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-%D \module
-%D [ file=supp-pdf,
-%D version=2006.09.02, % 2004.12.16,
-%D title=\CONTEXT\ Support Macros,
-%D subtitle=\METAPOST\ to \PDF\ conversion,
-%D author=Hans Hagen \& others (see text),
-%D date=\currentdate,
-%D copyright=\PRAGMA]
-%C
-%C This module is part of the \CONTEXT\ macro||package and is
-%C therefore copyrighted by \PRAGMA. See mreadme.pdf for
-%C details.
-
-\ifx\writestatus\undefined
- \immediate\write16{[Loading MPS to PDF converter (version 2006.09.02).]}
-\else
- \writestatus{loading}{Context Support Macros / PDF}
-\fi
-
-%D This module is not optimized because it is used outside
-%D \CONTEXT\ and we cannot forsee what interference will take
-%D place. We no longer load supp-mis. I got too tired of
-%D keeping track of interferences with non \CONTEXT\ usage so
-%D I moved the necessary code in here and use a derived version
-%D in \CONTEXT. When I have the time I will clean up some of the
-%D code that is of no use for non||\CONTEXT\ users.
-
-\ifx\contextversion\undefined
-
- \chardef\mptopdfstoredatcode\catcode`\@
-
- \catcode\string`@=11
-
- \def\unprotect
- {\let\@@mpstopdf@@unprotect \unprotect
- \let\@@mpstopdf@@protect \protect
- \edef\protect
- {\noexpand \let \noexpand \protect \noexpand \@@mpstopdf@@protect
- \noexpand \let \noexpand \unprotect \noexpand \@@mpstopdf@@unprotect
- % context specific
- \catcode\string`\noexpand @=\the\catcode\string`@
- \catcode\string`\noexpand !=\the\catcode\string`!
- \catcode\string`\noexpand ?=\the\catcode\string`?
- % latex specific
- \catcode\string`\noexpand /=\the\catcode\string`/
- \catcode\string`\noexpand -=\the\catcode\string`-
- \catcode\string`\noexpand :=\the\catcode\string`:
- \catcode\string`\noexpand ;=\the\catcode\string`;
- \catcode\string`\noexpand "=\the\catcode\string`"
- \catcode\string`\noexpand <=\the\catcode\string`<
- \catcode\string`\noexpand >=\the\catcode\string`>
- \catcode\string`\noexpand `=\the\catcode\string``}
- \catcode\string`@=11 \catcode\string`!=11 \catcode\string`?=11
- \catcode\string`/=12 \catcode\string`-=12
- \catcode\string`:=12 \catcode\string`;=12
- \catcode\string`>=12 \catcode\string`<=12
- \catcode\string`"=12 \catcode\string``=12 }
-
- \def\defineMPtoPDFfallbacks
- {% shortcuts
- \chardef\@@escape 0
- \chardef\@@begingroup 1
- \chardef\@@endgroup 2
- \chardef\@@endofline 5
- \chardef\@@ignore 9
- \chardef\@@space 10
- \chardef\@@letter 11
- \chardef\@@other 12
- \chardef\@@active 13
- \chardef\@@comment 14
- % placeholders
- \ifx\withoutpt \undefined \let\withoutpt \@@mptopdf@@withoutpt \fi
- \ifx\twodigitrounding \undefined \let\twodigitrounding \@@mptopdf@@twodigitrounding \fi
- \ifx\forgetall \undefined \let\forgetall \@@mptopdf@@forgetall \fi
- \ifx\uncatcodespecials \undefined \let\uncatcodespecials \@@mptopdf@@uncatcodespecials \fi
- \ifx\setnaturalcatcodes\undefined \let\setnaturalcatcodes\@@mptopdf@@setnaturalcatcodes \fi
- \ifx\dospecials \undefined \let\dospecials \@@mptopdf@@dospecials \fi}
-
- \def\@@mptopdf@@forgetall
- {\parskip0pt\leftskip0pt\parindent0pt\everypar{}}
-
- \def\@@mptopdf@@twodigitrounding#1%
- {#1}%
-
- \def\@@mptopdf@@uncatcodespecials
- {\def\do##1{\catcode`##1=\@@other}\dospecials
- \catcode`\ =\@@space
- \catcode`\^^L=\@@ignore
- \catcode`\^^M=\@@endofline
- \catcode`\^^?=\@@ignore}
-
- \def\@@mptopdf@@setnaturalcatcodes
- {\catcode`\!=\@@other \catcode`\?=\@@other \catcode`\@=\@@other
- \catcode`\#=\@@other \catcode`\&=\@@other \catcode`\|=\@@other
- \catcode`\$=\@@other \catcode`\^=\@@other \catcode`\_=\@@other
- \catcode`\*=\@@other \catcode`\/=\@@other
- \catcode`\-=\@@other \catcode`+=\@@other
- \catcode`\==\@@other \catcode`\<=\@@other \catcode`\>=\@@other
- \catcode`\"=\@@other \catcode`\'=\@@other \catcode`\`=\@@other
- \catcode`\:=\@@other \catcode`\;=\@@other
- \catcode`\,=\@@other \catcode`\.=\@@other \catcode`\~=\@@other
- \catcode`\(=\@@other \catcode`\)=\@@other
- \catcode`\{=\@@other \catcode`\}=\@@other
- \catcode`\\=\@@other \catcode`\%=\@@other}
-
- \def\@@mptopdf@@dospecials
- {\do\ \do\\\do\{\do\}\do\$%
- \do\#\do\^\do\_\do\&\do\%%
- \do\~\do\^^A\do\^^K}
-
- {
- \catcode`\.=12
- \catcode`\p=12
- \catcode`\t=12
- \gdef\@@MPTOPDF@@WITHOUTPT#1pt{#1}
- }
-
- \def\@@mptopdf@@withoutpt#1%
- {\expandafter\@@MPTOPDF@@WITHOUTPT#1}
-
-% \def\@@mptopdf@@newabove#1#2% \dimen \name
-% {#1#2%
-% \ifnum\expandafter\gobblesixarguments\meaning#2>20\else
-% \expandafter\@@mptopdf@@newabove\expandafter#1\expandafter#2%
-% \fi}
-
- \def\@@mptopdf@@stripnewabove#1%
- {\ifnum10<9#1 #1\else\expandafter\@@mptopdf@@stripnewabove\fi}%
-
- \def\@@mptopdf@@newabove\csname#1\endcsname#2% \dimen \name
- {\csname#1\endcsname#2%
- \ifnum\expandafter\@@mptopdf@@stripnewabove\meaning#2>20\else
- \@@mptopdf@@newabove\csname#1\endcsname#2%
- \fi}
-
- \@@mptopdf@@newabove \csname newcount\endcsname \scratchcounter
- \@@mptopdf@@newabove \csname newdimen\endcsname \scratchdimen
- \csname newbox\endcsname \scratchbox
-
- \expandafter \newif \csname ifdone\endcsname
-
- \catcode`\@=\mptopdfstoredatcode
-
-\else
-
- \let\defineMPtoPDFfallbacks\relax
-
-\fi
-
-%D These macros are written as generic as possible. Some
-%D general support macro's are loaded from a small module
-%D especially made for non \CONTEXT\ use. In this module I
-%D use a matrix transformation macro written by Tanmoy
-%D Bhattacharya. Thanks to extensive testing by Sebastian
-%D Ratz I was able to complete this module within reasonable
-%D time. This module has support for \METAPOST\ extensions
-%D built in.
-%D
-%D Daniel H. Luecking came up with a better (more precise)
-%D transformation method. You can recognize his comment by
-%D his initials. (We keep the old code around because it's a
-%D nice illustration on how a module like this evolves.)
-
-%D Beware, we cannot use \type{\zeropoint} here since it may be
-%D defined in the range \type{\dimen0} - 20 which we happen to use
-%D as scratch registers; inside context we may consider
-%D using dedicated registers.
-
-%D This module handles some \PDF\ conversion and insertions
-%D topics. By default, the macros use the \PDFTEX\ primitive
-%D \type{\pdfliteral} when available. Since \PDFTEX\ is now the
-%D default engine for \TEX\ distributions, we need a more complex
-%D test.
-
-\unprotect
-
-\ifx\PDFcode\undefined
- \ifx\pdfliteral\undefined
- \def\PDFcode#1{\special{PDF: #1}}
- \else\ifx\pdfoutput\undefined
- \def\PDFcode#1{\special{PDF: #1}}
- \else\ifcase\pdfoutput
- \def\PDFcode#1{\special{PDF: #1}}
- \else % pdftex as well as in pdf mode
- \let\PDFcode\pdfliteral
- \fi\fi\fi
-\else
- % we probably use context
-\fi
-
-%D First we define a handy constant:
-
-\bgroup \defineMPtoPDFfallbacks \catcode`\%=\@@other \xdef\letterpercent{\string%} \egroup
-
-%D \macros
-%D {pdfimage,pdfimages,pdfclippedimage}
-%D
-%D Starting with pdftex version 14, images are included more
-%D natural to the form embedding. This enables alternative
-%D images to be embedded.
-%D
-%D \starttyping
-%D \pdfimage <optional dimensions> {file}
-%D \pdfimages <optional dimensions> {high res file} {low res file}
-%D \stoptyping
-%D
-%D The first one replaces the pre||version||14 original,
-%D while the latter provides alternative images.
-%D
-%D The next macro is dedicated to Maarten Gelderman, who
-%D needed to paste prepared \PDF\ pages into conference
-%D proceedings.
-%D
-%D \starttyping
-%D \pdfclippedimage <optional dimensions> {file} {l} {r} {t} {b}
-%D \stoptyping
-
-\ifx\pdftexversion\undefined \else \ifnum\pdftexversion>13
-
- \def\pdfimage#1#%
- {\dopdfimage{#1}}
-
- \def\dopdfimage#1#2%
- {\immediate\pdfximage#1{#2}%
- \pdfrefximage\pdflastximage}
-
- \def\pdfimages#1#%
- {\dopdfimages{#1}}
-
- \def\dopdfimages#1#2#3%
- {\immediate\pdfximage#1{#2}%
- \immediate\pdfobj{[ << /Image \the\pdflastximage\space0 R /DefaultForPrinting true >> ]}%
- \immediate\pdfximage#1 attr {/Alternates \the\pdflastobj\space0 R}{#3}%
- \pdfrefximage\pdflastximage}
-
- \def\pdfclippedimage#1#% specs {file}{left}{right}{top}{bottom}
- {\dopdfclippedimage{#1}}
-
- \def\dopdfclippedimage#1#2#3#4#5#6%
- {\bgroup
- \pdfximage#1{#2}%
- \setbox\scratchbox\hbox
- {\pdfrefximage\pdflastximage}%
- \hsize\wd\scratchbox
- \advance\hsize -#3
- \advance\hsize -#4
- \vsize\ht\scratchbox
- \advance\vsize -#5
- \advance\vsize -#6
- \setbox\scratchbox\vbox to \vsize
- {\vskip-#5\hbox to \hsize{\hskip-#3\box\scratchbox\hss}}%
- \pdfxform\scratchbox
- \pdfrefxform\pdflastxform
- \egroup}
-
-\fi \fi
-
-%D If you want to save a few hash entries, you may prefer the
-%D less readable alternatives, like:
-%D
-%D \starttyping
-%D \def\pdfimage#1#% This one is less readable but needs no additional
-%D {\bgroup % hash entry for the second stage macro.
-%D \def\pdfimage##1%
-%D {\immediate\pdfximage##1{#2}%
-%D \pdfrefximage\pdflastximage\egroup}}
-%D \stoptyping
-
-%D For old times sake we provide a few aliases. These will be
-%D removed some day.
