diff options
Diffstat (limited to 'Build/source/utils/asymptote/doc')
| -rw-r--r-- | Build/source/utils/asymptote/doc/CAD.pdf | bin | 198487 -> 198543 bytes | |||
| -rw-r--r-- | Build/source/utils/asymptote/doc/FAQ/asy-faq.info | 2 | ||||
| -rwxr-xr-x | Build/source/utils/asymptote/doc/FAQ/install-sh | 443 | ||||
| -rw-r--r-- | Build/source/utils/asymptote/doc/TeXShopAndAsymptote.pdf | bin | 81303 -> 81270 bytes | |||
| -rw-r--r-- | Build/source/utils/asymptote/doc/asy-latex.dtx | 4 | ||||
| -rw-r--r-- | Build/source/utils/asymptote/doc/asy-latex.pdf | bin | 208908 -> 209130 bytes | |||
| -rw-r--r-- | Build/source/utils/asymptote/doc/asy.1 | 7 | ||||
| -rw-r--r-- | Build/source/utils/asymptote/doc/asyRefCard.pdf | bin | 121145 -> 121145 bytes | |||
| -rw-r--r-- | Build/source/utils/asymptote/doc/asymptote.pdf | bin | 1288667 -> 1303978 bytes | |||
| -rw-r--r-- | Build/source/utils/asymptote/doc/asymptote.sty | 4 | ||||
| -rw-r--r-- | Build/source/utils/asymptote/doc/asymptote.texi | 178 | ||||
| -rwxr-xr-x | Build/source/utils/asymptote/doc/install-sh | 443 | ||||
| -rw-r--r-- | Build/source/utils/asymptote/doc/latexmkrc | 3 | ||||
| -rw-r--r-- | Build/source/utils/asymptote/doc/latexmkrc_asydir | 4 | ||||
| -rw-r--r-- | Build/source/utils/asymptote/doc/png/asymptote.info | 6450 |
15 files changed, 3845 insertions, 3693 deletions
diff --git a/Build/source/utils/asymptote/doc/CAD.pdf b/Build/source/utils/asymptote/doc/CAD.pdf Binary files differindex 404c5f0e5b6..306c5309f15 100644 --- a/Build/source/utils/asymptote/doc/CAD.pdf +++ b/Build/source/utils/asymptote/doc/CAD.pdf diff --git a/Build/source/utils/asymptote/doc/FAQ/asy-faq.info b/Build/source/utils/asymptote/doc/FAQ/asy-faq.info index d2b3fcbec85..8a47fafe0cb 100644 --- a/Build/source/utils/asymptote/doc/FAQ/asy-faq.info +++ b/Build/source/utils/asymptote/doc/FAQ/asy-faq.info @@ -10,7 +10,7 @@ END-INFO-DIR-ENTRY File: asy-faq.info, Node: Top, Next: Question 1.1, Up: (dir) ASYMPTOTE FREQUENTLY ASKED QUESTIONS - 2023-02-09 + 2024-02-27 This is the list of Frequently Asked Questions about Asymptote (asy). diff --git a/Build/source/utils/asymptote/doc/FAQ/install-sh b/Build/source/utils/asymptote/doc/FAQ/install-sh index 7c56c9c0151..6781b987bdb 100755 --- a/Build/source/utils/asymptote/doc/FAQ/install-sh +++ b/Build/source/utils/asymptote/doc/FAQ/install-sh @@ -1,7 +1,7 @@ #!/bin/sh # install - install a program, script, or datafile -scriptversion=2023-11-23.18; # UTC +scriptversion=2009-04-28.21; # UTC # This originates from X11R5 (mit/util/scripts/install.sh), which was # later released in X11R6 (xc/config/util/install.sh) with the @@ -35,21 +35,25 @@ scriptversion=2023-11-23.18; # UTC # FSF changes to this file are in the public domain. # # Calling this script install-sh is preferred over install.sh, to prevent -# 'make' implicit rules from creating a file called install from it +# `make' implicit rules from creating a file called install from it # when there is no Makefile. # # This script is compatible with the BSD install script, but was written # from scratch. -tab=' ' nl=' ' -IFS=" $tab$nl" +IFS=" "" $nl" -# Set DOITPROG to "echo" to test this script. +# set DOITPROG to echo to test this script +# Don't use :- since 4.3BSD and earlier shells don't like it. doit=${DOITPROG-} -doit_exec=${doit:-exec} +if test -z "$doit"; then + doit_exec=exec +else + doit_exec=$doit +fi # Put in absolute file names if you don't have them in your path; # or use environment vars. @@ -64,16 +68,22 @@ mvprog=${MVPROG-mv} rmprog=${RMPROG-rm} stripprog=${STRIPPROG-strip} +posix_glob='?' +initialize_posix_glob=' + test "$posix_glob" != "?" || { + if (set -f) 2>/dev/null; then + posix_glob= + else + posix_glob=: + fi + } +' + posix_mkdir= # Desired mode of installed file. mode=0755 -# Create dirs (including intermediate dirs) using mode 755. -# This is like GNU 'install' as of coreutils 8.32 (2020). -mkdir_umask=22 - -backupsuffix= chgrpcmd= chmodcmd=$chmodprog chowncmd= @@ -87,7 +97,7 @@ dir_arg= dst_arg= copy_on_change=false -is_target_a_directory=possibly +no_target_directory= usage="\ Usage: $0 [OPTION]... [-T] SRCFILE DSTFILE @@ -104,29 +114,19 @@ Options: --version display version info and exit. -c (ignored) - -C install only if different (preserve data modification time) + -C install only if different (preserve the last data modification time) -d create directories instead of installing files. -g GROUP $chgrpprog installed files to GROUP. -m MODE $chmodprog installed files to MODE. -o USER $chownprog installed files to USER. - -p pass -p to $cpprog. -s $stripprog installed files. - -S SUFFIX attempt to back up existing files, with suffix SUFFIX. -t DIRECTORY install into DIRECTORY. -T report an error if DSTFILE is a directory. Environment variables override the default commands: CHGRPPROG CHMODPROG CHOWNPROG CMPPROG CPPROG MKDIRPROG MVPROG RMPROG STRIPPROG - -By default, rm is invoked with -f; when overridden with RMPROG, -it's up to you to specify -f if you want it. - -If -S is not specified, no backups are attempted. - -Report bugs to <bug-automake@gnu.org>. -GNU Automake home page: <https://www.gnu.org/software/automake/>. -General help using GNU software: <https://www.gnu.org/gethelp/>." +" while test $# -ne 0; do case $1 in @@ -137,62 +137,42 @@ while test $# -ne 0; do -d) dir_arg=true;; -g) chgrpcmd="$chgrpprog $2" - shift;; + shift;; --help) echo "$usage"; exit $?;; -m) mode=$2 - case $mode in - *' '* | *"$tab"* | *"$nl"* | *'*'* | *'?'* | *'['*) - echo "$0: invalid mode: $mode" >&2 - exit 1;; - esac - shift;; + case $mode in + *' '* | *' '* | *' +'* | *'*'* | *'?'* | *'['*) + echo "$0: invalid mode: $mode" >&2 + exit 1;; + esac + shift;; -o) chowncmd="$chownprog $2" - shift;; - - -p) cpprog="$cpprog -p";; + shift;; -s) stripcmd=$stripprog;; - -S) backupsuffix="$2" - shift;; - - -t) - is_target_a_directory=always - dst_arg=$2 - # Protect names problematic for 'test' and other utilities. - case $dst_arg in - -* | [=\(\)!]) dst_arg=./$dst_arg;; - esac - shift;; + -t) dst_arg=$2 + shift;; - -T) is_target_a_directory=never;; + -T) no_target_directory=true;; --version) echo "$0 $scriptversion"; exit $?;; - --) shift - break;; + --) shift + break;; - -*) echo "$0: invalid option: $1" >&2 - exit 1;; + -*) echo "$0: invalid option: $1" >&2 + exit 1;; *) break;; esac shift done -# We allow the use of options -d and -T together, by making -d -# take the precedence; this is for compatibility with GNU install. - -if test -n "$dir_arg"; then - if test -n "$dst_arg"; then - echo "$0: target directory not allowed when installing a directory." >&2 - exit 1 - fi -fi - if test $# -ne 0 && test -z "$dir_arg$dst_arg"; then # When -d is used, all remaining arguments are directories to create. # When -t is used, the destination is already specified. @@ -206,10 +186,6 @@ if test $# -ne 0 && test -z "$dir_arg$dst_arg"; then fi shift # arg dst_arg=$arg - # Protect names problematic for 'test' and other utilities. - case $dst_arg in - -* | [=\(\)!]) dst_arg=./$dst_arg;; - esac done fi @@ -218,26 +194,13 @@ if test $# -eq 0; then echo "$0: no input file specified." >&2 exit 1 fi - # It's OK to call 'install-sh -d' without argument. + # It's OK to call `install-sh -d' without argument. # This can happen when creating conditional directories. exit 0 fi if test -z "$dir_arg"; then - if test $# -gt 1 || test "$is_target_a_directory" = always; then - if test ! -d "$dst_arg"; then - echo "$0: $dst_arg: Is not a directory." >&2 - exit 1 - fi - fi -fi - -if test -z "$dir_arg"; then - do_exit='(exit $ret); exit $ret' - trap "ret=129; $do_exit" 1 - trap "ret=130; $do_exit" 2 - trap "ret=141; $do_exit" 13 - trap "ret=143; $do_exit" 15 + trap '(exit $?); exit' 1 2 13 15 # Set umask so as not to create temps with too-generous modes. # However, 'strip' requires both read and write access to temps. @@ -248,16 +211,16 @@ if test -z "$dir_arg"; then *[0-7]) if test -z "$stripcmd"; then - u_plus_rw= + u_plus_rw= else - u_plus_rw='% 200' + u_plus_rw='% 200' fi cp_umask=`expr '(' 777 - $mode % 1000 ')' $u_plus_rw`;; *) if test -z "$stripcmd"; then - u_plus_rw= + u_plus_rw= else - u_plus_rw=,u+rw + u_plus_rw=,u+rw fi cp_umask=$mode$u_plus_rw;; esac @@ -265,9 +228,9 @@ fi for src do - # Protect names problematic for 'test' and other utilities. + # Protect names starting with `-'. case $src in - -* | [=\(\)!]) src=./$src;; + -*) src=./$src;; esac if test -n "$dir_arg"; then @@ -275,10 +238,6 @@ do dstdir=$dst test -d "$dstdir" dstdir_status=$? - # Don't chown directories that already exist. - if test $dstdir_status = 0; then - chowncmd="" - fi else # Waiting for this to be detected by the "$cpprog $src $dsttmp" command @@ -293,150 +252,185 @@ do echo "$0: no destination specified." >&2 exit 1 fi + dst=$dst_arg + # Protect names starting with `-'. + case $dst in + -*) dst=./$dst;; + esac - # If destination is a directory, append the input filename. + # If destination is a directory, append the input filename; won't work + # if double slashes aren't ignored. if test -d "$dst"; then - if test "$is_target_a_directory" = never; then - echo "$0: $dst_arg: Is a directory" >&2 - exit 1 + if test -n "$no_target_directory"; then + echo "$0: $dst_arg: Is a directory" >&2 + exit 1 fi dstdir=$dst - dstbase=`basename "$src"` - case $dst in - */) dst=$dst$dstbase;; - *) dst=$dst/$dstbase;; - esac + dst=$dstdir/`basename "$src"` dstdir_status=0 else - dstdir=`dirname "$dst"` + # Prefer dirname, but fall back on a substitute if dirname fails. + dstdir=` + (dirname "$dst") 2>/dev/null || + expr X"$dst" : 'X\(.*[^/]\)//*[^/][^/]*/*$' \| \ + X"$dst" : 'X\(//\)[^/]' \| \ + X"$dst" : 'X\(//\)$' \| \ + X"$dst" : 'X\(/\)' \| . 2>/dev/null || + echo X"$dst" | + sed '/^X\(.*[^/]\)\/\/*[^/][^/]*\/*$/{ + s//\1/ + q + } + /^X\(\/\/\)[^/].*/{ + s//\1/ + q + } + /^X\(\/\/\)$/{ + s//\1/ + q + } + /^X\(\/\).*/{ + s//\1/ + q + } + s/.*/./; q' + ` + test -d "$dstdir" dstdir_status=$? fi fi - case $dstdir in - */) dstdirslash=$dstdir;; - *) dstdirslash=$dstdir/;; - esac - obsolete_mkdir_used=false if test $dstdir_status != 0; then case $posix_mkdir in '') - # With -d, create the new directory with the user-specified mode. - # Otherwise, rely on $mkdir_umask. - if test -n "$dir_arg"; then - mkdir_mode=-m$mode - else - mkdir_mode= - fi - - posix_mkdir=false - # The $RANDOM variable is not portable (e.g., dash). Use it - # here however when possible just to lower collision chance. - tmpdir=${TMPDIR-/tmp}/ins$RANDOM-$$ - - trap ' - ret=$? - rmdir "$tmpdir/a/b" "$tmpdir/a" "$tmpdir" 2>/dev/null - exit $ret - ' 0 - - # Because "mkdir -p" follows existing symlinks and we likely work - # directly in world-writeable /tmp, make sure that the '$tmpdir' - # directory is successfully created first before we actually test - # 'mkdir -p'. - if (umask $mkdir_umask && - $mkdirprog $mkdir_mode "$tmpdir" && - exec $mkdirprog $mkdir_mode -p -- "$tmpdir/a/b") >/dev/null 2>&1 - then - if test -z "$dir_arg" || { - # Check for POSIX incompatibilities with -m. - # HP-UX 11.23 and IRIX 6.5 mkdir -m -p sets group- or - # other-writable bit of parent directory when it shouldn't. - # FreeBSD 6.1 mkdir -m -p sets mode of existing directory. - test_tmpdir="$tmpdir/a" - ls_ld_tmpdir=`ls -ld "$test_tmpdir"` - case $ls_ld_tmpdir in - d????-?r-*) different_mode=700;; - d????-?--*) different_mode=755;; - *) false;; - esac && - $mkdirprog -m$different_mode -p -- "$test_tmpdir" && { - ls_ld_tmpdir_1=`ls -ld "$test_tmpdir"` - test "$ls_ld_tmpdir" = "$ls_ld_tmpdir_1" - } - } - then posix_mkdir=: - fi - rmdir "$tmpdir/a/b" "$tmpdir/a" "$tmpdir" + # Create intermediate dirs using mode 755 as modified by the umask. + # This is like FreeBSD 'install' as of 1997-10-28. + umask=`umask` + case $stripcmd.$umask in + # Optimize common cases. + *[2367][2367]) mkdir_umask=$umask;; + .*0[02][02] | .[02][02] | .[02]) mkdir_umask=22;; + + *[0-7]) + mkdir_umask=`expr $umask + 22 \ + - $umask % 100 % 40 + $umask % 20 \ + - $umask % 10 % 4 + $umask % 2 + `;; + *) mkdir_umask=$umask,go-w;; + esac + + # With -d, create the new directory with the user-specified mode. + # Otherwise, rely on $mkdir_umask. + if test -n "$dir_arg"; then + mkdir_mode=-m$mode else - # Remove any dirs left behind by ancient mkdir implementations. - rmdir ./$mkdir_mode ./-p ./-- "$tmpdir" 2>/dev/null + mkdir_mode= fi - trap '' 0;; + + posix_mkdir=false + case $umask in + *[123567][0-7][0-7]) + # POSIX mkdir -p sets u+wx bits regardless of umask, which + # is incompatible with FreeBSD 'install' when (umask & 300) != 0. + ;; + *) + tmpdir=${TMPDIR-/tmp}/ins$RANDOM-$$ + trap 'ret=$?; rmdir "$tmpdir/d" "$tmpdir" 2>/dev/null; exit $ret' 0 + + if (umask $mkdir_umask && + exec $mkdirprog $mkdir_mode -p -- "$tmpdir/d") >/dev/null 2>&1 + then + if test -z "$dir_arg" || { + # Check for POSIX incompatibilities with -m. + # HP-UX 11.23 and IRIX 6.5 mkdir -m -p sets group- or + # other-writeable bit of parent directory when it shouldn't. + # FreeBSD 6.1 mkdir -m -p sets mode of existing directory. + ls_ld_tmpdir=`ls -ld "$tmpdir"` + case $ls_ld_tmpdir in + d????-?r-*) different_mode=700;; + d????-?--*) different_mode=755;; + *) false;; + esac && + $mkdirprog -m$different_mode -p -- "$tmpdir" && { + ls_ld_tmpdir_1=`ls -ld "$tmpdir"` + test "$ls_ld_tmpdir" = "$ls_ld_tmpdir_1" + } + } + then posix_mkdir=: + fi + rmdir "$tmpdir/d" "$tmpdir" + else + # Remove any dirs left behind by ancient mkdir implementations. + rmdir ./$mkdir_mode ./-p ./-- 2>/dev/null + fi + trap '' 0;; + esac;; esac if $posix_mkdir && ( - umask $mkdir_umask && - $doit_exec $mkdirprog $mkdir_mode -p -- "$dstdir" + umask $mkdir_umask && + $doit_exec $mkdirprog $mkdir_mode -p -- "$dstdir" ) then : else - # mkdir does not conform to POSIX, + # The umask is ridiculous, or mkdir does not conform to POSIX, # or it failed possibly due to a race condition. Create the # directory the slow way, step by step, checking for races as we go. case $dstdir in - /*) prefix='/';; - [-=\(\)!]*) prefix='./';; - *) prefix='';; + /*) prefix='/';; + -*) prefix='./';; + *) prefix='';; esac + eval "$initialize_posix_glob" + oIFS=$IFS IFS=/ - set -f + $posix_glob set -f set fnord $dstdir shift - set +f + $posix_glob set +f IFS=$oIFS prefixes= for d do - test X"$d" = X && continue - - prefix=$prefix$d - if test -d "$prefix"; then - prefixes= - else - if $posix_mkdir; then - (umask $mkdir_umask && - $doit_exec $mkdirprog $mkdir_mode -p -- "$dstdir") && break - # Don't fail if two instances are running concurrently. - test -d "$prefix" || exit 1 - else - case $prefix in - *\'*) qprefix=`echo "$prefix" | sed "s/'/'\\\\\\\\''/g"`;; - *) qprefix=$prefix;; - esac - prefixes="$prefixes '$qprefix'" - fi - fi - prefix=$prefix/ + test -z "$d" && continue + + prefix=$prefix$d + if test -d "$prefix"; then + prefixes= + else + if $posix_mkdir; then + (umask=$mkdir_umask && + $doit_exec $mkdirprog $mkdir_mode -p -- "$dstdir") && break + # Don't fail if two instances are running concurrently. + test -d "$prefix" || exit 1 + else + case $prefix in + *\'*) qprefix=`echo "$prefix" | sed "s/'/'\\\\\\\\''/g"`;; + *) qprefix=$prefix;; + esac + prefixes="$prefixes '$qprefix'" + fi + fi + prefix=$prefix/ done if test -n "$prefixes"; then - # Don't fail if two instances are running concurrently. - (umask $mkdir_umask && - eval "\$doit_exec \$mkdirprog $prefixes") || - test -d "$dstdir" || exit 1 - obsolete_mkdir_used=true + # Don't fail if two instances are running concurrently. + (umask $mkdir_umask && + eval "\$doit_exec \$mkdirprog $prefixes") || + test -d "$dstdir" || exit 1 + obsolete_mkdir_used=true fi fi fi @@ -449,25 +443,14 @@ do else # Make a couple of temp file names in the proper directory. - dsttmp=${dstdirslash}_inst.$$_ - rmtmp=${dstdirslash}_rm.$$_ + dsttmp=$dstdir/_inst.$$_ + rmtmp=$dstdir/_rm.$$_ # Trap to clean up those temp files at exit. trap 'ret=$?; rm -f "$dsttmp" "$rmtmp" && exit $ret' 0 # Copy the file name to the temp name. - (umask $cp_umask && - { test -z "$stripcmd" || { - # Create $dsttmp read-write so that cp doesn't create it read-only, - # which would cause strip to fail. - if test -z "$doit"; then - : >"$dsttmp" # No need to fork-exec 'touch'. - else - $doit touch "$dsttmp" - fi - } - } && - $doit_exec $cpprog "$src" "$dsttmp") && + (umask $cp_umask && $doit_exec $cpprog "$src" "$dsttmp") && # and set any options; do chmod last to preserve setuid bits. # @@ -482,24 +465,20 @@ do # If -C, don't bother to copy if it wouldn't change the file. if $copy_on_change && - old=`LC_ALL=C ls -dlL "$dst" 2>/dev/null` && - new=`LC_ALL=C ls -dlL "$dsttmp" 2>/dev/null` && - set -f && + old=`LC_ALL=C ls -dlL "$dst" 2>/dev/null` && + new=`LC_ALL=C ls -dlL "$dsttmp" 2>/dev/null` && + + eval "$initialize_posix_glob" && + $posix_glob set -f && set X $old && old=:$2:$4:$5:$6 && set X $new && new=:$2:$4:$5:$6 && - set +f && + $posix_glob set +f && + test "$old" = "$new" && $cmpprog "$dst" "$dsttmp" >/dev/null 2>&1 then rm -f "$dsttmp" else - # If $backupsuffix is set, and the file being installed - # already exists, attempt a backup. Don't worry if it fails, - # e.g., if mv doesn't support -f. - if test -n "$backupsuffix" && test -f "$dst"; then - $doit $mvcmd -f "$dst" "$dst$backupsuffix" 2>/dev/null - fi - # Rename the file to the real destination. $doit $mvcmd -f "$dsttmp" "$dst" 2>/dev/null || @@ -507,24 +486,24 @@ do # to itself, or perhaps because mv is so ancient that it does not # support -f. { - # Now remove or move aside any old file at destination location. - # We try this two ways since rm can't unlink itself on some - # systems and the destination file might be busy for other - # reasons. In this case, the final cleanup might fail but the new - # file should still install successfully. - { - test ! -f "$dst" || - $doit $rmcmd "$dst" 2>/dev/null || - { $doit $mvcmd -f "$dst" "$rmtmp" 2>/dev/null && - { $doit $rmcmd "$rmtmp" 2>/dev/null; :; } - } || - { echo "$0: cannot unlink or rename $dst" >&2 - (exit 1); exit 1 - } - } && - - # Now rename the file to the real destination. - $doit $mvcmd "$dsttmp" "$dst" + # Now remove or move aside any old file at destination location. + # We try this two ways since rm can't unlink itself on some + # systems and the destination file might be busy for other + # reasons. In this case, the final cleanup might fail but the new + # file should still install successfully. + { + test ! -f "$dst" || + $doit $rmcmd -f "$dst" 2>/dev/null || + { $doit $mvcmd -f "$dst" "$rmtmp" 2>/dev/null && + { $doit $rmcmd -f "$rmtmp" 2>/dev/null; :; } + } || + { echo "$0: cannot unlink or rename $dst" >&2 + (exit 1); exit 1 + } + } && + + # Now rename the file to the real destination. + $doit $mvcmd "$dsttmp" "$dst" } fi || exit 1 @@ -533,9 +512,9 @@ do done # Local variables: -# eval: (add-hook 'before-save-hook 'time-stamp) +# eval: (add-hook 'write-file-hooks 'time-stamp) # time-stamp-start: "scriptversion=" # time-stamp-format: "%:y-%02m-%02d.%02H" -# time-stamp-time-zone: "UTC0" +# time-stamp-time-zone: "UTC" # time-stamp-end: "; # UTC" # End: diff --git a/Build/source/utils/asymptote/doc/TeXShopAndAsymptote.pdf b/Build/source/utils/asymptote/doc/TeXShopAndAsymptote.pdf Binary files differindex 9926852eec1..a43c2db07c5 100644 --- a/Build/source/utils/asymptote/doc/TeXShopAndAsymptote.pdf +++ b/Build/source/utils/asymptote/doc/TeXShopAndAsymptote.pdf diff --git a/Build/source/utils/asymptote/doc/asy-latex.dtx b/Build/source/utils/asymptote/doc/asy-latex.dtx index 211ad202b17..febf3f4c47e 100644 --- a/Build/source/utils/asymptote/doc/asy-latex.dtx +++ b/Build/source/utils/asymptote/doc/asy-latex.dtx @@ -38,7 +38,7 @@ Licence: GPL2+ %</driver> %<pkg>\ProvidesPackage{asymptote} %<*pkg> - [2021/12/29 v1.37 Asymptote style file for LaTeX] + [2024/02/26 v1.38 Asymptote style file for LaTeX] %</pkg> % %<*driver> @@ -165,7 +165,7 @@ Licence: GPL2+ % \end{macrocode} % % \begin{macrocode} -\InputIfFileExists{\jobname.pre}{}{} +\InputIfFileExists{\jobname.pre}{}{\typeout{No file \jobname.pre.}} % \end{macrocode} % % \subsection{Allocations} diff --git a/Build/source/utils/asymptote/doc/asy-latex.pdf b/Build/source/utils/asymptote/doc/asy-latex.pdf Binary files differindex 554016edc6b..6a6834ba30a 100644 --- a/Build/source/utils/asymptote/doc/asy-latex.pdf +++ b/Build/source/utils/asymptote/doc/asy-latex.pdf diff --git a/Build/source/utils/asymptote/doc/asy.1 b/Build/source/utils/asymptote/doc/asy.1 index 4738bebd4e1..41a4ece5f6a 100644 --- a/Build/source/utils/asymptote/doc/asy.1 +++ b/Build/source/utils/asymptote/doc/asy.1 @@ -242,7 +242,7 @@ PostScript offset [(0,0)]. Convert each output file to specified format. .TP .B \-o,\-outname name -Alternative output directory/filename. +Alternative output directory/file prefix. .TP .B \-outpipe n Output pipe [-1]. @@ -343,6 +343,9 @@ Use two-sided 3D lighting model for rendering [true]. .B \-u,\-user str General purpose user string. .TP +.B \-v3d +Embed 3D V3D graphics in PDF output [false]. +.TP .B \-v,\-verbose Increase verbosity level (can specify multiple times) 0. .TP @@ -368,7 +371,7 @@ Use webgl2 if available [false]. Show where listed variables are declared [false]. .TP .B \-wsl -Run asy under the Windows Subsystem for Linux. [false]. +Run asy under the Windows Subsystem for Linux [false]. .TP .B \-xasy Interactive mode for xasy [false]. diff --git a/Build/source/utils/asymptote/doc/asyRefCard.pdf b/Build/source/utils/asymptote/doc/asyRefCard.pdf Binary files differindex bdc97baa740..de22ab3176b 100644 --- a/Build/source/utils/asymptote/doc/asyRefCard.pdf +++ b/Build/source/utils/asymptote/doc/asyRefCard.pdf diff --git a/Build/source/utils/asymptote/doc/asymptote.pdf b/Build/source/utils/asymptote/doc/asymptote.pdf Binary files differindex b38e93f9c76..79ccc9346e3 100644 --- a/Build/source/utils/asymptote/doc/asymptote.pdf +++ b/Build/source/utils/asymptote/doc/asymptote.pdf diff --git a/Build/source/utils/asymptote/doc/asymptote.sty b/Build/source/utils/asymptote/doc/asymptote.sty index 2deb265a80c..a3b9dc79f01 100644 --- a/Build/source/utils/asymptote/doc/asymptote.sty +++ b/Build/source/utils/asymptote/doc/asymptote.sty @@ -17,9 +17,9 @@ %% Licence: GPL2+ %% \ProvidesPackage{asymptote} - [2021/12/29 v1.37 Asymptote style file for LaTeX] + [2024/02/26 v1.38 Asymptote style file for LaTeX] \def\Asymptote{{\tt Asymptote}} -\InputIfFileExists{\jobname.pre}{}{} +\InputIfFileExists{\jobname.pre}{}{\typeout{No file \jobname.pre.}} \newbox\ASYbox \newdimen\ASYdimen \newcounter{asy} diff --git a/Build/source/utils/asymptote/doc/asymptote.texi b/Build/source/utils/asymptote/doc/asymptote.texi index 7e159345478..3f16bb9d6e5 100644 --- a/Build/source/utils/asymptote/doc/asymptote.texi +++ b/Build/source/utils/asymptote/doc/asymptote.texi @@ -11,7 +11,7 @@ This file documents @code{Asymptote}, version @value{VERSION}. @url{https://asymptote.sourceforge.io} -Copyright @copyright{} 2004-23 Andy Hammerlindl, John Bowman, and Tom Prince. +Copyright @copyright{} 2004-24 Andy Hammerlindl, John Bowman, and Tom Prince. @quotation Permission is granted to copy, distribute and/or modify this document @@ -133,6 +133,10 @@ Arrays * Slices:: Python-style array slices +Import + +* Templated imports:: + Base modules * plain:: Default @code{Asymptote} base file @@ -2908,10 +2912,9 @@ the routine @verbatim pen rgb(string s); @end verbatim -@noindent -A pen can be converted to a hexadecimal string with +@item A pen can be converted to a hexadecimal string with @cindex @code{hex} -@item string hex(pen p); +@code{string hex(pen p);} Various shades and mixtures of the grayscale primary colors @code{black} and @code{white}, @acronym{RGB} primary colors @@ -3549,8 +3552,7 @@ The @code{options}, @code{script}, and @code{projection} parameters are only relevant for 3D pictures. If @code{defaultfilename} is an empty string, the prefix @code{outprefix()} will be used. -A @code{shipout()} command is added implicitly at file exit if no -previous @code{shipout} commands have been executed. +A @code{shipout()} command is added implicitly at file exit. @cindex @code{orientation} @cindex @code{Portrait} @cindex @code{Landscape} @@ -5286,7 +5288,7 @@ The @code{copy} function listed below provides a deep copy of an array. Every array @code{A} of type @code{T[]} has the virtual members @itemize @item @code{int length}, -@item @code{int cyclic}, +@item @code{bool cyclic}, @item @code{int[] keys}, @item @code{T push(T x)}, @item @code{void append(T[] a)}, @@ -5402,9 +5404,9 @@ element of the array @code{a}. This is equivalent to @cindex @code{map} @item T2[] map(T2 f(T1), T1[] a) -constructed by calling @code{mapArray("T1","T2")}, returns the array -obtained by applying the function @code{f} to each element of the -array @code{a}; +constructed by running @code{from mapArray(Src=T1, Dst=T2) access map;}, +returns the array obtained by applying the function @code{f} to each +element of the array @code{a}; @cindex @code{reverse} @item int[] reverse(int n) @@ -6122,9 +6124,6 @@ code s=quote { eval(s,true); // Outputs 1 @end verbatim -One application of @code{eval} is the creation of parametrized Asymptote -code, such as a map from one type to another (@pxref{map}). - @cindex @code{include} To include the contents of an existing file @code{graph} verbatim (as if the contents of the file were inserted at that point), use one of the forms: @@ -6144,6 +6143,61 @@ void list(string s, bool imports=false); Imported global functions and variables are also listed if @code{imports} is @code{true}. +@menu +* Templated imports:: +@end menu + +@node Templated imports +@subsection Templated imports +@cindex template + +@strong{Warning:} This feature is experimental: it has known issues and its behavior may change in the future. + +In Asymptote, it is possible to create modules that must have one or more +types specified when they are imported. The first executable line of any such +module must be of the form @code{typedef import(<types>)}, where +@code{<types>} is a list of required type parameters. For instance, +@verbatim +typedef import(T, S, Number); +@end verbatim +@noindent +could be the first line of a module that requires three type parameters. The +remaining code in the module can then use @code{T}, @code{S}, and @code{Number} +as types. + +To import such a module, one must specify the types to be used. For instance, +if the module above were named @code{templatedModule}, it could be accessed +for types @code{string}, @code{int[]}, and @code{real} with the import +command +@verbatim +access templatedModule(T=string, S=int[], Number=real) + as templatedModule_string_int_real; +@end verbatim +@noindent +Note that this is actually an @emph{access} command rather than an +@emph{import} command, so the names of types, functions, etc. would have to be +stated as e.g. @code{templatedModule_string_int_real.Wrapper_Number} rather than +just @code{Wrapper_Number} (where @code{Wrapper_Number} is a type defined in +@code{templatedModule.asy}). + +Alternatively, the module could be imported via a command like +@verbatim +from templatedModule(T=string, S=int[], Number=real) access + Wrapper_Number as Wrapper_real, + operator ==; +@end verbatim +@noindent +This command would automatically rename @code{Wrapper_Number} to +@code{Wrapper_real} and would also allow the use of any @code{operator ==} +overloads defined in the module. + +For more information, see the examples in +@url{https://github.com/vectorgraphics/asymptote/tree/647b6c5732ec94a48f0f0b2446f02c86888fe7e7/tests/template}. + +Issues: Certain standard features of almost any type (such as +@code{==}, @code{new}, and the ability to call static methods on the type) may +only be available for type arguments that are builtin or defined in the @code{plain} module. + @node Static, , Import, Programming @section Static @cindex @code{static} @@ -6331,9 +6385,7 @@ To store the figures in a separate directory named @code{asy}, one can define @verbatim \def\asydir{asy} @end verbatim -in @code{latexusage.tex} and put the contents of -@url{https://raw.githubusercontent.com/vectorgraphics/asymptote/HEAD/doc/latexmkrc_asydir} -in a file @code{latexmkrc} in the same directory. +in @code{latexusage.tex}. @noindent External @code{Asymptote} code can be included with @cindex @code{asyinclude} @@ -6911,6 +6963,7 @@ The points are connected using the interpolation specified by @code{join}: @item @code{operator ..} (piecewise Bezier cubic spline interpolation; the abbreviation @code{Spline} is also accepted); +@cindex @code{linear} @cindex @code{Hermite} @cindex @code{notaknot} @cindex @code{natural} @@ -6918,6 +6971,7 @@ the abbreviation @code{Spline} is also accepted); @cindex @code{clamped} @cindex @code{monotonic} @cindex @code{Hermite(splinetype splinetype} +@item @code{linear} (linear interpolation), @item @code{Hermite} (standard cubic spline interpolation using boundary condition @code{notaknot}, @code{natural}, @code{periodic}, @code{clamped(real slopea, real slopeb)}), or @code{monotonic}. @@ -8264,12 +8318,24 @@ The @acronym{PRC} specification is available from @url{https://web.archive.org/web/20081204104459/http://livedocs.adobe.com/acrobat_sdk/9/Acrobat9_HTMLHelp/API_References/PRCReference/PRC_Format_Specification/} @cindex @code{v3d} -@item Output a @code{V3D} portable compressed binary file for viewing with an -external viewer or conversion to an alternate 3D format with the Python -@code{pyv3d} library. The @code{V3D} specification and the +@item Output a @acronym{V3D} portable compressed vector graphics file +using @code{settings.outformat="v3d"}, which can be viewed +with an external viewer or converted to an alternate 3D format +using the Python @code{pyv3d} library. @acronym{V3D} content can be automatically embedded within +a @acronym{PDF} file using the options @code{settings.outformat="pdf"} and +@code{settings.v3d=true}. Alternatively, a V3D file @code{file.v3d} may be manually embedded +within a @acronym{PDF} file using the @code{media9} @code{LaTeX} package: +@verbatim +\includemedia[noplaybutton,width=100pt,height=200pt]{}{file.v3d}% +@end verbatim +An online @code{Javascript}-based V3D-aware @code{PDF} viewer is +available at +@url{https://github.com/vectorgraphics/pdfv3dReader}. + +The @acronym{V3D} specification and the @code{pyv3d} library are available at @url{https://github.com/vectorgraphics/v3d}. -A @code{V3D} file @code{file.v3d} may be imported and viewed by +A @acronym{V3D} file @code{file.v3d} may be imported and viewed by @code{Asymptote} either by specifying @code{file.v3d} on the command line @verbatim asy -V file.v3d @@ -9030,7 +9096,7 @@ picture vectorfield(path3 vector(pair v), triple f(pair z), pair a, pair b, arrowbar3 arrow=Arrow3, margin3 margin=PenMargin3) @end verbatim as illustrated in the examples @code{@uref{https://asymptote.sourceforge.io/gallery/3Dgraphs/vectorfield3.html,,vectorfield3}@uref{https://asymptote.sourceforge.io/gallery/3Dgraphs/vectorfield3.asy,,.asy}} and -@code{@uref{https://asymptote.sourceforge.io/gallery/3Dgraphs/vectorfieldsphere.html,,vectorfieldsphere}@uref{https://asymptote.sourceforge.io/gallery/3Dgraphs/vectorfieldsphere.asy,,.asy}}. +@code{@uref{https://asymptote.sourceforge.io/gallery/3Dwebgl/vectorfieldsphere.html,,vectorfieldsphere}@uref{https://asymptote.sourceforge.io/gallery/3Dwebgl/vectorfieldsphere.asy,,.asy}}. @node grid3, solids, graph3, Base modules @section @code{grid3} @@ -10307,7 +10373,7 @@ developed the @code{Asymptote Web Application} hosted at @c LocalWords: differentiable vectorization vectorized asydir normals quartic @c LocalWords: wavepacket kerned parametrized specular hyperboloid Bourke's @c LocalWords: Michail 0pt 1filll 's 3D labelpath3 2D graph3 0pt 3D -@c LocalWords: grid3 contour3 x86_64 psv a4 freeglut 'load ' +@c LocalWords: grid3 contour3 x86_64 psv a4 freeglut 'load ' 0pt 's @c LocalWords: 'asy 'lasy 'auto 5bp 1cm sqrtx01 4g extenda extendb @c LocalWords: bb llx 2S 100pt 3t bezier2 bool3 x0 angle1 angle2 z1 @c LocalWords: z2 before' struct X11 x11colors type1cm 12pt OT1 5mm @@ -10372,4 +10438,70 @@ developed the @code{Asymptote Web Application} hosted at @c LocalWords: renderers 2E ESC AsyGL 48kB 2n 100d 5z 5y 5unit 10cm @c LocalWords: unicode 144x144 Pedram Emami 204e 10x Ai Ai Ai Ai Ai @c LocalWords: Ai Ai Ai 5a 5E 5cm 2N 2E devicepixelratio 48kB 2n 5z -@c LocalWords: 100d 5y 5unit 144x144 +@c LocalWords: 100d 5y 5unit 144x144 2004-23 2004-24 top-level 3D +@c LocalWords: 1filll Command-line Command-Line command-line 2D 15 +@c LocalWords: high-order User-defined Python-style Templated V3D +@c LocalWords: coordinate-based high-quality high-level de-facto 56 +@c LocalWords: command-driven graphical-user-interface full-fledged +@c LocalWords: script-generated script-based fixed-sized ASYMPTOTE_ +@c LocalWords: user-written Debian-based self-extracting disable-gc +@c LocalWords: google-chrome installation-dependent microsoft-edge +@c LocalWords: ASYMPTOTE_PAPERTYPE Right-click ASYMPTOTE_DIR C-c 72 +@c LocalWords: ASYMPTOTE_HOME asymptote-x DCMAKE_INSTALL_PREFIX M-x +@c LocalWords: DCMAKE_C_FLAGS texinfo-tex system-wide asy-mode C-h +@c LocalWords: lasy-mode add-to-list 'load-path 'asy-mode asy-kate +@c LocalWords: 'lasy-mode 'asy-insinuate-latex 'auto-mode-alist 100 +@c LocalWords: two-mode-mode latex-mode space-separated apt-get 5bp +@c LocalWords: ASYMPTOTE_SITEDIR build-dep Vector_Graphics_Language +@c LocalWords: 1cm double-quoted 06 left-hand right-hand even-odd +@c LocalWords: two-dimensional three-dimensional 4g fixed-size a--b +@c LocalWords: bottom-left 45 10 picture-transformed plain_Label 2S +@c LocalWords: comma-separated boundary-drawing plain_boxes 100pt +@c LocalWords: z_0 c_0 z_1 c_1 1-t 3t third-order m_5 first-order +@c LocalWords: m_0 m_1 m_2 m_3 m_4 second-order 14 75 1986 x-I 360 +@c LocalWords: inflection-free Java-style user-defined built-in a-c +@c LocalWords: highest-precision floating-point element-by-element +@c LocalWords: a--b--c--cycle b-c counterclockwise-oriented 377 01 +@c LocalWords: C-style 1970 02 2007 24 60 non-zero z2-c z1-c b-a 68 +@c LocalWords: counter-clockwise t-floor 137 P--Q p--q cubic-spline +@c LocalWords: two-element non-default 255 6-character 140 180 375 +@c LocalWords: plain_pens z--z 12pt 2018 UTF-8 CJKfamily right-top +@c LocalWords: foreground--background left-bottom 5mm 90 25 25cm 50 +@c LocalWords: end-of-file one-dimensional 64-bit 32-bit C-like i-1 +@c LocalWords: end-of-line asy_history_ path-joining 3x 5x 3y 2x 2y +@c LocalWords: 602e-19 3sin 10cm 204e-19 non-function 17 L-values +@c LocalWords: so-called 10x 34 43 keyword-only 77 42 Keyword-only +@c LocalWords: 21 six-element zero-length n-k Ai_deriv Bi_deriv n-1 +@c LocalWords: zero_Ai zero_Bi zero_Ai_deriv zero_Bi_deriv i_scaled +@c LocalWords: k_scaled zero_J Newton-Raphson real-valued f_i T2 T1 +@c LocalWords: out-of-bounds higher-indexed Dst n-2 realschur schur +@c LocalWords: quasitriangular 19 33 white-space Python-like 12 103 +@c LocalWords: comma-separated-value non-cyclic 107 Non-bridging 5a +@c LocalWords: 866025403784439 non-private d-b templatedModule k-1 +@c LocalWords: templatedModule_string_int_real Wrapper_Number 36 5E +@c LocalWords: Wrapper_real higher-order Three-dimensional log-log +@c LocalWords: two-variable true-element higher-quality post-scaled +@c LocalWords: polar-coordinate auto-generated textbook-style 1000 +@c LocalWords: scientific-style graphwithderiv least-squares 5cm 38 +@c LocalWords: 256 32766 32761 divs quantized fillcontour 67 57 48 +@c LocalWords: shape-invariant 2010021-2010022 vice-versa ibl EXR +@c LocalWords: three_surface three_light plain_prethree image-based +@c LocalWords: pre-rendered imageDir imageURL cudareflect teapotIBL +@c LocalWords: patch-dependent vertex-dependent O--X 2N--2E--E 561 +@c LocalWords: vertex-specific three-dimensions Ctrl-q iframe 321 +@c LocalWords: frameborder 48kB stand-alone 2n 100d v3d pyv3d v2-c +@c LocalWords: importv3d v1-c O--O u--O v--O v--cycle x-0 5z y-0 5y +@c LocalWords: z-0 O--v u--v a-d b-d c-d near_earth c--c nslice 20 +@c LocalWords: O--1 5unit three_arrows diamond-shaped right-angled +@c LocalWords: 2-y public-domain in-depth field-defining 144x144 'e +@c LocalWords: ASYMPTOTE_CONFIG non-writable 200 semi-colon ctrl-C +@c LocalWords: asy_history auto-completion Button-1 Button-2 LSP +@c LocalWords: rsvg-convert librsvg2-tools dvisvgmMultipleFiles lsp +@c LocalWords: data-binary 'import lsp-mode 'package melpa 'asyls +@c LocalWords: 'package-archives package-initialize package-install +@c LocalWords: package-refresh-contents 'lsp-mode make-lsp-client +@c LocalWords: 'lsp-language-id-configuration lsp-register-client +@c LocalWords: new-connection lsp-stdio-connection activation-fn +@c LocalWords: lsp-activate-on major-modes server-id user-generated +@c LocalWords: line-based code-based plain_debugger Guib Skitsko +@c LocalWords: Chaumont Cheng diff --git a/Build/source/utils/asymptote/doc/install-sh b/Build/source/utils/asymptote/doc/install-sh index 7c56c9c0151..6781b987bdb 100755 --- a/Build/source/utils/asymptote/doc/install-sh +++ b/Build/source/utils/asymptote/doc/install-sh @@ -1,7 +1,7 @@ #!/bin/sh # install - install a program, script, or datafile -scriptversion=2023-11-23.18; # UTC +scriptversion=2009-04-28.21; # UTC # This originates from X11R5 (mit/util/scripts/install.sh), which was # later released in X11R6 (xc/config/util/install.sh) with the @@ -35,21 +35,25 @@ scriptversion=2023-11-23.18; # UTC # FSF changes to this file are in the public domain. # # Calling this script install-sh is preferred over install.sh, to prevent -# 'make' implicit rules from creating a file called install from it +# `make' implicit rules from creating a file called install from it # when there is no Makefile. # # This script is compatible with the BSD install script, but was written # from scratch. -tab=' ' nl=' ' -IFS=" $tab$nl" +IFS=" "" $nl" -# Set DOITPROG to "echo" to test this script. +# set DOITPROG to echo to test this script +# Don't use :- since 4.3BSD and earlier shells don't like it. doit=${DOITPROG-} -doit_exec=${doit:-exec} +if test -z "$doit"; then + doit_exec=exec +else + doit_exec=$doit +fi # Put in absolute file names if you don't have them in your path; # or use environment vars. @@ -64,16 +68,22 @@ mvprog=${MVPROG-mv} rmprog=${RMPROG-rm} stripprog=${STRIPPROG-strip} +posix_glob='?' +initialize_posix_glob=' + test "$posix_glob" != "?" || { + if (set -f) 2>/dev/null; then + posix_glob= + else + posix_glob=: + fi + } +' + posix_mkdir= # Desired mode of installed file. mode=0755 -# Create dirs (including intermediate dirs) using mode 755. -# This is like GNU 'install' as of coreutils 8.32 (2020). -mkdir_umask=22 - -backupsuffix= chgrpcmd= chmodcmd=$chmodprog chowncmd= @@ -87,7 +97,7 @@ dir_arg= dst_arg= copy_on_change=false -is_target_a_directory=possibly +no_target_directory= usage="\ Usage: $0 [OPTION]... [-T] SRCFILE DSTFILE @@ -104,29 +114,19 @@ Options: --version display version info and exit. -c (ignored) - -C install only if different (preserve data modification time) + -C install only if different (preserve the last data modification time) -d create directories instead of installing files. -g GROUP $chgrpprog installed files to GROUP. -m MODE $chmodprog installed files to MODE. -o USER $chownprog installed files to USER. - -p pass -p to $cpprog. -s $stripprog installed files. - -S SUFFIX attempt to back up existing files, with suffix SUFFIX. -t DIRECTORY install into DIRECTORY. -T report an error if DSTFILE is a directory. Environment variables override the default commands: CHGRPPROG CHMODPROG CHOWNPROG CMPPROG CPPROG MKDIRPROG MVPROG RMPROG STRIPPROG - -By default, rm is invoked with -f; when overridden with RMPROG, -it's up to you to specify -f if you want it. - -If -S is not specified, no backups are attempted. - -Report bugs to <bug-automake@gnu.org>. -GNU Automake home page: <https://www.gnu.org/software/automake/>. -General help using GNU software: <https://www.gnu.org/gethelp/>." +" while test $# -ne 0; do case $1 in @@ -137,62 +137,42 @@ while test $# -ne 0; do -d) dir_arg=true;; -g) chgrpcmd="$chgrpprog $2" - shift;; + shift;; --help) echo "$usage"; exit $?;; -m) mode=$2 - case $mode in - *' '* | *"$tab"* | *"$nl"* | *'*'* | *'?'* | *'['*) - echo "$0: invalid mode: $mode" >&2 - exit 1;; - esac - shift;; + case $mode in + *' '* | *' '* | *' +'* | *'*'* | *'?'* | *'['*) + echo "$0: invalid mode: $mode" >&2 + exit 1;; + esac + shift;; -o) chowncmd="$chownprog $2" - shift;; - - -p) cpprog="$cpprog -p";; + shift;; -s) stripcmd=$stripprog;; - -S) backupsuffix="$2" - shift;; - - -t) - is_target_a_directory=always - dst_arg=$2 - # Protect names problematic for 'test' and other utilities. - case $dst_arg in - -* | [=\(\)!]) dst_arg=./$dst_arg;; - esac - shift;; + -t) dst_arg=$2 + shift;; - -T) is_target_a_directory=never;; + -T) no_target_directory=true;; --version) echo "$0 $scriptversion"; exit $?;; - --) shift - break;; + --) shift + break;; - -*) echo "$0: invalid option: $1" >&2 - exit 1;; + -*) echo "$0: invalid option: $1" >&2 + exit 1;; *) break;; esac shift done -# We allow the use of options -d and -T together, by making -d -# take the precedence; this is for compatibility with GNU install. - -if test -n "$dir_arg"; then - if test -n "$dst_arg"; then - echo "$0: target directory not allowed when installing a directory." >&2 - exit 1 - fi -fi - if test $# -ne 0 && test -z "$dir_arg$dst_arg"; then # When -d is used, all remaining arguments are directories to create. # When -t is used, the destination is already specified. @@ -206,10 +186,6 @@ if test $# -ne 0 && test -z "$dir_arg$dst_arg"; then fi shift # arg dst_arg=$arg - # Protect names problematic for 'test' and other utilities. - case $dst_arg in - -* | [=\(\)!]) dst_arg=./$dst_arg;; - esac done fi @@ -218,26 +194,13 @@ if test $# -eq 0; then echo "$0: no input file specified." >&2 exit 1 fi - # It's OK to call 'install-sh -d' without argument. + # It's OK to call `install-sh -d' without argument. # This can happen when creating conditional directories. exit 0 fi if test -z "$dir_arg"; then - if test $# -gt 1 || test "$is_target_a_directory" = always; then - if test ! -d "$dst_arg"; then - echo "$0: $dst_arg: Is not a directory." >&2 - exit 1 - fi - fi -fi - -if test -z "$dir_arg"; then - do_exit='(exit $ret); exit $ret' - trap "ret=129; $do_exit" 1 - trap "ret=130; $do_exit" 2 - trap "ret=141; $do_exit" 13 - trap "ret=143; $do_exit" 15 + trap '(exit $?); exit' 1 2 13 15 # Set umask so as not to create temps with too-generous modes. # However, 'strip' requires both read and write access to temps. @@ -248,16 +211,16 @@ if test -z "$dir_arg"; then *[0-7]) if test -z "$stripcmd"; then - u_plus_rw= + u_plus_rw= else - u_plus_rw='% 200' + u_plus_rw='% 200' fi cp_umask=`expr '(' 777 - $mode % 1000 ')' $u_plus_rw`;; *) if test -z "$stripcmd"; then - u_plus_rw= + u_plus_rw= else - u_plus_rw=,u+rw + u_plus_rw=,u+rw fi cp_umask=$mode$u_plus_rw;; esac @@ -265,9 +228,9 @@ fi for src do - # Protect names problematic for 'test' and other utilities. + # Protect names starting with `-'. case $src in - -* | [=\(\)!]) src=./$src;; + -*) src=./$src;; esac if test -n "$dir_arg"; then @@ -275,10 +238,6 @@ do dstdir=$dst test -d "$dstdir" dstdir_status=$? - # Don't chown directories that already exist. - if test $dstdir_status = 0; then - chowncmd="" - fi else # Waiting for this to be detected by the "$cpprog $src $dsttmp" command @@ -293,150 +252,185 @@ do echo "$0: no destination specified." >&2 exit 1 fi + dst=$dst_arg + # Protect names starting with `-'. + case $dst in + -*) dst=./$dst;; + esac - # If destination is a directory, append the input filename. + # If destination is a directory, append the input filename; won't work + # if double slashes aren't ignored. if test -d "$dst"; then - if test "$is_target_a_directory" = never; then - echo "$0: $dst_arg: Is a directory" >&2 - exit 1 + if test -n "$no_target_directory"; then + echo "$0: $dst_arg: Is a directory" >&2 + exit 1 fi dstdir=$dst - dstbase=`basename "$src"` - case $dst in - */) dst=$dst$dstbase;; - *) dst=$dst/$dstbase;; - esac + dst=$dstdir/`basename "$src"` dstdir_status=0 else - dstdir=`dirname "$dst"` + # Prefer dirname, but fall back on a substitute if dirname fails. + dstdir=` + (dirname "$dst") 2>/dev/null || + expr X"$dst" : 'X\(.*[^/]\)//*[^/][^/]*/*$' \| \ + X"$dst" : 'X\(//\)[^/]' \| \ + X"$dst" : 'X\(//\)$' \| \ + X"$dst" : 'X\(/\)' \| . 2>/dev/null || + echo X"$dst" | + sed '/^X\(.*[^/]\)\/\/*[^/][^/]*\/*$/{ + s//\1/ + q + } + /^X\(\/\/\)[^/].*/{ + s//\1/ + q + } + /^X\(\/\/\)$/{ + s//\1/ + q + } + /^X\(\/\).*/{ + s//\1/ + q + } + s/.*/./; q' + ` + test -d "$dstdir" dstdir_status=$? fi fi - case $dstdir in - */) dstdirslash=$dstdir;; - *) dstdirslash=$dstdir/;; - esac - obsolete_mkdir_used=false if test $dstdir_status != 0; then case $posix_mkdir in '') - # With -d, create the new directory with the user-specified mode. - # Otherwise, rely on $mkdir_umask. - if test -n "$dir_arg"; then - mkdir_mode=-m$mode - else - mkdir_mode= - fi - - posix_mkdir=false - # The $RANDOM variable is not portable (e.g., dash). Use it - # here however when possible just to lower collision chance. - tmpdir=${TMPDIR-/tmp}/ins$RANDOM-$$ - - trap ' - ret=$? - rmdir "$tmpdir/a/b" "$tmpdir/a" "$tmpdir" 2>/dev/null - exit $ret - ' 0 - - # Because "mkdir -p" follows existing symlinks and we likely work - # directly in world-writeable /tmp, make sure that the '$tmpdir' - # directory is successfully created first before we actually test - # 'mkdir -p'. - if (umask $mkdir_umask && - $mkdirprog $mkdir_mode "$tmpdir" && - exec $mkdirprog $mkdir_mode -p -- "$tmpdir/a/b") >/dev/null 2>&1 - then - if test -z "$dir_arg" || { - # Check for POSIX incompatibilities with -m. - # HP-UX 11.23 and IRIX 6.5 mkdir -m -p sets group- or - # other-writable bit of parent directory when it shouldn't. - # FreeBSD 6.1 mkdir -m -p sets mode of existing directory. - test_tmpdir="$tmpdir/a" - ls_ld_tmpdir=`ls -ld "$test_tmpdir"` - case $ls_ld_tmpdir in - d????-?r-*) different_mode=700;; - d????-?--*) different_mode=755;; - *) false;; - esac && - $mkdirprog -m$different_mode -p -- "$test_tmpdir" && { - ls_ld_tmpdir_1=`ls -ld "$test_tmpdir"` - test "$ls_ld_tmpdir" = "$ls_ld_tmpdir_1" - } - } - then posix_mkdir=: - fi - rmdir "$tmpdir/a/b" "$tmpdir/a" "$tmpdir" + # Create intermediate dirs using mode 755 as modified by the umask. + # This is like FreeBSD 'install' as of 1997-10-28. + umask=`umask` + case $stripcmd.$umask in + # Optimize common cases. + *[2367][2367]) mkdir_umask=$umask;; + .*0[02][02] | .[02][02] | .[02]) mkdir_umask=22;; + + *[0-7]) + mkdir_umask=`expr $umask + 22 \ + - $umask % 100 % 40 + $umask % 20 \ + - $umask % 10 % 4 + $umask % 2 + `;; + *) mkdir_umask=$umask,go-w;; + esac + + # With -d, create the new directory with the user-specified mode. + # Otherwise, rely on $mkdir_umask. + if test -n "$dir_arg"; then + mkdir_mode=-m$mode else - # Remove any dirs left behind by ancient mkdir implementations. - rmdir ./$mkdir_mode ./-p ./-- "$tmpdir" 2>/dev/null + mkdir_mode= fi - trap '' 0;; + + posix_mkdir=false + case $umask in + *[123567][0-7][0-7]) + # POSIX mkdir -p sets u+wx bits regardless of umask, which + # is incompatible with FreeBSD 'install' when (umask & 300) != 0. + ;; + *) + tmpdir=${TMPDIR-/tmp}/ins$RANDOM-$$ + trap 'ret=$?; rmdir "$tmpdir/d" "$tmpdir" 2>/dev/null; exit $ret' 0 + + if (umask $mkdir_umask && + exec $mkdirprog $mkdir_mode -p -- "$tmpdir/d") >/dev/null 2>&1 + then + if test -z "$dir_arg" || { + # Check for POSIX incompatibilities with -m. + # HP-UX 11.23 and IRIX 6.5 mkdir -m -p sets group- or + # other-writeable bit of parent directory when it shouldn't. + # FreeBSD 6.1 mkdir -m -p sets mode of existing directory. + ls_ld_tmpdir=`ls -ld "$tmpdir"` + case $ls_ld_tmpdir in + d????-?r-*) different_mode=700;; + d????-?--*) different_mode=755;; + *) false;; + esac && + $mkdirprog -m$different_mode -p -- "$tmpdir" && { + ls_ld_tmpdir_1=`ls -ld "$tmpdir"` + test "$ls_ld_tmpdir" = "$ls_ld_tmpdir_1" + } + } + then posix_mkdir=: + fi + rmdir "$tmpdir/d" "$tmpdir" + else + # Remove any dirs left behind by ancient mkdir implementations. + rmdir ./$mkdir_mode ./-p ./-- 2>/dev/null + fi + trap '' 0;; + esac;; esac if $posix_mkdir && ( - umask $mkdir_umask && - $doit_exec $mkdirprog $mkdir_mode -p -- "$dstdir" + umask $mkdir_umask && + $doit_exec $mkdirprog $mkdir_mode -p -- "$dstdir" ) then : else - # mkdir does not conform to POSIX, + # The umask is ridiculous, or mkdir does not conform to POSIX, # or it failed possibly due to a race condition. Create the # directory the slow way, step by step, checking for races as we go. case $dstdir in - /*) prefix='/';; - [-=\(\)!]*) prefix='./';; - *) prefix='';; + /*) prefix='/';; + -*) prefix='./';; + *) prefix='';; esac + eval "$initialize_posix_glob" + oIFS=$IFS IFS=/ - set -f + $posix_glob set -f set fnord $dstdir shift - set +f + $posix_glob set +f IFS=$oIFS prefixes= for d do - test X"$d" = X && continue - - prefix=$prefix$d - if test -d "$prefix"; then - prefixes= - else - if $posix_mkdir; then - (umask $mkdir_umask && - $doit_exec $mkdirprog $mkdir_mode -p -- "$dstdir") && break - # Don't fail if two instances are running concurrently. - test -d "$prefix" || exit 1 - else - case $prefix in - *\'*) qprefix=`echo "$prefix" | sed "s/'/'\\\\\\\\''/g"`;; - *) qprefix=$prefix;; - esac - prefixes="$prefixes '$qprefix'" - fi - fi - prefix=$prefix/ + test -z "$d" && continue + + prefix=$prefix$d + if test -d "$prefix"; then + prefixes= + else + if $posix_mkdir; then + (umask=$mkdir_umask && + $doit_exec $mkdirprog $mkdir_mode -p -- "$dstdir") && break + # Don't fail if two instances are running concurrently. + test -d "$prefix" || exit 1 + else + case $prefix in + *\'*) qprefix=`echo "$prefix" | sed "s/'/'\\\\\\\\''/g"`;; + *) qprefix=$prefix;; + esac + prefixes="$prefixes '$qprefix'" + fi + fi + prefix=$prefix/ done if test -n "$prefixes"; then - # Don't fail if two instances are running concurrently. - (umask $mkdir_umask && - eval "\$doit_exec \$mkdirprog $prefixes") || - test -d "$dstdir" || exit 1 - obsolete_mkdir_used=true + # Don't fail if two instances are running concurrently. + (umask $mkdir_umask && + eval "\$doit_exec \$mkdirprog $prefixes") || + test -d "$dstdir" || exit 1 + obsolete_mkdir_used=true fi fi fi @@ -449,25 +443,14 @@ do else # Make a couple of temp file names in the proper directory. - dsttmp=${dstdirslash}_inst.$$_ - rmtmp=${dstdirslash}_rm.$$_ + dsttmp=$dstdir/_inst.$$_ + rmtmp=$dstdir/_rm.$$_ # Trap to clean up those temp files at exit. trap 'ret=$?; rm -f "$dsttmp" "$rmtmp" && exit $ret' 0 # Copy the file name to the temp name. - (umask $cp_umask && - { test -z "$stripcmd" || { - # Create $dsttmp read-write so that cp doesn't create it read-only, - # which would cause strip to fail. - if test -z "$doit"; then - : >"$dsttmp" # No need to fork-exec 'touch'. - else - $doit touch "$dsttmp" - fi - } - } && - $doit_exec $cpprog "$src" "$dsttmp") && + (umask $cp_umask && $doit_exec $cpprog "$src" "$dsttmp") && # and set any options; do chmod last to preserve setuid bits. # @@ -482,24 +465,20 @@ do # If -C, don't bother to copy if it wouldn't change the file. if $copy_on_change && - old=`LC_ALL=C ls -dlL "$dst" 2>/dev/null` && - new=`LC_ALL=C ls -dlL "$dsttmp" 2>/dev/null` && - set -f && + old=`LC_ALL=C ls -dlL "$dst" 2>/dev/null` && + new=`LC_ALL=C ls -dlL "$dsttmp" 2>/dev/null` && + + eval "$initialize_posix_glob" && + $posix_glob set -f && set X $old && old=:$2:$4:$5:$6 && set X $new && new=:$2:$4:$5:$6 && - set +f && + $posix_glob set +f && + test "$old" = "$new" && $cmpprog "$dst" "$dsttmp" >/dev/null 2>&1 then rm -f "$dsttmp" else - # If $backupsuffix is set, and the file being installed - # already exists, attempt a backup. Don't worry if it fails, - # e.g., if mv doesn't support -f. - if test -n "$backupsuffix" && test -f "$dst"; then - $doit $mvcmd -f "$dst" "$dst$backupsuffix" 2>/dev/null - fi - # Rename the file to the real destination. $doit $mvcmd -f "$dsttmp" "$dst" 2>/dev/null || @@ -507,24 +486,24 @@ do # to itself, or perhaps because mv is so ancient that it does not # support -f. { - # Now remove or move aside any old file at destination location. - # We try this two ways since rm can't unlink itself on some - # systems and the destination file might be busy for other - # reasons. In this case, the final cleanup might fail but the new - # file should still install successfully. - { - test ! -f "$dst" || - $doit $rmcmd "$dst" 2>/dev/null || - { $doit $mvcmd -f "$dst" "$rmtmp" 2>/dev/null && - { $doit $rmcmd "$rmtmp" 2>/dev/null; :; } - } || - { echo "$0: cannot unlink or rename $dst" >&2 - (exit 1); exit 1 - } - } && - - # Now rename the file to the real destination. - $doit $mvcmd "$dsttmp" "$dst" + # Now remove or move aside any old file at destination location. + # We try this two ways since rm can't unlink itself on some + # systems and the destination file might be busy for other + # reasons. In this case, the final cleanup might fail but the new + # file should still install successfully. + { + test ! -f "$dst" || + $doit $rmcmd -f "$dst" 2>/dev/null || + { $doit $mvcmd -f "$dst" "$rmtmp" 2>/dev/null && + { $doit $rmcmd -f "$rmtmp" 2>/dev/null; :; } + } || + { echo "$0: cannot unlink or rename $dst" >&2 + (exit 1); exit 1 + } + } && + + # Now rename the file to the real destination. + $doit $mvcmd "$dsttmp" "$dst" } fi || exit 1 @@ -533,9 +512,9 @@ do done # Local variables: -# eval: (add-hook 'before-save-hook 'time-stamp) +# eval: (add-hook 'write-file-hooks 'time-stamp) # time-stamp-start: "scriptversion=" # time-stamp-format: "%:y-%02m-%02d.%02H" -# time-stamp-time-zone: "UTC0" +# time-stamp-time-zone: "UTC" # time-stamp-end: "; # UTC" # End: diff --git a/Build/source/utils/asymptote/doc/latexmkrc b/Build/source/utils/asymptote/doc/latexmkrc index fbc52a98d2e..646594e4dad 100644 --- a/Build/source/utils/asymptote/doc/latexmkrc +++ b/Build/source/utils/asymptote/doc/latexmkrc @@ -1,4 +1,5 @@ -sub asy {return system("asy \"$_[0]\"");} +sub asy {return system("asy -o '$_[0]' '$_[0]'");} add_cus_dep("asy","eps",0,"asy"); add_cus_dep("asy","pdf",0,"asy"); add_cus_dep("asy","tex",0,"asy"); +push @generated_exts, "pre", "%R-[0-9]*.pdf", "%R-[0-9]*.prc", "%R-[0-9]*.tex", "%R-[0-9]*.out", "%R-[0-9]*.pbsdat", "%R.pbsdat", "%R-[0-9]*.eps", "%R-*.asy"
\ No newline at end of file diff --git a/Build/source/utils/asymptote/doc/latexmkrc_asydir b/Build/source/utils/asymptote/doc/latexmkrc_asydir deleted file mode 100644 index 043084e8e6d..00000000000 --- a/Build/source/utils/asymptote/doc/latexmkrc_asydir +++ /dev/null @@ -1,4 +0,0 @@ -sub asy {return system("asy -o asy/ '$_[0]'");} -add_cus_dep("asy","eps",0,"asy"); -add_cus_dep("asy","pdf",0,"asy"); -add_cus_dep("asy","tex",0,"asy"); diff --git a/Build/source/utils/asymptote/doc/png/asymptote.info b/Build/source/utils/asymptote/doc/png/asymptote.info index 78edd9ad026..c3633800c78 100644 --- a/Build/source/utils/asymptote/doc/png/asymptote.info +++ b/Build/source/utils/asymptote/doc/png/asymptote.info @@ -1,11 +1,11 @@ -This is asymptote.info, produced by makeinfo version 6.8 from +This is asymptote.info, produced by makeinfo version 7.0.2 from asymptote.texi. -This file documents 'Asymptote', version 2.85. +This file documents ‘Asymptote’, version 2.87. <https://asymptote.sourceforge.io> - Copyright (C) 2004-23 Andy Hammerlindl, John Bowman, and Tom Prince. + Copyright © 2004-24 Andy Hammerlindl, John Bowman, and Tom Prince. Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Lesser General Public License @@ -22,11 +22,11 @@ File: asymptote.info, Node: Top, Next: Description, Prev: (dir), Up: (dir) Asymptote ********* -This file documents 'Asymptote', version 2.85. +This file documents ‘Asymptote’, version 2.87. <https://asymptote.sourceforge.io> - Copyright (C) 2004-23 Andy Hammerlindl, John Bowman, and Tom Prince. + Copyright © 2004-24 Andy Hammerlindl, John Bowman, and Tom Prince. Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Lesser General Public License @@ -34,45 +34,45 @@ This file documents 'Asymptote', version 2.85. * Menu: -* Description:: What is 'Asymptote'? +* Description:: What is ‘Asymptote’? * Installation:: Downloading and installing * Tutorial:: Getting started * Drawing commands:: Four primitive graphics commands * Bezier curves:: Path connectors and direction specifiers -* Programming:: The 'Asymptote' vector graphics language -* LaTeX usage:: Embedding 'Asymptote' commands within 'LaTeX' -* Base modules:: Base modules shipped with 'Asymptote' +* Programming:: The ‘Asymptote’ vector graphics language +* LaTeX usage:: Embedding ‘Asymptote’ commands within ‘LaTeX’ +* Base modules:: Base modules shipped with ‘Asymptote’ * Options:: Command-line options -* Interactive mode:: Typing 'Asymptote' commands interactively +* Interactive mode:: Typing ‘Asymptote’ commands interactively * GUI:: Graphical user interface * Command-Line Interface:: Remote command-line interface * Language server protocol:: Help when writing code -* PostScript to Asymptote:: 'Asymptote' backend to 'pstoedit' +* PostScript to Asymptote:: ‘Asymptote’ backend to ‘pstoedit’ * Help:: Where to get help and submit bug reports * Debugger:: Squish those bugs! * Credits:: Contributions and acknowledgments * Index:: General index - -- The Detailed Node Listing -- + — The Detailed Node Listing — Installation -* UNIX binary distributions:: Prebuilt 'UNIX' binaries -* MacOS X binary distributions:: Prebuilt 'MacOS X' binaries -* Microsoft Windows:: Prebuilt 'Microsoft Windows' binary -* Configuring:: Configuring 'Asymptote' for your system -* Search paths:: Where 'Asymptote' looks for your files -* Compiling from UNIX source:: Building 'Asymptote' from scratch -* Editing modes:: Convenient 'emacs' and 'vim' modes +* UNIX binary distributions:: Prebuilt ‘UNIX’ binaries +* MacOS X binary distributions:: Prebuilt ‘MacOS X’ binaries +* Microsoft Windows:: Prebuilt ‘Microsoft Windows’ binary +* Configuring:: Configuring ‘Asymptote’ for your system +* Search paths:: Where ‘Asymptote’ looks for your files +* Compiling from UNIX source:: Building ‘Asymptote’ from scratch +* Editing modes:: Convenient ‘emacs’ and ‘vim’ modes * Git:: Getting the latest development source -* Uninstall:: Goodbye, 'Asymptote'! +* Uninstall:: Goodbye, ‘Asymptote’! Tutorial -* Drawing in batch mode:: Run 'Asymptote' on a text file -* Drawing in interactive mode:: Running 'Asymptote' interactively +* Drawing in batch mode:: Run ‘Asymptote’ on a text file +* Drawing in interactive mode:: Running ‘Asymptote’ interactively * Figure size:: Specifying the figure size -* Labels:: Adding 'LaTeX' labels +* Labels:: Adding ‘LaTeX’ labels * Paths:: Drawing lines and curves Drawing commands @@ -97,7 +97,7 @@ Programming * Functions:: Traditional and high-order functions * Arrays:: Dynamic vectors * Casts:: Implicit and explicit casts -* Import:: Importing external 'Asymptote' modules +* Import:: Importing external ‘Asymptote’ modules * Static:: Where to allocate your variable? Operators @@ -117,11 +117,15 @@ Arrays * Slices:: Python-style array slices +Import + +* Templated imports:: + Base modules -* plain:: Default 'Asymptote' base file +* plain:: Default ‘Asymptote’ base file * simplex:: Linear programming: simplex method -* math:: Extend 'Asymptote''s math capabilities +* math:: Extend ‘Asymptote’’s math capabilities * interpolate:: Interpolation routines * geometry:: Geometry routines * trembling:: Wavy lines @@ -137,9 +141,9 @@ Base modules * roundedpath:: Round the sharp corners of paths * animation:: Embedded PDF and MPEG movies * embed:: Embedding movies, sounds, and 3D objects -* slide:: Making presentations with 'Asymptote' -* MetaPost:: 'MetaPost' compatibility routines -* babel:: Interface to 'LaTeX' 'babel' package +* slide:: Making presentations with ‘Asymptote’ +* MetaPost:: ‘MetaPost’ compatibility routines +* babel:: Interface to ‘LaTeX’ ‘babel’ package * labelpath:: Drawing curved labels * labelpath3:: Drawing curved labels in 3D * annotate:: Annotate your PDF files @@ -161,8 +165,8 @@ Base modules Graphical User Interface -* GUI installation:: Installing 'xasy' -* GUI usage:: Using 'xasy' to edit objects +* GUI installation:: Installing ‘xasy’ +* GUI usage:: Using ‘xasy’ to edit objects @@ -171,93 +175,93 @@ File: asymptote.info, Node: Description, Next: Installation, Prev: Top, Up: 1 Description ************* -'Asymptote' is a powerful descriptive vector graphics language that +‘Asymptote’ is a powerful descriptive vector graphics language that provides a mathematical coordinate-based framework for technical -drawing. Labels and equations are typeset with 'LaTeX', for overall +drawing. Labels and equations are typeset with ‘LaTeX’, for overall document consistency, yielding the same high-quality level of -typesetting that 'LaTeX' provides for scientific text. By default it -produces 'PostScript' output, but it can also generate 'OpenGL', 'PDF', -'SVG', 'WebGL', 'V3D', and 'PRC' vector graphics, along with any format -that the 'ImageMagick' package can produce. You can even try it out in -your Web browser without installing it, using the 'Asymptote Web -Application' +typesetting that ‘LaTeX’ provides for scientific text. By default it +produces ‘PostScript’ output, but it can also generate ‘OpenGL’, ‘PDF’, +‘SVG’, ‘WebGL’, ‘V3D’, and ‘PRC’ vector graphics, along with any format +that the ‘ImageMagick’ package can produce. You can even try it out in +your Web browser without installing it, using the ‘Asymptote Web +Application’ <http://asymptote.ualberta.ca> It is also possible to send remote commands to this server via the curl utility (*note Command-Line Interface::). - A major advantage of 'Asymptote' over other graphics packages is that + A major advantage of ‘Asymptote’ over other graphics packages is that it is a high-level programming language, as opposed to just a graphics program: it can therefore exploit the best features of the script (command-driven) and graphical-user-interface (GUI) methods for -producing figures. The rudimentary GUI 'xasy' included with the package -allows one to move script-generated objects around. To make 'Asymptote' +producing figures. The rudimentary GUI ‘xasy’ included with the package +allows one to move script-generated objects around. To make ‘Asymptote’ accessible to the average user, this GUI is currently being developed into a full-fledged interface that can generate objects directly. However, the script portion of the language is now ready for general use -by users who are willing to learn a few simple 'Asymptote' graphics +by users who are willing to learn a few simple ‘Asymptote’ graphics commands (*note Drawing commands::). - 'Asymptote' is mathematically oriented (e.g. one can use complex -multiplication to rotate a vector) and uses 'LaTeX' to do the + ‘Asymptote’ is mathematically oriented (e.g. one can use complex +multiplication to rotate a vector) and uses ‘LaTeX’ to do the typesetting of labels. This is an important feature for scientific applications. It was inspired by an earlier drawing program (with a -weaker syntax and capabilities) called 'MetaPost'. +weaker syntax and capabilities) called ‘MetaPost’. - The 'Asymptote' vector graphics language provides: + The ‘Asymptote’ vector graphics language provides: - * a standard for typesetting mathematical figures, just as - TeX/'LaTeX' is the de-facto standard for typesetting equations. + • a standard for typesetting mathematical figures, just as + TeX/‘LaTeX’ is the de-facto standard for typesetting equations. - * 'LaTeX' typesetting of labels, for overall document consistency; + • ‘LaTeX’ typesetting of labels, for overall document consistency; - * the ability to generate and embed 3D vector WebGL graphics within + • the ability to generate and embed 3D vector WebGL graphics within HTML files; - * the ability to generate and embed 3D vector PRC graphics within PDF + • the ability to generate and embed 3D vector PRC graphics within PDF files; - * a natural coordinate-based framework for technical drawing, - inspired by 'MetaPost', with a much cleaner, powerful C++-like + • a natural coordinate-based framework for technical drawing, + inspired by ‘MetaPost’, with a much cleaner, powerful C++-like programming syntax; - * compilation of figures into virtual machine code for speed, without + • compilation of figures into virtual machine code for speed, without sacrificing portability; - * the power of a script-based language coupled to the convenience of + • the power of a script-based language coupled to the convenience of a GUI; - * customization using its own C++-like graphics programming language; + • customization using its own C++-like graphics programming language; - * sensible defaults for graphical features, with the ability to + • sensible defaults for graphical features, with the ability to override; - * a high-level mathematically oriented interface to the 'PostScript' + • a high-level mathematically oriented interface to the ‘PostScript’ language for vector graphics, including affine transforms and complex variables; - * functions that can create new (anonymous) functions; + • functions that can create new (anonymous) functions; - * deferred drawing that uses the simplex method to solve overall size + • deferred drawing that uses the simplex method to solve overall size constraint issues between fixed-sized objects (labels and arrowheads) and objects that should scale with figure size; - Many of the features of 'Asymptote' are written in the 'Asymptote' -language itself. While the stock version of 'Asymptote' is designed for -mathematics typesetting needs, one can write 'Asymptote' modules that + Many of the features of ‘Asymptote’ are written in the ‘Asymptote’ +language itself. While the stock version of ‘Asymptote’ is designed for +mathematics typesetting needs, one