtop vertices: p786(v477) p444(v313) p396(v27) between f41098 and f74662 - r166526 tested simplicialbot vertices: p360(v270) p275(v187) p396(v27) between f74662 and f17077 - r166522 tested simplicialtop vertices: p444(v313) p275(v187) p396(v27) between f22165 and f74662 - r168492 tested simplicialbot vertices: p614(v417) p736(v416) p360(v270) between f74662 and f32467 - r167065 tested simplicialbot vertices: p529(v204) p119(v112) p698(v38) between f74662 and f8116 - r167277 tested simplicialtop vertices: p18(v484) p861(v317) p275(v187) between f41163 and f74662 - r168246 tested simplicialbot vertices: p812(v648) p632(v292) p149(v58) between f74662 and f64883 - r168495 tested simplicialtop vertices: p736(v416) p360(v270) p703(v103) between f32454 and f74662 - r166678 tested simplicialtop vertices: p236(v248) p151(v143) p748(v77) between f12906 and f74662 - r165978 tested simplicialbot vertices: p861(v317) p275(v187) p703(v103) between f74662 and f22208 - r169135 tested simplicialbot vertices: p573(v589) p614(v417) p360(v270) between f74662 and f59637 - r165974 tested simplicialbot vertices: p934(v478) p861(v317) p703(v103) between f74662 and f41106 - r167873 tested simplicialbot vertices: p870(v314) p402(v188) p55(v31) between f74662 and f22173 - r166778 tested simplicialtop vertices: p178(v622) p713(v447) p632(v292) between f62214 and f74662 - r166721 tested simplicialbot vertices: p336(v653) p870(v314) p55(v31) between f74662 and f64927 - r166718 tested simplicialtop vertices: p336(v653) p141(v497) p55(v31) between f64930 and f74662 - r167709 tested simplicialbot vertices: p880(v479) p724(v107) p149(v58) between f74662 and f41114 - r167357 tested simplicialtop vertices: p880(v479) p361(v189) p149(v58) between f41116 and f74662 - r167617 tested simplicialbot vertices: p653(v468) p509(v306) p13(v171) between f74662 and f41021 - r167583 tested simplicialbot vertices: p632(v292) p361(v189) p149(v58) between f74662 and f19454 - r167395 tested simplicialbot vertices: p934(v478) p870(v314) p361(v189) between f74662 and f41108 - r167353 tested simplicialtop vertices: p880(v479) p870(v314) p361(v189) between f41117 and f74662 - r167614 tested simplicialbot vertices: p812(v648) p653(v468) p13(v171) between f74662 and f64887 - r167398 tested simplicialtop vertices: p934(v478) p870(v314) p402(v188) between f41101 and f74662 - r169104 tested simplicialbot vertices: p377(v654) p265(v315) p350(v56) between f74662 and f64933 - r168507 tested simplicialbot vertices: p934(v478) p265(v315) p402(v188) between f74662 and f41104 - r166782 tested simplicialtop vertices: p178(v622) p632(v292) p361(v189) between f62217 and f74662 - r168472 tested simplicialbot vertices: p336(v653) p880(v479) p870(v314) between f74662 and f64928 - r167705 tested simplicialtop vertices: p336(v653) p880(v479) p724(v107) between f64923 and f74662 - r168565 tested simplicialtop vertices: p934(v478) p265(v315) p703(v103) between f41103 and f74662 - r168512 tested simplicialbot vertices: p916(v656) p922(v482) p806(v481) between f74662 and f64957 - r166402 tested simplicialtop vertices: p324(v246) p801(v136) p750(v135) between f12890 and f74662 - r168561 tested simplicialbot vertices: p265(v315) p703(v103) p350(v56) between f74662 and f22183 - r169063 tested simplicialtop vertices: p736(v416) p703(v103) p350(v56) between f32453 and f74662 - r166456 tested simplicialtop vertices: p916(v656) p377(v654) p402(v188) between f64952 and f74662 - r168509 tested simplicialbot vertices: p916(v656) p377(v654) p922(v482) between f74662 and f64953 - r166452 tested simplicialtop vertices: p377(v654) p265(v315) p402(v188) between f64938 and f74662 - r169182 tested simplicialtop vertices: p934(v478) p861(v317) p361(v189) between f41109 and f74662 - r168249 tested simplicialtop vertices: p812(v648) p632(v292) p13(v171) between f64886 and f74662 - r168098 tested simplicialtop vertices: p95(v603) p573(v589) p996(v102) between f60870 and f74662 - r170748 tested simplicialbot vertices: p896(v762) p688(v735) p1(v421) between f74662 and f74835 - r166305 tested simplicialtop vertices: p685(v597) p372(v273) p684(v78) between f74774 and f74662 - r168974 tested vertices: p183(v595) p1(v421) p684(v78) between f74774 and f74662 - r166301 tested vertices: p183(v595) p372(v273) p684(v78) between f74662 and f74774 - r170753 tested simplicialtop vertices: p896(v762) p92(v425) p854(v274) between f74837 and f74662 - r170746 tested simplicialbot vertices: p896(v762) p1(v421) p684(v78) between f74662 and f74834 - r170762 tested simplicialbot vertices: p646(v764) p88(v600) p74(v253) between f74662 and f74854 - r169499 tested simplicialbot vertices: p688(v735) p139(v733) p1(v421) between f74662 and f74128 - r170665 tested simplicialbot vertices: p729(v753) p826(v419) p354(v271) between f74662 and f74727 - r170686 tested simplicialtop vertices: p977(v756) p683(v598) p245(v426) between f74756 and f74662 - r168244 tested simplicialbot vertices: p711(v580) p282(v408) p421(v259) between f74662 and f58466 - r168240 tested simplicialbot vertices: p711(v580) p421(v259) p318(v26) between f74662 and f58465 - r168363 tested simplicialtop vertices: p711(v580) p531(v226) p318(v26) between f58470 and f74662 - r169544 tested simplicialbot vertices: p948(v739) p145(v398) p465(v249) between f74662 and f74167 - r168431 tested simplicialtop vertices: p531(v226) p14(v67) p318(v26) between f10964 and f74662 - r168434 tested simplicialbot vertices: p421(v259) p14(v67) p318(v26) between f74662 and f13908 - r170314 tested simplicialtop vertices: p285(v745) p940(v539) p531(v226) between f74538 and f74662 - r167972 tested simplicialbot vertices: p850(v698) p421(v259) p825(v149) between f74662 and f66673 - r167968 tested simplicialtop vertices: p282(v408) p421(v259) p825(v149) between f29396 and f74662 - r168011 tested simplicialtop vertices: p511(v599) p225(v148) p382(v85) between f60834 and f74662 - r166034 tested simplicialbot vertices: p511(v599) p616(v424) p603(v157) between f74662 and f74842 - r166038 tested simplicialbot vertices: p511(v599) p603(v157) p382(v85) between f74662 and f74847 - r168383 tested simplicialbot vertices: p444(v313) p580(v158) p382(v85) between f74662 and f22170 - r167699 tested simplicialtop vertices: p156(v275) p603(v157) p382(v85) between f18796 and f74662 - r167695 tested simplicialtop vertices: p444(v313) p156(v275) p382(v85) between f22171 and f74662 - r168457 tested simplicialbot vertices: p786(v477) p156(v275) p396(v27) between f74662 and f41097 - r168925 tested simplicialbot vertices: p786(v477) p444(v313) p156(v275) between f74662 and f41099 - r168108 tested simplicialbot vertices: p683(v598) p156(v275) p603(v157) between f74662 and f60819 - r168617 tested simplicialtop vertices: p593(v601) p616(v424) p603(v157) between f74844 and f74662 - r167049 tested simplicialbot vertices: p511(v599) p225(v148) p866(v15) between f74662 and f60832 - r166315 tested simplicialtop vertices: p135(v602) p511(v599) p616(v424) between f60865 and f74662 - r168627 tested simplicialtop vertices: p8(v390) p731(v244) p274(v134) between f27399 and f74662 - r168624 tested simplicialtop vertices: p844(v555) p8(v390) p274(v134) between f58137 and f74662 - r166705 tested simplicialtop vertices: p873(v721) p844(v555) p586(v12) between f69698 and f74662 - r169169 tested simplicialbot vertices: p491(v725) p278(v239) p675(v137) between f74662 and f73920 - r168333 tested simplicialtop vertices: p906(v393) p192(v237) p212(v44) between f28903 and f74662 - r169131 tested simplicialbot vertices: p844(v555) p103(v378) p274(v134) between f74662 and f58136 - r166703 tested simplicialbot vertices: p873(v721) p8(v390) p586(v12) between f74662 and f73924 - r166699 tested simplicialbot vertices: p873(v721) p844(v555) p8(v390) between f74662 and f69699 - r168340 tested simplicialtop vertices: p268(v720) p844(v555) p103(v378) between f69581 and f74662 - r168337 tested simplicialtop vertices: p59(v722) p268(v720) p103(v378) between f69702 and f74662 - r167849 tested simplicialtop vertices: p12(v556) p103(v378) p274(v134) between f58140 and f74662 - r167846 tested simplicialbot vertices: p59(v722) p12(v556) p103(v378) between f74662 and f69700 - r166266 tested simplicialbot vertices: p12(v556) p906(v393) p192(v237) between f74662 and f58142 - r166262 tested simplicialtop vertices: p59(v722) p12(v556) p906(v393) between f71083 and f74662 - r168738 tested simplicialtop vertices: p59(v722) p906(v393) p277(v75) between f71082 and f74662 - r167966 tested simplicialbot vertices: p226(v723) p64(v380) p277(v75) between f74662 and f71092 - r169168 tested simplicialtop vertices: p203(v558) p278(v239) p675(v137) between f58159 and f74662 - r166112 tested simplicialbot vertices: p59(v722) p203(v558) p277(v75) between f74662 and f71080 - r166108 tested simplicialtop vertices: p226(v723) p203(v558) p277(v75) between f71093 and f74662 - r165859 tested vertices: p491(v725) p718(v559) p518(v43) between f74662 and f73383 - r167314 tested vertices: p491(v725) p667(v230) p827(v74) between f73383 and f74662 - r167318 tested simplicialbot vertices: p491(v725) p667(v230) p801(v136) between f74662 and f73383 - r167918 tested vertices: p491(v725) p278(v239) p801(v136) between f73383 and f74662 - r168548 tested vertices: p491(v725) p827(v74) p518(v43) between f73383 and f74662 - r167735 tested simplicialbot vertices: p226(v723) p203(v558) p278(v239) between f74662 and f71091 - r169167 tested simplicialbot vertices: p59(v722) p268(v720) p188(v238) between f74662 and f69701 - r167964 tested simplicialbot vertices: p64(v380) p801(v136) p277(v75) between f74662 and f25681 - r167731 tested simplicialtop vertices: p226(v723) p64(v380) p278(v239) between f71090 and f74662 - r167917 tested simplicialbot vertices: p64(v380) p278(v239) p801(v136) between f74662 and f25682 - r166473 tested simplicialbot vertices: p203(v558) p841(v379) p675(v137) between f74662 and f58160 - r169149 tested simplicialtop vertices: p59(v722) p203(v558) p188(v238) between f71081 and f74662 - r168778 tested simplicialtop vertices: p203(v558) p841(v379) p188(v238) between f58167 and f74662 - r168774 tested simplicialbot vertices: p268(v720) p841(v379) p188(v238) between f74662 and f69683 - r166478 tested simplicialtop vertices: p491(v725) p15(v557) p675(v137) between f73885 and f74662 - r168908 tested simplicialbot vertices: p268(v720) p15(v557) p841(v379) between f74662 and f69684 - r167126 tested simplicialbot vertices: p131(v550) p302(v374) p484(v232) between f74662 and f55303 - r167683 tested simplicialtop vertices: p284(v570) p667(v230) p322(v25) between f58361 and f74662 - r167122 tested simplicialbot vertices: p851(v551) p131(v550) p484(v232) between f74662 and f56396 - r166965 tested simplicialtop vertices: p131(v550) p998(v373) p926(v129) between f56388 and f74662 - r167687 tested simplicialtop vertices: p667(v230) p801(v136) p322(v25) between f11434 and f74662 - r167274 tested simplicialtop vertices: p131(v550) p302(v374) p827(v74) between f55302 and f74662 - r167826 tested simplicialtop vertices: p251(v549) p302(v374) p716(v236) between f55301 and f74662 - r168099 tested simplicialbot vertices: p131(v550) p328(v548) p827(v74) between f74662 and f56389 - r167829 tested simplicialbot vertices: p251(v549) p302(v374) p827(v74) between f74662 and f55298 - r168883 tested simplicialtop vertices: p851(v551) p131(v550) p926(v129) between f56395 and f74662 - r165855 tested simplicialbot vertices: p718(v559) p716(v236) p518(v43) between f74662 and f58169 - r166969 tested simplicialtop vertices: p131(v550) p328(v548) p998(v373) between f56390 and f74662 - r169049 tested simplicialbot vertices: p328(v548) p667(v230) p827(v74) between f74662 and f55293 - r169012 tested simplicialbot vertices: p251(v549) p827(v74) p518(v43) between f74662 and f55297 - r169175 tested simplicialtop vertices: p554(v430) p859(v427) p613(v295) between f36429 and f74662 - r169173 tested simplicialbot vertices: p859(v427) p613(v295) p22(v35) between f74662 and f35588 - r166139 tested simplicialbot vertices: p775(v621) p383(v440) p822(v88) between f74662 and f62198 - r167180 tested simplicialbot vertices: p554(v430) p966(v159) p159(v86) between f74662 and f36419 - r168780 tested simplicialtop vertices: p422(v510) p966(v159) p241(v20) between f48630 and f74662 - r167176 tested simplicialtop vertices: p557(v607) p554(v430) p966(v159) between f62061 and f74662 - r165721 tested simplicialtop vertices: p500(v619) p294(v618) p235(v167) between f62174 and f74662 - r170834 tested simplicialtop vertices: p392(v773) p471(v613) p10(v165) between f74948 and f74662 - r169154 tested simplicialbot vertices: p859(v427) p794(v276) p51(v160) between f74662 and f35586 - r168384 tested simplicialtop vertices: p10(v165) p22(v35) p430(v16) between f6593 and f74662 - r167936 tested simplicialtop vertices: p79(v429) p10(v165) p430(v16) between f36409 and f74662 - r167072 tested simplicialtop vertices: p471(v613) p379(v437) p714(v284) between f62110 and f74662 - r168047 tested simplicialbot vertices: p794(v276) p22(v35) p430(v16) between f74662 and f19109 - r168043 tested simplicialtop vertices: p859(v427) p794(v276) p22(v35) between f35585 and f74662 - r169004 tested simplicialbot vertices: p79(v429) p794(v276) p430(v16) between f74662 and f36406 - r168554 tested simplicialbot vertices: p714(v284) p10(v165) p22(v35) between f74662 and f19263 - r168992 tested simplicialtop vertices: p122(v606) p79(v429) p946(v9) between f62048 and f74662 - r167076 tested simplicialtop vertices: p471(v613) p714(v284) p10(v165) between f62109 and f74662 - r167569 tested simplicialbot vertices: p791(v616) p273(v615) p642(v438) between f74662 and f74963 - r167566 tested vertices: p791(v616) p642(v438) p945(v90) between f74662 and f74963 - r166054 tested simplicialbot vertices: p775(v621) p294(v618) p235(v167) between f74662 and f62200 - r165717 tested vertices: p659(v620) p500(v619) p235(v167) between f75015 and f74662 - r169025 tested vertices: p659(v620) p500(v619) p791(v616) between f74662 and f75015 - r167378 tested simplicialbot vertices: p500(v619) p117(v439) p442(v286) between f74662 and f74996 - r170841 tested simplicialbot vertices: p392(v773) p471(v613) p379(v437) between f74662 and f74955 - r170777 tested simplicialbot vertices: p638(v767) p511(v599) p866(v15) between f74662 and f74883 - r170837 tested simplicialbot vertices: p392(v773) p122(v606) p79(v429) between f74662 and f74951 - r170827 tested simplicialbot vertices: p297(v772) p86(v612) p997(v433) between f74662 and f74945 - r168533 tested simplicialbot vertices: p546(v432) p51(v160) p946(v9) between f74662 and f36998 - r167659 tested simplicialtop vertices: p343(v441) p383(v440) p206(v164) between f38427 and f74662 - r166821 tested simplicialbot vertices: p659(v620) p791(v616) p654(v287) between f74662 and f62192 - r170654 tested simplicialtop vertices: p2(v751) p988(v588) p120(v584) between f74715 and f74662 - r166817 tested simplicialtop vertices: p659(v620) p383(v440) p654(v287) between f62190 and f74662 - r168940 tested simplicialbot vertices: p343(v441) p383(v440) p654(v287) between f74662 and f38428 - r170779 tested simplicialbot vertices: p638(v767) p135(v602) p511(v599) between f74662 and f74884 - r167117 tested simplicialbot vertices: p122(v606) p84(v605) p228(v277) between f74662 and f74893 - r166491 tested simplicialtop vertices: p791(v616) p273(v615) p442(v286) between f62147 and f74662 - r166487 tested simplicialbot vertices: p656(v632) p273(v615) p442(v286) between f74662 and f63552 - r167760 tested simplicialtop vertices: p656(v632) p117(v439) p442(v286) between f74999 and f74662 - r169082 tested simplicialbot vertices: p581(v646) p775(v621) p142(v302) between f74662 and f64875 - r167294 tested simplicialtop vertices: p273(v615) p234(v285) p553(v166) between f62137 and f74662 - r168346 tested simplicialbot vertices: p775(v621) p659(v620) p383(v440) between f74662 and f62203 - r167291 tested simplicialtop vertices: p656(v632) p273(v615) p553(v166) between f63551 and f74662 - r168327 tested simplicialtop vertices: p794(v276) p51(v160) p946(v9) between f19106 and f74662 - r167382 tested nonconvex vertices: p500(v619) p791(v616) p442(v286) between f75017 and f74662 - r168586 tested simplicialtop vertices: p230(v714) p228(v277) p946(v9) between f66823 and f74662 - r168583 tested simplicialbot vertices: p230(v714) p546(v432) p946(v9) between f74662 and f66824 - r168907 tested simplicialbot vertices: p497(v608) p546(v432) p91(v278) between f74662 and f74917 - r168489 tested vertices: p497(v608) p546(v432) p51(v160) between f74917 and f74662 - r168600 tested vertices: p230(v714) p546(v432) p91(v278) between f74917 and f74662 - r168588 tested simplicialbot vertices: p122(v606) p228(v277) p946(v9) between f74662 and f62047 - r168323 tested simplicialtop vertices: p79(v429) p794(v276) p946(v9) between f36405 and f74662 - r170826 tested simplicialtop vertices: p297(v772) p86(v612) p312(v173) between f74944 and f74662 - r170833 tested simplicialbot vertices: p392(v773) p79(v429) p10(v165) between f74662 and f74947 - r166172 tested simplicialbot vertices: p557(v607) p789(v214) p698(v38) between f74662 and f62069 - r166135 tested simplicialbot vertices: p383(v440) p206(v164) p822(v88) between f74662 and f38417 - r165876 tested simplicialtop vertices: p557(v607) p255(v431) p91(v278) between f62064 and f74662 - r166169 tested simplicialbot vertices: p557(v607) p255(v431) p789(v214) between f74662 and f62066 - r165880 tested simplicialtop vertices: p497(v608) p557(v607) p91(v278) between f62077 and f74662 - r168070 tested simplicialbot vertices: p789(v214) p475(v119) p698(v38) between f74662 and f8954 - r166057 tested simplicialtop vertices: p581(v646) p775(v621) p294(v618) between f64872 and f74662 - r167503 tested simplicialbot vertices: p497(v608) p557(v607) p554(v430) between f74662 and f62078 - r167499 tested simplicialbot vertices: p497(v608) p554(v430) p859(v427) between f74662 and f62076 - r167817 tested simplicialbot vertices: p497(v608) p859(v427) p51(v160) between f74662 and f62075 - r168235 tested simplicialbot vertices: p422(v510) p966(v159) p698(v38) between f74662 and f48631 - r168233 tested simplicialtop vertices: p557(v607) p966(v159) p698(v38) between f62068 and f74662 - r170782 tested simplicialtop vertices: p638(v767) p674(v261) p866(v15) between f74881 and