-
-\ifx\pdftexversion\undefined \else \ifnum\pdftexversion>13
-
- \let\pdfform =\pdfxform
- \let\pdflastform=\pdflastxform
- \let\pdfrefform =\pdfrefxform
-
-\fi \fi
-
-%D The main conversion macro wraps the \PDF\ codes in a box
-%D that is output as an object. The graphics are embedded
-%D in~\type{q} and~\type{Q} and are scaled and positioned using
-%D one transform call (\type{cm}). This saves some additional
-%D scaling.
-
-%D \macros
-%D {convertMPtoPDF}
-%D
-%D The next set of macros implements \METAPOST\ to \PDF\
-%D conversion. Because we want to test as fast as possible, we
-%D first define the \POSTSCRIPT\ operators that \METAPOST\
-%D uses. We don't define irrelevant ones, because these are
-%D skipped anyway.
-
-%D The converter can be made a bit faster by replacing the
-%D two test macros (the ones with the many \type {\if's}) by
-%D a call to named branch macros (something \typ {\getvalue
-%D {xPSmoveto}}. For everyday documents with relatively
-%D small graphics the gain in speed can be neglected.
-
-\def \PScurveto {curveto}
-\def \PSlineto {lineto}
-\def \PSmoveto {moveto}
-\def \PSshowpage {showpage}
-\def \PSnewpath {newpath}
-\def \PSfshow {fshow}
-\def \PSclosepath {closepath}
-\def \PSfill {fill}
-\def \PSstroke {stroke}
-\def \PSclip {clip}
-\def \PSrlineto {rlineto}
-\def \PSsetlinejoin {setlinejoin}
-\def \PSsetlinecap {setlinecap}
-\def \PSsetmiterlimit {setmiterlimit}
-\def \PSsetgray {setgray}
-\def \PSsetrgbcolor {setrgbcolor}
-\def \PSsetcmykcolor {setcmykcolor}
-\def \PSsetdash {setdash}
-\def \PSgsave {gsave}
-\def \PSgrestore {grestore}
-\def \PStranslate {translate}
-\def \PSscale {scale}
-\def \PSconcat {concat}
-\def \PSdtransform {dtransform}
-\def \PSsetlinewidth {setlinewidth}
-\def \PSpop {pop}
-
-\def \PSnfont {nfont} % was needed for TUG98 proceedings
-\def \PSspecial {special} % extensions to MetaPost
-
-%D A previous version set \type {%} to ignore, which
-%D simplified the following definitions. At the start of
-%D conversion the percent character was made active again.
-%D Because the whole graphic is one paragraph (there are no
-%D empty lines) this does not give the desired effect. This
-%D went unnoticed untill Scott Pakin sent me a test file
-%D percent characters in a string. So, from now on we have
-%D to prefix the following strings with percentages.
-
-%D Some day I'll figure out a better solution (line by line reading
-%D using \ETEX).
-
-\edef \PSBoundingBox {\letterpercent\letterpercent BoundingBox:}
-\edef \PSHiResBoundingBox {\letterpercent\letterpercent HiResBoundingBox:}
-\edef \PSExactBoundingBox {\letterpercent\letterpercent ExactBoundingBox:}
-\edef \PSMetaPostSpecial {\letterpercent\letterpercent MetaPostSpecial:}
-\edef \PSMetaPostSpecials {\letterpercent\letterpercent MetaPostSpecials:}
-\edef \PSPage {\letterpercent\letterpercent Page:}
-\edef \PSBeginProlog {\letterpercent\letterpercent BeginProlog}
-\edef \PSEndProlog {\letterpercent\letterpercent EndProlog}
-\edef \PSEof {\letterpercent\letterpercent EOF}
-
-%D By the way, the \type {setcmykcolor} operator is not
-%D output by \METAPOST\ but can result from converting the
-%D \cap{RGB} color specifications, as implemented in
-%D \type{supp-mps}.
-
-%D In \POSTSCRIPT\ arguments precede the operators. Due to the
-%D fact that in some translations we need access to those
-%D arguments, and also because sometimes we have to skip them,
-%D we stack them up. The stack is one||dimensional for non path
-%D operators and two||dimensional for operators inside a path.
-%D This is because we have to save the whole path for
-%D (optional) postprocessing. Values are pushed onto the stack
-%D by:
-%D
-%D \starttyping
-%D \setMPargument {value}
-%D \stoptyping
-%D
-%D They can be retrieved by the short named macros:
-%D
-%D \starttyping
-%D \gMPa {number}
-%D \gMPs {number}
-%D \stoptyping
-%D
-%D When scanning a path specification, we also save the
-%D operator, using
-%D
-%D \starttyping
-%D \setMPkeyword {n}
-%D \stoptyping
-%D
-%D The path drawing operators are coded for speed: \type{clip},
-%D \type{stroke}, \type{fill} and \type{fillstroke} become
-%D 1, 2, 3 and~4.
-%D
-%D When processing the path this code can be retrieved
-%D using
-%D
-%D \starttyping
-%D \getMPkeyword % {n}
-%D \stoptyping
-%D
-%D When setting an argument, the exact position on the stack
-%D depends on the current value of the \COUNTERS\
-%D \type{\nofMPsegments} and \type{\nofMParguments}.
-
-\newcount\nofMPsegments
-\newcount\nofMParguments
-
-%D These variables hold the coordinates. The argument part of
-%D the stack is reset by:
-%D
-%D \starttyping
-%D \resetMPstack
-%D \stoptyping
-%D
-%D We use the prefix \type{@@MP} to keep the stack from
-%D conflicting with existing macros. To speed up things a bit
-%D more, we use the constant \type{\@@MP}.
-
-\def\@@MP{@@MP}
-
-\def\setMPargument% #1%
- {\advance\nofMParguments 1
- \expandafter\def
- \csname\@@MP\the\nofMPsegments\the\nofMParguments\endcsname} % {#1}
-
-\def\letMPargument
- {\advance\nofMParguments 1
- \expandafter\let
- \csname\@@MP\the\nofMPsegments\the\nofMParguments\endcsname}
-
-\def\setMPsequence#1 %
- {\advance\nofMParguments 1
- \expandafter\def
- \csname\@@MP\the\nofMPsegments\the\nofMParguments\endcsname{#1}%
- \handleMPsequence}
-
-\def\gMPa#1%
- {\csname\@@MP0\number#1\endcsname}
-
-\def\gMPs#1%
- {\csname\@@MP\the\nofMPsegments\number#1\endcsname}
-
-\def\dogMPa#1%
- {\expandafter\expandafter\expandafter\do\csname\@@MP0\number#1\endcsname}
-
-\def\setMPkeyword#1 %
- {\expandafter\def\csname\@@MP\the\nofMPsegments0\endcsname{#1}%
- \advance\nofMPsegments 1
- \nofMParguments0}
-
-\def\getMPkeyword% #1%
- {\csname\@@MP\the\nofMPsegments0\endcsname} % {\csname\@@MP#10\endcsname}
-
-\def\docleanupMPargument#1% we need this because args can have [ or ] pre/appended
- {\expandafter\edef\csname\@@MP\the\nofMPsegments\number#1\endcsname
- {\csname\@@MP\the\nofMPsegments\number#1\endcsname}}
-
-%D When we reset the stack, we can assume that all further
-%D comment is to be ignored and handled in strings.
-%D By redefining the reset macro after the first call, we
-%D save some run time. Only use this macro after all
-%D comments are processed and use the simple alternative
-%D when dealing with comments.
-
-\def\doresetMPstack
- {\nofMParguments0\relax}
-
-\def\resetMPstack
- {\let\handleMPgraphic\handleMPendgraphic
- \let\resetMPstack\doresetMPstack
- \resetMPstack}
-
-%D The arguments are saved with the preceding command
-%D \type{\do}. By default this command expands to nothing, but
-%D when we deal with strings it's used to strip off the
-%D \type{(} and \type{)}.
-%D
-%D Strings are kind of tricky, because characters can be
-%D passed verbatim \type{(hello)}, by octal number
-%D \type{(\005)} or as command \type{(\()}. We therefore
-%D cannot simply ignore \type{(} and \type{)}, the way we do
-%D with \type{[} and \type{]}. Another complication is that
-%D strings may contain characters that normally have a
-%D special meaning in \TEX, like \type{$} and \type{{}}.
-%D
-%D A previous solution made \type{\} an active character and
-%D let it look ahead for a number or characters. We had to
-%D abandon this scheme because of the need for verbatim
-%D support. The next solution involved some \CATCODE\
-%D trickery but works well.
-
-\def\octalMPcharacter#1#2#3%
- {\char'#1#2#3\relax}
-
-%D curly braces and squarly brackets are stored in the argument stack
-%D as part of strings, for instance in:
-%D
-%D \starttyping
-%D /fshow {exch findfont exch scalefont setfont show}bind def
-%D [3 3 ] 0 setdash
-%D \stoptyping
-%D
-%D but we need to keep them in situation like
-%D
-%D \starttyping
-%D ([bla bla] bla bla) ec-lmr10 9.96265 fshow
-%D ({bla bla} bla bla) ec-lmr10 9.96265 fshow
-%D \stoptyping
-%D
-%D So, when we store the snippets, we keep the special tokens, and
-%D when needed we either ignore or obey them
-
-\bgroup
-\defineMPtoPDFfallbacks
-\catcode`\|=\@@comment
-\catcode`\%=\@@active
-\catcode`\[=\@@active
-\catcode`\]=\@@active
-\catcode`\{=\@@active
-\catcode`\}=\@@active
-\catcode`B=\@@begingroup
-\catcode`E=\@@endgroup
-\gdef\keepMPspecials|
- B\let%\letterpercent|
- \def[B\noexpand[E|
- \def]B\noexpand]E|
- \def{B\noexpand{E|
- \def}B\noexpand}EE
-\gdef\ignoreMPspecials|
- B\let%\letterpercent|
- \def[BE|
- \def]BE|
- \def{BE|
- \def}BEE
-\gdef\obeyMPspecials|
- B\def%B\char 37\relax E|
- \def[B\char 91\relax E|
- \def]B\char 93\relax E|
- \def{B\char123\relax E|
- \def}B\char125\relax EE
-\gdef\setMPspecials|
- B\setnaturalcatcodes
- \catcode`\\=\@@escape
- \catcode`\%=\@@active
- \catcode`\[=\@@active
- \catcode`\]=\@@active
- \catcode`\{=\@@active
- \catcode`\}=\@@active
- \lccode`\-=0 | latex sets this to `\-
- \lccode`\%=`\% | otherwise it's seen as a number
- \def\(B\char40\relax E|
- \def\)B\char41\relax E|
- \def\\B\char92\relax E|
- \def\0B\octalMPcharacter0E|
- \def\1B\octalMPcharacter1E|
- \def\2B\octalMPcharacter2E|
- \def\3B\octalMPcharacter3E|
- \def\4B\octalMPcharacter4E|
- \def\5B\octalMPcharacter5E|
- \def\6B\octalMPcharacter6E|
- \def\7B\octalMPcharacter7E|
- \def\8B\octalMPcharacter8E|
- \def\9B\octalMPcharacter9EE
-\egroup
-
-%D We use the comment symbol as a sort of trigger. Beware!
-%D The whole graphic is seen as on eparagraph, which means
-%D that we cannot change the catcodes in between.
-
-\bgroup
-\defineMPtoPDFfallbacks
-\catcode`\%=\@@active
-\gdef\startMPscanning{\let%=\startMPconversion}
-\egroup
-
-%D In earlier versions we used the sequence
-%D
-%D \starttyping
-%D \expandafter\handleMPsequence\input filename\relax
-%D \stoptyping
-%D
-%D Persistent problems in \LATEX\ however forced us to use a
-%D different scheme. Every \POSTSCRIPT\ file starts with a
-%D \type{%}, so we temporary make this an active character
-%D that starts the scanning and redefines itself. (The problem
-%D originates in the redefinition by \LATEX\ of the
-%D \type{\input} primitive.)
-
-\def\startMPconversion
- {\keepMPspecials
- \handleMPsequence}
-
-%D Here comes the main loop. Most arguments are numbers. This
-%D means that they can be recognized by their \type{\lccode}.