can write ‘Asymptote’ modules that tailor it to specific applications; for example, a scientific graphing -module is available (*note graph::). Examples of 'Asymptote' code and +module is available (*note graph::). Examples of ‘Asymptote’ code and output, including animations, are available at <https://asymptote.sourceforge.io/gallery/> -Clicking on an example file name in this manual, like 'Pythagoras', will -display the PDF output, whereas clicking on its '.asy' extension will -show the corresponding 'Asymptote' code in a separate window. +Clicking on an example file name in this manual, like ‘Pythagoras’, will +display the PDF output, whereas clicking on its ‘.asy’ extension will +show the corresponding ‘Asymptote’ code in a separate window. Links to many external resources, including an excellent user-written -'Asymptote' tutorial can be found at +‘Asymptote’ tutorial can be found at <https://asymptote.sourceforge.io/links.html> - A quick reference card for 'Asymptote' is available at + A quick reference card for ‘Asymptote’ is available at <https://asymptote.sourceforge.io/asyRefCard.pdf> @@ -268,22 +272,22 @@ File: asymptote.info, Node: Installation, Next: Tutorial, Prev: Description, * Menu: -* UNIX binary distributions:: Prebuilt 'UNIX' binaries -* MacOS X binary distributions:: Prebuilt 'MacOS X' binaries -* Microsoft Windows:: Prebuilt 'Microsoft Windows' binary -* Configuring:: Configuring 'Asymptote' for your system -* Search paths:: Where 'Asymptote' looks for your files -* Compiling from UNIX source:: Building 'Asymptote' from scratch -* Editing modes:: Convenient 'emacs' and 'vim' modes +* UNIX binary distributions:: Prebuilt ‘UNIX’ binaries +* MacOS X binary distributions:: Prebuilt ‘MacOS X’ binaries +* Microsoft Windows:: Prebuilt ‘Microsoft Windows’ binary +* Configuring:: Configuring ‘Asymptote’ for your system +* Search paths:: Where ‘Asymptote’ looks for your files +* Compiling from UNIX source:: Building ‘Asymptote’ from scratch +* Editing modes:: Convenient ‘emacs’ and ‘vim’ modes * Git:: Getting the latest development source -* Uninstall:: Goodbye, 'Asymptote'! +* Uninstall:: Goodbye, ‘Asymptote’! After following the instructions for your specific distribution, please see also *note Configuring::. We recommend subscribing to new release announcements at <https://sourceforge.net/projects/asymptote> -Users may also wish to monitor the 'Asymptote' forum: +Users may also wish to monitor the ‘Asymptote’ forum: <https://sourceforge.net/p/asymptote/discussion/409349> @@ -292,24 +296,24 @@ File: asymptote.info, Node: UNIX binary distributions, Next: MacOS X binary di 2.1 UNIX binary distributions ============================= -We release both 'tgz' and RPM binary distributions of 'Asymptote'. The -root user can install the 'Linux x86_64' 'tgz' distribution of version -'x.xx' of 'Asymptote' with the commands: +We release both ‘tgz’ and RPM binary distributions of ‘Asymptote’. The +root user can install the ‘Linux x86_64’ ‘tgz’ distribution of version +‘x.xx’ of ‘Asymptote’ with the commands: tar -C / -zxf asymptote-x.xx.x86_64.tgz texhash -The 'texhash' command, which installs LaTeX style files, is optional. -The executable file will be '/usr/local/bin/asy') and example code will -be installed by default in '/usr/local/share/doc/asymptote/examples'. +The ‘texhash’ command, which installs LaTeX style files, is optional. +The executable file will be ‘/usr/local/bin/asy’) and example code will +be installed by default in ‘/usr/local/share/doc/asymptote/examples’. -Fedora users can easily install a recent version of 'Asymptote' with the +Fedora users can easily install a recent version of ‘Asymptote’ with the command dnf --enablerepo=rawhide install asymptote -To install the latest version of 'Asymptote' on a Debian-based +To install the latest version of ‘Asymptote’ on a Debian-based distribution (e.g. Ubuntu, Mepis, Linspire) follow the instructions for -compiling from 'UNIX' source (*note Compiling from UNIX source::). -Alternatively, Debian users can install one of Hubert Chan's prebuilt -'Asymptote' binaries from +compiling from ‘UNIX’ source (*note Compiling from UNIX source::). +Alternatively, Debian users can install one of Hubert Chan’s prebuilt +‘Asymptote’ binaries from <http://ftp.debian.org/debian/pool/main/a/asymptote> @@ -318,8 +322,8 @@ File: asymptote.info, Node: MacOS X binary distributions, Next: Microsoft Wind 2.2 MacOS X binary distributions ================================ -'MacOS X' users can either compile the 'UNIX' source code (*note -Compiling from UNIX source::) or install the 'Asymptote' binary +‘MacOS X’ users can either compile the ‘UNIX’ source code (*note +Compiling from UNIX source::) or install the ‘Asymptote’ binary available at <https://www.macports.org/> @@ -328,8 +332,8 @@ available at <https://brew.sh/> -Note that many 'MacOS X' (and FreeBSD) systems lack the GNU 'readline' -library. For full interactive functionality, GNU 'readline' version 4.3 +Note that many ‘MacOS X’ (and FreeBSD) systems lack the GNU ‘readline’ +library. For full interactive functionality, GNU ‘readline’ version 4.3 or later must be installed. @@ -338,29 +342,29 @@ File: asymptote.info, Node: Microsoft Windows, Next: Configuring, Prev: MacOS 2.3 Microsoft Windows ===================== -Users of the 'Microsoft Windows' operating system can install the -self-extracting 'Asymptote' executable 'asymptote-x.xx-setup.exe', where -'x.xx' denotes the latest version. +Users of the ‘Microsoft Windows’ operating system can install the +self-extracting ‘Asymptote’ executable ‘asymptote-x.xx-setup.exe’, where +‘x.xx’ denotes the latest version. A working TeX implementation (we recommend <https://www.tug.org/texlive> or <http://www.miktex.org>) will be -required to typeset labels. You will also need to install 'GPL -Ghostscript' version 9.56 or later from <https://www.ghostscript.com/>. +required to typeset labels. You will also need to install ‘GPL +Ghostscript’ version 9.56 or later from <https://www.ghostscript.com/>. - To view 'PostScript' output, you can install the program 'Sumatra -PDF' available from <https://www.sumatrapdfreader.org/>. + To view ‘PostScript’ output, you can install the program ‘Sumatra +PDF’ available from <https://www.sumatrapdfreader.org/>. - The 'ImageMagick' package from + The ‘ImageMagick’ package from <https://www.imagemagick.org/script/binary-releases.php> is required to support output formats other than HTML, PDF, SVG, and PNG -(*note convert::). The 'Python 3' interpreter from +(*note convert::). The ‘Python 3’ interpreter from <https://www.python.org> is only required if you wish to try out the graphical user interface (*note GUI::). -Example code will be installed by default in the 'examples' subdirectory -of the installation directory (by default, 'C:\Program -Files\Asymptote'). +Example code will be installed by default in the ‘examples’ subdirectory +of the installation directory (by default, ‘C:\Program +Files\Asymptote’). File: asymptote.info, Node: Configuring, Next: Search paths, Prev: Microsoft Windows, Up: Installation @@ -368,20 +372,20 @@ File: asymptote.info, Node: Configuring, Next: Search paths, Prev: Microsoft 2.4 Configuring =============== -In interactive mode, or when given the '-V' option (the default when -running 'Asymptote' on a single file under 'MSDOS'), 'Asymptote' will -automatically invoke your 'PostScript' viewer ('evince' under 'UNIX') to -display graphical output. The 'PostScript' viewer should be capable of -automatically redrawing whenever the output file is updated. The 'UNIX' -'PostScript' viewer 'gv' supports this (via a 'SIGHUP' signal). Users -of 'ggv' will need to enable 'Watch file' under 'Edit/PostScript Viewer -Preferences'. - - Configuration variables are most easily set as 'Asymptote' variables -in an optional configuration file 'config.asy' (*note configuration -file::). For example, the setting 'pdfviewer' specifies the location of +In interactive mode, or when given the ‘-V’ option (the default when +running ‘Asymptote’ on a single file under ‘MSDOS’), ‘Asymptote’ will +automatically invoke your ‘PostScript’ viewer (‘evince’ under ‘UNIX’) to +display graphical output. The ‘PostScript’ viewer should be capable of +automatically redrawing whenever the output file is updated. The ‘UNIX’ +‘PostScript’ viewer ‘gv’ supports this (via a ‘SIGHUP’ signal). Users +of ‘ggv’ will need to enable ‘Watch file’ under ‘Edit/PostScript Viewer +Preferences’. + + Configuration variables are most easily set as ‘Asymptote’ variables +in an optional configuration file ‘config.asy’ (*note configuration +file::). For example, the setting ‘pdfviewer’ specifies the location of the PDF viewer. Here are the default values of several important -configuration variables under 'UNIX': +configuration variables under ‘UNIX’: import settings; pdfviewer="acroread"; @@ -392,44 +396,44 @@ animate="animate"; gs="gs"; libgs=""; -Under 'MSDOS', the viewer settings 'htmlviewer', 'pdfviewer', -'psviewer', 'display', and 'animate' default to the string 'cmd', +Under ‘MSDOS’, the viewer settings ‘htmlviewer’, ‘pdfviewer’, +‘psviewer’, ‘display’, and ‘animate’ default to the string ‘cmd’, requesting the application normally associated with each file type. The -(installation-dependent) default values of 'gs' and 'libgs' are -determined automatically from the 'Microsoft Windows' registry. The -'gs' setting specifies the location of the 'PostScript' processor -'Ghostscript', available from <https://www.ghostscript.com/>. - -The configuration variable 'htmlviewer' specifies the browser to use to -display 3D 'WebGL' output. The default setting is 'google-chrome' under -'UNIX' and 'cmd' under 'Microsoft Windows'. Note that 'Internet -Explorer' does not support 'WebGL'; 'Microsoft Windows' users should set -their default html browser to 'chrome' or 'microsoft-edge'. By default, -2D and 3D 'HTML' images expand to the enclosing canvas; this can be -disabled by setting the configuration variable 'absolute' to 'true'. - - On 'UNIX' systems, to support automatic document reloading of 'PDF' -files in 'Adobe Reader', we recommend copying the file 'reload.js' from -the 'Asymptote' system directory (by default, -'/usr/local/share/asymptote' under 'UNIX' to -'~/.adobe/Acrobat/x.x/JavaScripts/', where 'x.x' represents the -appropriate 'Adobe Reader' version number. The automatic document +(installation-dependent) default values of ‘gs’ and ‘libgs’ are +determined automatically from the ‘Microsoft Windows’ registry. The +‘gs’ setting specifies the location of the ‘PostScript’ processor +‘Ghostscript’, available from <https://www.ghostscript.com/>. + +The configuration variable ‘htmlviewer’ specifies the browser to use to +display 3D ‘WebGL’ output. The default setting is ‘google-chrome’ under +‘UNIX’ and ‘cmd’ under ‘Microsoft Windows’. Note that ‘Internet +Explorer’ does not support ‘WebGL’; ‘Microsoft Windows’ users should set +their default html browser to ‘chrome’ or ‘microsoft-edge’. By default, +2D and 3D ‘HTML’ images expand to the enclosing canvas; this can be +disabled by setting the configuration variable ‘absolute’ to ‘true’. + + On ‘UNIX’ systems, to support automatic document reloading of ‘PDF’ +files in ‘Adobe Reader’, we recommend copying the file ‘reload.js’ from +the ‘Asymptote’ system directory (by default, +‘/usr/local/share/asymptote’ under ‘UNIX’ to +‘~/.adobe/Acrobat/x.x/JavaScripts/’, where ‘x.x’ represents the +appropriate ‘Adobe Reader’ version number. The automatic document reload feature must then be explicitly enabled by putting import settings; pdfreload=true; pdfreloadOptions="-tempFile"; -in the 'Asymptote' configuration file. This reload feature is not -useful under 'MSDOS' since the document cannot be updated anyway on that -operating system until it is first closed by 'Adobe Reader'. +in the ‘Asymptote’ configuration file. This reload feature is not +useful under ‘MSDOS’ since the document cannot be updated anyway on that +operating system until it is first closed by ‘Adobe Reader’. - The configuration variable 'dir' can be used to adjust the search + The configuration variable ‘dir’ can be used to adjust the search path (*note Search paths::). - By default, 'Asymptote' attempts to center the figure on the page, -assuming that the paper type is 'letter'. The default paper type may be -changed to 'a4' with the configuration variable 'papertype'. Alignment + By default, ‘Asymptote’ attempts to center the figure on the page, +assuming that the paper type is ‘letter’. The default paper type may be +changed to ‘a4’ with the configuration variable ‘papertype’. Alignment to other paper sizes can be obtained by setting the configuration -variables 'paperwidth' and 'paperheight'. +variables ‘paperwidth’ and ‘paperheight’. These additional configuration variables normally do not require adjustment: @@ -445,7 +449,7 @@ asygl disabled with the functions warn(string s); nowarn(string s); -or by directly modifying the string array 'settings.suppress', which +or by directly modifying the string array ‘settings.suppress’, which lists all disabled warnings. Configuration variables may also be set or overwritten with a @@ -455,15 +459,15 @@ asy -psviewer=evince -V venn Alternatively, system environment versions of the above configuration variables may be set in the conventional way. The corresponding environment variable name is obtained by converting the configuration -variable name to upper case and prepending 'ASYMPTOTE_': for example, to +variable name to upper case and prepending ‘ASYMPTOTE_’: for example, to set the environment variable ASYMPTOTE_PAPERTYPE="a4"; -under 'Microsoft Windows XP': - 1. Click on the 'Start' button; - 2. Right-click on 'My Computer'; - 3. Choose 'View system information'; - 4. Click the 'Advanced' tab; - 5. Click the 'Environment Variables' button. +under ‘Microsoft Windows XP’: + 1. Click on the ‘Start’ button; + 2. Right-click on ‘My Computer’; + 3. Choose ‘View system information’; + 4. Click the ‘Advanced’ tab; + 5. Click the ‘Environment Variables’ button. File: asymptote.info, Node: Search paths, Next: Compiling from UNIX source, Prev: Configuring, Up: Installation @@ -471,22 +475,22 @@ File: asymptote.info, Node: Search paths, Next: Compiling from UNIX source, P 2.5 Search paths ================ -In looking for 'Asymptote' files, 'asy' will search the following paths, +In looking for ‘Asymptote’ files, ‘asy’ will search the following paths, in the order listed: 1. The current directory; 2. A list of one or more directories specified by the configuration - variable 'dir' or environment variable 'ASYMPTOTE_DIR' (separated - by ':' under UNIX and ';' under 'MSDOS'); + variable ‘dir’ or environment variable ‘ASYMPTOTE_DIR’ (separated + by ‘:’ under UNIX and ‘;’ under ‘MSDOS’); 3. The directory specified by the environment variable - 'ASYMPTOTE_HOME'; if this variable is not set, the directory '.asy' - in the user's home directory ('%USERPROFILE%\.asy' under 'MSDOS') + ‘ASYMPTOTE_HOME’; if this variable is not set, the directory ‘.asy’ + in the user’s home directory (‘%USERPROFILE%\.asy’ under ‘MSDOS’) is used; - 4. The 'Asymptote' system directory (by default, - '/usr/local/share/asymptote' under 'UNIX' and 'C:\Program - Files\Asymptote' under 'MSDOS'). - 5. The 'Asymptote' examples directory (by default, - '/usr/local/share/doc/asymptote/examples' under 'UNIX' and - 'C:\Program Files\Asymptote\examples' under 'MSDOS'). + 4. The ‘Asymptote’ system directory (by default, + ‘/usr/local/share/asymptote’ under ‘UNIX’ and ‘C:\Program + Files\Asymptote’ under ‘MSDOS’). + 5. The ‘Asymptote’ examples directory (by default, + ‘/usr/local/share/doc/asymptote/examples’ under ‘UNIX’ and + ‘C:\Program Files\Asymptote\examples’ under ‘MSDOS’). File: asymptote.info, Node: Compiling from UNIX source, Next: Editing modes, Prev: Search paths, Up: Installation @@ -494,8 +498,8 @@ File: asymptote.info, Node: Compiling from UNIX source, Next: Editing modes, 2.6 Compiling from UNIX source ============================== -To compile and install a 'UNIX' executable from the source release -'asymptote-x.xx.src.tgz' in the subdirectory 'x.xx' under +To compile and install a ‘UNIX’ executable from the source release +‘asymptote-x.xx.src.tgz’ in the subdirectory ‘x.xx’ under <https://sourceforge.net/projects/asymptote/files/> @@ -507,10 +511,10 @@ cd asymptote-x.xx used; if it is old we recommend first putting <https://github.com/ivmai/bdwgc/releases/download/v8.0.4/gc-8.0.4.tar.gz> <https://www.ivmaisoft.com/_bin/atomic_ops/libatomic_ops-7.6.10.tar.gz> -in the 'Asymptote' source directory. +in the ‘Asymptote’ source directory. - On 'UNIX' platforms (other than 'MacOS X'), we recommend using -version '3.2.1' of the 'freeglut' library. To compile 'freeglut', + On ‘UNIX’ platforms (other than ‘MacOS X’), we recommend using +version ‘3.2.1’ of the ‘freeglut’ library. To compile ‘freeglut’, download <https://prdownloads.sourceforge.net/freeglut/freeglut-3.2.1.tar.gz> and type (as the root user): @@ -521,44 +525,44 @@ cmake -DCMAKE_INSTALL_PREFIX=/usr -DCMAKE_C_FLAGS=-fcommon . make make install - Then compile 'Asymptote' with the commands + Then compile ‘Asymptote’ with the commands ./configure make all make install -Be sure to use GNU 'make' (on non-GNU systems this command may be called -'gmake'). To build the documentation, you may need to install the -'texinfo-tex' package. If you get errors from a broken 'texinfo' or -'pdftex' installation, simply put +Be sure to use GNU ‘make’ (on non-GNU systems this command may be called +‘gmake’). To build the documentation, you may need to install the +‘texinfo-tex’ package. If you get errors from a broken ‘texinfo’ or +‘pdftex’ installation, simply put <https://asymptote.sourceforge.io/asymptote.pdf> -in the directory 'doc' and repeat the command 'make all'. +in the directory ‘doc’ and repeat the command ‘make all’. For a (default) system-wide installation, the last command should be done as the root user. To install without root privileges, change the -'./configure' command to +‘./configure’ command to ./configure --prefix=$HOME/asymptote One can disable use of the Boehm garbage collector by configuring -with './configure --disable-gc'. For a list of other configuration -options, say './configure --help'. For example, under 'MacOS X', one -can tell configure to use the 'clang' compilers and look for header +with ‘./configure --disable-gc’. For a list of other configuration +options, say ‘./configure --help’. For example, under ‘MacOS X’, one +can tell configure to use the ‘clang’ compilers and look for header files and libraries in nonstandard locations: ./configure CC=clang CXX=clang++ CPPFLAGS=-I/opt/local/include LDFLAGS=-L/opt/local/lib - If you are compiling 'Asymptote' with 'gcc', you will need a + If you are compiling ‘Asymptote’ with ‘gcc’, you will need a relatively recent version (e.g. 3.4.4 or later). For full interactive -functionality, you will need version 4.3 or later of the GNU 'readline' -library. The file 'gcc3.3.2curses.patch' in the 'patches' directory can +functionality, you will need version 4.3 or later of the GNU ‘readline’ +library. The file ‘gcc3.3.2curses.patch’ in the ‘patches’ directory can be used to patch the broken curses.h header file (or a local copy -thereof in the current directory) on some 'AIX' and 'IRIX' systems. +thereof in the current directory) on some ‘AIX’ and ‘IRIX’ systems. - The 'FFTW' library is only required if you want 'Asymptote' to be + The ‘FFTW’ library is only required if you want ‘Asymptote’ to be able to take Fourier transforms of data (say, to compute an audio power -spectrum). The 'GSL' library is only required if you require the +spectrum). The ‘GSL’ library is only required if you require the special functions that it supports. - If you don't want to install 'Asymptote' system wide, just make sure -the compiled binary 'asy' and GUI script 'xasy' are in your path and set -the configuration variable 'dir' to point to the directory 'base' (in -the top level directory of the 'Asymptote' source code). + If you don’t want to install ‘Asymptote’ system wide, just make sure +the compiled binary ‘asy’ and GUI script ‘xasy’ are in your path and set +the configuration variable ‘dir’ to point to the directory ‘base’ (in +the top level directory of the ‘Asymptote’ source code). File: asymptote.info, Node: Editing modes, Next: Git, Prev: Compiling from UNIX source, Up: Installation @@ -566,52 +570,52 @@ File: asymptote.info, Node: Editing modes, Next: Git, Prev: Compiling from UN 2.7 Editing modes ================= -Users of 'emacs' can edit 'Asymptote' code with the mode 'asy-mode', -after enabling it by putting the following lines in their '.emacs' -initialization file, replacing 'ASYDIR' with the location of the -'Asymptote' system directory (by default, '/usr/local/share/asymptote' -or 'C:\Program Files\Asymptote' under 'MSDOS'): +Users of ‘emacs’ can edit ‘Asymptote’ code with the mode ‘asy-mode’, +after enabling it by putting the following lines in their ‘.emacs’ +initialization file, replacing ‘ASYDIR’ with the location of the +‘Asymptote’ system directory (by default, ‘/usr/local/share/asymptote’ +or ‘C:\Program Files\Asymptote’ under ‘MSDOS’): (add-to-list 'load-path "ASYDIR") (autoload 'asy-mode "asy-mode.el" "Asymptote major mode." t) (autoload 'lasy-mode "asy-mode.el" "hybrid Asymptote/Latex major mode." t) (autoload 'asy-insinuate-latex "asy-mode.el" "Asymptote insinuate LaTeX." t) (add-to-list 'auto-mode-alist '("\\.asy$" . asy-mode)) -Particularly useful key bindings in this mode are 'C-c C-c', which -compiles and displays the current buffer, and the key binding 'C-c ?', +Particularly useful key bindings in this mode are ‘C-c C-c’, which +compiles and displays the current buffer, and the key binding ‘C-c ?’, which shows the available function prototypes for the command at the cursor. For full functionality you should also install the Apache -Software Foundation package 'two-mode-mode': +Software Foundation package ‘two-mode-mode’: <https://www.dedasys.com/freesoftware/files/two-mode-mode.el> -Once installed, you can use the hybrid mode 'lasy-mode' to edit a LaTeX -file containing embedded 'Asymptote' code (*note LaTeX usage::). This -mode can be enabled within 'latex-mode' with the key sequence 'M-x -lasy-mode <RET>'. On 'UNIX' systems, additional keywords will be -generated from all 'asy' files in the space-separated list of -directories specified by the environment variable 'ASYMPTOTE_SITEDIR'. -Further documentation of 'asy-mode' is available within 'emacs' by -pressing the sequence keys 'C-h f asy-mode <RET>'. +Once installed, you can use the hybrid mode ‘lasy-mode’ to edit a LaTeX +file containing embedded ‘Asymptote’ code (*note LaTeX usage::). This +mode can be enabled within ‘latex-mode’ with the key sequence ‘M-x +lasy-mode <RET>’. On ‘UNIX’ systems, additional keywords will be +generated from all ‘asy’ files in the space-separated list of +directories specified by the environment variable ‘ASYMPTOTE_SITEDIR’. +Further documentation of ‘asy-mode’ is available within ‘emacs’ by +pressing the sequence keys ‘C-h f asy-mode <RET>’. - Fans of 'vim' can customize 'vim' for 'Asymptote' with + Fans of ‘vim’ can customize ‘vim’ for ‘Asymptote’ with -'cp /usr/local/share/asymptote/asy.vim ~/.vim/syntax/asy.vim' +‘cp /usr/local/share/asymptote/asy.vim ~/.vim/syntax/asy.vim’ -and add the following to their '~/.vimrc' file: +and add the following to their ‘~/.vimrc’ file: augroup filetypedetect au BufNewFile,BufRead *.asy setf asy augroup END filetype plugin on - If any of these directories or files don't exist, just create them. -To set 'vim' up to run the current asymptote script using ':make' just -add to '~/.vim/ftplugin/asy.vim': + If any of these directories or files don’t exist, just create them. +To set ‘vim’ up to run the current asymptote script using ‘:make’ just +add to ‘~/.vim/ftplugin/asy.vim’: setlocal makeprg=asy\ % setlocal errorformat=%f:\ %l.%c:\ %m - Syntax highlighting support for the KDE editor 'Kate' can be enabled -by running 'asy-kate.sh' in the '/usr/local/share/asymptote' directory -and putting the generated 'asymptote.xml' file in -'~/.local/share/org.kde.syntax-highlighting/syntax/'. + Syntax highlighting support for the KDE editor ‘Kate’ can be enabled +by running ‘asy-kate.sh’ in the ‘/usr/local/share/asymptote’ directory +and putting the generated ‘asymptote.xml’ file in +‘~/.local/share/org.kde.syntax-highlighting/syntax/’. File: asymptote.info, Node: Git, Next: Uninstall, Prev: Editing modes, Up: Installation @@ -620,7 +624,7 @@ File: asymptote.info, Node: Git, Next: Uninstall, Prev: Editing modes, Up: I ======= The following commands are needed to install the latest development -version of 'Asymptote' using 'git': +version of ‘Asymptote’ using ‘git’: git clone https://github.com/vectorgraphics/asymptote cd asymptote @@ -629,8 +633,8 @@ cd asymptote make all make install -To compile without optimization, use the command 'make CFLAGS=-g'. On -'Ubuntu' systems, you may need to first install the required +To compile without optimization, use the command ‘make CFLAGS=-g’. On +‘Ubuntu’ systems, you may need to first install the required dependencies: apt-get build-dep asymptote @@ -640,11 +644,11 @@ File: asymptote.info, Node: Uninstall, Prev: Git, Up: Installation 2.9 Uninstall ============= -To uninstall a 'Linux x86_64' binary distribution, use the commands +To uninstall a ‘Linux x86_64’ binary distribution, use the commands tar -zxvf asymptote-x.xx.x86_64.tgz | xargs --replace=% rm /% texhash -To uninstall all 'Asymptote' files installed from a source distribution, +To uninstall all ‘Asymptote’ files installed from a source distribution, use the command make uninstall @@ -656,19 +660,19 @@ File: asymptote.info, Node: Tutorial, Next: Drawing commands, Prev: Installat * Menu: -* Drawing in batch mode:: Run 'Asymptote' on a text file -* Drawing in interactive mode:: Running 'Asymptote' interactively +* Drawing in batch mode:: Run ‘Asymptote’ on a text file +* Drawing in interactive mode:: Running ‘Asymptote’ interactively * Figure size:: Specifying the figure size -* Labels:: Adding 'LaTeX' labels +* Labels:: Adding ‘LaTeX’ labels * Paths:: Drawing lines and curves -A concise introduction to 'Asymptote' is given here. For a more -thorough introduction, see the excellent 'Asymptote' tutorial written by +A concise introduction to ‘Asymptote’ is given here. For a more +thorough introduction, see the excellent ‘Asymptote’ tutorial written by Charles Staats: <https://asymptote.sourceforge.io/asymptote_tutorial.pdf> - Another 'Asymptote' tutorial is available as a wiki, with images + Another ‘Asymptote’ tutorial is available as a wiki, with images rendered by an online Asymptote engine: <https://www.artofproblemsolving.com/wiki/?title=Asymptote_(Vector_Graphics_Language)> @@ -680,23 +684,23 @@ File: asymptote.info, Node: Drawing in batch mode, Next: Drawing in interactiv ========================= To draw a line from coordinate (0,0) to coordinate (100,100), create a -text file 'test.asy' containing +text file ‘test.asy’ containing draw((0,0)--(100,100)); Then execute the command asy -V test -Alternatively, 'MSDOS' users can drag and drop 'test.asy' onto the -Desktop 'asy' icon (or make 'Asymptote' the default application for the -extension 'asy'). +Alternatively, ‘MSDOS’ users can drag and drop ‘test.asy’ onto the +Desktop ‘asy’ icon (or make ‘Asymptote’ the default application for the +extension ‘asy’). -This method, known as _batch mode_, outputs a 'PostScript' file -'test.eps'. If you prefer PDF output, use the command line +This method, known as _batch mode_, outputs a ‘PostScript’ file +‘test.eps’. If you prefer PDF output, use the command line asy -V -f pdf test - In either case, the '-V' option opens up a viewer window so you can + In either case, the ‘-V’ option opens up a viewer window so you can immediately view the result: [./diagonal] -Here, the '--' connector joins the two points '(0,0)' and '(100,100)' +Here, the ‘--’ connector joins the two points ‘(0,0)’ and ‘(100,100)’ with a line segment. @@ -705,17 +709,17 @@ File: asymptote.info, Node: Drawing in interactive mode, Next: Figure size, P 3.2 Drawing in interactive mode =============================== -Another method is _interactive mode_, where 'Asymptote' reads individual +Another method is _interactive mode_, where ‘Asymptote’ reads individual commands as they are entered by the user. To try this out, enter -'Asymptote''s interactive mode by clicking on the 'Asymptote' icon or -typing the command 'asy'. Then type +‘Asymptote’’s interactive mode by clicking on the ‘Asymptote’ icon or +typing the command ‘asy’. Then type draw((0,0)--(100,100)); -followed by 'Enter', to obtain the above image. At this point you can -type further 'draw' commands, which will be added to the displayed -figure, 'erase' to clear the canvas, +followed by ‘Enter’, to obtain the above image. At this point you can +type further ‘draw’ commands, which will be added to the displayed +figure, ‘erase’ to clear the canvas, input test; -to execute all of the commands contained in the file 'test.asy', or -'quit' to exit interactive mode. You can use the arrow keys in +to execute all of the commands contained in the file ‘test.asy’, or +‘quit’ to exit interactive mode. You can use the arrow keys in interactive mode to edit previous lines. The tab key will automatically complete unambiguous words; otherwise, hitting tab again will show the possible choices. Further commands specific to interactive mode are @@ -727,20 +731,20 @@ File: asymptote.info, Node: Figure size, Next: Labels, Prev: Drawing in inter 3.3 Figure size =============== -In 'Asymptote', coordinates like '(0,0)' and '(100,100)', called -_pairs_, are expressed in 'PostScript' "big points" (1 'bp' = 1/72 -'inch') and the default line width is '0.5bp'. However, it is often -inconvenient to work directly in 'PostScript' coordinates. The next +In ‘Asymptote’, coordinates like ‘(0,0)’ and ‘(100,100)’, called +_pairs_, are expressed in ‘PostScript’ "big points" (1 ‘bp’ = 1/72 +‘inch’) and the default line width is ‘0.5bp’. However, it is often +inconvenient to work directly in ‘PostScript’ coordinates. The next example produces identical output to the previous example, by scaling -the line '(0,0)--(1,1)' to fit a rectangle of width '100.5 bp' and -height '100.5 bp' (the extra '0.5bp' accounts for the line width): +the line ‘(0,0)--(1,1)’ to fit a rectangle of width ‘100.5 bp’ and +height ‘100.5 bp’ (the extra ‘0.5bp’ accounts for the line width): size(100.5,100.5); draw((0,0)--(1,1)); [./diagonal] - One can also specify the size in 'pt' (1 'pt' = 1/72.27 'inch'), -'cm', 'mm', or 'inches'. Two nonzero size arguments (or a single size + One can also specify the size in ‘pt’ (1 ‘pt’ = 1/72.27 ‘inch’), +‘cm’, ‘mm’, or ‘inches’. Two nonzero size arguments (or a single size argument) restrict the size in both directions, preserving the aspect ratio. If 0 is given as a size argument, no restriction is made in that direction; the overall scaling will be determined by the other direction @@ -750,17 +754,17 @@ draw((0,0)--(2,1),Arrow); [./bigdiagonal] - To connect several points and create a cyclic path, use the 'cycle' + To connect several points and create a cyclic path, use the ‘cycle’ keyword: size(3cm); draw((0,0)--(1,0)--(1,1)--(0,1)--cycle); [./square] -For convenience, the path '(0,0)--(1,0)--(1,1)--(0,1)--cycle' may be -replaced with the predefined variable 'unitsquare', or equivalently, -'box((0,0),(1,1))'. +For convenience, the path ‘(0,0)--(1,0)--(1,1)--(0,1)--cycle’ may be +replaced with the predefined variable ‘unitsquare’, or equivalently, +‘box((0,0),(1,1))’. - To make the user coordinates represent multiples of exactly '1cm': + To make the user coordinates represent multiples of exactly ‘1cm’: unitsize(1cm); draw(unitsquare); @@ -770,8 +774,8 @@ File: asymptote.info, Node: Labels, Next: Paths, Prev: Figure size, Up: Tuto 3.4 Labels ========== -Adding labels is easy in 'Asymptote'; one specifies the label as a -double-quoted 'LaTeX' string, a coordinate, and an optional alignment +Adding labels is easy in ‘Asymptote’; one specifies the label as a +double-quoted ‘LaTeX’ string, a coordinate, and an optional alignment direction: size(3cm); draw(unitsquare); @@ -782,12 +786,12 @@ label("$D$",(0,1),NW); [./labelsquare] - 'Asymptote' uses the standard compass directions 'E=(1,0)', -'N=(0,1)', 'NE=unit(N+E)', and 'ENE=unit(E+NE)', etc., which along with -the directions 'up', 'down', 'right', and 'left' are defined as pairs in -the 'Asymptote' base module 'plain' (a user who has a local variable -named 'E' may access the compass direction 'E' by prefixing it with the -name of the module where it is defined: 'plain.E'). + ‘Asymptote’ uses the standard compass directions ‘E=(1,0)’, +‘N=(0,1)’, ‘NE=unit(N+E)’, and ‘ENE=unit(E+NE)’, etc., which along with +the directions ‘up’, ‘down’, ‘right’, and ‘left’ are defined as pairs in +the ‘Asymptote’ base module ‘plain’ (a user who has a local variable +named ‘E’ may access the compass direction ‘E’ by prefixing it with the +name of the module where it is defined: ‘plain.E’). File: asymptote.info, Node: Paths, Prev: Labels, Up: Tutorial @@ -801,23 +805,23 @@ size(100,0); draw((1,0){up}..{left}(0,1),Arrow); [./quartercircle] -Here the directions 'up' and 'left' in braces specify the outgoing and -incoming directions at the points '(1,0)' and '(0,1)', respectively. +Here the directions ‘up’ and ‘left’ in braces specify the outgoing and +incoming directions at the points ‘(1,0)’ and ‘(0,1)’, respectively. In general, a path is specified as a list of points (or other paths) -interconnected with '--', which denotes a straight line segment, or -'..', which denotes a cubic spline (*note Bezier curves::). Specifying -a final '..cycle' creates a cyclic path that connects smoothly back to +interconnected with ‘--’, which denotes a straight line segment, or +‘..’, which denotes a cubic spline (*note Bezier curves::). Specifying +a final ‘..cycle’ creates a cyclic path that connects smoothly back to the initial node, as in this approximation (accurate to within 0.06%) of a unit circle: path unitcircle=E..N..W..S..cycle; -An 'Asymptote' path, being connected, is equivalent to a 'PostScript -subpath'. The '^^' binary operator, which requests that the pen be +An ‘Asymptote’ path, being connected, is equivalent to a ‘PostScript +subpath’. The ‘^^’ binary operator, which requests that the pen be moved (without drawing or affecting endpoint curvatures) from the final point of the left-hand path to the initial point of the right-hand path, -may be used to group several 'Asymptote' paths into a 'path[]' array -(equivalent to a 'PostScript' path): +may be used to group several ‘Asymptote’ paths into a ‘path[]’ array +(equivalent to a ‘PostScript’ path): size(0,100); path unitcircle=E..N..W..S..cycle; path g=scale(2)*unitcircle; @@ -826,15 +830,15 @@ filldraw(unitcircle^^g,evenodd+yellow,black); [./superpath] -The 'PostScript' even-odd fill rule here specifies that only the region +The ‘PostScript’ even-odd fill rule here specifies that only the region bounded between the two unit circles is filled (*note fillrule::). In this example, the same effect can be achieved by using the default zero winding number fill rule, if one is careful to alternate the orientation of the paths: filldraw(unitcircle^^reverse(g),yellow,black); - The '^^' operator is used by the 'box(triple, triple)' function in -the module 'three' to construct the edges of a cube 'unitbox' without + The ‘^^’ operator is used by the ‘box(triple, triple)’ function in +the module ‘three’ to construct the edges of a cube ‘unitbox’ without retracing steps (*note three::): import three; @@ -854,7 +858,7 @@ label("(0,0,1)",(0,0,1),Z); [./cube] - See section *note graph:: (or the online 'Asymptote' gallery and + See section *note graph:: (or the online ‘Asymptote’ gallery and external links posted at <https://asymptote.sourceforge.io>) for further examples, including two-dimensional and interactive three-dimensional scientific graphs. Additional examples have been posted by Philippe @@ -867,25 +871,25 @@ File: asymptote.info, Node: Drawing commands, Next: Bezier curves, Prev: Tuto 4 Drawing commands ****************** -All of 'Asymptote''s graphical capabilities are based on four primitive -commands. The three 'PostScript' drawing commands 'draw', 'fill', and -'clip' add objects to a picture in the order in which they are executed, +All of ‘Asymptote’’s graphical capabilities are based on four primitive +commands. The three ‘PostScript’ drawing commands ‘draw’, ‘fill’, and +‘clip’ add objects to a picture in the order in which they are executed, with the most recently drawn object appearing on top. The labeling -command 'label' can be used to add text labels and external EPS images, -which will appear on top of the 'PostScript' objects (since this is +command ‘label’ can be used to add text labels and external EPS images, +which will appear on top of the ‘PostScript’ objects (since this is normally what one wants), but again in the relative order in which they were executed. After drawing objects on a picture, the picture can be -output with the 'shipout' function (*note shipout::). +output with the ‘shipout’ function (*note shipout::). - If you wish to draw 'PostScript' objects on top of labels (or -verbatim 'tex' commands; *note tex::), the 'layer' command may be used -to start a new 'PostScript/LaTeX' layer: + If you wish to draw ‘PostScript’ objects on top of labels (or +verbatim ‘tex’ commands; *note tex::), the ‘layer’ command may be used +to start a new ‘PostScript/LaTeX’ layer: void layer(picture pic=currentpicture); - The 'layer' function gives one full control over the order in which + The ‘layer’ function gives one full control over the order in which objects are drawn. Layers are drawn sequentially, with the most recent layer appearing on top. Within each layer, labels, images, and verbatim -'tex' commands are always drawn after the 'PostScript' objects in that +‘tex’ commands are always drawn after the ‘PostScript’ objects in that layer. A page break can be generated with the command @@ -913,60 +917,60 @@ void draw(picture pic=currentpicture, Label L="", path g, arrowbar arrow=None, arrowbar bar=None, margin margin=NoMargin, Label legend="", marker marker=nomarker); - Draw the path 'g' on the picture 'pic' using pen 'p' for drawing, -with optional drawing attributes (Label 'L', explicit label alignment -'align', arrows and bars 'arrow' and 'bar', margins 'margin', legend, -and markers 'marker'). Only one parameter, the path, is required. For -convenience, the arguments 'arrow' and 'bar' may be specified in either -order. The argument 'legend' is a Label to use in constructing an + Draw the path ‘g’ on the picture ‘pic’ using pen ‘p’ for drawing, +with optional drawing attributes (Label ‘L’, explicit label alignment +‘align’, arrows and bars ‘arrow’ and ‘bar’, margins ‘margin’, legend, +and markers ‘marker’). Only one parameter, the path, is required. For +convenience, the arguments ‘arrow’ and ‘bar’ may be specified in either +order. The argument ‘legend’ is a Label to use in constructing an optional legend entry. Bars are useful for indicating dimensions. The possible values of -'bar' are 'None', 'BeginBar', 'EndBar' (or equivalently 'Bar'), and -'Bars' (which draws a bar at both ends of the path). Each of these bar -specifiers (except for 'None') will accept an optional real argument -that denotes the length of the bar in 'PostScript' coordinates. The -default bar length is 'barsize(pen)'. - - The possible values of 'arrow' are 'None', 'Blank' (which draws no -arrows or path), 'BeginArrow', 'MidArrow', 'EndArrow' (or equivalently -'Arrow'), and 'Arrows' (which draws an arrow at both ends of the path). -All of the arrow specifiers except for 'None' and 'Blank' may be given -the optional arguments arrowhead 'arrowhead' (one of the predefined -arrowhead styles 'DefaultHead', 'SimpleHead', 'HookHead', 'TeXHead'), -real 'size' (arrowhead size in 'PostScript' coordinates), real 'angle' -(arrowhead angle in degrees), filltype 'filltype' (one of 'FillDraw', -'Fill', 'NoFill', 'UnFill', 'Draw') and (except for 'MidArrow' and -'Arrows') a real 'position' (in the sense of 'point(path p, real t)') +‘bar’ are ‘None’, ‘BeginBar’, ‘EndBar’ (or equivalently ‘Bar’), and +‘Bars’ (which draws a bar at both ends of the path). Each of these bar +specifiers (except for ‘None’) will accept an optional real argument +that denotes the length of the bar in ‘PostScript’ coordinates. The +default bar length is ‘barsize(pen)’. + + The possible values of ‘arrow’ are ‘None’, ‘Blank’ (which draws no +arrows or path), ‘BeginArrow’, ‘MidArrow’, ‘EndArrow’ (or equivalently +‘Arrow’), and ‘Arrows’ (which draws an arrow at both ends of the path). +All of the arrow specifiers except for ‘None’ and ‘Blank’ may be given +the optional arguments arrowhead ‘arrowhead’ (one of the predefined +arrowhead styles ‘DefaultHead’, ‘SimpleHead’, ‘HookHead’, ‘TeXHead’), +real ‘size’ (arrowhead size in ‘PostScript’ coordinates), real ‘angle’ +(arrowhead angle in degrees), filltype ‘filltype’ (one of ‘FillDraw’, +‘Fill’, ‘NoFill’, ‘UnFill’, ‘Draw’) and (except for ‘MidArrow’ and +‘Arrows’) a real ‘position’ (in the sense of ‘point(path p, real t)’) along the path where the tip of the arrow should be placed. The default -arrowhead size when drawn with a pen 'p' is 'arrowsize(p)'. There are -also arrow versions with slightly modified default values of 'size' and -'angle' suitable for curved arrows: 'BeginArcArrow', 'EndArcArrow' (or -equivalently 'ArcArrow'), 'MidArcArrow', and 'ArcArrows'. +arrowhead size when drawn with a pen ‘p’ is ‘arrowsize(p)’. There are +also arrow versions with slightly modified default values of ‘size’ and +‘angle’ suitable for curved arrows: ‘BeginArcArrow’, ‘EndArcArrow’ (or +equivalently ‘ArcArrow’), ‘MidArcArrow’, and ‘ArcArrows’. Margins can be used to shrink the visible portion of a path by -'labelmargin(p)' to avoid overlap with other drawn objects. Typical -values of 'margin' are 'NoMargin', 'BeginMargin', 'EndMargin' (or -equivalently 'Margin'), and 'Margins' (which leaves a margin at both -ends of the path). One may use 'Margin(real begin, real end=begin)' to +‘labelmargin(p)’ to avoid overlap with other drawn objects. Typical +values of ‘margin’ are ‘NoMargin’, ‘BeginMargin’, ‘EndMargin’ (or +equivalently ‘Margin’), and ‘Margins’ (which leaves a margin at both +ends of the path). One may use ‘Margin(real begin, real end=begin)’ to specify the size of the beginning and ending margin, respectively, in -multiples of the units 'labelmargin(p)' used for aligning labels. -Alternatively, 'BeginPenMargin', 'EndPenMargin' (or equivalently -'PenMargin'), 'PenMargins', 'PenMargin(real begin, real end=begin)' +multiples of the units ‘labelmargin(p)’ used for aligning labels. +Alternatively, ‘BeginPenMargin’, ‘EndPenMargin’ (or equivalently +‘PenMargin’), ‘PenMargins’, ‘PenMargin(real begin, real end=begin)’ specify a margin in units of the pen line width, taking account of the pen line width when drawing the path or arrow. For example, use -'DotMargin', an abbreviation for -'PenMargin(-0.5*dotfactor,0.5*dotfactor)', to draw from the usual +‘DotMargin’, an abbreviation for +‘PenMargin(-0.5*dotfactor,0.5*dotfactor)’, to draw from the usual beginning point just up to the boundary of an end dot of width -'dotfactor*linewidth(p)'. The qualifiers 'BeginDotMargin', -'EndDotMargin', and 'DotMargins' work similarly. The qualifier -'TrueMargin(real begin, real end=begin)' allows one to specify a margin -directly in 'PostScript' units, independent of the pen line width. +‘dotfactor*linewidth(p)’. The qualifiers ‘BeginDotMargin’, +‘EndDotMargin’, and ‘DotMargins’ work similarly. The qualifier +‘TrueMargin(real begin, real end=begin)’ allows one to specify a margin +directly in ‘PostScript’ units, independent of the pen line width. The use of arrows, bars, and margins is illustrated by the examples -'Pythagoras.asy' and 'sqrtx01.asy'. +‘Pythagoras.asy’ and ‘sqrtx01.asy’. - The legend for a picture 'pic' can be fit and aligned to a frame with + The legend for a picture ‘pic’ can be fit and aligned to a frame with the routine: frame legend(picture pic=currentpicture, int perline=1, real xmargin=legendmargin, real ymargin=xmargin, @@ -974,22 +978,22 @@ frame legend(picture pic=currentpicture, int perline=1, real hskip=legendhskip, real vskip=legendvskip, real maxwidth=0, real maxheight=0, bool hstretch=false, bool vstretch=false, pen p=currentpen); -Here 'xmargin' and 'ymargin' specify the surrounding x and y margins, -'perline' specifies the number of entries per line (default 1; 0 means -choose this number automatically), 'linelength' specifies the length of -the path lines, 'hskip' and 'vskip' specify the line skip (as a multiple -of the legend entry size), 'maxwidth' and 'maxheight' specify optional +Here ‘xmargin’ and ‘ymargin’ specify the surrounding x and y margins, +‘perline’ specifies the number of entries per line (default 1; 0 means +choose this number automatically), ‘linelength’ specifies the length of +the path lines, ‘hskip’ and ‘vskip’ specify the line skip (as a multiple +of the legend entry size), ‘maxwidth’ and ‘maxheight’ specify optional upper limits on the width and height of the resulting legend (0 means -unlimited), 'hstretch' and 'vstretch' allow the legend to stretch -horizontally or vertically, and 'p' specifies the pen used to draw the +unlimited), ‘hstretch’ and ‘vstretch’ allow the legend to stretch +horizontally or vertically, and ‘p’ specifies the pen used to draw the bounding box. The legend frame can then be added and aligned about a -point on a picture 'dest' using 'add' or 'attach' (*note add about::). +point on a picture ‘dest’ using ‘add’ or ‘attach’ (*note add about::). To draw a dot, simply draw a path containing a single point. The -'dot' command defined in the module 'plain' draws a dot having a +‘dot’ command defined in the module ‘plain’ draws a dot having a diameter equal to an explicit pen line width or the default line width -magnified by 'dotfactor' (6 by default), using the specified filltype -(*note filltype::) or 'dotfilltype' ('Fill' by default): +magnified by ‘dotfactor’ (6 by default), using the specified filltype +(*note filltype::) or ‘dotfilltype’ (‘Fill’ by default): void dot(frame f, pair z, pen p=currentpen, filltype filltype=dotfilltype); void dot(picture pic=currentpicture, pair z, pen p=currentpen, filltype filltype=dotfilltype); @@ -1003,10 +1007,10 @@ void dot(picture pic=currentpicture, path[] g, pen p=currentpen, void dot(picture pic=currentpicture, Label L, pen p=currentpen, filltype filltype=dotfilltype); - If the variable 'Label' is given as the 'Label' argument to the third -routine, the 'format' argument will be used to format a string based on -the dot location (here 'defaultformat' is '"$%.4g$"'). The fourth -routine draws a dot at every point of a pair array 'z'. One can also + If the variable ‘Label’ is given as the ‘Label’ argument to the third +routine, the ‘format’ argument will be used to format a string based on +the dot location (here ‘defaultformat’ is ‘"$%.4g$"’). The fourth +routine draws a dot at every point of a pair array ‘z’. One can also draw a dot at every node of a path: void dot(picture pic=currentpicture, Label[] L=new Label[], explicit path g, align align=RightSide, string format=defaultformat, @@ -1014,8 +1018,8 @@ void dot(picture pic=currentpicture, Label[] L=new Label[], See *note pathmarkers:: and *note markers:: for more general methods for marking path nodes. - To draw a fixed-sized object (in 'PostScript' coordinates) about the -user coordinate 'origin', use the routine + To draw a fixed-sized object (in ‘PostScript’ coordinates) about the +user coordinate ‘origin’, use the routine void draw(pair origin, picture pic=currentpicture, Label L="", path g, align align=NoAlign, pen p=currentpen, arrowbar arrow=None, arrowbar bar=None, margin margin=NoMargin, Label legend="", @@ -1029,18 +1033,18 @@ File: asymptote.info, Node: fill, Next: clip, Prev: draw, Up: Drawing comman void fill(picture pic=currentpicture, path g, pen p=currentpen); - Fill the interior region bounded by the cyclic path 'g' on the -picture 'pic', using the pen 'p'. + Fill the interior region bounded by the cyclic path ‘g’ on the +picture ‘pic’, using the pen ‘p’. - There is also a convenient 'filldraw' command, which fills the path + There is also a convenient ‘filldraw’ command, which fills the path and then draws in the boundary. One can specify separate pens for each operation: void filldraw(picture pic=currentpicture, path g, pen fillpen=currentpen, pen drawpen=currentpen); - This fixed-size version of 'fill' allows one to fill an object -described in 'PostScript' coordinates about the user coordinate -'origin': + This fixed-size version of ‘fill’ allows one to fill an object +described in ‘PostScript’ coordinates about the user coordinate +‘origin’: void fill(pair origin, picture pic=currentpicture, path g, pen p=currentpen); This is just a convenient abbreviation for the commands: @@ -1050,64 +1054,64 @@ add(pic,opic,origin); The routine void filloutside(picture pic=currentpicture, path g, pen p=currentpen); -fills the region exterior to the path 'g', out to the current boundary -of picture 'pic'. +fills the region exterior to the path ‘g’, out to the current boundary +of picture ‘pic’. Lattice gradient shading varying smoothly over a two-dimensional -array of pens 'p', using fill rule 'fillrule', can be produced with +array of pens ‘p’, using fill rule ‘fillrule’, can be produced with void latticeshade(picture pic=currentpicture, path g, bool stroke=false, pen fillrule=currentpen, pen[][] p) - If 'stroke=true', the region filled is the same as the region that -would be drawn by 'draw(pic,g,zerowinding)'; in this case the path 'g' -need not be cyclic. The pens in 'p' must belong to the same color -space. One can use the functions 'rgb(pen)' or 'cmyk(pen)' to promote + If ‘stroke=true’, the region filled is the same as the region that +would be drawn by ‘draw(pic,g,zerowinding)’; in this case the path ‘g’ +need not be cyclic. The pens in ‘p’ must belong to the same color +space. One can use the functions ‘rgb(pen)’ or ‘cmyk(pen)’ to promote pens to a higher color space, as illustrated in the example file -'latticeshading.asy'. +‘latticeshading.asy’. - Axial gradient shading varying smoothly from 'pena' to 'penb' in the -direction of the line segment 'a--b' can be achieved with + Axial gradient shading varying smoothly from ‘pena’ to ‘penb’ in the +direction of the line segment ‘a--b’ can be achieved with void axialshade(picture pic=currentpicture, path g, bool stroke=false, pen pena, pair a, bool extenda=true, pen penb, pair b, bool extendb=true); -The boolean parameters 'extenda' and 'extendb' indicate whether the -shading should extend beyond the axis endpoints 'a' and 'b'. An example -of axial shading is provided in the example file 'axialshade.asy'. +The boolean parameters ‘extenda’ and ‘extendb’ indicate whether the +shading should extend beyond the axis endpoints ‘a’ and ‘b’. An example +of axial shading is provided in the example file ‘axialshade.asy’. - Radial gradient shading varying smoothly from 'pena' on the circle -with center 'a' and radius 'ra' to 'penb' on the circle with center 'b' -and radius 'rb' is similar: + Radial gradient shading varying smoothly from ‘pena’ on the circle +with center ‘a’ and radius ‘ra’ to ‘penb’ on the circle with center ‘b’ +and radius ‘rb’ is similar: void radialshade(picture pic=currentpicture, path g, bool stroke=false, pen pena, pair a, real ra, bool extenda=true, pen penb, pair b, real rb, bool extendb=true); -The boolean parameters 'extenda' and 'extendb' indicate whether the -shading should extend beyond the radii 'a' and 'b'. Illustrations of -radial shading are provided in the example files 'shade.asy', -'ring.asy', and 'shadestroke.asy'. - - Gouraud shading using fill rule 'fillrule' and the vertex colors in -the pen array 'p' on a triangular lattice defined by the vertices 'z' -and edge flags 'edges' is implemented with +The boolean parameters ‘extenda’ and ‘extendb’ indicate whether the +shading should extend beyond the radii ‘a’ and ‘b’. Illustrations of +radial shading are provided in the example files ‘shade.asy’, +‘ring.asy’, and ‘shadestroke.asy’. + + Gouraud shading using fill rule ‘fillrule’ and the vertex colors in +the pen array ‘p’ on a triangular lattice defined by the vertices ‘z’ +and edge flags ‘edges’ is implemented with void gouraudshade(picture pic=currentpicture, path g, bool stroke=false, pen fillrule=currentpen, pen[] p, pair[] z, int[] edges); void gouraudshade(picture pic=currentpicture, path g, bool stroke=false, pen fillrule=currentpen, pen[] p, int[] edges); -In the second form, the elements of 'z' are taken to be successive nodes -of path 'g'. The pens in 'p' must belong to the same color space. +In the second form, the elements of ‘z’ are taken to be successive nodes +of path ‘g’. The pens in ‘p’ must belong to the same color space. Illustrations of Gouraud shading are provided in the example file -'Gouraud.asy'. The edge flags used in Gouraud shading are documented +‘Gouraud.asy’. The edge flags used in Gouraud shading are documented here: <https://www.adobe.com/content/dam/acom/en/devnet/postscript/pdfs/TN5600.SmoothShading.pdf> - Tensor product shading using clipping path 'g', fill rule 'fillrule' -on patches bounded by the n cyclic paths of length 4 in path array 'b', -using the vertex colors specified in the n \times 4 pen array 'p' and -internal control points in the n \times 4 array 'z', is implemented with + Tensor product shading using clipping path ‘g’, fill rule ‘fillrule’ +on patches bounded by the n cyclic paths of length 4 in path array ‘b’, +using the vertex colors specified in the n \times 4 pen array ‘p’ and +internal control points in the n \times 4 array ‘z’, is implemented with void tensorshade(picture pic=currentpicture, path[] g, bool stroke=false, pen fillrule=currentpen, pen[][] p, path[] b=g, pair[][] z=new pair[][]); -If the array 'z' is empty, Coons shading, in which the color control -points are calculated automatically, is used. The pens in 'p' must +If the array ‘z’ is empty, Coons shading, in which the color control +points are calculated automatically, is used. The pens in ‘p’ must belong to the same color space. A simpler interface for the case of a single patch (n=1) is also available: void tensorshade(picture pic=currentpicture, path g, bool stroke=false, @@ -1118,20 +1122,20 @@ a sequence using a given array of pens: void draw(picture pic=currentpicture, pen fillrule=currentpen, path[] g, pen[] p); Illustrations of tensor product and Coons shading are provided in the -example files 'tensor.asy', 'Coons.asy', 'BezierPatch.asy', and -'rainbow.asy'. +example files ‘tensor.asy’, ‘Coons.asy’, ‘BezierPatch.asy’, and +‘rainbow.asy’. More general shading possibilities are available using TeX engines that produce PDF output (*note texengines::): the routine void functionshade(picture pic=currentpicture, path[] g, bool stroke=false, pen fillrule=currentpen, string shader); -shades on picture 'pic' the interior of path 'g' according to fill rule -'fillrule' using the 'PostScript' calculator routine specified by the -string 'shader'; this routine takes 2 arguments, each in [0,1], and -returns 'colors(fillrule).length' color components. Function shading is -illustrated in the example 'functionshading.asy'. +shades on picture ‘pic’ the interior of path ‘g’ according to fill rule +‘fillrule’ using the ‘PostScript’ calculator routine specified by the +string ‘shader’; this routine takes 2 arguments, each in [0,1], and +returns ‘colors(fillrule).length’ color components. Function shading is +illustrated in the example ‘functionshading.asy’. - The following routine uses 'evenodd' clipping together with the '^^' + The following routine uses ‘evenodd’ clipping together with the ‘^^’ operator to unfill a region: void unfill(picture pic=currentpicture, path g); @@ -1145,13 +1149,13 @@ File: asymptote.info, Node: clip, Next: label, Prev: fill, Up: Drawing comma void clip(picture pic=currentpicture, path g, stroke=false, pen fillrule=currentpen); - Clip the current contents of picture 'pic' to the region bounded by -the path 'g', using fill rule 'fillrule' (*note fillrule::). If -'stroke=true', the clipped portion is the same as the region that would -be drawn with 'draw(pic,g,zerowinding)'; in this case the path 'g' need + Clip the current contents of picture ‘pic’ to the region bounded by +the path ‘g’, using fill rule ‘fillrule’ (*note fillrule::). If +‘stroke=true’, the clipped portion is the same as the region that would +be drawn with ‘draw(pic,g,zerowinding)’; in this case the path ‘g’ need not be cyclic. While clipping has no notion of depth (it transcends layers and even pages), one can localize clipping to a temporary -picture, which can then be added to 'pic'. For an illustration of +picture, which can then be added to ‘pic’. For an illustration of picture clipping, see the first example in *note LaTeX usage::. @@ -1163,12 +1167,12 @@ File: asymptote.info, Node: label, Prev: clip, Up: Drawing commands void label(picture pic=currentpicture, Label L, pair position, align align=NoAlign, pen p=currentpen, filltype filltype=NoFill) - Draw Label 'L' on picture 'pic' using pen 'p'. If 'align' is -'NoAlign', the label will be centered at user coordinate 'position'; -otherwise it will be aligned in the direction of 'align' and displaced -from 'position' by the 'PostScript' offset 'align*labelmargin(p)'. The -constant 'Align' can be used to align the bottom-left corner of the -label at 'position'. The Label 'L' can either be a string or the + Draw Label ‘L’ on picture ‘pic’ using pen ‘p’. If ‘align’ is +‘NoAlign’, the label will be centered at user coordinate ‘position’; +otherwise it will be aligned in the direction of ‘align’ and displaced +from ‘position’ by the ‘PostScript’ offset ‘align*labelmargin(p)’. The +constant ‘Align’ can be used to align the bottom-left corner of the +label at ‘position’. The Label ‘L’ can either be a string or the structure obtained by calling one of the functions Label Label(string s="", pair position, align align=NoAlign, pen p=nullpen, embed embed=Rotate, filltype filltype=NoFill); @@ -1180,79 +1184,79 @@ Label Label(Label L, align align=NoAlign, pen p=nullpen, embed embed=L.embed, filltype filltype=NoFill); The text of a Label can be scaled, slanted, rotated, or shifted by multiplying it on the left by an affine transform (*note Transforms::). -For example, 'rotate(45)*xscale(2)*L' first scales 'L' in the x +For example, ‘rotate(45)*xscale(2)*L’ first scales ‘L’ in the x direction and then rotates it counterclockwise by 45 degrees. The final -position of a Label can also be shifted by a 'PostScript' coordinate -translation: 'shift(10,0)*L'. An explicit pen specified within the -Label overrides other pen arguments. The 'embed' argument determines +position of a Label can also be shifted by a ‘PostScript’ coordinate +translation: ‘shift(10,0)*L’. An explicit pen specified within the +Label overrides other pen arguments. The ‘embed’ argument determines how the Label should transform with the embedding picture: -'Shift' +‘Shift’ only shift with embedding picture; -'Rotate' +‘Rotate’ only shift and rotate with embedding picture (default); -'Rotate(pair z)' - rotate with (picture-transformed) vector 'z'. +‘Rotate(pair z)’ + rotate with (picture-transformed) vector ‘z’. -'Slant' +‘Slant’ only shift, rotate, slant, and reflect with embedding picture; -'Scale' +‘Scale’ shift, rotate, slant, reflect, and scale with embedding picture. To add a label to a path, use void label(picture pic=currentpicture, Label L, path g, align align=NoAlign, pen p=currentpen, filltype filltype=NoFill); By default the label will be positioned at the midpoint of the path. -An alternative label position (in the sense of 'point(path p, real t)') -may be specified as a real value for 'position' in constructing the -Label. The position 'Relative(real)' specifies a location relative to +An alternative label position (in the sense of ‘point(path p, real t)’) +may be specified as a real value for ‘position’ in constructing the +Label. The position ‘Relative(real)’ specifies a location relative to the total arclength of the path. These convenient abbreviations are predefined: position BeginPoint=Relative(0); position MidPoint=Relative(0.5); position EndPoint=Relative(1); - Path labels are aligned in the direction 'align', which may be + Path labels are aligned in the direction ‘align’, which may be specified as an absolute compass direction (pair) or a direction -'Relative(pair)' measured relative to a north axis in the local -direction of the path. For convenience 'LeftSide', 'Center', and -'RightSide' are defined as 'Relative(W)', 'Relative((0,0))', and -'Relative(E)', respectively. Multiplying 'LeftSide' and 'RightSide' on +‘Relative(pair)’ measured relative to a north axis in the local +direction of the path. For convenience ‘LeftSide’, ‘Center’, and +‘RightSide’ are defined as ‘Relative(W)’, ‘Relative((0,0))’, and +‘Relative(E)’, respectively. Multiplying ‘LeftSide’ and ‘RightSide’ on the left by a real scaling factor will move the label further away from or closer to the path. - A label with a fixed-size arrow of length 'arrowlength' pointing to -'b' from direction 'dir' can be produced with the routine + A label with a fixed-size arrow of length ‘arrowlength’ pointing to +‘b’ from direction ‘dir’ can be produced with the routine void arrow(picture pic=currentpicture, Label L="", pair b, pair dir, real length=arrowlength, align align=NoAlign, pen p=currentpen, arrowbar arrow=Arrow, margin margin=EndMargin); If no alignment is specified (either in the Label or as an explicit -argument), the optional Label will be aligned in the direction 'dir', -using margin 'margin'. +argument), the optional Label will be aligned in the direction ‘dir’, +using margin ‘margin’. - The function 'string graphic(string name, string options="")' returns -a string that can be used to include an encapsulated 'PostScript' (EPS) -file. Here, 'name' is the name of the file to include and 'options' is + The function ‘string graphic(string name, string options="")’ returns +a string that can be used to include an encapsulated ‘PostScript’ (EPS) +file. Here, ‘name’ is the name of the file to include and ‘options’ is a string containing a comma-separated list of optional bounding box -('bb=llx lly urx ury'), width ('width=value'), height ('height=value'), -rotation ('angle=value'), scaling ('scale=factor'), clipping -('clip=bool'), and draft mode ('draft=bool') parameters. The 'layer()' +(‘bb=llx lly urx ury’), width (‘width=value’), height (‘height=value’), +rotation (‘angle=value’), scaling (‘scale=factor’), clipping +(‘clip=bool’), and draft mode (‘draft=bool’) parameters. The ‘layer()’ function can be used to force future objects to be drawn on top of the included image: label(graphic("file.eps","width=1cm"),(0,0),NE); layer(); - The 'string baseline(string s, string template="\strut")' function + The ‘string baseline(string s, string template="\strut")’ function can be used to enlarge the bounding box of labels to match a given template, so that their baselines will be typeset on a horizontal line. -See 'Pythagoras.asy' for an example. +See ‘Pythagoras.asy’ for an example. One can prevent labels from overwriting one another with the -'overwrite' pen attribute (*note overwrite::). +‘overwrite’ pen attribute (*note overwrite::). - The structure 'object' defined in 'plain_Label.asy' allows Labels and + The structure ‘object’ defined in ‘plain_Label.asy’ allows Labels and frames to be treated in a uniform manner. A group of objects may be packed together into single frame with the routine frame pack(pair align=2S ... object inset[]); @@ -1264,15 +1268,15 @@ object draw(picture pic=currentpicture, Label L, envelope e, object draw(picture pic=currentpicture, Label L, envelope e, pair position, real xmargin=0, real ymargin=xmargin, pen p=currentpen, filltype filltype=NoFill, bool above=true); -Here 'envelope' is a boundary-drawing routine such as 'box', 'roundbox', -or 'ellipse' defined in 'plain_boxes.asy' (*note envelope::). +Here ‘envelope’ is a boundary-drawing routine such as ‘box’, ‘roundbox’, +or ‘ellipse’ defined in ‘plain_boxes.asy’ (*note envelope::). - The function 'path[] texpath(Label L)' returns the path array that -TeX would fill to draw the Label 'L'. + The function ‘path[] texpath(Label L)’ returns the path array that +TeX would fill to draw the Label ‘L’. - The 'string minipage(string s, width=100pt)' function can be used to -format string 's' into a paragraph of width 'width'. This example uses -'minipage', 'clip', and 'graphic' to produce a CD label: + The ‘string minipage(string s, width=100pt)’ function can be used to +format string ‘s’ into a paragraph of width ‘width’. This example uses +‘minipage’, ‘clip’, and ‘graphic’ to produce a CD label: [./CDlabel] size(11.7cm,11.7cm); @@ -1299,7 +1303,7 @@ File: asymptote.info, Node: Bezier curves, Next: Programming, Prev: Drawing c *************** Each interior node of a cubic spline may be given a direction prefix or -suffix '{dir}': the direction of the pair 'dir' specifies the direction +suffix ‘{dir}’: the direction of the pair ‘dir’ specifies the direction of the incoming or outgoing tangent, respectively, to the curve at that node. Exterior nodes may be given direction specifiers only on their interior side. @@ -1330,10 +1334,10 @@ fraction t in [0,1] of each segment, not just for midpoints (t=1/2). The Bezier curve constructed in this manner has the following properties: - * It is entirely contained in the convex hull of the given four + • It is entirely contained in the convex hull of the given four points. - * It starts heading from the first endpoint to the first control + • It starts heading from the first endpoint to the first control point and finishes heading from the second control point to the second endpoint. @@ -1341,9 +1345,9 @@ properties: this: draw((0,0)..controls (0,100) and (100,100)..