f74662 - r168447 tested simplicialbot vertices: p500(v619) p294(v618) p117(v439) between f74662 and f62175 - r168310 tested simplicialtop vertices: p416(v614) p343(v441) p936(v50) between f62124 and f74662 - r167662 tested simplicialtop vertices: p343(v441) p206(v164) p936(v50) between f38425 and f74662 - r166078 tested simplicialbot vertices: p412(v623) p175(v466) p102(v17) between f74662 and f62227 - r167245 tested simplicialbot vertices: p108(v673) p175(v466) p509(v306) between f74662 and f65132 - r167578 tested simplicialtop vertices: p108(v673) p812(v648) p653(v468) between f65123 and f74662 - r169430 tested vertices: p139(v733) p77(v245) p891(v141) between f74031 and f74662 - r170757 tested simplicialbot vertices: p896(v762) p135(v602) p854(v274) between f74662 and f74840 - r169519 tested vertices: p804(v737) p567(v594) p986(v593) between f74793 and f74662 - r169300 tested vertices: p139(v733) p183(v595) p738(v420) between f74793 and f74662 - r169296 tested simplicialbot vertices: p139(v733) p183(v595) p1(v421) between f74662 and f74793 - r169358 tested vertices: p139(v733) p567(v594) p77(v245) between f74793 and f74662 - r169349 tested vertices: p139(v733) p986(v593) p738(v420) between f74662 and f74793 - r169377 tested vertices: p139(v733) p567(v594) p986(v593) between f74662 and f74793 - r169429 tested simplicialbot vertices: p205(v396) p77(v245) p891(v141) between f74662 and f28941 - r169329 tested simplicialbot vertices: p12(v556) p192(v237) p274(v134) between f74662 and f58139 - r170688 tested simplicialbot vertices: p977(v756) p617(v592) p900(v186) between f74662 and f74754 - r169525 tested simplicialtop vertices: p804(v737) p986(v593) p830(v391) between f74148 and f74662 - r169286 tested simplicialbot vertices: p139(v733) p981(v247) p891(v141) between f74662 and f74055 - r168814 tested vertices: p680(v563) p335(v385) p481(v47) between f74108 and f74662 - r169482 tested simplicialtop vertices: p139(v733) p74(v253) p828(v144) between f74108 and f74662 - r169318 tested vertices: p139(v733) p97(v573) p74(v253) between f74108 and f74662 - r169323 tested vertices: p139(v733) p97(v573) p455(v538) between f74662 and f74108 - r169324 tested vertices: p139(v733) p680(v563) p481(v47) between f74108 and f74662 - r169320 tested vertices: p139(v733) p455(v538) p481(v47) between f74662 and f74108 - r169331 tested vertices: p139(v733) p680(v563) p955(v139) between f74662 and f74108 - r169299 tested simplicialbot vertices: p183(v595) p738(v420) p372(v273) between f74662 and f74749 - r166294 tested vertices: p617(v592) p738(v420) p372(v273) between f74749 and f74662 - r170681 tested vertices: p977(v756) p617(v592) p372(v273) between f74749 and f74662 - r170581 tested simplicialtop vertices: p637(v493) p568(v324) p177(v106) between f45476 and f74662 - r169316 tested simplicialtop vertices: p981(v247) p324(v246) p212(v44) between f12901 and f74662 - r169310 tested vertices: p139(v733) p192(v237) p212(v44) between f74662 and f74060 - r169428 tested vertices: p139(v733) p901(v554) p274(v134) between f74662 and f74060 - r169330 tested vertices: p139(v733) p192(v237) p274(v134) between f74060 and f74662 - r169317 tested vertices: p139(v733) p981(v247) p212(v44) between f74060 and f74662 - r169527 tested simplicialbot vertices: p804(v737) p567(v594) p205(v396) between f74662 and f74143 - r169538 tested simplicialbot vertices: p87(v738) p46(v591) p636(v156) between f74662 and f74163 - r169537 tested simplicialtop vertices: p87(v738) p46(v591) p363(v83) between f74162 and f74662 - r169535 tested simplicialbot vertices: p87(v738) p830(v391) p744(v45) between f74662 and f74153 - r169545 tested simplicialtop vertices: p948(v739) p37(v552) p465(v249) between f74168 and f74662 - r169590 tested simplicialtop vertices: p319(v625) p682(v445) p238(v291) between f62250 and f74662 - r170269 tested simplicialtop vertices: p742(v578) p529(v204) p119(v112) between f58447 and f74662 - r158424 tested simplicialtop vertices: p4(v717) p470(v532) p446(v359) between f69517 and f74662 - r169965 tested simplicialtop vertices: p655(v642) p370(v470) p886(v98) between f63658 and f74662 - r170274 tested simplicialtop vertices: p171(v294) p468(v172) p781(v92) between f20132 and f74662 - r169928 tested simplicialtop vertices: p412(v623) p389(v443) p102(v17) between f62225 and f74662 - r170013 tested simplicialtop vertices: p818(v471) p386(v330) p963(v181) between f41046 and f74662 - r158407 tested simplicialbot vertices: p373(v703) p470(v532) p658(v370) between f74662 and f66720 - r169963 tested simplicialbot vertices: p655(v642) p370(v470) p746(v308) between f74662 and f63659 - r170196 tested simplicialtop vertices: p9(v340) p611(v79) p384(v2) between f22423 and f74662 - r157872 tested simplicialbot vertices: p691(v716) p641(v544) p658(v370) between f74662 and f68226 - r169593 tested simplicialtop vertices: p412(v623) p509(v306) p13(v171) between f62234 and f74662 - r170213 tested simplicialtop vertices: p601(v624) p493(v444) p327(v170) between f62246 and f74662 - r169910 tested simplicialtop vertices: p293(v574) p695(v403) p792(v257) between f58400 and f74662 - r169961 tested simplicialtop vertices: p849(v651) p370(v470) p746(v308) between f64906 and f74662 - r169957 tested simplicialbot vertices: p849(v651) p370(v470) p963(v181) between f74662 and f64908 - r170115 tested simplicialbot vertices: p422(v510) p33(v203) p241(v20) between f74662 and f48627 - r170267 tested simplicialtop vertices: p389(v443) p799(v289) p327(v170) between f39915 and f74662 - r170198 tested simplicialbot vertices: p897(v744) p9(v340) p611(v79) between f74662 and f74214 - r170242 tested simplicialtop vertices: p81(v672) p386(v330) p543(v196) between f65114 and f74662 - r169632 tested simplicialbot vertices: p18(v484) p861(v317) p361(v189) between f74662 and f41161 - r169959 tested simplicialbot vertices: p370(v470) p886(v98) p102(v17) between f74662 and f41039 - r170145 tested simplicialbot vertices: p799(v289) p327(v170) p781(v92) between f74662 and f19420 - r169846 tested simplicialtop vertices: p166(v629) p863(v293) p468(v172) between f62285 and f74662 - r170089 tested simplicialbot vertices: p747(v665) p319(v625) p124(v93) between f74662 and f65046 - r169630 tested simplicialtop vertices: p554(v430) p198(v174) p159(v86) between f36426 and f74662 - r169850 tested simplicialbot vertices: p863(v293) p468(v172) p781(v92) between f74662 and f19564 - r169831 tested simplicialtop vertices: p849(v651) p818(v471) p963(v181) between f64909 and f74662 - r170243 tested simplicialbot vertices: p562(v449) p473(v448) p863(v293) between f74662 and f40818 - r169657 tested simplicialbot vertices: p897(v744) p176(v577) p579(v406) between f74662 and f74212 - r158038 tested simplicialtop vertices: p641(v544) p658(v370) p644(v228) between f55263 and f74662 - r170231 tested simplicialbot vertices: p514(v730) p968(v520) p201(v349) between f74662 and f73966 - r170240 tested simplicialtop vertices: p81(v672) p175(v466) p386(v330) between f65112 and f74662 - r170278 tested simplicialbot vertices: p412(v623) p389(v443) p799(v289) between f74662 and f62230 - r169925 tested simplicialtop vertices: p389(v443) p886(v98) p102(v17) between f39142 and f74662 - r170155 tested simplicialbot vertices: p818(v471) p386(v330) p543(v196) between f74662 and f41057 - r169640 tested simplicialbot vertices: p444(v313) p275(v187) p580(v158) between f74662 and f22166 - r170273 tested simplicialbot vertices: p897(v744) p742(v578) p9(v340) between f74662 and f74215 - r169634 tested simplicialbot vertices: p81(v672) p597(v328) p543(v196) between f74662 and f65116 - r170010 tested simplicialbot vertices: p175(v466) p386(v330) p963(v181) between f74662 and f41002 - r170232 tested simplicialtop vertices: p514(v730) p173(v565) p201(v349) between f73967 and f74662 - r170272 tested simplicialtop vertices: p742(v578) p9(v340) p529(v204) between f58448 and f74662 - r170199 tested simplicialbot vertices: p9(v340) p529(v204) p384(v2) between f74662 and f22424 - r158097 tested simplicialtop vertices: p283(v541) p875(v371) p127(v168) between f55232 and f74662 - r158090 tested simplicialbot vertices: p271(v711) p911(v604) p596(v428) between f74662 and f66800 - r157267 tested simplicialtop vertices: p911(v604) p305(v543) p253(v70) between f60875 and f74662 - r158093 tested simplicialbot vertices: p283(v541) p875(v371) p763(v229) between f74662 and f55233 - r157868 tested simplicialtop vertices: p691(v716) p470(v532) p658(v370) between f68975 and f74662 - r158206 tested simplicialtop vertices: p658(v370) p524(v368) p644(v228) between f22993 and f74662 - r158292 tested simplicialtop vertices: p283(v541) p524(v368) p763(v229) between f54352 and f74662 - r157485 tested simplicialtop vertices: p373(v703) p470(v532) p670(v40) between f66723 and f74662 - r158294 tested simplicialbot vertices: p524(v368) p763(v229) p501(v128) between f74662 and f22967 - r158396 tested simplicialtop vertices: p373(v703) p763(v229) p501(v128) between f66717 and f74662 - r158409 tested simplicialtop vertices: p875(v371) p763(v229) p670(v40) between f22994 and f74662 - r157989 tested simplicialbot vertices: p658(v370) p524(v368) p501(v128) between