-%D This method saves a lot of processing time. We could
-%D speed up the conversion by handling the \type{path}
-%D seperately.
-
-\def\dohandleMPsequence#1%
- {\ifdone
- \ifcase\lccode`#1\relax
- \expandafter\expandafter\expandafter\dohandleMPsequenceA
- \else
- \expandafter\expandafter\expandafter\dohandleMPsequenceB
- \fi
- \else
- \expandafter\dohandleMPsequenceC
- \fi#1}
-
-\let\dohandleMPsequenceA\setMPsequence
-
-\def\installMPSkeywordN#1#2%
- {\expandafter\def\csname\@@MP:N:#1\endcsname{#2}}
-
-\def\installMPSshortcutN#1#2% todo: \let
- {\expandafter\let\csname\@@MP:N:#1\expandafter\endcsname\csname\@@MP:N:#2\endcsname}
-
-\def\dohandleMPsequenceB#1 %
- {\edef\somestring{#1}%
- \ifcsname\@@MP:N:\somestring\endcsname
- \csname\@@MP:N:\somestring\expandafter\endcsname
- \else
- \expandafter\handleMPgraphic
- \fi
- \handleMPsequence}
-
-\ifx\eTeXversion\undefined
- \def\dohandleMPsequenceB#1 %
- {\edef\somestring{#1}%
- \expandafter\ifx\csname\@@MP:N:\somestring\endcsname\relax
- \expandafter\handleMPgraphic
- \else
- \csname\@@MP:N:\somestring\expandafter\endcsname
- \fi
- \handleMPsequence}
-\fi
-
-\installMPSkeywordN \PSmoveto
- {\edef\lastMPmoveX{\gMPa1}%
- \edef\lastMPmoveY{\gMPa2}%
- \resetMPstack}
-\installMPSkeywordN \PSnewpath
- {\let\handleMPsequence\handleMPpath}
-\installMPSkeywordN \PSgsave
- {\PDFcode{q}%
- \resetMPstack}
-\installMPSkeywordN \PSgrestore
- {\PDFcode{Q}%
- \resetMPstack}
-\installMPSkeywordN \PSdtransform % == setlinewidth
- {\let\handleMPsequence\handleMPdtransform}
- % after that we will encounter more tokens until setlinewidth+pop
- % or pop+setlinewidth which we catch next; we explicitly need to
- % reset the stack since [] n setdash may follow; a more clever
- % approach would be to read on till the condition is met, but it's
- % the only pop / setlinewidth we will encounter so ...
-\installMPSkeywordN \PSsetlinewidth
- {% already handled in dtransform
- \resetMPstack}
-\installMPSkeywordN \PSpop
- {% already handled in dtransform
- \resetMPstack}
-\installMPSkeywordN \PSconcat
- {\cleanupMPconcat
- \PDFcode{\gMPa1 \gMPa2 \gMPa3 \gMPa4 \gMPa5 \gMPa6 cm}%
- \resetMPstack}
-\installMPSkeywordN \PSsetrgbcolor
- {\handleMPrgbcolor
- \resetMPstack}
-\installMPSkeywordN \PSsetcmykcolor
- {\handleMPcmykcolor
- \resetMPstack}
-\installMPSkeywordN \PSsetgray
- {\handleMPgraycolor
- \resetMPstack}
-\installMPSkeywordN \PStranslate
- {\PDFcode{1 0 0 1 \gMPa1 \gMPa2 cm}%
- \resetMPstack}
-\installMPSkeywordN \PSsetdash
- {\handleMPsetdash
- \resetMPstack}
-\installMPSkeywordN \PSsetlinejoin
- {\PDFcode{\gMPa1 j}%
- \resetMPstack}
-\installMPSkeywordN \PSsetmiterlimit
- {\PDFcode{\gMPa1 M}%
- \resetMPstack}
-\installMPSkeywordN \PSfshow
- {%\PDFcode{n}% removed !
- \handleMPfshow
- \resetMPstack}
-\installMPSkeywordN \PSsetlinecap
- {\PDFcode{\gMPa1 J}%
- \resetMPstack}
-\installMPSkeywordN \PSrlineto
- {\flushMPmoveto
- \PDFcode{\!MP\lastMPmoveX\space\!MP\lastMPmoveY\space l S}%
- \resetMPmoveto
- \resetMPstack}
-\installMPSkeywordN \PSscale
- {\PDFcode{\gMPa1 0 0 \gMPa2 0 0 cm}%
- \resetMPstack}
-\installMPSkeywordN \PSspecial
- {\handleMPspecialcommand
- \resetMPstack}
-
-\installMPSshortcutN {n} \PSnewpath
-\installMPSshortcutN {p} \PSclosepath
-\installMPSshortcutN {l} \PSlineto
-\installMPSshortcutN {r} \PSrlineto
-\installMPSshortcutN {m} \PSmoveto
-\installMPSshortcutN {c} \PScurveto
-\installMPSshortcutN {C} \PSsetcmykcolor
-\installMPSshortcutN {G} \PSsetgray
-\installMPSshortcutN {R} \PSsetrgbcolor
-\installMPSshortcutN {lj} \PSsetlinejoin
-\installMPSshortcutN {ml} \PSsetmiterlimit
-\installMPSshortcutN {lc} \PSsetlinecap
-\installMPSshortcutN {sd} \PSsetdash
-\installMPSshortcutN {S} \PSstroke
-\installMPSshortcutN {F} \PSfill
-\installMPSshortcutN {W} \PSclip
-
-\installMPSshortcutN {q} \PSgsave
-\installMPSshortcutN {Q} \PSgrestore
-
-\installMPSshortcutN {s} \PSscale
-\installMPSshortcutN {t} \PSconcat
-\installMPSshortcutN {P} \PSshowpage
-
-\installMPSkeywordN {hlw} {\PDFcode{\gMPa1 w}\resetMPstack}
-\installMPSkeywordN {vlw} {\PDFcode{\gMPa1 w}\resetMPstack}
-\installMPSkeywordN {rd} {\PDFcode{[] 0 d}\resetMPstack}
-
-\def\dohandleMPsequenceC#1 %
- {\edef\somestring{#1}%
- \handleMPgraphic % {#1}%
- \handleMPsequence}
-
-%D Since colors are not sensitive to transformations, they
-%D are sometimes used for signaling. Therefore, we handle them
-%D separately. The next macro can be redefined if needed.
-
-\def\handleMPrgbcolor
- {\PDFcode{\!MPgMPa1 \!MPgMPa2 \!MPgMPa3 rg
- \!MPgMPa1 \!MPgMPa2 \!MPgMPa3 RG}}
-
-\def\handleMPcmykcolor
- {\PDFcode{\!MPgMPa1 \!MPgMPa2 \!MPgMPa3 \!MPgMPa4 k
- \!MPgMPa1 \!MPgMPa2 \!MPgMPa3 \!MPgMPa4 K}}
-
-\def\handleMPgraycolor
- {\PDFcode{\!MPgMPa1 g
- \!MPgMPa1 G}}
-
-\def\handleMPspotcolor
- {\PDFcode{0 g
- 0 G}}
-
-%D Beginning and ending the graphics is taken care of by the
-%D macro \type{\handleMPgraphic}, which is redefined when
-%D the first graphics operator is met.
-
-\def\handleMPendgraphic % #1%
- {\ifx\somestring\PSshowpage
- \let\handleMPsequence\finishMPgraphic
- \else\ifx\somestring\PSEof
- \let\handleMPsequence\finishMPgraphic
- \else
- \letMPargument\somestring % {#1}%
- \fi\fi}
-
-\def\handleMPbegingraphic % #1%
- {\ifx\somestring\PSBoundingBox
- \def\handleMPsequence{\handleMPboundingbox1}%
- \else\ifx\somestring\PSHiResBoundingBox
- \def\handleMPsequence{\handleMPboundingbox2}%
- \else\ifx\somestring\PSExactBoundingBox
- \def\handleMPsequence{\handleMPboundingbox3}%
- \else\ifx\somestring\PSshowpage
- \let\handleMPsequence\finishMPgraphic
- \else\ifx\somestring\PSEof
- \let\handleMPsequence\finishMPgraphic
- \else\ifx\somestring\PSPage
- \let\handleMPsequence\handleMPpage
- \else\ifx\somestring\PSMetaPostSpecials
- \let\handleMPsequence\handleMPspecialscomment
- \else\ifx\somestring\PSMetaPostSpecial
- \let\handleMPsequence\handleMPspecialcomment
- \else\ifx\somestring\PSBeginProlog
- \let\handleMPsequence\handleMPprolog
- \else
- \letMPargument\somestring % {#1}%
- \fi\fi\fi\fi\fi\fi\fi\fi\fi}
-
-\let\handleMPgraphic=\handleMPbegingraphic
-
-%D New: we can best filter the prolog because nowdays it can contain
-%D quite some code.
-
-% hm, catcode mess, so we need to tweak %'s catcode here
-% \long\expandafter\def\expandafter\handleMPprolog\expandafter#\expandafter1\PSEndProlog%
-% but today i'm not in the mood for ugly stuff
-
-\long\def\handleMPprolog#1EndProlog %
- {\doresetMPstack
- \let\handleMPsequence\dohandleMPsequence
- \handleMPsequence}
-
-%D We check for three kind of bounding boxes: the normal one
-%D and two high precision ones:
-%D
-%D \starttyping
-%D BoundingBox: llx lly ucx ucy
-%D HiResBoundingBox: llx lly ucx ucy
-%D ExactBoundingBox: llx lly ucx ucy
-%D \stoptyping
-%D
-%D The original as well as the recalculated dimensions are
-%D saved for later use.
-
-\newif\ifskipemptyMPgraphic \skipemptyMPgraphicfalse
-
-\chardef\currentMPboundingbox=0
-
-\def\handleMPboundingbox#1#2 #3 #4 #5
- {\ifnum#1>\currentMPboundingbox
- \xdef\MPllx{#2}\xdef\MPlly{#3}%
- \xdef\MPurx{#4}\xdef\MPury{#5}%
- \dimen0=#2pt
- \dimen0=-\MPxscale\dimen0
- \dimen2=#3pt
- \dimen2=-\MPyscale\dimen2
- \xdef\MPxoffset{\withoutpt\the\dimen0}%
- \xdef\MPyoffset{\withoutpt\the\dimen2}%
- \dimen0=#2bp
- \dimen0=-\dimen0
- \dimen2=#3bp
- \dimen2=-\dimen2
- \advance\dimen0 #4bp
- \dimen0=\MPxscale\dimen0
- \xdef\MPwidth{\the\dimen0}%
- \advance\dimen2 #5bp
- \xdef\MPyshift{\the\dimen2}% unscaled
- \dimen2=\MPyscale\dimen2
- \xdef\MPheight{\the\dimen2}%
- \chardef\currentMPboundingbox#1\relax
- \fi
- \doresetMPstack
- \let\handleMPsequence\dohandleMPsequence
- \let\next\handleMPsequence
- \ifskipemptyMPgraphic
- \ifdim\MPheight=0pt\relax\ifdim\MPwidth=0pt\relax
- \def\next{\endinput\finishMPgraphic}%
- \fi\fi
- \fi
- \next}
-
-%D Unless defined otherwise, we simply ignore specialcomments.
-
-\def\handleMPspecialcomment
- {\doresetMPstack
- \let\handleMPsequence\dohandleMPsequence
- \handleMPsequence}
-
-\let\handleMPspecialscomment\handleMPspecialcomment
-
-%D We use the \type{page} comment as a signal that
-%D stackbuilding can be started.
-
-\def\handleMPpage #1 #2
- {\doresetMPstack
- \donetrue
- \let\handleMPsequence\dohandleMPsequence
- \handleMPsequence}
-
-%D The same applies to the special extensions.
