% \iffalse
% File: mfpic.dtx
% A part of mfpic 1.06 2011/03/08
%
% -------------------------------------------------------------------
%
% Copyright 2002--2011, Daniel H. Luecking
%
% Mfpic may be distributed and/or modified under the conditions of the
% LaTeX Project Public License, either version 1.3c of this license or (at
% your option) any later version. The latest version of this license is in
%    <http://www.latex-project.org/lppl.txt>
% and version 1.3c or later is part of all distributions of LaTeX version
% 2008/12/01 or later.
%
% Mfpic has maintenance status "author-maintained". The Current Maintainer
% is Daniel H. Luecking. There are several Base Interpreters: plain TeX, LaTeX,
% plain Metafont and plain MetaPost.
%
%<*driver>
\ProvidesFile{mfpic.dtx}
%</driver>
%<sty>\ProvidesPackage{mfpic}
%<*sty>
  [2011/03/08 v1.06. Macros for drawing with Metafont/MetaPost.]%
%</sty>
%<*driver>
\documentclass{ltxdoc}

\addtolength{\textwidth}{.5878pt}

\def\mytt{\upshape\mdseries\ttfamily}
\renewcommand\marg[1]{{\mytt\{#1\}}}
\renewcommand\oarg[1]{{\mytt [#1]}}
\renewcommand\parg[1]{{\mytt (#1)}}
\renewcommand \arg[1]{{\mytt \##1}}
\renewcommand\#{\char`\#\relax}
\renewcommand{\meta}[1]{{$\langle$\rmfamily\itshape#1\/$\rangle$}}
\DeclareRobustCommand\cs[1]{{\mytt\char`\\#1}}
\def\prog#1{{\mdseries\scshape #1}}
\def\grafbase{\prog{grafbase}}
\def\Grafbase{\prog{Grafbase}}
\def\mfpic{\prog{mfpic}}
\def\Mfpic{\prog{Mfpic}}
\def\MF{\prog{meta\-font}}
\def\MP{\prog{meta\-post}}
\def\CMF{\prog{Meta\-font}}
\def\CMP{\prog{Meta\-post}}
\def\opt#1{{\sffamily\upshape#1}}
\def\mfc#1{{\mytt#1}}
\let\env\mfc
\let\file\mfc
\let\gbc \mfc
\catcode`\_=12
\renewcommand\{{\char`\{}
\renewcommand\}{\char`\}}
\renewcommand\|{${}\mathrel{|}{}$}

\makeatletter
\newcommand\bsl{{\mytt\@backslashchar}}
% Stupid lists!
\def\@listi{\leftmargin\leftmargini
  \parsep \z@ \@plus\p@ \@minus\z@
  \topsep 4\p@ \@plus\p@ \@minus2\p@
  \itemsep\parsep}
\let\@listI\@listi \@listi
\renewcommand\labelitemi{\normalfont\bfseries \textendash}
\renewcommand\labelitemii{\textasteriskcentered}
\renewcommand\labelitemiii{\textperiodcentered}
\leftmargini\parindent
% Stupid index!
\def\usage#1{\textrm{#1}}
\def\index@prologue{\section*{Index}\markboth{Index}{Index}%
  Numbers refer to the page where the corresponding entry is described.
}
\def\IndexParms{%
  \parindent \z@ \columnsep 15pt
  \parskip 0pt plus 1pt
  \rightskip 5pt plus2em \mathsurround \z@
  \parfillskip-5pt \small
  % less hanging:
  \def\@idxitem{\par\hangindent 20pt}%
  \def\subitem{\@idxitem\hspace*{15pt}}%
  \def\subsubitem{\@idxitem\hspace*{25pt}}%
  \def\indexspace{\par\vspace{10pt plus 2pt minus 3pt}}}
\makeatother

\def\pdfTeX{\textrm{pdf\kern.04em\TeX}}
\def\pdfLaTeX{\textrm{pdf\kern.06em\LaTeX}}
\def\ConTeXt{\textrm{Con\kern-.16em\TeX\kern-0.06em t}}
\def\PiCTeX{\textrm{P\kern-.13em\lower.3ex\hbox{I}C\TeX}}

\title{The \mfpic{} package\thanks{This file has version number
        \fileversion, last revised \filedate. The code described here
        was developed by several people, notably Thomas Leathrum,
        Geoffrey Tobin and Dan Luecking. Dan wrote this documentation.}}
\author{Dan Luecking}
\date{\filedate}
\DisableCrossrefs
\CodelineIndex
\AlsoImplementation

\begin{document}
  \DeleteShortVerb{\|}
  \DocInput{mfpic.dtx}
\end{document}
%</driver>
%\fi
% \CheckSum{5145}
% \CharacterTable
%  {Upper-case    \A\B\C\D\E\F\G\H\I\J\K\L\M\N\O\P\Q\R\S\T\U\V\W\X\Y\Z
%   Lower-case    \a\b\c\d\e\f\g\h\i\j\k\l\m\n\o\p\q\r\s\t\u\v\w\x\y\z
%   Digits        \0\1\2\3\4\5\6\7\8\9
%   Exclamation   \!     Double quote  \"     Hash (number) \#
%   Dollar        \$     Percent       \%     Ampersand     \&
%   Acute accent  \'     Left paren    \(     Right paren   \)
%   Asterisk      \*     Plus          \+     Comma         \,
%   Minus         \-     Point         \.     Solidus       \/
%   Colon         \:     Semicolon     \;     Less than     \<
%   Equals        \=     Greater than  \>     Question mark \?