f74662 and f22992 - r157985 tested simplicialbot vertices: p373(v703) p658(v370) p501(v128) between f74662 and f66719 - r157496 tested simplicialtop vertices: p470(v532) p867(v221) p670(v40) between f52386 and f74662 - r157492 tested simplicialbot vertices: p875(v371) p867(v221) p670(v40) between f74662 and f23613 - r158208 tested simplicialbot vertices: p283(v541) p524(v368) p644(v228) between f74662 and f54351 - r157489 tested simplicialbot vertices: p373(v703) p763(v229) p670(v40) between f74662 and f66722 - r157659 tested simplicialtop vertices: p271(v711) p283(v541) p127(v168) between f66798 and f74662 - r158137 tested simplicialbot vertices: p271(v711) p596(v428) p127(v168) between f74662 and f66797 - r158204 tested simplicialtop vertices: p305(v543) p283(v541) p253(v70) between f55245 and f74662 - r157655 tested simplicialtop vertices: p271(v711) p911(v604) p283(v541) between f66801 and f74662 - r158202 tested simplicialbot vertices: p911(v604) p283(v541) p253(v70) between f74662 and f60878 - r170293 tested simplicialbot vertices: p4(v717) p470(v532) p574(v372) between f74662 and f69421 - r170292 tested simplicialtop vertices: p470(v532) p574(v372) p867(v221) between f52387 and f74662 - r169817 tested simplicialtop vertices: p498(v666) p166(v629) p808(v91) between f65060 and f74662 - r169934 tested simplicialbot vertices: p178(v622) p713(v447) p620(v32) between f74662 and f62213 - r169814 tested simplicialbot vertices: p498(v666) p166(v629) p473(v448) between f74662 and f65061 - r170225 tested simplicialbot vertices: p319(v625) p90(v491) p238(v291) between f74662 and f62252 - r169716 tested simplicialbot vertices: p498(v666) p473(v448) p238(v291) between f74662 and f65055 - r170263 tested simplicialtop vertices: p747(v665) p319(v625) p90(v491) between f65045 and f74662 - r170122 tested simplicialtop vertices: p166(v629) p473(v448) p863(v293) between f62286 and f74662 - r169720 tested simplicialtop vertices: p498(v666) p90(v491) p238(v291) between f65056 and f74662 - r169740 tested simplicialtop vertices: p166(v629) p898(v169) p808(v91) between f62283 and f74662 - r169736 tested simplicialtop vertices: p166(v629) p171(v294) p898(v169) between f62288 and f74662 - r170245 tested simplicialtop vertices: p443(v647) p487(v450) p781(v92) between f64880 and f74662 - r169930 tested simplicialtop vertices: p178(v622) p564(v442) p620(v32) between f62211 and f74662 - r170026 tested simplicialbot vertices: p171(v294) p898(v169) p620(v32) between f74662 and f19570 - r170020 tested simplicialbot vertices: p582(v628) p171(v294) p620(v32) between f74662 and f62275 - r170017 tested simplicialtop vertices: p582(v628) p713(v447) p620(v32) between f62276 and f74662 - r170260 tested simplicialtop vertices: p564(v442) p898(v169) p620(v32) between f38436 and f74662 - r170107 tested simplicialtop vertices: p582(v628) p487(v450) p713(v447) between f62279 and f74662 - r170028 tested simplicialbot vertices: p783(v627) p487(v450) p713(v447) between f74662 and f62270 - r170248 tested simplicialtop vertices: p443(v647) p404(v467) p487(v450) between f64881 and f74662 - r170032 tested simplicialbot vertices: p783(v627) p404(v467) p487(v450) between f74662 and f62273 - r170252 tested simplicialbot vertices: p443(v647) p404(v467) p799(v289) between f74662 and f64878 - r170181 tested simplicialbot vertices: p783(v627) p713(v447) p632(v292) between f74662 and f62268 - r170250 tested simplicialbot vertices: p443(v647) p799(v289) p781(v92) between f74662 and f64877 - r170175 tested simplicialtop vertices: p783(v627) p404(v467) p13(v171) between f62272 and f74662 - r170183 tested simplicialbot vertices: p783(v627) p632(v292) p13(v171) between f74662 and f62267 - r169940 tested simplicialbot vertices: p582(v628) p487(v450) p171(v294) between f74662 and f62278 - r170157 tested simplicialtop vertices: p412(v623) p404(v467) p799(v289) between f62232 and f74662 - r169936 tested simplicialtop vertices: p487(v450) p171(v294) p781(v92) between f40827 and f74662 - r170239 tested simplicialbot vertices: p809(v664) p773(v660) p602(v194) between f74662 and f65036 - r170063 tested simplicialbot vertices: p686(v667) p90(v491) p715(v325) between f74662 and f65064 - r169862 tested simplicialbot vertices: p686(v667) p6(v490) p808(v91) between f74662 and f65066 - r170037 tested simplicialtop vertices: p686(v667) p498(v666) p808(v91) between f65068 and f74662 - r170228 tested simplicialbot vertices: p260(v743) p293(v574) p884(v146) between f74662 and f74199 - r170141 tested simplicialbot vertices: p634(v671) p809(v664) p715(v325) between f74662 and f65104 - r170078 tested simplicialtop vertices: p809(v664) p6(v490) p602(v194) between f65035 and f74662 - r169866 tested simplicialbot vertices: p6(v490) p602(v194) p808(v91) between f74662 and f44983 - r169906 tested simplicialtop vertices: p260(v743) p293(v574) p792(v257) between f74204 and f74662 - r169919 tested simplicialbot vertices: p809(v664) p6(v490) p715(v325) between f74662 and f65027 - r169916 tested simplicialtop vertices: p686(v667) p6(v490) p715(v325) between f65063 and f74662 - r170061 tested simplicialbot vertices: p686(v667) p498(v666) p90(v491) between f74662 and f65069 - r170266 tested simplicialtop vertices: p747(v665) p90(v491) p715(v325) between f65044 and f74662 - r170295 tested simplicialtop vertices: p897(v744) p742(v578) p579(v406) between f74213 and f74662 - r170143 tested simplicialtop vertices: p634(v671) p747(v665) p715(v325) between f65101 and f74662 - r169857 tested simplicialtop vertices: p882(v670) p397(v507) p702(v506) between f65097 and f74662 - r170035 tested simplicialbot vertices: p634(v671) p747(v665) p745(v11) between f74662 and f65100 - r170068 tested simplicialbot vertices: p882(v670) p958(v669) p943(v495) between f74662 and f65092 - r170053 tested simplicialbot vertices: p882(v670) p397(v507) p918(v202) between f74662 and f65096 - r169853 tested simplicialtop vertices: p882(v670) p702(v506) p745(v11) between f65089 and f74662 - r169840 tested simplicialbot vertices: p397(v507) p702(v506) p42(v336) between f74662 and f48603 - r169968 tested simplicialbot vertices: p747(v665) p702(v506) p745(v11) between f74662 and f65050 - r169784 tested simplicialtop vertices: p634(v671) p943(v495) p745(v11) between f65099 and f74662 - r169979 tested simplicialtop vertices: p747(v665) p702(v506) p42(v336) between f65053 and f74662 - r169788 tested simplicialtop vertices: p634(v671) p809(v664) p943(v495) between f65105 and f74662 - r169993 tested simplicialbot vertices: p637(v493) p435(v326) p177(v106) between f74662 and f45477 - r169753 tested simplicialtop vertices: p94(v509) p918(v202) p477(v111) between f48613 and f74662 - r169750 tested simplicialbot vertices: p94(v509) p918(v202) p93(v52) between f74662 and f48617 - r169984 tested simplicialtop vertices: p260(v743) p320(v680) p378(v34) between f74206 and f74662 - r170257 tested simplicialbot vertices: p397(v507) p868(v337) p918(v202) between f74662 and f48599 - r169859 tested simplicialbot vertices: p882(v670) p918(v202) p477(v111) between f74662 and f65094 - r170255 tested simplicialtop vertices: p958(v669) p943(v495) p89(v327) between f65080 and f74662 - r169837 tested simplicialtop vertices: p397(v507) p868(v337) p42(v336) between f48600 and f74662 - r170015 tested simplicialbot vertices: p809(v664) p943(v495) p89(v327) between f74662 and f65030 - r170072 tested simplicialbot vertices: p882(v670) p943(v495) p745(v11) between f74662 and f65087 - r169695 tested simplicialbot vertices: p809(v664) p89(v327) p259(v195) between f74662 and f65033 - r169699 tested simplicialtop vertices: p809(v664) p637(v493) p259(v195) between f65037 and f74662 - r170207 tested simplicialtop vertices: p678(v575) p695(v403) p623(v255) between f58412 and f74662 - r169799 tested simplicialtop vertices: p958(v669) p7(v494) p477(v111) between f65077 and f74662 - r170254 tested simplicialtop vertices: p882(v670) p958(v669) p477(v111) between f65091 and f74662 - r170003 tested simplicialtop vertices: p7(v494) p314(v338) p477(v111) between f45487 and f74662 - r170000 tested simplicialbot vertices: p94(v509) p314(v338) p477(v111) between f74662 and f48614 - r169726 tested simplicialtop vertices: p747(v665) p42(v336) p124(v93) between f65052 and f74662 - r169723 tested simplicialbot vertices: p868(v337) p42(v336) p124(v93) between f74662 and f22389 - r170259 tested simplicialtop vertices: p868(v337) p918(v202) p93(v52) between f22385 and f74662 - r170135 tested simplicialbot vertices: p958(v669) p503(v668) p89(v327) between f74662 and f65081 - r170236 tested simplicialtop vertices: p503(v668) p89(v327) p259(v195) between f65075 and f74662 - r169795 tested simplicialtop vertices: p958(v669) p503(v668) p7(v494) between f65082 and f74662 - r169883 tested simplicialtop vertices: p320(v680) p259(v195) p378(v34) between f65237 and f74662 - r170244 tested simplicialtop vertices: p637(v493) p435(v326) p259(v195) between f45480 and f74662 - r170286 tested simplicialbot vertices: p320(v680) p308(v508) p119(v112) between f74662 and f65244 - r170097 tested simplicialtop vertices: p308(v508) p314(v338) p326(v61) between f48605 and f74662 - r169879 tested