-
-\def\handleMPspecialcommand
- {\doresetMPstack
- \let\handleMPsequence\dohandleMPsequence
- \handleMPsequence}
-
-%D \METAPOST\ draws its dots by moving to a location and
-%D invoking \type{0 0 rlineto}. This operator is not
-%D available in \PDF. Our solution is straightforward: we draw
-%D a line from $(current\_x, current\_y)$ to itself. This
-%D means that the arguments of the preceding \type{moveto} have
-%D to be saved.
-
-\def\lastMPmoveX{0}
-\def\lastMPmoveY{0}
-
-%D These saved coordinates are also used when we handle the
-%D texts. Text handling proved to be a bit of a nuisance, but
-%D finally I saw the light. It proved that we also had to
-%D take care of \type{(split arguments)}.
-
-% \def\setMPfshowfont#1#2%
-% {\font\temp=#1\space at #2\relax\temp}
-
-% \startMPcode
-% draw btex Ga toch effe f\kern0ptietsen?{}` etex ;
-% \stopMPcode
-
-\newtoks \everyMPshowfont
-
-\def\setMPfshowfont#1#2%
- {\font\temp=#1\space at #2\relax\temp
- \the\everyMPshowfont}
-
-\let\MPfshowcommand\empty
-
-%D The next hackery handles characters one by one. We only support this
-%D for the latest greatest \METAPOST\ binaries, the ones that escape
-%D problematic chars.
-
-\def\doflushMPtext#1%
- {\edef\!!stringa{#1}%
- \expandafter\dodoflushMPtext\!!stringa\relax}
-
-\def\dodoflushMPtext
- {\afterassignment\dododoflushMPtext\let\nexttoken=}
-
-\def\dododoflushMPtext
- {\ifx\nexttoken\relax
- % done
- \else\ifx\nexttoken\char
- \expandafter\expandafter\expandafter\dodododoflushMPtext
- \else
- {\nexttoken}%
- \expandafter\expandafter\expandafter\dodoflushMPtext
- \fi\fi}
-
-\def\dodododoflushMPtext
- {\afterassignment\dododododoflushMPtext\scratchcounter}
-
-\def\dododododoflushMPtext
- {{\char\scratchcounter}\let\next\dodoflushMPtext}
-
-\def\dohandleMPfshow
- {\bgroup
- \setbox\scratchbox\hbox
- {\obeyMPspecials
- \let\ \relax % mp breaks long lines and appends a \
- \edef\size{\gMPa\nofMParguments}%
- \ifx\size\PSnfont % round font size (to pt)
- \advance\nofMParguments -1
- \expandafter\scratchdimen\gMPa\nofMParguments pt\relax
- \ifdim\scratchdimen<1pt
- \def\size{1pt}%
- \else
- \advance\scratchdimen .5pt
- \def\size##1.##2\relax{\def\size{##1pt}}%
- \expandafter\size\the\scratchdimen\relax
- \fi
- \else
- \edef\size{\size bp}%
- \fi
- \advance\nofMParguments -1
- %\font\temp=\gMPa\nofMParguments\space at \size
- \let\temp\relax % to be sure
- \setMPfshowfont{\gMPa\nofMParguments}\size
- \advance\nofMParguments -1
- \temp
- \MPfshowcommand
- {\ifnum\nofMParguments=1
- \def\do(##1){##1}%
- \doflushMPtext{\dogMPa1}% only latest mp gets this treatment
- \else
- % we need to catch ( a ) (a a a) (\123 \123 \123) etc
- \scratchcounter1
- \def\dodo##1% Andreas Fieger's bug: (\304...)
- {\edef\!!stringa{##1\empty\empty}% and another one: ( 11) -> \ifx 11
- \ifx\!!stringa\MPspacechar\MPspacechar\else\expandafter##1\fi}%
- \def\do(##1{\dodo{##1}}%
- \dogMPa\scratchcounter\MPspacechar
- \let\do\relax
- \loop
- \advance\scratchcounter 1
- \ifnum\scratchcounter<\nofMParguments\relax
- \gMPa\scratchcounter\MPspacechar
- \repeat
- \def\do##1){\dodo{##1}}%
- \dogMPa\scratchcounter
- \fi
- \unskip}}%
- \setbox\scratchbox\hbox
- {\hskip\lastMPmoveX bp\raise\lastMPmoveY bp\box\scratchbox}%
- \ht\scratchbox0pt%
- \dp\scratchbox0pt%
- \wd\scratchbox0pt%
- \box\scratchbox
- \egroup}
-
-\let\handleMPfshow\dohandleMPfshow % so we can overload this one later
-
-%D You could consider the following definition to be the most
-%D natural one.
-
-% \def\MPspacechar{\space} % normal case
-
-\def\MPspacechar{\char32\relax} % old solution does not work with math
-
-%D However, the following implementation is more robust, since
-%D some fonts have funny visible spaces in the space slot. This
-%D gives a mismatch between the space that \METAPOST\ took into
-%D account and the \quote {natural} space. This only happens in
-%D labels, since \type {btex}||\type {etex} thingies don't have
-%D spaces. This phenomena showed up when preparing the
-%D \METAFUN\ manual, where Palatino fonts are used. We can
-%D safely assume that \METAPOST\ considers \type {\char32} to
-%D be the space.
-
-\def\MPspacechar{\setbox\scratchbox\hbox{\char32}\kern\wd\scratchbox}
-
-%D Well, this does not work with math fonts, so:
-
-\def\MPspacechar{\char32\relax}
-
-%D Most operators are just converted and keep their
-%D arguments. Dashes however need a bit different treatment,
-%D otherwise \PDF\ viewers complain loudly. Another
-%D complication is that one argument comes after the \type{]}.
-%D When reading the data, we simply ignore the array boundary
-%D characters. We save ourselves some redundant newlines and
-%D at the same time keep the output readable by packing the
-%D literals.
-
-\def\handleMPsetdash
- {\bgroup
- \ignoreMPspecials
- \def\somestring{[}%
- \scratchcounter1
- \loop
- \ifnum\scratchcounter<\nofMParguments
- \edef\somestring{\somestring\space\gMPa\scratchcounter}%
- \advance\scratchcounter 1
- \repeat
- \edef\somestring{\somestring]\gMPa\scratchcounter\space d}%
- \PDFcode{\somestring}%
- \egroup}
-
-%D The \type{setlinewidth} commands looks a bit complicated. There are
-%D two alternatives, that result in a similar look in both
-%D $x$- and $y$-dorection. As John Hobby says:
-%D
-%D \startnarrower \switchtobodyfont[ss]
-%D \starttyping
-%D x 0 dtransform exch truncate exch idtransform pop setlinewidth
-%D 0 y dtransform truncate idtransform setlinewidth pop
-%D \stoptyping
-%D
-%D These are just fancy versions of \type{x setlinewidth} and
-%D \type{y setlinewidth}. The \type{x 0 ...} form is used if
-%D the path is {\em primarily vertical}. It rounds the width
-%D so that vertical lines come out an integer number of pixels
-%D wide in device space. The \type{0 y ...} form does the same
-%D for paths that are {\em primarily horizontal}. The reason
-%D why I did this is Knuth insists on getting exactly the
-%D widths \TEX\ intends for the horizontal and vertical rules
-%D in \type{btex...etex} output. (Note that PostScript scan
-%D conversion rules cause a horizontal or vertical line of
-%D integer width $n$ in device space to come out $n+1$ pixels
-%D wide, regardless of the phase relative to the pixel grid.)
-%D \stopnarrower
-%D
-%D The common operator in these sequences is \type{dtransform},
-%D so we can use this one to trigger setting the linewidth.
-
-\def\handleMPdtransform
- {\ifdim\gMPa1 pt>0pt
- \PDFcode{\gMPa1 w}%
- \def\next##1 ##2 ##3 ##4 ##5 ##6 {\handleMPsequence}%
- \else
- \PDFcode{\gMPa2 w}%
- \def\next##1 ##2 ##3 ##4 {\handleMPsequence}%
- \fi
- \let\handleMPsequence\dohandleMPsequence
- \resetMPstack
- \next}
-
-%D The most complicated command is \type{concat}. \METAPOST\
-%D applies this operator to \type{stroke}. At that moment the
-%D points set by \type{curveto} and \type{moveto}, are already
-%D fixed. In \PDF\ however the \type{cm} operator affects the
-%D points as well as the pen (stroke). Like more \PDF\
-%D operators, \type{cm} is defined in a bit ambiguous way.
-%D The only save route for non||circular penshapes, is saving
-%D the path, recalculating the points and applying the
-%D transformation matrix in such a way that we can be sure
-%D that its behavior is well defined. This comes down to
-%D inverting the path and applying \type{cm} to that path as
-%D well as the pen. This all means that we have to save the
-%D path.
-
-%D In \METAPOST\ there are three ways to handle a path $p$:
-%D
-%D \starttyping
-%D draw p; fill p; filldraw p;
-%D \stoptyping
-%D
-%D The last case outputs a \type{gsave fill grestore} before
-%D \type{stroke}. Handling the path outside the main loops
-%D saves about 40\% run time.\footnote{We can save some more by
-%D following the \METAPOST\ output routine, but for the moment
-%D we keep things simple.} Switching between the main loop and
-%D the path loop is done by means of the recursely called
-%D macro \type{\handleMPsequence}.
-
-\def\handleMPpath
- {\chardef\finiMPpath0
- \let\closeMPpath\relax
- \let\flushMPpath\flushnormalMPpath
- \resetMPstack
- \nofMPsegments1
- \let\handleMPsequence\dohandleMPpath
- \dohandleMPpath}
-
-%D Most paths are drawn with simple round pens. Therefore we've
-%D split up the routine in two.
-
-\def\flushnormalMPsegment
- {\ifcase\getMPkeyword\relax
- \PDFcode{\!MPgMPs1 \!MPgMPs2 l}%
- \or
- \PDFcode{\!MPgMPs1 \!MPgMPs2 \!MPgMPs3 \!MPgMPs4 \!MPgMPs5 \!MPgMPs6 c}%
- \or
- \PDFcode{\!MP\lastMPmoveX\space\!MP\lastMPmoveY\space l}%
- \or
- \edef\lastMPmoveX{\gMPs1}% evt \!MP here
- \edef\lastMPmoveY{\gMPs2}%
- \PDFcode{\!MP\lastMPmoveX\space \!MP\lastMPmoveY\space m}%
- \fi}
-
-\def\flushconcatMPsegment
- {\ifcase\getMPkeyword\relax
- \doMPconcat{\gMPs1}\a{\gMPs2}\b%
- \PDFcode{\!MP\a\space\!MP\b\space l}%
- \or
- \doMPconcat{\gMPs1}\a{\gMPs2}\b%
- \doMPconcat{\gMPs3}\c{\gMPs4}\d%
- \doMPconcat{\gMPs5}\e{\gMPs6}\f%
- \PDFcode{\!MP\a\space\!MP\b\space
- \!MP\c\space\!MP\d\space
- \!MP\e\space\!MP\f\space c}%
- \or
- \bgroup
- \noMPtranslate
- \doMPconcat\lastMPmoveX\a\lastMPmoveY\b%
- \PDFcode{\!MP\a\space\!MP\b\space l S}%
- \egroup
- \or
- \edef\lastMPmoveX{\gMPs1}%
- \edef\lastMPmoveY{\gMPs2}%
- \doMPconcat\lastMPmoveX\a\lastMPmoveY\b%
- \PDFcode{\!MP\a\space\!MP\b\space m}%
- \fi}
-
-% \def\flushnormalMPpath
-% {\scratchcounter\nofMPsegments
-% \nofMPsegments 1
-% \loop
-% \flushnormalMPsegment
-% \advance\nofMPsegments 1
-% \ifnum\nofMPsegments<\scratchcounter
-% \repeat}
-%
-% \def\flushconcatMPpath
-% {\scratchcounter\nofMPsegments
-% \nofMPsegments 1
-% \loop
-% \flushconcatMPsegment
-% \advance\nofMPsegments 1
-% \ifnum\nofMPsegments<\scratchcounter
-% \repeat}
-%
-% an alternative is presented below: (no \def assignment)
-
-\def\doflushsomeMPpath
- {\dodoflushsomeMPpath
- \advance\nofMPsegments 1
- \ifnum\nofMPsegments<\scratchcounter
- \expandafter\doflushsomeMPpath
- \fi}
-
-\def\flushsomeMPpath
- {\scratchcounter\nofMPsegments
- \nofMPsegments 1
- \doflushsomeMPpath}
-
-\def\flushnormalMPpath{\let\dodoflushsomeMPpath\flushnormalMPsegment\flushsomeMPpath}
-
-%OLD \def\flushconcatMPpath{\let\dodoflushsomeMPpath\flushconcatMPsegment\flushsomeMPpath}
-
-%NEW pre-calculate 1/D so it needn't be repeated for each control point.
