summaryrefslogtreecommitdiff
path: root/Master/texmf-dist/doc/pdftex/manual/samplepdf/supp-pdf.tex
diff options
context:
space:
mode:
Diffstat (limited to 'Master/texmf-dist/doc/pdftex/manual/samplepdf/supp-pdf.tex')
-rw-r--r--Master/texmf-dist/doc/pdftex/manual/samplepdf/supp-pdf.tex2191
1 files changed, 2191 insertions, 0 deletions
diff --git a/Master/texmf-dist/doc/pdftex/manual/samplepdf/supp-pdf.tex b/Master/texmf-dist/doc/pdftex/manual/samplepdf/supp-pdf.tex
new file mode 100644
index 00000000000..184cfb81582
--- /dev/null
+++ b/Master/texmf-dist/doc/pdftex/manual/samplepdf/supp-pdf.tex
@@ -0,0 +1,2191 @@
+%D \module
+%D [ file=supp-pdf,
+%D version=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.
+
+%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.)
+
+% Beware, we cannot use \zeropoint here since it may be
+% defined in the range \dimen 0 - 20 which we happen to use
+% as scratch registers; inside context we may consider
+% using dedicated registers.
+
+% fails: ( ) vect10 9.96265 fshow % \040\040\040\040
+%
+% some optimizations are possible, but we need to be generic
+
+%D First we take care of non||\CONTEXT\ use (newlines needed,
+%D expandafter not -).
+
+\ifx \undefined \writestatus \input supp-mis.tex \relax \fi
+
+\ifx \undefined \convertMPtoPDF \else \expandafter \endinput \fi
+
+\ifx \undefined \StartLatexHack \else \StartLatexHack \fi
+
+%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.
+
+\writestatus{loading}{Context Support Macros / PDF (2004.03.26)}
+
+\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 \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 % no \m!systems for the sake of latex
+% \writestatus{systems}{Why not use pdf(e)TeX binaries?}
+% \protect
+% \expandafter\endinput
+% \fi
+
+\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 \macros
+%D {convertPDFtoPDF}
+%D
+%D \PDFTEX\ supports verbatim inclusion of \PDF\ code. The
+%D following macro takes care of inserting externally defined
+%D illustrations in \PDF\ format. According to a suggestion
+%D Tanmoy Bhattacharya posted to the \PDFTEX\ mailing list, we
+%D first skip lines until \type{stream} is reached and then
+%D copy lines until \type{endstream} is encountered. This
+%D scheme only works with vectorized graphics in which no
+%D indirect references to objects are used. Bitmaps also don't
+%D work. Interpreting their specifications is beyond the
+%D current implementation.
+%D
+%D \starttyping
+%D \convertPDFtoPDF
+%D {filename}
+%D {x scale} {y scale}
+%D {x offset } {y offset}
+%D {width} {height}
+%D \stoptyping
+%D
+%D When the scales are set to~1, the last last four values
+%D are the same as the bounding box, e.g.
+%D
+%D \starttyping
+%D \convertPDFtoPDF{mp-pra-1.pdf} {1} {1}{-1bp}{-1bp}{398bp}{398bp}
+%D \convertPDFtoPDF{mp-pra-1.pdf}{.5}{.5} {0bp} {0bp}{199bp}{199bp}
+%D \stoptyping
+%D
+%D Keep in mind, that this kind of copying only works for
+%D pure and valid pdf code (without fonts).
+
+%D The scanning and copying is straightforward and quite fast.
+%D To speed up things we use two constants.
+
+\def\@@PDFstream@@ {stream}
+\def\@@PDFendstream@@ {endstream}
+
+%D \macros
+%D {PDFmediaboxprefered}
+%D
+%D If needed, the macros can scan for the mediabox that
+%D specifies the dimensions and offsets of the graphic. When
+%D we say:
+%D
+%D \starttyping
+%D \PDFmediaboxpreferedtrue
+%D \stoptyping
+%D
+%D the mediabox present in the file superseded the user
+%D specified, already scaled and calculated offset and
+%D dimensions. Beware: the user supplied values are not the
+%D bounding box ones!
+
+%D This code has become obsolete.