simplicialbot vertices: p320(v680) p259(v195) p326(v61) between f74662 and f65238 - r170256 tested simplicialbot vertices: p242(v492) p695(v403) p623(v255) between f74662 and f45473 - r169913 tested simplicialbot vertices: p242(v492) p259(v195) p378(v34) between f74662 and f45438 - r170022 tested simplicialbot vertices: p242(v492) p435(v326) p259(v195) between f74662 and f45439 - r170024 tested simplicialtop vertices: p503(v668) p259(v195) p326(v61) between f65074 and f74662 - r169980 tested simplicialbot vertices: p260(v743) p320(v680) p742(v578) between f74662 and f74209 - r170100 tested simplicialtop vertices: p320(v680) p308(v508) p326(v61) between f65235 and f74662 - r169811 tested simplicialbot vertices: p7(v494) p314(v338) p326(v61) between f74662 and f45486 - r169808 tested simplicialbot vertices: p503(v668) p7(v494) p326(v61) between f74662 and f65071 - r170284 tested simplicialbot vertices: p999(v511) p159(v86) p241(v20) between f74662 and f48635 - r170203 tested simplicialbot vertices: p308(v508) p314(v338) p119(v112) between f74662 and f48606 - r169706 tested simplicialbot vertices: p153(v681) p768(v339) p33(v203) between f74662 and f65252 - r170042 tested simplicialbot vertices: p999(v511) p768(v339) p198(v174) between f74662 and f48633 - r169702 tested simplicialtop vertices: p153(v681) p422(v510) p33(v203) between f65249 and f74662 - r169843 tested simplicialtop vertices: p999(v511) p768(v339) p33(v203) between f48639 and f74662 - r170281 tested simplicialtop vertices: p153(v681) p94(v509) p314(v338) between f65247 and f74662 - r170279 tested simplicialbot vertices: p153(v681) p94(v509) p768(v339) between f74662 and f65253 - r170138 tested simplicialbot vertices: p153(v681) p422(v510) p314(v338) between f74662 and f65250 - r170282 tested simplicialtop vertices: p999(v511) p33(v203) p241(v20) between f48638 and f74662 - r170237 tested simplicialbot vertices: p999(v511) p198(v174) p159(v86) between f74662 and f48636 - r170206 tested simplicialtop vertices: p422(v510) p314(v338) p119(v112) between f48623 and f74662 - r170288 tested simplicialtop vertices: p320(v680) p742(v578) p119(v112) between f65245 and f74662 - r169997 tested simplicialtop vertices: p242(v492) p435(v326) p177(v106) between f45475 and f74662 - r170169 tested simplicialtop vertices: p242(v492) p695(v403) p378(v34) between f45440 and f74662 - r170230 tested simplicialbot vertices: p293(v574) p695(v403) p884(v146) between f74662 and f58399 - r170201 tested simplicialbot vertices: p260(v743) p579(v406) p792(v257) between f74662 and f74203 - r170165 tested simplicialtop vertices: p695(v403) p884(v146) p378(v34) between f29347 and f74662 - r170188 tested simplicialbot vertices: p260(v743) p884(v146) p378(v34) between f74662 and f74201 - r170312 tested simplicialbot vertices: p285(v745) p940(v539) p545(v126) between f74662 and f74531 - r170310 tested simplicialtop vertices: p34(v742) p282(v408) p960(v260) between f74190 and f74662 - r170311 tested simplicialbot vertices: p285(v745) p34(v742) p282(v408) between f74662 and f74529 - r170309 tested simplicialtop vertices: p285(v745) p711(v580) p282(v408) between f74527 and f74662 - r170317 tested simplicialbot vertices: p34(v742) p97(v573) p74(v253) between f74662 and f74195 - r170319 tested simplicialbot vertices: p34(v742) p195(v579) p960(v260) between f74662 and f74194 - r170318 tested simplicialtop vertices: p34(v742) p195(v579) p74(v253) between f74193 and f74662 - r170391 tested simplicialtop vertices: p678(v575) p623(v255) p177(v106) between f58405 and f74662 - r170631 tested simplicialbot vertices: p923(v748) p207(v488) p409(v147) between f74662 and f74688 - r170646 tested simplicialtop vertices: p779(v749) p329(v480) p548(v267) between f74704 and f74662 - r170643 tested simplicialbot vertices: p779(v749) p991(v414) p548(v267) between f74662 and f74706 - r170645 tested simplicialbot vertices: p779(v749) p590(v587) p991(v414) between f74662 and f74707 - r170648 tested simplicialtop vertices: p779(v749) p590(v587) p771(v154) between f74698 and f74662 - r170651 tested simplicialtop vertices: p881(v750) p590(v587) p991(v414) between f74711 and f74662 - r170649 tested simplicialtop vertices: p881(v750) p991(v414) p476(v269) between f74709 and f74662 ERRONEOUS OTHER FACET: - f75017 - flags: bottom upperDelaunay newfacet tested newmerge - merges: 1 - normal: -1.113e-12 1.107e-11 -1.237e-11 1 - offset: -0.4998369 - center: -0.02029539975225766 0.3750836276475107 -0.3275079122468065 0.4998368680877545 - vertices: p425(v780) p578(v779) p500(v619) p791(v616) p442(v286) - neighboring facets: f75003 f75012 f75013 f75015 f74662 - ridges: - r170873 tested simplicialtop simplicialbot vertices: p578(v779) p791(v616) p442(v286) between f75003 and f75017 - r170872 tested simplicialbot vertices: p425(v780) p500(v619) p442(v286) between f75017 and f75012 - r170874 tested simplicialtop simplicialbot vertices: p425(v780) p578(v779) p442(v286) between f75013 and f75017 - r170869 tested vertices: p425(v780) p500(v619) p791(v616) between f75015 and f75017 - r170875 tested simplicialtop simplicialbot vertices: p425(v780) p578(v779) p791(v616) between f75017 and f75015 - r167382 tested nonconvex vertices: p500(v619) p791(v616) p442(v286) between f75017 and f74662 While executing: rbox 1000 s W1e-13 P0 t1676184633 | qhull d Qbb Qc Q12 Tv Options selected for Qhull 2020.2.r 2020/08/31: run-id 944645485 delaunay Qbbound-last Qcoplanar-keep Q12-allow-wide Tverify _pre-merge _zero-centrum Qinterior-keep Pgood _max-width 1 Error-roundoff 1e-15 _one-merge 9.1e-15 Visible-distance 6e-15 U-max-coplanar 6e-15 Width-outside 1.2e-14 _wide-facet 3.6e-14 _maxoutside 1.5e-12 Last point added to hull was p425. Last merge was #69712. At error exit: Delaunay triangulation by the convex hull of 1001 points in 4-d: Number of input sites: 780 Total number of nearly incident points: 221 Number of Delaunay regions: 1554 Statistics for: rbox 1000 s W1e-13 P0 t1676184633 | qhull d Qbb Qc Q12 Tv Number of points processed: 780 Number of hyperplanes created: 74656 Number of facets in hull: 1629 Number of distance tests for qhull: 119788 Number of distance tests for merging: 6885970 Number of distance tests for checking: 0 Number of merged facets: 69929 Maximum distance of point above facet: 1.5e-12 (149.8x) Maximum distance of vertex below facet: -1.6e-12 (155.6x) precision problems (corrected unless 'Q0' or an error) 1267 flipped facets 157 coplanar horizon facets for new vertices 1 dupridges with multiple neighbors 44 dupridges with flip facet into good neighbor 1 dupridges with flip facet into good flip neighbor 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 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: 41 Total number of deleted points due to merging: 423 Total number of nearly incident points: 536 Number of Delaunay regions: 26 Number of non-simplicial Delaunay regions: 12 Statistics for: rbox 1000 s W1e-13 t1676184634 | qhull d Q12 Tv Number of points processed: 464 Number of hyperplanes created: 5818 Number of facets in hull: 50 Number of distance tests for qhull: 1898091 Number of distance tests for merging: 802308 Number of distance tests for checking: 50230 Number of merged facets: 5112 CPU seconds to compute hull (after input): 0.1327 Maximum distance of point above facet: 5.3e-13 (52.9x) Maximum distance of vertex below facet: -5.7e-14 (5.7x) Output completed. Verifying that all points are below outer planes of all facets. Will make 26000 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. Delaunay triangulation by the convex hull of 1000 points in 3-d: Number of input sites: 976 Total number of deleted points due to merging: 7 Total number of nearly incident points: 17 Number of Delaunay regions: 735 Number of non-simplicial Delaunay regions: 114 Statistics for: rbox 1000 s W1e-13 D2 t1676184634 | qhull d Tv Number of points processed: 983 Number of hyperplanes created: 4031 Number of facets in hull: 1404 Number of distance tests for qhull: 183778 Number of distance tests for merging: 55517 Number of distance tests for checking: 257268 Number of merged facets: 1046 CPU seconds to compute hull (after input): 0.02108 Maximum distance of point above facet: 1.8e-13 (32.4x) Maximum distance of vertex below facet: -1.2e-14 (2.2x) Output completed. Verifying that all points are below outer planes of all facets. Will make 735000 distance computations. set +v === check Qhull without merging Q0 Sun Feb 12 20:50:34 +14 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): 0.02614 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): 0.002405 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): 0.001354 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): 0.000107 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): 0.002489 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): 0.001955 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 944679099 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): 0.000703 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): 0.000699 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): 0.009728 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 