(100,0)); - However, it is usually more convenient to just use the '..' operator, -which tells 'Asymptote' to choose its own control points using the -algorithms described in Donald Knuth's monograph, The MetaFontbook, + However, it is usually more convenient to just use the ‘..’ operator, +which tells ‘Asymptote’ to choose its own control points using the +algorithms described in Donald Knuth’s monograph, The MetaFontbook, Chapter 14. The user can still customize the guide (or path) by specifying direction, tension, and curl values. @@ -1355,18 +1359,18 @@ draw((100,0)..tension 2 ..(100,100)..(0,100)); draw((100,0)..tension 3 and 2 ..(100,100)..(0,100)); draw((100,0)..tension atleast 2 ..(100,100)..(0,100)); - In these examples there is a space between '2' and '..'. This is -needed as '2.' is interpreted as a numerical constant. + In these examples there is a space between ‘2’ and ‘..’. This is +needed as ‘2.’ is interpreted as a numerical constant. The curl parameter specifies the curvature at the endpoints of a path (0 means straight; the default value of 1 means approximately circular): draw((100,0){curl 0}..(100,100)..{curl 0}(0,100)); - The 'MetaPost ...' path connector, which requests, when possible, an + The ‘MetaPost ...’ path connector, which requests, when possible, an inflection-free curve confined to a triangle defined by the endpoints -and directions, is implemented in 'Asymptote' as the convenient -abbreviation '::' for '..tension atleast 1 ..' (the ellipsis '...' is -used in 'Asymptote' to indicate a variable number of arguments; *note +and directions, is implemented in ‘Asymptote’ as the convenient +abbreviation ‘::’ for ‘..tension atleast 1 ..’ (the ellipsis ‘...’ is +used in ‘Asymptote’ to indicate a variable number of arguments; *note Rest arguments::). For example, compare draw((0,0){up}..(100,25){right}..(200,0){down}); @@ -1376,8 +1380,8 @@ draw((0,0){up}::(100,25){right}::(200,0){down}); [./colons] - The '---' connector is an abbreviation for '..tension atleast -infinity..' and the '&' connector concatenates two paths, after first + The ‘---’ connector is an abbreviation for ‘..tension atleast +infinity..’ and the ‘&’ connector concatenates two paths, after first stripping off the last node of the first path (which normally should coincide with the first node of the second path). @@ -1402,10 +1406,10 @@ File: asymptote.info, Node: Programming, Next: LaTeX usage, Prev: Bezier curv * Functions:: Traditional and high-order functions * Arrays:: Dynamic vectors * Casts:: Implicit and explicit casts -* Import:: Importing external 'Asymptote' modules +* Import:: Importing external ‘Asymptote’ modules * Static:: Where to allocate your variable? -Here is a short introductory example to the 'Asymptote' programming +Here is a short introductory example to the ‘Asymptote’ programming language that highlights the similarity of its control structures with those of C, C++, and Java: // This is a comment. @@ -1429,7 +1433,7 @@ for(int i=0; i < 10; ++i) { } - 'Asymptote' supports 'while', 'do', 'break', and 'continue' + ‘Asymptote’ supports ‘while’, ‘do’, ‘break’, and ‘continue’ statements just as in C/C++. It also supports the Java-style shorthand for iterating over all elements of an array: @@ -1447,51 +1451,51 @@ File: asymptote.info, Node: Data types, Next: Paths and guides, Prev: Program 6.1 Data types ============== -'Asymptote' supports the following data types (in addition to +‘Asymptote’ supports the following data types (in addition to user-defined types): -'void' +‘void’ The void type is used only by functions that take or return no arguments. -'bool' - a boolean type that can only take on the values 'true' or 'false'. +‘bool’ + a boolean type that can only take on the values ‘true’ or ‘false’. For example: bool b=true; - defines a boolean variable 'b' and initializes it to the value - 'true'. If no initializer is given: + defines a boolean variable ‘b’ and initializes it to the value + ‘true’. If no initializer is given: bool b; - the value 'false' is assumed. + the value ‘false’ is assumed. -'bool3' - an extended boolean type that can take on the values 'true', - 'default', or 'false'. A bool3 type can be cast to or from a bool. - The default initializer for bool3 is 'default'. +‘bool3’ + an extended boolean type that can take on the values ‘true’, + ‘default’, or ‘false’. A bool3 type can be cast to or from a bool. + The default initializer for bool3 is ‘default’. -'int' - an integer type; if no initializer is given, the implicit value '0' - is assumed. The minimum allowed value of an integer is 'intMin' - and the maximum value is 'intMax'. +‘int’ + an integer type; if no initializer is given, the implicit value ‘0’ + is assumed. The minimum allowed value of an integer is ‘intMin’ + and the maximum value is ‘intMax’. -'real' +‘real’ a real number; this should be set to the highest-precision native floating-point type on the architecture. The implicit initializer - for reals is '0.0'. Real numbers have precision 'realEpsilon', - with 'realDigits' significant digits. The smallest positive real - number is 'realMin' and the largest positive real number is - 'realMax'. The variables 'inf' and 'nan', along with the function - 'bool isnan(real x)' are useful when floating-point exceptions are - masked with the '-mask' command-line option (the default in + for reals is ‘0.0’. Real numbers have precision ‘realEpsilon’, + with ‘realDigits’ significant digits. The smallest positive real + number is ‘realMin’ and the largest positive real number is + ‘realMax’. The variables ‘inf’ and ‘nan’, along with the function + ‘bool isnan(real x)’ are useful when floating-point exceptions are + masked with the ‘-mask’ command-line option (the default in interactive mode). -'pair' +‘pair’ complex number, that is, an ordered pair of real components - '(x,y)'. The real and imaginary parts of a pair 'z' can read as - 'z.x' and 'z.y'. We say that 'x' and 'y' are virtual members of + ‘(x,y)’. The real and imaginary parts of a pair ‘z’ can read as + ‘z.x’ and ‘z.y’. We say that ‘x’ and ‘y’ are virtual members of the data element pair; they cannot be directly modified, however. - The implicit initializer for pairs is '(0.0,0.0)'. + The implicit initializer for pairs is ‘(0.0,0.0)’. There are a number of ways to take the complex conjugate of a pair: pair z=(3,4); @@ -1499,284 +1503,284 @@ user-defined types): z=z.x-I*z.y; z=conj(z); - Here 'I' is the pair '(0,1)'. A number of built-in functions are + Here ‘I’ is the pair ‘(0,1)’. A number of built-in functions are defined for pairs: - 'pair conj(pair z)' - returns the conjugate of 'z'; + ‘pair conj(pair z)’ + returns the conjugate of ‘z’; - 'real length(pair z)' - returns the complex modulus |'z'| of its argument 'z'. For + ‘real length(pair z)’ + returns the complex modulus |‘z’| of its argument ‘z’. For example, pair z=(3,4); length(z); - returns the result 5. A synonym for 'length(pair)' is - 'abs(pair)'. The function 'abs2(pair z)' returns |'z'|^2; + returns the result 5. A synonym for ‘length(pair)’ is + ‘abs(pair)’. The function ‘abs2(pair z)’ returns |‘z’|^2; - 'real angle(pair z, bool warn=true)' - returns the angle of 'z' in radians in the interval - [-'pi','pi'] or '0' if 'warn' is 'false' and 'z=(0,0)' (rather + ‘real angle(pair z, bool warn=true)’ + returns the angle of ‘z’ in radians in the interval + [-‘pi’,‘pi’] or ‘0’ if ‘warn’ is ‘false’ and ‘z=(0,0)’ (rather than producing an error); - 'real degrees(pair z, bool warn=true)' - returns the angle of 'z' in degrees in the interval [0,360) or - '0' if 'warn' is 'false' and 'z=(0,0)' (rather than producing + ‘real degrees(pair z, bool warn=true)’ + returns the angle of ‘z’ in degrees in the interval [0,360) or + ‘0’ if ‘warn’ is ‘false’ and ‘z=(0,0)’ (rather than producing an error); - 'pair unit(pair z)' - returns a unit vector in the direction of the pair 'z'; + ‘pair unit(pair z)’ + returns a unit vector in the direction of the pair ‘z’; - 'pair expi(real angle)' - returns a unit vector in the direction 'angle' measured in + ‘pair expi(real angle)’ + returns a unit vector in the direction ‘angle’ measured in radians; - 'pair dir(real degrees)' - returns a unit vector in the direction 'degrees' measured in + ‘pair dir(real degrees)’ + returns a unit vector in the direction ‘degrees’ measured in degrees; - 'real xpart(pair z)' - returns 'z.x'; + ‘real xpart(pair z)’ + returns ‘z.x’; - 'real ypart(pair z)' - returns 'z.y'; + ‘real ypart(pair z)’ + returns ‘z.y’; - 'pair realmult(pair z, pair w)' - returns the element-by-element product '(z.x*w.x,z.y*w.y)'; + ‘pair realmult(pair z, pair w)’ + returns the element-by-element product ‘(z.x*w.x,z.y*w.y)’; - 'real dot(explicit pair z, explicit pair w)' - returns the dot product 'z.x*w.x+z.y*w.y'; + ‘real dot(explicit pair z, explicit pair w)’ + returns the dot product ‘z.x*w.x+z.y*w.y’; - 'real cross(explicit pair z, explicit pair w)' - returns the 2D scalar product 'z.x*w.y-z.y*w.x'; + ‘real cross(explicit pair z, explicit pair w)’ + returns the 2D scalar product ‘z.x*w.y-z.y*w.x’; - 'real orient(pair a, pair b, pair c);' - returns a positive (negative) value if 'a--b--c--cycle' is + ‘real orient(pair a, pair b, pair c);’ + returns a positive (negative) value if ‘a--b--c--cycle’ is oriented counterclockwise (clockwise) or zero if all three points are colinear. Equivalently, a positive (negative) - value is returned if 'c' lies to the left (right) of the line - through 'a' and 'b' or zero if 'c' lies on this line. The + value is returned if ‘c’ lies to the left (right) of the line + through ‘a’ and ‘b’ or zero if ‘c’ lies on this line. The value returned can be expressed in terms of the 2D scalar - cross product as 'cross(a-c,b-c)', which is the determinant + cross product as ‘cross(a-c,b-c)’, which is the determinant |a.x a.y 1| |b.x b.y 1| |c.x c.y 1| - 'real incircle(pair a, pair b, pair c, pair d);' - returns a positive (negative) value if 'd' lies inside + ‘real incircle(pair a, pair b, pair c, pair d);’ + returns a positive (negative) value if ‘d’ lies inside (outside) the circle passing through the - counterclockwise-oriented points 'a,b,c' or zero if 'd' lies + counterclockwise-oriented points ‘a,b,c’ or zero if ‘d’ lies on the this circle. The value returned is the determinant |a.x a.y a.x^2+a.y^2 1| |b.x b.y b.x^2+b.y^2 1| |c.x c.y c.x^2+c.y^2 1| |d.x d.y d.x^2+d.y^2 1| - 'pair minbound(pair z, pair w)' - returns '(min(z.x,w.x),min(z.y,w.y))'; + ‘pair minbound(pair z, pair w)’ + returns ‘(min(z.x,w.x),min(z.y,w.y))’; - 'pair maxbound(pair z, pair w)' - returns '(max(z.x,w.x),max(z.y,w.y))'. + ‘pair maxbound(pair z, pair w)’ + returns ‘(max(z.x,w.x),max(z.y,w.y))’. -'triple' - an ordered triple of real components '(x,y,z)' used for +‘triple’ + an ordered triple of real components ‘(x,y,z)’ used for three-dimensional drawings. The respective components of a triple - 'v' can read as 'v.x', 'v.y', and 'v.z'. The implicit initializer - for triples is '(0.0,0.0,0.0)'. + ‘v’ can read as ‘v.x’, ‘v.y’, and ‘v.z’. The implicit initializer + for triples is ‘(0.0,0.0,0.0)’. Here are the built-in functions for triples: - 'real length(triple v)' - returns the length |'v'| of its argument 'v'. A synonym for - 'length(triple)' is 'abs(triple)'. The function 'abs2(triple - v)' returns |'v'|^2; - - 'real polar(triple v, bool warn=true)' - returns the colatitude of 'v' measured from the z axis in - radians or '0' if 'warn' is 'false' and 'v=O' (rather than + ‘real length(triple v)’ + returns the length |‘v’| of its argument ‘v’. A synonym for + ‘length(triple)’ is ‘abs(triple)’. The function ‘abs2(triple + v)’ returns |‘v’|^2; + + ‘real polar(triple v, bool warn=true)’ + returns the colatitude of ‘v’ measured from the z axis in + radians or ‘0’ if ‘warn’ is ‘false’ and ‘v=O’ (rather than producing an error); - 'real azimuth(triple v, bool warn=true)' - returns the longitude of 'v' measured from the x axis in - radians or '0' if 'warn' is 'false' and 'v.x=v.y=0' (rather + ‘real azimuth(triple v, bool warn=true)’ + returns the longitude of ‘v’ measured from the x axis in + radians or ‘0’ if ‘warn’ is ‘false’ and ‘v.x=v.y=0’ (rather than producing an error); - 'real colatitude(triple v, bool warn=true)' - returns the colatitude of 'v' measured from the z axis in - degrees or '0' if 'warn' is 'false' and 'v=O' (rather than + ‘real colatitude(triple v, bool warn=true)’ + returns the colatitude of ‘v’ measured from the z axis in + degrees or ‘0’ if ‘warn’ is ‘false’ and ‘v=O’ (rather than producing an error); - 'real latitude(triple v, bool warn=true)' - returns the latitude of 'v' measured from the xy plane in - degrees or '0' if 'warn' is 'false' and 'v=O' (rather than + ‘real latitude(triple v, bool warn=true)’ + returns the latitude of ‘v’ measured from the xy plane in + degrees or ‘0’ if ‘warn’ is ‘false’ and ‘v=O’ (rather than producing an error); - 'real longitude(triple v, bool warn=true)' - returns the longitude of 'v' measured from the x axis in - degrees or '0' if 'warn' is 'false' and 'v.x=v.y=0' (rather + ‘real longitude(triple v, bool warn=true)’ + returns the longitude of ‘v’ measured from the x axis in + degrees or ‘0’ if ‘warn’ is ‘false’ and ‘v.x=v.y=0’ (rather than producing an error); - 'triple unit(triple v)' - returns a unit triple in the direction of the triple 'v'; + ‘triple unit(triple v)’ + returns a unit triple in the direction of the triple ‘v’; - 'triple expi(real polar, real azimuth)' - returns a unit triple in the direction '(polar,azimuth)' + ‘triple expi(real polar, real azimuth)’ + returns a unit triple in the direction ‘(polar,azimuth)’ measured in radians; - 'triple dir(real colatitude, real longitude)' + ‘triple dir(real colatitude, real longitude)’ returns a unit triple in the direction - '(colatitude,longitude)' measured in degrees; + ‘(colatitude,longitude)’ measured in degrees; - 'real xpart(triple v)' - returns 'v.x'; + ‘real xpart(triple v)’ + returns ‘v.x’; - 'real ypart(triple v)' - returns 'v.y'; + ‘real ypart(triple v)’ + returns ‘v.y’; - 'real zpart(triple v)' - returns 'v.z'; + ‘real zpart(triple v)’ + returns ‘v.z’; - 'real dot(triple u, triple v)' - returns the dot product 'u.x*v.x+u.y*v.y+u.z*v.z'; + ‘real dot(triple u, triple v)’ + returns the dot product ‘u.x*v.x+u.y*v.y+u.z*v.z’; - 'triple cross(triple u, triple v)' + ‘triple cross(triple u, triple v)’ returns the cross product - '(u.y*v.z-u.z*v.y,u.z*v.x-u.x*v.z,u.x*v.y-v.x*u.y)'; + ‘(u.y*v.z-u.z*v.y,u.z*v.x-u.x*v.z,u.x*v.y-v.x*u.y)’; - 'triple minbound(triple u, triple v)' - returns '(min(u.x,v.x),min(u.y,v.y),min(u.z,v.z))'; + ‘triple minbound(triple u, triple v)’ + returns ‘(min(u.x,v.x),min(u.y,v.y),min(u.z,v.z))’; - 'triple maxbound(triple u, triple v)' - returns '(max(u.x,v.x),max(u.y,v.y),max(u.z,v.z)'). + ‘triple maxbound(triple u, triple v)’ + returns ‘(max(u.x,v.x),max(u.y,v.y),max(u.z,v.z)’). -'string' - a character string, implemented using the STL 'string' class. +‘string’ + a character string, implemented using the STL ‘string’ class. - Strings delimited by double quotes ('"') are subject to the + Strings delimited by double quotes (‘"’) are subject to the following mappings to allow the use of double quotes in TeX - (e.g. for using the 'babel' package, *note babel::): - - * \" maps to " - * \\ maps to \\ - - Strings delimited by single quotes (''') have the same mappings as - character strings in ANSI 'C': - - * \' maps to ' - * \" maps to " - * \? maps to ? - * \\ maps to backslash - * \a maps to alert - * \b maps to backspace - * \f maps to form feed - * \n maps to newline - * \r maps to carriage return - * \t maps to tab - * \v maps to vertical tab - * \0-\377 map to corresponding octal byte - * \x0-\xFF map to corresponding hexadecimal byte - - The implicit initializer for strings is the empty string '""'. - Strings may be concatenated with the '+' operator. In the - following string functions, position '0' denotes the start of the + (e.g. for using the ‘babel’ package, *note babel::): + + • \" maps to " + • \\ maps to \\ + + Strings delimited by single quotes (‘'’) have the same mappings as + character strings in ANSI ‘C’: + + • \’ maps to ’ + • \" maps to " + • \? maps to ? + • \\ maps to backslash + • \a maps to alert + • \b maps to backspace + • \f maps to form feed + • \n maps to newline + • \r maps to carriage return + • \t maps to tab + • \v maps to vertical tab + • \0-\377 map to corresponding octal byte + • \x0-\xFF map to corresponding hexadecimal byte + + The implicit initializer for strings is the empty string ‘""’. + Strings may be concatenated with the ‘+’ operator. In the + following string functions, position ‘0’ denotes the start of the string: - 'int length(string s)' - returns the length of the string 's'; - - 'int find(string s, string t, int pos=0)' - returns the position of the first occurrence of string 't' in - string 's' at or after position 'pos', or -1 if 't' is not a - substring of 's'; - - 'int rfind(string s, string t, int pos=-1)' - returns the position of the last occurrence of string 't' in - string 's' at or before position 'pos' (if 'pos'=-1, at the - end of the string 's'), or -1 if 't' is not a substring of - 's'; - - 'string insert(string s, int pos, string t)' - returns the string formed by inserting string 't' at position - 'pos' in 's'; - - 'string erase(string s, int pos, int n)' - returns the string formed by erasing the string of length 'n' - (if 'n'=-1, to the end of the string 's') at position 'pos' in - 's'; - - 'string substr(string s, int pos, int n=-1)' - returns the substring of 's' starting at position 'pos' and of - length 'n' (if 'n'=-1, until the end of the string 's'); - - 'string reverse(string s)' - returns the string formed by reversing string 's'; - - 'string replace(string s, string before, string after)' - returns a string with all occurrences of the string 'before' - in the string 's' changed to the string 'after'; - - 'string replace(string s, string[][] table)' - returns a string constructed by translating in string 's' all - occurrences of the string 'before' in an array 'table' of - string pairs {'before','after'} to the corresponding string - 'after'; - - 'string[] split(string s, string delimiter="")' - returns an array of strings obtained by splitting 's' into - substrings delimited by 'delimiter' (an empty delimiter + ‘int length(string s)’ + returns the length of the string ‘s’; + + ‘int find(string s, string t, int pos=0)’ + returns the position of the first occurrence of string ‘t’ in + string ‘s’ at or after position ‘pos’, or -1 if ‘t’ is not a + substring of ‘s’; + + ‘int rfind(string s, string t, int pos=-1)’ + returns the position of the last occurrence of string ‘t’ in + string ‘s’ at or before position ‘pos’ (if ‘pos’=-1, at the + end of the string ‘s’), or -1 if ‘t’ is not a substring of + ‘s’; + + ‘string insert(string s, int pos, string t)’ + returns the string formed by inserting string ‘t’ at position + ‘pos’ in ‘s’; + + ‘string erase(string s, int pos, int n)’ + returns the string formed by erasing the string of length ‘n’ + (if ‘n’=-1, to the end of the string ‘s’) at position ‘pos’ in + ‘s’; + + ‘string substr(string s, int pos, int n=-1)’ + returns the substring of ‘s’ starting at position ‘pos’ and of + length ‘n’ (if ‘n’=-1, until the end of the string ‘s’); + + ‘string reverse(string s)’ + returns the string formed by reversing string ‘s’; + + ‘string replace(string s, string before, string after)’ + returns a string with all occurrences of the string ‘before’ + in the string ‘s’ changed to the string ‘after’; + + ‘string replace(string s, string[][] table)’ + returns a string constructed by translating in string ‘s’ all + occurrences of the string ‘before’ in an array ‘table’ of + string pairs {‘before’,‘after’} to the corresponding string + ‘after’; + + ‘string[] split(string s, string delimiter="")’ + returns an array of strings obtained by splitting ‘s’ into + substrings delimited by ‘delimiter’ (an empty delimiter signifies a space, but with duplicate delimiters discarded); - 'string[] array(string s)' - returns an array of strings obtained by splitting 's' into + ‘string[] array(string s)’ + returns an array of strings obtained by splitting ‘s’ into individual characters. The inverse operation is provided by - 'operator +(...string[] a)'. + ‘operator +(...string[] a)’. - 'string format(string s, int n, string locale="")' - returns a string containing 'n' formatted according to the - C-style format string 's' using locale 'locale' (or the + ‘string format(string s, int n, string locale="")’ + returns a string containing ‘n’ formatted according to the + C-style format string ‘s’ using locale ‘locale’ (or the current locale if an empty string is specified), following the - behaviour of the C function 'fprintf'), except that only one + behaviour of the C function ‘fprintf’), except that only one data field is allowed. - 'string format(string s=defaultformat, bool forcemath=false, string s=defaultseparator, real x, string locale="")' - returns a string containing 'x' formatted according to the - C-style format string 's' using locale 'locale' (or the + ‘string format(string s=defaultformat, bool forcemath=false, string s=defaultseparator, real x, string locale="")’ + returns a string containing ‘x’ formatted according to the + C-style format string ‘s’ using locale ‘locale’ (or the current locale if an empty string is specified), following the - behaviour of the C function 'fprintf'), except that only one + behaviour of the C function ‘fprintf’), except that only one data field is allowed, trailing zeros are removed by default - (unless '#' is specified), and if 's' specifies math mode or - 'forcemath=true', TeX is used to typeset scientific notation - using the 'defaultseparator="\!\times\!";'; + (unless ‘#’ is specified), and if ‘s’ specifies math mode or + ‘forcemath=true’, TeX is used to typeset scientific notation + using the ‘defaultseparator="\!\times\!";’; - 'int hex(string s);' - casts a hexadecimal string 's' to an integer; + ‘int hex(string s);’ + casts a hexadecimal string ‘s’ to an integer; - 'int ascii(string s);' - returns the ASCII code for the first character of string 's'; + ‘int ascii(string s);’ + returns the ASCII code for the first character of string ‘s’; - 'string string(real x, int digits=realDigits)' - casts 'x' to a string using precision 'digits' and the C + ‘string string(real x, int digits=realDigits)’ + casts ‘x’ to a string using precision ‘digits’ and the C locale; - 'string locale(string s="")' + ‘string locale(string s="")’ sets the locale to the given string, if nonempty, and returns the current locale; - 'string time(string format="%a %b %d %T %Z %Y")' + ‘string time(string format="%a %b %d %T %Z %Y")’ returns the current time formatted by the ANSI C routine - 'strftime' according to the string 'format' using the current + ‘strftime’ according to the string ‘format’ using the current locale. Thus time(); time("%a %b %d %H:%M:%S %Z %Y"); are equivalent ways of returning the current time in the - default format used by the 'UNIX' 'date' command; + default format used by the ‘UNIX’ ‘date’ command; - 'int seconds(string t="", string format="")' + ‘int seconds(string t="", string format="")’ returns the time measured in seconds after the Epoch (Thu Jan 01 00:00:00 UTC 1970) as determined by the ANSI C routine - 'strptime' according to the string 'format' using the current - locale, or the current time if 't' is the empty string. Note - that the '"%Z"' extension to the POSIX 'strptime' + ‘strptime’ according to the string ‘format’ using the current + locale, or the current time if ‘t’ is the empty string. Note + that the ‘"%Z"’ extension to the POSIX ‘strptime’ specification is ignored by the current GNU C Library. If an error occurs, the value -1 is returned. Here are some examples: @@ -1784,49 +1788,49 @@ user-defined types): seconds(time("%b %d %r %z %Y"),"%b %d %r %z %Y"); seconds(time("%b %d %r %Z %Y"),"%b %d %r "+time("%Z")+" %Y"); 1+(seconds()-seconds("Jan 1","%b %d"))/(24*60*60); - The last example returns today's ordinal date, measured from + The last example returns today’s ordinal date, measured from the beginning of the year. - 'string time(int seconds, string format="%a %b %d %T %Z %Y")' - returns the time corresponding to 'seconds' seconds after the + ‘string time(int seconds, string format="%a %b %d %T %Z %Y")’ + returns the time corresponding to ‘seconds’ seconds after the Epoch (Thu Jan 01 00:00:00 UTC 1970) formatted by the ANSI C - routine 'strftime' according to the string 'format' using the + routine ‘strftime’ according to the string ‘format’ using the current locale. For example, to return the date corresponding to 24 hours ago: time(seconds()-24*60*60); - 'int system(string s)' - 'int system(string[] s)' - if the setting 'safe' is false, call the arbitrary system - command 's'; + ‘int system(string s)’ + ‘int system(string[] s)’ + if the setting ‘safe’ is false, call the arbitrary system + command ‘s’; - 'void asy(string format, bool overwrite=false ... string[] s)' - conditionally process each file name in array 's' in a new - environment, using format 'format', overwriting the output - file only if 'overwrite' is true; + ‘void asy(string format, bool overwrite=false ... string[] s)’ + conditionally process each file name in array ‘s’ in a new + environment, using format ‘format’, overwriting the output + file only if ‘overwrite’ is true; - 'void abort(string s="")' + ‘void abort(string s="")’ aborts execution (with a non-zero return code in batch mode); - if string 's' is nonempty, a diagnostic message constructed - from the source file, line number, and 's' is printed; + if string ‘s’ is nonempty, a diagnostic message constructed + from the source file, line number, and ‘s’ is printed; - 'void assert(bool b, string s="")' - aborts execution with an error message constructed from 's' if - 'b=false'; + ‘void assert(bool b, string s="")’ + aborts execution with an error message constructed from ‘s’ if + ‘b=false’; - 'void exit()' + ‘void exit()’ exits (with a zero error return code in batch mode); - 'void sleep(int seconds)' + ‘void sleep(int seconds)’ pauses for the given number of seconds; - 'void usleep(int microseconds)' + ‘void usleep(int microseconds)’ pauses for the given number of microseconds; - 'void beep()' + ‘void beep()’ produces a beep on the console; - As in C/C++, complicated types may be abbreviated with 'typedef' (see + As in C/C++, complicated types may be abbreviated with ‘typedef’ (see the example in *note Functions::). @@ -1835,37 +1839,37 @@ File: asymptote.info, Node: Paths and guides, Next: Pens, Prev: Data types, 6.2 Paths and guides ==================== -'path' +‘path’ a cubic spline resolved into a fixed path. The implicit - initializer for paths is 'nullpath'. + initializer for paths is ‘nullpath’. - For example, the routine 'circle(pair c, real r)', which returns a - Bezier curve approximating a circle of radius 'r' centered on 'c', - is based on 'unitcircle' (*note unitcircle::): + For example, the routine ‘circle(pair c, real r)’, which returns a + Bezier curve approximating a circle of radius ‘r’ centered on ‘c’, + is based on ‘unitcircle’ (*note unitcircle::): path circle(pair c, real r) { return shift(c)*scale(r)*unitcircle; } If high accuracy is needed, a true circle may be produced with the - routine 'Circle' defined in the module 'graph': + routine ‘Circle’ defined in the module ‘graph’: import graph; path Circle(pair c, real r, int n=nCircle); - A circular arc consistent with 'circle' centered on 'c' with radius - 'r' from 'angle1' to 'angle2' degrees, drawing counterclockwise if - 'angle2 >= angle1', can be constructed with + A circular arc consistent with ‘circle’ centered on ‘c’ with radius + ‘r’ from ‘angle1’ to ‘angle2’ degrees, drawing counterclockwise if + ‘angle2 >= angle1’, can be constructed with path arc(pair c, real r, real angle1, real angle2); One may also specify the direction explicitly: path arc(pair c, real r, real angle1, real angle2, bool direction); Here the direction can be specified as CCW (counter-clockwise) or - CW (clockwise). For convenience, an arc centered at 'c' from pair - 'z1' to 'z2' (assuming '|z2-c|=|z1-c|') in the may also be + CW (clockwise). For convenience, an arc centered at ‘c’ from pair + ‘z1’ to ‘z2’ (assuming ‘|z2-c|=|z1-c|’) in the may also be constructed with path arc(pair c, explicit pair z1, explicit pair z2, bool direction=CCW) If high accuracy is needed, true arcs may be produced with routines - in the module 'graph' that produce Bezier curves with 'n' control + in the module ‘graph’ that produce Bezier curves with ‘n’ control points: import graph; path Arc(pair c, real r, real angle1, real angle2, bool direction, @@ -1880,7 +1884,7 @@ File: asymptote.info, Node: Paths and guides, Next: Pens, Prev: Data types, return shift(c)*scale(a,b)*unitcircle; } - A brace can be constructed between pairs 'a' and 'b' with + A brace can be constructed between pairs ‘a’ and ‘b’ with path brace(pair a, pair b, real amplitude=bracedefaultratio*length(b-a)); This example illustrates the use of all five guide connectors @@ -1905,246 +1909,246 @@ File: asymptote.info, Node: Paths and guides, Next: Pens, Prev: Data types, Here are some useful functions for paths: - 'int length(path p);' - This is the number of (linear or cubic) segments in path 'p'. - If 'p' is cyclic, this is the same as the number of nodes in - 'p'. + ‘int length(path p);’ + This is the number of (linear or cubic) segments in path ‘p’. + If ‘p’ is cyclic, this is the same as the number of nodes in + ‘p’. - 'int size(path p);' - This is the number of nodes in the path 'p'. If 'p' is - cyclic, this is the same as 'length(p)'. + ‘int size(path p);’ + This is the number of nodes in the path ‘p’. If ‘p’ is + cyclic, this is the same as ‘length(p)’. - 'bool cyclic(path p);' - returns 'true' iff path 'p' is cyclic. + ‘bool cyclic(path p);’ + returns ‘true’ iff path ‘p’ is cyclic. - 'bool straight(path p, int i);' - returns 'true' iff the segment of path 'p' between node 'i' - and node 'i+1' is straight. + ‘bool straight(path p, int i);’ + returns ‘true’ iff the segment of path ‘p’ between node ‘i’ + and node ‘i+1’ is straight. - 'bool piecewisestraight(path p)' - returns 'true' iff the path 'p' is piecewise straight. + ‘bool piecewisestraight(path p)’ + returns ‘true’ iff the path ‘p’ is piecewise straight. - 'pair point(path p, int t);' - If 'p' is cyclic, return the coordinates of node 't' mod - 'length(p)'. Otherwise, return the coordinates of node 't', - unless 't' < 0 (in which case 'point(0)' is returned) or 't' > - 'length(p)' (in which case 'point(length(p))' is returned). + ‘pair point(path p, int t);’ + If ‘p’ is cyclic, return the coordinates of node ‘t’ mod + ‘length(p)’. Otherwise, return the coordinates of node ‘t’, + unless ‘t’ < 0 (in which case ‘point(0)’ is returned) or ‘t’ > + ‘length(p)’ (in which case ‘point(length(p))’ is returned). - 'pair point(path p, real t);' + ‘pair point(path p, real t);’ This returns the coordinates of the point between node - 'floor(t)' and 'floor(t)+1' corresponding to the cubic spline - parameter 't-floor(t)' (*note Bezier curves::). If 't' lies - outside the range [0,'length(p)'], it is first reduced modulo - 'length(p)' in the case where 'p' is cyclic or else converted - to the corresponding endpoint of 'p'. - - 'pair dir(path p, int t, int sign=0, bool normalize=true);' - If 'sign < 0', return the direction (as a pair) of the - incoming tangent to path 'p' at node 't'; if 'sign > 0', - return the direction of the outgoing tangent. If 'sign=0', + ‘floor(t)’ and ‘floor(t)+1’ corresponding to the cubic spline + parameter ‘t-floor(t)’ (*note Bezier curves::). If ‘t’ lies + outside the range [0,‘length(p)’], it is first reduced modulo + ‘length(p)’ in the case where ‘p’ is cyclic or else converted + to the corresponding endpoint of ‘p’. + + ‘pair dir(path p, int t, int sign=0, bool normalize=true);’ + If ‘sign < 0’, return the direction (as a pair) of the + incoming tangent to path ‘p’ at node ‘t’; if ‘sign > 0’, + return the direction of the outgoing tangent. If ‘sign=0’, the mean of these two directions is returned. - 'pair dir(path p, real t, bool normalize=true);' - returns the direction of the tangent to path 'p' at the point - between node 'floor(t)' and 'floor(t)+1' corresponding to the - cubic spline parameter 't-floor(t)' (*note Bezier curves::). + ‘pair dir(path p, real t, bool normalize=true);’ + returns the direction of the tangent to path ‘p’ at the point + between node ‘floor(t)’ and ‘floor(t)+1’ corresponding to the + cubic spline parameter ‘t-floor(t)’ (*note Bezier curves::). - 'pair dir(path p)' + ‘pair dir(path p)’ returns dir(p,length(p)). - 'pair dir(path p, path q)' + ‘pair dir(path p, path q)’ returns unit(dir(p)+dir(q)). - 'pair accel(path p, int t, int sign=0);' - If 'sign < 0', return the acceleration of the incoming path - 'p' at node 't'; if 'sign > 0', return the acceleration of the - outgoing path. If 'sign=0', the mean of these two + ‘pair accel(path p, int t, int sign=0);’ + If ‘sign < 0’, return the acceleration of the incoming path + ‘p’ at node ‘t’; if ‘sign > 0’, return the acceleration of the + outgoing path. If ‘sign=0’, the mean of these two accelerations is returned. - 'pair accel(path p, real t);' - returns the acceleration of the path 'p' at the point 't'. + ‘pair accel(path p, real t);’ + returns the acceleration of the path ‘p’ at the point ‘t’. - 'real radius(path p, real t);' - returns the radius of curvature of the path 'p' at the point - 't'. + ‘real radius(path p, real t);’ + returns the radius of curvature of the path ‘p’ at the point + ‘t’. - 'pair precontrol(path p, int t);' - returns the precontrol point of 'p' at node 't'. + ‘pair precontrol(path p, int t);’ + returns the precontrol point of ‘p’ at node ‘t’. - 'pair precontrol(path p, real t);' - returns the effective precontrol point of 'p' at parameter - 't'. + ‘pair precontrol(path p, real t);’ + returns the effective precontrol point of ‘p’ at parameter + ‘t’. - 'pair postcontrol(path p, int t);' - returns the postcontrol point of 'p' at node 't'. + ‘pair postcontrol(path p, int t);’ + returns the postcontrol point of ‘p’ at node ‘t’. - 'pair postcontrol(path p, real t);' - returns the effective postcontrol point of 'p' at parameter - 't'. + ‘pair postcontrol(path p, real t);’ + returns the effective postcontrol point of ‘p’ at parameter + ‘t’. - 'real arclength(path p);' + ‘real arclength(path p);’ returns the length (in user coordinates) of the piecewise - linear or cubic curve that path 'p' represents. + linear or cubic curve that path ‘p’ represents. - 'real arctime(path p, real L);' + ‘real arctime(path p, real L);’ returns the path "time", a real number between 0 and the - length of the path in the sense of 'point(path p, real t)', at + length of the path in the sense of ‘point(path p, real t)’, at which the cumulative arclength (measured from the beginning of - the path) equals 'L'. + the path) equals ‘L’. - 'pair arcpoint(path p, real L);' - returns 'point(p,arctime(p,L))'. + ‘pair arcpoint(path p, real L);’ + returns ‘point(p,arctime(p,L))’. - 'real dirtime(path p, pair z);' + ‘real dirtime(path p, pair z);’ returns the first "time", a real number between 0 and the - length of the path in the sense of 'point(path, real)', at - which the tangent to the path has the direction of pair 'z', + length of the path in the sense of ‘point(path, real)’, at + which the tangent to the path has the direction of pair ‘z’, or -1 if this never happens. - 'real reltime(path p, real l);' - returns the time on path 'p' at the relative fraction 'l' of + ‘real reltime(path p, real l);’ + returns the time on path ‘p’ at the relative fraction ‘l’ of its arclength. - 'pair relpoint(path p, real l);' - returns the point on path 'p' at the relative fraction 'l' of + ‘pair relpoint(path p, real l);’ + returns the point on path ‘p’ at the relative fraction ‘l’ of its arclength. - 'pair midpoint(path p);' - returns the point on path 'p' at half of its arclength. + ‘pair midpoint(path p);’ + returns the point on path ‘p’ at half of its arclength. - 'path reverse(path p);' - returns a path running backwards along 'p'. + ‘path reverse(path p);’ + returns a path running backwards along ‘p’. - 'path subpath(path p, int a, int b);' - returns the subpath of 'p' running from node 'a' to node 'b'. - If 'a' > 'b', the direction of the subpath is reversed. + ‘path subpath(path p, int a, int b);’ + returns the subpath of ‘p’ running from node ‘a’ to node ‘b’. + If ‘a’ > ‘b’, the direction of the subpath is reversed. - 'path subpath(path p, real a, real b);' - returns the subpath of 'p' running from path time 'a' to path - time 'b', in the sense of 'point(path, real)'. If 'a' > 'b', + ‘path subpath(path p, real a, real b);’ + returns the subpath of ‘p’ running from path time ‘a’ to path + time ‘b’, in the sense of ‘point(path, real)’. If ‘a’ > ‘b’, the direction of the subpath is reversed. - 'real[] intersect(path p, path q, real fuzz=-1);' - If 'p' and 'q' have at least one intersection point, return a + ‘real[] intersect(path p, path q, real fuzz=-1);’ + If ‘p’ and ‘q’ have at least one intersection point, return a real array of length 2 containing the times representing the - respective path times along 'p' and 'q', in the sense of - 'point(path, real)', for one such intersection point (as - chosen by the algorithm described on page 137 of 'The - MetaFontbook'). The computations are performed to the - absolute error specified by 'fuzz', or if 'fuzz < 0', to + respective path times along ‘p’ and ‘q’, in the sense of + ‘point(path, real)’, for one such intersection point (as + chosen by the algorithm described on page 137 of ‘The + MetaFontbook’). The computations are performed to the + absolute error specified by ‘fuzz’, or if ‘fuzz < 0’, to machine precision. If the paths do not intersect, return a real array of length 0. - 'real[][] intersections(path p, path q, real fuzz=-1);' + ‘real[][] intersections(path p, path q, real fuzz=-1);’ Return all (unless there are infinitely many) intersection - times of paths 'p' and 'q' as a sorted array of real arrays of + times of paths ‘p’ and ‘q’ as a sorted array of real arrays of length 2 (*note sort::). The computations are performed to - the absolute error specified by 'fuzz', or if 'fuzz < 0', to + the absolute error specified by ‘fuzz’, or if ‘fuzz < 0’, to machine precision. - 'real[] intersections(path p, explicit pair a, explicit pair b, real fuzz=-1);' + ‘real[] intersections(path p, explicit pair a, explicit pair b, real fuzz=-1);’ Return all (unless there are infinitely many) intersection - times of path 'p' with the (infinite) line through points 'a' - and 'b' as a sorted array. The intersections returned are + times of path ‘p’ with the (infinite) line through points ‘a’ + and ‘b’ as a sorted array. The intersections returned are guaranteed to be correct to within the absolute error - specified by 'fuzz', or if 'fuzz < 0', to machine precision. + specified by ‘fuzz’, or if ‘fuzz < 0’, to machine precision. - 'real[] times(path p, real x)' - returns all intersection times of path 'p' with the vertical - line through '(x,0)'. + ‘real[] times(path p, real x)’ + returns all intersection times of path ‘p’ with the vertical + line through ‘(x,0)’. - 'real[] times(path p, explicit pair z)' - returns all intersection times of path 'p' with the horizontal - line through '(0,z.y)'. + ‘real[] times(path p, explicit pair z)’ + returns all intersection times of path ‘p’ with the horizontal + line through ‘(0,z.y)’. - 'real[] mintimes(path p)' + ‘real[] mintimes(path p)’ returns an array of length 2 containing times at which path - 'p' reaches its minimal horizontal and vertical extents, + ‘p’ reaches its minimal horizontal and vertical extents, respectively. - 'real[] maxtimes(path p)' + ‘real[] maxtimes(path p)’ returns an array of length 2 containing times at which path - 'p' reaches its maximal horizontal and vertical extents, + ‘p’ reaches its maximal horizontal and vertical extents, respectively. - 'pair intersectionpoint(path p, path q, real fuzz=-1);' + ‘pair intersectionpoint(path p, path q, real fuzz=-1);’ returns the intersection point - 'point(p,intersect(p,q,fuzz)[0])'. + ‘point(p,intersect(p,q,fuzz)[0])’. - 'pair[] intersectionpoints(path p, path q, real fuzz=-1);' + ‘pair[] intersectionpoints(path p, path q, real fuzz=-1);’ returns an array containing all intersection points of the - paths 'p' and 'q'. + paths ‘p’ and ‘q’. - 'pair extension(pair P, pair Q, pair p, pair q);' + ‘pair extension(pair P, pair Q, pair p, pair q);’ returns the intersection point of the extensions of the line - segments 'P--Q' and 'p--q', or if the lines are parallel, - '(infinity,infinity)'. + segments ‘P--Q’ and ‘p--q’, or if the lines are parallel, + ‘(infinity,infinity)’. - 'slice cut(path p, path knife, int n);' - returns the portions of path 'p' before and after the 'n'th - intersection of 'p' with path 'knife' as a structure 'slice' + ‘slice cut(path p, path knife, int n);’ + returns the portions of path ‘p’ before and after the ‘n’th + intersection of ‘p’ with path ‘knife’ as a structure ‘slice’ (if no intersection exist is found, the entire path is - considered to be 'before' the intersection): + considered to be ‘before’ the intersection): struct slice { path before,after; } - The argument 'n' is treated as modulo the number of + The argument ‘n’ is treated as modulo the number of intersections. - 'slice firstcut(path p, path knife);' - equivalent to 'cut(p,knife,0);' Note that 'firstcut.after' - plays the role of the 'MetaPost cutbefore' command. + ‘slice firstcut(path p, path knife);’ + equivalent to ‘cut(p,knife,0);’ Note that ‘firstcut.after’ + plays the role of the ‘MetaPost cutbefore’ command. - 'slice lastcut(path p, path knife);' - equivalent to 'cut(p,knife,-1);' Note that 'lastcut.before' - plays the role of the 'MetaPost cutafter' command. + ‘slice lastcut(path p, path knife);’ + equivalent to ‘cut(p,knife,-1);’ Note that ‘lastcut.before’ + plays the role of the ‘MetaPost cutafter’ command. - 'path buildcycle(... path[] p);' + ‘path buildcycle(... path[] p);’ This returns the path surrounding a region bounded by a list of two or more consecutively intersecting paths, following the - behaviour of the 'MetaPost buildcycle' command. + behaviour of the ‘MetaPost buildcycle’ command. - 'pair min(path p);' + ‘pair min(path p);’ returns the pair (left,bottom) for the path bounding box of - path 'p'. + path ‘p’. - 'pair max(path p);' + ‘pair max(path p);’ returns the pair (right,top) for the path bounding box of path - 'p'. + ‘p’. - 'int windingnumber(path p, pair z);' - returns the winding number of the cyclic path 'p' relative to - the point 'z'. The winding number is positive if the path - encircles 'z' in the counterclockwise direction. If 'z' lies - on 'p' the constant 'undefined' (defined to be the largest odd + ‘int windingnumber(path p, pair z);’ + returns the winding number of the cyclic path ‘p’ relative to + the point ‘z’. The winding number is positive if the path + encircles ‘z’ in the counterclockwise direction. If ‘z’ lies + on ‘p’ the constant ‘undefined’ (defined to be the largest odd integer) is returned. - 'bool interior(int windingnumber, pen fillrule)' - returns true if 'windingnumber' corresponds to an interior - point according to 'fillrule'. + ‘bool interior(int windingnumber, pen fillrule)’ + returns true if ‘windingnumber’ corresponds to an interior + point according to ‘fillrule’. - 'bool inside(path p, pair z, pen fillrule=currentpen);' - returns 'true' iff the point 'z' lies inside or on the edge of - the region bounded by the cyclic path 'p' according to the - fill rule 'fillrule' (*note fillrule::). + ‘bool inside(path p, pair z, pen fillrule=currentpen);’ + returns ‘true’ iff the point ‘z’ lies inside or on the edge of + the region bounded by the cyclic path ‘p’ according to the + fill rule ‘fillrule’ (*note fillrule::). - 'int inside(path p, path q, pen fillrule=currentpen);' - returns '1' if the cyclic path 'p' strictly contains 'q' - according to the fill rule 'fillrule' (*note fillrule::), '-1' - if the cyclic path 'q' strictly contains 'p', and '0' + ‘int inside(path p, path q, pen fillrule=currentpen);’ + returns ‘1’ if the cyclic path ‘p’ strictly contains ‘q’ + according to the fill rule ‘fillrule’ (*note fillrule::), ‘-1’ + if the cyclic path ‘q’ strictly contains ‘p’, and ‘0’ otherwise. - 'pair inside(path p, pen fillrule=currentpen);' - returns an arbitrary point strictly inside a cyclic path 'p' - according to the fill rule 'fillrule' (*note fillrule::). + ‘pair inside(path p, pen fillrule=currentpen);’ + returns an arbitrary point strictly inside a cyclic path ‘p’ + according to the fill rule ‘fillrule’ (*note fillrule::). - 'path[] strokepath(path g, pen p=currentpen);' - returns the path array that 'PostScript' would fill in drawing - path 'g' with pen 'p'. + ‘path[] strokepath(path g, pen p=currentpen);’ + returns the path array that ‘PostScript’ would fill in drawing + path ‘g’ with pen ‘p’. -'guide' +‘guide’ an unresolved cubic spline (list of cubic-spline nodes and control - points). The implicit initializer for a guide is 'nullpath'; this + points). The implicit initializer for a guide is ‘nullpath’; this is useful for building up a guide within a loop. A guide is similar to a path except that the computation of the @@ -2199,51 +2203,51 @@ File: asymptote.info, Node: Paths and guides, Next: Pens, Prev: Data types, elements of a guide without actually resolving the guide to a fixed path (except for internal cycles, which are resolved): - 'int size(guide g);' - Analogous to 'size(path p)'. + ‘int size(guide g);’ + Analogous to ‘size(path p)’. - 'int length(guide g);' - Analogous to 'length(path p)'. + ‘int length(guide g);’ + Analogous to ‘length(path p)’. - 'bool cyclic(path p);' - Analogous to 'cyclic(path p)'. + ‘bool cyclic(path p);’ + Analogous to ‘cyclic(path p)’. - 'pair point(guide g, int t);' - Analogous to 'point(path p, int t)'. + ‘pair point(guide g, int t);’ + Analogous to ‘point(path p, int t)’. - 'guide reverse(guide g);' - Analogous to 'reverse(path p)'. If 'g' is cyclic and also + ‘guide reverse(guide g);’ + Analogous to ‘reverse(path p)’. If ‘g’ is cyclic and also contains a secondary cycle, it is first solved to a path, then - reversed. If 'g' is not cyclic but contains an internal + reversed. If ‘g’ is not cyclic but contains an internal cycle, only the internal cycle is solved before reversal. If there are no internal cycles, the guide is reversed but not solved to a path. - 'pair[] dirSpecifier(guide g, int i);' + ‘pair[] dirSpecifier(guide g, int i);’ This returns a pair array of length 2 containing the outgoing (in element 0) and incoming (in element 1) direction - specifiers (or '(0,0)' if none specified) for the segment of - guide 'g' between nodes 'i' and 'i+1'. + specifiers (or ‘(0,0)’ if none specified) for the segment of + guide ‘g’ between nodes ‘i’ and ‘i+1’. - 'pair[] controlSpecifier(guide g, int i);' - If the segment of guide 'g' between nodes 'i' and 'i+1' has + ‘pair[] controlSpecifier(guide g, int i);’ + If the segment of guide ‘g’ between nodes ‘i’ and ‘i+1’ has explicit outgoing and incoming control points, they are returned as elements 0 and 1, respectively, of a two-element array. Otherwise, an empty array is returned. - 'tensionSpecifier tensionSpecifier(guide g, int i);' + ‘tensionSpecifier tensionSpecifier(guide g, int i);’ This returns the tension specifier for the segment of guide - 'g' between nodes 'i' and 'i+1'. The individual components of - the 'tensionSpecifier' type can be accessed as the virtual - members 'in', 'out', and 'atLeast'. + ‘g’ between nodes ‘i’ and ‘i+1’. The individual components of + the ‘tensionSpecifier’ type can be accessed as the virtual + members ‘in’, ‘out’, and ‘atLeast’. - 'real[] curlSpecifier(guide g);' + ‘real[] curlSpecifier(guide g);’ This returns an array containing the initial curl specifier (in element 0) and final curl specifier (in element 1) for - guide 'g'. + guide ‘g’. As a technical detail we note that a direction specifier given to - 'nullpath' modifies the node on the other side: the guides + ‘nullpath’ modifies the node on the other side: the guides a..{up}nullpath..b; c..nullpath{up}..d; e..{up}nullpath{down}..f; @@ -2258,110 +2262,110 @@ File: asymptote.info, Node: Pens, Next: Transforms, Prev: Paths and guides, 6.3 Pens ======== -In 'Asymptote', pens provide a context for the four basic drawing +In ‘Asymptote’, pens provide a context for the four basic drawing commands (*note Drawing commands::). They are used to specify the following drawing attributes: color, line type, line width, line cap, line join, fill rule, text alignment, font, font size, pattern, overwrite mode, and calligraphic transforms on the pen nib. The default -pen used by the drawing routines is called 'currentpen'. This provides -the same functionality as the 'MetaPost' command 'pickup'. The implicit -initializer for pens is 'defaultpen'. +pen used by the drawing routines is called ‘currentpen’. This provides +the same functionality as the ‘MetaPost’ command ‘pickup’. The implicit +initializer for pens is ‘defaultpen’. Pens may be added together with the nonassociative binary operator -'+'. This will add the colors of the two pens. All other non-default +‘+’. This will add the colors of the two pens. All other non-default attributes of the rightmost pen will override those of the leftmost pen. -Thus, one can obtain a yellow dashed pen by saying 'dashed+red+green' or -'red+green+dashed' or 'red+dashed+green'. The binary operator '*' can +Thus, one can obtain a yellow dashed pen by saying ‘dashed+red+green’ or +‘red+green+dashed’ or ‘red+dashed+green’. The binary operator ‘*’ can be used to scale the color of a pen by a real number, until it saturates with one or more color components equal to 1. - * Colors are specified using one of the following colorspaces: - 'pen gray(real g);' - This produces a grayscale color, where the intensity 'g' lies + • Colors are specified using one of the following colorspaces: + ‘pen gray(real g);’ + This produces a grayscale color, where the intensity ‘g’ lies in the interval [0,1], with 0.0 denoting black and 1.0 denoting white. - 'pen rgb(real r, real g, real b);' + ‘pen rgb(real r, real g, real b);’ This produces an RGB color, where each of the red, green, and - blue intensities 'r', 'g', 'b', lies in the interval [0,1]. + blue intensities ‘r’, ‘g’, ‘b’, lies in the interval [0,1]. - 'pen RGB(int r, int g, int b);' + ‘pen RGB(int r, int g, int b);’ This produces an RGB color, where each of the red, green, and - blue intensities 'r', 'g', 'b', lies in the interval [0,255]. + blue intensities ‘r’, ‘g’, ‘b’, lies in the interval [0,255]. - 'pen cmyk(real c, real m, real y, real k);' + ‘pen cmyk(real c, real m, real y, real k);’ This produces a CMYK color, where each of the cyan, magenta, - yellow, and black intensities 'c', 'm', 'y', 'k', lies in the + yellow, and black intensities ‘c’, ‘m’, ‘y’, ‘k’, lies in the interval [0,1]. - 'pen invisible;' + ‘pen invisible;’ This special pen writes in invisible ink, but adjusts the bounding box as if something had been drawn (like the - '\phantom' command in TeX). The function 'bool - invisible(pen)' can be used to test whether a pen is + ‘\phantom’ command in TeX). The function ‘bool + invisible(pen)’ can be used to test whether a pen is invisible. - The default color is 'black'; this may be changed with the routine - 'defaultpen(pen)'. The function 'colorspace(pen p)' returns the - colorspace of pen 'p' as a string ('"gray"', '"rgb"', '"cmyk"', or - '""'). + The default color is ‘black’; this may be changed with the routine + ‘defaultpen(pen)’. The function ‘colorspace(pen p)’ returns the + colorspace of pen ‘p’ as a string (‘"gray"’, ‘"rgb"’, ‘"cmyk"’, or + ‘""’). - The function 'real[] colors(pen)' returns the color components of a - pen. The functions 'pen gray(pen)', 'pen rgb(pen)', and 'pen - cmyk(pen)' return new pens obtained by converting their arguments + The function ‘real[] colors(pen)’ returns the color components of a + pen. The functions ‘pen gray(pen)’, ‘pen rgb(pen)’, and ‘pen + cmyk(pen)’ return new pens obtained by converting their arguments to the respective color spaces. The function - 'colorless(pen=currentpen)' returns a copy of its argument with the + ‘colorless(pen=currentpen)’ returns a copy of its argument with the color attributes stripped (to avoid color mixing). A 6-character RGB hexadecimal string can be converted to a pen with the routine pen rgb(string s); - A pen can be converted to a hexadecimal string with - * string hex(pen p); + • A pen can be converted to a hexadecimal string with ‘string hex(pen + p);’ - Various shades and mixtures of the grayscale primary colors 'black' - and 'white', RGB primary colors 'red', 'green', and 'blue', and RGB - secondary colors 'cyan', 'magenta', and 'yellow' are defined as - named colors, along with the CMYK primary colors 'Cyan', 'Magenta', - 'Yellow', and 'Black', in the module 'plain': + Various shades and mixtures of the grayscale primary colors ‘black’ + and ‘white’, RGB primary colors ‘red’, ‘green’, and ‘blue’, and RGB + secondary colors ‘cyan’, ‘magenta’, and ‘yellow’ are defined as + named colors, along with the CMYK primary colors ‘Cyan’, ‘Magenta’, + ‘Yellow’, and ‘Black’, in the module ‘plain’: [./colors] - The standard 140 RGB 'X11' colors can be imported with the command + The standard 140 RGB ‘X11’ colors can be imported with the command import x11colors; and the standard 68 CMYK TeX colors can be imported with the command import texcolors; Note that there is some overlap between these two standards and the - definitions of some colors (e.g. 'Green') actually disagree. + definitions of some colors (e.g. ‘Green’) actually disagree. - 'Asymptote' also comes with a 'asycolors.sty' 'LaTeX' package that - defines to 'LaTeX' CMYK versions of 'Asymptote''s predefined - colors, so that they can be used directly within 'LaTeX' strings. - Normally, such colors are passed to 'LaTeX' via a pen argument; + ‘Asymptote’ also comes with a ‘asycolors.sty’ ‘LaTeX’ package that + defines to ‘LaTeX’ CMYK versions of ‘Asymptote’’s predefined + colors, so that they can be used directly within ‘LaTeX’ strings. + Normally, such colors are passed to ‘LaTeX’ via a pen argument; however, to change the color of only a portion of a string, say for a slide presentation, (*note slide::) it may be desirable to - specify the color directly to 'LaTeX'. This file can be passed to - 'LaTeX' with the 'Asymptote' command + specify the color directly to ‘LaTeX’. This file can be passed to + ‘LaTeX’ with the ‘Asymptote’ command usepackage("asycolors"); - The structure 'hsv' defined in 'plain_pens.asy' may be used to - convert between HSV and RGB spaces, where the hue 'h' is an angle - in [0,360) and the saturation 's' and value 'v' lie in '[0,1]': + The structure ‘hsv’ defined in ‘plain_pens.asy’ may be used to + convert between HSV and RGB spaces, where the hue ‘h’ is an angle + in [0,360) and the saturation ‘s’ and value ‘v’ lie in ‘[0,1]’: pen p=hsv(180,0.5,0.75); write(p); // ([default], red=0.375, green=0.75, blue=0.75) hsv q=p; write(q.h,q.s,q.v); // 180 0.5 0.75 - * Line types are specified with the function 'pen linetype(real[] a, - real offset=0, bool scale=true, bool adjust=true)', where 'a' is an - array of real array numbers. The optional parameter 'offset' + • Line types are specified with the function ‘pen linetype(real[] a, + real offset=0, bool scale=true, bool adjust=true)’, where ‘a’ is an + array of real array numbers. The optional parameter ‘offset’ specifies where in the pattern to begin. The first number - specifies how far (if 'scale' is 'true', in units of the pen line - width; otherwise in 'PostScript' units) to draw with the pen on, + specifies how far (if ‘scale’ is ‘true’, in units of the pen line + width; otherwise in ‘PostScript’ units) to draw with the pen on, the second number specifies how far to draw with the pen off, and - so on. If 'adjust' is 'true', these spacings are automatically - adjusted by 'Asymptote' to fit the arclength of the path. Here are + so on. If ‘adjust’ is ‘true’, these spacings are automatically + adjusted by ‘Asymptote’ to fit the arclength of the path. Here are the predefined line types: pen solid=linetype(new real[]); pen dotted=linetype(new real[] {0,4}); @@ -2374,16 +2378,16 @@ with one or more color components equal to 1. [./linetype] - The default line type is 'solid'; this may be changed with - 'defaultpen(pen)'. The line type of a pen can be determined with - the functions 'real[] linetype(pen p=currentpen)', 'real offset(pen - p)', 'bool scale(pen p)', and 'bool adjust(pen p)'. + The default line type is ‘solid’; this may be changed with + ‘defaultpen(pen)’. The line type of a pen can be determined with + the functions ‘real[] linetype(pen p=currentpen)’, ‘real offset(pen + p)’, ‘bool scale(pen p)’, and ‘bool adjust(pen p)’. - * The pen line width is specified in 'PostScript' units with 'pen - linewidth(real)'. The default line width is 0.5 bp; this value may - be changed with 'defaultpen(pen)'. The line width of a pen is - returned by 'real linewidth(pen p=currentpen)'. For convenience, - in the module 'plain_pens' we define + • The pen line width is specified in ‘PostScript’ units with ‘pen + linewidth(real)’. The default line width is 0.5 bp; this value may + be changed with ‘defaultpen(pen)’. The line width of a pen is + returned by ‘real linewidth(pen p=currentpen)’. For convenience, + in the module ‘plain_pens’ we define void defaultpen(real w) {defaultpen(linewidth(w));} pen operator +(pen p, real w) {return p+linewidth(w);} pen operator +(real w, pen p) {return linewidth(w)+p;} @@ -2391,90 +2395,90 @@ with one or more color components equal to 1. defaultpen(2); pen p=red+0.5; - * A pen with a specific 'PostScript' line cap is returned on calling - 'linecap' with an integer argument: + • A pen with a specific ‘PostScript’ line cap is returned on calling + ‘linecap’ with an integer argument: pen squarecap=linecap(0); pen roundcap=linecap(1); pen extendcap=linecap(2); - The default line cap, 'roundcap', may be changed with - 'defaultpen(pen)'. The line cap of a pen is returned by 'int - linecap(pen p=currentpen)'. + The default line cap, ‘roundcap’, may be changed with + ‘defaultpen(pen)’. The line cap of a pen is returned by ‘int + linecap(pen p=currentpen)’. - * A pen with a specific 'PostScript' join style is returned on - calling 'linejoin' with an integer argument: + • A pen with a specific ‘PostScript’ join style is returned on + calling ‘linejoin’ with an integer argument: pen miterjoin=linejoin(0); pen roundjoin=linejoin(1); pen beveljoin=linejoin(2); - The default join style, 'roundjoin', may be changed with - 'defaultpen(pen)'.The join style of a pen is returned by 'int - linejoin(pen p=currentpen)'. + The default join style, ‘roundjoin’, may be changed with + ‘defaultpen(pen)’.The join style of a pen is returned by ‘int + linejoin(pen p=currentpen)’. - * A pen with a specific 'PostScript' miter limit is returned by - calling 'miterlimit(real)'. The default miterlimit, '10.0', may be - changed with 'defaultpen(pen)'. The miter limit of a pen is - returned by 'real miterlimit(pen p=currentpen)'. + • A pen with a specific ‘PostScript’ miter limit is returned by + calling ‘miterlimit(real)’. The default miterlimit, ‘10.0’, may be + changed with ‘defaultpen(pen)’. The miter limit of a pen is + returned by ‘real miterlimit(pen p=currentpen)’. - * A pen with a specific 'PostScript' fill rule is returned on calling - 'fillrule' with an integer argument: + • A pen with a specific ‘PostScript’ fill rule is returned on calling + ‘fillrule’ with an integer argument: pen zerowinding=fillrule(0); pen evenodd=fillrule(1); The fill rule, which identifies the algorithm used to determine the - insideness of a path or array of paths, only affects the 'clip', - 'fill', and 'inside' functions. For the 'zerowinding' fill rule, a - point 'z' is outside the region bounded by a path if the number of + insideness of a path or array of paths, only affects the ‘clip’, + ‘fill’, and ‘inside’ functions. For the ‘zerowinding’ fill rule, a + point ‘z’ is outside the region bounded by a path if the number of upward intersections of the path with the horizontal line - 'z--z+infinity' minus the number of downward intersections is zero. - For the 'evenodd' fill rule, 'z' is considered to be outside the + ‘z--z+infinity’ minus the number of downward intersections is zero. + For the ‘evenodd’ fill rule, ‘z’ is considered to be outside the region if the total number of such intersections is even. The - default fill rule, 'zerowinding', may be changed with - 'defaultpen(pen)'. The fill rule of a pen is returned by 'int - fillrule(pen p=currentpen)'. + default fill rule, ‘zerowinding’, may be changed with + ‘defaultpen(pen)’. The fill rule of a pen is returned by ‘int + fillrule(pen p=currentpen)’. - * A pen with a specific text alignment setting is returned on calling - 'basealign' with an integer argument: + • A pen with a specific text alignment setting is returned on calling + ‘basealign’ with an integer argument: pen nobasealign=basealign(0); pen basealign=basealign(1); - The default setting, 'nobasealign',which may be changed with - 'defaultpen(pen)', causes the label alignment routines to use the - full label bounding box for alignment. In contrast, 'basealign' + The default setting, ‘nobasealign’,which may be changed with + ‘defaultpen(pen)’, causes the label alignment routines to use the + full label bounding box for alignment. In contrast, ‘basealign’ requests that the TeX baseline be respected. The base align - setting of a pen is returned by 'int basealign(pen p=currentpen)'. + setting of a pen is returned by ‘int basealign(pen p=currentpen)’. - * The font size is specified in TeX points (1 pt = 1/72.27 inches) - with the function 'pen fontsize(real size, real - lineskip=1.2*size)'. The default font size, 12pt, may be changed - with 'defaultpen(pen)'. Nonstandard font sizes may require + • The font size is specified in TeX points (1 pt = 1/72.27 inches) + with the function ‘pen fontsize(real size, real + lineskip=1.2*size)’. The default font size, 12pt, may be changed + with ‘defaultpen(pen)’. Nonstandard font sizes may require inserting import fontsize; - at the beginning of the file (this requires the 'type1cm' package + at the beginning of the file (this requires the ‘type1cm’ package available from <http://mirror.ctan.org/macros/latex/contrib/type1cm/> - and included in recent 'LaTeX' distributions). The font size and - line skip of a pen can be examined with the routines 'real - fontsize(pen p=currentpen)' and 'real lineskip(pen p=currentpen)', + and included in recent ‘LaTeX’ distributions). The font size and + line skip of a pen can be examined with the routines ‘real + fontsize(pen p=currentpen)’ and ‘real lineskip(pen p=currentpen)’, respectively. - * A pen using a specific LaTeX NFSS font is returned by calling the - function 'pen font(string encoding, string family, string series, - string shape)'. The default setting, 'font("OT1","cmr","m","n")', + • A pen using a specific LaTeX NFSS font is returned by calling the + function ‘pen font(string encoding, string family, string series, + string shape)’. The default setting, ‘font("OT1","cmr","m","n")’, corresponds to 12pt Computer Modern Roman; this may be changed with - 'defaultpen(pen)'. The font setting of a pen is returned by - 'string font(pen p=currentpen)'. + ‘defaultpen(pen)’. The font setting of a pen is returned by + ‘string font(pen p=currentpen)’. Alternatively, one may select a fixed-size TeX font (on which - 'fontsize' has no effect) like '"cmr12"' (12pt Computer Modern - Roman) or '"pcrr"' (Courier) using the function 'pen font(string - name)'. An optional size argument can also be given to scale the - font to the requested size: 'pen font(string name, real size)'. + ‘fontsize’ has no effect) like ‘"cmr12"’ (12pt Computer Modern + Roman) or ‘"pcrr"’ (Courier) using the function ‘pen font(string + name)’. An optional size argument can also be given to scale the + font to the requested size: ‘pen font(string name, real size)’. - A nonstandard font command can be generated with 'pen - fontcommand(string)'. + A nonstandard font command can be generated with ‘pen + fontcommand(string)’. - A convenient interface to the following standard 'PostScript' fonts + A convenient interface to the following standard ‘PostScript’ fonts is also provided: pen AvantGarde(string series="m", string shape="n"); pen Bookman(string series="m", string shape="n"); @@ -2487,11 +2491,11 @@ with one or more color components equal to 1. pen Symbol(string series="m", string shape="n"); pen ZapfDingbats(string series="m", string shape="n"); - * Starting with the 2018/04/01 release, LaTeX takes UTF-8 as the new + • Starting with the 2018/04/01 release, LaTeX takes UTF-8 as the new default