%   Commercial at \@     Left bracket  \[     Backslash     \\
%   Right bracket \]     Circumflex    \^     Underscore    \_
%   Grave accent  \`     Left brace    \{     Vertical bar  \|
%   Right brace   \}     Tilde         \~}
%
% \GetFileInfo{mfpic.dtx}
% \maketitle
%
% \begin{abstract}
% An environment, \env{mfpic}, is defined, within which commands can be
% used for drawing pictures, especially of mathematical objects and
% functions. These commands actually write code to an external file to be
% processed through \MF{} or \MP{} (depending on package options) to
% produce the picture. The picture is then included on a second pass
% through \TeX.
%
% This file documents the source code. See \file{mfpic-doc.pdf}/\file{tex}
% for the user documentation, or \file{mfpguide.pdf}/\file{tex}) for an
% introductory guide.
% \end{abstract}
%
% \StopEventually{\PrintIndex}
% \tableofcontents
%
%
% \section{Introductory setup}\label{intro}
%
% \Mfpic{} is designed to work with plain \TeX, \LaTeX, \pdfTeX, and
% \pdfLaTeX. I consistently use it with eplain and AMS\LaTeX{}
% without problems. Users have reported succesfully using it with \AmSTeX.
% It has \emph{not} been successfully used with \ConTeXt.
%
% \subsection{Versions numbers, category codes, etc.}\label{category}
%
% Almost all the various category code settings we do were prompted by
% an \mfpic{} user who had sent a bug report and had to send along his
% modified version of \file{mfpic.tex}. It had been modified so that
% \cs{message}\,s and \cs{write}\,s would do the right thing in latex
% files where various punctuation were made active (e.g., with
% \file{french.sty}).
%
% We keep track of version numbers here. We store the version and date
% in macros and later we write this version information to the
% output file, The \cs{mfpicversion} is 100 times the numeric part of the
% version. The output file can compare this number with the corresponding
% value in \file{grafbase} and detect installations where there is a
% mismatch.
%    \begin{macrocode}
%<*tex>
\ifx\mfpfileversion\UndEfInEd\else\expandafter\endinput\fi%
{%
  \catcode\lq\.12 \catcode\lq\/12%
  \gdef\mfpfileversion{1.06}%
  \gdef\mfpfiledate{2011/02/25}%
  \gdef\mfpicversion{106}%
}%
%    \end{macrocode}
%
% A bug in older versions of some support files is triggered by the macro
% \cs{+}, which is an \cs{outer} macro in plain \TeX. Here we save the
% current definition and then give it a nonouter meaning.
%    \begin{macrocode}
\let\mfpsaveplus\+%
\let\+\tabalign%
%    \end{macrocode}
%
% We now get rid of unusually catcoded punctuation, space and EOL.
% We save all the current category codes in the macro \cs{mfp@restoreALL}
% and restore them at the end by executing this command.
% We assume that letters, numbers, `\texttt\bsl', `\texttt\{', `\texttt\}',
% `\texttt\#' and `\texttt\%' have the usual categories. However, styles
% (e.g., \prog{french}) that make punctuation active foul up \cs{write}\,s
% of MF/MP code. This can still occur in user-generated \cs{write}\,s, so
% maybe some of this code should be added in \cs{mfpic} or \cs{mfsrc}
% command, too.