944679099 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 944679099 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 Sun Feb 12 20:50:35 +14 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): 0.09198 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): 0.09014 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 944679099 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): 0.004489 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): 0.004376 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: - GIT: - news: - Geomview: - news group: - FAQ: - email: qhull@qhull.org - bug reports: qhull_bug@qhull.org Geometry Center 2019/05/03 1 qhull(1) qhull(1) The sections are: - INTRODUCTION - DESCRIPTION, a description of Qhull - IMPRECISION, how Qhull handles imprecision - OPTIONS - Input and output options - Additional input/output formats - Precision options - Geomview options - Print options - Qhull options - Trace options - BUGS - E-MAIL - SEE ALSO - AUTHORS - ACKNOWLEGEMENTS This man page briefly describes all Qhull options. Please report any mismatches with Qhull's html manual (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. Geometry Center 2019/05/03 2 qhull(1) qhull(1) Qhull implements the Quickhull algorithm for convex hull. This algorithm combines the 2-d Quickhull algorithm with the n-d beneath-beyond algorithm [c.f., Preparata & Shamos '85]. It is similar to the randomized algorithms of Clarkson and others [Clarkson et al. '93]. The main advantages of Quickhull are output sensitive performance, reduced space requirements, and automatic handling of pre- cision problems. The data structure produced by Qhull consists of vertices, ridges, and facets. A vertex is a point of the input set. A ridge is a set of d vertices and two neighboring facets. For example in 3-d, a ridge is an edge of the polyhedron. A facet is a set of ridges, a set of neighboring facets, a set of incident vertices, and a hyperplane equation. For simplicial facets, the ridges are defined by the vertices and neighboring facets. When Qhull merges two facets, it produces a non-simplicial facet. A non-simplicial facet has more than d neighbors and may share more than one ridge with a neighbor. IMPRECISION Since Qhull uses floating point arithmetic, roundoff error may occur for each calculation. This causes problems for most geometric algorithms. Qhull automatically sets option 'C-0' in 2-d, 3-d, and 4-d, or option 'Qx' in 5-d and higher. These options han- dle precision problems by merging facets. Alternatively, use option 'QJ' to joggle the input. With 'C-0', Qhull merges non-convex facets while con- structing the hull. The remaining facets are clearly con- vex. With 'Qx', Qhull merges coplanar horizon facets, flipped facets, concave facets and duplicated ridges. It merges coplanar facets after constructing the hull. With 'Qx', coplanar points may be missed, but it appears to be unlikely. To guarantee triangular output, joggle the input with option 'QJ'. Facet merging will not occur. OPTIONS To get a list of the most important options, execute 'qhull -?'. 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'), Geometry Center 2019/05/03 3 qhull(1) qhull(1) and tracing ('T'). Main options: default Compute the convex hull of the input points. Report a summary of the result. d Compute the Delaunay triangulation by lifting the input points to a paraboloid. The 'o' option prints the input points and facets. The 'QJ' option guarantees triangular output. The 'Ft' option prints a triangulation. It adds points (the centrums) to non-simplicial facets. v Compute the Voronoi diagram from the Delaunay tri- angulation. The 'p' option prints the Voronoi ver- tices. The 'o' option prints the Voronoi vertices and the vertices in each Voronoi region. It lists regions in site id order. The 'Fv' option prints each ridge of the Voronoi diagram. The first or zero'th vertex indicates the infinity vertex. Its coordinates are qh_INFINITE (-10.101). It indi- cates unbounded Voronoi regions or degenerate Delaunay triangles. Hn,n,... Compute halfspace intersection about [n,n,0,...]. The input is a set of halfspaces defined in the same format as 'n', 'Fo', and 'Fi'. Use 'Fp' to print the intersection points. Use 'Fv' to list the intersection points for each halfspace. The other output formats display the dual convex hull. The point [n,n,n,...] is a feasible point for the halfspaces, i.e., a point that is inside all of the halfspaces (Hx+b <= 0). The default coordinate value is 0. The input may start with a feasible point. If so, use 'H' by itself. The input starts with a feasi- ble point when the first number is the dimension, the second number is "1", and the coordinates com- plete a line. The 'FV' option produces a feasible point for a convex hull. d Qu Compute the furthest-site Delaunay triangulation from the upper convex hull. The 'o' option prints the input points and facets. The 'QJ' option guar- antees triangular otuput. You can also use facets. v Qu Compute the furthest-site Voronoi diagram. The 'p' option prints the Voronoi vertices. The 'o' option prints the Voronoi vertices and the vertices in Geometry Center 2019/05/03 4 qhull(1) qhull(1) each Voronoi region. The 'Fv' option prints each ridge of the Voronoi diagram. The first or zero'th vertex indicates the infinity vertex at infinity. Its coordinates are qh_INFINITE (-10.101). It indicates unbounded Voronoi regions and degenerate Delaunay triangles. Qt Triangulated output. Input/Output options: f Print 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= << ". If the object is 2-d, it can be visualized by "Show[Graphics[list]] ". For 3-d objects the command is "Show[Graphics3D[list]]". n Output the normal equation for each facet. Qhull prints the dimension (plus one), the number of facets, and the normals for each facet. The facet's offset follows its normal coefficients. o Output the facets in OFF file format. Qhull prints the dimension, number of points, number of facets, and number of ridges. Then it prints the Geometry Center 2019/05/03 5 qhull(1) qhull(1) coordinates of the input points and the vertices for each facet. Each facet is on a separate line. The first number is the number of vertices. The remainder are the indices of the corresponding points. The vertices are oriented in 2-d, 3-d, and in simplicial facets. For 2-d Voronoi diagrams, the vertices are sorted by adjacency, but not oriented. In 3-d and higher, the Voronoi vertices are sorted by index. See the 'v' option for more information. p Output the coordinates of each vertex point. Qhull prints the dimension, the number of points, and the coordinates for each vertex. With the 'Gc' and 'Gi' options, it also prints coplanar and interior points. For Voronoi diagrams, it prints the coor- dinates of each Voronoi vertex. s Print a summary to stderr. If no output options are specified, a summary goes to stdout. The summary lists the number of input points, the dimension, the number of vertices in the convex hull, the number of facets in the convex hull, the number of good facets (if 'Pg'), and statistics. The last two statistics (if needed) measure the maximum distance from a point or vertex to a facet. The number in parenthesis (e.g., 2.1x) is the ratio between the maximum distance and the worst-case distance due to merging two simplicial facets. Precision options An Maximum angle given as a cosine. If the angle between a pair of facet normals is greater than n, Qhull merges one of the facets into a neighbor. If 'n' is negative, Qhull tests angles after adding each point to the hull (pre-merging). If 'n' is posi- tive, Qhull tests angles after constructing the hull (post-merging). Both pre- and post-merging can be defined. Option 'C0' or 'C-0' is set if the corresponding 'Cn' or 'C-n' is not set. If 'Qx' is set, then 'A- n' and 'C-n' are checked after the hull is con- structed and before 'An' and 'Cn' are checked. Cn Centrum radius. If a centrum is less than n below a neighboring facet, Qhull merges one of the facets. If 'n' is negative or '-0', Qhull tests and merges facets after adding each point to the hull. This is called "pre-merging". If 'n' is Geometry Center 2019/05/03 6 qhull(1) qhull(1) positive, Qhull tests for convexity after con- structing the hull ("post-merging"). Both pre- and post-merging can be defined. For 5-d and higher, 'Qx' should be used instead of 'C-n'. Otherwise, most or all facets may be merged together. En Maximum roundoff error for distance computations. Rn Randomly perturb distance computations up to +/- n * max_coord. This option perturbs every distance, hyperplane, and angle computation. To use time as the random number seed, use option 'QR-1'. Vn Minimum distance for a facet to be visible. A facet is visible if the distance from the point to the facet is greater than 'Vn'. Without merging, the default value for 'Vn' is the round-off error ('En'). With merging, the default value is the pre-merge centrum ('C-n') in 2-d or 3--d, or three times that in other dimensions. If the outside width is specified ('Wn'), the maximum, default value for 'Vn' is 'Wn'. Un Maximum