input encoding. However, you can still set different input encoding (so as the font, font encoding or even language context). - Here is an example for 'cp1251' and Russian language in Cyrillic - script (font encoding 'T2A'): + Here is an example for ‘cp1251’ and Russian language in Cyrillic + script (font encoding ‘T2A’): texpreamble("\usepackage[math]{anttor}"); texpreamble("\usepackage[T2A]{fontenc}"); texpreamble("\usepackage[cp1251]{inputenc}"); @@ -2501,43 +2505,43 @@ with one or more color components equal to 1. <https://ctan.org/pkg/cjk> The following commands enable the CJK song family (within a label, you can also temporarily switch to another family, say kai, by - prepending '"\CJKfamily{kai}"' to the label string): + prepending ‘"\CJKfamily{kai}"’ to the label string): texpreamble("\usepackage{CJK} \AtBeginDocument{\begin{CJK*}{GBK}{song}} \AtEndDocument{\clearpage\end{CJK*}}"); - * The transparency of a pen can be changed with the command: + • The transparency of a pen can be changed with the command: pen opacity(real opacity=1, string blend="Compatible"); - The opacity can be varied from '0' (fully transparent) to the - default value of '1' (opaque), and 'blend' specifies one of the - following foreground-background blending operations: + The opacity can be varied from ‘0’ (fully transparent) to the + default value of ‘1’ (opaque), and ‘blend’ specifies one of the + following foreground–background blending operations: "Compatible","Normal","Multiply","Screen","Overlay","SoftLight", "HardLight","ColorDodge","ColorBurn","Darken","Lighten","Difference", "Exclusion","Hue","Saturation","Color","Luminosity", as described in <https://www.adobe.com/content/dam/acom/en/devnet/pdf/pdfs/PDF32000_2008.pdf>. - Since 'PostScript' does not support transparency, this feature is - only effective with the '-f pdf' output format option; other + Since ‘PostScript’ does not support transparency, this feature is + only effective with the ‘-f pdf’ output format option; other formats can be produced from the resulting PDF file with the - 'ImageMagick' 'convert' program. Labels are always drawn with an - 'opacity' of 1. A simple example of transparent filling is - provided in the example file 'transparency.asy'. - - * 'PostScript' commands within a 'picture' may be used to create a - tiling pattern, identified by the string 'name', for 'fill' and - 'draw' operations by adding it to the global 'PostScript' frame - 'currentpatterns', with optional left-bottom margin 'lb' and - right-top margin 'rt'. + ‘ImageMagick’ ‘convert’ program. Labels are always drawn with an + ‘opacity’ of 1. A simple example of transparent filling is + provided in the example file ‘transparency.asy’. + + • ‘PostScript’ commands within a ‘picture’ may be used to create a + tiling pattern, identified by the string ‘name’, for ‘fill’ and + ‘draw’ operations by adding it to the global ‘PostScript’ frame + ‘currentpatterns’, with optional left-bottom margin ‘lb’ and + right-top margin ‘rt’. import patterns; void add(string name, picture pic, pair lb=0, pair rt=0); - To 'fill' or 'draw' using pattern 'name', use the pen - 'pattern("name")'. For example, rectangular tilings can be - constructed using the routines 'picture tile(real Hx=5mm, real - Hy=0, pen p=currentpen, filltype filltype=NoFill)', 'picture - checker(real Hx=5mm, real Hy=0, pen p=currentpen)', and 'picture - brick(real Hx=5mm, real Hy=0, pen p=currentpen)' defined in module - 'patterns': + To ‘fill’ or ‘draw’ using pattern ‘name’, use the pen + ‘pattern("name")’. For example, rectangular tilings can be + constructed using the routines ‘picture tile(real Hx=5mm, real + Hy=0, pen p=currentpen, filltype filltype=NoFill)’, ‘picture + checker(real Hx=5mm, real Hy=0, pen p=currentpen)’, and ‘picture + brick(real Hx=5mm, real Hy=0, pen p=currentpen)’ defined in module + ‘patterns’: size(0,90); import patterns; @@ -2554,9 +2558,9 @@ with one or more color components equal to 1. [./tile] - Hatch patterns can be generated with the routines 'picture - hatch(real H=5mm, pair dir=NE, pen p=currentpen)', 'picture - crosshatch(real H=5mm, pen p=currentpen)': + Hatch patterns can be generated with the routines ‘picture + hatch(real H=5mm, pair dir=NE, pen p=currentpen)’, ‘picture + crosshatch(real H=5mm, pen p=currentpen)’: size(0,100); import patterns; @@ -2571,12 +2575,12 @@ with one or more color components equal to 1. [./hatch] - You may need to turn off aliasing in your 'PostScript' viewer for + You may need to turn off aliasing in your ‘PostScript’ viewer for patterns to appear correctly. Custom patterns can easily be - constructed, following the examples in module 'patterns'. The + constructed, following the examples in module ‘patterns’. The tiled pattern can even incorporate shading (*note gradient shading::), as illustrated in this example (not included in the - manual because not all printers support 'PostScript' 3): + manual because not all printers support ‘PostScript’ 3): size(0,100); import patterns; @@ -2590,10 +2594,10 @@ with one or more color components equal to 1. filldraw(unitcircle,pattern("shadedtiling")); - * One can specify a custom pen nib as an arbitrary polygonal path - with 'pen makepen(path)'; this path represents the mark to be drawn + • One can specify a custom pen nib as an arbitrary polygonal path + with ‘pen makepen(path)’; this path represents the mark to be drawn for paths containing a single point. This pen nib path can be - recovered from a pen with 'path nib(pen)'. Unlike in 'MetaPost', + recovered from a pen with ‘path nib(pen)’. Unlike in ‘MetaPost’, the path need not be convex: size(200); @@ -2608,39 +2612,39 @@ with one or more color components equal to 1. [./makepen] - The value 'nullpath' represents a circular pen nib (the default); + The value ‘nullpath’ represents a circular pen nib (the default); an elliptical pen can be achieved simply by multiplying the pen by - a transform: 'yscale(2)*currentpen'. + a transform: ‘yscale(2)*currentpen’. - * One can prevent labels from overwriting one another by using the - pen attribute 'overwrite', which takes a single argument: + • One can prevent labels from overwriting one another by using the + pen attribute ‘overwrite’, which takes a single argument: - 'Allow' + ‘Allow’ Allow labels to overwrite one another. This is the default - behaviour (unless overridden with 'defaultpen(pen)'. + behaviour (unless overridden with ‘defaultpen(pen)’. - 'Suppress' + ‘Suppress’ Suppress, with a warning, each label that would overwrite another label. - 'SuppressQuiet' + ‘SuppressQuiet’ Suppress, without warning, each label that would overwrite another label. - 'Move' + ‘Move’ Move a label that would overwrite another out of the way and issue a warning. As this adjustment is during the final - output phase (in 'PostScript' coordinates) it could result in + output phase (in ‘PostScript’ coordinates) it could result in a larger figure than requested. - 'MoveQuiet' + ‘MoveQuiet’ Move a label that would overwrite another out of the way, without warning. As this adjustment is during the final - output phase (in 'PostScript' coordinates) it could result in + output phase (in ‘PostScript’ coordinates) it could result in a larger figure than requested. - The routine 'defaultpen()' returns the current default pen -attributes. Calling the routine 'resetdefaultpen()' resets all pen + The routine ‘defaultpen()’ returns the current default pen +attributes. Calling the routine ‘resetdefaultpen()’ resets all pen default attributes to their initial values. @@ -2649,51 +2653,51 @@ File: asymptote.info, Node: Transforms, Next: Frames and pictures, Prev: Pens 6.4 Transforms ============== -'Asymptote' makes extensive use of affine transforms. A pair '(x,y)' is -transformed by the transform 't=(t.x,t.y,t.xx,t.xy,t.yx,t.yy)' to -'(x',y')', where +‘Asymptote’ makes extensive use of affine transforms. A pair ‘(x,y)’ is +transformed by the transform ‘t=(t.x,t.y,t.xx,t.xy,t.yx,t.yy)’ to +‘(x',y')’, where x' = t.x + t.xx * x + t.xy * y y' = t.y + t.yx * x + t.yy * y -This is equivalent to the 'PostScript' transformation '[t.xx t.yx t.xy -t.yy t.x t.y]'. +This is equivalent to the ‘PostScript’ transformation ‘[t.xx t.yx t.xy +t.yy t.x t.y]’. Transforms can be applied to pairs, guides, paths, pens, strings, transforms, frames, and pictures by multiplication (via the binary -operator '*') on the left (*note circle:: for an example). Transforms +operator ‘*’) on the left (*note circle:: for an example). Transforms can be composed with one another and inverted with the function -'transform inverse(transform t)'; they can also be raised to any integer -power with the '^' operator. +‘transform inverse(transform t)’; they can also be raised to any integer +power with the ‘^’ operator. The built-in transforms are: -'transform identity;' +‘transform identity;’ the identity transform; -'transform shift(pair z);' - translates by the pair 'z'; -'transform shift(real x, real y);' - translates by the pair '(x,y)'; -'transform xscale(real x);' - scales by 'x' in the x direction; -'transform yscale(real y);' - scales by 'y' in the y direction; -'transform scale(real s);' - scale by 's' in both x and y directions; -'transform scale(real x, real y);' - scale by 'x' in the x direction and by 'y' in the y direction; -'transform slant(real s);' - maps '(x,y)' -> '(x+s*y,y)'; -'transform rotate(real angle, pair z=(0,0));' - rotates by 'angle' in degrees about 'z'; -'transform reflect(pair a, pair b);' - reflects about the line 'a--b'. -'transform zeroTransform;' +‘transform shift(pair z);’ + translates by the pair ‘z’; +‘transform shift(real x, real y);’ + translates by the pair ‘(x,y)’; +‘transform xscale(real x);’ + scales by ‘x’ in the x direction; +‘transform yscale(real y);’ + scales by ‘y’ in the y direction; +‘transform scale(real s);’ + scale by ‘s’ in both x and y directions; +‘transform scale(real x, real y);’ + scale by ‘x’ in the x direction and by ‘y’ in the y direction; +‘transform slant(real s);’ + maps ‘(x,y)’ –> ‘(x+s*y,y)’; +‘transform rotate(real angle, pair z=(0,0));’ + rotates by ‘angle’ in degrees about ‘z’; +‘transform reflect(pair a, pair b);’ + reflects about the line ‘a--b’. +‘transform zeroTransform;’ the zero transform; - The implicit initializer for transforms is 'identity()'. The -routines 'shift(transform t)' and 'shiftless(transform t)' return the -transforms '(t.x,t.y,0,0,0,0)' and '(0,0,t.xx,t.xy,t.yx,t.yy)' -respectively. The function 'bool isometry(transform t)' can be used to -test if 't' is an isometry (preserves distance). + The implicit initializer for transforms is ‘identity()’. The +routines ‘shift(transform t)’ and ‘shiftless(transform t)’ return the +transforms ‘(t.x,t.y,0,0,0,0)’ and ‘(0,0,t.xx,t.xy,t.yx,t.yy)’ +respectively. The function ‘bool isometry(transform t)’ can be used to +test if ‘t’ is an isometry (preserves distance). File: asymptote.info, Node: Frames and pictures, Next: Files, Prev: Transforms, Up: Programming @@ -2701,27 +2705,27 @@ File: asymptote.info, Node: Frames and pictures, Next: Files, Prev: Transform 6.5 Frames and pictures ======================= -'frame' - Frames are canvases for drawing in 'PostScript' coordinates. While +‘frame’ + Frames are canvases for drawing in ‘PostScript’ coordinates. While working with frames directly is occasionally necessary for constructing deferred drawing routines, pictures are usually more convenient to work with. The implicit initializer for frames is - 'newframe'. The function 'bool empty(frame f)' returns 'true' only - if the frame 'f' is empty. A frame may be erased with the - 'erase(frame)' routine. The functions 'pair min(frame)' and 'pair - max(frame)' return the (left,bottom) and (right,top) coordinates of - the frame bounding box, respectively. The contents of frame 'src' - may be appended to frame 'dest' with the command + ‘newframe’. The function ‘bool empty(frame f)’ returns ‘true’ only + if the frame ‘f’ is empty. A frame may be erased with the + ‘erase(frame)’ routine. The functions ‘pair min(frame)’ and ‘pair + max(frame)’ return the (left,bottom) and (right,top) coordinates of + the frame bounding box, respectively. The contents of frame ‘src’ + may be appended to frame ‘dest’ with the command void add(frame dest, frame src); or prepended with void prepend(frame dest, frame src); - A frame obtained by aligning frame 'f' in the direction 'align', in - a manner analogous to the 'align' argument of 'label' (*note + A frame obtained by aligning frame ‘f’ in the direction ‘align’, in + a manner analogous to the ‘align’ argument of ‘label’ (*note label::), is returned by frame align(frame f, pair align); To draw or fill a box or ellipse around a label or frame and return - the boundary as a path, use one of the predefined 'envelope' + the boundary as a path, use one of the predefined ‘envelope’ routines path box(frame f, Label L="", real xmargin=0, real ymargin=xmargin, pen p=currentpen, @@ -2733,92 +2737,92 @@ File: asymptote.info, Node: Frames and pictures, Next: Files, Prev: Transform real ymargin=xmargin, pen p=currentpen, filltype filltype=NoFill, bool above=true); -'picture' +‘picture’ Pictures are high-level structures (*note Structures::) defined in - the module 'plain' that provide canvases for drawing in user - coordinates. The default picture is called 'currentpicture'. A + the module ‘plain’ that provide canvases for drawing in user + coordinates. The default picture is called ‘currentpicture’. A new picture can be created like this: picture pic; - Anonymous pictures can be made by the expression 'new picture'. + Anonymous pictures can be made by the expression ‘new picture’. - The 'size' routine specifies the dimensions of the desired picture: + The ‘size’ routine specifies the dimensions of the desired picture: void size(picture pic=currentpicture, real x, real y=x, bool keepAspect=Aspect); - If the 'x' and 'y' sizes are both 0, user coordinates will be - interpreted as 'PostScript' coordinates. In this case, the - transform mapping 'pic' to the final output frame is 'identity()'. + If the ‘x’ and ‘y’ sizes are both 0, user coordinates will be + interpreted as ‘PostScript’ coordinates. In this case, the + transform mapping ‘pic’ to the final output frame is ‘identity()’. - If exactly one of 'x' or 'y' is 0, no size restriction is imposed + If exactly one of ‘x’ or ‘y’ is 0, no size restriction is imposed in that direction; it will be scaled the same as the other direction. - If 'keepAspect' is set to 'Aspect' or 'true', the picture will be + If ‘keepAspect’ is set to ‘Aspect’ or ‘true’, the picture will be scaled with its aspect ratio preserved such that the final width is - no more than 'x' and the final height is no more than 'y'. + no more than ‘x’ and the final height is no more than ‘y’. - If 'keepAspect' is set to 'IgnoreAspect' or 'false', the picture - will be scaled in both directions so that the final width is 'x' - and the height is 'y'. + If ‘keepAspect’ is set to ‘IgnoreAspect’ or ‘false’, the picture + will be scaled in both directions so that the final width is ‘x’ + and the height is ‘y’. - To make the user coordinates of picture 'pic' represent multiples - of 'x' units in the x direction and 'y' units in the y direction, + To make the user coordinates of picture ‘pic’ represent multiples + of ‘x’ units in the x direction and ‘y’ units in the y direction, use void unitsize(picture pic=currentpicture, real x, real y=x); - When nonzero, these 'x' and 'y' values override the corresponding - size parameters of picture 'pic'. + When nonzero, these ‘x’ and ‘y’ values override the corresponding + size parameters of picture ‘pic’. The routine void size(picture pic=currentpicture, real xsize, real ysize, pair min, pair max); forces the final picture scaling to map the user coordinates - 'box(min,max)' to a region of width 'xsize' and height 'ysize' + ‘box(min,max)’ to a region of width ‘xsize’ and height ‘ysize’ (when these parameters are nonzero). Alternatively, calling the routine transform fixedscaling(picture pic=currentpicture, pair min, pair max, pen p=nullpen, bool warn=false); - will cause picture 'pic' to use a fixed scaling to map user - coordinates in 'box(min,max)' to the (already specified) picture - size, taking account of the width of pen 'p'. A warning will be + will cause picture ‘pic’ to use a fixed scaling to map user + coordinates in ‘box(min,max)’ to the (already specified) picture + size, taking account of the width of pen ‘p’. A warning will be issued if the final picture exceeds the specified size. - A picture 'pic' can be fit to a frame and output to a file - 'prefix'.'format' using image format 'format' by calling the - 'shipout' function: + A picture ‘pic’ can be fit to a frame and output to a file + ‘prefix’.‘format’ using image format ‘format’ by calling the + ‘shipout’ function: void shipout(string prefix=defaultfilename, picture pic=currentpicture, orientation orientation=orientation, string format="", bool wait=false, bool view=true, string options="", string script="", light light=currentlight, projection P=currentprojection) - The default output format, 'PostScript', may be changed with the - '-f' or '-tex' command-line options. The 'options', 'script', and - 'projection' parameters are only relevant for 3D pictures. If - 'defaultfilename' is an empty string, the prefix 'outprefix()' will + The default output format, ‘PostScript’, may be changed with the + ‘-f’ or ‘-tex’ command-line options. The ‘options’, ‘script’, and + ‘projection’ parameters are only relevant for 3D pictures. If + ‘defaultfilename’ is an empty string, the prefix ‘outprefix()’ will be used. - A 'shipout()' command is added implicitly at file exit if no - previous 'shipout' commands have been executed. The default page - orientation is 'Portrait'; this may be modified by changing the - variable 'orientation'. To output in landscape mode, simply set - the variable 'orientation=Landscape' or issue the command + A ‘shipout()’ command is added implicitly at file exit. The + default page orientation is ‘Portrait’; this may be modified by + changing the variable ‘orientation’. To output in landscape mode, + simply set the variable ‘orientation=Landscape’ or issue the + command shipout(Landscape); - To rotate the page by -90 degrees, use the orientation 'Seascape'. - The orientation 'UpsideDown' rotates the page by 180 degrees. + To rotate the page by -90 degrees, use the orientation ‘Seascape’. + The orientation ‘UpsideDown’ rotates the page by 180 degrees. - A picture 'pic' can be explicitly fit to a frame by calling + A picture ‘pic’ can be explicitly fit to a frame by calling frame pic.fit(real xsize=pic.xsize, real ysize=pic.ysize, bool keepAspect=pic.keepAspect); The default size and aspect ratio settings are those given to the - 'size' command (which default to '0', '0', and 'true', + ‘size’ command (which default to ‘0’, ‘0’, and ‘true’, respectively). The transformation that would currently be used to - fit a picture 'pic' to a frame is returned by the member function - 'pic.calculateTransform()'. + fit a picture ‘pic’ to a frame is returned by the member function + ‘pic.calculateTransform()’. In certain cases (e.g. 2D graphs) where only an approximate size - estimate for 'pic' is available, the picture fitting routine + estimate for ‘pic’ is available, the picture fitting routine frame pic.scale(real xsize=this.xsize, real ysize=this.ysize, bool keepAspect=this.keepAspect); (which scales the resulting frame, including labels and fixed-size @@ -2830,56 +2834,56 @@ File: asymptote.info, Node: Frames and pictures, Next: Files, Prev: Transform frame bbox(picture pic=currentpicture, real xmargin=0, real ymargin=xmargin, pen p=currentpen, filltype filltype=NoFill); - Here 'filltype' specifies one of the following fill types: - 'FillDraw' + Here ‘filltype’ specifies one of the following fill types: + ‘FillDraw’ Fill the interior and draw the boundary. - 'FillDraw(real xmargin=0, real ymargin=xmargin, pen fillpen=nullpen,' - 'pen drawpen=nullpen)' If 'fillpen' is 'nullpen', fill with - the drawing pen; otherwise fill with pen 'fillpen'. If - 'drawpen' is 'nullpen', draw the boundary with 'fillpen'; - otherwise with 'drawpen'. An optional margin of 'xmargin' and - 'ymargin' can be specified. + ‘FillDraw(real xmargin=0, real ymargin=xmargin, pen fillpen=nullpen,’ + ‘pen drawpen=nullpen)’ If ‘fillpen’ is ‘nullpen’, fill with + the drawing pen; otherwise fill with pen ‘fillpen’. If + ‘drawpen’ is ‘nullpen’, draw the boundary with ‘fillpen’; + otherwise with ‘drawpen’. An optional margin of ‘xmargin’ and + ‘ymargin’ can be specified. - 'Fill' + ‘Fill’ Fill the interior. - 'Fill(real xmargin=0, real ymargin=xmargin, pen p=nullpen)' - If 'p' is 'nullpen', fill with the drawing pen; otherwise fill - with pen 'p'. An optional margin of 'xmargin' and 'ymargin' + ‘Fill(real xmargin=0, real ymargin=xmargin, pen p=nullpen)’ + If ‘p’ is ‘nullpen’, fill with the drawing pen; otherwise fill + with pen ‘p’. An optional margin of ‘xmargin’ and ‘ymargin’ can be specified. - 'NoFill' + ‘NoFill’ Do not fill. - 'Draw' + ‘Draw’ Draw only the boundary. - 'Draw(real xmargin=0, real ymargin=xmargin, pen p=nullpen)' - If 'p' is 'nullpen', draw the boundary with the drawing pen; - otherwise draw with pen 'p'. An optional margin of 'xmargin' - and 'ymargin' can be specified. + ‘Draw(real xmargin=0, real ymargin=xmargin, pen p=nullpen)’ + If ‘p’ is ‘nullpen’, draw the boundary with the drawing pen; + otherwise draw with pen ‘p’. An optional margin of ‘xmargin’ + and ‘ymargin’ can be specified. - 'UnFill' + ‘UnFill’ Clip the region. - 'UnFill(real xmargin=0, real ymargin=xmargin)' - Clip the region and surrounding margins 'xmargin' and - 'ymargin'. + ‘UnFill(real xmargin=0, real ymargin=xmargin)’ + Clip the region and surrounding margins ‘xmargin’ and + ‘ymargin’. - 'RadialShade(pen penc, pen penr)' - Fill varying radially from 'penc' at the center of the - bounding box to 'penr' at the edge. + ‘RadialShade(pen penc, pen penr)’ + Fill varying radially from ‘penc’ at the center of the + bounding box to ‘penr’ at the edge. - 'RadialShadeDraw(real xmargin=0, real ymargin=xmargin, pen penc,' - 'pen penr, pen drawpen=nullpen)' Fill with RadialShade and + ‘RadialShadeDraw(real xmargin=0, real ymargin=xmargin, pen penc,’ + ‘pen penr, pen drawpen=nullpen)’ Fill with RadialShade and draw the boundary. For example, to draw a bounding box around a picture with a 0.25 cm margin and output the resulting frame, use the command: shipout(bbox(0.25cm)); - A 'picture' may be fit to a frame with the background color pen - 'p', using the function 'bbox(p,Fill)'. + A ‘picture’ may be fit to a frame with the background color pen + ‘p’, using the function ‘bbox(p,Fill)’. To pad a picture to a precise size in both directions, fit the picture to a frame using the function @@ -2890,43 +2894,43 @@ File: asymptote.info, Node: Frames and pictures, Next: Files, Prev: Transform pair min(picture pic, user=false); pair max(picture pic, user=false); pair size(picture pic, user=false); - calculate the bounds that picture 'pic' would have if it were + calculate the bounds that picture ‘pic’ would have if it were currently fit to a frame using its default size specification. If - 'user' is 'false' the returned value is in 'PostScript' + ‘user’ is ‘false’ the returned value is in ‘PostScript’ coordinates, otherwise it is in user coordinates. The function pair point(picture pic=currentpicture, pair dir, bool user=true); is a convenient way of determining the point on the bounding box of - 'pic' in the direction 'dir' relative to its center, ignoring the + ‘pic’ in the direction ‘dir’ relative to its center, ignoring the contributions from fixed-size objects (such as labels and - arrowheads). If 'user' is 'true' the returned value is in user - coordinates, otherwise it is in 'PostScript' coordinates. + arrowheads). If ‘user’ is ‘true’ the returned value is in user + coordinates, otherwise it is in ‘PostScript’ coordinates. The function pair truepoint(picture pic=currentpicture, pair dir, bool user=true); - is identical to 'point', except that it also accounts for - fixed-size objects, using the scaling transform that picture 'pic' + is identical to ‘point’, except that it also accounts for + fixed-size objects, using the scaling transform that picture ‘pic’ would have if currently fit to a frame using its default size - specification. If 'user' is 'true' the returned value is in user - coordinates, otherwise it is in 'PostScript' coordinates. + specification. If ‘user’ is ‘true’ the returned value is in user + coordinates, otherwise it is in ‘PostScript’ coordinates. Sometimes it is useful to draw objects on separate pictures and add - one picture to another using the 'add' function: + one picture to another using the ‘add’ function: void add(picture src, bool group=true, filltype filltype=NoFill, bool above=true); void add(picture dest, picture src, bool group=true, filltype filltype=NoFill, bool above=true); - The first example adds 'src' to 'currentpicture'; the second one - adds 'src' to 'dest'. The 'group' option specifies whether or not + The first example adds ‘src’ to ‘currentpicture’; the second one + adds ‘src’ to ‘dest’. The ‘group’ option specifies whether or not the graphical user interface should treat all of the elements of - 'src' as a single entity (*note GUI::), 'filltype' requests - optional background filling or clipping, and 'above' specifies - whether to add 'src' above or below existing objects. + ‘src’ as a single entity (*note GUI::), ‘filltype’ requests + optional background filling or clipping, and ‘above’ specifies + whether to add ‘src’ above or below existing objects. - There are also routines to add a picture or frame 'src' specified - in postscript coordinates to another picture 'dest' (or - 'currentpicture') about the user coordinate 'position': + There are also routines to add a picture or frame ‘src’ specified + in postscript coordinates to another picture ‘dest’ (or + ‘currentpicture’) about the user coordinate ‘position’: void add(picture src, pair position, bool group=true, filltype filltype=NoFill, bool above=true); void add(picture dest, picture src, pair position, @@ -2937,12 +2941,12 @@ File: asymptote.info, Node: Frames and pictures, Next: Files, Prev: Transform pair align, bool group=true, filltype filltype=NoFill, bool above=true); - The optional 'align' argument in the last form specifies a + The optional ‘align’ argument in the last form specifies a direction to use for aligning the frame, in a manner analogous to - the 'align' argument of 'label' (*note label::). However, one key - difference is that when 'align' is not specified, labels are + the ‘align’ argument of ‘label’ (*note label::). However, one key + difference is that when ‘align’ is not specified, labels are centered, whereas frames and pictures are aligned so that their - origin is at 'position'. Illustrations of frame alignment can be + origin is at ‘position’. Illustrations of frame alignment can be found in the examples *note errorbars:: and *note image::. If you want to align three or more subpictures, group them two at a time: @@ -2969,9 +2973,9 @@ File: asymptote.info, Node: Frames and pictures, Next: Files, Prev: Transform [./subpictures] - Alternatively, one can use 'attach' to automatically increase the - size of picture 'dest' to accommodate adding a frame 'src' about - the user coordinate 'position': + Alternatively, one can use ‘attach’ to automatically increase the + size of picture ‘dest’ to accommodate adding a frame ‘src’ about + the user coordinate ‘position’: void attach(picture dest=currentpicture, frame src, pair position=0, bool group=true, filltype filltype=NoFill, bool above=true); @@ -2983,28 +2987,28 @@ File: asymptote.info, Node: Frames and pictures, Next: Files, Prev: Transform specification), use the function void erase(picture pic=currentpicture); - To save a snapshot of 'currentpicture', 'currentpen', and - 'currentprojection', use the function 'save()'. + To save a snapshot of ‘currentpicture’, ‘currentpen’, and + ‘currentprojection’, use the function ‘save()’. - To restore a snapshot of 'currentpicture', 'currentpen', and - 'currentprojection', use the function 'restore()'. + To restore a snapshot of ‘currentpicture’, ‘currentpen’, and + ‘currentprojection’, use the function ‘restore()’. Many further examples of picture and frame operations are provided - in the base module 'plain'. + in the base module ‘plain’. - It is possible to insert verbatim 'PostScript' commands in a + It is possible to insert verbatim ‘PostScript’ commands in a picture with one of the routines void postscript(picture pic=currentpicture, string s); void postscript(picture pic=currentpicture, string s, pair min, pair max) - Here 'min' and 'max' can be used to specify explicit bounds - associated with the resulting 'PostScript' code. + Here ‘min’ and ‘max’ can be used to specify explicit bounds + associated with the resulting ‘PostScript’ code. - Verbatim TeX commands can be inserted in the intermediate 'LaTeX' + Verbatim TeX commands can be inserted in the intermediate ‘LaTeX’ output file with one of the functions void tex(picture pic=currentpicture, string s); void tex(picture pic=currentpicture, string s, pair min, pair max) - Here 'min' and 'max' can be used to specify explicit bounds + Here ‘min’ and ‘max’ can be used to specify explicit bounds associated with the resulting TeX code. To issue a global TeX command (such as a TeX macro definition) in @@ -3020,7 +3024,7 @@ File: asymptote.info, Node: Frames and pictures, Next: Files, Prev: Transform void usepackage(string s, string options=""); provides a convenient abbreviation for texpreamble("\usepackage["+options+"]{"+s+"}"); - that can be used for importing 'LaTeX' packages. + that can be used for importing ‘LaTeX’ packages. File: asymptote.info, Node: Files, Next: Variable initializers, Prev: Frames and pictures, Up: Programming @@ -3028,7 +3032,7 @@ File: asymptote.info, Node: Files, Next: Variable initializers, Prev: Frames 6.6 Files ========= -'Asymptote' can read and write text files (including comma-separated +‘Asymptote’ can read and write text files (including comma-separated value) files and portable XDR (External Data Representation) binary files. @@ -3038,47 +3042,47 @@ input(string name="", bool check=true, string comment="#", string mode=""); file fin=input("test.txt"); real a=fin; - If the optional boolean argument 'check' is 'false', no check will be + If the optional boolean argument ‘check’ is ‘false’, no check will be made that the file exists. If the file does not exist or is not -readable, the function 'bool error(file)' will return 'true'. The first -character of the string 'comment' specifies a comment character. If +readable, the function ‘bool error(file)’ will return ‘true’. The first +character of the string ‘comment’ specifies a comment character. If this character is encountered in a data file, the remainder of the line is ignored. When reading strings, a comment character followed immediately by another comment character is treated as a single literal -comment character. If 'Asymptote' is compiled with support for -'libcurl', 'name' can be a URL. +comment character. If ‘Asymptote’ is compiled with support for +‘libcurl’, ‘name’ can be a URL. - Unless the '-noglobalread' command-line option is specified, one can + Unless the ‘-noglobalread’ command-line option is specified, one can change the current working directory for read operations to the contents -of the string 's' with the function 'string cd(string s)', which returns -the new working directory. If 'string s' is empty, the path is reset to +of the string ‘s’ with the function ‘string cd(string s)’, which returns +the new working directory. If ‘string s’ is empty, the path is reset to the value it had at program startup. When reading pairs, the enclosing parenthesis are optional. Strings are also read by assignment, by reading characters up to but not -including a newline. In addition, 'Asymptote' provides the function -'string getc(file)' to read the next character (treating the comment +including a newline. In addition, ‘Asymptote’ provides the function +‘string getc(file)’ to read the next character (treating the comment character as an ordinary character) and return it as a string. - A file named 'name' can be open for output with + A file named ‘name’ can be open for output with file output(string name="", bool update=false, string comment="#", string mode=""); -If 'update=false', any existing data in the file will be erased and only -write operations can be used on the file. If 'update=true', any +If ‘update=false’, any existing data in the file will be erased and only +write operations can be used on the file. If ‘update=true’, any existing data will be preserved, the position will be set to the end-of-file, and both reading and writing operations will be enabled. For security reasons, writing to files in directories other than the -current directory is allowed only if the '-globalwrite' (or '-nosafe') +current directory is allowed only if the ‘-globalwrite’ (or ‘-nosafe’) command-line option is specified. Reading from files in other -directories is allowed unless the '-noglobalread' command-line option is -specified. The function 'string mktemp(string s)' may be used to create +directories is allowed unless the ‘-noglobalread’ command-line option is +specified. The function ‘string mktemp(string s)’ may be used to create and return the name of a unique temporary file in the current directory -based on the string 's'. +based on the string ‘s’. - There are two special files: 'stdin', which reads from the keyboard, -and 'stdout', which writes to the terminal. The implicit initializer -for files is 'null'. + There are two special files: ‘stdin’, which reads from the keyboard, +and ‘stdout’, which writes to the terminal. The implicit initializer +for files is ‘null’. - Data of a built-in type 'T' can be written to an output file by + Data of a built-in type ‘T’ can be written to an output file by calling one of the functions write(string s="", T x, suffix suffix=endl ... T[]); write(file file, string s="", T x, suffix suffix=none ... T[]); @@ -3087,61 +3091,61 @@ write(file file=stdout, T[][]); write(file file=stdout, T[][][]); write(suffix suffix=endl); write(file file, suffix suffix=none); - If 'file' is not specified, 'stdout' is used and terminated by + If ‘file’ is not specified, ‘stdout’ is used and terminated by default with a newline. If specified, the optional identifying string -'s' is written before the data 'x'. An arbitrary number of data values +‘s’ is written before the data ‘x’. An arbitrary number of data values may be listed when writing scalars or one-dimensional arrays. The -'suffix' may be one of the following: 'none' (do nothing), 'flush' -(output buffered data), 'endl' (terminate with a newline and flush), -'newl' (terminate with a newline), 'DOSendl' (terminate with a DOS -newline and flush), 'DOSnewl' (terminate with a DOS newline), 'tab' -(terminate with a tab), or 'comma' (terminate with a comma). Here are +‘suffix’ may be one of the following: ‘none’ (do nothing), ‘flush’ +(output buffered data), ‘endl’ (terminate with a newline and flush), +‘newl’ (terminate with a newline), ‘DOSendl’ (terminate with a DOS +newline and flush), ‘DOSnewl’ (terminate with a DOS newline), ‘tab’ +(terminate with a tab), or ‘comma’ (terminate with a comma). Here are some simple examples of data output: file fout=output("test.txt"); write(fout,1); // Writes "1" write(fout); // Writes a new line write(fout,"List: ",1,2,3); // Writes "List: 1 2 3" - A file may be opened with 'mode="xdr"', to read or write double + A file may be opened with ‘mode="xdr"’, to read or write double precision (64-bit) reals and single precision (32-bit) integers in Sun -Microsystem's XDR (External Data Representation) portable binary format -(available on all 'UNIX' platforms). Alternatively, a file may also be -opened with 'mode="binary"' to read or write double precision reals and +Microsystem’s XDR (External Data Representation) portable binary format +(available on all ‘UNIX’ platforms). Alternatively, a file may also be +opened with ‘mode="binary"’ to read or write double precision reals and single precision integers in the native (nonportable) machine binary format, or to read the entire file into a string. The virtual member -functions 'file singlereal(bool b=true)' and 'file singleint(bool -b=true)' be used to change the precision of real and integer I/O -operations, respectively, for an XDR or binary file 'f'. Similarly, the -function 'file signedint(bool b=true)' can be used to modify the -signedness of integer reads and writes for an XDR or binary file 'f'. - - The virtual members 'name', 'mode', 'singlereal', 'singleint', and -'signedint' may be used to query the respective parameters for a given +functions ‘file singlereal(bool b=true)’ and ‘file singleint(bool +b=true)’ be used to change the precision of real and integer I/O +operations, respectively, for an XDR or binary file ‘f’. Similarly, the +function ‘file signedint(bool b=true)’ can be used to modify the +signedness of integer reads and writes for an XDR or binary file ‘f’. + + The virtual members ‘name’, ‘mode’, ‘singlereal’, ‘singleint’, and +‘signedint’ may be used to query the respective parameters for a given file. One can test a file for end-of-file with the boolean function -'eof(file)', end-of-line with 'eol(file)', and for I/O errors with -'error(file)'. One can flush the output buffers with 'flush(file)', -clear a previous I/O error with 'clear(file)', and close the file with -'close(file)'. The function 'int precision(file file=stdout, int -digits=0)' sets the number of digits of output precision for 'file' to -'digits', provided 'digits' is nonzero, and returns the previous -precision setting. The function 'int tell(file)' returns the current -position in a file relative to the beginning. The routine 'seek(file -file, int pos)' can be used to change this position, where a negative -value for the position 'pos' is interpreted as relative to the -end-of-file. For example, one can rewind a file 'file' with the command -'seek(file,0)' and position to the final character in the file with -'seek(file,-1)'. The command 'seekeof(file)' sets the position to the +‘eof(file)’, end-of-line with ‘eol(file)’, and for I/O errors with +‘error(file)’. One can flush the output buffers with ‘flush(file)’, +clear a previous I/O error with ‘clear(file)’, and close the file with +‘close(file)’. The function ‘int precision(file file=stdout, int +digits=0)’ sets the number of digits of output precision for ‘file’ to +‘digits’, provided ‘digits’ is nonzero, and returns the previous +precision setting. The function ‘int tell(file)’ returns the current +position in a file relative to the beginning. The routine ‘seek(file +file, int pos)’ can be used to change this position, where a negative +value for the position ‘pos’ is interpreted as relative to the +end-of-file. For example, one can rewind a file ‘file’ with the command +‘seek(file,0)’ and position to the final character in the file with +‘seek(file,-1)’. The command ‘seekeof(file)’ sets the position to the end of the file. - Assigning 'settings.scroll=n' for a positive integer 'n' requests a -pause after every 'n' output lines to 'stdout'. One may then press -'Enter' to continue to the next 'n' output lines, 's' followed by -'Enter' to scroll without further interruption, or 'q' followed by -'Enter' to quit the current output operation. If 'n' is negative, the + Assigning ‘settings.scroll=n’ for a positive integer ‘n’ requests a +pause after every ‘n’ output lines to ‘stdout’. One may then press +‘Enter’ to continue to the next ‘n’ output lines, ‘s’ followed by +‘Enter’ to scroll without further interruption, or ‘q’ followed by +‘Enter’ to quit the current output operation. If ‘n’ is negative, the output scrolls a page at a time (i.e. by one less than the current -number of display lines). The default value, 'settings.scroll=0', +number of display lines). The default value, ‘settings.scroll=0’, specifies continuous scrolling. The routines @@ -3155,38 +3159,38 @@ pair getpair(string name="", pair default=0, string prompt="", bool store=true); triple gettriple(string name="", triple default=(0,0,0), string prompt="", bool store=true); -defined in the module 'plain' may be used to prompt for a value from -'stdin' using the GNU 'readline' library. If 'store=true', the history -of values for 'name' is stored in the file '".asy_history_"+name' (*note +defined in the module ‘plain’ may be used to prompt for a value from +‘stdin’ using the GNU ‘readline’ library. If ‘store=true’, the history +of values for ‘name’ is stored in the file ‘".asy_history_"+name’ (*note history::). The most recent value in the history will be used to provide a default value for subsequent runs. The default value -(initially 'default') is displayed after 'prompt'. These functions are +(initially ‘default’) is displayed after ‘prompt’. These functions are based on the internal routines string readline(string prompt="", string name="", bool tabcompletion=false); void saveline(string name, string value, bool store=true); - Here, 'readline' prompts the user with the default value formatted -according to 'prompt', while 'saveline' is used to save the string -'value' in a local history named 'name', optionally storing the local -history in a file '".asy_history_"+name'. - - The routine 'history(string name, int n=1)' can be used to look up -the 'n' most recent values (or all values up to 'historylines' if 'n=0') -entered for string 'name'. The routine 'history(int n=0)' returns the + Here, ‘readline’ prompts the user with the default value formatted +according to ‘prompt’, while ‘saveline’ is used to save the string +‘value’ in a local history named ‘name’, optionally storing the local +history in a file ‘".asy_history_"+name’. + + The routine ‘history(string name, int n=1)’ can be used to look up +the ‘n’ most recent values (or all values up to ‘historylines’ if ‘n=0’) +entered for string ‘name’. The routine ‘history(int n=0)’ returns the interactive history. For example, write(output("transcript.asy"),history()); -outputs the interactive history to the file 'transcript.asy'. +outputs the interactive history to the file ‘transcript.asy’. - The function 'int delete(string s)' deletes the file named by the -string 's'. Unless the '-globalwrite' (or '-nosafe') option is enabled, -the file must reside in the current directory. The function 'int -rename(string from, string to)' may be used to rename file 'from' to -file 'to'. Unless the '-globalwrite' (or '-nosafe') option is enabled, + The function ‘int delete(string s)’ deletes the file named by the +string ‘s’. Unless the ‘-globalwrite’ (or ‘-nosafe’) option is enabled, +the file must reside in the current directory. The function ‘int +rename(string from, string to)’ may be used to rename file ‘from’ to +file ‘to’. Unless the ‘-globalwrite’ (or ‘-nosafe’) option is enabled, this operation is restricted to the current directory. The functions int convert(string args="", string file="", string format=""); int animate(string args="", string file="", string format=""); -call the 'ImageMagick' commands 'convert' and 'animate', respectively, -with the arguments 'args' and the file name constructed from the strings -'file' and 'format'. +call the ‘ImageMagick’ commands ‘convert’ and ‘animate’, respectively, +with the arguments ‘args’ and the file name constructed from the strings +‘file’ and ‘format’. File: asymptote.info, Node: Variable initializers, Next: Structures, Prev: Files, Up: Programming @@ -3194,56 +3198,56 @@ File: asymptote.info, Node: Variable initializers, Next: Structures, Prev: Fi 6.7 Variable initializers ========================= -A variable can be assigned a value when it is declared, as in 'int x=3;' -where the variable 'x' is assigned the value '3'. As well as literal -constants such as '3', arbitary expressions can be used as initializers, -as in 'real x=2*sin(pi/2);'. +A variable can be assigned a value when it is declared, as in ‘int x=3;’ +where the variable ‘x’ is assigned the value ‘3’. As well as literal +constants such as ‘3’, arbitary expressions can be used as initializers, +as in ‘real x=2*sin(pi/2);’. A variable is not added to the namespace until after the initializer is evaluated, so for example, in int x=2; int x=5*x; -the 'x' in the initializer on the second line refers to the variable 'x' +the ‘x’ in the initializer on the second line refers to the variable ‘x’ declared on the first line. The second line, then, declares a variable -'x' shadowing the original 'x' and initializes it to the value '10'. +‘x’ shadowing the original ‘x’ and initializes it to the value ‘10’. Variables of most types can be declared without an explicit initializer and they will be initialized by the default initializer of that type: - * Variables of the numeric types 'int', 'real', and 'pair' are all - initialized to zero; variables of type 'triple' are initialized to - 'O=(0,0,0)'. - * 'boolean' variables are initialized to 'false'. - * 'string' variables are initialized to the empty string. - * 'transform' variables are initialized to the identity + • Variables of the numeric types ‘int’, ‘real’, and ‘pair’ are all + initialized to zero; variables of type ‘triple’ are initialized to + ‘O=(0,0,0)’. + • ‘boolean’ variables are initialized to ‘false’. + • ‘string’ variables are initialized to the empty string. + • ‘transform’ variables are initialized to the identity transformation. - * 'path' and 'guide' variables are initialized to 'nullpath'. - * 'pen' variables are initialized to the default pen. - * 'frame' and 'picture' variables are initialized to empty frames and + • ‘path’ and ‘guide’ variables are initialized to ‘nullpath’. + • ‘pen’ variables are initialized to the default pen. + • ‘frame’ and ‘picture’ variables are initialized to empty frames and pictures, respectively. - * 'file' variables are initialized to 'null'. + • ‘file’ variables are initialized to ‘null’. The default initializers for user-defined array, structure, and function types are explained in their respective sections. Some types, -such as 'code', do not have default initializers. When a variable of +such as ‘code’, do not have default initializers. When a variable of such a type is introduced, the user must initialize it by explicitly giving it a value. - The default initializer for any type 'T' can be redeclared by -defining the function 'T operator init()'. For instance, 'int' + The default initializer for any type ‘T’ can be redeclared by +defining the function ‘T operator init()’. For instance, ‘int’ variables are usually initialized to zero, but in int operator init() { return 3; } int y; -the variable 'y' is initialized to '3'. This example was given for +the variable ‘y’ is initialized to ‘3’. This example was given for illustrative purposes; redeclaring the initializers of built-in types is -not recommended. Typically, 'operator init' is used to define sensible +not recommended. Typically, ‘operator init’ is used to define sensible defaults for user-defined types. - The special type 'var' may be used to infer the type of a variable + The special type ‘var’ may be used to infer the type of a variable from its initializer. If the initializer is an expression of a unique type, then the variable will be defined with that type. For instance, var x=5; @@ -3254,7 +3258,7 @@ int x=5; real y=4.3; pen reddash=red+dashed; - 'var' may also be used with the extended 'for' loop syntax. + ‘var’ may also be used with the extended ‘for’ loop syntax. int[] a = {1,2,3}; for (var x : a) @@ -3268,11 +3272,11 @@ File: asymptote.info, Node: Structures, Next: Operators, Prev: Variable initi Users may also define their own data types as structures, along with user-defined operators, much as in C++. By default, structure members -are 'public' (may be read and modified anywhere in the code), but may be -optionally declared 'restricted' (readable anywhere but writeable only -inside the structure where they are defined) or 'private' (readable and +are ‘public’ (may be read and modified anywhere in the code), but may be +optionally declared ‘restricted’ (readable anywhere but writeable only +inside the structure where they are defined) or ‘private’ (readable and writable only inside the structure). In a structure definition, the -keyword 'this' can be used as an expression to refer to the enclosing +keyword ‘this’ can be used as an expression to refer to the enclosing structure. Any code at the top-level scope within the structure is executed on initialization. @@ -3285,13 +3289,13 @@ T foo; T bar=foo; bar.x=5; - The variable 'foo' holds a reference to an instance of the structure -'T'. When 'bar' is assigned the value of 'foo', it too now holds a -reference to the same instance as 'foo' does. The assignment 'bar.x=5' -changes the value of the field 'x' in that instance, so that 'foo.x' -will also be equal to '5'. + The variable ‘foo’ holds a reference to an instance of the structure +‘T’. When ‘bar’ is assigned the value of ‘foo’, it too now holds a +reference to the same instance as ‘foo’ does. The assignment ‘bar.x=5’ +changes the value of the field ‘x’ in that instance, so that ‘foo.x’ +will also be equal to ‘5’. - The expression 'new T' creates a new instance of the structure 'T' + The expression ‘new T’ creates a new instance of the structure ‘T’ and returns a reference to that instance. In creating the new instance, any code in the body of the record definition is executed. For example: int Tcount=0; @@ -3302,13 +3306,13 @@ struct T { T foo=new T; T foo; -Here, 'new T' produces a new instance of the class, which causes -'Tcount' to be incremented, tracking the number of instances produced. -The declarations 'T foo=new T' and 'T foo' are equivalent: the second -form implicitly creates a new instance of 'T'. That is, after the -definition of a structure 'T', a variable of type 'T' is initialized to -a new instance ('new T') by default. During the definition of the -structure, however, variables of type 'T' are initialized to 'null' by +Here, ‘new T’ produces a new instance of the class, which causes +‘Tcount’ to be incremented, tracking the number of instances produced. +The declarations ‘T foo=new T’ and ‘T foo’ are equivalent: the second +form implicitly creates a new instance of ‘T’. That is, after the +definition of a structure ‘T’, a variable of type ‘T’ is initialized to +a new instance (‘new T’) by default. During the definition of the +structure, however, variables of type ‘T’ are initialized to ‘null’ by default. This special behaviour is to avoid infinite recursion of creating new instances in code such as struct tree { @@ -3317,18 +3321,18 @@ struct tree { tree right; } - The expression 'null' can be cast to any structure type to yield a + The expression ‘null’ can be cast to any structure type to yield a null reference, a reference that does not actually refer to any instance of the structure. Trying to use a field of a null reference will cause an error. - The function 'bool alias(T,T)' checks to see if two structure + The function ‘bool alias(T,T)’ checks to see if two structure references refer to the same instance of the structure (or both to -'null'). In the example at the beginning of this section, -'alias(foo,bar)' would return true, but 'alias(foo,new T)' would return -false, as 'new T' creates a new instance of the structure 'T'. The -boolean operators '==' and '!=' are by default equivalent to 'alias' and -'!alias' respectively, but may be overwritten for a particular type (for +‘null’). In the example at the beginning of this section, +‘alias(foo,bar)’ would return true, but ‘alias(foo,new T)’ would return +false, as ‘new T’ creates a new instance of the structure ‘T’. The +boolean operators ‘==’ and ‘!=’ are by default equivalent to ‘alias’ and +‘!alias’ respectively, but may be overwritten for a particular type (for example, to do a deep comparison). Here is a simple example that illustrates the use of structures: @@ -3352,7 +3356,7 @@ write((s+s).f(0)); // Outputs 2 It is often convenient to have functions that construct new instances -of a structure. Say we have a 'Person' structure: +of a structure. Say we have a ‘Person’ structure: struct Person { string firstname; string lastname; @@ -3362,11 +3366,11 @@ Person joe; joe.firstname="Joe"; joe.lastname="Jones"; Creating a new Person is a chore; it takes three lines to create a new -instance and to initialize its fields (that's still considerably less +instance and to initialize its fields (that’s still considerably less effort than creating a new person in real life, though). We can reduce the work by defining a constructor function -'Person(string,string)': +‘Person(string,string)’: struct Person { string firstname; string lastname; @@ -3382,11 +3386,11 @@ struct Person { Person joe=Person.Person("Joe", "Jones"); While it is now easier than before to create a new instance, we still -have to refer to the constructor by the qualified name 'Person.Person'. +have to refer to the constructor by the qualified name ‘Person.Person’. If we add the line from Person unravel Person; immediately after the structure definition, then the constructor can be -used without qualification: 'Person joe=Person("Joe", "Jones");'. +used without qualification: ‘Person joe=Person("Joe", "Jones");’. The constructor is now easy to use, but it is quite a hassle to define. If you write a lot of constructors, you will find that you are @@ -3395,11 +3399,11 @@ neighbourhood Asymptote developers have devised a way to automate much of the process. If, in the body of a structure, Asymptote encounters the definition -of a function of the form 'void operator init(ARGS)', it implicitly -defines a constructor function of the arguments 'ARGS' that uses the -'void operator init' function to initialize a new instance of the +of a function of the form ‘void operator init(ARGS)’, it implicitly +defines a constructor function of the arguments ‘ARGS’ that uses the +‘void operator init’ function to initialize a new instance of the structure. That is, it essentially defines the following constructor -(assuming the structure is called 'Foo'): +(assuming the structure is called ‘Foo’): static Foo Foo(ARGS) { Foo instance=new Foo; @@ -3409,7 +3413,7 @@ structure. That is, it essentially defines the following constructor This constructor is also implicitly copied to the enclosing scope after the end of the structure definition, so that it can used -subsequently without qualifying it by the structure name. Our 'Person' +subsequently without qualifying it by the structure name. Our ‘Person’ example can thus be implemented as: struct Person { string firstname; @@ -3423,24 +3427,24 @@ struct Person { Person joe=Person("Joe", "Jones"); - The use of 'operator init' to implicitly define constructors should + The use of ‘operator init’ to implicitly define constructors should not be confused with its use to define default values for variables (*note Variable initializers::). Indeed, in the first case, the return -type of the 'operator init' must be 'void' while in the second, it must -be the (non-'void') type of the variable. - - The function 'cputime()' returns a structure 'cputime' with -cumulative CPU times broken down into the fields 'parent.user', -'parent.system', 'child.user', and 'child.system', along with the -cumulative wall clock time in 'parent.clock', all measured in seconds. -For convenience, the incremental fields 'change.user', 'change.system', -and 'change.clock' indicate the change in the corresponding fields since -the last call to 'cputime()'. The function +type of the ‘operator init’ must be ‘void’ while in the second, it must +be the (non-‘void’) type of the variable. + + The function ‘cputime()’ returns a structure ‘cputime’ with +cumulative CPU times broken down into the fields ‘parent.user’, +‘parent.system’, ‘child.user’, and ‘child.system’, along with the +cumulative wall clock time in ‘parent.clock’, all measured in seconds. +For convenience, the incremental fields ‘change.user’, ‘change.system’, +and ‘change.clock’ indicate the change in the corresponding fields since +the last call to ‘cputime()’. The function void write(file file=stdout, string s="", cputime c, string format=cputimeformat, suffix suffix=none); -displays the incremental user cputime followed by "u", the incremental -system cputime followed by "s", the total user cputime followed by "U", -and the total system cputime followed by "S". +displays the incremental user cputime followed by “u”, the incremental +system cputime followed by “s”, the total user cputime followed by “U”, +and the total system cputime followed by “S”. Much like in C++, casting (*note Casts::) provides for an elegant implementation of structure inheritance, including virtual functions: @@ -3475,8 +3479,8 @@ c.f(); // Outputs 1; write(c.parent.x); // Outputs 2; write(c.y); // Outputs 3; - For further examples of structures, see 'Legend' and 'picture' in the -'Asymptote' base module 'plain'. + For further examples of structures, see ‘Legend’ and ‘picture’ in the +‘Asymptote’ base module ‘plain’. File: asymptote.info, Node: Operators, Next: Implicit scaling, Prev: Structures, Up: Programming @@ -3496,73 +3500,73 @@ File: asymptote.info, Node: Arithmetic & logical, Next: Self & prefix operator 6.9.1 Arithmetic & logical operators ------------------------------------ -'Asymptote' uses the standard binary arithmetic operators. However, +‘Asymptote’ uses the standard binary arithmetic operators. However, when one integer is divided by another, both arguments are converted to real values before dividing and a real quotient is returned (since this -is typically what is intended; otherwise one can use the function 'int -quotient(int x, int y)', which returns greatest integer less than or -equal to 'x/y'). In all other cases both operands are promoted to the +is typically what is intended; otherwise one can use the function ‘int +quotient(int x, int y)’, which returns greatest integer less than or +equal to ‘x/y’). In all other cases both operands are promoted to the same type, which will also be the type of the result: -'+' +‘+’ addition -'-' +‘-’ subtraction -'*' +‘*’ multiplication -'/' +‘/’ division -'#' - integer division; equivalent to 'quotient(x,y)'. Noting that the - 'Python3' community adopted our comment symbol ('//') for integer +‘#’ + integer division; equivalent to ‘quotient(x,y)’. Noting that the + ‘Python3’ community adopted our comment symbol (‘//’) for integer division, we decided to reciprocate and use their comment symbol - for integer division in 'Asymptote'! -'%' + for integer division in ‘Asymptote’! +‘%’ modulo; the result always has the same sign as the divisor. In - particular, this makes 'q*(p # q)+p % q == p' for all integers 'p' - and nonzero integers 'q'. -'^' + particular, this makes ‘q*(p # q)+p % q == p’ for all integers ‘p’ + and nonzero integers ‘q’. +‘^’ power; if the exponent (second argument) is an int, recursive multiplication is used; otherwise, logarithms and exponentials are - used ('**' is a synonym for '^'). + used (‘**’ is a synonym for ‘^’). The usual boolean operators are also defined: -'==' +‘==’ equals -'!=' +‘!=’ not equals -'<' +‘<’ less than -'<=' +‘<=’ less than or equals -'>=' +‘>=’ greater than or equals -'>' +‘>’ greater than -'&&' +‘&&’ and (with conditional evaluation of right-hand argument) -'&' +‘&’ and -'||' +‘||’ or (with conditional evaluation of right-hand argument) -'|' +‘|’ or -'^' +‘^’ xor -'!' +‘!’ not - 'Asymptote' also supports the C-like conditional syntax: + ‘Asymptote’ also supports the C-like conditional syntax: bool positive=(pi > 0) ? true : false; - The function 'T interp(T a, T b, real t)' returns '(1-t)*a+t*b' for -nonintegral built-in arithmetic types 'T'. If 'a' and 'b' are pens, + The function ‘T interp(T a, T b, real t)’ returns ‘(1-t)*a+t*b’ for +nonintegral built-in arithmetic types ‘T’. If ‘a’ and ‘b’ are pens, they are first promoted to the same color space. - 'Asymptote' also defines bitwise functions 'int AND(int,int)', 'int -OR(int,int)', 'int XOR(int,int)', 'int NOT(int)', 'int CLZ(int)' (count -leading zeros), 'int CTZ(int)' (count trailing zeros), 'int -popcount(int)' (count bits populated by ones), and 'int bitreverse(int -a, int bits)' (reverse bits within a word of length bits). + ‘Asymptote’ also defines bitwise functions ‘int AND(int,int)’, ‘int +OR(int,int)’, ‘int XOR(int,int)’, ‘int NOT(int)’, ‘int CLZ(int)’ (count +leading zeros), ‘int CTZ(int)’ (count trailing zeros), ‘int +popcount(int)’ (count bits populated by ones), and ‘int bitreverse(int +a, int bits)’ (reverse bits within a word of length bits). File: asymptote.info, Node: Self & prefix operators, Next: User-defined operators, Prev: Arithmetic & logical, Up: Operators @@ -3570,9 +3574,9 @@ File: asymptote.info, Node: Self & prefix operators, Next: User-defined operat 6.9.2 Self & prefix operators ----------------------------- -As in C, each of the arithmetic operators '+', '-', '*', '/', '#', '%', -and '^' can be used as a self operator. The prefix operators '++' -(increment by one) and '--' (decrement by one) are also defined. For +As in C, each of the arithmetic operators ‘+’, ‘-’, ‘*’, ‘/’, ‘#’, ‘%’, +and ‘^’ can be used as a self operator. The prefix operators ‘++’ +(increment by one) and ‘--’ (decrement by one) are also defined. For example, int i=1; i += 2; @@ -3583,11 +3587,11 @@ int i=1; i=i+2; int j=i=i+1; - However, postfix operators like 'i++' and 'i--' are not defined -(because of the inherent ambiguities that would arise with the '--' -path-joining operator). In the rare instances where 'i++' and 'i--' are -really needed, one can substitute the expressions '(++i-1)' and -'(--i+1)', respectively. + However, postfix operators like ‘i++’ and ‘i--’ are not defined +(because of the inherent ambiguities that would arise with the ‘--’ +path-joining operator). In the rare instances where ‘i++’ and ‘i--’ are +really needed, one can substitute the expressions ‘(++i-1)’ and +‘(--i+1)’, respectively. File: asymptote.info, Node: User-defined operators, Prev: Self & prefix operators, Up: Operators @@ -3595,14 +3599,14 @@ File: asymptote.info, Node: User-defined operators, Prev: Self & prefix operat 6.9.3 User-defined operators ---------------------------- -The following symbols may be used with 'operator' to define or redefine +The following symbols may be used with ‘operator’ to define or redefine operators on structures and built-in types: - + * / % ^ ! < > == != <= >= & | ^^ .. :: -- --- ++ << >> $ $$ @ @@ <> The operators on the second line have precedence one higher than the -boolean operators '<', '>', '<=', and '>='. +boolean operators ‘<’, ‘>’, ‘<=’, and ‘>=’. - Guide operators like '..' may be overloaded, say, to write a user + Guide operators like ‘..’ may be overloaded, say, to write a user function that produces a new guide from a given guide: guide dots(... guide[] g)=operator ..; @@ -3673,14 +3677,14 @@ File: asymptote.info, Node: Functions, Next: Arrays, Prev: Implicit scaling, * Rest arguments:: Functions with a variable number of arguments * Mathematical functions:: Standard libm functions -'Asymptote' functions are treated as variables with a signature +‘Asymptote’ functions are treated as variables with a signature (non-function variables have null signatures). Variables with the same name are allowed, so long as they have distinct signatures. Function arguments are passed by value. To pass an argument by reference, simply enclose it in a structure (*note Structures::). - Here are some significant features of 'Asymptote' functions: + Here are some significant features of ‘Asymptote’ functions: 1. Variables with signatures (functions) and without signatures (nonfunction variables) are distinct: @@ -3715,11 +3719,11 @@ reference, simply enclose it in a structure (*note Structures::). intop addby7=adder(7); write(addby7(1)); // Writes 8. - 5. One may redefine a function 'f', even for calls to 'f' in + 5. One may redefine a function ‘f’, even for calls to ‘f’ in previously declared functions, by assigning another (anonymous or - named) function to it. However, if 'f' is overloaded by a new + named) function to it. However, if ‘f’ is overloaded by a new function definition, previous calls will still access the original - version of 'f', as illustrated in this example: + version of ‘f’, as illustrated in this example: void f() { write("hi"); } @@ -3756,14 +3760,14 @@ reference, simply enclose it in a structure (*note Structures::). g(true); // Writes true, then writes false. - 'Asymptote' is the only language we know of that treats functions as + ‘Asymptote’ is the only language we know of that treats functions as variables, but allows overloading by distinguishing variables based on their signatures. Functions are allowed to call themselves recursively. As in C++, infinite nested recursion will generate a stack overflow (reported as a segmentation fault, unless a fully working version of the GNU library -'libsigsegv' (e.g. 2.4 or later) is installed at configuration time). +‘libsigsegv’ (e.g. 2.4 or later) is installed at configuration time). File: asymptote.info, Node: Default arguments, Next: Named arguments, Prev: Functions, Up: Functions @@ -3771,17 +3775,17 @@ File: asymptote.info, Node: Default arguments, Next: Named arguments, Prev: F 6.11.1 Default arguments ------------------------ -'Asymptote' supports a more flexible mechanism for default function +‘Asymptote’ supports a more flexible mechanism for default function arguments than C++: they may appear anywhere in the function prototype. Because certain data types are implicitly cast to more sophisticated types (*note Casts::) one can often avoid ambiguities by ordering function arguments from the simplest to the most complicated. For example, given real f(int a=1, real b=0) {return a+b;} -then 'f(1)' returns 1.0, but 'f(1.0)' returns 2.0. +then ‘f(1)’ returns 1.0, but ‘f(1.0)’ returns 2.0. The value of a default argument is determined by evaluating the given -'Asymptote' expression in the scope where the called function is +‘Asymptote’ expression in the scope where the called function is defined. @@ -3795,8 +3799,8 @@ appear in a function declaration. Named (keyword) arguments make calling functions with multiple arguments easier. Unlike in the C and C++ languages, an assignment in a function argument is interpreted as an assignment to a parameter of the same name in the function signature, -_not within the local scope_. The command-line option '-d' may be used -to check 'Asymptote' code for cases where a named argument may be +_not within the local scope_. The command-line option ‘-d’ may be used +to check ‘Asymptote’ code for cases where a named argument may be mistaken for a local assignment. When matching arguments to signatures, first all of the keywords are @@ -3806,13 +3810,13 @@ int f(int x, int y) { return 10x+y; } write(f(4,x=3)); -outputs 34, as 'x' is already matched when we try to match the unnamed -argument '4', so it gets matched to the next item, 'y'. +outputs 34, as ‘x’ is already matched when we try to match the unnamed +argument ‘4’, so it gets matched to the next item, ‘y’. For the rare occasions where it is desirable to assign a value to local variable within a function argument (generally _not_ a good programming practice), simply enclose the assignment in parentheses. -For example, given the definition of 'f' in the previous example, +For example, given the definition of ‘f’ in the previous example, int x; write(f(4,(x=3))); is equivalent to the statements @@ -3821,11 +3825,11 @@ x=3; write(f(4,3)); and outputs 43. - Parameters can be specified as "keyword-only" by putting 'keyword' -immediately before the parameter name, as in 'int f(int keyword x)' or -'int f(int keyword x=77)'. This forces the caller of the function to + Parameters can be specified as “keyword-only” by putting ‘keyword’ +immediately before the parameter name, as in ‘int f(int keyword x)’ or +‘int f(int keyword x=77)’. This forces the caller of the function to use a named argument to give a value for this parameter. That is, -'f(x=42)' is legal, but 'f(25)' is not. Keyword-only parameters must be +‘f(x=42)’ is legal, but ‘f(25)’ is not. Keyword-only parameters must be listed after normal parameters in a function definition. As a technical detail, we point out that, since variables of the same @@ -3834,16 +3838,16 @@ int f(int x, int x()) { return x+x(); } int seven() {return 7;} -is legal in 'Asymptote', with 'f(2,seven)' returning 9. A named +is legal in ‘Asymptote’, with ‘f(2,seven)’ returning 9. A named argument matches the first unmatched formal of the same name, so -'f(x=2,x=seven)' is an equivalent call, but 'f(x=seven,2)' is not, as -the first argument is matched to the first formal, and 'int ()' cannot -be implicitly cast to 'int'. Default arguments do not affect which -formal a named argument is matched to, so if 'f' were defined as +‘f(x=2,x=seven)’ is an equivalent call, but ‘f(x=seven,2)’ is not, as +the first argument is matched to the first formal, and ‘int ()’ cannot +be implicitly cast to ‘int’. Default arguments do not affect which +formal a named argument is matched to, so if ‘f’ were defined as int f(int x=3, int x()) { return x+x(); } -then 'f(x=seven)' would be illegal, even though 'f(seven)' obviously +then ‘f(x=seven)’ would be illegal, even though ‘f(seven)’ obviously would be allowed. @@ -3877,7 +3881,7 @@ subtract(10); // returns 10 subtract(); // illegal Putting an argument into a rest array is called _packing_. One can -give an explicit list of arguments for the rest argument, so 'subtract' +give an explicit list of arguments for the rest argument, so ‘subtract’ could alternatively be implemented as int subtract(int start ... int[] subs) { return start - sum(... subs); @@ -3885,26 +3889,26 @@ int subtract(int start ... int[] subs) { One can even combine normal arguments with rest arguments: sum(1,2,3 ... new int[] {4,5,6}); // returns 21 -This builds a new six-element array that is passed to 'sum' as 'nums'. +This builds a new six-element array that is passed to ‘sum’ as ‘nums’. The opposite operation, _unpacking_, is not allowed: subtract(... new int[] {10, 1, 2}); is illegal, as the start formal is not matched. If no arguments are packed, then a zero-length array (as opposed to -'null') is bound to the rest parameter. Note that default arguments are +‘null’) is bound to the rest parameter. Note that default arguments are ignored for rest formals and the rest argument is not bound to a keyword. In some cases, keyword-only parameters are helpful to avoid arguments intended for the rest parameter to be assigned to other parameters. For -example, here the use of 'keyword' is to avoid 'pnorm(1.0,2.0,0.3)' -matching '1.0' to 'p'. +example, here the use of ‘keyword’ is to avoid ‘pnorm(1.0,2.0,0.3)’ +matching ‘1.0’ to ‘p’. real pnorm(real keyword p=2.0 ... real[] v) { return sum(v^p)^(1/p); } - The overloading resolution in 'Asymptote' is similar to the function + The overloading resolution in ‘Asymptote’ is similar to the function matching rules used in C++. Every argument match is given a score. Exact matches score better than matches with casting, and matches with formals (regardless of casting) score better than packing an argument @@ -3940,84 +3944,84 @@ File: asymptote.info, Node: Mathematical functions, Prev: Rest arguments, Up: 6.11.4 Mathematical functions ----------------------------- -'Asymptote' has built-in versions of the standard 'libm' mathematical -real(real) functions 'sin', 'cos', 'tan', 'asin', 'acos', 'atan', 'exp', -'log', 'pow10', 'log10', 'sinh', 'cosh', 'tanh', 'asinh', 'acosh', -'atanh', 'sqrt', 'cbrt', 'fabs', 'expm1', 'log1p', as well as the -identity function 'identity'. 'Asymptote' also defines the order 'n' -Bessel functions of the first kind 'Jn(int n, real)' and second kind -'Yn(int n, real)', as well as the gamma function 'gamma', the error -function 'erf', and the complementary error function 'erfc'. The -standard real(real, real) functions 'atan2', 'hypot', 'fmod', -'remainder' are also included. - - The functions 'degrees(real radians)' and 'radians(real degrees)' can +‘Asymptote’ has built-in versions of the standard ‘libm’ mathematical +real(real) functions ‘sin’, ‘cos’, ‘tan’, ‘asin’, ‘acos’, ‘atan’, ‘exp’, +‘log’, ‘pow10’, ‘log10’, ‘sinh’, ‘cosh’, ‘tanh’, ‘asinh’, ‘acosh’, +‘atanh’, ‘sqrt’, ‘cbrt’, ‘fabs’, ‘expm1’, ‘log1p’, as well as the +identity function ‘identity’. ‘Asymptote’ also defines the order ‘n’ +Bessel functions of the first kind ‘Jn(int n, real)’ and second kind +‘Yn(int n, real)’, as well as the gamma function ‘gamma’, the error +function ‘erf’, and the complementary error function ‘erfc’. The +standard real(real, real) functions ‘atan2’, ‘hypot’, ‘fmod’, +‘remainder’ are also included. + + The functions ‘degrees(real radians)’ and ‘radians(real degrees)’ can be used to convert between radians and degrees. The function -'Degrees(real radians)' returns the angle in degrees in the interval -[0,360). For convenience, 'Asymptote' defines variants 'Sin', 'Cos', -'Tan', 'aSin', 'aCos', and 'aTan' of the standard trigonometric +‘Degrees(real radians)’ returns the angle in degrees in the interval +[0,360). For convenience, ‘Asymptote’ defines variants ‘Sin’, ‘Cos’, +‘Tan’, ‘aSin’, ‘aCos’, and ‘aTan’ of the standard trigonometric functions that use degrees rather than radians. We also define complex -versions of the 'sqrt', 'sin', 'cos', 'exp', 'log', and 'gamma' +versions of the ‘sqrt’, ‘sin’, ‘cos’, ‘exp’, ‘log’, and ‘gamma’ functions. - The functions 'floor', 'ceil', and 'round' differ from their usual + The functions ‘floor’, ‘ceil’, and ‘round’ differ from their usual definitions in that they all return an int value rather than a real -(since that is normally what one wants). The functions 'Floor', 'Ceil', -and 'Round' are respectively similar, except that if the result cannot -be converted to a valid int, they return 'intMax' for positive arguments -and 'intMin' for negative arguments, rather than generating an integer -overflow. We also define a function 'sgn', which returns the sign of +(since that is normally what one wants). The functions ‘Floor’, ‘Ceil’, +and ‘Round’ are respectively similar, except that if the result cannot +be converted to a valid int, they return ‘intMax’ for positive arguments +and ‘intMin’ for negative arguments, rather than generating an integer +overflow. We also define a function ‘sgn’, which returns the sign of its real argument as an integer (-1, 0, or 1). - There is an 'abs(int)' function, as well as an 'abs(real)' function -(equivalent to 'fabs(real)'), an 'abs(pair)' function (equivalent to -'length(pair)'). + There is an ‘abs(int)’ function, as well as an ‘abs(real)’ function +(equivalent to ‘fabs(real)’), an ‘abs(pair)’ function (equivalent to +‘length(pair)’). - Random numbers can be seeded with 'srand(int)' and generated with the -'int rand()' function, which returns a random integer between 0 and the -integer 'randMax'. The 'unitrand()' function returns a random number + Random numbers can be seeded with ‘srand(int)’ and generated with the +‘int rand()’ function, which returns a random integer between 0 and the +integer ‘randMax’. The ‘unitrand()’ function returns a random number uniformly distributed in the interval [0,1]. A Gaussian random number -generator 'Gaussrand' and a collection of statistics routines, including -'histogram', are provided in the module 'stats'. The functions -'factorial(int n)', which returns n!, and 'choose(int n, int k)', which +generator ‘Gaussrand’ and a collection of statistics routines, including +‘histogram’, are provided in the module ‘stats’. The functions +‘factorial(int n)’, which returns n!, and ‘choose(int n, int k)’, which returns n!/(k!(n-k)!), are also defined. When configured with the GNU Scientific Library (GSL), available from -<https://www.gnu.org/software/gsl/>, 'Asymptote' contains an internal -module 'gsl' that defines the airy functions 'Ai(real)', 'Bi(real)', -'Ai_deriv(real)', 'Bi_deriv(real)', 'zero_Ai(int)', 'zero_Bi(int)', -'zero_Ai_deriv(int)', 'zero_Bi_deriv(int)', the Bessel functions 'I(int, -real)', 'K(int, real)', 'j(int, real)', 'y(int, real)', 'i_scaled(int, -real)', 'k_scaled(int, real)', 'J(real, real)', 'Y(real, real)', -'I(real, real)', 'K(real, real)', 'zero_J(real, int)', the elliptic -functions 'F(real, real)', 'E(real, real)', and 'P(real, real)', the -Jacobi elliptic functions 'real[] sncndn(real,real)', the -exponential/trigonometric integrals 'Ei', 'Si', and 'Ci', the Legendre -polynomials 'Pl(int, real)', and the Riemann zeta function 'zeta(real)'. -For example, to compute the sine integral 'Si' of 1.0: +<https://www.gnu.org/software/gsl/>, ‘Asymptote’ contains an internal +module ‘gsl’ that defines the airy functions ‘Ai(real)’, ‘Bi(real)’, +‘Ai_deriv(real)’, ‘Bi_deriv(real)’, ‘zero_Ai(int)’, ‘zero_Bi(int)’, +‘zero_Ai_deriv(int)’, ‘zero_Bi_deriv(int)’, the Bessel functions ‘I(int, +real)’, ‘K(int, real)’, ‘j(int, real)’, ‘y(int, real)’, ‘i_scaled(int, +real)’, ‘k_scaled(int, real)’, ‘J(real, real)’, ‘Y(real, real)’, +‘I(real, real)’, ‘K(real, real)’, ‘zero_J(real, int)’, the elliptic +functions ‘F(real, real)’, ‘E(real, real)’, and ‘P(real, real)’, the +Jacobi elliptic functions ‘real[] sncndn(real,real)’, the +exponential/trigonometric integrals ‘Ei’, ‘Si’, and ‘Ci’, the Legendre +polynomials ‘Pl(int, real)’, and the Riemann zeta function ‘zeta(real)’. +For example, to compute the sine integral ‘Si’ of 1.0: import gsl; write(Si(1.0)); - 'Asymptote' also provides a few general purpose numerical routines: + ‘Asymptote’ also provides a few general purpose numerical routines: -'real newton(int iterations=100, real f(real), real fprime(real), real x, bool verbose=false);' +‘real newton(int iterations=100, real f(real), real fprime(real), real x, bool verbose=false);’ Use Newton-Raphson iteration to solve for a root of a real-valued - differentiable function 'f', given its derivative 'fprime' and an - initial guess 'x'. Diagnostics for each iteration are printed if - 'verbose=true'. If the iteration fails after the maximum allowed - number of loops ('iterations'), 'realMax' is returned. + differentiable function ‘f’, given its derivative ‘fprime’ and an + initial guess ‘x’. Diagnostics for each iteration are printed if + ‘verbose=true’. If the iteration fails after the maximum allowed + number of loops (‘iterations’), ‘realMax’ is returned. -'real newton(int iterations=100, real f(real), real fprime(real), real x1, real x2, bool verbose=false);' +‘real newton(int iterations=100, real f(real), real fprime(real), real x1, real x2, bool verbose=false);’ Use bracketed Newton-Raphson bisection to solve for a root of a - real-valued differentiable function 'f' within an interval - ['x1','x2'] (on which the endpoint values of 'f' have opposite - signs), given its derivative 'fprime'. Diagnostics for each - iteration are printed if 'verbose=true'. If the iteration fails - after the maximum allowed number of loops ('iterations'), 'realMax' + real-valued differentiable function ‘f’ within an interval + [‘x1’,‘x2’] (on which the endpoint values of ‘f’ have opposite + signs), given its derivative ‘fprime’. Diagnostics for each + iteration are printed if ‘verbose=true’. If the iteration fails + after the maximum allowed number of loops (‘iterations’), ‘realMax’ is returned. -'real simpson(real f(real), real a, real b, real acc=realEpsilon, real dxmax=b-a)' - returns the integral of 'f' from 'a' to 'b' using adaptive Simpson +‘real simpson(real f(real), real a, real b, real acc=realEpsilon, real dxmax=b-a)’ + returns the integral of ‘f’ from ‘a’ to ‘b’ using adaptive Simpson integration. @@ -4030,69 +4034,69 @@ File: asymptote.info, Node: Arrays, Next: Casts, Prev: Functions, Up: Progra * Slices:: Python-style array slices -Appending '[]' to a built-in or user-defined type yields an array. The -array element 'i' of an array 'A' can be accessed as 'A[i]'. By +Appending ‘[]’ to a built-in or user-defined type yields an array. The +array element ‘i’ of an array ‘A’ can be accessed as ‘A[i]’. By default, attempts to access or assign to an array element using a negative index generates an error. Reading an array element with an index beyond the length of the array also generates an error; however, assignment to an element beyond the length of the array causes the array to be resized to accommodate the new element. One can also index an -array 'A' with an integer array 'B': the array 'A[B]' is formed by -indexing array 'A' with successive elements of array 'B'. A convenient +array ‘A’ with an integer array ‘B’: the array ‘A[B]’ is formed by +indexing array ‘A’ with successive elements of array ‘B’. A convenient Java-style shorthand exists for iterating over all elements of an array; see *note array iteration::. The declaration real[] A; -initializes 'A' to be an empty (zero-length) array. Empty arrays should +initializes ‘A’ to be an empty (zero-length) array. Empty arrays should be distinguished from null arrays. If we say real[] A=null; -then 'A' cannot be dereferenced at all (null arrays have no length and +then ‘A’ cannot be dereferenced at all (null arrays have no length and cannot be read from or assigned to). Arrays can be explicitly initialized like this: real[] A={0,1,2}; - Array assignment in 'Asymptote' does a shallow copy: only the pointer -is copied (if one copy if modified, the other will be too). The 'copy' + Array assignment in ‘Asymptote’ does a shallow copy: only the pointer +is copied (if one copy if modified, the other will be too). The ‘copy’ function listed below provides a deep copy of an array. - Every array 'A' of type 'T[]' has the virtual members - * 'int length', - * 'int cyclic', - * 'int[] keys', - * 'T push(T x)', - * 'void append(T[] a)', - * 'T pop()', - * 'void insert(int i ... T[] x)', - * 'void delete(int i, int j=i)', - * 'void delete()', and - * 'bool initialized(int n)'. - - The member 'A.length' evaluates to the length of the array. Setting -'A.cyclic=true' signifies that array indices should be reduced modulo + Every array ‘A’ of type ‘T[]’ has the virtual members + • ‘int length’, + • ‘bool cyclic’, + • ‘int[] keys’, + • ‘T push(T x)’, + • ‘void append(T[] a)’, + • ‘T pop()’, + • ‘void insert(int i ... T[] x)’, + • ‘void delete(int i, int j=i)’, + • ‘void delete()’, and + • ‘bool initialized(int n)’. + + The member ‘A.length’ evaluates to the length of the array. Setting +‘A.cyclic=true’ signifies that array indices should be reduced modulo the current array length. Reading from or writing to a nonempty cyclic array never leads to out-of-bounds errors or array resizing. - The member 'A.keys' evaluates to an array of integers containing the + The member ‘A.keys’ evaluates to an array of integers containing the indices of initialized entries in the array in ascending order. Hence, -for an array of length 'n' with all entries initialized, 'A.keys' -evaluates to '{0,1,...,n-1}'. A new keys array is produced each time -'A.keys' is evaluated. - - The functions 'A.push' and 'A.append' append their arguments onto the -end of the array, while 'A.insert(int i ... T[] x)' inserts 'x' into the -array at index 'i'. For convenience 'A.push' returns the pushed item. -The function 'A.pop()' pops and returns the last element, while -'A.delete(int i, int j=i)' deletes elements with indices in the range -['i','j'], shifting the position of all higher-indexed elements down. -If no arguments are given, 'A.delete()' provides a convenient way of -deleting all elements of 'A'. The routine 'A.initialized(int n)' can be -used to examine whether the element at index 'n' is initialized. Like -all 'Asymptote' functions, 'push', 'append', 'pop', 'insert', 'delete', -and 'initialized' can be "pulled off" of the array and used on their +for an array of length ‘n’ with all entries initialized, ‘A.keys’ +evaluates to ‘{0,1,...,n-1}’. A new keys array is produced each time +‘A.keys’ is evaluated. + + The functions ‘A.push’ and ‘A.append’ append their arguments onto the +end of the array, while ‘A.insert(int i ... T[] x)’ inserts ‘x’ into the +array at index ‘i’. For convenience ‘A.push’ returns the pushed item. +The function ‘A.pop()’ pops and returns the last element, while +‘A.delete(int i, int j=i)’ deletes elements with indices in the range +[‘i’,‘j’], shifting the position of all higher-indexed elements down. +If no arguments are given, ‘A.delete()’ provides a convenient way of +deleting all elements of ‘A’. The routine ‘A.initialized(int n)’ can be +used to examine whether the element at index ‘n’ is initialized. Like +all ‘Asymptote’ functions, ‘push’, ‘append’, ‘pop’, ‘insert’, ‘delete’, +and ‘initialized’ can be "pulled off" of the array and used on their own. For example, int[] A={1}; A.push(2); // A now contains {1,2}. @@ -4107,111 +4111,111 @@ A.insert(1,3); // A now contains {2,3}. A.insert(1 ... A); // A now contains {2,2,3,3} A.insert(2,4,5); // A now contains {2,2,4,5,3,3}. - The '[]' suffix can also appear after the variable name; this is + The ‘[]’ suffix can also appear after the variable name; this is sometimes convenient for declaring a list of variables and arrays of the same type: real a,A[]; -This declares 'a' to be 'real' and implicitly declares 'A' to be of type -'real[]'. +This declares ‘a’ to be ‘real’ and implicitly declares ‘A’ to be of type +‘real[]’. - In the following list of built-in array functions, 'T' represents a -generic type. Note that the internal functions 'alias', 'array', -'copy', 'concat', 'sequence', 'map', and 'transpose', which depend on -type 'T[]', are defined only after the first declaration of a variable -of type 'T[]'. + In the following list of built-in array functions, ‘T’ represents a +generic type. Note that the internal functions ‘alias’, ‘array’, +‘copy’, ‘concat’, ‘sequence’, ‘map’, and ‘transpose’, which depend on +type ‘T[]’, are defined only after the first declaration of a variable +of type ‘T[]’. -'new T[]' - returns a new empty array of type 'T[]'; +‘new T[]’ + returns a new empty array of type ‘T[]’; -'new T[] {list}' - returns a new array of type 'T[]' initialized with 'list' (a comma +‘new T[] {list}’ + returns a new array of type ‘T[]’ initialized with ‘list’ (a comma delimited list of elements); -'new T[n]' - returns a new array of 'n' elements of type 'T[]'. These 'n' array +‘new T[n]’ + returns a new array of ‘n’ elements of type ‘T[]’. These ‘n’ array elements are not initialized unless they are arrays themselves (in which case they are each initialized to empty arrays); -'T[] array(int n, T value, int depth=intMax)' - returns an array consisting of 'n' copies of 'value'. If 'value' - is itself an array, a deep copy of 'value' is made for each entry. - If 'depth' is specified, this deep copying only recurses to the +‘T[] array(int n, T value, int depth=intMax)’ + returns an array consisting of ‘n’ copies of ‘value’. If ‘value’ + is itself an array, a deep copy of ‘value’ is made for each entry. + If ‘depth’ is specified, this deep copying only recurses to the specified number of levels; -'int[] sequence(int n)' - if 'n >= 1' returns the array '{0,1,...,n-1}' (otherwise returns a +‘int[] sequence(int n)’ + if ‘n >= 1’ returns the array ‘{0,1,...,n-1}’ (otherwise returns a null array); -'int[] sequence(int n, int m)' - if 'm >= n' returns an array '{n,n+1,...,m}' (otherwise returns a +‘int[] sequence(int n, int m)’ + if ‘m >= n’ returns an array ‘{n,n+1,...,m}’ (otherwise returns a null array); -'int[] sequence(int n, int m, int skip)' - if 'm >= n' returns an array '{n,n+1,...,m}' skipping by 'skip' +‘int[] sequence(int n, int m, int skip)’ + if ‘m >= n’ returns an array ‘{n,n+1,...,m}’ skipping by ‘skip’ (otherwise returns a null array); -'T[] sequence(T f(int), int n)' - if 'n >= 1' returns the sequence '{f_i :i=0,1,...n-1}' given a - function 'T f(int)' and integer 'int n' (otherwise returns a null +‘T[] sequence(T f(int), int n)’ + if ‘n >= 1’ returns the sequence ‘{f_i :i=0,1,...n-1}’ given a + function ‘T f(int)’ and integer ‘int n’ (otherwise returns a null array); -'T[] map(T f(T), T[] a)' - returns the array obtained by applying the function 'f' to each - element of the array 'a'. This is equivalent to 'sequence(new - T(int i) {return f(a[i]);},a.length)'; +‘T[] map(T f(T), T[] a)’ + returns the array obtained by applying the function ‘f’ to each + element of the array ‘a’. This is equivalent to ‘sequence(new + T(int i) {return f(a[i]);},a.length)’; -'T2[] map(T2 f(T1), T1[] a)' - constructed by calling 'mapArray("T1","T2")', returns the array - obtained by applying the function 'f' to each element of the array - 'a'; +‘T2[] map(T2 f(T1), T1[] a)’ + constructed by running ‘from mapArray(Src=T1, Dst=T2) access map;’, + returns the array obtained by applying the function ‘f’ to each + element of the array ‘a’; -'int[] reverse(int n)' - if 'n >= 1' returns the array '{n-1,n-2,...,0}' (otherwise returns +‘int[] reverse(int n)’ + if ‘n >= 1’ returns the array ‘{n-1,n-2,...,0}’ (otherwise returns a null array); -'int[] complement(int[] a, int n)' - returns the complement of the integer array 'a' in - '{0,1,2,...,n-1}', so that 'b[complement(a,b.length)]' yields the - complement of 'b[a]'; +‘int[] complement(int[] a, int n)’ + returns the complement of the integer array ‘a’ in + ‘{0,1,2,...,n-1}’, so that ‘b[complement(a,b.length)]’ yields the + complement of ‘b[a]’; -'real[] uniform(real a, real b, int n)' - if 'n >= 1' returns a uniform partition of '[a,b]' into 'n' +‘real[] uniform(real a, real b, int n)’ + if ‘n >= 1’ returns a uniform partition of ‘[a,b]’ into ‘n’ subintervals (otherwise returns a null array); -'int find(bool[] a, int n=1)' - returns the index of the 'n'th 'true' value in the boolean array - 'a' or -1 if not found. If 'n' is negative, search backwards from - the end of the array for the '-n'th value; +‘int find(bool[] a, int n=1)’ + returns the index of the ‘n’th ‘true’ value in the boolean array + ‘a’ or -1 if not found. If ‘n’ is negative, search backwards from + the end of the array for the ‘-n’th value; -'int[] findall(bool[] a)' - returns the indices of all 'true' values in the boolean array 'a'; +‘int[] findall(bool[] a)’ + returns the indices of all ‘true’ values in the boolean array ‘a’; -'int search(T[] a, T key)' - For built-in ordered types 'T', searches a sorted array 'a' of 'n' - elements for k, returning the index 'i' if 'a[i] <= key < a[i+1]', - '-1' if 'key' is less than all elements of 'a', or 'n-1' if 'key' - is greater than or equal to the last element of 'a'; +‘int search(T[] a, T key)’ + For built-in ordered types ‘T’, searches a sorted array ‘a’ of ‘n’ + elements for k, returning the index ‘i’ if ‘a[i] <= key < a[i+1]’, + ‘-1’ if ‘key’ is less than all elements of ‘a’, or ‘n-1’ if ‘key’ + is greater than or equal to the last element of ‘a’; -'int search(T[] a, T key, bool less(T i, T j))' - searches an array 'a' sorted in ascending order such that element - 'i' precedes element 'j' if 'less(i,j)' is true; +‘int search(T[] a, T key, bool less(T i, T j))’ + searches an array ‘a’ sorted in ascending order such that element + ‘i’ precedes element ‘j’ if ‘less(i,j)’ is true; -'T[] copy(T[] a)' - returns a deep copy of the array 'a'; +‘T[] copy(T[] a)’ + returns a deep copy of the array ‘a’; -'T[] concat(... T[][] a)' +‘T[] concat(... T[][] a)’ returns a new array formed by concatenating the given one-dimensional arrays given as arguments; -'bool alias(T[] a, T[] b)' - returns 'true' if the arrays 'a' and 'b' are identical; +‘bool alias(T[] a, T[] b)’ + returns ‘true’ if the arrays ‘a’ and ‘b’ are identical; -'T[] sort(T[] a)' - For built-in ordered types 'T', returns a copy of 'a' sorted in +‘T[] sort(T[] a)’ + For built-in ordered types ‘T’, returns a copy of ‘a’ sorted in ascending order; -'T[][] sort(T[][] a)' - For built-in ordered types 'T', returns a copy of 'a' with the rows +‘T[][] sort(T[][] a)’ + For built-in ordered types ‘T’, returns a copy of ‘a’ with the rows sorted by the first column, breaking ties with successively higher columns. For example: string[][] a={{"bob","9"},{"alice","5"},{"pete","7"}, @@ -4225,53 +4229,53 @@ of type 'T[]'. bob 9 pete 7 -'T[] sort(T[] a, bool less(T i, T j), bool stable=true)' - returns a copy of 'a' sorted in ascending order such that element - 'i' precedes element 'j' if 'less(i,j)' is true, subject to (if - 'stable' is 'true') the stability constraint that the original - order of elements 'i' and 'j' is preserved if 'less(i,j)' and - 'less(j,i)' are both 'false'; +‘T[] sort(T[] a, bool less(T i, T j), bool stable=true)’ + returns a copy of ‘a’ sorted in ascending order such that element + ‘i’ precedes element ‘j’ if ‘less(i,j)’ is true, subject to (if + ‘stable’ is ‘true’) the stability constraint that the original + order of elements ‘i’ and ‘j’ is preserved if ‘less(i,j)’ and + ‘less(j,i)’ are both ‘false’; -'T[][] transpose(T[][] a)' - returns the transpose of 'a'; +‘T[][] transpose(T[][] a)’ + returns the transpose of ‘a’; -'T[][][] transpose(T[][][] a, int[] perm)' - returns the 3D transpose of 'a' obtained by applying the - permutation 'perm' of 'new int[]{0,1,2}' to the indices of each +‘T[][][] transpose(T[][][] a, int[] perm)’ + returns the 3D transpose of ‘a’ obtained by applying the + permutation ‘perm’ of ‘new int[]{0,1,2}’ to the indices of each entry; -'T sum(T[] a)' - for arithmetic types 'T', returns the sum of 'a'. In the case - where 'T' is 'bool', the number of true elements in 'a' is +‘T sum(T[] a)’ + for arithmetic types ‘T’, returns the sum of ‘a’. In the case + where ‘T’ is ‘bool’, the number of true elements in ‘a’ is returned; -'T min(T[] a)' -'T min(T[][] a)' -'T min(T[][][] a)' - for built-in ordered types 'T', returns the minimum element of 'a'; +‘T min(T[] a)’ +‘T min(T[][] a)’ +‘T min(T[][][] a)’ + for built-in ordered types ‘T’, returns the minimum element of ‘a’; -'T max(T[] a)' -'T max(T[][] a)' -'T max(T[][][] a)' - for built-in ordered types 'T', returns the maximum element of 'a'; +‘T max(T[] a)’ +‘T max(T[][] a)’ +‘T max(T[][][] a)’ + for built-in ordered types ‘T’, returns the maximum element of ‘a’; -'T[] min(T[] a, T[] b)' - for built-in ordered types 'T', and arrays 'a' and 'b' of the same +‘T[] min(T[] a, T[] b)’ + for built-in ordered types ‘T’, and arrays ‘a’ and ‘b’ of the same length, returns an array composed of the minimum of the - corresponding elements of 'a' and 'b'; + corresponding elements of ‘a’ and ‘b’; -'T[] max(T[] a, T[] b)' - for built-in ordered types 'T', and arrays 'a' and 'b' of the same +‘T[] max(T[] a, T[] b)’ + for built-in ordered types ‘T’, and arrays ‘a’ and ‘b’ of the same length, returns an array composed of the maximum of the - corresponding elements of 'a' and 'b'; + corresponding elements of ‘a’ and ‘b’; -'pair[] pairs(real[] x, real[] y);' - for arrays 'x' and 'y' of the same length, returns the pair array - 'sequence(new pair(int i) {return (x[i],y[i]);},x.length)'; +‘pair[] pairs(real[] x, real[] y);’ + for arrays ‘x’ and ‘y’ of the same length, returns the pair array + ‘sequence(new pair(int i) {return (x[i],y[i]);},x.length)’; -'pair[] fft(pair[] a, int sign=1)' - returns the unnormalized Fast Fourier Transform of 'a' (if the - optional 'FFTW' package is installed), using the given 'sign'. +‘pair[] fft(pair[] a, int sign=1)’ + returns the unnormalized Fast Fourier Transform of ‘a’ (if the + optional ‘FFTW’ package is installed), using the given ‘sign’. Here is a simple example: int n=4; pair[] f=sequence(n); @@ -4283,45 +4287,45 @@ of type 'T[]'. write(); write(f/n); -'pair[][] fft(pair[][] a, int sign=1)' - returns the unnormalized two-dimensional Fourier transform of 'a' - using the given 'sign'; +‘pair[][] fft(pair[][] a, int sign=1)’ + returns the unnormalized two-dimensional Fourier transform of ‘a’ + using the given ‘sign’; -'pair[][][] fft(pair[][][] a, int sign=1)' - returns the unnormalized three-dimensional Fourier transform of 'a' - using the given 'sign'; +‘pair[][][] fft(pair[][][] a, int sign=1)’ + returns the unnormalized three-dimensional Fourier transform of ‘a’ + using the given ‘sign’; -'realschur schur(real[][] a)' - returns a struct 'realschur' containing a unitary matrix 'U' and a - quasitriangular matrix 'T' such that 'a=U*T*transpose(U)'; +‘realschur schur(real[][] a)’ + returns a struct ‘realschur’ containing a unitary matrix ‘U’ and a + quasitriangular matrix ‘T’ such that ‘a=U*T*transpose(U)’; -'schur schur(pair[][] a)' - returns a struct 'schur' containing a unitary matrix 'U' and a - triangular matrix 'T' such that 'a=U*T*conj(transpose(U))'; +‘schur schur(pair[][] a)’ + returns a struct ‘schur’ containing a unitary matrix ‘U’ and a + triangular matrix ‘T’ such that ‘a=U*T*conj(transpose(U))’; -'real dot(real[] a, real[] b)' - returns the dot product of the vectors 'a' and 'b'; +‘real dot(real[] a, real[] b)’ + returns the dot product of the vectors ‘a’ and ‘b’; -'pair dot(pair[] a, pair[] b)' - returns the complex dot product 'sum(a*conj(b))' of the vectors 'a' - and 'b'; +‘pair dot(pair[] a, pair[] b)’ + returns the complex dot product ‘sum(a*conj(b))’ of the vectors ‘a’ + and ‘b’; -'real[] tridiagonal(real[] a, real[] b, real[] c, real[] f);' - Solve the periodic tridiagonal problem L'x'='f' and return the - solution 'x', where 'f' is an n vector and L is the n \times n +‘real[] tridiagonal(real[] a, real[] b, real[] c, real[] f);’ + Solve the periodic tridiagonal problem L‘x’=‘f’ and return the + solution ‘x’, where ‘f’ is an n vector and L is the n \times n matrix [ b[0] c[0] a[0] ] [ a[1] b[1] c[1] ] [ a[2] b[2] c[2] ] [ ... ] [ c[n-1] a[n-1] b[n-1] ] - For Dirichlet boundary conditions (denoted here by 'u[-1]' and - 'u[n]'), replace 'f[0]' by 'f[0]-a[0]u[-1]' and - 'f[n-1]-c[n-1]u[n]'; then set 'a[0]=c[n-1]=0'; + For Dirichlet boundary conditions (denoted here by ‘u[-1]’ and + ‘u[n]’), replace ‘f[0]’ by ‘f[0]-a[0]u[-1]’ and + ‘f[n-1]-c[n-1]u[n]’; then set ‘a[0]=c[n-1]=0’; -'real[] solve(real[][] a, real[] b, bool warn=true)' - Solve the linear equation 'a'x='b' by LU decomposition and return - the solution x, where 'a' is an n \times n matrix and 'b' is an +‘real[] solve(real[][] a, real[] b, bool warn=true)’ + Solve the linear equation ‘a’x=‘b’ by LU decomposition and return + the solution x, where ‘a’ is an n \times n matrix and ‘b’ is an array of length n. For example: import math; real[][] a={{1,-2,3,0},{4,-5,6,2},{-7,-8,10,5},{1,50,1,-2}}; @@ -4331,83 +4335,83 @@ of type 'T[]'. write(b); write(); write(x); write(); write(a*x); - If 'a' is a singular matrix and 'warn' is 'false', return an empty - array. If the matrix 'a' is tridiagonal, the routine 'tridiagonal' + If ‘a’ is a singular matrix and ‘warn’ is ‘false’, return an empty + array. If the matrix ‘a’ is tridiagonal, the routine ‘tridiagonal’ provides a more efficient algorithm (*note tridiagonal::); -'real[][] solve(real[][] a, real[][] b, bool warn=true)' - Solve the linear equation 'a'x='b' and return the solution x, where - 'a' is an n \times n matrix and 'b' is an n \times m matrix. If - 'a' is a singular matrix and 'warn' is 'false', return an empty +‘real[][] solve(real[][] a, real[][] b, bool warn=true)’ + Solve the linear equation ‘a’x=‘b’ and return the solution x, where + ‘a’ is an n \times n matrix and ‘b’ is an n \times m matrix. If + ‘a’ is a singular matrix and ‘warn’ is ‘false’, return an empty matrix; -'real[][] identity(int n);' +‘real[][] identity(int n);’ returns the n \times n identity matrix; -'real[][] diagonal(... real[] a)' +‘real[][] diagonal(... real[] a)’ returns the diagonal matrix with diagonal entries given by a; -'real[][] inverse(real[][] a)' - returns the inverse of a square matrix 'a'; +‘real[][] inverse(real[][] a)’ + returns the inverse of a square matrix ‘a’; -'real[] quadraticroots(real a, real b, real c);' +‘real[] quadraticroots(real a, real b, real c);’ This numerically robust solver returns the real roots of the quadratic equation ax^2+bx+c=0, in ascending order. Multiple roots are listed separately; -'pair[] quadraticroots(explicit pair a, explicit pair b, explicit pair c);' +‘pair[] quadraticroots(explicit pair a, explicit pair b, explicit pair c);’ This numerically robust solver returns the complex roots of the quadratic equation ax^2+bx+c=0; -'real[] cubicroots(real a, real b, real c, real d);' +‘real[] cubicroots(real a, real b, real c, real d);’ This numerically robust solver returns the real roots of the cubic equation ax^3+bx^2+cx+d=0. Multiple roots are listed separately. - 'Asymptote' includes a full set of vectorized array instructions for + ‘Asymptote’ includes a full set of vectorized array instructions for arithmetic (including self) and logical operations. These element-by-element instructions are implemented in C++ code for speed. Given real[] a={1,2}; real[] b={3,2}; -then 'a == b' and 'a >= 2' both evaluate to the vector '{false, true}'. -To test whether all components of 'a' and 'b' agree, use the boolean -function 'all(a == b)'. One can also use conditionals like '(a >= 2) ? -a : b', which returns the array '{3,2}', or 'write((a >= 2) ? a : null', -which returns the array '{2}'. +then ‘a == b’ and ‘a >= 2’ both evaluate to the vector ‘{false, true}’. +To test whether all components of ‘a’ and ‘b’ agree, use the boolean +function ‘all(a == b)’. One can also use conditionals like ‘(a >= 2) ? +a : b’, which returns the array ‘{3,2}’, or ‘write((a >= 2) ? a : null’, +which returns the array ‘{2}’. - All of the standard built-in 'libm' functions of signature -'real(real)' also take a real array as an argument, effectively like an -implicit call to 'map'. + All of the standard built-in ‘libm’ functions of signature +‘real(real)’ also take a real array as an argument, effectively like an +implicit call to ‘map’. As with other built-in types, arrays of the basic data types can be read in by assignment. In this example, the code file fin=input("test.txt"); real[] A=fin; -reads real values into 'A' until the end-of-file is reached (or an I/O +reads real values into ‘A’ until the end-of-file is reached (or an I/O error occurs). - The virtual members 'dimension', 'line', 'csv', 'word', and 'read' of + The virtual members ‘dimension’, ‘line’, ‘csv’, ‘word’, and ‘read’ of a file are useful for reading arrays. For example, if line mode is set -with 'file line(bool b=true)', then reading will stop once the end of +with ‘file line(bool b=true)’, then reading will stop once the end of the line is reached instead: file fin=input("test.txt"); real[] A=fin.line(); Since string reads by default read up to the end of line anyway, line mode normally has no effect on string array reads. However, there is a -white-space delimiter mode for reading strings, 'file word(bool -b=true)', which causes string reads to respect white-space delimiters, +white-space delimiter mode for reading strings, ‘file word(bool +b=true)’, which causes string reads to respect white-space delimiters, instead of the default end-of-line delimiter: file fin=input("test.txt").line().word(); real[] A=fin; - Another useful mode is comma-separated-value mode, 'file csv(bool -b=true)', which causes reads to respect comma delimiters: + Another useful mode is comma-separated-value mode, ‘file csv(bool +b=true)’, which causes reads to respect comma delimiters: file fin=input("test.txt").csv(); real[] A=fin; - To restrict the number of values read, use the 'file dimension(int)' + To restrict the number of values read, use the ‘file dimension(int)’ function: file fin=input("test.txt"); real[] A=fin.dimension(10); @@ -4426,16 +4430,16 @@ real[][][] B=fin.dimension(2,3,4); Sometimes the array dimensions are stored with the data as integer fields at the beginning of an array. Such 1, 2, or 3 dimensional arrays -can be read in with the virtual member functions 'read(1)', 'read(2)', -or 'read(3)', respectively: +can be read in with the virtual member functions ‘read(1)’, ‘read(2)’, +or ‘read(3)’, respectively: file fin=input("test.txt"); real[] A=fin.read(1); real[][] B=fin.read(2); real[][][] C=fin.read(3); One, two, and three-dimensional arrays of the basic data types can be -output with the functions 'write(file,T[])', 'write(file,T[][])', -'write(file,T[][][])', respectively. +output with the functions ‘write(file,T[])’, ‘write(file,T[][])’, +‘write(file,T[][][])’, respectively. File: asymptote.info, Node: Slices, Prev: Arrays, Up: Arrays @@ -4444,14 +4448,14 @@ File: asymptote.info, Node: Slices, Prev: Arrays, Up: Arrays ------------- Asymptote allows a section of an array to be addressed as a slice using -a Python-like syntax. If 'A' is an array, the expression 'A[m:n]' -returns a new array consisting of the elements of 'A' with indices from -'m' up to but not including 'n'. For example, +a Python-like syntax. If ‘A’ is an array, the expression ‘A[m:n]’ +returns a new array consisting of the elements of ‘A’ with indices from +‘m’ up to but not including ‘n’. For example, int[] x={0,1,2,3,4,5,6,7,8,9}; int[] y=x[2:6]; // y={2,3,4,5}; int[] z=x[5:10]; // z={5,6,7,8,9}; - If the left index is omitted, it is taken be '0'. If the right index + If the left index is omitted, it is taken be ‘0’. If the right index is omitted it is taken to be the length of the array. If both are omitted, the slice then goes from the start of the array to the end, producing a non-cyclic deep copy of the array. For example: @@ -4464,8 +4468,8 @@ int[] w=x[:]; // w={0,1,2,3,4,5,6,7,8,9}, distinct from array x. either of the indices. If the indices exceed the length of the array, however, they are politely truncated to that length. - For cyclic arrays, the slice 'A[m:n]' still consists of the cells -with indices in the set ['m','n'), but now negative values and values + For cyclic arrays, the slice ‘A[m:n]’ still consists of the cells +with indices in the set [‘m’,‘n’), but now negative values and values beyond the length of the array are allowed. The indices simply wrap around. For example: @@ -4497,26 +4501,26 @@ toppings[0:3]=new string[] {"tomato"}; // Now toppings={"tomato", "bacon", "lettuce"} If an array is assigned to a slice of itself, a copy of the original -array is assigned to the slice. That is, code such as 'x[m:n]=x' is -equivalent to 'x[m:n]=copy(x)'. One can use the shorthand 'x[m:m]=y' to -insert the contents of the array 'y' into the array 'x' starting at the -location just before 'x[m]'. +array is assigned to the slice. That is, code such as ‘x[m:n]=x’ is +equivalent to ‘x[m:n]=copy(x)’. One can use the shorthand ‘x[m:m]=y’ to +insert the contents of the array ‘y’ into the array ‘x’ starting at the +location just before ‘x[m]’. For a cyclic array, a slice is bridging if it addresses cells up to the end of the array and then continues on to address cells at the start -of the array. For instance, if 'A' is a cyclic array of length 10, -'A[8:12]', 'A[-3:1]', and 'A[5:25]' are bridging slices whereas -'A[3:7]', 'A[7:10]', 'A[-3:0]' and 'A[103:107]' are not. Bridging +of the array. For instance, if ‘A’ is a cyclic array of length 10, +‘A[8:12]’, ‘A[-3:1]’, and ‘A[5:25]’ are bridging slices whereas +‘A[3:7]’, ‘A[7:10]’, ‘A[-3:0]’ and ‘A[103:107]’ are not. Bridging slices can only be assigned to if the number of elements in the slice is exactly equal to the number of elements we are assigning to it. Otherwise, there is no clear way to decide which of the new entries -should be 'A[0]' and an error is reported. Non-bridging slices may be +should be ‘A[0]’ and an error is reported. Non-bridging slices may be assigned an array of any length. - For a cyclic array 'A' an expression of the form -'A[A.length:A.length]' is equivalent to the expression 'A[0:0]' and so + For a cyclic array ‘A’ an expression of the form +‘A[A.length:A.length]’ is equivalent to the expression ‘A[0:0]’ and so assigning to this slice will insert values at the start of the array. -'A.append()' can be used to insert values at the end of the array. +‘A.append()’ can be used to insert values at the end of the array. It is illegal to assign to a slice of a cyclic array that repeats any of the cells. @@ -4527,14 +4531,14 @@ File: asymptote.info, Node: Casts, Next: Import, Prev: Arrays, Up: Programmi 6.13 Casts ========== -'Asymptote' implicitly casts 'int' to 'real', 'int' to 'pair', 'real' to -'pair', 'pair' to 'path', 'pair' to 'guide', 'path' to 'guide', 'guide' -to 'path', 'real' to 'pen', 'pair[]' to 'guide[]', 'pair[]' to 'path[]', -'path' to 'path[]', and 'guide' to 'path[]', along with various -three-dimensional casts defined in module 'three'. Implicit casts are +‘Asymptote’ implicitly casts ‘int’ to ‘real’, ‘int’ to ‘pair’, ‘real’ to +‘pair’, ‘pair’ to ‘path’, ‘pair’ to ‘guide’, ‘path’ to ‘guide’, ‘guide’ +to ‘path’, ‘real’ to ‘pen’, ‘pair[]’ to ‘guide[]’, ‘pair[]’ to ‘path[]’, +‘path’ to ‘path[]’, and ‘guide’ to ‘path[]’, along with various +three-dimensional casts defined in module ‘three’. Implicit casts are automatically attempted on assignment and when trying to match function calls with possible function signatures. Implicit casting can be -inhibited by declaring individual arguments 'explicit' in the function +inhibited by declaring individual arguments ‘explicit’ in the function signature, say to avoid an ambiguous function call in the following example, which outputs 0: int f(pair a) {return 0;} @@ -4542,7 +4546,7 @@ int f(explicit real x) {return 1;} write(f(0)); - Other conversions, say 'real' to 'int' or 'real' to 'string', require + Other conversions, say ‘real’ to ‘int’ or ‘real’ to ‘string’, require an explicit cast: int i=(int) 2.5; string s=(string) 2.5; @@ -4550,16 +4554,16 @@ string s=(string) 2.5; real[] a={2.5,-3.5}; int[] b=(int []) a; write(stdout,b); // Outputs 2,-3 - In situations where casting from a string to a type 'T' fails, an + In situations where casting from a string to a type ‘T’ fails, an uninitialized variable is returned; this condition can be detected with -the function 'bool initialized(T);' +the function ‘bool initialized(T);’ int i=(int) "2.5"; assert(initialized(i),"Invalid cast."); real x=(real) "2.5a"; assert(initialized(x),"Invalid cast."); - Casting to user-defined types is also possible using 'operator cast': + Casting to user-defined types is also possible using ‘operator cast’: struct rpair { real radius; real angle; @@ -4580,13 +4584,13 @@ some code one wants all integers to represent multiples of 100. To convert them to reals, one would first want to multiply them by 100. However, the straightforward implementation real operator cast(int x) {return x*100;} -is equivalent to an infinite recursion, since the result 'x*100' needs +is equivalent to an infinite recursion, since the result ‘x*100’ needs itself to be cast from an integer to a real. Instead, we want to use the standard conversion of int to real: real convert(int x) {return x*100;} real operator cast(int x)=convert; - Explicit casts are implemented similarly, with 'operator ecast'. + Explicit casts are implemented similarly, with ‘operator ecast’. File: asymptote.info, Node: Import, Next: Static, Prev: Casts, Up: Programming @@ -4594,21 +4598,21 @@ File: asymptote.info, Node: Import, Next: Static, Prev: Casts, Up: Programmi 6.14 Import =========== -While 'Asymptote' provides many features by default, some applications -require specialized features contained in external 'Asymptote' modules. +While ‘Asymptote’ provides many features by default, some applications +require specialized features contained in external ‘Asymptote’ modules. For instance, the lines access graph; graph.axes(); draw x and y axes on a two-dimensional graph. Here, the command looks -up the module under the name 'graph' in a global dictionary of modules -and puts it in a new variable named 'graph'. The module is a structure, +up the module under the name ‘graph’ in a global dictionary of modules +and puts it in a new variable named ‘graph’. The module is a structure, and we can refer to its fields as we usually would with a structure. Often, one wants to use module functions without having to specify the module name. The code from graph access axes; -adds the 'axes' field of 'graph' into the local name space, so that -subsequently, one can just write 'axes()'. If the given name is +adds the ‘axes’ field of ‘graph’ into the local name space, so that +subsequently, one can just write ‘axes()’. If the given name is overloaded, all types and variables of that name are added. To add more than one name, just use a comma-separated list: from graph access axes, xaxis, yaxis; @@ -4618,7 +4622,7 @@ of a module to the local name space: from graph access *; Similarly, one can add the non-private fields and types of a -structure to the local environment with the 'unravel' keyword: +structure to the local environment with the ‘unravel’ keyword: struct matrix { real a,b,c,d; } @@ -4638,8 +4642,8 @@ import graph; is a convenient abbreviation for the commands access graph; unravel graph; - That is, 'import graph' first loads a module into a structure called -'graph' and then adds its non-private fields and types to the local + That is, ‘import graph’ first loads a module into a structure called +‘graph’ and then adds its non-private fields and types to the local environment. This way, if a member variable (or function) is overwritten with a local variable (or function of the same signature), the original one can still be accessed by qualifying it with the module @@ -4648,15 +4652,15 @@ name. Wild card importing will work fine in most cases, but one does not usually know all of the internal types and variables of a module, which can also change as the module writer adds or changes features of the -module. As such, it is prudent to add 'import' commands at the start of -an 'Asymptote' file, so that imported names won't shadow locally defined +module. As such, it is prudent to add ‘import’ commands at the start of +an ‘Asymptote’ file, so that imported names won’t shadow locally defined functions. Still, imported names may shadow other imported names, depending on the order in which they were imported, and imported functions may cause overloading resolution problems if they have the same name as local functions defined later. To rename modules or fields when adding them to the local -environment, use 'as': +environment, use ‘as’: access graph as graph2d; from graph access xaxis as xline, yaxis as yline; @@ -4666,9 +4670,9 @@ import graph as graph2d; access graph as graph2d; unravel graph2d; - Except for a few built-in modules, such as 'settings', all modules -are implemented as 'Asymptote' files. When looking up a module that has -not yet been loaded, 'Asymptote' searches the standard search paths + Except for a few built-in modules, such as ‘settings’, all modules +are implemented as ‘Asymptote’ files. When looking up a module that has +not yet been loaded, ‘Asymptote’ searches the standard search paths (*note Search paths::) for the matching file. The file corresponding to that name is read and the code within it is interpreted as the body of a structure defining the module. @@ -4676,64 +4680,110 @@ structure defining the module. If the file name contains nonalphanumeric characters, enclose it with quotation marks: -'access "/usr/local/share/asymptote/graph.asy" as graph;' +‘access "/usr/local/share/asymptote/graph.asy" as graph;’ -'from "/usr/local/share/asymptote/graph.asy" access axes;' +‘from "/usr/local/share/asymptote/graph.asy" access axes;’ -'import "/usr/local/share/asymptote/graph.asy" as graph;' +‘import "/usr/local/share/asymptote/graph.asy" as graph;’ - If 'Asymptote' is compiled with support for 'libcurl', the file name -can even be a URL: 'import + If ‘Asymptote’ is compiled with support for ‘libcurl’, the file name +can even be a URL: ‘import "https://raw.githubusercontent.com/vectorgraphics/asymptote/HEAD/doc/axis3.asy" -as axis3;' +as axis3;’ It is an error if modules import themselves (or each other in a cycle). The module name to be imported must be known at compile time. - However, you can import an 'Asymptote' module determined by the -string 's' at runtime like this: + However, you can import an ‘Asymptote’ module determined by the +string ‘s’ at runtime like this: eval("import "+s,true); To conditionally execute an array of asy files, use void asy(string format, bool overwrite ... string[] s); - The file will only be processed, using output format 'format', if -overwrite is 'true' or the output file is missing. + The file will only be processed, using output format ‘format’, if +overwrite is ‘true’ or the output file is missing. - One can evaluate an 'Asymptote' expression (without any return value, -however) contained in the string 's' with: + One can evaluate an ‘Asymptote’ expression (without any return value, +however) contained in the string ‘s’ with: void eval(string s, bool embedded=false); - It is not necessary to terminate the string 's' with a semicolon. If -'embedded' is 'true', the string will be evaluated at the top level of -the current environment. If 'embedded' is 'false' (the default), the + It is not necessary to terminate the string ‘s’ with a semicolon. If +‘embedded’ is ‘true’, the string will be evaluated at the top level of +the current environment. If ‘embedded’ is ‘false’ (the default), the string will be evaluated in an independent environment, sharing the same -'settings' module (*note settings::). +‘settings’ module (*note settings::). - One can evaluate arbitrary 'Asymptote' code (which may contain + One can evaluate arbitrary ‘Asymptote’ code (which may contain unescaped quotation marks) with the command void eval(code s, bool embedded=false); - Here 'code' is a special type used with 'quote {}' to enclose -'Asymptote code' like this: + Here ‘code’ is a special type used with ‘quote {}’ to enclose +‘Asymptote code’ like this: real a=1; code s=quote { write(a); }; eval(s,true); // Outputs 1 - One application of 'eval' is the creation of parametrized Asymptote -code, such as a map from one type to another (*note map::). - - To include the contents of an existing file 'graph' verbatim (as if + To include the contents of an existing file ‘graph’ verbatim (as if the contents of the file were inserted at that point), use one of the forms: include graph; -'include "/usr/local/share/asymptote/graph.asy";' +‘include "/usr/local/share/asymptote/graph.asy";’ To list all global functions and variables defined in a module named -by the contents of the string 's', use the function +by the contents of the string ‘s’, use the function void list(string s, bool imports=false); -Imported global functions and variables are also listed if 'imports' is -'true'. +Imported global functions and variables are also listed if ‘imports’ is +‘true’. + +* Menu: + +* Templated imports:: + + +File: asymptote.info, Node: Templated imports, Up: Import + +6.14.1 Templated imports +------------------------ + +*Warning:* This feature is experimental: it has known issues and its +behavior may change in the future. + + In Asymptote, it is possible to create modules that must have one or +more types specified when they are imported. The first executable line +of any such module must be of the form ‘typedef import(<types>)’, where +‘<types>’ is a list of required type parameters. For instance, +typedef import(T, S, Number); +could be the first line of a module that requires three type parameters. +The remaining code in the module can then use ‘T’, ‘S’, and ‘Number’ as +types. + + To import such a module, one must specify the types to be used. For +instance, if the module above were named ‘templatedModule’, it could be +accessed for types ‘string’, ‘int[]’, and ‘real’ with the import command +access templatedModule(T=string, S=int[], Number=real) + as templatedModule_string_int_real; +Note that this is actually an _access_ command rather than an _import_ +command, so the names of types, functions, etc. would have to be stated +as e.g. ‘templatedModule_string_int_real.Wrapper_Number’ rather than +just ‘Wrapper_Number’ (where ‘Wrapper_Number’ is a type defined in +‘templatedModule.asy’). + + Alternatively, the module could be imported via a command like +from templatedModule(T=string, S=int[], Number=real) access + Wrapper_Number as Wrapper_real, + operator ==; +This command would automatically rename ‘Wrapper_Number’ to +‘Wrapper_real’ and would also allow the use of any ‘operator ==’ +overloads defined in the module. + + For more information, see the examples in +<https://github.com/vectorgraphics/asymptote/tree/647b6c5732ec94a48f0f0b2446f02c86888fe7e7/tests/template>. + + Issues: Certain standard features of almost any type (such as ‘==’, +‘new’, and the ability to call static methods on the type) may only be +available for type arguments that are builtin or defined in the ‘plain’ +module. File: asymptote.info, Node: Static, Prev: Import, Up: Programming @@ -4754,8 +4804,8 @@ struct s { } } -there is one instance of the variable 'c' for each object 's' (as -opposed to each call of 'count'). +there is one instance of the variable ‘c’ for each object ‘s’ (as +opposed to each call of ‘count’). Similarly, in int factorial(int n) { @@ -4767,8 +4817,8 @@ int factorial(int n) { return helper(n); } -there is one instance of 'x' for every call to 'factorial' (and not for -every call to 'helper'), so this is a correct, but ugly, implementation +there is one instance of ‘x’ for every call to ‘factorial’ (and not for +every call to ‘helper’), so this is a correct, but ugly, implementation of factorial. Similarly, a static variable declared within a structure is allocated @@ -4779,7 +4829,7 @@ struct A { } } -creates one object 'z' for each object of type 'A' created. +creates one object ‘z’ for each object of type ‘A’ created. In this example, int pow(int n, int k) { @@ -4796,7 +4846,7 @@ int pow(int n, int k) { return A.x; } -there is one instance of 'x' for each call to 'pow', so this is an ugly +there is one instance of ‘x’ for each call to ‘pow’, so this is an ugly implementation of exponentiation. Loop constructs allocate a new frame in every iteration. This is so @@ -4811,8 +4861,8 @@ for(int i=0; i < 10; ++i) { } f(); - Here, every iteration of the loop has its own variable 'x', so 'f()' -will write '5'. If a variable in a loop is declared static, it will be + Here, every iteration of the loop has its own variable ‘x’, so ‘f()’ +will write ‘5’. If a variable in a loop is declared static, it will be allocated where the enclosing function or structure was defined (just as if it were declared static outside of the loop). For instance, in: void f() { @@ -4821,8 +4871,8 @@ void f() { static int y; } } -both 'x' and 'y' will be allocated in the same place, which is also -where 'f' is allocated. +both ‘x’ and ‘y’ will be allocated in the same place, which is also +where ‘f’ is allocated. Statements may also be declared static, in which case they are run at the place where the enclosing function or structure is defined. @@ -4840,7 +4890,7 @@ struct A { pair A; int y=A.x; -does the 'A' in 'A.x' refer to the structure or to the pair variable. +does the ‘A’ in ‘A.x’ refer to the structure or to the pair variable. It is the convention in Asymptote that, if there is a non-function variable with the same name as the qualifier, the qualifier refers to that variable, and not to the type. This is regardless of what fields @@ -4849,21 +4899,21 @@ the variable actually possesses. File: asymptote.info, Node: LaTeX usage, Next: Base modules, Prev: Programming, Up: Top -7 'LaTeX' usage +7 ‘LaTeX’ usage *************** -'Asymptote' comes with a convenient 'LaTeX' style file 'asymptote.sty' -(v1.36 or later required) that makes 'LaTeX' 'Asymptote'-aware. -Entering 'Asymptote' code directly into the 'LaTeX' source file, at the +‘Asymptote’ comes with a convenient ‘LaTeX’ style file ‘asymptote.sty’ +(v1.36 or later required) that makes ‘LaTeX’ ‘Asymptote’-aware. +Entering ‘Asymptote’ code directly into the ‘LaTeX’ source file, at the point where it is needed, keeps figures organized and avoids the need to invent new file names for each figure. Simply add the line -'\usepackage{asymptote}' at the beginning of your file and enclose your -'Asymptote' code within a '\begin{asy}...\end{asy}' environment. As -with the 'LaTeX' 'comment' environment, the '\end{asy}' command must +‘\usepackage{asymptote}’ at the beginning of your file and enclose your +‘Asymptote’ code within a ‘\begin{asy}...\end{asy}’ environment. As +with the ‘LaTeX’ ‘comment’ environment, the ‘\end{asy}’ command must appear on a line by itself, with no trailing commands/comments. A blank -line is not allowed after '\begin{asy}'. +line is not allowed after ‘\begin{asy}’. - The sample 'LaTeX' file below, named 'latexusage.tex', can be run as + The sample ‘LaTeX’ file below, named ‘latexusage.tex’, can be run as follows: latex latexusage asy latexusage-*.asy @@ -4873,50 +4923,47 @@ or pdflatex latexusage asy latexusage-*.asy pdflatex latexusage -To switch between using inline Asymptote code with 'latex' and -'pdflatex' you may first need to remove the files 'latexusage-*.tex'. +To switch between using inline Asymptote code with ‘latex’ and +‘pdflatex’ you may first need to remove the files ‘latexusage-*.tex’. - An even better method for processing a 'LaTeX' file with embedded -'Asymptote' code is to use the 'latexmk' utility from + An even better method for processing a ‘LaTeX’ file with embedded +‘Asymptote’ code is to use the ‘latexmk’ utility from <http://mirror.ctan.org/support/latexmk/> after putting the contents of <https://raw.githubusercontent.com/vectorgraphics/asymptote/HEAD/doc/latexmkrc> -in a file 'latexmkrc' in the same directory. The command +in a file ‘latexmkrc’ in the same directory. The command latexmk -pdf latexusage -will then call 'Asymptote' automatically, recompiling only the figures +will then call ‘Asymptote’ automatically, recompiling only the figures that have changed. Since each figure is compiled in a separate system process, this method also tends to use less memory. To store the -figures in a separate directory named 'asy', one can define +figures in a separate directory named ‘asy’, one can define \def\asydir{asy} - in 'latexusage.tex' and put the contents of -<https://raw.githubusercontent.com/vectorgraphics/asymptote/HEAD/doc/latexmkrc_asydir> -in a file 'latexmkrc' in the same directory. External 'Asymptote' code -can be included with + in ‘latexusage.tex’. External ‘Asymptote’ code can be included with \asyinclude[<options>]{<filename.asy>} -so that 'latexmk' will recognize when the code is changed. Note that -'latexmk' requires 'perl', available from <https://www.perl.org/>. +so that ‘latexmk’ will recognize when the code is changed. Note that +‘latexmk’ requires ‘perl’, available from <https://www.perl.org/>. - One can specify 'width', 'height', 'keepAspect', 'viewportwidth', -'viewportheight', 'attach', and 'inline'. 'keyval'-style options to the -'asy' and 'asyinclude' environments. Three-dimensional PRC files may + One can specify ‘width’, ‘height’, ‘keepAspect’, ‘viewportwidth’, +‘viewportheight’, ‘attach’, and ‘inline’. ‘keyval’-style options to the +‘asy’ and ‘asyinclude’ environments. Three-dimensional PRC files may either be embedded within the page (the default) or attached as -annotated (but printable) attachments, using the 'attach' option and the -'attachfile2' (or older 'attachfile') 'LaTeX' package. The 'inline' -option generates inline 'LaTeX' code instead of EPS or PDF files. This -makes 2D LaTeX symbols visible to the '\begin{asy}...\end{asy}' +annotated (but printable) attachments, using the ‘attach’ option and the +‘attachfile2’ (or older ‘attachfile’) ‘LaTeX’ package. The ‘inline’ +option generates inline ‘LaTeX’ code instead of EPS or PDF files. This +makes 2D LaTeX symbols visible to the ‘\begin{asy}...\end{asy}’ environment. In this mode, Asymptote correctly aligns 2D LaTeX symbols -defined outside of '\begin{asy}...\end{asy}', but treats their size as -zero; an optional second string can be given to 'Label' to provide an +defined outside of ‘\begin{asy}...