+
+% \newif\ifPDFmediaboxprefered
+
+\def\setPDFboundingbox#1#2#3#4#5#6%
+ {\dimen0=#1\dimen0=#5\dimen0
+ \ScaledPointsToBigPoints{\number\dimen0}\PDFxoffset
+ \dimen0=#3\dimen0=#5\dimen0
+ \xdef\PDFwidth{\the\dimen0}%
+ \dimen0=#2\dimen0=#6\dimen0
+ \ScaledPointsToBigPoints{\number\dimen0}\PDFyoffset
+ \dimen0=#4\dimen0=#6\dimen0
+ \xdef\PDFheight{\the\dimen0}%
+ \global\let\PDFxoffset\PDFxoffset
+ \global\let\PDFyoffset\PDFyoffset}
+
+\def\setPDFmediabox#1[#2 #3 #4 #5]#6\done
+ {\dimen2=#2bp\dimen2=-\dimen2 % \dimen2=-#2bp also works since tex handles --
+ \dimen4=#3bp\dimen4=-\dimen4 % \dimen4=-#3bp also works since tex handles --
+ \dimen6=#4bp\advance\dimen6 \dimen2
+ \dimen8=#5bp\advance\dimen8 \dimen4
+ \setPDFboundingbox{\dimen2}{\dimen4}{\dimen6}{\dimen8}\PDFxscale\PDFyscale}
+
+% \def\checkPDFmediabox#1/MediaBox#2#3\done
+% {\ifx#2\relax \else
+% \message{mediabox}%
+% \setPDFmediabox#2#3\done
+% \fi}
+
+%D We use the general macro \type{\doprocessfile} and feed this
+%D with a line handling macro that changes it's behavior when
+%D the stream operators are encountered.
+
+% \def\handlePDFline
+% {\ifx\@@PDFstream@@\fileline
+% \let\doprocessPDFline\copyPDFobject
+% \startPDFtoPDF
+% \else\ifPDFmediaboxprefered
+% \expandafter\checkPDFmediabox\fileline/MediaBox\relax\done
+% \fi\fi}
+
+% \def\copyPDFobject
+% {\ifx\@@PDFendstream@@\fileline
+% \ifPDFmediaboxprefered
+% \let\doprocessPDFline\findPDFmediabox
+% \else
+% \let\doprocessPDFline\relax
+% \fi
+% \else
+% \advance\scratchcounter 1
+% \PDFcode{\fileline}%
+% \fi}
+
+% \def\findPDFmediabox
+% {\expandafter\checkPDFmediabox\fileline/MediaBox\relax\done}
+
+%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 \starttyping
+%D \def\startPDFtoPDF%
+%D {\setbox0=\vbox\bgroup
+%D \message{[PDF to PDF \PDFfilename}%
+%D \forgetall
+%D \scratchcounter=0
+%D \let\stopPDFtoPDF=\dostopPDFtoPDF}
+%D
+%D \def\dostopPDFtoPDF%
+%D {\ifnum\scratchcounter<0 \scratchcounter=1 \fi
+%D \message{(\the\scratchcounter\space lines)]}%
+%D \egroup
+%D \wd0=\PDFwidth
+%D \vbox to \PDFheight
+%D {\forgetall
+%D \vfill
+%D \PDFcode{q}%
+%D \PDFcode{1 0 0 1 \PDFxoffset\space \PDFyoffset\space cm}%
+%D \PDFcode{\PDFxscale\space 0 0 \PDFyscale\space 0 0 cm}%
+%D \box0
+%D \PDFcode{Q}}}
+%D
+%D \def\stopPDFtoPDF%
+%D {\message{[PDF to PDF \PDFfilename\space not found]}}
+%D
+%D \def\convertPDFtoPDF#1#2#3#4#5#6#7%
+%D {\bgroup
+%D \def\PDFfilename{#1}%
+%D \def\PDFxscale {#2}%
+%D \def\PDFyscale {#3}%
+%D \setPDFboundingbox{#4}{#5}{#6}{#7}{1}{1}%
+%D \uncatcodespecials
+%D \endlinechar=-1
+%D \let\doprocessPDFline=\handlePDFline
+%D \doprocessfile\scratchread\PDFfilename\doprocessPDFline
+%D \stopPDFtoPDF
+%D \egroup}
+
+\def\convertPDFtoPDF#1#2#3#4#5#6#7%
+ {\message{[PDF to PDF use \string\PDFcode instead]}%
+ \vbox{use the direct method instead}}
+
+%D \macros
+%D {dogetPDFmediabox}
+%D
+%D The next macro can be used to find the mediabox of a \PDF\
+%D illustration.