%    \begin{macrocode}
{%
  \catcode61\space12\relax% 61=equal sign
  \catcode32=10\relax%      32=space
  \catcode13=5 %            13=EOL
  \catcode96=12 %           96=left quote
  \catcode`\@=11
  \gdef\MFPsavecodes{%
    \edef\mfp@restoreNLchar{\newlinechar\number\newlinechar\relax}%
    \edef\mfp@restoreELchar{\endlinechar\number\endlinechar\relax}%
    \edef\mfp@restoreSP{\catcode32=\number\catcode32\relax}%
    \edef\mfp@restoreEOL{\catcode13=\number\catcode13\relax}%
    \edef\mfp@restoreALL{\mfp@restorecode{=}\mfp@restorecode{@}%
      \mfp@restorecode{$}\mfp@restorecode{:}\mfp@restorecode{;}%
      \mfp@restorecode{.}\mfp@restorecode{,}\mfp@restorecode{!}%
      \mfp@restorecode{?}\mfp@restorecode{(}\mfp@restorecode{)}%
      \mfp@restorecode{[}\mfp@restorecode{]}\mfp@restorecode{<}%
      \mfp@restorecode{>}\mfp@restorecode{*}\mfp@restorecode{/}%
      \mfp@restorecode{+}\mfp@restorecode{-}\mfp@restorecode{"}%
      \mfp@restorecode{'}\mfp@restorecode{_}\mfp@restorecode{`}%
      \mfp@restoreEOL\mfp@restoreSP\catcode10=\number\catcode10
      \mfp@restoreNLchar\mfp@restoreELchar}}%
  \gdef\mfp@restorecode#1{\catcode`\string#1=\number\catcode`#1\relax}%
  \ifx\@makeother\UndEfInEd \gdef\@makeother#1{\catcode`#1=12\relax}\fi
  \gdef\MFPsanitize{\endlinechar13 \newlinechar10
    \catcode10=12 \catcode13=5 \catcode`\$=3 \catcode`\ =10
    \@makeother\:\@makeother\;\@makeother\.\@makeother\,%
    \@makeother\!\@makeother\?\@makeother\(\@makeother\)%
    \@makeother\[\@makeother\]\@makeother\>\@makeother\<%
    \@makeother\/\@makeother\*\@makeother\+\@makeother\-%
    \@makeother\'\@makeother\"\@makeother\_\@makeother\`%
    \@makeother\=\@makeother\@}%
}%
\MFPsavecodes\MFPsanitize
\catcode`@11
\chardef\mfp@ctrlJ 10 \chardef\mfp@ctrlM 13
%    \end{macrocode}
%
% \cs{MFPsavecodes} saves a bunch of things that must have (mostly)
% normal settings \cs{mfp@restoreALL} will be invoked at the end of the
% file to restore all the values.
%
% \cs{MFPsanitize} sets (almost) everything to normal. It can be used to
% redo these settings inside some other macro, should that ever become
% necessary. Characters 10 and 13 are \verb|^^J| and \verb|^^M|,
% control-J and control-M.
%
% \subsection{Debugging and messages}\label{debug}
%
% \DescribeMacro{\mfpicdebug}
% To turn on debugging before option processing, the user must make sure
% \cs{mfpicdebug} is defined. \cs{mfp@DBlog} writes it contents to the
% log file only if debugging is on.
% \DescribeMacro{\ifmfpicdebug}
% The switch \cs {ifmfpicdebug} is normally set to true if the user loads
% \mfpic{} with the \opt{debug} option, or sets it directly with
% \cs{mfpicdebugtrue} after loading.
%    \begin{macrocode}
\newif\ifmfpicdebug
\ifx\mfpicdebug\UndEfInEd \mfpicdebugfalse
\else \mfpicdebugtrue
\fi
\def\mfp@DBlog#1{%
  \ifmfpicdebug{\let\@msgbreak\mfp@errbrk\wlog{Mfpic debug: #1}}\fi}%
%    \end{macrocode}
%
% We need to write various kinds of messages to the screen and log file.
% \cs{mfp@msg} is only used in the definition of the others and to write a
% blank line. We always use the second, which identifies the source of the
% message, or the third, which adds the word `warning'. The fourth is for
% errors and provides for help if a user presses `\texttt h' in response
% to the message. The bit with the spaces is to get a hanging indentation
% with text properly aligned on screen. The basic \cs{mfp@msg} defines
% \cs{@nl} to place the \cs{newlinechar}, for multiline messages. We
% also define \cs{@nl} in \cs{mfp@write} for new lines in writing to a
% file. We do not define it at all at the outer level.