\end{asy}’, but treats their size as +zero; an optional second string can be given to ‘Label’ to provide an estimate of the unknown label size. - Note that if the 'latex' TeX engine is used with the 'inline' option, + Note that if the ‘latex’ TeX engine is used with the ‘inline’ option, labels might not show up in DVI viewers that cannot handle raw -'PostScript' code. One can use 'dvips'/'dvipdf' to produce -'PostScript'/PDF output (we recommend using the modified version of -'dvipdf' in the 'Asymptote' patches directory, which accepts the 'dvips --z' hyperdvi option). +‘PostScript’ code. One can use ‘dvips’/‘dvipdf’ to produce +‘PostScript’/PDF output (we recommend using the modified version of +‘dvipdf’ in the ‘Asymptote’ patches directory, which accepts the ‘dvips +-z’ hyperdvi option). - Here now is 'latexusage.tex': + Here now is ‘latexusage.tex’: \documentclass[12pt]{article} % Use this form to include EPS (latex) or PDF (pdflatex) files: @@ -5045,13 +5092,13 @@ File: asymptote.info, Node: Base modules, Next: Options, Prev: LaTeX usage, 8 Base modules ************** -'Asymptote' currently ships with the following base modules: +‘Asymptote’ currently ships with the following base modules: * Menu: -* plain:: Default 'Asymptote' base file +* plain:: Default ‘Asymptote’ base file * simplex:: Linear programming: simplex method -* math:: Extend 'Asymptote''s math capabilities +* math:: Extend ‘Asymptote’’s math capabilities * interpolate:: Interpolation routines * geometry:: Geometry routines * trembling:: Wavy lines @@ -5067,9 +5114,9 @@ File: asymptote.info, Node: Base modules, Next: Options, Prev: LaTeX usage, * roundedpath:: Round the sharp corners of paths * animation:: Embedded PDF and MPEG movies * embed:: Embedding movies, sounds, and 3D objects -* slide:: Making presentations with 'Asymptote' -* MetaPost:: 'MetaPost' compatibility routines -* babel:: Interface to 'LaTeX' 'babel' package +* slide:: Making presentations with ‘Asymptote’ +* MetaPost:: ‘MetaPost’ compatibility routines +* babel:: Interface to ‘LaTeX’ ‘babel’ package * labelpath:: Drawing curved labels * labelpath3:: Drawing curved labels in 3D * annotate:: Annotate your PDF files @@ -5092,118 +5139,118 @@ File: asymptote.info, Node: Base modules, Next: Options, Prev: LaTeX usage, File: asymptote.info, Node: plain, Next: simplex, Prev: Base modules, Up: Base modules -8.1 'plain' +8.1 ‘plain’ =========== -This is the default 'Asymptote' base file, which defines key parts of -the drawing language (such as the 'picture' structure). +This is the default ‘Asymptote’ base file, which defines key parts of +the drawing language (such as the ‘picture’ structure). - By default, an implicit 'private import plain;' occurs before + By default, an implicit ‘private import plain;’ occurs before translating a file and before the first command given in interactive mode. This also applies when translating files for module definitions -(except when translating 'plain', of course). This means that the types -and functions defined in 'plain' are accessible in almost all -'Asymptote' code. Use the '-noautoplain' command-line option to disable +(except when translating ‘plain’, of course). This means that the types +and functions defined in ‘plain’ are accessible in almost all +‘Asymptote’ code. Use the ‘-noautoplain’ command-line option to disable this feature. File: asymptote.info, Node: simplex, Next: math, Prev: plain, Up: Base modules -8.2 'simplex' +8.2 ‘simplex’ ============= This module solves the two-variable linear programming problem using the -simplex method. It is used by the module 'plain' for automatic sizing +simplex method. It is used by the module ‘plain’ for automatic sizing of pictures. File: asymptote.info, Node: math, Next: interpolate, Prev: simplex, Up: Base modules -8.3 'math' +8.3 ‘math’ ========== -This module extends 'Asymptote''s mathematical capabilities with useful +This module extends ‘Asymptote’’s mathematical capabilities with useful functions such as -'void drawline(picture pic=currentpicture, pair P, pair Q, pen p=currentpen);' - draw the visible portion of the (infinite) line going through 'P' - and 'Q', without altering the size of picture 'pic', using pen 'p'. +‘void drawline(picture pic=currentpicture, pair P, pair Q, pen p=currentpen);’ + draw the visible portion of the (infinite) line going through ‘P’ + and ‘Q’, without altering the size of picture ‘pic’, using pen ‘p’. -'real intersect(triple P, triple Q, triple n, triple Z);' +‘real intersect(triple P, triple Q, triple n, triple Z);’ returns the intersection time of the extension of the line segment - 'PQ' with the plane perpendicular to 'n' and passing through 'Z'. + ‘PQ’ with the plane perpendicular to ‘n’ and passing through ‘Z’. -'triple intersectionpoint(triple n0, triple P0, triple n1, triple P1);' +‘triple intersectionpoint(triple n0, triple P0, triple n1, triple P1);’ Return any point on the intersection of the two planes with normals - 'n0' and 'n1' passing through points 'P0' and 'P1', respectively. - If the planes are parallel, return '(infinity,infinity,infinity)'. + ‘n0’ and ‘n1’ passing through points ‘P0’ and ‘P1’, respectively. + If the planes are parallel, return ‘(infinity,infinity,infinity)’. -'pair[] quarticroots(real a, real b, real c, real d, real e);' +‘pair[] quarticroots(real a, real b, real c, real d, real e);’ returns the four complex roots of the quartic equation ax^4+bx^3+cx^2+dx+e=0. -'real time(path g, real x, int n=0, real fuzz=-1)' - returns the 'n'th intersection time of path 'g' with the vertical +‘real time(path g, real x, int n=0, real fuzz=-1)’ + returns the ‘n’th intersection time of path ‘g’ with the vertical line through x. -'real time(path g, explicit pair z, int n=0, real fuzz=-1)' - returns the 'n'th intersection time of path 'g' with the horizontal - line through '(0,z.y)'. +‘real time(path g, explicit pair z, int n=0, real fuzz=-1)’ + returns the ‘n’th intersection time of path ‘g’ with the horizontal + line through ‘(0,z.y)’. -'real value(path g, real x, int n=0, real fuzz=-1)' - returns the 'n'th 'y' value of 'g' at 'x'. +‘real value(path g, real x, int n=0, real fuzz=-1)’ + returns the ‘n’th ‘y’ value of ‘g’ at ‘x’. -'real value(path g, explicit pair z, int n=0, real fuzz=-1)' - returns the 'n'th 'x' value of 'g' at 'y=z.y'. +‘real value(path g, explicit pair z, int n=0, real fuzz=-1)’ + returns the ‘n’th ‘x’ value of ‘g’ at ‘y=z.y’. -'real slope(path g, real x, int n=0, real fuzz=-1)' - returns the 'n'th slope of 'g' at 'x'. +‘real slope(path g, real x, int n=0, real fuzz=-1)’ + returns the ‘n’th slope of ‘g’ at ‘x’. -'real slope(path g, explicit pair z, int n=0, real fuzz=-1)' - returns the 'n'th slope of 'g' at 'y=z.y'. +‘real slope(path g, explicit pair z, int n=0, real fuzz=-1)’ + returns the ‘n’th slope of ‘g’ at ‘y=z.y’. int[][] segment(bool[] b) returns the indices of consecutive - true-element segments of bool[] 'b'. + true-element segments of bool[] ‘b’. -'real[] partialsum(real[] a)' - returns the partial sums of a real array 'a'. +‘real[] partialsum(real[] a)’ + returns the partial sums of a real array ‘a’. -'real[] partialsum(real[] a, real[] dx)' - returns the partial 'dx'-weighted sums of a real array 'a'. +‘real[] partialsum(real[] a, real[] dx)’ + returns the partial ‘dx’-weighted sums of a real array ‘a’. -'bool increasing(real[] a, bool strict=false)' - returns, if 'strict=false', whether 'i > j' implies 'a[i] >= a[j]', - or if 'strict=true', whether 'i > j' implies implies 'a[i] > a[j]'. +‘bool increasing(real[] a, bool strict=false)’ + returns, if ‘strict=false’, whether ‘i > j’ implies ‘a[i] >= a[j]’, + or if ‘strict=true’, whether ‘i > j’ implies implies ‘a[i] > a[j]’. -'int unique(real[] a, real x)' - if the sorted array 'a' does not contain 'x', insert it - sequentially, returning the index of 'x' in the resulting array. +‘int unique(real[] a, real x)’ + if the sorted array ‘a’ does not contain ‘x’, insert it + sequentially, returning the index of ‘x’ in the resulting array. -'bool lexorder(pair a, pair b)' - returns the strict lexicographical partial order of 'a' and 'b'. +‘bool lexorder(pair a, pair b)’ + returns the strict lexicographical partial order of ‘a’ and ‘b’. -'bool lexorder(triple a, triple b)' - returns the strict lexicographical partial order of 'a' and 'b'. +‘bool lexorder(triple a, triple b)’ + returns the strict lexicographical partial order of ‘a’ and ‘b’. File: asymptote.info, Node: interpolate, Next: geometry, Prev: math, Up: Base modules -8.4 'interpolate' +8.4 ‘interpolate’ ================= This module implements Lagrange, Hermite, and standard cubic spline -interpolation in 'Asymptote', as illustrated in the example -'interpolate1.asy'. +interpolation in ‘Asymptote’, as illustrated in the example +‘interpolate1.asy’. File: asymptote.info, Node: geometry, Next: trembling, Prev: interpolate, Up: Base modules -8.5 'geometry' +8.5 ‘geometry’ ============== This module, written by Philippe Ivaldi, provides an extensive set of -geometry routines, including 'perpendicular' symbols and a 'triangle' -structure. Link to the documentation for the 'geometry' module are +geometry routines, including ‘perpendicular’ symbols and a ‘triangle’ +structure. Link to the documentation for the ‘geometry’ module are posted here: <https://asymptote.sourceforge.io/links.html>, including an extensive set of examples, <https://web.archive.org/web/20201130113133/http://www.piprime.fr/files/asymptote/geometry/>, @@ -5213,45 +5260,45 @@ and an index: File: asymptote.info, Node: trembling, Next: stats, Prev: geometry, Up: Base modules -8.6 'trembling' +8.6 ‘trembling’ =============== This module, written by Philippe Ivaldi and illustrated in the example -'floatingdisk.asy', allows one to draw wavy lines, as if drawn by hand. +‘floatingdisk.asy’, allows one to draw wavy lines, as if drawn by hand. File: asymptote.info, Node: stats, Next: patterns, Prev: trembling, Up: Base modules -8.7 'stats' +8.7 ‘stats’ =========== This module implements a Gaussian random number generator and a -collection of statistics routines, including 'histogram' and -'leastsquares'. +collection of statistics routines, including ‘histogram’ and +‘leastsquares’. File: asymptote.info, Node: patterns, Next: markers, Prev: stats, Up: Base modules -8.8 'patterns' +8.8 ‘patterns’ ============== -This module implements 'PostScript' tiling patterns and includes several +This module implements ‘PostScript’ tiling patterns and includes several convenient pattern generation routines. File: asymptote.info, Node: markers, Next: map, Prev: patterns, Up: Base modules -8.9 'markers' +8.9 ‘markers’ ============= This module implements specialized routines for marking paths and angles. The principal mark routine provided by this module is markroutine markinterval(int n=1, frame f, bool rotated=false); -which centers 'n' copies of frame 'f' within uniformly space intervals +which centers ‘n’ copies of frame ‘f’ within uniformly space intervals in arclength along the path, optionally rotated by the angle of the local tangent. - The 'marker' (*note marker::) routine can be used to construct new + The ‘marker’ (*note marker::) routine can be used to construct new markers from these predefined frames: frame stickframe(int n=1, real size=0, pair space=0, real angle=0, @@ -5266,9 +5313,9 @@ frame tildeframe(int n=1, real size=0, pair space=0, real angle=0, pair offset=0, pen p=currentpen); For convenience, this module also constructs the markers -'StickIntervalMarker', 'CrossIntervalMarker', 'CircleBarIntervalMarker', -and 'TildeIntervalMarker' from the above frames. The example -'markers1.asy' illustrates the use of these markers: +‘StickIntervalMarker’, ‘CrossIntervalMarker’, ‘CircleBarIntervalMarker’, +and ‘TildeIntervalMarker’ from the above frames. The example +‘markers1.asy’ illustrates the use of these markers: [./markers1] @@ -5279,7 +5326,7 @@ void markangle(picture pic=currentpicture, Label L="", pair A, pair O, pair B, arrowbar arrow=None, pen p=currentpen, margin margin=NoMargin, marker marker=nomarker); -as illustrated in the example 'markers2.asy'. +as illustrated in the example ‘markers2.asy’. [./markers2] @@ -5287,11 +5334,11 @@ as illustrated in the example 'markers2.asy'. File: asymptote.info, Node: map, Next: tree, Prev: markers, Up: Base modules -8.10 'map' +8.10 ‘map’ ========== This module creates a struct parameterized by the types specified in -strings 'key' and 'value', mapping keys to values with a specified +strings ‘key’ and ‘value’, mapping keys to values with a specified default: import map; @@ -5308,7 +5355,7 @@ write(M.lookup("y")); File: asymptote.info, Node: tree, Next: binarytree, Prev: map, Up: Base modules -8.11 'tree' +8.11 ‘tree’ =========== This module implements an example of a dynamic binary search tree. @@ -5316,12 +5363,12 @@ This module implements an example of a dynamic binary search tree. File: asymptote.info, Node: binarytree, Next: drawtree, Prev: tree, Up: Base modules -8.12 'binarytree' +8.12 ‘binarytree’ ================= This module can be used to draw an arbitrary binary tree and includes an input routine for the special case of a binary search tree, as -illustrated in the example 'binarytreetest.asy': +illustrated in the example ‘binarytreetest.asy’: import binarytree; picture pic,pic2; @@ -5341,134 +5388,134 @@ add(pic2.fit(),(0,0),10S); File: asymptote.info, Node: drawtree, Next: syzygy, Prev: binarytree, Up: Base modules -8.13 'drawtree' +8.13 ‘drawtree’ =============== -This is a simple tree drawing module used by the example 'treetest.asy'. +This is a simple tree drawing module used by the example ‘treetest.asy’. File: asymptote.info, Node: syzygy, Next: feynman, Prev: drawtree, Up: Base modules -8.14 'syzygy' +8.14 ‘syzygy’ ============= This module automates the drawing of braids, relations, and syzygies, along with the corresponding equations, as illustrated in the example -'knots.asy'. +‘knots.asy’. File: asymptote.info, Node: feynman, Next: roundedpath, Prev: syzygy, Up: Base modules -8.15 'feynman' +8.15 ‘feynman’ ============== This module, contributed by Martin Wiebusch, is useful for drawing -Feynman diagrams, as illustrated by the examples 'eetomumu.asy' and -'fermi.asy'. +Feynman diagrams, as illustrated by the examples ‘eetomumu.asy’ and +‘fermi.asy’. File: asymptote.info, Node: roundedpath, Next: animation, Prev: feynman, Up: Base modules -8.16 'roundedpath' +8.16 ‘roundedpath’ ================== This module, contributed by Stefan Knorr, is useful for rounding the sharp corners of paths, as illustrated in the example file -'roundpath.asy'. +‘roundpath.asy’. File: asymptote.info, Node: animation, Next: embed, Prev: roundedpath, Up: Base modules -8.17 'animation' +8.17 ‘animation’ ================ This module allows one to generate animations, as illustrated by the -files 'wheel.asy', 'wavepacket.asy', and 'cube.asy' in the 'animations' +files ‘wheel.asy’, ‘wavepacket.asy’, and ‘cube.asy’ in the ‘animations’ subdirectory of the examples directory. These animations use the -'ImageMagick' 'convert' program to merge multiple images into a GIF or +‘ImageMagick’ ‘convert’ program to merge multiple images into a GIF or MPEG movie. - The related 'animate' module, derived from the 'animation' module, + The related ‘animate’ module, derived from the ‘animation’ module, generates higher-quality portable clickable PDF movies, with optional controls. This requires installing the module <http://mirror.ctan.org/macros/latex/contrib/animate/animate.sty> -(version 2007/11/30 or later) in a new directory 'animate' in the local -'LaTeX' directory (for example, in -'/usr/local/share/texmf/tex/latex/animate'). On 'UNIX' systems, one -must then execute the command 'texhash'. - - The example 'pdfmovie.asy' in the 'animations' directory, along with -the slide presentations 'slidemovies.asy' and 'intro', illustrate the -use of embedded PDF movies. The examples 'inlinemovie.tex' and -'inlinemovie3.tex' show how to generate and embed PDF movies directly -within a 'LaTeX' file (*note LaTeX usage::). The member function +(version 2007/11/30 or later) in a new directory ‘animate’ in the local +‘LaTeX’ directory (for example, in +‘/usr/local/share/texmf/tex/latex/animate’). On ‘UNIX’ systems, one +must then execute the command ‘texhash’. + + The example ‘pdfmovie.asy’ in the ‘animations’ directory, along with +the slide presentations ‘slidemovies.asy’ and ‘intro’, illustrate the +use of embedded PDF movies. The examples ‘inlinemovie.tex’ and +‘inlinemovie3.tex’ show how to generate and embed PDF movies directly +within a ‘LaTeX’ file (*note LaTeX usage::). The member function string pdf(fit fit=NoBox, real delay=animationdelay, string options="", bool keep=settings.keep, bool multipage=true); -of the 'animate' structure accepts any of the 'animate.sty' options, as +of the ‘animate’ structure accepts any of the ‘animate.sty’ options, as described here: <http://mirror.ctan.org/macros/latex/contrib/animate/doc/animate.pdf> File: asymptote.info, Node: embed, Next: slide, Prev: animation, Up: Base modules -8.18 'embed' +8.18 ‘embed’ ============ -This module provides an interface to the 'LaTeX' package (included with -'MikTeX') +This module provides an interface to the ‘LaTeX’ package (included with +‘MikTeX’) <http://mirror.ctan.org/macros/latex/contrib/media9> for embedding movies, sounds, and 3D objects into a PDF document. A more portable method for embedding movie files, which should work -on any platform and does not require the 'media9' package, is provided -by using the 'external' module instead of 'embed'. +on any platform and does not require the ‘media9’ package, is provided +by using the ‘external’ module instead of ‘embed’. Examples of the above two interfaces is provided in the file -'embeddedmovie.asy' in the 'animations' subdirectory of the examples -directory and in 'externalmovie.asy'. For a higher quality embedded -movie generated directly by 'Asymptote', use the 'animate' module along -with the 'animate.sty' package to embed a portable PDF animation (*note +‘embeddedmovie.asy’ in the ‘animations’ subdirectory of the examples +directory and in ‘externalmovie.asy’. For a higher quality embedded +movie generated directly by ‘Asymptote’, use the ‘animate’ module along +with the ‘animate.sty’ package to embed a portable PDF animation (*note animate::). - An example of embedding 'U3D' code is provided in the file -'embeddedu3d'. + An example of embedding ‘U3D’ code is provided in the file +‘embeddedu3d’. File: asymptote.info, Node: slide, Next: MetaPost, Prev: embed, Up: Base modules -8.19 'slide' +8.19 ‘slide’ ============ This module provides a simple yet high-quality facility for making presentation slides, including portable embedded PDF animations (see the -file 'slidemovies.asy'). A simple example is provided in -'slidedemo.asy'. +file ‘slidemovies.asy’). A simple example is provided in +‘slidedemo.asy’. File: asymptote.info, Node: MetaPost, Next: babel, Prev: slide, Up: Base modules -8.20 'MetaPost' +8.20 ‘MetaPost’ =============== -This module provides some useful routines to help 'MetaPost' users -migrate old 'MetaPost' code to 'Asymptote'. Further contributions here +This module provides some useful routines to help ‘MetaPost’ users +migrate old ‘MetaPost’ code to ‘Asymptote’. Further contributions here are welcome. - Unlike 'MetaPost', 'Asymptote' does not implicitly solve linear -equations and therefore does not have the notion of a 'whatever' -unknown. The routine 'extension' (*note extension::) provides a useful -replacement for a common use of 'whatever': finding the intersection -point of the lines through 'P', 'Q' and 'p', 'q'. For less common -occurrences of 'whatever', one can use the built-in explicit linear -equation solver 'solve' instead. + Unlike ‘MetaPost’, ‘Asymptote’ does not implicitly solve linear +equations and therefore does not have the notion of a ‘whatever’ +unknown. The routine ‘extension’ (*note extension::) provides a useful +replacement for a common use of ‘whatever’: finding the intersection +point of the lines through ‘P’, ‘Q’ and ‘p’, ‘q’. For less common +occurrences of ‘whatever’, one can use the built-in explicit linear +equation solver ‘solve’ instead. File: asymptote.info, Node: babel, Next: labelpath, Prev: MetaPost, Up: Base modules -8.21 'babel' +8.21 ‘babel’ ============ -This module implements the 'LaTeX' 'babel' package in 'Asymptote'. For +This module implements the ‘LaTeX’ ‘babel’ package in ‘Asymptote’. For example: import babel; babel("german"); @@ -5476,155 +5523,156 @@ babel("german"); File: asymptote.info, Node: labelpath, Next: labelpath3, Prev: babel, Up: Base modules -8.22 'labelpath' +8.22 ‘labelpath’ ================ -This module uses the 'PSTricks' 'pstextpath' macro to fit labels along a +This module uses the ‘PSTricks’ ‘pstextpath’ macro to fit labels along a path (properly kerned, as illustrated in the example file -'curvedlabel.asy'), using the command +‘curvedlabel.asy’), using the command void labelpath(picture pic=currentpicture, Label L, path g, string justify=Centered, pen p=currentpen); -Here 'justify' is one of 'LeftJustified', 'Centered', or -'RightJustified'. The x component of a shift transform applied to the +Here ‘justify’ is one of ‘LeftJustified’, ‘Centered’, or +‘RightJustified’. The x component of a shift transform applied to the Label is interpreted as a shift along the curve, whereas the y component is interpreted as a shift away from the curve. All other Label -transforms are ignored. This module requires the 'latex' tex engine and -inherits the limitations of the 'PSTricks' '\pstextpath' macro. +transforms are ignored. This module requires the ‘latex’ tex engine and +inherits the limitations of the ‘PSTricks’ ‘\pstextpath’ macro. File: asymptote.info, Node: labelpath3, Next: annotate, Prev: labelpath, Up: Base modules -8.23 'labelpath3' +8.23 ‘labelpath3’ ================= This module, contributed by Jens Schwaiger, implements a 3D version of -'labelpath' that does not require the 'PSTricks' package. An example is -provided in 'curvedlabel3.asy'. +‘labelpath’ that does not require the ‘PSTricks’ package. An example is +provided in ‘curvedlabel3.asy’. File: asymptote.info, Node: annotate, Next: CAD, Prev: labelpath3, Up: Base modules -8.24 'annotate' +8.24 ‘annotate’ =============== -This module supports PDF annotations for viewing with 'Adobe Reader', +This module supports PDF annotations for viewing with ‘Adobe Reader’, via the function void annotate(picture pic=currentpicture, string title, string text, pair position); -Annotations are illustrated in the example file 'annotation.asy'. -Currently, annotations are only implemented for the 'latex' (default) -and 'tex' TeX engines. +Annotations are illustrated in the example file ‘annotation.asy’. +Currently, annotations are only implemented for the ‘latex’ (default) +and ‘tex’ TeX engines. File: asymptote.info, Node: CAD, Next: graph, Prev: annotate, Up: Base modules -8.25 'CAD' +8.25 ‘CAD’ ========== This module, contributed by Mark Henning, provides basic pen definitions and measurement functions for simple 2D CAD drawings according to DIN -15. It is documented separately, in the file 'CAD.pdf'. +15. It is documented separately, in the file ‘CAD.pdf’. File: asymptote.info, Node: graph, Next: palette, Prev: CAD, Up: Base modules -8.26 'graph' +8.26 ‘graph’ ============ This module implements two-dimensional linear and logarithmic graphs, including automatic scale and tick selection (with the ability to -override manually). A graph is a 'guide' (that can be drawn with the +override manually). A graph is a ‘guide’ (that can be drawn with the draw command, with an optional legend) constructed with one of the following routines: - * guide graph(picture pic=currentpicture, real f(real), real a, real b, + • guide graph(picture pic=currentpicture, real f(real), real a, real b, int n=ngraph, real T(real)=identity, interpolate join=operator --); guide[] graph(picture pic=currentpicture, real f(real), real a, real b, int n=ngraph, real T(real)=identity, bool3 cond(real), interpolate join=operator --); - Returns a graph using the scaling information for picture 'pic' - (*note automatic scaling::) of the function 'f' on the interval - ['T'('a'),'T'('b')], sampling at 'n' points evenly spaced in - ['a','b'], optionally restricted by the bool3 function 'cond' on - ['a','b']. If 'cond' is: - * 'true', the point is added to the existing guide; - * 'default', the point is added to a new guide; - * 'false', the point is omitted and a new guide is begun. + Returns a graph using the scaling information for picture ‘pic’ + (*note automatic scaling::) of the function ‘f’ on the interval + [‘T’(‘a’),‘T’(‘b’)], sampling at ‘n’ points evenly spaced in + [‘a’,‘b’], optionally restricted by the bool3 function ‘cond’ on + [‘a’,‘b’]. If ‘cond’ is: + • ‘true’, the point is added to the existing guide; + • ‘default’, the point is added to a new guide; + • ‘false’, the point is omitted and a new guide is begun. The points are connected using the interpolation specified by - 'join': + ‘join’: - * 'operator --' (linear interpolation; the abbreviation - 'Straight' is also accepted); + • ‘operator --’ (linear interpolation; the abbreviation + ‘Straight’ is also accepted); - * 'operator ..' (piecewise Bezier cubic spline interpolation; - the abbreviation 'Spline' is also accepted); + • ‘operator ..’ (piecewise Bezier cubic spline interpolation; + the abbreviation ‘Spline’ is also accepted); - * 'Hermite' (standard cubic spline interpolation using boundary - condition 'notaknot', 'natural', 'periodic', 'clamped(real - slopea, real slopeb)'), or 'monotonic'. The abbreviation - 'Hermite' is equivalent to 'Hermite(notaknot)' for nonperiodic - data and 'Hermite(periodic)' for periodic data). + • ‘linear’ (linear interpolation), + • ‘Hermite’ (standard cubic spline interpolation using boundary + condition ‘notaknot’, ‘natural’, ‘periodic’, ‘clamped(real + slopea, real slopeb)’), or ‘monotonic’. The abbreviation + ‘Hermite’ is equivalent to ‘Hermite(notaknot)’ for nonperiodic + data and ‘Hermite(periodic)’ for periodic data). - * guide graph(picture pic=currentpicture, real x(real), real y(real), + • guide graph(picture pic=currentpicture, real x(real), real y(real), real a, real b, int n=ngraph, real T(real)=identity, interpolate join=operator --); guide[] graph(picture pic=currentpicture, real x(real), real y(real), real a, real b, int n=ngraph, real T(real)=identity, bool3 cond(real), interpolate join=operator --); - Returns a graph using the scaling information for picture 'pic' of - the parametrized function ('x'(t),'y'(t)) for t in the interval - ['T'('a'),'T'('b')], sampling at 'n' points evenly spaced in - ['a','b'], optionally restricted by the bool3 function 'cond' on - ['a','b'], using the given interpolation type. + Returns a graph using the scaling information for picture ‘pic’ of + the parametrized function (‘x’(t),‘y’(t)) for t in the interval + [‘T’(‘a’),‘T’(‘b’)], sampling at ‘n’ points evenly spaced in + [‘a’,‘b’], optionally restricted by the bool3 function ‘cond’ on + [‘a’,‘b’], using the given interpolation type. - * guide graph(picture pic=currentpicture, pair z(real), real a, real b, + • guide graph(picture pic=currentpicture, pair z(real), real a, real b, int n=ngraph, real T(real)=identity, interpolate join=operator --); guide[] graph(picture pic=currentpicture, pair z(real), real a, real b, int n=ngraph, real T(real)=identity, bool3 cond(real), interpolate join=operator --); - Returns a graph using the scaling information for picture 'pic' of - the parametrized function 'z'(t) for t in the interval - ['T'('a'),'T'('b')], sampling at 'n' points evenly spaced in - ['a','b'], optionally restricted by the bool3 function 'cond' on - ['a','b'], using the given interpolation type. + Returns a graph using the scaling information for picture ‘pic’ of + the parametrized function ‘z’(t) for t in the interval + [‘T’(‘a’),‘T’(‘b’)], sampling at ‘n’ points evenly spaced in + [‘a’,‘b’], optionally restricted by the bool3 function ‘cond’ on + [‘a’,‘b’], using the given interpolation type. - * guide graph(picture pic=currentpicture, pair[] z, + • guide graph(picture pic=currentpicture, pair[] z, interpolate join=operator --); guide[] graph(picture pic=currentpicture, pair[] z, bool3[] cond, interpolate join=operator --); - Returns a graph using the scaling information for picture 'pic' of - the elements of the array 'z', optionally restricted to those - indices for which the elements of the boolean array 'cond' are - 'true', using the given interpolation type. + Returns a graph using the scaling information for picture ‘pic’ of + the elements of the array ‘z’, optionally restricted to those + indices for which the elements of the boolean array ‘cond’ are + ‘true’, using the given interpolation type. - * guide graph(picture pic=currentpicture, real[] x, real[] y, + • guide graph(picture pic=currentpicture, real[] x, real[] y, interpolate join=operator --); guide[] graph(picture pic=currentpicture, real[] x, real[] y, bool3[] cond, interpolate join=operator --); - Returns a graph using the scaling information for picture 'pic' of - the elements of the arrays ('x','y'), optionally restricted to - those indices for which the elements of the boolean array 'cond' - are 'true', using the given interpolation type. + Returns a graph using the scaling information for picture ‘pic’ of + the elements of the arrays (‘x’,‘y’), optionally restricted to + those indices for which the elements of the boolean array ‘cond’ + are ‘true’, using the given interpolation type. - * guide polargraph(picture pic=currentpicture, real f(real), real a, + • guide polargraph(picture pic=currentpicture, real f(real), real a, real b, int n=ngraph, interpolate join=operator --); Returns a polar-coordinate graph using the scaling information for - picture 'pic' of the function 'f' on the interval ['a','b'], - sampling at 'n' evenly spaced points, with the given interpolation + picture ‘pic’ of the function ‘f’ on the interval [‘a’,‘b’], + sampling at ‘n’ evenly spaced points, with the given interpolation type. - * guide polargraph(picture pic=currentpicture, real[] r, real[] theta, + • guide polargraph(picture pic=currentpicture, real[] r, real[] theta, interpolate join=operator--); Returns a polar-coordinate graph using the scaling information for - picture 'pic' of the elements of the arrays ('r','theta'), using + picture ‘pic’ of the elements of the arrays (‘r’,‘theta’), using the given interpolation type. @@ -5632,42 +5680,42 @@ following routines: An axis can be drawn on a picture with one of the following commands: - * void xaxis(picture pic=currentpicture, Label L="", axis axis=YZero, + • void xaxis(picture pic=currentpicture, Label L="", axis axis=YZero, real xmin=-infinity, real xmax=infinity, pen p=currentpen, ticks ticks=NoTicks, arrowbar arrow=None, bool above=false); - Draw an x axis on picture 'pic' from x='xmin' to x='xmax' using pen - 'p', optionally labelling it with Label 'L'. The relative label + Draw an x axis on picture ‘pic’ from x=‘xmin’ to x=‘xmax’ using pen + ‘p’, optionally labelling it with Label ‘L’. The relative label location along the axis (a real number from [0,1]) defaults to 1 (*note Label::), so that the label is drawn at the end of the axis. - An infinite value of 'xmin' or 'xmax' specifies that the + An infinite value of ‘xmin’ or ‘xmax’ specifies that the corresponding axis limit will be automatically determined from the - picture limits. The optional 'arrow' argument takes the same - values as in the 'draw' command (*note arrows::). The axis is - drawn before any existing objects in 'pic' unless 'above=true'. - The axis placement is determined by one of the following 'axis' + picture limits. The optional ‘arrow’ argument takes the same + values as in the ‘draw’ command (*note arrows::). The axis is + drawn before any existing objects in ‘pic’ unless ‘above=true’. + The axis placement is determined by one of the following ‘axis’ types: - 'YZero(bool extend=true)' + ‘YZero(bool extend=true)’ Request an x axis at y=0 (or y=1 on a logarithmic axis) extending to the full dimensions of the picture, unless - 'extend'=false. + ‘extend’=false. - 'YEquals(real Y, bool extend=true)' - Request an x axis at y='Y' extending to the full dimensions of - the picture, unless 'extend'=false. + ‘YEquals(real Y, bool extend=true)’ + Request an x axis at y=‘Y’ extending to the full dimensions of + the picture, unless ‘extend’=false. - 'Bottom(bool extend=false)' + ‘Bottom(bool extend=false)’ Request a bottom axis. - 'Top(bool extend=false)' + ‘Top(bool extend=false)’ Request a top axis. - 'BottomTop(bool extend=false)' + ‘BottomTop(bool extend=false)’ Request a bottom and top axis. Custom axis types can be created by following the examples in the - module 'graph.asy'. One can easily override the default values for + module ‘graph.asy’. One can easily override the default values for the standard axis types: import graph; @@ -5685,8 +5733,8 @@ following routines: YZero=YZero(); - The default tick option is 'NoTicks'. The options 'LeftTicks', - 'RightTicks', or 'Ticks' can be used to draw ticks on the left, + The default tick option is ‘NoTicks’. The options ‘LeftTicks’, + ‘RightTicks’, or ‘Ticks’ can be used to draw ticks on the left, right, or both sides of the path, relative to the direction in which the path is drawn. These tick routines accept a number of optional arguments: @@ -5699,68 +5747,68 @@ following routines: If any of these parameters are omitted, reasonable defaults will be chosen: - 'Label format' - override the default tick label format ('defaultformat', + ‘Label format’ + override the default tick label format (‘defaultformat’, initially "$%.4g$"), rotation, pen, and alignment (for - example, 'LeftSide', 'Center', or 'RightSide') relative to the - axis. To enable 'LaTeX' math mode fonts, the format string - should begin and end with '$' *note format::. If the format - string is 'trailingzero', trailing zeros will be added to the - tick labels; if the format string is '"%"', the tick label + example, ‘LeftSide’, ‘Center’, or ‘RightSide’) relative to the + axis. To enable ‘LaTeX’ math mode fonts, the format string + should begin and end with ‘$’ *note format::. If the format + string is ‘trailingzero’, trailing zeros will be added to the + tick labels; if the format string is ‘"%"’, the tick label will be suppressed; - 'ticklabel' - is a function 'string(real x)' returning the label (by - default, format(format.s,x)) for each major tick value 'x'; - 'bool beginlabel' + ‘ticklabel’ + is a function ‘string(real x)’ returning the label (by + default, format(format.s,x)) for each major tick value ‘x’; + ‘bool beginlabel’ include the first label; - 'bool endlabel' + ‘bool endlabel’ include the last label; - 'int N' + ‘int N’ when automatic scaling is enabled (the default; *note automatic scaling::), divide a linear axis evenly into this many intervals, separated by major ticks; for a logarithmic axis, this is the number of decades between labelled ticks; - 'int n' + ‘int n’ divide each interval into this many subintervals, separated by minor ticks; - 'real Step' - the tick value spacing between major ticks (if 'N'='0'); - 'real step' - the tick value spacing between minor ticks (if 'n'='0'); - 'bool begin' + ‘real Step’ + the tick value spacing between major ticks (if ‘N’=‘0’); + ‘real step’ + the tick value spacing between minor ticks (if ‘n’=‘0’); + ‘bool begin’ include the first major tick; - 'bool end' + ‘bool end’ include the last major tick; - 'tickmodifier modify;' - an optional function that takes and returns a 'tickvalue' - structure having real[] members 'major' and 'minor' consisting + ‘tickmodifier modify;’ + an optional function that takes and returns a ‘tickvalue’ + structure having real[] members ‘major’ and ‘minor’ consisting of the tick values (to allow modification of the automatically generated tick values); - 'real Size' - the size of the major ticks (in 'PostScript' coordinates); - 'real size' - the size of the minor ticks (in 'PostScript' coordinates); - 'bool extend;' + ‘real Size’ + the size of the major ticks (in ‘PostScript’ coordinates); + ‘real size’ + the size of the minor ticks (in ‘PostScript’ coordinates); + ‘bool extend;’ extend the ticks between two axes (useful for drawing a grid on the graph); - 'pen pTick' + ‘pen pTick’ an optional pen used to draw the major ticks; - 'pen ptick' + ‘pen ptick’ an optional pen used to draw the minor ticks. - For convenience, the predefined tickmodifiers 'OmitTick(... real[] - x)', 'OmitTickInterval(real a, real b)', and - 'OmitTickIntervals(real[] a, real[] b)' can be used to remove + For convenience, the predefined tickmodifiers ‘OmitTick(... real[] + x)’, ‘OmitTickInterval(real a, real b)’, and + ‘OmitTickIntervals(real[] a, real[] b)’ can be used to remove specific auto-generated ticks and their labels. The - 'OmitFormat(string s=defaultformat ... real[] x)' ticklabel can be + ‘OmitFormat(string s=defaultformat ... real[] x)’ ticklabel can be used to remove specific tick labels but not the corresponding - ticks. The tickmodifier 'NoZero' is an abbreviation for - 'OmitTick(0)' and the ticklabel 'NoZeroFormat' is an abbrevation - for 'OmitFormat(0)'. + ticks. The tickmodifier ‘NoZero’ is an abbreviation for + ‘OmitTick(0)’ and the ticklabel ‘NoZeroFormat’ is an abbrevation + for ‘OmitFormat(0)’. It is also possible to specify custom tick locations with - 'LeftTicks', 'RightTicks', and 'Ticks' by passing explicit real - arrays 'Ticks' and (optionally) 'ticks' containing the locations of + ‘LeftTicks’, ‘RightTicks’, and ‘Ticks’ by passing explicit real + arrays ‘Ticks’ and (optionally) ‘ticks’ containing the locations of the major and minor ticks, respectively: ticks LeftTicks(Label format="", ticklabel ticklabel=null, bool beginlabel=true, bool endlabel=true, @@ -5768,42 +5816,42 @@ following routines: real Size=0, real size=0, bool extend=false, pen pTick=nullpen, pen ptick=nullpen) - * void yaxis(picture pic=currentpicture, Label L="", axis axis=XZero, + • void yaxis(picture pic=currentpicture, Label L="", axis axis=XZero, real ymin=-infinity, real ymax=infinity, pen p=currentpen, ticks ticks=NoTicks, arrowbar arrow=None, bool above=false, bool autorotate=true); - Draw a y axis on picture 'pic' from y='ymin' to y='ymax' using pen - 'p', optionally labelling it with a Label 'L' that is autorotated - unless 'autorotate=false'. The relative location of the label (a + Draw a y axis on picture ‘pic’ from y=‘ymin’ to y=‘ymax’ using pen + ‘p’, optionally labelling it with a Label ‘L’ that is autorotated + unless ‘autorotate=false’. The relative location of the label (a real number from [0,1]) defaults to 1 (*note Label::). An infinite - value of 'ymin' or 'ymax' specifies that the corresponding axis + value of ‘ymin’ or ‘ymax’ specifies that the corresponding axis limit will be automatically determined from the picture limits. - The optional 'arrow' argument takes the same values as in the - 'draw' command (*note arrows::). The axis is drawn before any - existing objects in 'pic' unless 'above=true'. The tick type is - specified by 'ticks' and the axis placement is determined by one of - the following 'axis' types: + The optional ‘arrow’ argument takes the same values as in the + ‘draw’ command (*note arrows::). The axis is drawn before any + existing objects in ‘pic’ unless ‘above=true’. The tick type is + specified by ‘ticks’ and the axis placement is determined by one of + the following ‘axis’ types: - 'XZero(bool extend=true)' + ‘XZero(bool extend=true)’ Request a y axis at x=0 (or x=1 on a logarithmic axis) extending to the full dimensions of the picture, unless - 'extend'=false. + ‘extend’=false. - 'XEquals(real X, bool extend=true)' - Request a y axis at x='X' extending to the full dimensions of - the picture, unless 'extend'=false. + ‘XEquals(real X, bool extend=true)’ + Request a y axis at x=‘X’ extending to the full dimensions of + the picture, unless ‘extend’=false. - 'Left(bool extend=false)' + ‘Left(bool extend=false)’ Request a left axis. - 'Right(bool extend=false)' + ‘Right(bool extend=false)’ Request a right axis. - 'LeftRight(bool extend=false)' + ‘LeftRight(bool extend=false)’ Request a left and right axis. - * For convenience, the functions + • For convenience, the functions void xequals(picture pic=currentpicture, Label L="", real x, bool extend=false, real ymin=-infinity, real ymax=infinity, pen p=currentpen, ticks ticks=NoTicks, bool above=true, @@ -5813,48 +5861,48 @@ following routines: bool extend=false, real xmin=-infinity, real xmax=infinity, pen p=currentpen, ticks ticks=NoTicks, bool above=true, arrowbar arrow=None); - can be respectively used to call 'yaxis' and 'xaxis' with the - appropriate axis types 'XEquals(x,extend)' and 'YEquals(y,extend)'. + can be respectively used to call ‘yaxis’ and ‘xaxis’ with the + appropriate axis types ‘XEquals(x,extend)’ and ‘YEquals(y,extend)’. This is the recommended way of drawing vertical or horizontal lines and axes at arbitrary locations. - * void axes(picture pic=currentpicture, Label xlabel="", Label ylabel="", + • void axes(picture pic=currentpicture, Label xlabel="", Label ylabel="", bool extend=true, pair min=(-infinity,-infinity), pair max=(infinity,infinity), pen p=currentpen, arrowbar arrow=None, bool above=false); - This convenience routine draws both x and y axes on picture 'pic' - from 'min' to 'max', with optional labels 'xlabel' and 'ylabel' and - any arrows specified by 'arrow'. The axes are drawn on top of - existing objects in 'pic' only if 'above=true'. + This convenience routine draws both x and y axes on picture ‘pic’ + from ‘min’ to ‘max’, with optional labels ‘xlabel’ and ‘ylabel’ and + any arrows specified by ‘arrow’. The axes are drawn on top of + existing objects in ‘pic’ only if ‘above=true’. - * void axis(picture pic=currentpicture, Label L="", path g, + • void axis(picture pic=currentpicture, Label L="", path g, pen p=currentpen, ticks ticks, ticklocate locate, arrowbar arrow=None, int[] divisor=new int[], bool above=false, bool opposite=false); - This routine can be used to draw on picture 'pic' a general axis - based on an arbitrary path 'g', using pen 'p'. One can optionally - label the axis with Label 'L' and add an arrow 'arrow'. The tick - type is given by 'ticks'. The optional integer array 'divisor' + This routine can be used to draw on picture ‘pic’ a general axis + based on an arbitrary path ‘g’, using pen ‘p’. One can optionally + label the axis with Label ‘L’ and add an arrow ‘arrow’. The tick + type is given by ‘ticks’. The optional integer array ‘divisor’ specifies what tick divisors to try in the attempt to produce - uncrowded tick labels. A 'true' value for the flag 'opposite' + uncrowded tick labels. A ‘true’ value for the flag ‘opposite’ identifies an unlabelled secondary axis (typically drawn opposite a primary axis). The axis is drawn before any existing objects in - 'pic' unless 'above=true'. The tick locator 'ticklocate' is + ‘pic’ unless ‘above=true’. The tick locator ‘ticklocate’ is constructed by the routine ticklocate ticklocate(real a, real b, autoscaleT S=defaultS, real tickmin=-infinity, real tickmax=infinity, real time(real)=null, pair dir(real)=zero); - where 'a' and 'b' specify the respective tick values at - 'point(g,0)' and 'point(g,length(g))', 'S' specifies the - autoscaling transformation, the function 'real time(real v)' - returns the time corresponding to the value 'v', and 'pair dir(real - t)' returns the absolute tick direction as a function of 't' (zero + where ‘a’ and ‘b’ specify the respective tick values at + ‘point(g,0)’ and ‘point(g,length(g))’, ‘S’ specifies the + autoscaling transformation, the function ‘real time(real v)’ + returns the time corresponding to the value ‘v’, and ‘pair dir(real + t)’ returns the absolute tick direction as a function of ‘t’ (zero means draw the tick perpendicular to the axis). - * These routines are useful for manually putting ticks and labels on - axes (if the variable 'Label' is given as the 'Label' argument, the - 'format' argument will be used to format a string based on the tick + • These routines are useful for manually putting ticks and labels on + axes (if the variable ‘Label’ is given as the ‘Label’ argument, the + ‘format’ argument will be used to format a string based on the tick location): void xtick(picture pic=currentpicture, Label L="", explicit pair z, pair dir=N, string format="", @@ -5907,8 +5955,8 @@ following routines: 2. The next example draws a scientific-style graph with a legend. The position of the legend can be adjusted either explicitly or by using the graphical user interface (*note GUI::). If an - 'UnFill(real xmargin=0, real ymargin=xmargin)' or 'Fill(pen)' - option is specified to 'add', the legend will obscure any + ‘UnFill(real xmargin=0, real ymargin=xmargin)’ or ‘Fill(pen)’ + option is specified to ‘add’, the legend will obscure any underlying objects. Here we illustrate how to clip the portion of the picture covered by a label: @@ -5931,7 +5979,7 @@ following routines: [./lineargraph0] - To specify a fixed size for the graph proper, use 'attach': + To specify a fixed size for the graph proper, use ‘attach’: import graph; size(250,200,IgnoreAspect); @@ -6011,23 +6059,23 @@ following routines: marker marker(path g, markroutine markroutine=marknodes, pen p=currentpen, filltype filltype=NoFill, bool above=true); - using the path 'unitcircle' (*note filltype::), are drawn below + using the path ‘unitcircle’ (*note filltype::), are drawn below each node. Any frame can be converted to a marker, using marker marker(frame f, markroutine markroutine=marknodes, bool above=true); In the right-hand graph, the unit n-sided regular polygon - 'polygon(int n)' and the unit n-point cyclic cross 'cross(int n, - bool round=true, real r=0)' (where 'r' is an optional "inner" + ‘polygon(int n)’ and the unit n-point cyclic cross ‘cross(int n, + bool round=true, real r=0)’ (where ‘r’ is an optional “inner” radius) are used to build a custom marker frame. Here - 'markuniform(bool centered=false, int n, bool rotated=false)' adds - this frame at 'n' uniformly spaced points along the arclength of + ‘markuniform(bool centered=false, int n, bool rotated=false)’ adds + this frame at ‘n’ uniformly spaced points along the arclength of the path, optionally rotated by the angle of the local tangent to the path (if centered is true, the frames will be centered within - 'n' evenly spaced arclength intervals). Alternatively, one can use - markroutine 'marknodes' to request that the marks be placed at each - Bezier node of the path, or markroutine 'markuniform(pair z(real - t), real a, real b, int n)' to place marks at points 'z(t)' for n - evenly spaced values of 't' in '[a,b]'. + ‘n’ evenly spaced arclength intervals). Alternatively, one can use + markroutine ‘marknodes’ to request that the marks be placed at each + Bezier node of the path, or markroutine ‘markuniform(pair z(real + t), real a, real b, int n)’ to place marks at points ‘z(t)’ for n + evenly spaced values of ‘t’ in ‘[a,b]’. These markers are predefined: marker[] Mark={ @@ -6043,7 +6091,7 @@ following routines: marker(invert*polygon(3),Fill),marker(diamond,Fill) }; - The example also illustrates the 'errorbar' routines: + The example also illustrates the ‘errorbar’ routines: void errorbars(picture pic=currentpicture, pair[] z, pair[] dp, pair[] dm={}, bool[] cond={}, pen p=currentpen, @@ -6054,8 +6102,8 @@ following routines: bool[] cond={}, pen p=currentpen, real size=0); Here, the positive and negative extents of the error are given by - the absolute values of the elements of the pair array 'dp' and the - optional pair array 'dm'. If 'dm' is not specified, the positive + the absolute values of the elements of the pair array ‘dp’ and the + optional pair array ‘dm’. If ‘dm’ is not specified, the positive and negative extents of the error are assumed to be equal. import graph; @@ -6168,14 +6216,14 @@ following routines: to xlimits(picture pic=currentpicture, real min=-infinity, real max=infinity, bool crop=NoCrop); - and the analogous function 'ylimits' can be uncommented to set the - respective axes limits for picture 'pic' to the specified 'min' and - 'max' values. Alternatively, the function + and the analogous function ‘ylimits’ can be uncommented to set the + respective axes limits for picture ‘pic’ to the specified ‘min’ and + ‘max’ values. Alternatively, the function void limits(picture pic=currentpicture, pair min, pair max, bool crop=NoCrop); can be used to limit the axes to the box having opposite vertices - at the given pairs). Existing objects in picture 'pic' will be - cropped to lie within the given limits if 'crop'='Crop'. The - function 'crop(picture pic)' can be used to crop a graph to the + at the given pairs). Existing objects in picture ‘pic’ will be + cropped to lie within the given limits if ‘crop’=‘Crop’. The + function ‘crop(picture pic)’ can be used to crop a graph to the current graph limits. import graph; @@ -6198,9 +6246,9 @@ following routines: The function guide graphwithderiv(pair f(real), pair fprime(real), real a, real b, int n=ngraph#10); - can be used to construct the graph of the parametric function 'f' - on '[a,b]' with the control points of the 'n' Bezier segments - determined by the specified derivative 'fprime': + can be used to construct the graph of the parametric function ‘f’ + on ‘[a,b]’ with the control points of the ‘n’ Bezier segments + determined by the specified derivative ‘fprime’: unitsize(2cm); import graph; pair F(real t) { @@ -6236,22 +6284,22 @@ following routines: [./scaledgraph] Axis scaling can be requested and/or automatic selection of the - axis limits can be inhibited with one of these 'scale' routines: + axis limits can be inhibited with one of these ‘scale’ routines: void scale(picture pic=currentpicture, scaleT x, scaleT y); void scale(picture pic=currentpicture, bool xautoscale=true, bool yautoscale=xautoscale, bool zautoscale=yautoscale); - This sets the scalings for picture 'pic'. The 'graph' routines - accept an optional 'picture' argument for determining the + This sets the scalings for picture ‘pic’. The ‘graph’ routines + accept an optional ‘picture’ argument for determining the appropriate scalings to use; if none is given, it uses those set - for 'currentpicture'. + for ‘currentpicture’. - Two frequently used scaling routines 'Linear' and 'Log' are - predefined in 'graph'. + Two frequently used scaling routines ‘Linear’ and ‘Log’ are + predefined in ‘graph’. All picture coordinates (including those in paths and those given - to the 'label' and 'limits' functions) are always treated as linear + to the ‘label’ and ‘limits’ functions) are always treated as linear (post-scaled) coordinates. Use pair Scale(picture pic=currentpicture, pair z); to convert a graph coordinate into a scaled picture coordinate. @@ -6262,15 +6310,15 @@ following routines: real ScaleY(picture pic=currentpicture, real y); The predefined scaling routines can be given two optional boolean - arguments: 'automin=false' and 'automax=automin'. These default to - 'false' but can be respectively set to 'true' to enable automatic - selection of "nice" axis minimum and maximum values. The 'Linear' + arguments: ‘automin=false’ and ‘automax=automin’. These default to + ‘false’ but can be respectively set to ‘true’ to enable automatic + selection of "nice" axis minimum and maximum values. The ‘Linear’ scaling can also take as optional final arguments a multiplicative - scaling factor and intercept (e.g. for a depth axis, 'Linear(-1)' + scaling factor and intercept (e.g. for a depth axis, ‘Linear(-1)’ requests axis reversal). For example, to draw a log/log graph of a function, use - 'scale(Log,Log)': + ‘scale(Log,Log)’: import graph; size(200,200,IgnoreAspect); @@ -6378,11 +6426,11 @@ following routines: [./brokenaxis] - 9. 'Asymptote' can draw secondary axes with the routines + 9. ‘Asymptote’ can draw secondary axes with the routines picture secondaryX(picture primary=currentpicture, void f(picture)); picture secondaryY(picture primary=currentpicture, void f(picture)); - In this example, 'secondaryY' is used to draw a secondary linear y + In this example, ‘secondaryY’ is used to draw a secondary linear y axis against a primary logarithmic y axis: import graph; texpreamble("\def\Arg{\mathop {\rm Arg}\nolimits}"); @@ -6449,7 +6497,7 @@ following routines: [./secondaryaxis] - 10. Here is a histogram example, which uses the 'stats' module. + 10. Here is a histogram example, which uses the ‘stats’ module. import graph; import stats; @@ -6472,7 +6520,7 @@ following routines: [./histogram] 11. Here is an example of reading column data in from a file and a - least-squares fit, using the 'stats' module. + least-squares fit, using the ‘stats’ module. size(400,200,IgnoreAspect); import graph; @@ -6531,7 +6579,7 @@ following routines: [./leastsquares] - 12. Here is an example that illustrates the general 'axis' routine. + 12. Here is an example that illustrates the general ‘axis’ routine. import graph; size(0,100); @@ -6546,7 +6594,7 @@ following routines: [./generalaxis] - 13. To draw a vector field of 'n' arrows evenly spaced along the + 13. To draw a vector field of ‘n’ arrows evenly spaced along the arclength of a path, use the routine picture vectorfield(path vector(real), path g, int n, bool truesize=false, pen p=currentpen, arrowbar arrow=Arrow); @@ -6585,7 +6633,7 @@ following routines: [./flow] - 14. To draw a vector field of 'nx'\times'ny' arrows in 'box(a,b)', use + 14. To draw a vector field of ‘nx’\times‘ny’ arrows in ‘box(a,b)’, use the routine picture vectorfield(path vector(pair), pair a, pair b, int nx=nmesh, int ny=nx, bool truesize=false, @@ -6606,9 +6654,9 @@ following routines: [./vectorfield] 15. The following scientific graphs, which illustrate many features of - 'Asymptote''s graphics routines, were generated from the examples - 'diatom.asy' and 'westnile.asy', using the comma-separated data in - 'diatom.csv' and 'westnile.csv'. + ‘Asymptote’’s graphics routines, were generated from the examples + ‘diatom.asy’ and ‘westnile.asy’, using the comma-separated data in + ‘diatom.csv’ and ‘westnile.csv’. [./diatom] @@ -6618,46 +6666,46 @@ following routines: File: asymptote.info, Node: palette, Next: three, Prev: graph, Up: Base modules -8.27 'palette' +8.27 ‘palette’ ============== -'Asymptote' can also generate color density images and palettes. The -following palettes are predefined in 'palette.asy': +‘Asymptote’ can also generate color density images and palettes. The +following palettes are predefined in ‘palette.asy’: -'pen[] Grayscale(int NColors=256)' +‘pen[] Grayscale(int NColors=256)’ a grayscale palette; -'pen[] Rainbow(int NColors=32766)' +‘pen[] Rainbow(int NColors=32766)’ a rainbow spectrum; -'pen[] BWRainbow(int NColors=32761)' +‘pen[] BWRainbow(int NColors=32761)’ a rainbow spectrum tapering off to black/white at the ends; -'pen[] BWRainbow2(int NColors=32761)' +‘pen[] BWRainbow2(int NColors=32761)’ a double rainbow palette tapering off to black/white at the ends, with a linearly scaled intensity. -'pen[] Wheel(int NColors=32766)' +‘pen[] Wheel(int NColors=32766)’ a full color wheel palette; -'pen[] Gradient(int NColors=256 ... pen[] p)' +‘pen[] Gradient(int NColors=256 ... pen[] p)’ a palette varying linearly over the specified array of pens, using NColors in each interpolation interval; - The function 'cmyk(pen[] Palette)' may be used to convert any of + The function ‘cmyk(pen[] Palette)’ may be used to convert any of these palettes to the CMYK colorspace. - A color density plot using palette 'palette' can be generated from a -function 'f'(x,y) and added to a picture 'pic': + A color density plot using palette ‘palette’ can be generated from a +function ‘f’(x,y) and added to a picture ‘pic’: bounds image(picture pic=currentpicture, real f(real, real), range range=Full, pair initial, pair final, int nx=ngraph, int ny=nx, pen[] palette, int divs=0, bool antialias=false) - The function 'f' will be sampled at 'nx' and 'ny' evenly spaced -points over a rectangle defined by the points 'initial' and 'final', -respecting the current graphical scaling of 'pic'. The color space is + The function ‘f’ will be sampled at ‘nx’ and ‘ny’ evenly spaced +points over a rectangle defined by the points ‘initial’ and ‘final’, +respecting the current graphical scaling of ‘pic’. The color space is scaled according to the z axis scaling (*note automatic scaling::). If -'divs' > 1, the palette is quantized to 'divs'-1 values. A 'bounds' +‘divs’ > 1, the palette is quantized to ‘divs’-1 values. A ‘bounds’ structure for the function values is returned: struct bounds { real min; @@ -6667,16 +6715,16 @@ struct bounds { } This information can be used for generating an optional palette bar. The palette color space corresponds to a range of values specified by -the argument 'range', which can be 'Full', 'Automatic', or an explicit -range 'Range(real min, real max)'. Here 'Full' specifies a range +the argument ‘range’, which can be ‘Full’, ‘Automatic’, or an explicit +range ‘Range(real min, real max)’. Here ‘Full’ specifies a range varying from the minimum to maximum values of the function over the -sampling interval, while 'Automatic' selects "nice" limits. The -examples 'fillcontour.asy' and 'imagecontour.asy' illustrate how level +sampling interval, while ‘Automatic’ selects "nice" limits. The +examples ‘fillcontour.asy’ and ‘imagecontour.asy’ illustrate how level sets (contour lines) can be drawn on a color density plot (*note contour::). A color density plot can also be generated from an explicit real[][] -array 'data': +array ‘data’: bounds image(picture pic=currentpicture, real[][] f, range range=Full, pair initial, pair final, pen[] palette, int divs=0, bool transpose=(initial.x < final.x && initial.y < final.y), @@ -6687,7 +6735,7 @@ convention (first index: x, second index: y) rather than the usual matrix convention (first index: -y, second index: x). To construct an image from an array of irregularly spaced points and -an array of values 'f' at these points, use one of the routines +an array of values ‘f’ at these points, use one of the routines bounds image(picture pic=currentpicture, pair[] z, real[] f, range range=Full, pen[] palette) bounds image(picture pic=currentpicture, real[] x, real[] y, real[] f, @@ -6698,11 +6746,11 @@ void palette(picture pic=currentpicture, Label L="", bounds bounds, pair initial, pair final, axis axis=Right, pen[] palette, pen p=currentpen, paletteticks ticks=PaletteTicks, bool copy=true, bool antialias=false); - The color space of 'palette' is taken to be over bounds 'bounds' with -scaling given by the z scaling of 'pic'. The palette orientation is -specified by 'axis', which may be one of 'Right', 'Left', 'Top', or -'Bottom'. The bar is drawn over the rectangle from 'initial' to -'final'. The argument 'paletteticks' is a special tick type (*note + The color space of ‘palette’ is taken to be over bounds ‘bounds’ with +scaling given by the z scaling of ‘pic’. The palette orientation is +specified by ‘axis’, which may be one of ‘Right’, ‘Left’, ‘Top’, or +‘Bottom’. The bar is drawn over the rectangle from ‘initial’ to +‘final’. The argument ‘paletteticks’ is a special tick type (*note ticks::) that takes the following arguments: paletteticks PaletteTicks(Label format="", ticklabel ticklabel=null, bool beginlabel=true, bool endlabel=true, @@ -6765,7 +6813,7 @@ palette("$f(x,y)$",range,(0,200),(100,250),Top,Palette, [./logimage] One can also draw an image directly from a two-dimensional pen array -or a function 'pen f(int, int)': +or a function ‘pen f(int, int)’: void image(picture pic=currentpicture, pen[][] data, pair initial, pair final, bool transpose=(initial.x < final.x && initial.y < final.y), @@ -6823,7 +6871,7 @@ image(f,N,N,(0,0),(300,300),antialias=true); [./penfunctionimage] - For convenience, the module 'palette' also defines functions that may + For convenience, the module ‘palette’ also defines functions that may be used to construct a pen array from a given function and palette: pen[] palette(real[] f, pen[] palette); pen[][] palette(real[][] f, pen[] palette); @@ -6831,18 +6879,18 @@ pen[][] palette(real[][] f, pen[] palette); File: asymptote.info, Node: three, Next: obj, Prev: palette, Up: Base modules -8.28 'three' +8.28 ‘three’ ============ -This module fully extends the notion of guides and paths in 'Asymptote' +This module fully extends the notion of guides and paths in ‘Asymptote’ to three dimensions. It introduces the new types guide3, path3, and surface. Guides in three dimensions are specified with the same syntax -as in two dimensions except that triples '(x,y,z)' are used in place of -pairs '(x,y)' for the nodes and direction specifiers. This -generalization of John Hobby's spline algorithm is shape-invariant under +as in two dimensions except that triples ‘(x,y,z)’ are used in place of +pairs ‘(x,y)’ for the nodes and direction specifiers. This +generalization of John Hobby’s spline algorithm is shape-invariant under three-dimensional rotation, scaling, and shifting, and reduces in the -planar case to the two-dimensional algorithm used in 'Asymptote', -'MetaPost', and 'MetaFont' [cf. J. C. Bowman, Proceedings in Applied +planar case to the two-dimensional algorithm used in ‘Asymptote’, +‘MetaPost’, and ‘MetaFont’ [cf. J. C. Bowman, Proceedings in Applied Mathematics and Mechanics, 7:1, 2010021-2010022 (2007)]. For example, a unit circle in the XY plane may be filled and drawn @@ -6869,13 +6917,13 @@ dot(g,red); [./saddle] - Module 'three' provides constructors for converting two-dimensional + Module ‘three’ provides constructors for converting two-dimensional paths to three-dimensional ones, and vice-versa: path3 path3(path p, triple plane(pair)=XYplane); path path(path3 p, pair P(triple)=xypart); A Bezier surface, the natural two-dimensional generalization of -Bezier curves, is defined in 'three_surface.asy' as a structure +Bezier curves, is defined in ‘three_surface.asy’ as a structure containing an array of Bezier patches. Surfaces may drawn with one of the routines void draw(picture pic=currentpicture, surface s, int nu=1, int nv=1, @@ -6891,10 +6939,10 @@ void draw(picture pic=currentpicture, surface s, int nu=1, int nv=1, light light=currentlight, light meshlight=nolight, string name="", render render=defaultrender); - The parameters 'nu' and 'nv' specify the number of subdivisions for -drawing optional mesh lines for each Bezier patch. The optional 'name' + The parameters ‘nu’ and ‘nv’ specify the number of subdivisions for +drawing optional mesh lines for each Bezier patch. The optional ‘name’ parameter is used as a prefix for naming the surface patches in the PRC -model tree. Here material is a structure defined in 'three_light.asy': +model tree. Here material is a structure defined in ‘three_light.asy’: struct material { pen[] p; // diffusepen,emissivepen,specularpen real opacity; @@ -6903,8 +6951,8 @@ struct material { real fresnel0; } These material properties are used to implement physically based -rendering (PBR) using light properties defined in 'plain_prethree.asy' -and 'three_light.asy': +rendering (PBR) using light properties defined in ‘plain_prethree.asy’ +and ‘three_light.asy’: struct light { real[][] diffuse; real[][] specular; @@ -6925,38 +6973,38 @@ light Headlamp=light(gray(0.8),specular=gray(0.7), currentlight=Headlamp; light nolight; - The 'currentlight.background' (or 'background' member of the -specified 'light') can be used to set the background colour for 2D (or -3D) images. The default background is white for 'HTML' images and + The ‘currentlight.background’ (or ‘background’ member of the +specified ‘light’) can be used to set the background colour for 2D (or +3D) images. The default background is white for ‘HTML’ images and transparent for all other formats. One can request a completely -transparent background for 3D 'WebGL' images with -'currentlight.background=black+opacity(0.0);' +transparent background for 3D ‘WebGL’ images with +‘currentlight.background=black+opacity(0.0);’ Asymptote also supports image-based lighting with the setting -'settings.ibl=true'. This uses pre-rendered EXR images from the -directory specified by '-imageDir' (which defaults to 'ibl') or, for -'WebGL' rendering, the URL specified by '-imageURL' (which defaults to +‘settings.ibl=true’. This uses pre-rendered EXR images from the +directory specified by ‘-imageDir’ (which defaults to ‘ibl’) or, for +‘WebGL’ rendering, the URL specified by ‘-imageURL’ (which defaults to <https://vectorgraphics.gitlab.io/asymptote/ibl>). Additional rendered -images can be generated on an 'NVIDIA' GPU using the 'reflect' program -in the 'cudareflect' subdirectory of the 'Asymptote' source directory. +images can be generated on an ‘NVIDIA’ GPU using the ‘reflect’ program +in the ‘cudareflect’ subdirectory of the ‘Asymptote’ source directory. Sample Bezier surfaces are contained in the example files -'BezierSurface.asy', 'teapot.asy', 'teapotIBL.asy', and -'parametricsurface.asy'. +‘BezierSurface.asy’, ‘teapot.asy’, ‘teapotIBL.asy’, and +‘parametricsurface.asy’. - The structure 'render' contains specialized rendering options -documented at the beginning of module 'three'. + The structure ‘render’ contains specialized rendering options +documented at the beginning of module ‘three’. - The examples 'elevation.asy' and 'sphericalharmonic.asy' illustrate + The examples ‘elevation.asy’ and ‘sphericalharmonic.asy’ illustrate how to draw a surface with patch-dependent colors. The examples -'vertexshading.asy' and 'smoothelevation.asy' illustrate -vertex-dependent colors, which are supported by 'Asymptote''s native -'OpenGL'/'WebGL' renderers and the two-dimensional vector output format -('settings.render=0'). Since the PRC output format does not currently +‘vertexshading.asy’ and ‘smoothelevation.asy’ illustrate +vertex-dependent colors, which are supported by ‘Asymptote’’s native +‘OpenGL’/‘WebGL’ renderers and the two-dimensional vector output format +(‘settings.render=0’). Since the PRC output format does not currently support vertex shading of Bezier surfaces, PRC patches are shaded with the mean of the four vertex colors. - A surface can be constructed from a cyclic 'path3' with the + A surface can be constructed from a cyclic ‘path3’ with the constructor surface surface(path3 external, triple[] internal=new triple[], pen[] colors=new pen[], bool3 planar=default); @@ -6969,16 +7017,16 @@ draw(surface(unitcircle3,new pen[] {red,green,blue,black}),nolight); The first example draws a Bezier patch and the second example draws a Bezier triangle. The third and fourth examples are planar surfaces. The last example constructs a patch with vertex-specific colors. A -three-dimensional planar surface in the plane 'plane' can be constructed -from a two-dimensional cyclic path 'g' with the constructor +three-dimensional planar surface in the plane ‘plane’ can be constructed +from a two-dimensional cyclic path ‘g’ with the constructor surface surface(path p, triple plane(pair)=XYplane); and then filled: draw(surface((0,0)--E+2N--2E--E+N..0.2E..cycle),red); -Planar Bezier surfaces patches are constructed using Orest Shardt's -'bezulate' routine, which decomposes (possibly nonsimply connected) -regions bounded (according to the 'zerowinding' fill rule) by simple +Planar Bezier surfaces patches are constructed using Orest Shardt’s +‘bezulate’ routine, which decomposes (possibly nonsimply connected) +regions bounded (according to the ‘zerowinding’ fill rule) by simple cyclic paths (intersecting only at the endpoints) into subregions -bounded by cyclic paths of length '4' or less. +bounded by cyclic paths of length ‘4’ or less. A more efficient routine also exists for drawing tessellations composed of many 3D triangles, with specified vertices, and optional @@ -6986,40 +7034,40 @@ normals or vertex colors: void draw(picture pic=currentpicture, triple[] v, int[][] vi, triple[] n={}, int[][] ni=vi, material m=currentpen, pen[] p={}, int[][] pi=vi, light light=currentlight); - Here, the triple array 'v' lists the (typically distinct) vertices, -while the array 'vi' contains integer arrays of length 3 containing the -indices of the elements in 'v' that form the vertices of each triangle. -Similarly, the arguments 'n' and 'ni' contain optional normal data and -'p' and 'pi' contain optional pen vertex data. If more than one normal + Here, the triple array ‘v’ lists the (typically distinct) vertices, +while the array ‘vi’ contains integer arrays of length 3 containing the +indices of the elements in ‘v’ that form the vertices of each triangle. +Similarly, the arguments ‘n’ and ‘ni’ contain optional normal data and +‘p’ and ‘pi’ contain optional pen vertex data. If more than one normal or pen is specified for a vertex, the last one is used. An example of -this tessellation facility is given in 'triangles.asy'. +this tessellation facility is given in ‘triangles.asy’. Arbitrary thick three-dimensional curves and line caps (which the -'OpenGL' standard does not require implementations to provide) are +‘OpenGL’ standard does not require implementations to provide) are constructed with tube tube(path3 p, real width, render render=defaultrender); -this returns a tube structure representing a tube of diameter 'width' -centered approximately on 'g'. The tube structure consists of a surface -'s' and the actual tube center, path3 'center'. Drawing thick lines as -tubes can be slow to render, especially with the 'Adobe Reader' -renderer. The setting 'thick=false' can be used to disable this feature -and force all lines to be drawn with 'linewidth(0)' (one pixel wide, +this returns a tube structure representing a tube of diameter ‘width’ +centered approximately on ‘g’. The tube structure consists of a surface +‘s’ and the actual tube center, path3 ‘center’. Drawing thick lines as +tubes can be slow to render, especially with the ‘Adobe Reader’ +renderer. The setting ‘thick=false’ can be used to disable this feature +and force all lines to be drawn with ‘linewidth(0)’ (one pixel wide, regardless of the resolution). By default, mesh and contour lines in three-dimensions are always drawn thin, unless an explicit line width is -given in the pen parameter or the setting 'thin' is set to 'false'. The -pens 'thin()' and 'thick()' defined in 'plain_pens.asy' can also be used +given in the pen parameter or the setting ‘thin’ is set to ‘false’. The +pens ‘thin()’ and ‘thick()’ defined in ‘plain_pens.asy’ can also be used to override these defaults for specific draw commands. -There are six choices for viewing 3D 'Asymptote' output: +There are six choices for viewing 3D ‘Asymptote’ output: - 1. Use the native 'Asymptote' adaptive 'OpenGL'-based renderer (with - the command-line option '-V' and the default settings - 'outformat=""' and 'render=-1'). On 'UNIX' systems with graphics + 1. Use the native ‘Asymptote’ adaptive ‘OpenGL’-based renderer (with + the command-line option ‘-V’ and the default settings + ‘outformat=""’ and ‘render=-1’). On ‘UNIX’ systems with graphics support for multisampling, the sample width can be controlled with - the setting 'multisample'. The ratio of physical to logical screen - pixels can be specified with the setting 'devicepixelratio'. An + the setting ‘multisample’. The ratio of physical to logical screen + pixels can be specified with the setting ‘devicepixelratio’. An initial screen position can be specified with the pair setting - 'position', where negative values are interpreted as relative to + ‘position’, where negative values are interpreted as relative to the corresponding maximum screen dimension. The default settings import settings; leftbutton=new string[] {"rotate","zoom","shift","pan"}; @@ -7028,120 +7076,130 @@ There are six choices for viewing 3D 'Asymptote' output: wheelup=new string[] {"zoomin"}; wheeldown=new string[] {"zoomout"}; bind the mouse buttons as follows: - * Left: rotate - * Shift Left: zoom - * Ctrl Left: shift viewport - * Alt Left: pan - * Wheel Up: zoom in - * Wheel Down: zoom out - * Right: zoom - * Shift Right: rotate about the X axis - * Ctrl Right: rotate about the Y axis - * Alt Right: rotate about the Z axis + • Left: rotate + • Shift Left: zoom + • Ctrl Left: shift viewport + • Alt Left: pan + • Wheel Up: zoom in + • Wheel Down: zoom out + • Right: zoom + • Shift Right: rotate about the X axis + • Ctrl Right: rotate about the Y axis + • Alt Right: rotate about the Z axis The keyboard bindings are: - * h: home - * f: toggle fitscreen - * x: spin about the X axis - * y: spin about the Y axis - * z: spin about the Z axis - * s: stop spinning - * m: rendering mode (solid/patch/mesh) - * e: export - * c: show camera parameters - * p: play animation - * r: reverse animation - * : step animation - * +: expand - * =: expand - * >: expand - * -: shrink - * _: shrink - * <: shrink - * q: exit - * Ctrl-q: exit - - 2. Generate 'WebGL' interactive vector graphics output with the the - command-line option and '-f html' (or the setting - 'outformat="html"'). The resulting 3D HTML file can then be viewed + • h: home + • f: toggle fitscreen + • x: spin about the X axis + • y: spin about the Y axis + • z: spin about the Z axis + • s: stop spinning + • m: rendering mode (solid/patch/mesh) + • e: export + • c: show camera parameters + • p: play animation + • r: reverse animation + • : step animation + • +: expand + • =: expand + • >: expand + • -: shrink + • _: shrink + • <: shrink + • q: exit + • Ctrl-q: exit + + 2. Generate ‘WebGL’ interactive vector graphics output with the the + command-line option and ‘-f html’ (or the setting + ‘outformat="html"’). The resulting 3D HTML file can then be viewed directly in any modern desktop or mobile browser, or even embedded within another web page: <iframe src="logo3.html" width="561" height="321" frameborder="0"> </iframe> - Normally, 'WebGL' files generated by 'Asymptote' are dynamically + Normally, ‘WebGL’ files generated by ‘Asymptote’ are dynamically remeshed to fit the browser window dimensions. However, the - setting 'absolute=true' can be used to force the image to be + setting ‘absolute=true’ can be used to force the image to be rendered at its designed size (accounting for multiple device - pixels per 'css' pixel). + pixels per ‘css’ pixel). - The interactive 'WebGL' files produced by 'Asymptote' use the - default mouse and (many of the same) key bindings as the 'OpenGL' - renderer. Zooming via the mouse wheel of a 'WebGL' image embedded + The interactive ‘WebGL’ files produced by ‘Asymptote’ use the + default mouse and (many of the same) key bindings as the ‘OpenGL’ + renderer. Zooming via the mouse wheel of a ‘WebGL’ image embedded within another page is disabled until the image is activated by a - click or touch event and will remain enabled until the 'ESC' key is + click or touch event and will remain enabled until the ‘ESC’ key is pressed. By default, viewing the 3D HTML files generated by Asymptote - requires network access to download the 'AsyGL' rendering library, + requires network access to download the ‘AsyGL’ rendering library, which is normally cached by the browser for future use. However, - the setting 'offline=true' can be used to embed this small (about + the setting ‘offline=true’ can be used to embed this small (about 48kB) library within a stand-alone HTML file that can be viewed offline. - 3. Render the scene to a specified rasterized format 'outformat' at - the resolution of 'n' pixels per 'bp', as specified by the setting - 'render=n'. A negative value of 'n' is interpreted as '|2n|' for - EPS and PDF formats and '|n|' for other formats. The default value - of 'render' is -1. By default, the scene is internally rendered at + 3. Render the scene to a specified rasterized format ‘outformat’ at + the resolution of ‘n’ pixels per ‘bp’, as specified by the setting + ‘render=n’. A negative value of ‘n’ is interpreted as ‘|2n|’ for + EPS and PDF formats and ‘|n|’ for other formats. The default value + of ‘render’ is -1. By default, the scene is internally rendered at twice the specified resolution; this can be disabled by setting - 'antialias=1'. High resolution rendering is done by tiling the + ‘antialias=1’. High resolution rendering is done by tiling the image. If your graphics card allows it, the rendering can be made - more efficient by increasing the maximum tile size 'maxtile' to - your screen dimensions (indicated by 'maxtile=(0,0)'. If your + more efficient by increasing the maximum tile size ‘maxtile’ to + your screen dimensions (indicated by ‘maxtile=(0,0)’. If your video card generates unwanted black stripes in the output, try - setting the horizontal and vertical components of 'maxtiles' to + setting the horizontal and vertical components of ‘maxtiles’ to something less than your screen dimensions. The tile size is also - limited by the setting 'maxviewport', which restricts the maximum + limited by the setting ‘maxviewport’, which restricts the maximum width and height of the viewport. Some graphics drivers support - batch mode ('-noV') rendering in an iconified window; this can be - enabled with the setting 'iconify=true'. + batch mode (‘-noV’) rendering in an iconified window; this can be + enabled with the setting ‘iconify=true’. 