+%D
+%D \starttyping
+%D \dogetPDFmediabox
+%D {filename}
+%D {new dimen}{new dimen}{new dimen}{new dimen}
+%D \stoptyping
+%D
+%D Beware of dimen clashes: this macro uses the 5~default
+%D scratch registers! When no file or mediabox is found, the
+%D dimensions are zeroed.
+
+\def\dogetPDFmediabox#1#2#3#4#5%
+ {\bgroup
+ \def\PDFxscale{1}%
+ \def\PDFyscale{1}%
+ \uncatcodespecials
+ \endlinechar\minusone
+ \def\checkPDFtypepage##1/Type /Page##2##3\done%
+ {\ifx##2\relax
+ \else\if##2s% accept /Page and /Pages
+ \let\doprocessPDFline\findPDFmediabox
+ \else
+ \let\doprocessPDFline\findPDFmediabox
+ \fi\fi}%
+ \def\findPDFtypepage
+ {\expandafter\checkPDFtypepage\fileline/Type /Page\relax\done}%
+ \def\checkPDFmediabox##1/MediaBox##2##3\done%
+ {\ifx##2\relax \else
+ \setPDFmediabox##2##3\done
+ \fileprocessedtrue
+ \fi}%
+ \def\findPDFmediabox
+ {\expandafter\checkPDFmediabox\fileline/MediaBox\relax\done}%
+ \let\doprocessPDFline\findPDFtypepage
+ \doprocessfile\scratchread{#1}\doprocessPDFline
+ \egroup
+ \ifx\PDFxoffset\undefined
+ #2\zeropoint
+ #3\zeropoint
+ #4\zeropoint
+ #5\zeropoint
+ \else
+ #2=\PDFxoffset\onebasepoint
+ #3=\PDFyoffset\onebasepoint
+ #4=\PDFwidth
+ #5=\PDFheight
+ \fi}
+
+%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.
+
+\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:}
+
+%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 \plusone
+ \expandafter\def
+ \csname\@@MP\the\nofMPsegments\the\nofMParguments\endcsname} % {#1}
+
+\def\letMPargument
+ {\advance\nofMParguments \plusone
+ \expandafter\let
+ \csname\@@MP\the\nofMPsegments\the\nofMParguments\endcsname}
+
+\def\setMPsequence#1 %
+ {\advance\nofMParguments \plusone
+ \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%
+ {\@EAEAEA\do\csname\@@MP0\number#1\endcsname}
+
+\def\setMPkeyword#1 %
+ {\expandafter\def\csname\@@MP\the\nofMPsegments0\endcsname{#1}%
+ \advance\nofMPsegments \plusone
+ \nofMParguments\zerocount}
+
+\def\getMPkeyword% #1%
+ {\csname\@@MP\the\nofMPsegments0\endcsname} % {\csname\@@MP#10\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
+ {\nofMParguments\zerocount}
+
+\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}
+
+\bgroup
+\catcode`\|=\@@comment
+\catcode`\%=\@@active
+\catcode`\[=\@@active
+\catcode`\]=\@@active
+\catcode`\{=\@@active
+\catcode`\}=\@@active
+\catcode`B=\@@begingroup
+\catcode`E=\@@endgroup
+\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
+\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
+ {\ignoreMPspecials
+ \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\@EAEAEA{\expandafter\expandafter\expandafter} % to be sure
+
+\def\dohandleMPsequence#1%
+ {\ifdone
+ \ifcase\lccode`#1\relax
+ \@EAEAEA\dohandleMPsequenceA
+ \else
+ \@EAEAEA\dohandleMPsequenceB
+ \fi
+ \else
+ \@EA\dohandleMPsequenceC
+ \fi#1}
+
+%\def\dohandleMPsequenceA#1 %
+% {\setMPargument{#1}%
+% \handleMPsequence}
+
+\let\dohandleMPsequenceA\setMPsequence
+
+\def\dohandleMPsequenceB#1 %
+ {\edef\somestring{#1}%
+ \ifx\somestring\PSmoveto
+ \edef\lastMPmoveX{\gMPa1}%
+ \edef\lastMPmoveY{\gMPa2}%
+ \PDFcode{\!MPgMPa1 \!MPgMPa2 m}%
+ \resetMPstack
+ \else\ifx\somestring\PSnewpath
+ \let\handleMPsequence\handleMPpath
+ \else\ifx\somestring\PSgsave
+ \PDFcode{q}%
+ \resetMPstack
+ \else\ifx\somestring\PSgrestore
+ \PDFcode{Q}%
+ \resetMPstack
+ \else\ifx\somestring\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 ...