-
-\def\flushconcatMPpath
- {\MPreciprocaldeterminant
- \let\dodoflushsomeMPpath\flushconcatMPsegment\flushsomeMPpath}
-
-%D The transformation of the coordinates is handled by one of
-%D the macros Tanmoy posted to the \PDFTEX\ mailing list.
-%D I rewrote and optimized the original macro to suit the other
-%D macros in this module.
-%D
-%D \starttyping
-%D \doMPconcat {x position} \xresult {y position} \yresult
-%D \stoptyping
-%D
-%D By setting the auxiliary \DIMENSIONS\ \type{\dimen0} upto
-%D \type{\dimen10} only once per path, we save over 20\% run
-%D time. Some more speed was gained by removing some parameter
-%D passing. These macros can be optimized a bit more by using
-%D more constants. There is however not much need for further
-%D optimization because penshapes usually are round and
-%D therefore need no transformation. Nevertheless we move the
-%D factor to the outer level and use a bit different \type{pt}
-%D removal macro. Although the values represent base points,
-%D we converted them to pure points, simply because those can
-%D be converted back.
-
-%OLD \mathchardef\MPconcatfactor=256 % beware don't remove spaces before it
-
-%OLD \def\doMPreducedimen#1
-%OLD {\count0\MPconcatfactor
-%OLD \advance\dimen#1 \ifdim\dimen#1>0pt .5\else -.5\fi\count0
-%OLD \divide\dimen#1 \count0\relax}
-
-%OLD % too inaccurate (see old pragma logo)
-%OLD
-%OLD \def\doMPreducedimen#1
-%OLD {\count0=\MPconcatfactor
-%OLD \divide\dimen#1 \count0\relax}
-
-%OLD \def\doMPreducedimen#1
-%OLD {\advance\dimen#1 \ifdim\dimen#1>0pt .5\else -.5\fi\MPconcatfactor
-%OLD \divide\dimen#1 \MPconcatfactor}
-
-%D The transformation code is rewritten by Daniel H. Luecking who
-%D describes his patch as follows:
-%D
-%D We would like to divide 1 by $X$, but all divisions are integer so
-%D for accuracy we want to convert to large integers and make sure the
-%D integer quotient has as many significant digits as possible. Thus we
-%D need to replace $1/X$ with $M/N$ where $N$ is as large as possible
-%D and $M/N$ is as large as possible. Also for simplicity $M$ should be
-%D a power of 2. So we make $M = 2^{30}$ \footnote{$2^{31} - 1$ is the
-%D largest legal integer. Using it (and simply ignoring the inaccuracy
-%D caused by $-1$) turns out to be at least as accurate in all cases,
-%D and more accurate in some.} (largest legal power of 2) and adjust
-%D $X$ downward (if necessary) to the the range $1-2^{16}$. This gives
-%D at least 15 significant binary digits, (almost as accurate as
-%D \METAPOST\ for numbers near 1) or almost 5 significant figures
-%D (decimal).
-
-\newcount\MPscratchCnt
-\newdimen\MPscratchDim % will be assigned global
-
-\def\MPadjustdimen % sets \MPscratchDim and \MPscratchCnt
- {\MPscratchCnt0
- \doMPadjustdimen}
-
-\def\doMPadjustdimen
- {\ifdim\MPscratchDim>1pt
- \divide\MPscratchDim 2
- \advance\MPscratchCnt 1
- \expandafter\doMPadjustdimen
- \fi}
-
-%OLD \def\doMPexpanddimen#1
-%OLD {\multiply\dimen#1 \MPconcatfactor\relax}
-
-%D DHL: When viewed as an integer, $1 \hbox{pt}=2^{16}$ so $2^{32}/X$
-%D is the right way to do $(1 \hbox{pt})/(X \hbox{pt})$ and get the
-%D answer in points. But we are limited to $2^{30}/X$. However, we
-%D actually do $[ 2^{30} / (X/2^K) ]*2^{2-K}$ where $K$ is the number
-%D of halvings it takes to bring $X$ below $1 \hbox{pt}$. If $K$ is 0
-%D or 1 we readjust by multiplying by 4 or 2, otherwise by halving
-%D $(K-2)$ times \type {\MPscratchCnt} holds the value of $K$ from
-%D \type {\MPadjustdimen}.
-
-\def\MPreadjustdimen % acts on \MPscratchDim and MPscratchCnt
- {\ifcase\MPscratchCnt
- \multiply\scratchdimen 4
- \or
- \multiply\scratchdimen 2
- \else
- \expandafter\doMPreadjustdimen
- \fi}
-
-\def\doMPreadjustdimen
- {\ifnum\MPscratchCnt>2
- \divide\scratchdimen 2
- \advance\MPscratchCnt -1
- \expandafter\doMPreadjustdimen
- \fi}
-
-\def\MPreciprocaldeterminant
- {\scratchdimen\withoutpt\the\dimen0 \dimen6 % s_x*s_y
- \advance\scratchdimen - \withoutpt\the\dimen2 \dimen4 % s_x*s_y - r_x*r_y
- \ifdim\scratchdimen<0pt % we need a positive dimension
- \scratchdimen-\scratchdimen % for \MPadjustdimen (?)
- \doMPreciprocal
- \scratchdimen-\scratchdimen
- \else
- \doMPreciprocal
- \fi
- \edef\MPreciprocal{\withoutpt\the\scratchdimen}}
-
-\newcount\MPnumerator \MPnumerator = 1073741824 % 2^{30}
-
-% todo: dimexpr
-
-\def\doMPreciprocal % replace \scratchdimen with its reciprocal
- {\ifdim\scratchdimen=1pt \else
- \MPadjustdimen
- \scratchcounter\MPnumerator
- \divide\scratchcounter\scratchdimen
- \scratchdimen1\scratchcounter % 1 needed !
- \MPreadjustdimen
- \fi}
-
-%OLD \def\presetMPconcat
-%OLD {\dimen 0=\gMPs1pt \doMPreducedimen 0 % r_x
-%OLD \dimen 2=\gMPs2pt \doMPreducedimen 2 % s_x
-%OLD \dimen 4=\gMPs3pt \doMPreducedimen 4 % s_y
-%OLD \dimen 6=\gMPs4pt \doMPreducedimen 6 % r_y
-%OLD \dimen 8=\gMPs5pt \doMPreducedimen 8 % t_x
-%OLD \dimen10=\gMPs6pt \doMPreducedimen10 } % t_y
-%OLD
-%OLD \def\presetMPscale
-%OLD {\dimen 0=\gMPs1pt \doMPreducedimen 0
-%OLD \dimen 2=0pt
-%OLD \dimen 4=0pt
-%OLD \dimen 6=\gMPs2pt \doMPreducedimen 6
-%OLD \dimen 8=0pt
-%OLD \dimen10=0pt}
-
-\def\cleanupMPconcat
- {\ignoreMPspecials
- \docleanupMPargument1%
- \docleanupMPargument6%
- \keepMPspecials}
-
-\def\presetMPconcat
- {\dimen 0=\gMPs1pt % s_x
- \dimen 2=\gMPs2pt % r_x
- \dimen 4=\gMPs3pt % r_y
- \dimen 6=\gMPs4pt % s_y
- \dimen 8=\gMPs5pt % t_x
- \dimen10=\gMPs6pt} % t_y
-
-\def\presetMPscale
- {\dimen 0=\gMPs1pt
- \dimen 2=0pt
- \dimen 4=0pt
- \dimen 6=\gMPs2pt
- \dimen 8=0pt
- \dimen10=0pt}
-
-\def\noMPtranslate % use this one grouped
- {\dimen 8=0pt % t_x
- \dimen10=0pt} % t_y
-
-%D \starttyping
-%D \def\doMPconcat#1#2#3#4%
-%D {\dimen12=#1 pt \doMPreducedimen12 % p_x
-%D \dimen14=#3 pt \doMPreducedimen14 % p_y
-%D %
-%D \dimen16 \dimen 0
-%D \multiply \dimen16 \dimen 6
-%D \dimen20 \dimen 2
-%D \multiply \dimen20 \dimen 4
-%D \advance \dimen16 -\dimen20
-%D %
-%D \dimen18 \dimen12
-%D \multiply \dimen18 \dimen 6
-%D \dimen20 \dimen14
-%D \multiply \dimen20 \dimen 4
-%D \advance \dimen18 -\dimen20
-%D \dimen20 \dimen 4
-%D \multiply \dimen20 \dimen10
-%D \advance \dimen18 \dimen20
-%D \dimen20 \dimen 6
-%D \multiply \dimen20 \dimen 8
-%D \advance \dimen18 -\dimen20
-%D %
-%D \multiply \dimen12 -\dimen 2
-%D \multiply \dimen14 \dimen 0
-%D \advance \dimen12 \dimen14
-%D \dimen20 \dimen 2
-%D \multiply \dimen20 \dimen 8
-%D \advance \dimen12 \dimen20
-%D \dimen20 \dimen 0
-%D \multiply \dimen20 \dimen10
-%D \advance \dimen12 -\dimen20
-%D %
-%D \doMPreducedimen16
-%D \divide \dimen18 \dimen16 \doMPexpanddimen18
-%D \divide \dimen12 \dimen16 \doMPexpanddimen12
-%D %
-%D \edef#2{\withoutpt\the\dimen18}% % p_x^\prime
-%D \edef#4{\withoutpt\the\dimen12}} % p_y^\prime
-%D \stoptyping
-
-%D The following optimization resulted from some tests by
-%D and email exchanges with Sanjoy Mahajan.