%    \begin{macrocode}
\def\mfp@msg#1{%
  {\newlinechar\mfp@ctrlJ\def\@nl{^^J}\immediate\write16{#1}}}%
\def\mfp@spaces{\space\space\space\space\space\space}%
\def\mfp@msgbrk{^^J\mfp@spaces\space}%
\def\mfp@errbrk{\mfp@msgbrk\mfp@spaces}%
\def\mfp@warnbrk{\mfp@errbrk\space\space}%
\def\Mfpic@msg#1{{\let\@msgbreak\mfp@msgbrk\mfp@msg{Mfpic: #1}}}%
\def\Mfpic@warn#1{%
  {\let\@msgbreak\mfp@warnbrk\mfp@msg{\@nl Mfpic warning: #1}}}%
\def\mfp@errmsg#1#2{{\newlinechar\mfp@ctrlJ\let\@msgbreak\mfp@errbrk
   \errhelp{#2}\errmessage{Mfpic error: #1}}}%
%    \end{macrocode}
%
% In \TeX{} 3.x we can identify the line being processed when a message is
% issued. We do not support \TeX{} 2.x.  The command \cs{mfp@lineno} is
% for information written into the output file.
%    \begin{macrocode}
\def\mfp@lineno{line \number\inputlineno\space in the TeX source}%
%    \end{macrocode}
%
% \subsection{Detecting the format}\label{format}
%
% To detect its environment, \mfpic{} needs to test whether certain
% commands are defined. We usually use the positive version
% \cs{mfp@ifdefined}. The \cs{@xp} in it is used to `expand away' the rest
% of a conditional. \cs{@XP} does this from two levels deep in a
% conditional. Since our check uses \cs{@firstoftwo} and
% \cs{@secondoftwo}, we cannot use it to check \emph{their} existence (but
% we could use other means).
%
% \cs{mfp@ifundefined} checks its argument to see if it is defined.
% If so, it gobbles all code up to \cs{mfp@enddef}. Otherwise that code is
% executed. This avoids reading code prematurely (category code changes).
%
% We also copy \LaTeX's \cs{@ifundefined} since we have at least five
% places where we need to supply the name without a backslash.
%    \begin{macrocode}
\let\@xp\expandafter
\def\@XP{\@xp\@xp\@xp}%
\long\def\@firstoftwo#1#2{#1}%
\long\def\@secondoftwo#1#2{#2}%
\def\mfp@ifdefined#1{%
  \ifx#1\UndEfInEd \@xp\@secondoftwo
  \else\ifx#1\relax \@XP\@secondoftwo
  \else \@XP\@firstoftwo
  \fi\fi}%
\mfp@ifdefined\@empty{}{\def\@empty{}}%
\mfp@ifdefined\@gobble{}{\def\@gobble#1{}}%
\mfp@ifdefined\@firstofone{}{\long\def\@firstofone#1{#1}}%
\mfp@ifdefined\on@line{}%
  {\def\on@line{ on input line \number\inputlineno}}%
\let\mfp@enddef\@empty
\long\def\mfp@gobbledef#1\mfp@enddef{}%
\def\mfp@ifundefined#1{\mfp@ifdefined#1\mfp@gobbledef\@empty}%
\mfp@ifundefined\@ifundefined
  \def\@ifundefined#1{%
    \@xp\ifx\csname #1\endcsname\relax \@xp\@firstoftwo
    \else \@xp\@secondoftwo
    \fi}%
\mfp@enddef
%    \end{macrocode}
%
% The following might be useful in patching things or adding to
% \cs{mfp@additions}.
%    \begin{macrocode}
\mfp@ifundefined\g@addto@macro
  \long\def\g@addto@macro#1#2{%
    \begingroup
      \toks@\@xp{#1#2}%
      \xdef#1{\the\toks@}%
    \endgroup}%
\mfp@enddef
\mfp@ifundefined\g@prependto@macro
  \long\def\g@prependto@macro#1#2{%
    \begingroup
      \toks@{#2}\toks2\@xp{#1}%
      \xdef#1{\the\toks@\the\toks2}%
    \endgroup}%
\mfp@enddef
%    \end{macrocode}
%
% We test for LaTeX. We assume plain\TeX{}, or something compatible,
% except in a few places where LaTeX{} does thing differently. \Mfpic{}
% didn't work in \ConTeXt{} the last few times I tried.