+ \else\ifx\somestring\PSsetlinewidth
+ % already handled in dtransform
+ \resetMPstack
+ \else\ifx\somestring\PSpop
+ % already handled in dtransform
+ \resetMPstack
+ \else\ifx\somestring\PSconcat
+ \PDFcode{\gMPa1 \gMPa2 \gMPa3 \gMPa4 \gMPa5 \gMPa6 cm}%
+ \resetMPstack
+ \else\ifx\somestring\PSsetrgbcolor
+ \handleMPrgbcolor
+ \resetMPstack
+ \else\ifx\somestring\PSsetcmykcolor
+ \handleMPcmykcolor
+ \resetMPstack
+ \else\ifx\somestring\PSsetgray
+ \handleMPgraycolor
+ \resetMPstack
+ \else\ifx\somestring\PStranslate
+ \PDFcode{1 0 0 1 \gMPa1 \gMPa2 cm}%
+ \resetMPstack
+ \else\ifx\somestring\PSsetdash
+ \handleMPsetdash
+ \resetMPstack
+ \else\ifx\somestring\PSsetlinejoin
+ \PDFcode{\gMPa1 j}%
+ \resetMPstack
+ \else\ifx\somestring\PSsetmiterlimit
+ \PDFcode{\gMPa1 M}%
+ \resetMPstack
+ \else\ifx\somestring\PSfshow
+ \PDFcode{n}%
+ \handleMPfshow
+ \resetMPstack
+ \else\ifx\somestring\PSsetlinecap
+ \PDFcode{\gMPa1 J}%
+ \resetMPstack
+ \else\ifx\somestring\PSrlineto
+ \PDFcode{\!MP\lastMPmoveX\space\!MP\lastMPmoveY\space l S}%
+ \resetMPstack
+ \else\ifx\somestring\PSscale
+ \PDFcode{\gMPa1 0 0 \gMPa2 0 0 cm}%
+ \resetMPstack
+ \else\ifx\somestring\PSspecial
+ \handleMPspecialcommand
+ \resetMPstack
+ \else
+ \handleMPgraphic% {#1}%
+ \fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi
+ \handleMPsequence}
+
+\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
+ \letMPargument\somestring % {#1}%
+ \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\PSPage
+ \let\handleMPsequence\handleMPpage
+ \else\ifx\somestring\PSMetaPostSpecials
+ \let\handleMPsequence\handleMPspecialscomment
+ \else\ifx\somestring\PSMetaPostSpecial
+ \let\handleMPsequence\handleMPspecialcomment
+ \else
+ \letMPargument\somestring % {#1}%
+ \fi\fi\fi\fi\fi\fi\fi}
+
+\let\handleMPgraphic=\handleMPbegingraphic
+
+%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=#2\onepoint
+ \dimen0=-\MPxscale\dimen0
+ \dimen2=#3\onepoint
+ \dimen2=-\MPyscale\dimen2
+ \xdef\MPxoffset{\withoutpt\the\dimen0}%
+ \xdef\MPyoffset{\withoutpt\the\dimen2}%
+ \dimen0=#2\onebasepoint
+ \dimen0=-\dimen0
+ \dimen2=#3\onebasepoint
+ \dimen2=-\dimen2
+ \advance\dimen0 #4\onebasepoint
+ \dimen0=\MPxscale\dimen0
+ \xdef\MPwidth{\the\dimen0}%
+ \advance\dimen2 #5\onebasepoint
+ \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=\zeropoint\relax\ifdim\MPwidth=\zeropoint\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}
+
+\let\MPfshowcommand\empty
+
+\def\dohandleMPfshow
+ {\bgroup
+ \setbox\scratchbox\hbox
+ {\obeyMPspecials
+ \edef\size{\gMPa\nofMParguments}%
+ \ifx\size\PSnfont % round font size (to pt)
+ \advance\nofMParguments \minusone
+ \expandafter\scratchdimen\gMPa\nofMParguments\onepoint\relax
+ \ifdim\scratchdimen<\onepoint
+ \def\size{1pt}%
+ \else
+ \advance\scratchdimen .5\onepoint
+ \def\size##1.##2\relax{\def\size{##1pt}}%
+ \expandafter\size\the\scratchdimen\relax
+ \fi
+ \else
+ \edef\size{\size bp}%
+ \fi
+ \advance\nofMParguments \minusone
+ %\font\temp=\gMPa\nofMParguments\space at \size
+ \let\temp\relax % to be sure
+ \setMPfshowfont{\gMPa\nofMParguments}\size
+ \advance\nofMParguments \minusone
+ \temp
+ \MPfshowcommand
+ {\ifnum\nofMParguments=\plusone
+ \def\do(##1){##1}%
+ \dogMPa1%
+ \else
+ % we need to catch ( a ) (a a a) (\123 \123 \123) etc
+ \scratchcounter\plusone
+ \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 \plusone