4. Embed the 3D PRC format in a PDF file and view the resulting PDF - file with version '9.0' or later of 'Adobe Reader'. This requires - 'settings.outformat="pdf"' and 'settings.prc=true', which can be - specified by the command-line options '-f pdf' and '-f prc', put in - the 'Asymptote' configuration file (*note configuration file::), or - specified in the script before module 'three' (or 'graph3') is - imported. The 'media9' LaTeX package is also required (*note - embed::). The example '100d.asy' illustrates how one can generate - a list of predefined views (see '100d.views'). A stationary - preview image with a resolution of 'n' pixels per 'bp' can be - embedded with the setting 'render=n'; this allows the file to be - viewed with other 'PDF' viewers. Alternatively, the file - 'externalprc.tex' illustrates how the resulting PRC and rendered - image files can be extracted and processed in a separate 'LaTeX' + file with version ‘9.0’ or later of ‘Adobe Reader’. This requires + ‘settings.outformat="pdf"’ and ‘settings.prc=true’, which can be + specified by the command-line options ‘-f pdf’ and ‘-f prc’, put in + the ‘Asymptote’ configuration file (*note configuration file::), or + specified in the script before module ‘three’ (or ‘graph3’) is + imported. The ‘media9’ LaTeX package is also required (*note + embed::). The example ‘100d.asy’ illustrates how one can generate + a list of predefined views (see ‘100d.views’). A stationary + preview image with a resolution of ‘n’ pixels per ‘bp’ can be + embedded with the setting ‘render=n’; this allows the file to be + viewed with other ‘PDF’ viewers. Alternatively, the file + ‘externalprc.tex’ illustrates how the resulting PRC and rendered + image files can be extracted and processed in a separate ‘LaTeX’ file. However, see *note LaTeX usage:: for an easier way to embed - three-dimensional 'Asymptote' pictures within 'LaTeX'. For + three-dimensional ‘Asymptote’ pictures within ‘LaTeX’. For specialized applications where only the raw PRC file is required, - specify 'settings.outformat="prc"'. The PRC specification is + specify ‘settings.outformat="prc"’. The PRC specification is available from <https://web.archive.org/web/20081204104459/http://livedocs.adobe.com/acrobat_sdk/9/Acrobat9_HTMLHelp/API_References/PRCReference/PRC_Format_Specification/> - 5. Output a 'V3D' portable compressed binary file for viewing with an - external viewer or conversion to an alternate 3D format with the - Python 'pyv3d' library. The 'V3D' specification and the 'pyv3d' - library are available at <https://github.com/vectorgraphics/v3d>. - A 'V3D' file 'file.v3d' may be imported and viewed by 'Asymptote' - either by specifying 'file.v3d' on the command line + 5. Output a V3D portable compressed vector graphics file using + ‘settings.outformat="v3d"’, which can be viewed with an external + viewer or converted to an alternate 3D format using the Python + ‘pyv3d’ library. V3D content can be automatically embedded within + a PDF file using the options ‘settings.outformat="pdf"’ and + ‘settings.v3d=true’. Alternatively, a V3D file ‘file.v3d’ may be + manually embedded within a PDF file using the ‘media9’ ‘LaTeX’ + package: + \includemedia[noplaybutton,width=100pt,height=200pt]{}{file.v3d}% + An online ‘Javascript’-based V3D-aware ‘PDF’ viewer is available at + <https://github.com/vectorgraphics/pdfv3dReader>. + + The V3D specification and the ‘pyv3d’ library are available at + <https://github.com/vectorgraphics/v3d>. A V3D file ‘file.v3d’ may + be imported and viewed by ‘Asymptote’ either by specifying + ‘file.v3d’ on the command line asy -V file.v3d - or using the 'v3d' module and 'importv3d' function in interactive - mode (or within an 'Asymptote' file): + or using the ‘v3d’ module and ‘importv3d’ function in interactive + mode (or within an ‘Asymptote’ file): import v3d; importv3d("file.v3d"); 6. Project the scene to a two-dimensional vector (EPS or PDF) format - with 'render=0'. Only limited support for hidden surface removal, + with ‘render=0’. Only limited support for hidden surface removal, lighting, and transparency is available with this approach (*note PostScript3D::). @@ -7154,121 +7212,121 @@ void size3(picture pic=currentpicture, real x, real y=x, real z=y, A simplex linear programming problem is then solved to produce a 3D version of a frame (actually implemented as a 3D picture). The result is then fit with another application of deferred drawing to the viewport -dimensions corresponding to the usual two-dimensional picture 'size' -parameters. The global pair 'viewportmargin' may be used to add +dimensions corresponding to the usual two-dimensional picture ‘size’ +parameters. The global pair ‘viewportmargin’ may be used to add horizontal and vertical margins to the viewport dimensions. -Alternatively, a minimum 'viewportsize' may be specified. A 3D picture -'pic' can be explicitly fit to a 3D frame by calling +Alternatively, a minimum ‘viewportsize’ may be specified. A 3D picture +‘pic’ can be explicitly fit to a 3D frame by calling frame pic.fit3(projection P=currentprojection); -and then added to picture 'dest' about 'position' with +and then added to picture ‘dest’ about ‘position’ with void add(picture dest=currentpicture, frame src, triple position=(0,0,0)); - For convenience, the 'three' module defines 'O=(0,0,0)', 'X=(1,0,0)', -'Y=(0,1,0)', and 'Z=(0,0,1)', along with a unitcircle in the XY plane: + For convenience, the ‘three’ module defines ‘O=(0,0,0)’, ‘X=(1,0,0)’, +‘Y=(0,1,0)’, and ‘Z=(0,0,1)’, along with a unitcircle in the XY plane: path3 unitcircle3=X..Y..-X..-Y..cycle; A general (approximate) circle can be drawn perpendicular to the -direction 'normal' with the routine +direction ‘normal’ with the routine path3 circle(triple c, real r, triple normal=Z); - A circular arc centered at 'c' with radius 'r' from -'c+r*dir(theta1,phi1)' to 'c+r*dir(theta2,phi2)', drawing + A circular arc centered at ‘c’ with radius ‘r’ from +‘c+r*dir(theta1,phi1)’ to ‘c+r*dir(theta2,phi2)’, drawing counterclockwise relative to the normal vector -'cross(dir(theta1,phi1),dir(theta2,phi2))' if 'theta2 > theta1' or if -'theta2 == theta1' and 'phi2 >= phi1', can be constructed with +‘cross(dir(theta1,phi1),dir(theta2,phi2))’ if ‘theta2 > theta1’ or if +‘theta2 == theta1’ and ‘phi2 >= phi1’, can be constructed with path3 arc(triple c, real r, real theta1, real phi1, real theta2, real phi2, triple normal=O); - The normal must be explicitly specified if 'c' and the endpoints are -colinear. If 'r' < 0, the complementary arc of radius '|r|' is -constructed. For convenience, an arc centered at 'c' from triple 'v1' -to 'v2' (assuming '|v2-c|=|v1-c|') in the direction CCW + The normal must be explicitly specified if ‘c’ and the endpoints are +colinear. If ‘r’ < 0, the complementary arc of radius ‘|r|’ is +constructed. For convenience, an arc centered at ‘c’ from triple ‘v1’ +to ‘v2’ (assuming ‘|v2-c|=|v1-c|’) in the direction CCW (counter-clockwise) or CW (clockwise) may also be constructed with path3 arc(triple c, triple v1, triple v2, triple normal=O, bool direction=CCW); -When high accuracy is needed, the routines 'Circle' and 'Arc' defined in -'graph3' may be used instead. See *note GaussianSurface:: for an +When high accuracy is needed, the routines ‘Circle’ and ‘Arc’ defined in +‘graph3’ may be used instead. See *note GaussianSurface:: for an example of a three-dimensional circular arc. - The representation 'O--O+u--O+u+v--O+v--cycle' of the plane passing -through point 'O' with normal 'cross(u,v)' is returned by + The representation ‘O--O+u--O+u+v--O+v--cycle’ of the plane passing +through point ‘O’ with normal ‘cross(u,v)’ is returned by path3 plane(triple u, triple v, triple O=O); - A three-dimensional box with opposite vertices at triples 'v1' and -'v2' may be drawn with the function + A three-dimensional box with opposite vertices at triples ‘v1’ and +‘v2’ may be drawn with the function path3[] box(triple v1, triple v2); For example, a unit box is predefined as path3[] unitbox=box(O,(1,1,1)); - 'Asymptote' also provides optimized definitions for the -three-dimensional paths 'unitsquare3' and 'unitcircle3', along with the -surfaces 'unitdisk', 'unitplane', 'unitcube', 'unitcylinder', -'unitcone', 'unitsolidcone', 'unitfrustum(real t1, real t2)', -'unitsphere', and 'unithemisphere'. + ‘Asymptote’ also provides optimized definitions for the +three-dimensional paths ‘unitsquare3’ and ‘unitcircle3’, along with the +surfaces ‘unitdisk’, ‘unitplane’, ‘unitcube’, ‘unitcylinder’, +‘unitcone’, ‘unitsolidcone’, ‘unitfrustum(real t1, real t2)’, +‘unitsphere’, and ‘unithemisphere’. These projections to two dimensions are predefined: -'oblique' -'oblique(real angle)' - The point '(x,y,z)' is projected to '(x-0.5z,y-0.5z)'. If an +‘oblique’ +‘oblique(real angle)’ + The point ‘(x,y,z)’ is projected to ‘(x-0.5z,y-0.5z)’. If an optional real argument is given, the negative z axis is drawn at - this angle in degrees. The projection 'obliqueZ' is a synonym for - 'oblique'. + this angle in degrees. The projection ‘obliqueZ’ is a synonym for + ‘oblique’. -'obliqueX' -'obliqueX(real angle)' - The point '(x,y,z)' is projected to '(y-0.5x,z-0.5x)'. If an +‘obliqueX’ +‘obliqueX(real angle)’ + The point ‘(x,y,z)’ is projected to ‘(y-0.5x,z-0.5x)’. If an optional real argument is given, the negative x axis is drawn at this angle in degrees. -'obliqueY' -'obliqueY(real angle)' - The point '(x,y,z)' is projected to '(x+0.5y,z+0.5y)'. If an +‘obliqueY’ +‘obliqueY(real angle)’ + The point ‘(x,y,z)’ is projected to ‘(x+0.5y,z+0.5y)’. If an optional real argument is given, the positive y axis is drawn at this angle in degrees. -'orthographic(triple camera, triple up=Z, triple target=O, +‘orthographic(triple camera, triple up=Z, triple target=O, real zoom=1, pair viewportshift=0, bool showtarget=true, - bool center=false)' + bool center=false)’ This projects from three to two dimensions using the view as seen - at a point infinitely far away in the direction 'unit(camera)', - orienting the camera so that, if possible, the vector 'up' points + at a point infinitely far away in the direction ‘unit(camera)’, + orienting the camera so that, if possible, the vector ‘up’ points upwards. Parallel lines are projected to parallel lines. The - bounding volume is expanded to include 'target' if - 'showtarget=true'. If 'center=true', the target will be adjusted + bounding volume is expanded to include ‘target’ if + ‘showtarget=true’. If ‘center=true’, the target will be adjusted to the center of the bounding volume. -'orthographic(real x, real y, real z, triple up=Z, triple target=O, +‘orthographic(real x, real y, real z, triple up=Z, triple target=O, real zoom=1, pair viewportshift=0, bool showtarget=true, - bool center=false)' + bool center=false)’ This is equivalent to orthographic((x,y,z),up,target,zoom,viewportshift,showtarget,center) The routine triple camera(real alpha, real beta); can be used to compute the camera position with the x axis below - the horizontal at angle 'alpha', the y axis below the horizontal at - angle 'beta', and the z axis up. + the horizontal at angle ‘alpha’, the y axis below the horizontal at + angle ‘beta’, and the z axis up. -'perspective(triple camera, triple up=Z, triple target=O, +‘perspective(triple camera, triple up=Z, triple target=O, real zoom=1, real angle=0, pair viewportshift=0, bool showtarget=true, bool autoadjust=true, - bool center=autoadjust)' + bool center=autoadjust)’ This projects from three to two dimensions, taking account of - perspective, as seen from the location 'camera' looking at - 'target', orienting the camera so that, if possible, the vector - 'up' points upwards. If 'autoadjust=true', the camera will + perspective, as seen from the location ‘camera’ looking at + ‘target’, orienting the camera so that, if possible, the vector + ‘up’ points upwards. If ‘autoadjust=true’, the camera will automatically be adjusted to lie outside the bounding volume for - all possible interactive rotations about 'target'. If - 'center=true', the target will be adjusted to the center of the + all possible interactive rotations about ‘target’. If + ‘center=true’, the target will be adjusted to the center of the bounding volume. -'perspective(real x, real y, real z, triple up=Z, triple target=O, +‘perspective(real x, real y, real z, triple up=Z, triple target=O, real zoom=1, real angle=0, pair viewportshift=0, bool showtarget=true, bool autoadjust=true, - bool center=autoadjust)' + bool center=autoadjust)’ This is equivalent to perspective((x,y,z),up,target,zoom,angle,viewportshift,showtarget, autoadjust,center) -The default projection, 'currentprojection', is initially set to -'perspective(5,4,2)'. +The default projection, ‘currentprojection’, is initially set to +‘perspective(5,4,2)’. We also define standard orthographic views used in technical drawing: projection LeftView=orthographic(-X,showtarget=true); @@ -7281,10 +7339,10 @@ The function void addViews(picture dest=currentpicture, picture src, projection[][] views=SixViewsUS, bool group=true, filltype filltype=NoFill); -adds to picture 'dest' an array of views of picture 'src' using the -layout projection[][] 'views'. The default layout 'SixViewsUS' aligns -the projection 'FrontView' below 'TopView' and above 'BottomView', to -the right of 'LeftView' and left of 'RightView' and 'BackView'. The +adds to picture ‘dest’ an array of views of picture ‘src’ using the +layout projection[][] ‘views’. The default layout ‘SixViewsUS’ aligns +the projection ‘FrontView’ below ‘TopView’ and above ‘BottomView’, to +the right of ‘LeftView’ and left of ‘RightView’ and ‘BackView’. The predefined layouts are: projection[][] ThreeViewsUS={{TopView}, {FrontView,RightView}}; @@ -7307,44 +7365,44 @@ projection[][] SixViews={{FrontView,TopView,RightView}, A triple or path3 can be projected to a pair or path, with -'project(triple, projection P=currentprojection)' or 'project(path3, -projection P=currentprojection)'. +‘project(triple, projection P=currentprojection)’ or ‘project(path3, +projection P=currentprojection)’. It is occasionally useful to be able to invert a projection, sending -a pair 'z' onto the plane perpendicular to 'normal' and passing through -'point': +a pair ‘z’ onto the plane perpendicular to ‘normal’ and passing through +‘point’: triple invert(pair z, triple normal, triple point, projection P=currentprojection); -A pair 'z' on the projection plane can be inverted to a triple with the +A pair ‘z’ on the projection plane can be inverted to a triple with the routine triple invert(pair z, projection P=currentprojection); -A pair direction 'dir' on the projection plane can be inverted to a -triple direction relative to a point 'v' with the routine +A pair direction ‘dir’ on the projection plane can be inverted to a +triple direction relative to a point ‘v’ with the routine triple invert(pair dir, triple v, projection P=currentprojection). Three-dimensional objects may be transformed with one of the following built-in transform3 types (the identity transformation is -'identity4'): - -'shift(triple v)' - translates by the triple 'v'; -'xscale3(real x)' - scales by 'x' in the x direction; -'yscale3(real y)' - scales by 'y' in the y direction; -'zscale3(real z)' - scales by 'z' in the z direction; -'scale3(real s)' - scales by 's' in the x, y, and z directions; -'scale(real x, real y, real z)' - scales by 'x' in the x direction, by 'y' in the y direction, and by - 'z' in the z direction; -'rotate(real angle, triple v)' - rotates by 'angle' in degrees about the axis 'O--v'; -'rotate(real angle, triple u, triple v)' - rotates by 'angle' in degrees about the axis 'u--v'; -'reflect(triple u, triple v, triple w)' - reflects about the plane through 'u', 'v', and 'w'. +‘identity4’): + +‘shift(triple v)’ + translates by the triple ‘v’; +‘xscale3(real x)’ + scales by ‘x’ in the x direction; +‘yscale3(real y)’ + scales by ‘y’ in the y direction; +‘zscale3(real z)’ + scales by ‘z’ in the z direction; +‘scale3(real s)’ + scales by ‘s’ in the x, y, and z directions; +‘scale(real x, real y, real z)’ + scales by ‘x’ in the x direction, by ‘y’ in the y direction, and by + ‘z’ in the z direction; +‘rotate(real angle, triple v)’ + rotates by ‘angle’ in degrees about the axis ‘O--v’; +‘rotate(real angle, triple u, triple v)’ + rotates by ‘angle’ in degrees about the axis ‘u--v’; +‘reflect(triple u, triple v, triple w)’ + reflects about the plane through ‘u’, ‘v’, and ‘w’. When not multiplied on the left by a transform3, three-dimensional TeX Labels are drawn as Bezier surfaces directly on the projection @@ -7354,70 +7412,70 @@ void label(picture pic=currentpicture, Label L, triple position, light light=nolight, string name="", render render=defaultrender, interaction interaction= settings.autobillboard ? Billboard : Embedded) -The optional 'name' parameter is used as a prefix for naming the label -patches in the PRC model tree. The default interaction is 'Billboard', +The optional ‘name’ parameter is used as a prefix for naming the label +patches in the PRC model tree. The default interaction is ‘Billboard’, which means that labels are rotated interactively so that they always -face the camera. The interaction 'Embedded' means that the label -interacts as a normal '3D' surface, as illustrated in the example -'billboard.asy'. Alternatively, a label can be transformed from the -'XY' plane by an explicit transform3 or mapped to a specified -two-dimensional plane with the predefined transform3 types 'XY', 'YZ', -'ZX', 'YX', 'ZY', 'ZX'. There are also modified versions of these -transforms that take an optional argument 'projection -P=currentprojection' that rotate and/or flip the label so that it is +face the camera. The interaction ‘Embedded’ means that the label +interacts as a normal ‘3D’ surface, as illustrated in the example +‘billboard.asy’. Alternatively, a label can be transformed from the +‘XY’ plane by an explicit transform3 or mapped to a specified +two-dimensional plane with the predefined transform3 types ‘XY’, ‘YZ’, +‘ZX’, ‘YX’, ‘ZY’, ‘ZX’. There are also modified versions of these +transforms that take an optional argument ‘projection +P=currentprojection’ that rotate and/or flip the label so that it is more readable from the initial viewpoint. - A transform3 that projects in the direction 'dir' onto the plane with -normal 'n' through point 'O' is returned by + A transform3 that projects in the direction ‘dir’ onto the plane with +normal ‘n’ through point ‘O’ is returned by transform3 planeproject(triple n, triple O=O, triple dir=n); One can use triple normal(path3 p); -to find the unit normal vector to a planar three-dimensional path 'p'. -As illustrated in the example 'planeproject.asy', a transform3 that -projects in the direction 'dir' onto the plane defined by a planar path -'p' is returned by +to find the unit normal vector to a planar three-dimensional path ‘p’. +As illustrated in the example ‘planeproject.asy’, a transform3 that +projects in the direction ‘dir’ onto the plane defined by a planar path +‘p’ is returned by transform3 planeproject(path3 p, triple dir=normal(p)); The functions surface extrude(path p, triple axis=Z); surface extrude(Label L, triple axis=Z); -return the surface obtained by extruding path 'p' or Label 'L' along -'axis'. +return the surface obtained by extruding path ‘p’ or Label ‘L’ along +‘axis’. - Three-dimensional versions of the path functions 'length', 'size', -'point', 'dir', 'accel', 'radius', 'precontrol', 'postcontrol', -'arclength', 'arctime', 'reverse', 'subpath', 'intersect', -'intersections', 'intersectionpoint', 'intersectionpoints', 'min', -'max', 'cyclic', and 'straight' are also defined. + Three-dimensional versions of the path functions ‘length’, ‘size’, +‘point’, ‘dir’, ‘accel’, ‘radius’, ‘precontrol’, ‘postcontrol’, +‘arclength’, ‘arctime’, ‘reverse’, ‘subpath’, ‘intersect’, +‘intersections’, ‘intersectionpoint’, ‘intersectionpoints’, ‘min’, +‘max’, ‘cyclic’, and ‘straight’ are also defined. The routine real[] intersect(path3 p, surface s, real fuzz=-1); returns a real array of length 3 containing the intersection times, if -any, of a path 'p' with a surface 's'. The routine +any, of a path ‘p’ with a surface ‘s’. The routine real[][] intersections(path3 p, surface s, real fuzz=-1); returns all (unless there are infinitely many) intersection times of a -path 'p' with a surface 's' as a sorted array of real arrays of length +path ‘p’ with a surface ‘s’ as a sorted array of real arrays of length 3, and triple[] intersectionpoints(path3 p, surface s, real fuzz=-1); returns the corresponding intersection points. Here, the computations -are performed to the absolute error specified by 'fuzz', or if 'fuzz < -0', to machine precision. The routine +are performed to the absolute error specified by ‘fuzz’, or if ‘fuzz < +0’, to machine precision. The routine real orient(triple a, triple b, triple c, triple d); -is a numerically robust computation of 'dot(cross(a-d,b-d),c-d)', which +is a numerically robust computation of ‘dot(cross(a-d,b-d),c-d)’, which is the determinant |a.x a.y a.z 1| |b.x b.y b.z 1| |c.x c.y c.z 1| |d.x d.y d.z 1| - The result is negative (positive) if 'a', 'b', 'c' appear in -counterclockwise (clockwise) order when viewed from 'd' or zero if all + The result is negative (positive) if ‘a’, ‘b’, ‘c’ appear in +counterclockwise (clockwise) order when viewed from ‘d’ or zero if all four points are coplanar. The routine real insphere(triple a, triple b, triple c, triple d, triple e); -returns a positive (negative) value if 'e' lies inside (outside) the -sphere passing through points 'a,b,c,d' oriented so that -'dot(cross(a-d,b-d),c-d)' is positive, or zero if all five points are +returns a positive (negative) value if ‘e’ lies inside (outside) the +sphere passing through points ‘a,b,c,d’ oriented so that +‘dot(cross(a-d,b-d),c-d)’ is positive, or zero if all five points are cospherical. The value returned is the determinant |a.x a.y a.z a.x^2+a.y^2+a.z^2 1| |b.x b.y b.z b.x^2+b.y^2+b.z^2 1| @@ -7451,55 +7509,55 @@ yaxis3(Label(XY()*"$y$",align=-3X),red,above=true); [./join3] Three-dimensional versions of bars or arrows can be drawn with one of -the specifiers 'None', 'Blank', 'BeginBar3', 'EndBar3' (or equivalently -'Bar3'), 'Bars3', 'BeginArrow3', 'MidArrow3', 'EndArrow3' (or -equivalently 'Arrow3'), 'Arrows3', 'BeginArcArrow3', 'EndArcArrow3' (or -equivalently 'ArcArrow3'), 'MidArcArrow3', and 'ArcArrows3'. -Three-dimensional bars accept the optional arguments '(real size=0, -triple dir=O)'. If 'size=O', the default bar length is used; if -'dir=O', the bar is drawn perpendicular to the path and the initial +the specifiers ‘None’, ‘Blank’, ‘BeginBar3’, ‘EndBar3’ (or equivalently +‘Bar3’), ‘Bars3’, ‘BeginArrow3’, ‘MidArrow3’, ‘EndArrow3’ (or +equivalently ‘Arrow3’), ‘Arrows3’, ‘BeginArcArrow3’, ‘EndArcArrow3’ (or +equivalently ‘ArcArrow3’), ‘MidArcArrow3’, and ‘ArcArrows3’. +Three-dimensional bars accept the optional arguments ‘(real size=0, +triple dir=O)’. If ‘size=O’, the default bar length is used; if +‘dir=O’, the bar is drawn perpendicular to the path and the initial viewing direction. The predefined three-dimensional arrowhead styles -are 'DefaultHead3', 'HookHead3', 'TeXHead3'. Versions of the +are ‘DefaultHead3’, ‘HookHead3’, ‘TeXHead3’. Versions of the two-dimensional arrowheads lifted to three-dimensional space and aligned -according to the initial viewpoint (or an optionally specified 'normal' -vector) are also defined: 'DefaultHead2(triple normal=O)', -'HookHead2(triple normal=O)', 'TeXHead2(triple normal=O)'. These are -illustrated in the example 'arrows3.asy'. - - Module 'three' also defines the three-dimensional margins -'NoMargin3', 'BeginMargin3', 'EndMargin3', 'Margin3', 'Margins3', -'BeginPenMargin2', 'EndPenMargin2', 'PenMargin2', 'PenMargins2', -'BeginPenMargin3', 'EndPenMargin3', 'PenMargin3', 'PenMargins3', -'BeginDotMargin3', 'EndDotMargin3', 'DotMargin3', 'DotMargins3', -'Margin3', and 'TrueMargin3'. +according to the initial viewpoint (or an optionally specified ‘normal’ +vector) are also defined: ‘DefaultHead2(triple normal=O)’, +‘HookHead2(triple normal=O)’, ‘TeXHead2(triple normal=O)’. These are +illustrated in the example ‘arrows3.asy’. + + Module ‘three’ also defines the three-dimensional margins +‘NoMargin3’, ‘BeginMargin3’, ‘EndMargin3’, ‘Margin3’, ‘Margins3’, +‘BeginPenMargin2’, ‘EndPenMargin2’, ‘PenMargin2’, ‘PenMargins2’, +‘BeginPenMargin3’, ‘EndPenMargin3’, ‘PenMargin3’, ‘PenMargins3’, +‘BeginDotMargin3’, ‘EndDotMargin3’, ‘DotMargin3’, ‘DotMargins3’, +‘Margin3’, and ‘TrueMargin3’. The routine void pixel(picture pic=currentpicture, triple v, pen p=currentpen, real width=1); -can be used to draw on picture 'pic' a pixel of width 'width' at -position 'v' using pen 'p'. +can be used to draw on picture ‘pic’ a pixel of width ‘width’ at +position ‘v’ using pen ‘p’. Further three-dimensional examples are provided in the files -'near_earth.asy', 'conicurv.asy', and (in the 'animations' subdirectory) -'cube.asy'. +‘near_earth.asy’, ‘conicurv.asy’, and (in the ‘animations’ subdirectory) +‘cube.asy’. Limited support for projected vector graphics (effectively -three-dimensional nonrendered 'PostScript') is available with the -setting 'render=0'. This currently only works for piecewise planar -surfaces, such as those produced by the parametric 'surface' routines in -the 'graph3' module. Surfaces produced by the 'solids' module will also -be properly rendered if the parameter 'nslices' is sufficiently large. +three-dimensional nonrendered ‘PostScript’) is available with the +setting ‘render=0’. This currently only works for piecewise planar +surfaces, such as those produced by the parametric ‘surface’ routines in +the ‘graph3’ module. Surfaces produced by the ‘solids’ module will also +be properly rendered if the parameter ‘nslices’ is sufficiently large. - In the module 'bsp', hidden surface removal of planar pictures is + In the module ‘bsp’, hidden surface removal of planar pictures is implemented using a binary space partition and picture clipping. A -planar path is first converted to a structure 'face' derived from -'picture'. A 'face' may be given to a two-dimensional drawing routine -in place of any 'picture' argument. An array of such faces may then be +planar path is first converted to a structure ‘face’ derived from +‘picture’. A ‘face’ may be given to a two-dimensional drawing routine +in place of any ‘picture’ argument. An array of such faces may then be drawn, removing hidden surfaces: void add(picture pic=currentpicture, face[] faces, projection P=currentprojection); - Labels may be projected to two dimensions, using projection 'P', onto -the plane passing through point 'O' with normal 'cross(u,v)' by + Labels may be projected to two dimensions, using projection ‘P’, onto +the plane passing through point ‘O’ with normal ‘cross(u,v)’ by multiplying it on the left by the transform transform transform(triple u, triple v, triple O=O, projection P=currentprojection); @@ -7531,24 +7589,24 @@ add(faces); File: asymptote.info, Node: obj, Next: graph3, Prev: three, Up: Base modules -8.29 'obj' +8.29 ‘obj’ ========== This module allows one to construct surfaces from simple obj files, as -illustrated in the example files 'galleon.asy' and 'triceratops.asy'. +illustrated in the example files ‘galleon.asy’ and ‘triceratops.asy’. File: asymptote.info, Node: graph3, Next: grid3, Prev: obj, Up: Base modules -8.30 'graph3' +8.30 ‘graph3’ ============= This module implements three-dimensional versions of the functions in -'graph.asy'. To draw an x axis in three dimensions, use the routine +‘graph.asy’. To draw an x axis in three dimensions, use the routine void xaxis3(picture pic=currentpicture, Label L="", axis axis=YZZero, real xmin=-infinity, real xmax=infinity, pen p=currentpen, ticks3 ticks=NoTicks3, arrowbar3 arrow=None, bool above=false); -Analogous routines 'yaxis' and 'zaxis' can be used to draw y and z axes +Analogous routines ‘yaxis’ and ‘zaxis’ can be used to draw y and z axes in three dimensions. There is also a routine for drawing all three axis: void axes3(picture pic=currentpicture, @@ -7566,16 +7624,16 @@ axis YZZero(triple align=O, bool extend=false); axis XZZero(triple align=O, bool extend=false); axis XYZero(triple align=O, bool extend=false); axis Bounds(int type=Both, int type2=Both, triple align=O, bool extend=false); -The optional 'align' parameter to these routines can be used to specify -the default axis and tick label alignments. The 'Bounds' axis accepts -two type parameters, each of which must be one of 'Min', 'Max', or -'Both'. These parameters specify which of the four possible +The optional ‘align’ parameter to these routines can be used to specify +the default axis and tick label alignments. The ‘Bounds’ axis accepts +two type parameters, each of which must be one of ‘Min’, ‘Max’, or +‘Both’. These parameters specify which of the four possible three-dimensional bounding box edges should be drawn. - The three-dimensional tick options are 'NoTicks3', 'InTicks', -'OutTicks', and 'InOutTicks'. These specify the tick directions for the -'Bounds' axis type; other axis types inherit the direction that would be -used for the 'Bounds(Min,Min)' axis. + The three-dimensional tick options are ‘NoTicks3’, ‘InTicks’, +‘OutTicks’, and ‘InOutTicks’. These specify the tick directions for the +‘Bounds’ axis type; other axis types inherit the direction that would be +used for the ‘Bounds(Min,Min)’ axis. Here is an example of a helix and bounding box axes with ticks and axis labels, using orthographic projection: @@ -7636,7 +7694,7 @@ axis(Label("C",position=0,align=15X),g,InTicks(endlabel=false,8,end=false), [./generalaxis3] - Surface plots of matrices and functions over the region 'box(a,b)' in + Surface plots of matrices and functions over the region ‘box(a,b)’ in the XY plane are also implemented: surface surface(real[][] f, pair a, pair b, bool[][] cond={}); surface surface(real[][] f, pair a, pair b, splinetype xsplinetype, @@ -7659,24 +7717,24 @@ surface surface(triple f(pair z), pair a, pair b, int nu=nmesh, int nv=nu, splinetype[] usplinetype, splinetype[] vsplinetype=Spline, bool cond(pair z)=null); The final two versions draw parametric surfaces for a function f(u,v) -over the parameter space 'box(a,b)', as illustrated in the example -'parametricsurface.asy'. An optional splinetype 'Spline' may be -specified. The boolean array or function 'cond' can be used to control +over the parameter space ‘box(a,b)’, as illustrated in the example +‘parametricsurface.asy’. An optional splinetype ‘Spline’ may be +specified. The boolean array or function ‘cond’ can be used to control which surface mesh cells are actually drawn (by default all mesh cells -over 'box(a,b)' are drawn). +over ‘box(a,b)’ are drawn). - One can also construct the surface generated by rotating a path 'g' -between 'angle1' to 'angle2' (in degrees) sampled 'n' times about the -line 'c--c+axis': + One can also construct the surface generated by rotating a path ‘g’ +between ‘angle1’ to ‘angle2’ (in degrees) sampled ‘n’ times about the +line ‘c--c+axis’: surface surface(triple c, path3 g, triple axis, int n=nslice, real angle1=0, real angle2=360, pen color(int i, real j)=null); -The optional argument 'color(int i, real j)' can be used to override the -surface color at the point obtained by rotating vertex 'i' by angle 'j' +The optional argument ‘color(int i, real j)’ can be used to override the +surface color at the point obtained by rotating vertex ‘i’ by angle ‘j’ (in degrees). Surface lighting is illustrated in the example files -'parametricsurface.asy' and 'sinc.asy'. Lighting can be disabled by -setting 'light=nolight', as in this example of a Gaussian surface: +‘parametricsurface.asy’ and ‘sinc.asy’. Lighting can be disabled by +setting ‘light=nolight’, as in this example of a Gaussian surface: import graph3; size(200,0); @@ -7700,27 +7758,27 @@ draw(s,lightgray,meshpen=black+thick(),nolight,render(merge=true)); label("$O$",O,-Z+Y,red); [./GaussianSurface] -A mesh can be drawn without surface filling by specifying 'nullpen' for +A mesh can be drawn without surface filling by specifying ‘nullpen’ for the surfacepen. - A vector field of 'nu'\times'nv' arrows on a parametric surface 'f' -over 'box(a,b)' can be drawn with the routine + A vector field of ‘nu’\times‘nv’ arrows on a parametric surface ‘f’ +over ‘box(a,b)’ can be drawn with the routine picture vectorfield(path3 vector(pair v), triple f(pair z), pair a, pair b, int nu=nmesh, int nv=nu, bool truesize=false, real maxlength=truesize ? 0 : maxlength(f,a,b,nu,nv), bool cond(pair z)=null, pen p=currentpen, arrowbar3 arrow=Arrow3, margin3 margin=PenMargin3) - as illustrated in the examples 'vectorfield3.asy' and -'vectorfieldsphere.asy'. + as illustrated in the examples ‘vectorfield3.asy’ and +‘vectorfieldsphere.asy’. File: asymptote.info, Node: grid3, Next: solids, Prev: graph3, Up: Base modules -8.31 'grid3' +8.31 ‘grid3’ ============ This module, contributed by Philippe Ivaldi, can be used for drawing 3D -grids. Here is an example (further examples can be found in 'grid3.asy' +grids. Here is an example (further examples can be found in ‘grid3.asy’ and at <https://web.archive.org/web/20201130113133/http://www.piprime.fr/files/asymptote/grid3/>): import grid3; @@ -7746,13 +7804,13 @@ zaxis3(Label("$z$",position=EndPoint,align=(-1,0.5)),Bounds(Min,Min), File: asymptote.info, Node: solids, Next: tube, Prev: grid3, Up: Base modules -8.32 'solids' +8.32 ‘solids’ ============= -This solid geometry module defines a structure 'revolution' that can be +This solid geometry module defines a structure ‘revolution’ that can be used to fill and draw surfaces of revolution. The following example uses it to display the outline of a circular cylinder of radius 1 with -axis 'O--1.5unit(Y+Z)' with perspective projection: +axis ‘O--1.5unit(Y+Z)’ with perspective projection: import solids; size(0,100); @@ -7763,9 +7821,9 @@ draw(r,heavygreen); [./cylinderskeleton] Further illustrations are provided in the example files -'cylinder.asy', 'cones.asy', 'hyperboloid.asy', and 'torus.asy'. +‘cylinder.asy’, ‘cones.asy’, ‘hyperboloid.asy’, and ‘torus.asy’. - The structure 'skeleton' contains the three-dimensional wireframe + The structure ‘skeleton’ contains the three-dimensional wireframe used to visualize a volume of revolution: struct skeleton { struct curve { @@ -7781,21 +7839,21 @@ struct skeleton { File: asymptote.info, Node: tube, Next: flowchart, Prev: solids, Up: Base modules -8.33 'tube' +8.33 ‘tube’ =========== -This module extends the 'tube' surfaces constructed in -'three_arrows.asy' to arbitrary cross sections, colors, and spine +This module extends the ‘tube’ surfaces constructed in +‘three_arrows.asy’ to arbitrary cross sections, colors, and spine transformations. The routine surface tube(path3 g, coloredpath section, transform T(real)=new transform(real t) {return identity();}, real corner=1, real relstep=0); -draws a tube along 'g' with cross section 'section', after applying the -transformation 'T(t)' at 'point(g,t)'. The parameter 'corner' controls -the number of elementary tubes at the angular points of 'g'. A nonzero -value of 'relstep' specifies a fixed relative time step (in the sense of -'relpoint(g,t)') to use in constructing elementary tubes along 'g'. The -type 'coloredpath' is a generalization of 'path' to which a 'path' can +draws a tube along ‘g’ with cross section ‘section’, after applying the +transformation ‘T(t)’ at ‘point(g,t)’. The parameter ‘corner’ controls +the number of elementary tubes at the angular points of ‘g’. A nonzero +value of ‘relstep’ specifies a fixed relative time step (in the sense of +‘relpoint(g,t)’) to use in constructing elementary tubes along ‘g’. The +type ‘coloredpath’ is a generalization of ‘path’ to which a ‘path’ can be cast: struct coloredpath { @@ -7803,15 +7861,15 @@ struct coloredpath pen[] pens(real); int colortype=coloredSegments; } -Here 'p' defines the cross section and the method 'pens(real t)' returns +Here ‘p’ defines the cross section and the method ‘pens(real t)’ returns an array of pens (interpreted as a cyclic array) used for shading the -tube patches at 'relpoint(g,t)'. If 'colortype=coloredSegments', the +tube patches at ‘relpoint(g,t)’. If ‘colortype=coloredSegments’, the tube patches are filled as if each segment of the section was colored -with the pen returned by 'pens(t)', whereas if 'colortype=coloredNodes', +with the pen returned by ‘pens(t)’, whereas if ‘colortype=coloredNodes’, the tube components are vertex shaded as if the nodes of the section were colored. - A 'coloredpath' can be constructed with one of the routines: + A ‘coloredpath’ can be constructed with one of the routines: coloredpath coloredpath(path p, pen[] pens(real), int colortype=coloredSegments); coloredpath coloredpath(path p, pen[] pens=new pen[] {currentpen}, @@ -7821,24 +7879,24 @@ In the second case, the pens are independent of the relative time. In the third case, the array of pens contains only one pen, which depends of the relative time. - The casting of 'path' to 'coloredpath' allows the use of a 'path' -instead of a 'coloredpath'; in this case the shading behaviour is the + The casting of ‘path’ to ‘coloredpath’ allows the use of a ‘path’ +instead of a ‘coloredpath’; in this case the shading behaviour is the default shading behavior for a surface. - An example of 'tube' is provided in the file 'trefoilknot.asy'. + An example of ‘tube’ is provided in the file ‘trefoilknot.asy’. Further examples can be found at <https://web.archive.org/web/20201130113133/http://www.piprime.fr/files/asymptote/tube>. File: asymptote.info, Node: flowchart, Next: contour, Prev: tube, Up: Base modules -8.34 'flowchart' +8.34 ‘flowchart’ ================ This module provides routines for drawing flowcharts. The primary -structure is a 'block', which represents a single block on the +structure is a ‘block’, which represents a single block on the flowchart. The following eight functions return a position on the -appropriate edge of the block, given picture transform 't': +appropriate edge of the block, given picture transform ‘t’: pair block.top(transform t=identity()); pair block.left(transform t=identity()); @@ -7853,8 +7911,8 @@ To obtain an arbitrary position along the boundary of the block in user coordinates, use: pair block.position(real x, transform t=identity()); -The center of the block in user coordinates is stored in 'block.center' -and the block size in 'PostScript' coordinates is given by 'block.size'. +The center of the block in user coordinates is stored in ‘block.center’ +and the block size in ‘PostScript’ coordinates is given by ‘block.size’. A frame containing the block is returned by frame block.draw(pen p=currentpen); @@ -7862,7 +7920,7 @@ frame block.draw(pen p=currentpen); The following block generation routines accept a Label, string, or frame for their object argument: -"rectangular block with an optional header (and padding 'dx' around header and body):" +“rectangular block with an optional header (and padding ‘dx’ around header and body):” block rectangle(object header, object body, pair center=(0,0), pen headerpen=mediumgray, pen bodypen=invisible, pen drawpen=currentpen, @@ -7875,45 +7933,45 @@ frame for their object argument: real dx=3, real minwidth=minblockwidth, real minheight=minblockheight); -"parallelogram block:" +“parallelogram block:” block parallelogram(object body, pair center=(0,0), pen fillpen=invisible, pen drawpen=currentpen, real dx=3, real slope=2, real minwidth=minblockwidth, real minheight=minblockheight); -"diamond-shaped block:" +“diamond-shaped block:” block diamond(object body, pair center=(0,0), pen fillpen=invisible, pen drawpen=currentpen, real ds=5, real dw=1, real height=20, real minwidth=minblockwidth, real minheight=minblockheight); -"circular block:" +“circular block:” block circle(object body, pair center=(0,0), pen fillpen=invisible, pen drawpen=currentpen, real dr=3, real mindiameter=mincirclediameter); -"rectangular block with rounded corners:" +“rectangular block with rounded corners:” block roundrectangle(object body, pair center=(0,0), pen fillpen=invisible, pen drawpen=currentpen, real ds=5, real dw=0, real minwidth=minblockwidth, real minheight=minblockheight); -"rectangular block with beveled edges:" +“rectangular block with beveled edges:” block bevel(object body, pair center=(0,0), pen fillpen=invisible, pen drawpen=currentpen, real dh=5, real dw=5, real minwidth=minblockwidth, real minheight=minblockheight); - To draw paths joining the pairs in 'point' with right-angled lines, + To draw paths joining the pairs in ‘point’ with right-angled lines, use the routine: path path(pair point[] ... flowdir dir[]); -The entries in 'dir' identify whether successive segments between the -pairs specified by 'point' should be drawn in the 'Horizontal' or -'Vertical' direction. +The entries in ‘dir’ identify whether successive segments between the +pairs specified by ‘point’ should be drawn in the ‘Horizontal’ or +‘Vertical’ direction. Here is a simple flowchart example (see also the example -'controlsystem.asy'): +‘controlsystem.asy’): size(0,300); @@ -7948,36 +8006,36 @@ add(new void(picture pic, transform t) { File: asymptote.info, Node: contour, Next: contour3, Prev: flowchart, Up: Base modules -8.35 'contour' +8.35 ‘contour’ ============== This module draws contour lines. To construct contours corresponding to -the values in a real array 'c' for a function 'f' on 'box(a,b)', use the +the values in a real array ‘c’ for a function ‘f’ on ‘box(a,b)’, use the routine guide[][] contour(real f(real, real), pair a, pair b, real[] c, int nx=ngraph, int ny=nx, interpolate join=operator --, int subsample=1); -The integers 'nx' and 'ny' define the resolution. The default -resolution, 'ngraph x ngraph' (here 'ngraph' defaults to '100') can be +The integers ‘nx’ and ‘ny’ define the resolution. The default +resolution, ‘ngraph x ngraph’ (here ‘ngraph’ defaults to ‘100’) can be increased for greater accuracy. The default interpolation operator is -'operator --' (linear). Spline interpolation ('operator ..') may +‘operator --’ (linear). Spline interpolation (‘operator ..’) may produce smoother contours but it can also lead to overshooting. The -'subsample' parameter indicates the number of interior points that -should be used to sample contours within each '1 x 1' box; the default -value of '1' is usually sufficient. +‘subsample’ parameter indicates the number of interior points that +should be used to sample contours within each ‘1 x 1’ box; the default +value of ‘1’ is usually sufficient. To construct contours for an array of data values on a uniform -two-dimensional lattice on 'box(a,b)', use +two-dimensional lattice on ‘box(a,b)’, use guide[][] contour(real[][] f, pair a, pair b, real[] c, interpolate join=operator --, int subsample=1); To construct contours for an array of data values on a nonoverlapping -regular mesh specified by the two-dimensional array 'z', +regular mesh specified by the two-dimensional array ‘z’, guide[][] contour(pair[][] z, real[][] f, real[] c, interpolate join=operator --, int subsample=1); -To construct contours for an array of values 'f' specified at -irregularly positioned points 'z', use the routine +To construct contours for an array of values ‘f’ specified at +irregularly positioned points ‘z’, use the routine guide[][] contour(pair[] z, real[] f, real[] c, interpolate join=operator --); The contours themselves can be drawn with one of the routines void draw(picture pic=currentpicture, Label[] L=new Label[], @@ -7986,7 +8044,7 @@ void draw(picture pic=currentpicture, Label[] L=new Label[], void draw(picture pic=currentpicture, Label[] L=new Label[], guide[][] g, pen[] p); - The following simple example draws the contour at value '1' for the + The following simple example draws the contour at value ‘1’ for the function z=x^2+y^2, which is a unit circle: import contour; size(75); @@ -7997,7 +8055,7 @@ draw(contour(f,(-1,-1),(1,1),new real[] {1})); [./onecontour] The next example draws and labels multiple contours for the function -z=x^2-y^2 with the resolution '100 x 100', using a dashed pen for +z=x^2-y^2 with the resolution ‘100 x 100’, using a dashed pen for negative contours and a solid pen for positive (and zero) contours: import contour; @@ -8134,7 +8192,7 @@ draw(contour(points,values,new real[]{0.25,0.5,1},operator ..),blue); [./irregularcontour] In the above example, the contours of irregularly spaced data are -constructed by first creating a triangular mesh from an array 'z' of +constructed by first creating a triangular mesh from an array ‘z’ of pairs: int[][] triangulate(pair[] z); @@ -8161,39 +8219,39 @@ for(int i=0; i < np; ++i) [./triangulate] - The example 'Gouraudcontour.asy' illustrates how to produce color -density images over such irregular triangular meshes. 'Asymptote' uses -a robust version of Paul Bourke's Delaunay triangulation algorithm based + The example ‘Gouraudcontour.asy’ illustrates how to produce color +density images over such irregular triangular meshes. ‘Asymptote’ uses +a robust version of Paul Bourke’s Delaunay triangulation algorithm based on the public-domain exact arithmetic predicates written by Jonathan Shewchuk. File: asymptote.info, Node: contour3, Next: smoothcontour3, Prev: contour, Up: Base modules -8.36 'contour3' +8.36 ‘contour3’ =============== This module draws surfaces described as the null space of real-valued -functions of (x,y,z) or 'real[][][]' matrices. Its usage is illustrated -in the example file 'magnetic.asy'. +functions of (x,y,z) or ‘real[][][]’ matrices. Its usage is illustrated +in the example file ‘magnetic.asy’. File: asymptote.info, Node: smoothcontour3, Next: slopefield, Prev: contour3, Up: Base modules -8.37 'smoothcontour3' +8.37 ‘smoothcontour3’ ===================== This module, written by Charles Staats, draws implicitly defined surfaces with smooth appearance. The purpose of this module is similar -to that of 'contour3': given a real-valued function f(x,y,z), construct +to that of ‘contour3’: given a real-valued function f(x,y,z), construct the surface described by the equation f(x,y,z) = 0. The -'smoothcontour3' module generally produces nicer results than -'contour3', but takes longer to compile. Additionally, the algorithm +‘smoothcontour3’ module generally produces nicer results than +‘contour3’, but takes longer to compile. Additionally, the algorithm assumes that the function and the surface are both smooth; if they are -not, then 'contour3' may be a better choice. +not, then ‘contour3’ may be a better choice. - To construct the null surface of a function 'f(triple)' or -'ff(real,real,real)' over 'box(a,b)', use the routine + To construct the null surface of a function ‘f(triple)’ or +‘ff(real,real,real)’ over ‘box(a,b)’, use the routine surface implicitsurface(real f(triple)=null, real ff(real,real,real)=null, triple a, @@ -8205,18 +8263,18 @@ surface implicitsurface(real f(triple)=null, int keyword nz=n, int keyword maxdepth=8, bool usetriangles=true); -The optional parameter 'overlapedges' attempts to compensate for an -artifact that can cause the renderer to "see through" the boundary -between patches. Although it defaults to 'false', it should usually be -set to 'true'. The example 'genustwo.asy' illustrates the use of this +The optional parameter ‘overlapedges’ attempts to compensate for an +artifact that can cause the renderer to “see through” the boundary +between patches. Although it defaults to ‘false’, it should usually be +set to ‘true’. The example ‘genustwo.asy’ illustrates the use of this function. Additional examples, together with a more in-depth -explanation of the module's usage and pitfalls, are available at +explanation of the module’s usage and pitfalls, are available at <https://github.com/charlesstaats/smoothcontour3>. File: asymptote.info, Node: slopefield, Next: ode, Prev: smoothcontour3, Up: Base modules -8.38 'slopefield' +8.38 ‘slopefield’ ================= To draw a slope field for the differential equation dy/dx=f(x,y) (or @@ -8225,23 +8283,23 @@ picture slopefield(real f(real,real), pair a, pair b, int nx=nmesh, int ny=nx, real tickfactor=0.5, pen p=currentpen, arrowbar arrow=None); -Here, the points 'a' and 'b' are the lower left and upper right corners -of the rectangle in which the slope field is to be drawn, 'nx' and 'ny' +Here, the points ‘a’ and ‘b’ are the lower left and upper right corners +of the rectangle in which the slope field is to be drawn, ‘nx’ and ‘ny’ are the respective number of ticks in the x and y directions, -'tickfactor' is the fraction of the minimum cell dimension to use for -drawing ticks, and 'p' is the pen to use for drawing the slope fields. -The return value is a picture that can be added to 'currentpicture' via -the 'add(picture)' command. +‘tickfactor’ is the fraction of the minimum cell dimension to use for +drawing ticks, and ‘p’ is the pen to use for drawing the slope fields. +The return value is a picture that can be added to ‘currentpicture’ via +the ‘add(picture)’ command. The function path curve(pair c, real f(real,real), pair a, pair b); -takes a point ('c') and a slope field-defining function 'f' and returns, -as a path, the curve passing through that point. The points 'a' and 'b' +takes a point (‘c’) and a slope field-defining function ‘f’ and returns, +as a path, the curve passing through that point. The points ‘a’ and ‘b’ represent the rectangular boundaries over which the curve is interpolated. - Both 'slopefield' and 'curve' alternatively accept a function 'real -f(real)' that depends on x only, as seen in this example: + Both ‘slopefield’ and ‘curve’ alternatively accept a function ‘real +f(real)’ that depends on x only, as seen in this example: import slopefield; @@ -8256,10 +8314,10 @@ draw(curve((0,0),func,(-3,-3),(3,3)),red); File: asymptote.info, Node: ode, Prev: slopefield, Up: Base modules -8.39 'ode' +8.39 ‘ode’ ========== -The 'ode' module, illustrated in the example 'odetest.asy', implements a +The ‘ode’ module, illustrated in the example ‘odetest.asy’, implements a number of explicit numerical integration schemes for ordinary differential equations. @@ -8269,8 +8327,8 @@ File: asymptote.info, Node: Options, Next: Interactive mode, Prev: Base modul 9 Command-line options ********************** -Type 'asy -h' to see the full list of command-line options supported by -'Asymptote': +Type ‘asy -h’ to see the full list of command-line options supported by +‘Asymptote’: Usage: ../asy [options] [file ...] Options (negate boolean options by replacing - with -no): @@ -8352,7 +8410,7 @@ Options (negate boolean options by replacing - with -no): -offline Produce offline html files [false] -O,-offset pair PostScript offset [(0,0)] -f,-outformat format Convert each output file to specified format --o,-outname name Alternative output directory/filename +-o,-outname name Alternative output directory/file prefix -outpipe n Output pipe [-1] -paperheight bp Default page height [0] -paperwidth bp Default page width [0] @@ -8388,6 +8446,7 @@ Options (negate boolean options by replacing - with -no): -twice Run LaTeX twice (to resolve references) [false] -twosided Use two-sided 3D lighting model for rendering [true] -u,-user str General purpose user string +-v3d Embed 3D V3D graphics in PDF output [false] -v,-verbose Increase verbosity level (can specify multiple times) 0 -version Show version; command-line only -vibrateTime ms WebGL shift mode vibrate duration [25] @@ -8396,7 +8455,7 @@ Options (negate boolean options by replacing - with -no): -warn str Enable warning; command-line only -webgl2 Use webgl2 if available [false] -where Show where listed variables are declared [false] --wsl Run asy under the Windows Subsystem for Linux. [false] +-wsl Run asy under the Windows Subsystem for Linux [false] -xasy Interactive mode for xasy [false] -zoomPinchCap limit WebGL maximum zoom pinch [100] -zoomPinchFactor n WebGL zoom pinch sensitivity [10] @@ -8404,30 +8463,30 @@ Options (negate boolean options by replacing - with -no): -zoomstep step Mouse motion zoom step [0.1] - All boolean options can be negated by prepending 'no' to the option + All boolean options can be negated by prepending ‘no’ to the option name. - If no arguments are given, 'Asymptote' runs in interactive mode + If no arguments are given, ‘Asymptote’ runs in interactive mode (*note Interactive mode::). In this case, the default output file is -'out.eps'. +‘out.eps’. - If '-' is given as the file argument, 'Asymptote' reads from standard + If ‘-’ is given as the file argument, ‘Asymptote’ reads from standard input. If multiple files are specified, they are treated as separate -'Asymptote' runs. +‘Asymptote’ runs. - If the string 'autoimport' is nonempty, a module with this name is + If the string ‘autoimport’ is nonempty, a module with this name is automatically imported for each run as the final step in loading module -'plain'. +‘plain’. - Default option values may be entered as 'Asymptote' code in a -configuration file named 'config.asy' (or the file specified by the -environment variable 'ASYMPTOTE_CONFIG' or '-config' option). -'Asymptote' will look for this file in its usual search path (*note + Default option values may be entered as ‘Asymptote’ code in a +configuration file named ‘config.asy’ (or the file specified by the +environment variable ‘ASYMPTOTE_CONFIG’ or ‘-config’ option). +‘Asymptote’ will look for this file in its usual search path (*note Search paths::). Typically the configuration file is placed in the -'.asy' directory in the user's home directory ('%USERPROFILE%\.asy' -under 'MSDOS'). Configuration variables are accessed using the long +‘.asy’ directory in the user’s home directory (‘%USERPROFILE%\.asy’ +under ‘MSDOS’). Configuration variables are accessed using the long form of the option names: import settings; outformat="pdf"; @@ -8437,94 +8496,94 @@ batchMask=false; interactiveMask=true; Command-line options override these defaults. Most configuration variables may also be changed at runtime. The advanced configuration -variables 'dvipsOptions', 'hyperrefOptions', 'convertOptions', -'gsOptions', 'htmlviewerOptions', 'psviewerOptions', 'pdfviewerOptions', -'pdfreloadOptions', 'glOptions', and 'dvisvgmOptions' allow specialized +variables ‘dvipsOptions’, ‘hyperrefOptions’, ‘convertOptions’, +‘gsOptions’, ‘htmlviewerOptions’, ‘psviewerOptions’, ‘pdfviewerOptions’, +‘pdfreloadOptions’, ‘glOptions’, and ‘dvisvgmOptions’ allow specialized options to be passed as a string to the respective applications or -libraries. The default value of 'hyperrefOptions' is -'setpagesize=false,unicode,pdfborder=0 0 0'. +libraries. The default value of ‘hyperrefOptions’ is +‘setpagesize=false,unicode,pdfborder=0 0 0’. If you insert import plain; settings.autoplain=true; at the beginning of the configuration file, it can contain arbitrary -'Asymptote' code. +‘Asymptote’ code. - The default output format is EPS for the (default) 'latex' and 'tex' -tex engine and PDF for the 'pdflatex', 'xelatex', 'context', 'luatex', -and 'lualatex' tex engines. Alternative output formats may be produced -using the '-f' option (or 'outformat' setting). + The default output format is EPS for the (default) ‘latex’ and ‘tex’ +tex engine and PDF for the ‘pdflatex’, ‘xelatex’, ‘context’, ‘luatex’, +and ‘lualatex’ tex engines. Alternative output formats may be produced +using the ‘-f’ option (or ‘outformat’ setting). - To produce SVG output, you will need 'dvisvgm' (version 2.6.3 or + To produce SVG output, you will need ‘dvisvgm’ (version 2.6.3 or later) from <https://dvisvgm.de>. You might need to adjust the -configuration variable 'libgs' to point to the location of your -'Ghostscript' library 'libgs.so' (or to an empty string, depending on -how 'dvisvgm' was configured). The 2.13.1 version (or later) of -'dvisvgm' can display SVG output (used by the 'xasy' editor) for -embedded EPS, PDF, PNG, and JPEG images included with the 'graphic()' +configuration variable ‘libgs’ to point to the location of your +‘Ghostscript’ library ‘libgs.so’ (or to an empty string, depending on +how ‘dvisvgm’ was configured). The 2.13.1 version (or later) of +‘dvisvgm’ can display SVG output (used by the ‘xasy’ editor) for +embedded EPS, PDF, PNG, and JPEG images included with the ‘graphic()’ function. - 'Asymptote' can also produce any output format supported by the -'ImageMagick' 'convert' program (version 6.3.5 or later recommended; an -'Invalid Parameter' error message indicates that the 'MSDOS' utility -'convert' is being used instead of the one that comes with -'ImageMagick'). The optional setting '-render n' requests an output -resolution of 'n' pixels per 'bp'. Antialiasing is controlled by the -parameter 'antialias', which by default specifies a sampling width of 2 -pixels. To give other options to 'convert', use the 'convertOptions' -setting or call convert manually. This example emulates how 'Asymptote' -produces antialiased 'tiff' output at one pixel per 'bp': + ‘Asymptote’ can also produce any output format supported by the +‘ImageMagick’ ‘convert’ program (version 6.3.5 or later recommended; an +‘Invalid Parameter’ error message indicates that the ‘MSDOS’ utility +‘convert’ is being used instead of the one that comes with +‘ImageMagick’). The optional setting ‘-render n’ requests an output +resolution of ‘n’ pixels per ‘bp’. Antialiasing is controlled by the +parameter ‘antialias’, which by default specifies a sampling width of 2 +pixels. To give other options to ‘convert’, use the ‘convertOptions’ +setting or call convert manually. This example emulates how ‘Asymptote’ +produces antialiased ‘tiff’ output at one pixel per ‘bp’: asy -o - venn | convert -alpha Off -density 144x144 -geometry 50%x eps:- venn.tiff - If the option '-nosafe' is given, 'Asymptote' runs in unsafe mode. -This enables the 'int system(string s)' and 'int system(string[] s)' + If the option ‘-nosafe’ is given, ‘Asymptote’ runs in unsafe mode. +This enables the ‘int system(string s)’ and ‘int system(string[] s)’ calls, allowing one to execute arbitrary shell commands. The default -mode, '-safe', disables this call. +mode, ‘-safe’, disables this call. - A 'PostScript' offset may be specified as a pair (in 'bp' units) with -the '-O' option: + A ‘PostScript’ offset may be specified as a pair (in ‘bp’ units) with +the ‘-O’ option: asy -O 0,0 file -The default offset is zero. The pair 'aligndir' specifies an optional +The default offset is zero. The pair ‘aligndir’ specifies an optional direction on the boundary of the page (mapped to the rectangle [-1,1]\times[-1,1]) to which the picture should be aligned; the default -value '(0,0)' species center alignment. +value ‘(0,0)’ species center alignment. - The '-c' ('command') option may be used to execute arbitrary -'Asymptote' code on the command line as a string. It is not necessary -to terminate the string with a semicolon. Multiple '-c' options are + The ‘-c’ (‘command’) option may be used to execute arbitrary +‘Asymptote’ code on the command line as a string. It is not necessary +to terminate the string with a semicolon. Multiple ‘-c’ options are executed in the order they are given. For example asy -c 2+2 -c "sin(1)" -c "size(100); draw(unitsquare)" produces the output 4 0.841470984807897 -and draws a unitsquare of size '100'. +and draws a unitsquare of size ‘100’. - The '-u' ('user') option may be used to specify arbitrary 'Asymptote' + The ‘-u’ (‘user’) option may be used to specify arbitrary ‘Asymptote’ settings on the command line as a string. It is not necessary to -terminate the string with a semicolon. Multiple '-u' options are -executed in the order they are given. Command-line code like '-u -x=sqrt(2)' can be executed within a module like this: +terminate the string with a semicolon. Multiple ‘-u’ options are +executed in the order they are given. Command-line code like ‘-u +x=sqrt(2)’ can be executed within a module like this: real x; usersetting(); write(x); - When the '-l' ('listvariables') option is used with file arguments, + When the ‘-l’ (‘listvariables’) option is used with file arguments, only global functions and variables defined in the specified file(s) are listed. - Additional debugging output is produced with each additional '-v' + Additional debugging output is produced with each additional ‘-v’ option: -'-v' +‘-v’ Display top-level module and final output file names. -'-vv' - Also display imported and included module names and final 'LaTeX' - and 'dvips' processing information. -'-vvv' - Also output 'LaTeX' bidirectional pipe diagnostics. -'-vvvv' +‘-vv’ + Also display imported and included module names and final ‘LaTeX’ + and ‘dvips’ processing information. +‘-vvv’ + Also output ‘LaTeX’ bidirectional pipe diagnostics. +‘-vvvv’ Also output knot guide solver diagnostics. -'-vvvvv' - Also output 'Asymptote' traceback diagnostics. +‘-vvvvv’ + Also output ‘Asymptote’ traceback diagnostics. File: asymptote.info, Node: Interactive mode, Next: GUI, Prev: Options, Up: Top @@ -8532,22 +8591,22 @@ File: asymptote.info, Node: Interactive mode, Next: GUI, Prev: Options, Up: 10 Interactive mode ******************* -Interactive mode is entered by executing the command 'asy' with no file -arguments. When the '-multiline' option is disabled (the default), each -line must be a complete 'Asymptote' statement (unless explicitly -continued by a final backslash character '\'); it is not necessary to +Interactive mode is entered by executing the command ‘asy’ with no file +arguments. When the ‘-multiline’ option is disabled (the default), each +line must be a complete ‘Asymptote’ statement (unless explicitly +continued by a final backslash character ‘\’); it is not necessary to terminate input lines with a semicolon. If one assigns -'settings.multiline=true', interactive code can be entered over multiple +‘settings.multiline=true’, interactive code can be entered over multiple lines; in this mode, the automatic termination of interactive input lines by a semicolon is inhibited. Multiline mode is useful for cutting -and pasting 'Asymptote' code directly into the interactive input buffer. +and pasting ‘Asymptote’ code directly into the interactive input buffer. Interactive mode can be conveniently used as a calculator: expressions entered at the interactive prompt (for which a corresponding -'write' function exists) are automatically evaluated and written to -'stdout'. If the expression is non-writable, its type signature will be +‘write’ function exists) are automatically evaluated and written to +‘stdout’. If the expression is non-writable, its type signature will be printed out instead. In either case, the expression can be referred to -using the symbol '%' in the next line input at the prompt. For example: +using the symbol ‘%’ in the next line input at the prompt. For example: > 2+3 5 > %*4 @@ -8561,47 +8620,47 @@ using the symbol '%' in the next line input at the prompt. For example: > %.size(200,0) > - The '%' symbol, when used as a variable, is shorthand for the -identifier 'operator answer', which is set by the prompt after each + The ‘%’ symbol, when used as a variable, is shorthand for the +identifier ‘operator answer’, which is set by the prompt after each written expression evaluation. The following special commands are supported only in interactive mode and must be entered immediately after the prompt: -'help' +‘help’ view the manual; -'erase' - erase 'currentpicture'; -'reset' - reset the 'Asymptote' environment to its initial state, except for +‘erase’ + erase ‘currentpicture’; +‘reset’ + reset the ‘Asymptote’ environment to its initial state, except for changes to the settings module (*note settings::), the current directory (*note cd::), and breakpoints (*note Debugger::); -'input FILE' - does an interactive reset, followed by the command 'include FILE'. - If the file name 'FILE' contains nonalphanumeric characters, +‘input FILE’ + does an interactive reset, followed by the command ‘include FILE’. + If the file name ‘FILE’ contains nonalphanumeric characters, enclose it with quotation marks. A trailing semi-colon followed by - optional 'Asymptote' commands may be entered on the same line. -'quit' - exit interactive mode ('exit' is a synonym; the abbreviation 'q' is - also accepted unless there exists a top-level variable named 'q'). + optional ‘Asymptote’ commands may be entered on the same line. +‘quit’ + exit interactive mode (‘exit’ is a synonym; the abbreviation ‘q’ is + also accepted unless there exists a top-level variable named ‘q’). A history of the most recent 1000 (this number can be changed with - the 'historylines' configuration variable) previous commands will - be retained in the file '.asy/history' in the user's home directory - (unless the command-line option '-localhistory' was specified, in - which case the history will be stored in the file '.asy_history' in + the ‘historylines’ configuration variable) previous commands will + be retained in the file ‘.asy/history’ in the user’s home directory + (unless the command-line option ‘-localhistory’ was specified, in + which case the history will be stored in the file ‘.asy_history’ in the current directory). - Typing 'ctrl-C' interrupts the execution of 'Asymptote' code and + Typing ‘ctrl-C’ interrupts the execution of ‘Asymptote’ code and returns control to the interactive prompt. - Interactive mode is implemented with the GNU 'readline' library, with + Interactive mode is implemented with the GNU ‘readline’ library, with command history and auto-completion. To customize the key bindings, see: <https://tiswww.case.edu/php/chet/readline/readline.html> - The file 'asymptote.py' in the 'Asymptote' system directory provides -an alternative way of entering 'Asymptote' commands interactively, -coupled with the full power of 'Python'. Copy this file to your 'Python -path' and then execute from within 'Python 3' the commands + The file ‘asymptote.py’ in the ‘Asymptote’ system directory provides +an alternative way of entering ‘Asymptote’ commands interactively, +coupled with the full power of ‘Python’. Copy this file to your ‘Python +path’ and then execute from within ‘Python 3’ the commands from asymptote import * g=asy() g.size(200) @@ -8619,13 +8678,13 @@ File: asymptote.info, Node: GUI, Next: Command-Line Interface, Prev: Interact * Menu: -* GUI installation:: Installing 'xasy' -* GUI usage:: Using 'xasy' to edit objects +* GUI installation:: Installing ‘xasy’ +* GUI usage:: Using ‘xasy’ to edit objects In the event that adjustments to the final figure are required, the -preliminary Graphical User Interface (GUI) 'xasy' included with -'Asymptote' allows you to move graphical objects and draw new ones. The -modified figure can then be saved as a normal 'Asymptote' file. +preliminary Graphical User Interface (GUI) ‘xasy’ included with +‘Asymptote’ allows you to move graphical objects and draw new ones. The +modified figure can then be saved as a normal ‘Asymptote’ file. File: asymptote.info, Node: GUI installation, Next: GUI usage, Prev: GUI, Up: GUI @@ -8633,22 +8692,22 @@ File: asymptote.info, Node: GUI installation, Next: GUI usage, Prev: GUI, Up 11.1 GUI installation ===================== -As 'xasy' is written in the interactive scripting language 'Python/Qt', -it requires 'Python' (<https://www.python.org>), along with the 'Python' -packages 'pyqt5', 'cson', and 'numpy': +As ‘xasy’ is written in the interactive scripting language ‘Python/Qt’, +it requires ‘Python’ (<https://www.python.org>), along with the ‘Python’ +packages ‘pyqt5’, ‘cson’, and ‘numpy’: pip3 install cson numpy pyqt5 PyQt5.sip - Pictures are deconstructed into the SVG image format. Since 'Qt5' -does not support 'SVG' clipping, you will need the 'rsvg-convert' -utility, which is part of the 'librsvg2-tools' package on 'UNIX' systems -and the 'librsvg' package on 'MacOS X'; under 'Microsoft Windows', it is + Pictures are deconstructed into the SVG image format. Since ‘Qt5’ +does not support ‘SVG’ clipping, you will need the ‘rsvg-convert’ +utility, which is part of the ‘librsvg2-tools’ package on ‘UNIX’ systems +and the ‘librsvg’ package on ‘MacOS X’; under ‘Microsoft Windows’, it is available as <https://sourceforge.net/projects/tumagcc/files/rsvg-convert-2.40.20.7z> Deconstruction of a picture into its components is fastest when using -the 'LaTeX' TeX engine. The default setting 'dvisvgmMultipleFiles=true' +the ‘LaTeX’ TeX engine. The default setting ‘dvisvgmMultipleFiles=true’ speeds up deconstruction under PDF TeX engines. @@ -8658,7 +8717,7 @@ File: asymptote.info, Node: GUI usage, Prev: GUI installation, Up: GUI ============== The arrow keys (or mouse wheel) are convenient for temporarily raising -and lowering objects within 'xasy', allowing an object to be selected. +and lowering objects within ‘xasy’, allowing an object to be selected. Pressing the arrow keys will pan while the shift key is held and zoom while the control key is held. The mouse wheel will pan while the alt or shift keys is held and zoom while the control key is held. In @@ -8681,45 +8740,45 @@ File: asymptote.info, Node: Command-Line Interface, Next: PostScript to Asympt 12 Command-Line Interface ************************* -'Asymptote' code may be sent to the <http://asymptote.ualberta.ca> +‘Asymptote’ code may be sent to the <http://asymptote.ualberta.ca> server directly from the command line, specifying any options directly in the URL: - * SVG output: + • SVG output: - 'curl --data-binary 'import venn;' - 'asymptote.ualberta.ca:10007?f=svg' | display -' + ‘curl --data-binary 'import venn;' + 'asymptote.ualberta.ca:10007?f=svg' | display -’ - * HTML output: + • HTML output: - 'curl --data-binary + ‘curl --data-binary @/usr/local/share/doc/asymptote/examples/Klein.asy - 'asymptote.ualberta.ca:10007' -o Klein.html' + 'asymptote.ualberta.ca:10007' -o Klein.html’ - * V3D output: + • V3D output: - 'curl --data-binary 'import teapot;' - 'asymptote.ualberta.ca:10007?f=v3d' -o teapot.v3d' + ‘curl --data-binary 'import teapot;' + 'asymptote.ualberta.ca:10007?f=v3d' -o teapot.v3d’ - * PDF output with rendered bitmap at 2 pixels per bp: + • PDF output with rendered bitmap at 2 pixels per bp: - 'curl --data-binary 'import teapot;' - 'asymptote.ualberta.ca:10007?f=pdf' -o teapot.pdf' + ‘curl --data-binary 'import teapot;' + 'asymptote.ualberta.ca:10007?f=pdf' -o teapot.pdf’ - * PDF output with rendered bitmap at 4 pixels per bp: + • PDF output with rendered bitmap at 4 pixels per bp: - 'curl --data-binary 'import teapot;' - 'asymptote.ualberta.ca:10007?f=pdf&render=4' -o teapot.pdf' + ‘curl --data-binary 'import teapot;' + 'asymptote.ualberta.ca:10007?f=pdf&render=4' -o teapot.pdf’ - * PRC output: + • PRC output: - 'curl --data-binary 'import teapot;' - 'asymptote.ualberta.ca:10007?f=pdf&prc' -o teapot.pdf' + ‘curl --data-binary 'import teapot;' + 'asymptote.ualberta.ca:10007?f=pdf&prc' -o teapot.pdf’ - * PRC output with rendered preview bitmap at 4 pixels per bp: + • PRC output with rendered preview bitmap at 4 pixels per bp: - 'curl --data-binary 'import teapot;' - 'asymptote.ualberta.ca:10007?f=pdf&prc&render=4' -o teapot.pdf' + ‘curl --data-binary 'import teapot;' + 'asymptote.ualberta.ca:10007?f=pdf&prc&render=4' -o teapot.pdf’ The source code for the command-line interface is available at <https://github.com/vectorgraphics/asymptote-http-server>. @@ -8730,27 +8789,27 @@ File: asymptote.info, Node: Language server protocol, Next: PostScript to Asym 13 Language server protocol *************************** -Under 'UNIX' and 'MacOS X', 'Asymptote' supports features of the +Under ‘UNIX’ and ‘MacOS X’, ‘Asymptote’ supports features of the Language Server Protocol (LSP) (https://en.wikipedia.org/wiki/Language_Server_Protocol), including -function signature and variable matching. Under 'MSWindows', -'Asymptote' currently supports LSP only when compiled within the -'Windows Subsystem for Linux'. +function signature and variable matching. Under ‘MSWindows’, +‘Asymptote’ currently supports LSP only when compiled within the +‘Windows Subsystem for Linux’. - 'Emacs' users can enable the 'Asymptote' language server protocol by -installing 'lsp-mode' using the following procedure: + ‘Emacs’ users can enable the ‘Asymptote’ language server protocol by +installing ‘lsp-mode’ using the following procedure: - * Add to the '.emacs' initialization file: + • Add to the ‘.emacs’ initialization file: (require 'package) (add-to-list 'package-archives '("melpa" . "https://melpa.org/packages/") t) (package-initialize) - * Launch emacs and execute + • Launch emacs and execute M-x package-refresh-contents M-x package-install - and select 'lsp-mode'. + and select ‘lsp-mode’. - * Add to the '.emacs' initialization file: + • Add to the ‘.emacs’ initialization file: (require 'lsp-mode) (add-to-list 'lsp-language-id-configuration '(asy-mode . "asymptote")) @@ -8762,27 +8821,27 @@ installing 'lsp-mode' using the following procedure: ) ) - * Launch emacs and execute + • Launch emacs and execute M-x lsp File: asymptote.info, Node: PostScript to Asymptote, Next: Help, Prev: Command-Line Interface, Up: Top -14 'PostScript' to 'Asymptote' +14 ‘PostScript’ to ‘Asymptote’ ****************************** -The excellent 'PostScript' editor 'pstoedit' (version 3.50 or later; +The excellent ‘PostScript’ editor ‘pstoedit’ (version 3.50 or later; available from <https://sourceforge.net/projects/pstoedit/>) includes an -'Asymptote' backend. Unlike virtually all other 'pstoedit' backends, -this driver includes native clipping, even-odd fill rule, 'PostScript' -subpath, and full image support. Here is an example: 'asy -V -/usr/local/share/doc/asymptote/examples/venn.asy' +‘Asymptote’ backend. Unlike virtually all other ‘pstoedit’ backends, +this driver includes native clipping, even-odd fill rule, ‘PostScript’ +subpath, and full image support. Here is an example: ‘asy -V +/usr/local/share/doc/asymptote/examples/venn.asy’ pstoedit -f asy venn.eps test.asy asy -V test -If the line widths aren't quite correct, try giving 'pstoedit' the -'-dis' option. If the fonts aren't typeset correctly, try giving -'pstoedit' the '-dt' option. +If the line widths aren’t quite correct, try giving ‘pstoedit’ the +‘-dis’ option. If the fonts aren’t typeset correctly, try giving +‘pstoedit’ the ‘-dt’ option. File: asymptote.info, Node: Help, Next: Debugger, Prev: PostScript to Asymptote, Up: Top @@ -8792,30 +8851,30 @@ File: asymptote.info, Node: Help, Next: Debugger, Prev: PostScript to Asympto A list of frequently asked questions (FAQ) is maintained at <https://asymptote.sourceforge.io/FAQ> -Questions on installing and using 'Asymptote' that are not addressed in -the FAQ should be sent to the 'Asymptote' forum: +Questions on installing and using ‘Asymptote’ that are not addressed in +the FAQ should be sent to the ‘Asymptote’ forum: <https://sourceforge.net/p/asymptote/discussion/409349> Including an example that illustrates what you are trying to do will -help you get useful feedback. 'LaTeX' problems can often be diagnosed -with the '-vv' or '-vvv' command-line options. Contributions in the -form of patches or 'Asymptote' modules can be posted here: +help you get useful feedback. ‘LaTeX’ problems can often be diagnosed +with the ‘-vv’ or ‘-vvv’ command-line options. Contributions in the +form of patches or ‘Asymptote’ modules can be posted here: <https://sourceforge.net/p/asymptote/patches> To receive announcements of upcoming releases, please subscribe to -'Asymptote' at +‘Asymptote’ at <https://sourceforge.net/projects/asymptote/> -If you find a bug in 'Asymptote', please check (if possible) whether the -bug is still present in the latest 'git' developmental code (*note +If you find a bug in ‘Asymptote’, please check (if possible) whether the +bug is still present in the latest ‘git’ developmental code (*note Git::) before submitting a bug report. New bugs can be reported at <https://github.com/vectorgraphics/asymptote/issues> To see if the bug has already been fixed, check bugs with Status -'Closed' and recent lines in +‘Closed’ and recent lines in <https://asymptote.sourceforge.io/ChangeLog> - 'Asymptote' can be configured with the optional GNU library -'libsigsegv', available from <https://www.gnu.org/software/libsigsegv/>, -which allows one to distinguish user-generated 'Asymptote' stack + ‘Asymptote’ can be configured with the optional GNU library +‘libsigsegv’, available from <https://www.gnu.org/software/libsigsegv/>, +which allows one to distinguish user-generated ‘Asymptote’ stack overflows (*note stack overflow::) from true segmentation faults (due to -internal C++ programming errors; please submit the 'Asymptote' code that +internal C++ programming errors; please submit the ‘Asymptote’ code that generates such segmentation faults along with your bug report). @@ -8826,17 +8885,17 @@ File: asymptote.info, Node: Debugger, Next: Credits, Prev: Help, Up: Top Asymptote now includes a line-based (as opposed to code-based) debugger that can assist the user in following flow control. To set a break -point in file 'file' at line 'line', use the command +point in file ‘file’ at line ‘line’, use the command void stop(string file, int line, code s=quote{}); -The optional argument 's' may be used to conditionally set the variable -'ignore' in 'plain_debugger.asy' to 'true'. For example, the first 10 -instances of this breakpoint will be ignored (the variable 'int count=0' -is defined in 'plain_debugger.asy'): +The optional argument ‘s’ may be used to conditionally set the variable +‘ignore’ in ‘plain_debugger.asy’ to ‘true’. For example, the first 10 +instances of this breakpoint will be ignored (the variable ‘int count=0’ +is defined in ‘plain_debugger.asy’): stop("test",2,quote{ignore=(++count <= 10);}); - To set a break point in file 'file' at the first line containing the -string 'text', use + To set a break point in file ‘file’ at the first line containing the +string ‘text’, use void stop(string file, string text, code s=quote{}); To list all breakpoints, use: @@ -8848,37 +8907,37 @@ void clear(); The following commands may be entered at the debugging prompt: -'h' +‘h’ help; -'c' +‘c’ continue execution; -'i' +‘i’ step to the next instruction; -'s' +‘s’ step to the next executable line; -'n' +‘n’ step to the next executable line in the current file; -'f' +‘f’ step to the next file; -'r' +‘r’ return to the file associated with the most recent breakpoint; -'t' - toggle tracing ('-vvvvv') mode; +‘t’ + toggle tracing (‘-vvvvv’) mode; -'q' +‘q’ quit debugging and end execution; -'x' +‘x’ exit the debugger and run to completion. -Arbitrary 'Asymptote' code may also be entered at the debugging prompt; -however, since the debugger is implemented with 'eval', currently only +Arbitrary ‘Asymptote’ code may also be entered at the debugging prompt; +however, since the debugger is implemented with ‘eval’, currently only top-level (global) variables can be displayed or modified. The debugging prompt may be entered manually with the call @@ -8890,24 +8949,24 @@ File: asymptote.info, Node: Credits, Next: Index, Prev: Debugger, Up: Top 17 Acknowledgments ****************** -Financial support for the development of 'Asymptote' was generously +Financial support for the development of ‘Asymptote’ was generously provided by the Natural Sciences and Engineering Research Council of Canada, the Pacific Institute for Mathematical Sciences, and the University of Alberta Faculty of Science. We also would like to acknowledge the previous work of John D. Hobby, -author of the program 'MetaPost' that inspired the development of -'Asymptote', and Donald E. Knuth, author of TeX and 'MetaFont' (on which -'MetaPost' is based). +author of the program ‘MetaPost’ that inspired the development of +‘Asymptote’, and Donald E. Knuth, author of TeX and ‘MetaFont’ (on which +‘MetaPost’ is based). - The authors of 'Asymptote' are Andy Hammerlindl, John Bowman, and Tom -Prince. Sean Healy designed the 'Asymptote' logo. Other contributors + The authors of ‘Asymptote’ are Andy Hammerlindl, John Bowman, and Tom +Prince. Sean Healy designed the ‘Asymptote’ logo. Other contributors include Orest Shardt, Jesse Frohlich, Michail Vidiassov, Charles Staats, Philippe Ivaldi, Olivier Guibé, Radoslav Marinov, Jeff Samuelson, Chris Savage, Jacques Pienaar, Mark Henning, Steve Melenchuk, Martin Wiebusch, -Stefan Knorr, Supakorn "Jamie" Rassameemasmuang, Jacob Skitsko, Joseph -Chaumont, and Oliver Cheng. Pedram Emami developed the 'Asymptote Web -Application' hosted at <http://asymptote.ualberta.ca>: +Stefan Knorr, Supakorn “Jamie” Rassameemasmuang, Jacob Skitsko, Joseph +Chaumont, and Oliver Cheng. Pedram Emami developed the ‘Asymptote Web +Application’ hosted at <http://asymptote.ualberta.ca>: <https://github.com/vectorgraphics/asymptoteWebApplication> @@ -8959,9 +9018,9 @@ Index * ---: Bezier curves. (line 84) * -=: Self & prefix operators. (line 6) -* -c: Options. (line 226) -* -l: Options. (line 245) -* -u: Options. (line 236) +* -c: Options. (line 227) +* -l: Options. (line 246) +* -u: Options. (line 237) * -V: Configuring. (line 6) * -V <1>: Drawing in batch mode. (line 16) @@ -8974,7 +9033,7 @@ Index * 2D graphs: graph. (line 6) * 3D graphs: graph3. (line 6) * 3D grids: grid3. (line 6) -* 3D PostScript: three. (line 655) +* 3D PostScript: three. (line 665) * :: Arithmetic & logical. (line 61) * ::: Bezier curves. (line 70) @@ -9014,7 +9073,7 @@ Index * absolute <1>: three. (line 241) * accel: Paths and guides. (line 126) * accel <1>: Paths and guides. (line 132) -* accel <2>: three. (line 556) +* accel <2>: three. (line 566) * access: Import. (line 6) * access <1>: Import. (line 45) * acknowledgments: Credits. (line 6) @@ -9028,8 +9087,8 @@ Index (line 217) * add <1>: Frames and pictures. (line 231) -* add <2>: three. (line 332) -* addViews: three. (line 449) +* add <2>: three. (line 342) +* addViews: three. (line 459) * adjust: Pens. (line 123) * Ai: Mathematical functions. (line 48) @@ -9040,7 +9099,7 @@ Index * alias: Structures. (line 62) * alias <1>: Arrays. (line 183) * Align: label. (line 12) -* aligndir: Options. (line 218) +* aligndir: Options. (line 219) * all: Arrays. (line 350) * Allow: Pens. (line 363) * and: Bezier curves. (line 56) @@ -9054,21 +9113,21 @@ Index * animation <1>: animation. (line 6) * annotate: annotate. (line 6) * antialias: three. (line 261) -* antialias <1>: Options. (line 187) +* antialias <1>: Options. (line 188) * append: Files. (line 38) * append <1>: Arrays. (line 39) * arc: Paths and guides. (line 24) * Arc: Paths and guides. (line 37) -* arc <1>: three. (line 343) +* arc <1>: three. (line 353) * ArcArrow: draw. (line 26) -* ArcArrow3: three. (line 622) +* ArcArrow3: three. (line 632) * ArcArrows: draw. (line 26) -* ArcArrows3: three. (line 622) +* ArcArrows3: three. (line 632) * arclength: Paths and guides. (line 153) -* arclength <1>: three. (line 556) +* arclength <1>: three. (line 566) * arcpoint: Paths and guides. (line 163) * arctime: Paths and guides. (line 157) -* arctime <1>: three. (line 556) +* arctime <1>: three. (line 566) * arguments: Default arguments. (line 6) * arithmetic operators: Arithmetic & logical. (line 6) @@ -9082,10 +9141,10 @@ Index * arrow keys: Drawing in interactive mode. (line 11) * arrow keys <1>: GUI usage. (line 6) -* Arrow3: three. (line 622) +* Arrow3: three. (line 632) * arrows: draw. (line 26) * Arrows: draw. (line 26) -* Arrows3: three. (line 622) +* Arrows3: three. (line 632) * as: Import. (line 67) * ascii: Data types. (line 309) * ascii <1>: Data types. (line 309) @@ -9104,11 +9163,11 @@ Index * asy-mode: Editing modes. (line 6) * asy.vim: Editing modes. (line 32) * asygl: Configuring. (line 69) -* asyinclude: LaTeX usage. (line 45) +* asyinclude: LaTeX usage. (line 42) * Asymptote Web Application: Description. (line 6) * asymptote.sty: LaTeX usage. (line 6) * asymptote.xml: Editing modes. (line 48) -* ASYMPTOTE_CONFIG: Options. (line 158) +* ASYMPTOTE_CONFIG: Options. (line 159) * atan: Mathematical functions. (line 6) * aTan: Mathematical functions. @@ -9120,15 +9179,15 @@ Index * atleast: Bezier curves. (line 56) * attach: Frames and pictures. (line 276) -* attach <1>: LaTeX usage. (line 50) -* attach <2>: graph. (line 406) -* autoadjust: three. (line 418) -* autoimport: Options. (line 154) -* automatic scaling: graph. (line 710) -* automatic scaling <1>: graph. (line 710) +* attach <1>: LaTeX usage. (line 47) +* attach <2>: graph. (line 407) +* autoadjust: three. (line 428) +* autoimport: Options. (line 155) +* automatic scaling: graph. (line 711) +* automatic scaling <1>: graph. (line 711) * axialshade: fill. (line 43) -* axis: graph. (line 924) -* axis <1>: graph. (line 1006) +* axis: graph. (line 925) +* axis <1>: graph. (line 1007) * axis <2>: graph3. (line 66) * axis <3>: graph3. (line 82) * azimuth: Data types. (line 154) @@ -9137,11 +9196,11 @@ Index * background <1>: three. (line 97) * background color: Frames and pictures. (line 180) -* BackView: three. (line 442) +* BackView: three. (line 452) * Bar: draw. (line 19) -* Bar3: three. (line 622) +* Bar3: three. (line 632) * Bars: draw. (line 19) -* Bars3: three. (line 622) +* Bars3: three. (line 632) * barsize: draw. (line 19) * base modules: Base modules. (line 6) * basealign: Pens. (line 181) @@ -9150,18 +9209,18 @@ Index (line 6) * beep: Data types. (line 382) * BeginArcArrow: draw. (line 26) -* BeginArcArrow3: three. (line 622) +* BeginArcArrow3: three. (line 632) * BeginArrow: draw. (line 26) -* BeginArrow3: three. (line 622) +* BeginArrow3: three. (line 632) * BeginBar: draw. (line 19) -* BeginBar3: three. (line 622) +* BeginBar3: three. (line 632) * BeginDotMargin: draw. (line 42) -* BeginDotMargin3: three. (line 638) +* BeginDotMargin3: three. (line 648) * BeginMargin: draw. (line 42) -* BeginMargin3: three. (line 638) +* BeginMargin3: three. (line 648) * BeginPenMargin: draw. (line 42) -* BeginPenMargin2: three. (line 638) -* BeginPenMargin3: three. (line 638) +* BeginPenMargin2: three. (line 648) +* BeginPenMargin3: three. (line 648) * BeginPoint: label. (line 55) * Bessel: Mathematical functions. (line 48) @@ -9173,7 +9232,7 @@ Index * bezulate: three. (line 146) * Bi: Mathematical functions. (line 48) -* Billboard: three. (line 526) +* Billboard: three. (line 536) * binary: Files. (line 80) * binary format: Files. (line 80) * binary operators: Arithmetic & logical. @@ -9198,9 +9257,9 @@ Index * bool3: Data types. (line 25) * boolean operators: Arithmetic & logical. (line 6) -* Bottom: graph. (line 132) -* BottomTop: graph. (line 138) -* BottomView: three. (line 442) +* Bottom: graph. (line 133) +* BottomTop: graph. (line 139) +* BottomView: three. (line 452) * bounding box: Frames and pictures. (line 180) * bounds: palette. (line 43) @@ -9209,15 +9268,15 @@ Index (line 25) * box <1>: Frames and pictures. (line 130) -* box <2>: three. (line 365) -* box <3>: three. (line 367) +* box <2>: three. (line 375) +* box <3>: three. (line 377) * bp: Drawing in batch mode. (line 23) * brace: Paths and guides. (line 51) * break: Programming. (line 48) * breakpoints: Debugger. (line 21) * brick: Pens. (line 285) -* broken axis: graph. (line 821) +* broken axis: graph. (line 822) * bug reports: Help. (line 19) * buildcycle: Paths and guides. (line 270) * Button-1: GUI. (line 6) @@ -9228,7 +9287,7 @@ Index * CAD: CAD. (line 6) * calculateTransform: Frames and pictures. (line 118) -* camera: three. (line 412) +* camera: three. (line 422) * casts: Casts. (line 6) * cbrt: Mathematical functions. (line 6) @@ -9236,7 +9295,7 @@ Index * ceil: Mathematical functions. (line 26) * Center: label. (line 60) -* center: three. (line 395) +* center: three. (line 405) * checker: Pens. (line 285) * Chinese: Pens. (line 244) * choose: Mathematical functions. @@ -9245,7 +9304,7 @@ Index (line 48) * circle: Paths and guides. (line 10) * Circle: Paths and guides. (line 18) -* circle <1>: three. (line 339) +* circle <1>: three. (line 349) * circle <2>: flowchart. (line 61) * circlebarframe: markers. (line 18) * CJK: Pens. (line 244) @@ -9284,13 +9343,13 @@ Index * conditional <1>: Arithmetic & logical. (line 61) * config: Configuring. (line 69) -* config <1>: Options. (line 158) +* config <1>: Options. (line 159) * configuration file: Configuring. (line 15) -* configuration file <1>: Options. (line 158) +* configuration file <1>: Options. (line 159) * configuring: Configuring. (line 6) * conj: Data types. (line 62) * constructors: Structures. (line 91) -* context: Options. (line 187) +* context: Options. (line 188) * continue: Programming. (line 48) * continue <1>: Debugger. (line 31) * contour: contour. (line 6) @@ -9301,8 +9360,8 @@ Index * convert: Configuring. (line 69) * convert <1>: Files. (line 159) * convert <2>: animation. (line 6) -* convert <3>: Options. (line 187) -* convertOptions: Options. (line 173) +* convert <3>: Options. (line 188) +* convertOptions: Options. (line 174) * Coons shading: fill. (line 78) * copy: Arrays. (line 176) * cos: Mathematical functions. @@ -9312,11 +9371,11 @@ Index * cosh: Mathematical functions. (line 6) * cputime: Structures. (line 169) -* crop: graph. (line 639) -* cropping graphs: graph. (line 639) +* crop: graph. (line 640) +* cropping graphs: graph. (line 640) * cross: Data types. (line 106) * cross <1>: Data types. (line 197) -* cross <2>: graph. (line 480) +* cross <2>: graph. (line 481) * crossframe: markers. (line 22) * crosshatch: Pens. (line 302) * csv: Arrays. (line 382) @@ -9328,11 +9387,11 @@ Index * curlSpecifier: Paths and guides. (line 408) * currentlight: three. (line 76) * currentpen: Pens. (line 6) -* currentprojection: three. (line 439) +* currentprojection: three. (line 449) * curve: slopefield. (line 20) -* custom axis types: graph. (line 141) -* custom mark routine: graph. (line 577) -* custom tick locations: graph. (line 233) +* custom axis types: graph. (line 142) +* custom mark routine: graph. (line 578) +* custom tick locations: graph. (line 234) * cut: Paths and guides. (line 251) * cycle: Figure size. (line 29) * cycle <1>: Paths. (line 16) @@ -9340,7 +9399,7 @@ Index * cyclic: Paths and guides. (line 85) * cyclic <1>: Paths and guides. (line 376) * cyclic <2>: Arrays. (line 39) -* cyclic <3>: three. (line 556) +* cyclic <3>: three. (line 566) * Cyrillic: Pens. (line 238) * dashdotted: Pens. (line 102) * dashed: Pens. (line 102) @@ -9352,9 +9411,9 @@ Index * declaration: Programming. (line 26) * deconstruct: GUI usage. (line 6) * default arguments: Default arguments. (line 6) -* defaultformat: graph. (line 175) +* defaultformat: graph. (line 176) * DefaultHead: draw. (line 26) -* DefaultHead3: three. (line 622) +* DefaultHead3: three. (line 632) * defaultpen: Pens. (line 49) * defaultpen <1>: Pens. (line 122) * defaultpen <2>: Pens. (line 127) @@ -9382,7 +9441,7 @@ Index * dir <1>: Data types. (line 90) * dir <2>: Data types. (line 181) * dir <3>: Paths and guides. (line 109) -* dir <4>: three. (line 556) +* dir <4>: three. (line 566) * direction specifier: Bezier curves. (line 6) * directory: Files. (line 26) * dirSpecifier: Paths and guides. (line 390) @@ -9397,11 +9456,11 @@ Index * dot <3>: Arrays. (line 279) * dot <4>: Arrays. (line 282) * DotMargin: draw. (line 42) -* DotMargin3: three. (line 638) +* DotMargin3: three. (line 648) * DotMargins: draw. (line 42) -* DotMargins3: three. (line 638) +* DotMargins3: three. (line 648) * dotted: Pens. (line 102) -* double deferred drawing: three. (line 317) +* double deferred drawing: three. (line 327) * double precision: Files. (line 80) * draw: Drawing commands. (line 34) * draw <1>: draw. (line 6) @@ -9414,11 +9473,11 @@ Index * drawline: math. (line 9) * drawtree: drawtree. (line 6) * dvips: Configuring. (line 69) -* dvipsOptions: Options. (line 173) +* dvipsOptions: Options. (line 174) * dvisvgm: Configuring. (line 69) -* dvisvgm <1>: Options. (line 192) +* dvisvgm <1>: Options. (line 193) * dvisvgmMultipleFiles: GUI installation. (line 20) -* dvisvgmOptions: Options. (line 173) +* dvisvgmOptions: Options. (line 174) * E: Labels. (line 18) * E <1>: Mathematical functions. (line 48) @@ -9433,24 +9492,24 @@ Index * else: Programming. (line 26) * emacs: Editing modes. (line 6) * embed: embed. (line 6) -* Embedded: three. (line 526) +* Embedded: three. (line 536) * emissivepen: three. (line 66) * empty: Frames and pictures. (line 7) * EndArcArrow: draw. (line 26) -* EndArcArrow3: three. (line 622) +* EndArcArrow3: three. (line 632) * EndArrow: draw. (line 26) -* EndArrow3: three. (line 622) +* EndArrow3: three. (line 632) * EndBar: draw. (line 19) -* EndBar3: three. (line 622) +* EndBar3: three. (line 632) * EndDotMargin: draw. (line 42) -* EndDotMargin3: three. (line 638) +* EndDotMargin3: three. (line 648) * endl: Files. (line 65) * EndMargin: draw. (line 42) -* EndMargin3: three. (line 638) +* EndMargin3: three. (line 648) * EndPenMargin: draw. (line 42) -* EndPenMargin2: three. (line 638) -* EndPenMargin3: three. (line 638) +* EndPenMargin2: three. (line 648) +* EndPenMargin3: three. (line 648) * EndPoint: label. (line 55) * envelope: Frames and pictures. (line 25) @@ -9460,7 +9519,7 @@ Index * eol: Files. (line 97) * eol <1>: Arrays. (line 364) * EPS: label. (line 78) -* EPS <1>: Options. (line 187) +* EPS <1>: Options. (line 188) * erase: Drawing in interactive mode. (line 11) * erase <1>: Data types. (line 257) @@ -9474,8 +9533,8 @@ Index (line 6) * error: Files. (line 16) * error <1>: Files. (line 97) -* error bars: graph. (line 531) -* errorbars: graph. (line 480) +* error bars: graph. (line 532) +* errorbars: graph. (line 481) * eval: Import. (line 102) * eval <1>: Import. (line 112) * evenodd: Paths. (line 37) @@ -9497,12 +9556,12 @@ Index * extension: Paths and guides. (line 246) * extension <1>: MetaPost. (line 10) * external: embed. (line 11) -* extrude: three. (line 550) +* extrude: three. (line 560) * F: Mathematical functions. (line 48) * fabs: Mathematical functions. (line 6) -* face: three. (line 662) +* face: three. (line 672) * factorial: Mathematical functions. (line 39) * Fedora: UNIX binary distributions. @@ -9533,7 +9592,7 @@ Index * firstcut: Paths and guides. (line 262) * fit: Frames and pictures. (line 113) -* fit3: three. (line 330) +* fit3: three. (line 340) * fixedscaling: Frames and pictures. (line 81) * floor: Mathematical functions. @@ -9551,13 +9610,13 @@ Index * fontsize: Pens. (line 192) * for: Programming. (line 26) * format: Data types. (line 290) -* format <1>: Options. (line 187) +* format <1>: Options. (line 188) * forum: Help. (line 6) * frame: Frames and pictures. (line 7) * freshnel0: three. (line 66) * from: Import. (line 16) -* FrontView: three. (line 442) +* FrontView: three. (line 452) * function declarations: Functions. (line 79) * Function shading: fill. (line 100) * function shading: fill. (line 100) @@ -9580,7 +9639,7 @@ Index * globalwrite: Files. (line 40) * globalwrite <1>: Files. (line 154) * glOptions: three. (line 261) -* glOptions <1>: Options. (line 173) +* glOptions <1>: Options. (line 174) * GNU Scientific Library: Mathematical functions. (line 48) * gouraudshade: fill. (line 63) @@ -9589,21 +9648,21 @@ Index * graph: graph. (line 6) * graph3: graph3. (line 6) * graphic: label. (line 78) -* graphic <1>: Options. (line 192) +* graphic <1>: Options. (line 193) * graphical user interface: GUI. (line 6) -* graphwithderiv: graph. (line 670) +* graphwithderiv: graph. (line 671) * gray: Pens. (line 25) * grayscale: Pens. (line 25) * Grayscale: palette. (line 9) * grid: Pens. (line 285) -* grid <1>: graph. (line 766) +* grid <1>: graph. (line 767) * grid3: grid3. (line 6) * gs: Configuring. (line 15) * GSL: Compiling from UNIX source. (line 62) * gsl: Mathematical functions. (line 48) -* gsOptions: Options. (line 173) +* gsOptions: Options. (line 174) * GUI: GUI. (line 6) * GUI installation: GUI installation. (line 6) * GUI usage: GUI usage. (line 6) @@ -9611,7 +9670,7 @@ Index * guide3: three. (line 6) * hatch: Pens. (line 302) * Headlamp: three. (line 76) -* height: LaTeX usage. (line 50) +* height: LaTeX usage. (line 47) * help: Interactive mode. (line 42) * help <1>: Help. (line 6) * help <2>: Debugger. (line 30) @@ -9621,20 +9680,20 @@ Index * hex <1>: Pens. (line 64) * hexadecimal: Data types. (line 306) * hexadecimal <1>: Pens. (line 62) -* hidden surface removal: three. (line 662) +* hidden surface removal: three. (line 672) * histogram: Mathematical functions. (line 39) * history: Files. (line 147) * history <1>: Interactive mode. (line 54) * historylines: Interactive mode. (line 58) * HookHead: draw. (line 26) -* HookHead3: three. (line 622) +* HookHead3: three. (line 632) * Horizontal: flowchart. (line 77) * HTML5: three. (line 233) * htmlviewer: Configuring. (line 15) * htmlviewer <1>: Configuring. (line 38) -* htmlviewerOptions: Options. (line 173) -* hyperrefOptions: Options. (line 173) +* htmlviewerOptions: Options. (line 174) +* hyperrefOptions: Options. (line 174) * hypot: Mathematical functions. (line 6) * I: Mathematical functions. @@ -9645,7 +9704,7 @@ Index * identity <1>: Mathematical functions. (line 6) * identity <2>: Arrays. (line 321) -* identity4: three. (line 494) +* identity4: three. (line 504) * if: Programming. (line 26) * IgnoreAspect: Frames and pictures. (line 63) @@ -9654,17 +9713,17 @@ Index * image-based lighting: three. (line 104) * ImageMagick: Configuring. (line 69) * ImageMagick <1>: animation. (line 6) -* ImageMagick <2>: Options. (line 187) +* ImageMagick <2>: Options. (line 188) * images: palette. (line 6) * implicit casts: Casts. (line 6) * implicit linear solver: MetaPost. (line 10) * implicit scaling: Implicit scaling. (line 6) * implicitsurface: smoothcontour3. (line 16) * import: Import. (line 45) -* importv3d: three. (line 308) +* importv3d: three. (line 318) * inches: Figure size. (line 18) * incircle: Data types. (line 120) -* include: Import. (line 134) +* include: Import. (line 131) * including images: label. (line 78) * increasing: math. (line 55) * inf: Data types. (line 35) @@ -9672,7 +9731,7 @@ Index * initialized: Arrays. (line 39) * initializers: Variable initializers. (line 6) -* inline: LaTeX usage. (line 50) +* inline: LaTeX usage. (line 47) * InOutTicks: graph3. (line 35) * input: Files. (line 10) * input <1>: Files. (line 12) @@ -9684,7 +9743,7 @@ Index * inside: Paths and guides. (line 294) * inside <1>: Paths and guides. (line 299) * inside <2>: Paths and guides. (line 305) -* insphere: three. (line 585) +* insphere: three. (line 595) * inst: Debugger. (line 35) * installation: Installation. (line 6) * int: Data types. (line 30) @@ -9703,23 +9762,23 @@ Index * interpolate: interpolate. (line 6) * intersect: Paths and guides. (line 195) * intersect <1>: math. (line 13) -* intersect <2>: three. (line 556) +* intersect <2>: three. (line 566) * intersectionpoint: Paths and guides. (line 238) * intersectionpoint <1>: math. (line 17) -* intersectionpoint <2>: three. (line 556) +* intersectionpoint <2>: three. (line 566) * intersectionpoints: Paths and guides. (line 242) -* intersectionpoints <1>: three. (line 556) -* intersectionpoints <2>: three. (line 569) +* intersectionpoints <1>: three. (line 566) +* intersectionpoints <2>: three. (line 579) * intersections: Paths and guides. (line 206) * intersections <1>: Paths and guides. (line 213) -* intersections <2>: three. (line 556) -* intersections <3>: three. (line 562) +* intersections <2>: three. (line 566) +* intersections <3>: three. (line 572) * InTicks: graph3. (line 35) * intMax: Data types. (line 30) * intMin: Data types. (line 30) * inverse: Transforms. (line 16) * inverse <1>: Arrays. (line 327) -* invert: three. (line 484) +* invert: three. (line 494) * invisible: Pens. (line 43) * isnan: Data types. (line 35) * i_scaled: Mathematical functions. @@ -9737,7 +9796,7 @@ Index (line 59) * keepAspect <1>: Frames and pictures. (line 63) -* keepAspect <2>: LaTeX usage. (line 50) +* keepAspect <2>: LaTeX usage. (line 47) * keyboard bindings:: three. (line 211) * keys: Arrays. (line 39) * keyword: Named arguments. (line 37) @@ -9750,20 +9809,20 @@ Index * Label: draw. (line 101) * label <1>: label. (line 6) * Label <1>: label. (line 14) -* Label <2>: graph. (line 330) -* label <2>: three. (line 520) +* Label <2>: graph. (line 331) +* label <2>: three. (line 530) * labelpath: labelpath. (line 6) * labelpath3: labelpath3. (line 6) -* labelx: graph. (line 330) -* labely: graph. (line 330) +* labelx: graph. (line 331) +* labely: graph. (line 331) * Landscape: Frames and pictures. - (line 104) + (line 103) * language context: Pens. (line 235) * language server protocol: Language server protocol. (line 6) * lastcut: Paths and guides. (line 266) * lasy-mode: Editing modes. (line 6) -* latex: Options. (line 187) +* latex: Options. (line 188) * LaTeX NFSS fonts: Pens. (line 206) * LaTeX usage: LaTeX usage. (line 6) * latexmk: LaTeX usage. (line 30) @@ -9771,16 +9830,16 @@ Index * latticeshade: fill. (line 32) * layer: Drawing commands. (line 16) * leastsquares: stats. (line 6) -* leastsquares <1>: graph. (line 947) -* Left: graph. (line 269) -* LeftRight: graph. (line 275) +* leastsquares <1>: graph. (line 948) +* Left: graph. (line 270) +* LeftRight: graph. (line 276) * LeftSide: label. (line 60) -* LeftTicks: graph. (line 160) -* LeftTicks <1>: graph. (line 233) -* LeftView: three. (line 442) +* LeftTicks: graph. (line 161) +* LeftTicks <1>: graph. (line 234) +* LeftView: three. (line 452) * legend: Drawing commands. (line 34) * legend <1>: draw. (line 65) -* legend <2>: graph. (line 424) +* legend <2>: graph. (line 425) * Legendre: Mathematical functions. (line 48) * length: Data types. (line 65) @@ -9789,22 +9848,23 @@ Index * length <3>: Paths and guides. (line 76) * length <4>: Paths and guides. (line 373) * length <5>: Arrays. (line 39) -* length <6>: three. (line 556) +* length <6>: three. (line 566) * letter: Configuring. (line 63) * lexorder: math. (line 63) * lexorder <1>: math. (line 66) * libcurl: Import. (line 94) -* libgs: Options. (line 192) +* libgs: Options. (line 193) * libm routines: Mathematical functions. (line 6) * libsigsegv: Functions. (line 100) * libsigsegv <1>: Help. (line 27) * light: three. (line 76) -* limits: graph. (line 639) +* limits: graph. (line 640) * line: Arrays. (line 364) * line <1>: Arrays. (line 368) * line mode: Arrays. (line 364) -* Linear: graph. (line 710) +* linear: graph. (line 36) +* Linear: graph. (line 711) * linecap: Pens. (line 139) * linejoin: Pens. (line 149) * lineskip: Pens. (line 192) @@ -9813,14 +9873,14 @@ Index * locale: Data types. (line 316) * log: Mathematical functions. (line 6) -* Log: graph. (line 710) -* log-log graph: graph. (line 744) +* Log: graph. (line 711) +* log-log graph: graph. (line 745) * log10: Mathematical functions. (line 6) * log1p: Mathematical functions. (line 6) -* log2 graph: graph. (line 800) -* logarithmic graph: graph. (line 744) +* log2 graph: graph. (line 801) +* logarithmic graph: graph. (line 745) * logical operators: Arithmetic & logical. (line 6) * longdashdotted: Pens. (line 102) @@ -9829,8 +9889,8 @@ Index * loop: Programming. (line 26) * LSP: Language server protocol. (line 6) -* lualatex: Options. (line 187) -* luatex: Options. (line 187) +* lualatex: Options. (line 188) +* luatex: Options. (line 188) * MacOS X binary distributions: MacOS X binary distributions. (line 6) * MacOS X configuration: Compiling from UNIX source. @@ -9841,17 +9901,17 @@ Index * map <2>: map. (line 6) * Margin: draw. (line 42) * Margin <1>: draw. (line 42) -* Margin3: three. (line 638) -* Margin3 <1>: three. (line 638) +* Margin3: three. (line 648) +* Margin3 <1>: three. (line 648) * Margins: draw. (line 42) -* margins: three. (line 323) -* Margins3: three. (line 638) -* mark: graph. (line 480) +* margins: three. (line 333) +* Margins3: three. (line 648) +* mark: graph. (line 481) * markangle: markers. (line 35) -* marker: graph. (line 480) +* marker: graph. (line 481) * markers: markers. (line 6) -* marknodes: graph. (line 480) -* markuniform: graph. (line 480) +* marknodes: graph. (line 481) +* markuniform: graph. (line 481) * mask: Data types. (line 35) * material: three. (line 66) * math: math. (line 6) @@ -9862,7 +9922,7 @@ Index (line 7) * max <2>: Arrays. (line 230) * max <3>: Arrays. (line 240) -* max <4>: three. (line 556) +* max <4>: three. (line 566) * maxbound: Data types. (line 134) * maxbound <1>: Data types. (line 205) * maxtile: three. (line 261) @@ -9877,9 +9937,9 @@ Index * MetaPost whatever: MetaPost. (line 10) * Microsoft Windows: Microsoft Windows. (line 6) * MidArcArrow: draw. (line 26) -* MidArcArrow3: three. (line 622) +* MidArcArrow3: three. (line 632) * MidArrow: draw. (line 26) -* MidArrow3: three. (line 622) +* MidArrow3: three. (line 632) * MidPoint: label. (line 55) * midpoint: Paths and guides. (line 180) * min: Paths and guides. (line 275) @@ -9887,7 +9947,7 @@ Index (line 7) * min <2>: Arrays. (line 225) * min <3>: Arrays. (line 235) -* min <4>: three. (line 556) +* min <4>: three. (line 566) * minbound: Data types. (line 131) * minbound <1>: Data types. (line 202) * minipage: label. (line 116) @@ -9931,16 +9991,16 @@ Index * noglobalread <1>: Files. (line 40) * nolight: three. (line 76) * NoMargin: draw. (line 42) -* NoMargin3: three. (line 638) +* NoMargin3: three. (line 648) * None: draw. (line 19) * None <1>: draw. (line 26) * none: Files. (line 65) -* normal: three. (line 542) -* nosafe: Options. (line 213) +* normal: three. (line 552) +* nosafe: Options. (line 214) * NOT: Arithmetic & logical. (line 68) * notaknot: graph. (line 36) -* NoTicks: graph. (line 160) +* NoTicks: graph. (line 161) * NoTicks3: graph3. (line 35) * null: Structures. (line 6) * nullpen: label. (line 14) @@ -9948,19 +10008,19 @@ Index (line 140) * nullpen <2>: Frames and pictures. (line 149) -* NURBS: three. (line 422) -* O: three. (line 335) +* NURBS: three. (line 432) +* O: three. (line 345) * obj: obj. (line 6) -* oblique: three. (line 378) -* obliqueX: three. (line 385) -* obliqueY: three. (line 391) -* obliqueZ: three. (line 378) +* oblique: three. (line 388) +* obliqueX: three. (line 395) +* obliqueY: three. (line 401) +* obliqueZ: three. (line 388) * ode: ode. (line 6) * offset: Pens. (line 123) -* offset <1>: Options. (line 218) -* OmitTick: graph. (line 223) -* OmitTickInterval: graph. (line 223) -* OmitTickIntervals: graph. (line 223) +* offset <1>: Options. (line 219) +* OmitTick: graph. (line 224) +* OmitTickInterval: graph. (line 224) +* OmitTickIntervals: graph. (line 224) * opacity: Pens. (line 254) * opacity <1>: three. (line 66) * open: Files. (line 12) @@ -9981,15 +10041,15 @@ Index * OR: Arithmetic & logical. (line 68) * orient: Data types. (line 108) -* orient <1>: three. (line 573) +* orient <1>: three. (line 583) * orientation: Frames and pictures. - (line 104) -* orthographic: three. (line 395) + (line 103) +* orthographic: three. (line 405) * outformat: three. (line 184) * outprefix: Frames and pictures. (line 91) * output: Files. (line 38) -* output <1>: Options. (line 187) +* output <1>: Options. (line 188) * OutTicks: graph3. (line 35) * overloading functions: Functions. (line 55) * overwrite: Pens. (line 360) @@ -10007,7 +10067,7 @@ Index * paperwidth: Configuring. (line 63) * parallelogram: flowchart. (line 47) * parametric surface: graph3. (line 99) -* parametrized curve: graph. (line 639) +* parametrized curve: graph. (line 640) * partialsum: math. (line 49) * partialsum <1>: math. (line 52) * patch-dependent colors: three. (line 119) @@ -10015,55 +10075,55 @@ Index * path <1>: Paths and guides. (line 7) * path <2>: three. (line 42) * path <3>: flowchart. (line 77) -* path markers: graph. (line 480) +* path markers: graph. (line 481) * path3: three. (line 6) * path3 <1>: three. (line 42) * path[]: Paths. (line 23) * patterns: Pens. (line 271) * patterns <1>: patterns. (line 6) * PBR: three. (line 74) -* PDF: Options. (line 187) -* pdflatex: Options. (line 187) -* pdfreloadOptions: Options. (line 173) +* PDF: Options. (line 188) +* pdflatex: Options. (line 188) +* pdfreloadOptions: Options. (line 174) * pdfviewer: Configuring. (line 15) -* pdfviewerOptions: Options. (line 173) +* pdfviewerOptions: Options. (line 174) * pen: Pens. (line 6) * PenMargin: draw. (line 42) -* PenMargin2: three. (line 638) -* PenMargin3: three. (line 638) +* PenMargin2: three. (line 648) +* PenMargin3: three. (line 648) * PenMargins: draw. (line 42) -* PenMargins2: three. (line 638) -* PenMargins3: three. (line 638) +* PenMargins2: three. (line 648) +* PenMargins3: three. (line 648) * periodic: graph. (line 36) * perl: LaTeX usage. (line 30) * perpendicular: geometry. (line 6) -* perspective: three. (line 422) +* perspective: three. (line 432) * physically based rendering: three. (line 74) * picture: Frames and pictures. (line 39) * picture alignment: Frames and pictures. (line 231) * piecewisestraight: Paths and guides. (line 92) -* pixel: three. (line 645) +* pixel: three. (line 655) * Pl: Mathematical functions. (line 48) * plain: plain. (line 6) * planar: three. (line 128) -* plane: three. (line 361) -* planeproject: three. (line 539) +* plane: three. (line 371) +* planeproject: three. (line 549) * point: Paths and guides. (line 95) * point <1>: Paths and guides. (line 379) -* point <2>: three. (line 556) +* point <2>: three. (line 566) * polar: Data types. (line 149) -* polargraph: graph. (line 88) -* polygon: graph. (line 480) +* polargraph: graph. (line 89) +* polygon: graph. (line 481) * pop: Arrays. (line 39) * Portrait: Frames and pictures. - (line 104) + (line 103) * position: three. (line 76) * position <1>: three. (line 184) * postcontrol: Paths and guides. (line 146) -* postcontrol <1>: three. (line 556) +* postcontrol <1>: three. (line 566) * postfix operators: Self & prefix operators. (line 19) * postscript: Frames and pictures. @@ -10075,7 +10135,7 @@ Index * prc: three. (line 279) * precision: Files. (line 97) * precontrol: Paths and guides. (line 139) -* precontrol <1>: three. (line 556) +* precontrol <1>: three. (line 566) * prefix operators: Self & prefix operators. (line 6) * private: Structures. (line 6) @@ -10083,7 +10143,7 @@ Index * pstoedit: PostScript to Asymptote. (line 6) * psviewer: Configuring. (line 15) -* psviewerOptions: Options. (line 173) +* psviewerOptions: Options. (line 174) * pt: Figure size. (line 18) * public: Structures. (line 6) * push: Arrays. (line 39) @@ -10107,7 +10167,7 @@ Index * radians: Mathematical functions. (line 17) * radius: Paths and guides. (line 135) -* radius <1>: three. (line 556) +* radius <1>: three. (line 566) * Rainbow: palette. (line 12) * rand: Mathematical functions. (line 39) @@ -10137,7 +10197,7 @@ Index * rename: Files. (line 156) * render: three. (line 46) * render <1>: three. (line 184) -* render <2>: Options. (line 187) +* render <2>: Options. (line 188) * replace: Data types. (line 270) * resetdefaultpen: Pens. (line 387) * rest arguments: Rest arguments. (line 6) @@ -10149,7 +10209,7 @@ Index * reverse <1>: Paths and guides. (line 183) * reverse <2>: Paths and guides. (line 382) * reverse <3>: Arrays. (line 145) -* reverse <4>: three. (line 556) +* reverse <4>: three. (line 566) * rewind: Files. (line 97) * rfind: Data types. (line 247) * rgb: Pens. (line 30) @@ -10157,13 +10217,13 @@ Index * rgb <2>: Pens. (line 62) * Riemann zeta function: Mathematical functions. (line 48) -* Right: graph. (line 272) +* Right: graph. (line 273) * RightSide: label. (line 60) -* RightTicks: graph. (line 160) -* RightTicks <1>: graph. (line 233) -* RightView: three. (line 442) +* RightTicks: graph. (line 161) +* RightTicks <1>: graph. (line 234) +* RightView: three. (line 452) * Rotate: label. (line 36) -* rotate: three. (line 510) +* rotate: three. (line 520) * Rotate(pair z): label. (line 39) * round: Mathematical functions. (line 26) @@ -10176,7 +10236,7 @@ Index * runtime imports: Import. (line 102) * Russian: Pens. (line 238) * S: Labels. (line 18) -* safe: Options. (line 213) +* safe: Options. (line 214) * save: Frames and pictures. (line 288) * saveline: Files. (line 139) @@ -10184,23 +10244,23 @@ Index * scale: Pens. (line 123) * scale <1>: Transforms. (line 34) * scale <2>: Transforms. (line 36) -* scale <3>: graph. (line 710) -* Scale <1>: graph. (line 727) -* scale <4>: three. (line 509) -* scale3: three. (line 507) -* scaled graph: graph. (line 690) +* scale <3>: graph. (line 711) +* Scale <1>: graph. (line 728) +* scale <4>: three. (line 519) +* scale3: three. (line 517) +* scaled graph: graph. (line 691) * schur: Arrays. (line 271) * schur <1>: Arrays. (line 275) -* scientific graph: graph. (line 387) +* scientific graph: graph. (line 388) * scroll: Files. (line 113) * search: Arrays. (line 166) * search <1>: Arrays. (line 172) * search paths: Search paths. (line 6) * Seascape: Frames and pictures. (line 110) -* secondary axis: graph. (line 853) -* secondaryX: graph. (line 853) -* secondaryY: graph. (line 853) +* secondary axis: graph. (line 854) +* secondaryX: graph. (line 854) +* secondaryY: graph. (line 854) * seconds: Data types. (line 330) * seek: Files. (line 97) * seekeof: Files. (line 97) @@ -10210,7 +10270,7 @@ Index (line 6) * sequence: Arrays. (line 118) * settings: Configuring. (line 15) -* settings <1>: Options. (line 158) +* settings <1>: Options. (line 159) * sgn: Mathematical functions. (line 26) * shading: fill. (line 32) @@ -10218,12 +10278,12 @@ Index * shift: Transforms. (line 26) * shift <1>: Transforms. (line 28) * shift <2>: Transforms. (line 46) -* shift <3>: three. (line 499) +* shift <3>: three. (line 509) * shiftless: Transforms. (line 46) * shininess: three. (line 66) * shipout: Frames and pictures. (line 91) -* showtarget: three. (line 395) +* showtarget: three. (line 405) * Si: Mathematical functions. (line 48) * signedint: Files. (line 80) @@ -10243,9 +10303,9 @@ Index * singlereal <1>: Files. (line 93) * sinh: Mathematical functions. (line 6) -* SixViews: three. (line 457) -* SixViewsFR: three. (line 457) -* SixViewsUS: three. (line 457) +* SixViews: three. (line 467) +* SixViewsFR: three. (line 467) +* SixViewsUS: three. (line 467) * size: Figure size. (line 6) * size <1>: Paths and guides. (line 81) * size <2>: Paths and guides. (line 370) @@ -10253,9 +10313,9 @@ Index (line 48) * size <4>: Frames and pictures. (line 74) -* size <5>: three. (line 556) -* size <6>: Options. (line 187) -* size3: three. (line 320) +* size <5>: three. (line 566) +* size <6>: Options. (line 188) +* size3: three. (line 330) * Slant: label. (line 42) * slant: Transforms. (line 38) * sleep: Data types. (line 376) @@ -10299,7 +10359,7 @@ Index * stop: Debugger. (line 10) * straight: Paths and guides. (line 88) * Straight: graph. (line 30) -* straight <1>: three. (line 556) +* straight <1>: three. (line 566) * strftime: Data types. (line 321) * strftime <1>: Data types. (line 346) * string: Data types. (line 208) @@ -10311,7 +10371,7 @@ Index * struct: Structures. (line 6) * structures: Structures. (line 6) * subpath: Paths and guides. (line 186) -* subpath <1>: three. (line 556) +* subpath <1>: three. (line 566) * subpictures: Frames and pictures. (line 113) * substr: Data types. (line 262) @@ -10325,9 +10385,9 @@ Index * surface <3>: three. (line 142) * surface <4>: graph3. (line 99) * surface <5>: graph3. (line 128) -* SVG: Options. (line 192) +* SVG: Options. (line 193) * system: Data types. (line 354) -* system <1>: Options. (line 213) +* system <1>: Options. (line 214) * syzygy: syzygy. (line 6) * tab: Files. (line 65) * tab completion: Drawing in interactive mode. @@ -10338,8 +10398,9 @@ Index (line 20) * tanh: Mathematical functions. (line 6) -* target: three. (line 395) +* target: three. (line 405) * tell: Files. (line 97) +* template: Templated imports. (line 6) * tension: Bezier curves. (line 56) * tension <1>: three. (line 6) * tensionSpecifier: Paths and guides. (line 402) @@ -10348,32 +10409,32 @@ Index * tessellation: three. (line 154) * tex: Frames and pictures. (line 305) -* tex <1>: Options. (line 187) +* tex <1>: Options. (line 188) * TeX fonts: Pens. (line 213) * TeX string: Data types. (line 208) * texcommand: Configuring. (line 69) * TeXHead: draw. (line 26) -* TeXHead3: three. (line 622) +* TeXHead3: three. (line 632) * texpath: Configuring. (line 69) * texpath <1>: label. (line 113) * texpreamble: Frames and pictures. (line 314) * texreset: Frames and pictures. (line 318) -* textbook graph: graph. (line 360) +* textbook graph: graph. (line 361) * tgz: UNIX binary distributions. (line 6) * thick: three. (line 166) * thin: three. (line 166) * this: Structures. (line 6) * three: three. (line 6) -* ThreeViews: three. (line 457) -* ThreeViewsFR: three. (line 457) -* ThreeViewsUS: three. (line 457) -* tick: graph. (line 330) -* ticks: graph. (line 160) -* Ticks: graph. (line 160) -* Ticks <1>: graph. (line 233) +* ThreeViews: three. (line 467) +* ThreeViewsFR: three. (line 467) +* ThreeViewsUS: three. (line 467) +* tick: graph. (line 331) +* ticks: graph. (line 161) +* Ticks: graph. (line 161) +* Ticks <1>: graph. (line 234) * tildeframe: markers. (line 24) * tile: Pens. (line 285) * tilings: Pens. (line 271) @@ -10383,13 +10444,13 @@ Index * time <3>: math. (line 30) * times: Paths and guides. (line 220) * times <1>: Paths and guides. (line 224) -* Top: graph. (line 135) -* TopView: three. (line 442) +* Top: graph. (line 136) +* TopView: three. (line 452) * trace: Debugger. (line 50) -* trailingzero: graph. (line 175) +* trailingzero: graph. (line 176) * transform: Transforms. (line 6) -* transform <1>: three. (line 531) -* transform3: three. (line 494) +* transform <1>: three. (line 541) +* transform3: three. (line 504) * transparency: Pens. (line 254) * transparent: three. (line 97) * transpose: Arrays. (line 212) @@ -10404,7 +10465,7 @@ Index (line 48) * triple: Data types. (line 137) * TrueMargin: draw. (line 42) -* TrueMargin3: three. (line 638) +* TrueMargin3: three. (line 648) * tube: three. (line 166) * tube <1>: tube. (line 6) * tutorial: Tutorial. (line 6) @@ -10425,10 +10486,10 @@ Index * unit: Data types. (line 83) * unit <1>: Data types. (line 174) * unitbox: Paths. (line 44) -* unitbox <1>: three. (line 367) +* unitbox <1>: three. (line 377) * unitcircle: Paths. (line 17) * unitcircle <1>: Paths. (line 17) -* unitcircle <2>: three. (line 335) +* unitcircle <2>: three. (line 345) * unitrand: Mathematical functions. (line 39) * unitsize: Figure size. (line 39) @@ -10438,10 +10499,10 @@ Index (line 6) * unpacking: Rest arguments. (line 39) * unravel: Import. (line 29) -* up: three. (line 395) +* up: three. (line 405) * update: Files. (line 38) * UpsideDown: Frames and pictures. - (line 104) + (line 103) * UpsideDown <1>: Frames and pictures. (line 111) * URL: Import. (line 94) @@ -10458,8 +10519,8 @@ Index (line 55) * variable initializers: Variable initializers. (line 6) -* vectorfield: graph. (line 1022) -* vectorfield <1>: graph. (line 1061) +* vectorfield: graph. (line 1023) +* vectorfield <1>: graph. (line 1062) * vectorfield3: graph3. (line 167) * vectorization: Arrays. (line 343) * verbatim: Frames and pictures. @@ -10467,10 +10528,10 @@ Index * vertex-dependent colors: three. (line 119) * Vertical: flowchart. (line 77) * Viewport: three. (line 76) -* viewportheight: LaTeX usage. (line 50) -* viewportmargin: three. (line 323) -* viewportsize: three. (line 323) -* viewportwidth: LaTeX usage. (line 50) +* viewportheight: LaTeX usage. (line 47) +* viewportmargin: three. (line 333) +* viewportsize: three. (line 333) +* viewportwidth: LaTeX usage. (line 47) * views: three. (line 279) * vim: Editing modes. (line 32) * virtual functions: Structures. (line 182) @@ -10483,53 +10544,53 @@ Index * while: Programming. (line 48) * White: three. (line 76) * white-space string delimiter mode: Arrays. (line 374) -* width: LaTeX usage. (line 50) +* width: LaTeX usage. (line 47) * windingnumber: Paths and guides. (line 283) * word: Arrays. (line 374) * write: Files. (line 57) * write <1>: Arrays. (line 413) -* X: three. (line 335) +* X: three. (line 345) * xasy: GUI. (line 6) * xaxis3: graph3. (line 7) * xdr: Files. (line 80) -* xelatex: Options. (line 187) -* XEquals: graph. (line 265) -* xequals: graph. (line 278) -* xlimits: graph. (line 639) +* xelatex: Options. (line 188) +* XEquals: graph. (line 266) +* xequals: graph. (line 279) +* xlimits: graph. (line 640) * XOR: Arithmetic & logical. (line 68) * xpart: Data types. (line 94) * xpart <1>: Data types. (line 185) * xscale: Transforms. (line 30) -* xscale3: three. (line 501) -* xtick: graph. (line 330) -* XY: three. (line 516) -* XY <1>: three. (line 531) +* xscale3: three. (line 511) +* xtick: graph. (line 331) +* XY: three. (line 526) +* XY <1>: three. (line 541) * XYEquals: graph3. (line 21) * XYZero: graph3. (line 21) * XZEquals: graph3. (line 21) -* XZero: graph. (line 260) +* XZero: graph. (line 261) * XZZero: graph3. (line 21) * Y: Mathematical functions. (line 6) * Y <1>: Mathematical functions. (line 48) -* Y <2>: three. (line 335) +* Y <2>: three. (line 345) * yaxis3: graph3. (line 7) -* YEquals: graph. (line 128) -* yequals: graph. (line 278) -* ylimits: graph. (line 639) +* YEquals: graph. (line 129) +* yequals: graph. (line 279) +* ylimits: graph. (line 640) * ypart: Data types. (line 97) * ypart <1>: Data types. (line 188) * yscale: Transforms. (line 32) -* yscale3: three. (line 503) -* ytick: graph. (line 330) -* YX: three. (line 531) -* YZ: three. (line 531) +* yscale3: three. (line 513) +* ytick: graph. (line 331) +* YX: three. (line 541) +* YZ: three. (line 541) * YZEquals: graph3. (line 21) -* YZero: graph. (line 123) +* YZero: graph. (line 124) * YZZero: graph3. (line 21) -* Z: three. (line 335) +* Z: three. (line 345) * zaxis3: graph3. (line 7) * zeroTransform: Transforms. (line 44) * zerowinding: Pens. (line 164) @@ -10546,161 +10607,162 @@ Index * zeta: Mathematical functions. (line 48) * zpart: Data types. (line 191) -* zscale3: three. (line 505) -* ZX: three. (line 531) -* ZX <1>: three. (line 531) -* ZY: three. (line 531) +* zscale3: three. (line 515) +* ZX: three. (line 541) +* ZX <1>: three. (line 541) +* ZY: three. (line 541) Tag Table: -Node: Top570 -Node: Description7317 -Node: Installation11564 -Node: UNIX binary distributions12610 -Node: MacOS X binary distributions13733 -Node: Microsoft Windows14321 -Node: Configuring15518 -Node: Search paths19737 -Node: Compiling from UNIX source20745 -Node: Editing modes23896 -Node: Git26334 -Node: Uninstall26841 -Node: Tutorial27187 -Node: Drawing in batch mode28034 -Node: Drawing in interactive mode28910 -Node: Figure size29942 -Node: Labels31537 -Node: Paths32365 -Ref: unitcircle32981 -Node: Drawing commands34922 -Node: draw36730 -Ref: arrows37912 -Node: fill43427 -Ref: gradient shading44473 -Node: clip49087 -Node: label49836 -Ref: Label50436 -Node: Bezier curves56293 -Node: Programming60193 -Ref: array iteration61946 -Node: Data types62113 -Ref: format72881 -Node: Paths and guides77327 -Ref: circle77581 -Ref: extension87281 -Node: Pens94091 -Ref: fillrule101782 -Ref: basealign102686 -Ref: transparency106368 -Ref: makepen109962 -Ref: overwrite110846 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