distance below a facet for a point to be coplanar to the facet. The default value is 'Vn'. Wn Minimum outside width of the hull. Points are added to the convex hull only if they are clearly outside of a facet. A point is outside of a facet if its distance to the facet is greater than 'Wn'. The normal value for 'Wn' is 'En'. If the user specifies pre-merging and does not set 'Wn', than 'Wn' is set to the premerge 'Cn' and maxco- ord*(1-An). Additional input/output formats Fa Print area for each facet. For Delaunay triangula- tions, the area is the area of the triangle. For Voronoi diagrams, the area is the area of the dual facet. Use 'PAn' for printing the n largest facets, and option 'PFn' for printing facets larger than 'n'. The area for non-simplicial facets is the sum of the areas for each ridge to the centrum. Vertices far below the facet's hyperplane are ignored. The reported area may be significantly less than the actual area. Geometry Center 2019/05/03 7 qhull(1) qhull(1) FA Compute the total area and volume for option 's'. It is an approximation for non-simplicial facets (see 'Fa'). Fc Print coplanar points for each facet. The output starts with the number of facets. Then each facet is printed one per line. Each line is the number of coplanar points followed by the point ids. Option 'Qi' includes the interior points. Each coplanar point (interior point) is assigned to the facet it is furthest above (resp., least below). FC Print centrums for each facet. The output starts with the dimension followed by the number of facets. Then each facet centrum is printed, one per line. Fd Read input in cdd format with homogeneous points. The input starts with comments. The first comment is reported in the summary. Data starts after a "begin" line. The next line is the number of points followed by the dimension+1 and "real" or "integer". Then the points are listed with a leading "1" or "1.0". The data ends with an "end" line. For halfspaces ('Fd Hn,n,...'), the input format is the same. Each halfspace starts with its offset. The sign of the offset is the opposite of Qhull's convention. FD Print normals ('n', 'Fo', 'Fi') or points ('p') in cdd format. The first line is the command line that invoked Qhull. Data starts with a "begin" line. The next line is the number of normals or points followed by the dimension+1 and "real". Then the normals or points are listed with the offset before the coefficients. The offset for points is 1.0. The offset for normals has the opposite sign. The data ends with an "end" line. FF Print facets (as in 'f') without printing the ridges. Fi Print inner planes for each facet. The inner plane is below all vertices. Fi Print separating hyperplanes for bounded, inner regions of the Voronoi diagram. The first line is the number of ridges. Then each hyperplane is printed, one per line. A line starts with the num- ber of indices and floats. The first pair lists adjacent input sites, the next d floats are the normalized coefficients for the hyperplane, and the Geometry Center 2019/05/03 8 qhull(1) qhull(1) 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 Geometry Center 2019/05/03 9 qhull(1) qhull(1) facet of the dual polytope. The "infinity" point [-10.101,-10.101,...] indicates an unbounded intersection. FP For each coplanar point ('Qc') print the point id of the nearest vertex, the point id, the facet id, and the distance. FQ Print command used for qhull and input. Fs Print a summary. The first line consists of the number of integers ("7"), followed by the dimen- sion, the number of points, the number of vertices, the number of facets, the number of vertices selected for output, the number of facets selected for output, the number of coplanar points selected for output. The second line consists of the number of reals ("2"), followed by the maxmimum offset to an outer plane and and minimum offset to an inner plane. Roundoff is included. Later versions of Qhull may produce additional integers or reals. FS Print the size of the hull. The first line con- sists of the number of integers ("0"). The second line consists of the number of reals ("2"), fol- lowed by the total facet area, and the total vol- ume. Later versions of Qhull may produce addi- tional integers or reals. The total volume measures the volume of the inter- section of the halfspaces defined by each facet. Both area and volume are approximations for non- simplicial facets. See option 'Fa'. Ft Print a triangulation with added points for non- simplicial facets. The first line is the dimension and the second line is the number of points and the number of facets. The points follow, one per line, then the facets follow as a list of point indices. With option points include the point-at-infinity. Fv Print vertices for each facet. The first line is the number of facets. Then each facet is printed, one per line. Each line is the number of vertices followed by the corresponding point ids. Vertices are listed in the order they were added to the hull (the last one is first). Fv Print all ridges of a Voronoi diagram. The first line is the number of ridges. Then each ridge is printed, one per line. A line starts with the num- ber of indices. The first pair lists adjacent Geometry Center 2019/05/03 10 qhull(1) qhull(1) input sites, the remaining indices list Voronoi vertices. Vertex '0' indicates the vertex-at- infinity (i.e., an unbounded ray). In 3-d, the vertices are listed in order. See 'Fi' and 'Fo' for separating hyperplanes. FV Print average vertex. The average vertex is a fea- sible point for halfspace intersection. Fx List extreme points (vertices) of the convex hull. The first line is the number of points. The other lines give the indices of the corresponding points. The first point is '0'. In 2-d, the points occur in counter-clockwise order; otherwise they occur in input order. For Delaunay triangulations, 'Fx' lists the extreme points of the input sites. The points are unordered. Geomview options G Produce a file for viewing with Geomview. Without other options, Qhull displays edges in 2-d, outer planes in 3-d, and ridges in 4-d. A ridge can be explicit or implicit. An explicit ridge is a dim-1 dimensional simplex between two facets. In 4-d, the explicit ridges are triangles. When displaying a ridge in 4-d, Qhull projects the ridge's vertices to one of its facets' hyperplanes. Use 'Gh' to project ridges to the intersection of both hyper- planes. Ga Display all input points as dots. Gc Display the centrum for each facet in 3-d. The centrum is defined by a green radius sitting on a blue plane. The plane corresponds to the facet's hyperplane. The radius is defined by 'C-n' or 'Cn'. GDn Drop dimension n in 3-d or 4-d. The result is a 2-d or 3-d object. Gh Display hyperplane intersections in 3-d and 4-d. In 3-d, the intersection is a black line. It lies on two neighboring hyperplanes (c.f., the blue squares associated with centrums ('Gc')). In 4-d, the ridges are projected to the intersection of both hyperplanes. Gi Display inner planes in 2-d and 3-d. The inner plane of a facet is below all of its vertices. It is parallel to the facet's hyperplane. The inner plane's color is the opposite (1-r,1-g,1-b) of the Geometry Center 2019/05/03 11 qhull(1) qhull(1) outer plane. Its edges are determined by the ver- tices. Gn Do not display inner or outer planes. By default, Geomview displays the precise plane (no merging) or both inner and output planes (merging). Under merging, Geomview does not display the inner plane if the the difference between inner and outer is too small. Go Display outer planes in 2-d and 3-d. The outer plane of a facet is above all input points. It is parallel to the facet's hyperplane. Its color is determined by the facet's normal, and its edges are determined by the vertices. Gp Display coplanar points and vertices as radii. A radius defines a ball which corresponds to the imprecision of the point. The imprecision is the maximum of the roundoff error, the centrum radius, and maxcoord * (1-An). It is at least 1/20'th of the maximum coordinate, and ignores post-merging if pre-merging is done. Gr Display ridges in 3-d. A ridge connects the two vertices that are shared by neighboring facets. Ridges are always displayed in 4-d. Gt A 3-d Delaunay triangulation looks like a convex hull with interior facets. Option 'Gt' removes the outside ridges to reveal the outermost facets. It automatically sets options 'Gr' and 'GDn'. Gv Display vertices as spheres. The radius of the sphere corresponds to the imprecision of the data. See 'Gp' for determining the radius. Print options PAn Only the n largest facets are marked good for printing. Unless 'PG' is set, 'Pg' is automati- cally set. Pdk:n Drop facet from output if normal[k] <= n. The option 'Pdk' uses the default value of 0 for n. PDk:n Drop facet from output if normal[k] >= n. The option 'PDk' uses the default value of 0 for n. PFn Only facets with area at least 'n' are marked good for printing. Unless 'PG' is set, 'Pg' is automat- ically set. Geometry Center 2019/05/03 12 qhull(1) qhull(1) Pg Print only good facets. A good facet is either visible from a point (the 'QGn' option) or includes a point (the 'QVn' option). It also meets the requirements of 'Pdk' and 'PDk' options. Option 'Pg' is automatically set for options '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. Geometry Center 2019/05/03 13 qhull(1) qhull(1) QBk:n Scale the k'th coordinate of the input points. After scaling, the upper bound will be n. 