-%D
-%D \starttyping
-%D \def\doMPconcat#1#2#3#4%
-%D {\dimen12=#1 pt \doMPreducedimen12 % p_x
-%D \dimen14=#3 pt \doMPreducedimen14 % p_y
-%D %
-%D \dimen16 \dimen 0
-%D \multiply \dimen16 \dimen 6
-%D \dimen20 \dimen 2
-%D \multiply \dimen20 \dimen 4
-%D \advance \dimen16 -\dimen20
-%D %
-%D \dimen18 \dimen12
-%D \multiply \dimen18 \dimen 6
-%D \dimen20 \dimen14
-%D \multiply \dimen20 \dimen 4
-%D \advance \dimen18 -\dimen20
-%D \dimen20 \dimen 4
-%D \multiply \dimen20 \dimen10
-%D \advance \dimen18 \dimen20
-%D \dimen20 \dimen 6
-%D \multiply \dimen20 \dimen 8
-%D \advance \dimen18 -\dimen20
-%D %
-%D \multiply \dimen12 -\dimen 2
-%D \multiply \dimen14 \dimen 0
-%D \advance \dimen12 \dimen14
-%D \dimen20 \dimen 2
-%D \multiply \dimen20 \dimen 8
-%D \advance \dimen12 \dimen20
-%D \dimen20 \dimen 0
-%D \multiply \dimen20 \dimen10
-%D \advance \dimen12 -\dimen20
-%D %
-%D %\ifdim\dimen16>1pt % oeps, can be < 1pt too
-%D \ifdim\dimen16=1pt \else
-%D \ifdim\dimen16>\MPconcatfactor pt
-%D \doMPreducedimen16
-%D \divide \dimen18 \dimen16 \doMPexpanddimen18
-%D \divide \dimen12 \dimen16 \doMPexpanddimen12
-%D \else
-%D \divide \dimen18 \dimen16 \doMPexpanddimen18 \doMPexpanddimen18
-%D \divide \dimen12 \dimen16 \doMPexpanddimen12 \doMPexpanddimen12
-%D \fi
-%D \fi
-%D %
-%D \edef#2{\withoutpt\the\dimen18}% % p_x^\prime
-%D \edef#4{\withoutpt\the\dimen12}} % p_y^\prime
-%D \stoptyping
-%D
-%D But, this one is still too inaccurate, so we now have:
-
-% \def\doMPconcat#1#2#3#4%
-% {\dimen12=#1pt % p_x
-% \dimen14=#3pt % p_y
-% %
-% % we should test for >-1024 too, but for the moment take the gamble
-% \chardef\MPfactor1\ifdim\dimen12<1024pt \ifdim\dimen14<1024pt 6\fi\fi
-% %
-% \multiply\dimen12 \MPfactor
-% \multiply\dimen14 \MPfactor
-% %
-% \doMPreducedimen12
-% \doMPreducedimen14
-% %
-% \dimen16 \dimen 0
-% \multiply \dimen16 \dimen 6
-% \dimen20 \dimen 2
-% \multiply \dimen20 \dimen 4
-% \advance \dimen16 -\dimen20
-% %
-% \dimen18 \dimen12
-% \multiply \dimen18 \dimen 6
-% \dimen20 \dimen14
-% \multiply \dimen20 \dimen 4
-% \advance \dimen18 -\dimen20
-% \dimen20 \dimen 4
-% \multiply \dimen20 \dimen10
-% \advance \dimen18 \dimen20
-% \dimen20 \dimen 6
-% \multiply \dimen20 \dimen 8
-% \advance \dimen18 -\dimen20
-% %
-% \multiply \dimen12 -\dimen 2
-% \multiply \dimen14 \dimen 0
-% \advance \dimen12 \dimen14
-% \dimen20 \dimen 2
-% \multiply \dimen20 \dimen 8
-% \advance \dimen12 \dimen20
-% \dimen20 \dimen 0
-% \multiply \dimen20 \dimen10
-% \advance \dimen12 -\dimen20
-% %
-% \ifdim\dimen16=1pt \else
-% \ifdim\dimen16>\MPconcatfactor pt
-% \doMPreducedimen16
-% \divide \dimen18 \dimen16 \doMPexpanddimen18
-% \divide \dimen12 \dimen16 \doMPexpanddimen12
-% \else
-% \divide \dimen18 \dimen16 \doMPexpanddimen18 \doMPexpanddimen18
-% \divide \dimen12 \dimen16 \doMPexpanddimen12 \doMPexpanddimen12
-% \fi
-% \fi
-% %
-% \divide\dimen18 \MPfactor
-% \divide\dimen12 \MPfactor
-% %
-% \edef#2{\withoutpt\the\dimen18}% % p_x^\prime
-% \edef#4{\withoutpt\the\dimen12}} % p_y^\prime
-
-%D We cannot use \type {\beginETEX} here since in plain we
-%D get \type {\outer} problems, sigh.
-
-%OLD \beginTEX
-%OLD
-%OLD \def\MPcriteriumA {512pt} % scale
-%OLD \def\MPcriteriumB {2pt} % scale
-%OLD
-%OLD \endTEX
-%OLD
-%OLD \ifx\MPcriteriumA\undefined
-%OLD
-%OLD \newdimen\MPcriteriumA \MPcriteriumA=512pt
-%OLD \newdimen\MPcriteriumB \MPcriteriumB= 2pt
-%OLD
-%OLD \fi
-
-%OLD \def\doMPconcat#1#2#3#4%
-%OLD {\dimen12=#1pt % p_x
-%OLD \dimen14=#3pt % p_y
-%OLD %
-%OLD \chardef\MPfactor0
-%OLD \ifdim\dimen4<\MPcriteriumB\ifdim\dimen4>-\MPcriteriumB
-%OLD \ifdim\dimen6<\MPcriteriumB\ifdim\dimen6>-\MPcriteriumB
-%OLD \ifdim\dimen8<\MPcriteriumB\ifdim\dimen8>-\MPcriteriumB
-%OLD \ifdim\dimen10<\MPcriteriumB\ifdim\dimen10>-\MPcriteriumB
-%OLD \chardef\MPfactor1
-%OLD \fi\fi
-%OLD \fi\fi
-%OLD \fi\fi
-%OLD \fi\fi
-%OLD \ifcase\MPfactor % spurious 0 removed
-%OLD \chardef\MPfactor1
-%OLD \ifdim\dimen12<\MPcriteriumA\ifdim\dimen12>-\MPcriteriumA
-%OLD \ifdim\dimen14<\MPcriteriumA\ifdim\dimen14>-\MPcriteriumA
-%OLD \chardef\MPfactor16
-%OLD \fi\fi
-%OLD \fi\fi
-%OLD \fi
-%OLD %
-%OLD \multiply\dimen12 \MPfactor
-%OLD \multiply\dimen14 \MPfactor
-%OLD %
-%OLD \doMPreducedimen12
-%OLD \doMPreducedimen14
-%OLD %
-%OLD \dimen16 \dimen 0
-%OLD \multiply \dimen16 \dimen 6
-%OLD \dimen20 \dimen 2
-%OLD \multiply \dimen20 \dimen 4
-%OLD \advance \dimen16 -\dimen20
-%OLD %
-%OLD \dimen18 \dimen12
-%OLD \multiply \dimen18 \dimen 6
-%OLD \dimen20 \dimen14
-%OLD \multiply \dimen20 \dimen 4
-%OLD \advance \dimen18 -\dimen20
-%OLD \dimen20 \dimen 4
-%OLD \multiply \dimen20 \dimen10
-%OLD \advance \dimen18 \dimen20
-%OLD \dimen20 \dimen 6
-%OLD \multiply \dimen20 \dimen 8
-%OLD \advance \dimen18 -\dimen20
-%OLD %
-%OLD \multiply \dimen12 -\dimen 2
-%OLD \multiply \dimen14 \dimen 0
-%OLD \advance \dimen12 \dimen14
-%OLD \dimen20 \dimen 2
-%OLD \multiply \dimen20 \dimen 8
-%OLD \advance \dimen12 \dimen20
-%OLD \dimen20 \dimen 0
-%OLD \multiply \dimen20 \dimen10
-%OLD \advance \dimen12 -\dimen20
-%OLD %
-%OLD \ifdim\dimen16=1pt \else
-%OLD \ifdim\dimen16>\MPconcatfactor 1pt \relax
-%OLD \doMPreducedimen16
-%OLD \divide \dimen18 \dimen16 \doMPexpanddimen18
-%OLD \divide \dimen12 \dimen16 \doMPexpanddimen12
-%OLD \else
-%OLD \divide \dimen18 \dimen16 \doMPexpanddimen18 \doMPexpanddimen18
-%OLD \divide \dimen12 \dimen16 \doMPexpanddimen12 \doMPexpanddimen12
-%OLD \fi
-%OLD \fi
-%OLD %
-%OLD \divide\dimen18 \MPfactor
-%OLD \divide\dimen12 \MPfactor
-%OLD %
-%OLD \edef#2{\withoutpt\the\dimen18}% % p_x^\prime
-%OLD \edef#4{\withoutpt\the\dimen12}} % p_y^\prime
-
-%D DHL: Ideally, $r_x$, $r_y$, $s_x$, $s_y$ should be in macros, not
-%D dimensions (they are scalar quantities after all, not lengths). I
-%D suppose the authors decided to do calculations with integer
-%D arithmetic instead of using real factors because it's faster.
-%D However, the actual macros test slower, possibly because I've
-%D omitted three nested loops. In my test files, my approach is more
-%D accurate. It is also far simpler and overflow does not seem to be a
-%D significant concern. The scale factors written by Metapost are (?)
-%D always $<=1$ (it scales coordinates internally) and coordinates are
-%D always likely to be less than \type {\maxdimen}.
-%D
-%D If this should ever cause problems, the scale factors can be reduced.
-
-% \def\doMPconcat#1#2#3#4%
-% {\dimen12=#1pt % p_x % #1pt
-% \dimen14=#3pt % p_y % #3pt
-% \advance\dimen12 -\dimen8 % p_x - t_x
-% \advance\dimen14 -\dimen10 % p_y - t_y
-% \dimen18=\withoutpt\the\dimen6 \dimen12 % s_y(p_x - t_x)
-% \advance\dimen18 -\withoutpt\the\dimen4 \dimen14 % - r_y(p_y-t_y)
-% \dimen14=\withoutpt\the\dimen0 \dimen14 % s_x(p_y-t_y)
-% \advance\dimen14 -\withoutpt\the\dimen2 \dimen12 % - r_x(p_x-t_x)
-% % \MPscratchDim contains precomputed 1/D:
-% \dimen18=\withoutpt\the\MPscratchDim \dimen18
-% \dimen14=\withoutpt\the\MPscratchDim \dimen14
-% \edef#2{\withoutpt\the\dimen18}% % p_x^\prime
-% \edef#4{\withoutpt\the\dimen14}} % p_y^\prime
-
-\def\doMPconcat#1#2#3#4%
- {\dimen12=#1pt % p_x % #1pt
- \dimen14=#3pt % p_y % #3pt
- \advance\dimen12 -\dimen8 % p_x - t_x
- \advance\dimen14 -\dimen10 % p_y - t_y
- \dimen18=\withoutpt\the\dimen6 \dimen12 % s_y(p_x - t_x)
- \advance\dimen18 -\withoutpt\the\dimen4 \dimen14 % - r_y(p_y-t_y)
- \dimen14=\withoutpt\the\dimen0 \dimen14 % s_x(p_y-t_y)
- \advance\dimen14 -\withoutpt\the\dimen2 \dimen12 % - r_x(p_x-t_x)
- % \MPreciprocal contains precomputed 1/D:
- \dimen18=\MPreciprocal\dimen18
- \dimen14=\MPreciprocal\dimen14
- \edef#2{\withoutpt\the\dimen18}% % p_x^\prime
- \edef#4{\withoutpt\the\dimen14}} % p_y^\prime
-
-% faster but not that often used
-%
-% \def\doMPconcat#1#2#3#4%
-% {\dimen12\dimexpr#1\points-\dimen 8\relax % p_x-t_x
-% \dimen14\dimexpr#3\points-\dimen10\relax % p_y-t_y
-% \dimen18\dimexpr\withoutpt\the\dimen6\dimen12-\withoutpt\the\dimen4\dimen14\relax % s_y(p_x-t_x)-r_y(p_y-t_y)
-% \dimen14\dimexpr\withoutpt\the\dimen0\dimen14-\withoutpt\the\dimen2\dimen12\relax % s_x(p_y-t_y)-r_x(p_x-t_x)
-% \edef#2{\withoutpt\the\dimexpr\MPreciprocal\dimen18\relax}% % p_x^\prime
-% \edef#4{\withoutpt\the\dimexpr\MPreciprocal\dimen14\relax}} % p_y^\prime
-
-%D One reason for Daniel to write this patch was that at small sizes
-%D the accuracy was less than optimal. Here is a test that demonstrates
-%D that his alternative is pretty good:
-%D
-%D \startlinecorrection
-%D \startMPcode
-%D for i = 5cm,1cm,5mm,1mm,.5mm,.1mm,.01mm :
-%D draw fullcircle scaled i withpen pencircle xscaled (i/10) yscaled (i/20) rotated 45 ;
-%D endfor ;
-%D \stopMPcode
-%D \stoplinecorrection
-
-%D The following explanation of the conversion process was
-%D posted to the \PDFTEX\ mailing list by Tanmoy. The original
-%D macro was part of a set of macro's that included sinus and
-%D cosinus calculations as well as scaling and translating. The
-%D \METAPOST\ to \PDF\ conversion however only needs
-%D transformation.