+ \ifnum\scratchcounter<\nofMParguments\relax
+ \gMPa\scratchcounter\MPspacechar
+ \repeat
+ \def\do##1){\dodo{##1}}%
+ \dogMPa\scratchcounter
+ \fi
+ \unskip}}%
+ %
+ % this fails in some versions of pdftex
+ %
+ % \dimen0=\lastMPmoveY bp
+ % \advance\dimen0 by \ht0
+ % \ScaledPointsToBigPoints{\number\dimen0}\lastMPmoveY
+ % \PDFcode{n q 1 0 0 1 \lastMPmoveX\space\lastMPmoveY\space cm}%
+ % \dimen0=\ht0
+ % \advance\dimen0 by \dp0
+ % \box0
+ % \vskip-\dimen0
+ % \PDFcode{Q}%
+ % \egroup}
+ %
+ \setbox\scratchbox\hbox
+ {\hskip\lastMPmoveX\onebasepoint\raise\lastMPmoveY\onebasepoint\box\scratchbox}%
+ \ht\scratchbox\zeropoint
+ \dp\scratchbox\zeropoint
+ \wd\scratchbox\zeropoint
+ \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
+ \def\somestring{[}%
+ \scratchcounter\plusone
+ \loop
+ \ifnum\scratchcounter<\nofMParguments
+ \edef\somestring{\somestring\space\gMPa\scratchcounter}%
+ \advance\scratchcounter \plusone
+ \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\onepoint>\zeropoint
+ \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.\footnoot{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
+ \nofMPsegments\plusone
+ \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 S}%
+ \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\plusone
+% \loop
+% \flushnormalMPsegment
+% \advance\nofMPsegments \plusone
+% \ifnum\nofMPsegments<\scratchcounter
+% \repeat}
+%
+% \def\flushconcatMPpath
+% {\scratchcounter\nofMPsegments
+% \nofMPsegments\plusone
+% \loop
+% \flushconcatMPsegment
+% \advance\nofMPsegments \plusone
+% \ifnum\nofMPsegments<\scratchcounter
+% \repeat}
+%
+% an alternative is presented below: (no \def assignment)
+
+\def\doflushsomeMPpath
+ {\dodoflushsomeMPpath
+ \advance\nofMPsegments \plusone
+ \ifnum\nofMPsegments<\scratchcounter
+ \expandafter\doflushsomeMPpath
+ \fi}
+
+\def\flushsomeMPpath
+ {\scratchcounter\nofMPsegments
+ \nofMPsegments\plusone
+ \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>\zeropoint .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>\zeropoint .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 $X4, 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 $X4 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
+ {\MPscratchCnt\zerocount
+ \doMPadjustdimen}
+
+\def\doMPadjustdimen
+ {\ifdim\MPscratchDim>\onepoint
+ \divide\MPscratchDim 2
+ \advance\MPscratchCnt \plusone
+ \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 $X4 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\MPscratchDim 4
+ \or
+ \multiply\MPscratchDim 2
+ \else
+ \expandafter\doMPreadjustdimen
+ \fi}
+
+\def\doMPreadjustdimen
+ {\ifnum\MPscratchCnt > 2
+ \divide\MPscratchDim 2
+ \advance\MPscratchCnt \minusone
+ \expandafter\doMPreadjustdimen
+ \fi}
+
+\def\MPreciprocaldeterminant
+ {\MPscratchDim\withoutpt\the\dimen0 \dimen6 % s_x*s_y
+ \advance\MPscratchDim - \withoutpt\the\dimen2 \dimen4 % s_x*s_y - r_x*r_y
+ \ifdim\MPscratchDim<\zeropoint % we need a positive dimension
+ \MPscratchDim-\MPscratchDim % for \MPadjustdimen
+ \doMPreciprocal
+ \MPscratchDim-\MPscratchDim
+ \else
+ \doMPreciprocal
+ \fi}
+
+\newcount\MPnumerator \MPnumerator = 1073741824 % 2^{30}
+
+% todo: dimexpr
+
+\def\doMPreciprocal % replace \MPscratchDim with its reciprocal
+ {\ifdim\MPscratchDim=\onepoint \else
+ \MPadjustdimen
+ \scratchcounter\MPnumerator
+ \divide\scratchcounter\MPscratchDim
+ \MPscratchDim1\scratchcounter % 1 needed !