'QBk' scales to +0.5. Qc Keep coplanar points with the nearest facet. Out- put formats 'p', 'f', 'Gp', 'Fc', 'FN', and 'FP' will print the points. Qf Partition points to the furthest outside facet. Qg Only build good facets. With the 'Qg' option, Qhull will only build those facets that it needs to determine the good facets in the output. See 'QGn', 'QVn', and 'PdD' for defining good facets, and 'Pg' and 'PG' for printing good facets and their neighbors. QGn A facet is good (see 'Qg' and 'Pg') if it is visi- ble from point n. If n < 0, a facet is good if it is not visible from point n. Point n is not added to the hull (unless 'TCn' or 'TPn'). With rbox, use the 'Pn,m,r' option to define your point; it will be point 0 (QG0). Qi Keep interior points with the nearest facet. Out- put formats 'p', 'f', 'Gp', 'FN', 'FP', and 'Fc' will print the points. QJn Joggle each input coordinate by adding a random number in [-n,n]. If a precision error occurs, then qhull increases n and tries again. It does not increase n beyond a certain value, and it stops after a certain number of attempts [see user.h]. Option 'QJ' selects a default value for n. The output will be simplicial. For Delaunay triangula- tions, 'QJn' sets 'Qbb' to scale the last coordi- nate (not if 'Qbk:n' or 'QBk:n' is set). 'QJn' is deprecated for Voronoi diagrams. See also 'Qt'. Qm Only process points that would otherwise increase max_outside. Other points are treated as coplanar or interior points. Qr Process random outside points instead of furthest ones. This makes Qhull equivalent to the random- ized incremental algorithms. CPU time is not reported since the randomization is inefficient. QRn Randomly rotate the input points. If n=0, use time as the random number seed. If n>0, use n as the random number seed. If n=-1, don't rotate but use time as the random number seed. For Delaunay tri- angulations ('d' and 'v'), rotate about the last axis. Geometry Center 2019/05/03 14 qhull(1) qhull(1) Qs Search all points for the initial simplex. Qt Triangulated output. Triangulate non-simplicial facets. 'Qt' is deprecated for Voronoi diagrams. See also 'QJn' Qv Test vertex neighbors for convexity after post- merging. To use the 'Qv' option, you also need to set a merge option (e.g., 'Qx' or 'C-0'). QVn A good facet (see 'Qg' and 'Pg') includes point n. If n<0, then a good facet does not include point n. The point is either in the initial simplex or it is the first point added to the hull. Option 'QVn' may not be used with merging. 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 '/build/qhull-2020.2' create-stamp debian/debhelper-build-stamp dh_testroot -O--buildsystem=cmake dh_prep -O--buildsystem=cmake debian/rules override_dh_auto_install make[1]: Entering directory '/build/qhull-2020.2' dh_auto_install --buildsystem=cmake cd obj-x86_64-linux-gnu && make -j16 install DESTDIR=/build/qhull-2020.2/debian/tmp AM_UPDATE_INFO_DIR=no "INSTALL=install --strip-program=true" make[2]: Entering directory '/build/qhull-2020.2/obj-x86_64-linux-gnu' /usr/bin/cmake -S/build/qhull-2020.2 -B/build/qhull-2020.2/obj-x86_64-linux-gnu --check-build-system CMakeFiles/Makefile.cmake 0 make -f CMakeFiles/Makefile2 preinstall make[3]: Entering directory '/build/qhull-2020.2/obj-x86_64-linux-gnu' make[3]: Nothing to be done for 'preinstall'. make[3]: Leaving directory '/build/qhull-2020.2/obj-x86_64-linux-gnu' Install the project... /usr/bin/cmake -P cmake_install.cmake -- 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/build/qhull-2020.2/debian/tmp/usr/share/doc/libqhull-dev/qhull/html/qh--cone.gif -- Installing: /build/qhull-2020.2/debian/tmp/usr/share/doc/libqhull-dev/qhull/html/qh--4d.gif -- Installing: /build/qhull-2020.2/debian/tmp/usr/share/doc/libqhull-dev/qhull/html/qdelau_f.htm -- Installing: /build/qhull-2020.2/debian/tmp/usr/share/doc/libqhull-dev/qhull/html/qdelaun.htm -- Installing: /build/qhull-2020.2/debian/tmp/usr/share/doc/libqhull-dev/qhull/html/qconvex.htm -- Installing: /build/qhull-2020.2/debian/tmp/usr/share/doc/libqhull-dev/qhull/html/normal_voronoi_knauss_oesterle.jpg -- Installing: /build/qhull-2020.2/debian/tmp/usr/share/doc/libqhull-dev/qhull/html/index.htm -- Installing: /build/qhull-2020.2/debian/tmp/usr/share/doc/libqhull-dev/qhull/src/Changes.txt make[2]: Leaving directory '/build/qhull-2020.2/obj-x86_64-linux-gnu' make[1]: Leaving directory '/build/qhull-2020.2' debian/rules execute_after_dh_auto_install make[1]: Entering directory '/build/qhull-2020.2' 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 '/build/qhull-2020.2' dh_install -O--buildsystem=cmake dh_installdocs -O--buildsystem=cmake debian/rules override_dh_installchangelogs make[1]: Entering directory '/build/qhull-2020.2' dh_installchangelogs src/Changes.txt make[1]: Leaving directory '/build/qhull-2020.2' dh_installexamples -O--buildsystem=cmake dh_installman -O--buildsystem=cmake dh_installsystemduser -O--buildsystem=cmake dh_perl -O--buildsystem=cmake debian/rules execute_before_dh_link-indep make[1]: Entering directory '/build/qhull-2020.2' mkdir -p debian/libqhull-doc/usr/share/doc/libqhull-dev/qhull/src/libqhull_r 'debian/libqhull-doc/usr/share/doc/libqhull-dev/qhull/src/libqhull_r/geom_r.h' -> '/usr/include/libqhull_r/geom_r.h' 'debian/libqhull-doc/usr/share/doc/libqhull-dev/qhull/src/libqhull_r/io_r.h' -> '/usr/include/libqhull_r/io_r.h' 'debian/libqhull-doc/usr/share/doc/libqhull-dev/qhull/src/libqhull_r/libqhull_r.h' -> '/usr/include/libqhull_r/libqhull_r.h' 'debian/libqhull-doc/usr/share/doc/libqhull-dev/qhull/src/libqhull_r/mem_r.h' -> '/usr/include/libqhull_r/mem_r.h' 'debian/libqhull-doc/usr/share/doc/libqhull-dev/qhull/src/libqhull_r/merge_r.h' -> '/usr/include/libqhull_r/merge_r.h' 'debian/libqhull-doc/usr/share/doc/libqhull-dev/qhull/src/libqhull_r/poly_r.h' -> '/usr/include/libqhull_r/poly_r.h' 'debian/libqhull-doc/usr/share/doc/libqhull-dev/qhull/src/libqhull_r/qhull_ra.h' -> '/usr/include/libqhull_r/qhull_ra.h' 'debian/libqhull-doc/usr/share/doc/libqhull-dev/qhull/src/libqhull_r/qset_r.h' -> '/usr/include/libqhull_r/qset_r.h' 'debian/libqhull-doc/usr/share/doc/libqhull-dev/qhull/src/libqhull_r/random_r.h' -> '/usr/include/libqhull_r/random_r.h' 'debian/libqhull-doc/usr/share/doc/libqhull-dev/qhull/src/libqhull_r/stat_r.h' -> '/usr/include/libqhull_r/stat_r.h' 'debian/libqhull-doc/usr/share/doc/libqhull-dev/qhull/src/libqhull_r/user_r.h' -> '/usr/include/libqhull_r/user_r.h' make[1]: Leaving directory '/build/qhull-2020.2' dh_link -O--buildsystem=cmake dh_strip_nondeterminism -O--buildsystem=cmake debian/rules override_dh_compress make[1]: Entering directory '/build/qhull-2020.2' dh_compress -X.c -X.h -X.txt make[1]: Leaving directory '/build/qhull-2020.2' dh_fixperms -O--buildsystem=cmake dh_missing -O--buildsystem=cmake dh_dwz -a -O--buildsystem=cmake dh_strip -a -O--buildsystem=cmake dh_makeshlibs -a -O--buildsystem=cmake dh_shlibdeps -a -O--buildsystem=cmake dh_installdeb -O--buildsystem=cmake dh_gencontrol -O--buildsystem=cmake dh_md5sums -O--buildsystem=cmake dh_builddeb -O--buildsystem=cmake dpkg-deb: building package 'libqhull8.0' in '../libqhull8.0_2020.2-3_amd64.deb'. dpkg-deb: building package 'libqhull8.0-dbgsym' in '../libqhull8.0-dbgsym_2020.2-3_amd64.deb'. dpkg-deb: building package 'libqhull-r8.0-dbgsym' in '../libqhull-r8.0-dbgsym_2020.2-3_amd64.deb'. dpkg-deb: building package 'libqhull-r8.0' in '../libqhull-r8.0_2020.2-3_amd64.deb'. dpkg-deb: building package 'libqhullcpp8.0' in '../libqhullcpp8.0_2020.2-3_amd64.deb'. dpkg-deb: building package 'libqhullcpp8.0-dbgsym' in '../libqhullcpp8.0-dbgsym_2020.2-3_amd64.deb'. dpkg-deb: building package 'libqhull-doc' in '../libqhull-doc_2020.2-3_all.deb'. dpkg-deb: building package 'libqhull-dev' in '../libqhull-dev_2020.2-3_amd64.deb'. dpkg-deb: building package 'qhull-bin' in '../qhull-bin_2020.2-3_amd64.deb'. dpkg-deb: building package 'qhull-bin-dbgsym' in '../qhull-bin-dbgsym_2020.2-3_amd64.deb'. dpkg-genbuildinfo --build=binary dpkg-genchanges --build=binary >../qhull_2020.2-3_amd64.changes dpkg-genchanges: info: binary-only upload (no source code included) dpkg-source --after-build . dpkg-buildpackage: info: binary-only upload (no source included) dpkg-genchanges: info: not including original source code in upload I: copying local configuration I: user script /srv/workspace/pbuilder/2609468/tmp/hooks/B01_cleanup starting I: user script /srv/workspace/pbuilder/2609468/tmp/hooks/B01_cleanup finished I: unmounting dev/ptmx filesystem I: unmounting dev/pts filesystem I: unmounting dev/shm filesystem I: unmounting proc filesystem I: unmounting sys filesystem I: cleaning the build env I: removing directory /srv/workspace/pbuilder/2609468 and its subdirectories I: Current time: Sun Feb 12 20:50:44 +14 2023 I: pbuilder-time-stamp: 1676184644