-
-%M \start \switchtobodyfont [ss]
-
-%D Given a point $(U_x, U_y)$ in user coordinates, the business
-%D of \POSTSCRIPT\ is to convert it to device space. Let us say
-%D that the device space coordinates are $(D_x, D_y)$. Then, in
-%D \POSTSCRIPT\ $(D_x, D_y)$ can be written in terms of
-%D $(U_x, U_y)$ in matrix notation, either as
-%D
-%D \placeformula
-%D \startformula
-%D \pmatrix{D_x&D_y&1\cr} = \pmatrix{U_x&U_y&1\cr}
-%D \pmatrix{s_x&r_x&0\cr
-%D r_y&s_y&0\cr
-%D t_x&t_y&1\cr}
-%D \stopformula
-%D
-%D or
-%D
-%D \placeformula
-%D \startformula
-%D \pmatrix{D_x\cr D_y\cr 1} = \pmatrix{s_x&r_y&t_x\cr
-%D r_x&s_y&t_y\cr
-%D 0 &0 &1 \cr}
-%D \pmatrix{U_x\cr
-%D U_y\cr
-%D 1 \cr}
-%D \stopformula
-%D
-%D both of which is a shorthand for the same set of equations:
-%D
-%D \placeformula
-%D \startformula
-%D D_x = s_x U_x + r_y U_y + t_x
-%D \stopformula
-%D
-%D \placeformula
-%D \startformula
-%D D_y = r_x U_x + s_y U_y + t_y
-%D \stopformula
-%D
-%D which define what is called an `affine transformation'.
-%D
-%D \POSTSCRIPT\ represents the `transformation matrix' as a
-%D six element matrix instead of a $3\times 3$ array because
-%D three of the elements are always~0, 0 and~1. Thus the above
-%D transformation is written in postscript as $[s_x\, r_x\,
-%D r_y\, s_y\, t_x\, t_y]$. However, when doing any
-%D calculations, it is useful to go back to the original
-%D matrix notation (whichever: I will use the second) and
-%D continue from there.
-%D
-%D As an example, if the current transformation matrix is
-%D $[s_x\, r_x\, r_y\, s_y\, t_x\, t_y]$ and you say \typ{[a b
-%D c d e f] concat}, this means:
-%D
-%D \startnarrower
-%D Take the user space coordinates and transform them to an
-%D intermediate set of coordinates using array $[a\, b\, c\, d\,
-%D e\, f]$ as the transformation matrix.
-%D
-%D Take the intermediate set of coordinates and change them to
-%D device coordinates using array $[s_x\, r_x\, r_y\, s_y\, t_x\, t_y]$
-%D as the transformation matrix.
-%D \stopnarrower
-%D
-%D Well, what is the net effect? In matrix notation, it is
-%D
-%D \placeformula
-%D \startformula
-%D \pmatrix{I_x\cr I_y\cr 1\cr} = \pmatrix{a&c&e\cr
-%D b&d&f\cr
-%D 0&0&1\cr}
-%D \pmatrix{U_x\cr
-%D U_y\cr
-%D 1 \cr}
-%D \stopformula
-%D
-%D \placeformula
-%D \startformula
-%D \pmatrix{D_y\cr D_y\cr 1\cr} = \pmatrix{s_x&r_y&t_x\cr
-%D r_x&s_y&t_y\cr
-%D 0 &0 &1 \cr}
-%D \pmatrix{I_x\cr
-%D I_y\cr
-%D 1 \cr}
-%D \stopformula
-%D
-%D where $(I_x, I_y)$ is the intermediate coordinate.
-%D
-%D Now, the beauty of the matrix notation is that when there is
-%D a chain of such matrix equations, one can always compose
-%D them into one matrix equation using the standard matrix
-%D composition law. The composite matrix from two matrices can
-%D be derived very easily: the element in the $i$\high{th}
-%D horizontal row and $j$\high{th} vertical column is
-%D calculated by`multiplying' the $i$\high{th} row of the first
-%D matrix and the $j$\high{th} column of the second matrix (and
-%D summing over the elements). Thus, in the above:
-%D
-%D \placeformula
-%D \startformula
-%D \pmatrix{D_x\cr D_y\cr 1} = \pmatrix{s_x^\prime&r_y^\prime&t_x^\prime\cr
-%D r_x^\prime&s_y^\prime&t_y^\prime\cr
-%D 0 &0 &0 \cr}
-%D \pmatrix{U_x\cr
-%D U_y\cr
-%D 1 \cr}
-%D \stopformula
-%D
-%D with
-%D
-%D \placeformula
-%D \startformula
-%D \eqalign
-%D {s_x^\prime & = s_x a + r_y b \cr
-%D r_x^\prime & = r_x a + s_y b \cr
-%D r_y^\prime & = s_x c + r_y d \cr
-%D s_y^\prime & = r_x c + s_y d \cr
-%D t_x^\prime & = s_x e + r_y f + t_x \cr
-%D t_y^\prime & = r_x e + s_y f + t_y \cr}
-%D \stopformula
-
-%D In fact, the same rule is true not only when one is going
-%D from user coordinates to device coordinates, but whenever
-%D one is composing two `transformations' together
-%D (transformations are `associative'). Note that the formula
-%D is not symmetric: you have to keep track of which
-%D transformation existed before (i.e.\ the equivalent of
-%D $[s_x\, r_x\, r_y\, s_y\, t_x\, t_y]$) and which was
-%D specified later (i.e.\ the equivalent of $[a\, b\, c\, d\,
-%D e\, f]$). Note also that the language can be rather
-%D confusing: the one specified later `acts earlier',
-%D converting the user space coordinates to intermediate
-%D coordinates, which are then acted upon by the pre||existing
-%D transformation. The important point is that order of
-%D transformation matrices cannot be flipped (transformations
-%D are not `commutative').
-%D
-%D Now what does it mean to move a transformation matrix
-%D before a drawing? What it means is that given a point
-%D $(P_x, P_y)$ we need a different set of coordinates
-%D $(P_x^\prime, P_y^\prime)$ such that if the transformation
-%D acts on $(P_x^\prime, P_y^\prime)$, they produce $(P_x,
-%D P_y)$. That is we need to solve the set of equations:
-%D
-%D \placeformula
-%D \startformula
-%D \pmatrix{P_x\cr P_y\cr 1\cr} = \pmatrix{s_x&r_y&t_x\cr
-%D r_x&s_y&t_y\cr
-%D 0 &0 &1 \cr}
-%D \pmatrix{P_x^\prime\cr
-%D P_y^\prime\cr
-%D 1 \cr}
-%D \stopformula
-%D
-%D Again matrix notation comes in handy (i.e. someone has
-%D already solved the problem for us): we need the inverse
-%D transformation matrix. The inverse transformation matrix can
-%D be calculated very easily:
-%D
-%D \placeformula
-%D \startformula
-%D \pmatrix{P_x^\prime\cr P_y^\prime\cr 1\cr} =
-%D \pmatrix{s_x^\prime&r_y^\prime&t_x^\prime\cr
-%D r_x^\prime&s_y^\prime&t_y^\prime\cr
-%D 0 &0 &1 \cr}
-%D \pmatrix{P_x\cr
-%D P_y\cr
-%D 1 \cr}
-%D \stopformula
-%D
-%D where, the inverse transformation matrix is given by
-%D
-%D \placeformula
-%D \startformula
-%D \eqalign
-%D {D & = s_x s_y - r_x r_y \cr
-%D s_x^\prime & = s_y / D \cr
-%D s_y^\prime & = s_x / D \cr
-%D r_x^\prime & = - r_x / D \cr
-%D r_y^\prime & = - r_y / D \cr
-%D t_x^\prime & = ( - s_y t_x + r_y t_y ) / D \cr
-%D t_y^\prime & = ( r_x t_x - s_x t_y ) / D \cr}
-%D \stopformula
-%D
-%D And you can see that when expanded out, this does
-%D give the formulas:
-%D
-%D \placeformula
-%D \startformula
-%D P_x^\prime = { { s_y(p_x-t_x) + r_y(t_y-p_y) } \over
-%D { s_x s_y-r_x r_y } }
-%D \stopformula
-%D
-%D \placeformula
-%D \startformula
-%D P_y^\prime = { { s_x(p_y-t_y) + r_x(t_x-p_x) } \over
-%D { s_x*s_y-r_x*r_y } }
-%D \stopformula
-%D
-%D The code works by representing a real number by converting
-%D it to a dimension to be put into a \DIMENSION\ register: 2.3 would
-%D be represented as 2.3pt for example. In this scheme,
-%D multiplying two numbers involves multiplying the \DIMENSION\
-%D registers and dividing by 65536. Accuracy demands that the
-%D division be done as late as possible, but overflow
-%D considerations need early division.
-%D
-%D Division involves dividing the two \DIMENSION\ registers and
-%D multiplying the result by 65536. Again, accuracy would
-%D demand that the numerator be multiplied (and|/|or the
-%D denominator divided) early: but that can lead to overflow
-%D which needs to be avoided.
-%D
-%D If nothing is known about the numbers to start with (in
-%D concat), I have chosen to divide the 65536 as a 256 in each
-%D operand. However, in the series calculating the sine and
-%D cosine, I know that the terms are small (because I never
-%D have an angle greater than 45 degrees), so I chose to
-%D apportion the factor in a different way.
-
-%M \stop
-
-%D The path is output using the values saved on the stack. If
-%D needed, all coordinates are recalculated.
-
-\def\finishMPpath
- {\PDFcode{\ifcase\finiMPpath W n\or S\or f\or B\fi}}
-
-\def\processMPpath
- {\checkMPpath
- \ifcase\nofMPsegments\else
- \flushMPpath
- \closeMPpath
- \finishMPpath
- \fi
- \let\handleMPsequence\dohandleMPsequence
- \resetMPstack
- \nofMPsegments0
- \handleMPsequence}
-
-%D The following \METAPOST\ code is quite valid but, when
-%D processed and converted to \PDF, will make a file
-%D unprintable on a Hewlett Packard printer (from Acrobat
-%D $v<=5$). Who is to blame, the driver of the OS layer in
-%D between, is hard to determine, so we add an additional
-%D check.
-%D
-%D \starttyping
-%D clip currentpicture to origin -- cycle ;
-%D setbounds currentpicture to fullsquare scaled 5cm ;
-%D \stoptyping
-
-\def\checkMPpath
- {\ifcase\finiMPpath
- \ifnum\nofMPsegments<3 % n is one ahead
- \message{omitting zero clip path}%
- \nofMPsegments0
- \fi
- \fi}
-
-%D In \PDF\ the \type{cm} operator must precede the path
-%D specification. We therefore can output the \type{cm} at
-%D the moment we encounter it.
-
-\def\handleMPpathconcat
- {\presetMPconcat
- \PDFcode{\gMPs1 \gMPs2 \gMPs3 \gMPs4 \gMPs5 \gMPs6 cm}%
- \resetMPstack}
-
-\def\handleMPpathscale
- {\presetMPscale
- \PDFcode{\gMPs1 0 0 \gMPs2 0 0 cm}%
- \resetMPstack}
-
-%D This macro interprets the path and saves it as compact as
-%D possible.