+ \MPreadjustdimen
+ \fi}
+
+%OLD \def\presetMPconcat
+%OLD {\dimen 0=\gMPs1\onepoint \doMPreducedimen 0 % r_x
+%OLD \dimen 2=\gMPs2\onepoint \doMPreducedimen 2 % s_x
+%OLD \dimen 4=\gMPs3\onepoint \doMPreducedimen 4 % s_y
+%OLD \dimen 6=\gMPs4\onepoint \doMPreducedimen 6 % r_y
+%OLD \dimen 8=\gMPs5\onepoint \doMPreducedimen 8 % t_x
+%OLD \dimen10=\gMPs6\onepoint \doMPreducedimen10 } % t_y
+%OLD
+%OLD \def\presetMPscale
+%OLD {\dimen 0=\gMPs1\onepoint \doMPreducedimen 0
+%OLD \dimen 2 \zeropoint
+%OLD \dimen 4 \zeropoint
+%OLD \dimen 6=\gMPs2\onepoint \doMPreducedimen 6
+%OLD \dimen 8 \zeropoint
+%OLD \dimen10 \zeropoint}
+
+\def\presetMPconcat
+ {\dimen 0=\gMPs1\onepoint % s_x
+ \dimen 2=\gMPs2\onepoint % r_x
+ \dimen 4=\gMPs3\onepoint % r_y
+ \dimen 6=\gMPs4\onepoint % s_y
+ \dimen 8=\gMPs5\onepoint % t_x
+ \dimen10=\gMPs6\onepoint} % t_y
+
+\def\presetMPscale
+ {\dimen 0=\gMPs1\onepoint
+ \dimen 2 \zeropoint
+ \dimen 4 \zeropoint
+ \dimen 6=\gMPs2\onepoint
+ \dimen 8 \zeropoint
+ \dimen10 \zeropoint}
+
+\def\noMPtranslate % use this one grouped
+ {\dimen 8 \zeropoint % t_x
+ \dimen10 \zeropoint} % 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\MPfactor\zerocount
+%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\MPfactor\plusone
+%OLD \fi\fi
+%OLD \fi\fi
+%OLD \fi\fi
+%OLD \fi\fi
+%OLD \ifcase\MPfactor % spurious 0 removed
+%OLD \chardef\MPfactor\plusone
+%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=\onepoint \else
+%OLD \ifdim\dimen16>\MPconcatfactor \onepoint \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_x4, $s_y$ 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 % #1\onepoint
+ \dimen14=#3pt % p_y % #3\onepoint
+ \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
+
+%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
+ \nofMPsegments\zerocount
+ \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}%
+ \nofMPsegments\zerocount
+ \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
+ \@EA\dohandleMPpathA
+ \else
+ \@EA\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
+ \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}
+
+%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
+ \ifx\pdfdecimaldigits\undefined\else \pdfdecimaldigits=5 \fi % new
+ \setbox\scratchbox\vbox\bgroup
+ \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}
+
+\def\doprocessMPtoPDFfile#1#2#3% file xscale yscale
+ {% the following line is needed for latex where onepoint is not
+ % onepoint but a number (maxdimen); some day i'll make a latex
+ % variant of this file so that i no longer have to deal with such
+ % issues; then i'll also speed up this module using a few context
+ % tricks
+ %
+ \let\onepoint\onerealpoint
+ %
+ \setMPspecials
+ \the\everyMPtoPDFconversion
+ \catcode`\^^M=\@@endofline
+ \startMPscanning