-
-\def\dohandleMPpath#1%
- {\ifcase\lccode`#1\relax
- \expandafter\dohandleMPpathA
- \else
- \expandafter\dohandleMPpathB
- \fi#1}
-
-%\def\dohandleMPpathA#1 %
-% {\setMPargument{#1}%
-% \handleMPsequence}
-
-\let\dohandleMPpathA\setMPsequence
-
-% \def\dohandleMPpathB#1 %
-% {\def\somestring{#1}%
-% \ifx\somestring\PSlineto
-% \setMPkeyword0
-% \else\ifx\somestring\PScurveto
-% \setMPkeyword1
-% \else\ifx\somestring\PSrlineto
-% \setMPkeyword2
-% \else\ifx\somestring\PSmoveto
-% \setMPkeyword3
-% \else\ifx\somestring\PSclip
-% % \chardef\finiMPpath0 % already
-% \let\handleMPsequence\processMPpath
-% \else\ifx\somestring\PSgsave
-% \chardef\finiMPpath3
-% \else\ifx\somestring\PSgrestore
-% \else\ifx\somestring\PSfill
-% \ifcase\finiMPpath
-% \chardef\finiMPpath2
-% \let\handleMPsequence\processMPpath
-% \fi
-% \else\ifx\somestring\PSstroke
-% \ifcase\finiMPpath
-% \chardef\finiMPpath1
-% \fi
-% \let\handleMPsequence\processMPpath
-% \else\ifx\somestring\PSclosepath
-% \def\closeMPpath{\PDFcode{h}}%
-% \else\ifx\somestring\PSconcat
-% \cleanupMPconcat
-% \let\flushMPpath\flushconcatMPpath
-% \handleMPpathconcat
-% \else\ifx\somestring\PSscale
-% \let\flushMPpath\flushconcatMPpath
-% \handleMPpathscale
-% \fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi
-% \handleMPsequence}
-
-\def\installMPSkeywordP#1#2%
- {\expandafter\def\csname\@@MP:P:#1\endcsname{#2}}
-
-\def\installMPSshortcutP#1#2% todo: \let
- {\expandafter\let\csname\@@MP:P:#1\expandafter\endcsname\csname\@@MP:P:#2\endcsname}
-
-\def\dohandleMPpathB#1 %
- {\def\somestring{#1}%
- \ifcsname\@@MP:P:\somestring\endcsname
- \csname\@@MP:P:\somestring\expandafter\endcsname
- \fi
- \handleMPsequence}
-
-\ifx\eTeXversion\undefined
- \def\dohandleMPpathB#1 %
- {\def\somestring{#1}%
- \csname\@@MP:P:\somestring\endcsname
- \handleMPsequence}
-\fi
-
-\installMPSkeywordP \PSlineto
- {\setMPkeyword0 }
-\installMPSkeywordP \PScurveto
- {\setMPkeyword1 }
-\installMPSkeywordP \PSrlineto
- {\setMPkeyword2 }
-\installMPSkeywordP \PSmoveto
- {\edef\lastMPmoveX{\gMPs1}%
- \edef\lastMPmoveY{\gMPs2}%
- \resetMPstack
- \setMPkeyword3 }
-\installMPSkeywordP \PSclip
- {% \chardef\finiMPpath\zerocount % already
- \let\handleMPsequence\processMPpath}
-\installMPSkeywordP \PSgsave
- {\chardef\finiMPpath3 }
-\installMPSkeywordP \PSgrestore
- {}
-\installMPSkeywordP \PSfill
- {\ifcase\finiMPpath
- \chardef\finiMPpath2
- \let\handleMPsequence\processMPpath
- \fi}
-\installMPSkeywordP \PSstroke
- {\ifcase\finiMPpath
- \chardef\finiMPpath1
- \fi
- \let\handleMPsequence\processMPpath}
-\installMPSkeywordP \PSclosepath
- {\def\closeMPpath{\PDFcode{h}}}
-\installMPSkeywordP \PSconcat
- {\cleanupMPconcat
- \let\flushMPpath\flushconcatMPpath
- \handleMPpathconcat}
-\installMPSkeywordP \PSscale
- {\let\flushMPpath\flushconcatMPpath
- \handleMPpathscale}
-
-\installMPSshortcutP {l} \PSlineto
-\installMPSshortcutP {r} \PSrlineto
-\installMPSshortcutP {m} \PSmoveto
-\installMPSshortcutP {c} \PScurveto
-
-\installMPSshortcutP {q} \PSgsave
-\installMPSshortcutP {Q} \PSgrestore
-\installMPSshortcutP {S} \PSstroke
-\installMPSshortcutP {F} \PSfill
-\installMPSshortcutP {B} \PSgsave
-\installMPSshortcutP {W} \PSclip
-\installMPSshortcutP {p} \PSclosepath
-
-\installMPSshortcutP {s} \PSscale
-\installMPSshortcutP {t} \PSconcat
-
-%D The main conversion command is:
-%D
-%D \starttyping
-%D \convertMPtoPDF {filename} {x scale} {y scale}
-%D \stoptyping
-%D
-%D The dimensions are derived from the bounding box. So we
-%D only have to say:
-%D
-%D \starttyping
-%D \convertMPtoPDF{mp-pra-1.eps}{1}{1}
-%D \convertMPtoPDF{mp-pra-1.eps}{.5}{.5}
-%D \stoptyping
-
-%D \macros
-%D {makeMPintoPDFobject,lastPDFMPobject}
-%D
-%D For experts there are a few more options. When attributes
-%D are to be added, the code must be embedded in an object
-%D accompanied with the appropriate directives. One can
-%D influence this process with \type {\makeMPintoPDFobject}.
-%D
-%D This option defaults to~0, because \CONTEXT\ takes care
-%D of objects at another level, which saves some bytes.
-%D
-%D \starttabulate[|l|l|p|]
-%D \NC 0 \NC never \NC don't use an object \NC\NR
-%D \NC 1 \NC always \NC always use an object \NC\NR
-%D \NC 2 \NC optional \NC use object when needed \NC\NR
-%D \stoptabulate
-%D
-%D The last object number used is avaliable in the macro
-%D \type {\lastPDFMPobject}.
-
-\ifx\makeMPintoPDFobject\undefined \chardef\makeMPintoPDFobject=0 \fi
-
-\def\lastPDFMPobject{0}
-
-%D The additional code needed can be made available in the
-%D (global) macro \type {\currentPDFresources}.
-
-\let\currentPDFresources\empty
-
-\newtoks\everyMPtoPDFconversion
-
-\def\convertMPtoPDF % #1#2#3%
- {\bgroup
- \defineMPtoPDFfallbacks
- \ifx\pdfdecimaldigits\undefined\else \pdfdecimaldigits=5 \fi % new
- \setbox\scratchbox\vbox\bgroup
- \xdef\MPheight{0pt}%
- \xdef\MPwidth {0pt}%
- \forgetall
- \offinterlineskip
- \startMPresources
- \doprocessMPtoPDFfile} %
-
-%D The next one is kind of private and probably will become obsolete):
-
-\def\processMPtoPDFfile % file xscale yscale
- {\bgroup
- \let\finishMPgraphic\egroup
- \doprocessMPtoPDFfile}
-
-\let\setMPextensions\relax
-
-\def\doprocessMPtoPDFfile#1#2#3% file xscale yscale
- {\setMPspecials
- \setMPextensions
- \the\everyMPtoPDFconversion
- \catcode`\^^M=\@@endofline
- \startMPscanning
- \let\do\empty
- \xdef\MPxscale{#2}%
- \xdef\MPyscale{#3}%
- \xdef\MPxoffset{0}%
- \xdef\MPyoffset{0}%
- \xdef\MPyshift{0pt}%
- \donefalse
- \let\handleMPsequence\dohandleMPsequence
- \message{[MP to PDF]}% was: [MP to PDF #1] but there is a (#1) anyway
- \input#1\relax}
-
-\def\PDFMPformoffset
- {\ifx\objectoffset\undefined0pt\else\objectoffset\fi}
-
-\chardef\blackoutMPgraphic0 % in ConTeXt 1
-
-\def\finishMPgraphic
- {\stopMPresources
- \egroup
- \setbox\scratchbox\vbox
- {\forgetall
- \hbox
- {\PDFcode{q \MPxscale\space 0 0 \MPyscale\space \MPxoffset\space \MPyoffset\space cm}%
- \ifcase\blackoutMPgraphic\or\PDFcode{0 g 0 G}\fi
- \lower\MPyshift\box\scratchbox % unscaled shift
- \PDFcode{Q}}}%
- \ht\scratchbox\MPheight
- \wd\scratchbox\MPwidth
- \dp\scratchbox0pt\relax
- \dopackageMPgraphic\scratchbox
- \egroup
- \endinput}
-
-%D Alternative for \PDFTEX. We cannot come up with something more contexy
-%D because this module is also used in \LATEX.
-
-\def\dopackageMPgraphic#1% #1 = boxregister
- {%\ifx\pdfxform\undefined
- % \chardef\makeMPintoPDFobject0 % no pdftex at all
- %\else\ifx\pdftexversion\undefined
- % \chardef\makeMPintoPDFobject0 % no pdftex at all
- %\else\ifnum\pdftexversion<14
- % \chardef\makeMPintoPDFobject0 % no resource support
- %\else
- % % keep the default value
- %\fi\fi\fi
- \ifcase\makeMPintoPDFobject\or\or\ifx\currentPDFresources\empty\else
- % an existing value of 2 signals object support (set elsewhere)
- \chardef\makeMPintoPDFobject1
- \fi\fi
- \ifcase\makeMPintoPDFobject
- \box#1%
- \or
- \scratchdimen\PDFMPformoffset\relax
- \ifdim\scratchdimen>0pt % compensate for error
- \setbox#1\vbox spread 2\scratchdimen
- {\forgetall\vss\hbox spread 2\scratchdimen{\hss\box#1\hss}\vss}%
- \fi
- \setMPPDFobject{\currentPDFresources}{#1}%
- \ifdim\scratchdimen>0pt % compensate for error
- \vbox to \MPheight
- {\forgetall\vss\hbox to \MPwidth{\hss\getMPPDFobject\hss}\vss}%
- \else
- \getMPPDFobject
- \fi
- \global\let\currentPDFresources\empty
- \else
- \box#1%
- \fi}
-
-\def\setMPPDFobject#1#2% resources boxnumber
- {\ifx\pdfxform\undefined
- \def\getMPPDFobject{\box#2}%
- \else\ifx\pdftexversion\undefined
- \def\getMPPDFobject{\box#2}%
- \else\ifnum\pdftexversion<14
- \def\getMPPDFobject{\box#2}%
- \else
- \ifx\everyPDFxform\undefined\else\the\everyPDFxform\fi
- \immediate\pdfxform resources{#1}#2%
- \edef\getMPPDFobject{\noexpand\pdfrefxform\the\pdflastxform}%
- \fi\fi\fi}
-
-\let\getMPPDFobject\relax
-
-%D \macros
-%D {deleteMPgraphic,
-%D startMPresources,
-%D stopMPresources}
-%D
-%D Here are a few hooks for \CONTEXT\ specific things.
-
-\ifx\deleteMPgraphic\undefined
- \def\deleteMPgraphic#1{}
-\fi
-
-\ifx\startMPresources\undefined
- \let\startMPresources\relax
- \let\stopMPresources\relax
-\fi
-
-%D \macros
-%D {twodigitMPoutput}
-%D
-%D We can limit the precision to two digits after the comma
-%D by saying:
-%D
-%D \starttyping
-%D \twodigitMPoutput
-%D \stoptyping
-%D
-%D This option only works in \CONTEXT\ combined with \ETEX.
-
-\def\twodigitMPoutput
- {\let\!MP \twodigitrounding
- \def\!MPgMPs##1{\twodigitrounding{\gMPs##1}}%
- \def\!MPgMPa##1{\twodigitrounding{\gMPa##1}}}
-
-\let\!MP \empty
-\let\!MPgMPa\gMPa
-\let\!MPgMPs\gMPs
-
-%D This kind of conversion is possible because \METAPOST\
-%D does all the calculations. Converting other \POSTSCRIPT\
-%D files would drive both me and \TEX\ crazy.
-
-\protect \endinput