+ \let\do\empty
+ \xdef\MPxscale{#2}%
+ \xdef\MPyscale{#3}%
+ \xdef\MPxoffset{0}%
+ \xdef\MPyoffset{0}%
+ \xdef\MPyshift{\zeropoint}%
+ \donefalse
+ \let\handleMPsequence\dohandleMPsequence
+ \message{[MP to PDF]}% was: [MP to PDF #1] but there is a (#1) anyway
+ \input#1\relax}
+
+% strange rounding/clip in pdftex/viewer
+%
+% \def\finishMPgraphic
+% {\stopMPresources
+% \egroup
+% \ifx\pdftexversion\undefined\else\ifnum\pdftexversion<14 % for the moment
+% \chardef\makeMPintoPDFobject=0
+% \fi\fi
+% \ifcase\makeMPintoPDFobject\or\or\ifx\currentPDFresources\empty\else
+% \chardef\makeMPintoPDFobject=1
+% \fi\fi
+% \setbox\scratchbox=\vbox
+% {\forgetall
+% \hbox
+% {\PDFcode{q \MPxscale\space 0 0 \MPyscale\space \MPxoffset\space \MPyoffset\space cm}%
+% \lower\MPyshift\box\scratchbox % unscaled shift
+% \PDFcode{Q}}}%
+% \ht\scratchbox\MPheight
+% \wd\scratchbox\MPwidth
+% \dp\scratchbox\zeropoint
+% \ifcase\makeMPintoPDFobject
+% \box\scratchbox
+% \or
+% \immediate\pdfxform resources{\currentPDFresources}\scratchbox
+% \xdef\lastPDFMPobject{\the\pdflastxform}%
+% \pdfrefxform\lastPDFMPobject
+% \global\let\currentPDFresources\empty
+% \else
+% \box\scratchbox
+% \fi
+% \egroup}
+%
+% funny clip in viewer
+%
+% \setbox\scratchbox=\vbox
+% {\forgetall
+% \dimen0=\MPllx bp
+% \dimen2=\MPlly bp
+% \setbox\scratchbox=\hbox{\hskip-\dimen0\raise-\dimen2\box\scratchbox}%
+% \ht\scratchbox=\zeropoint
+% \dp\scratchbox=\zeropoint
+% \wd\scratchbox=\zeropoint
+% \hbox
+% {\PDFcode{q \MPxscale\space 0 0 \MPyscale\space 0 0 cm}%
+% \lower\MPshift\box\scratchbox
+% \PDFcode{Q}}}%
+
+% \let\PDFMPformoffset\zeropoint
+
+\def\PDFMPformoffset
+ {\ifx\objectoffset\undefined\zeropoint\else\objectoffset\fi}
+
+\def\finishMPgraphic
+ {\stopMPresources
+ \egroup
+ \setbox\scratchbox\vbox
+ {\forgetall
+ \hbox
+ {\PDFcode{q \MPxscale\space 0 0 \MPyscale\space \MPxoffset\space \MPyoffset\space cm}%
+ \lower\MPyshift\box\scratchbox % unscaled shift
+ \PDFcode{Q}}}%
+ \ht\scratchbox\MPheight
+ \wd\scratchbox\MPwidth
+ \dp\scratchbox\zeropoint\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\makeMPintoPDFobject\zerocount % no pdftex at all
+ %\else\ifx\pdftexversion\undefined
+ % \chardef\makeMPintoPDFobject\zerocount % no pdftex at all
+ %\else\ifnum\pdftexversion<14
+ % \chardef\makeMPintoPDFobject\zerocount % 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\makeMPintoPDFobject\plusone
+ \fi\fi
+ \ifcase\makeMPintoPDFobject
+ \box#1%
+ \or
+ \scratchdimen\PDFMPformoffset\relax
+ \ifdim\scratchdimen>\zeropoint % 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>\zeropoint % 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
+ \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.
+
+\ifx\undefined\StopLatexHack \else \StopLatexHack \fi
+
+\protect \endinput