%
% Here we see if \cs{documentstyle} is defined, and then make sure
% we are not in \AmSTeX{}. We used to detect \AmSTeX{} by checking
% \cs{fmtname}. This leads to problems if some other format inputs
% \file{amstex.tex} and redefined \cs{fmtname}. Thus we will now check
% \cs{amstexloaded@}.
%    \begin{macrocode}
\newif\ifmfp@latex \mfp@latexfalse
\mfp@ifdefined\documentstyle
 {\ifx \amstexloaded@\relax \mfp@DBlog{AmS-TeX detected.}%
  \else \mfp@DBlog{LaTeX detected.}\mfp@latextrue
  \fi}%
 {\mfp@DBlog{Neither LaTeX nor AmS-TeX detected.}}%
%    \end{macrocode}
%
% We are in \LaTeXe{}, as opposed to \LaTeX2.09, if \cs{documentclass}
% is defined. The \file{mfpic.sty} now assumes \LaTeXe{}. It might still
% be possible to use \LaTeX{}2.09 with \cs{input mfpic}, but I don't
% care enough to test it.
%    \begin{macrocode}
\newif\ifmfp@latexe \mfp@latexefalse
\mfp@ifdefined\documentclass
  {\mfp@latexetrue \mfp@DBlog{LaTeX2e detected.}}%
  {\mfp@DBlog{Not LaTeX2e.}}%
%    \end{macrocode}
%
% We now test \cs{pdfoutput} to see if pdf support is needed.
%    \begin{macrocode}
\newif\ifmfp@pdf \mfp@pdffalse
\mfp@ifdefined\pdfoutput
 {\mfp@DBlog{PdfTeX detected...}%
  \ifnum\pdfoutput<1 \mfp@DBlog{...with dvi output.}%
  \else \mfp@pdftrue \mfp@DBlog{...with PDF output.}%
  \fi}%
 {\mfp@DBlog{Not pdfTeX.}}%
%    \end{macrocode}
%
% \subsection{Blank line and spacing hacks}\label{spacing}
%
% In order for commands to always read their arguments correctly,
% we need EOLs to have their normal category codes, but then a
% blank line will end a paragraph, and we would like blank lines to be
% ignored inside an \env{mfpic} environment. Therefore we turn off
% \cs{par} inside that environment, and then need(?) to turn it back on
% inside \cs{tlabel} and \cs{tcaption}. \cs{@@par} (in \LaTeX) and
% \cs{endgraf} (in plain \TeX) should equal the primitive \cs{par}.
%    \begin{macrocode}
\ifmfp@latex \else \let\@@par\endgraf \fi
\def\mfp@restorepar{\let\par\@@par}%
%    \end{macrocode}
%
% Some \mfpic{} commands end with \cs{ignorespaces}. For some others a
% better choice is the \LaTeX{} strategy of conditionally ignoring spaces.
%    \begin{macrocode}
\mfp@ifdefined\@namedef{}%
  {\def\@namedef#1{\@xp\def\csname #1\endcsname}}%
\mfp@ifdefined\@namelet{}%
  {\def\@namelet#1{\@xp\let\csname #1\endcsname}}%
\mfp@ifdefined\@nameuse{}%
  {\def\@nameuse#1{\csname #1\endcsname}}%
\mfp@ifundefined\@bsphack
  \@nameuse{newskip}\@savsk
  \@nameuse{newcount}\@savsf
  \def\@bsphack{\relax
    \ifhmode \@savsk\lastskip \@savsf\spacefactor \fi}%
  \def\@esphack{\relax
    \ifhmode \spacefactor\@savsf
    \ifdim\@savsk>\z@ \ignorespaces
    \fi\fi}%
\mfp@enddef
%    \end{macrocode}
%
% \subsection{Warning if commands are already defined}
%
% We sometimes (either by accident or by choice) redefine things defined
% in some formats. For the accidental redefinitions we want to be told,
% and since we cannot assume \LaTeX{} with its \cs{newcommand}, we define
% a simple check and print a warning when it happens.
%    \begin{macrocode}
\mfp@DBlog{Defining test for previous definitions of macros.}%
\def\mfp@testdef#1{%
  \ifx#1\UndEfInEd
  \else\ifx#1\relax
    \Mfpic@warn{\string#1 was previouly defined to be \string\relax.}%
  \else
    \Mfpic@warn{\string#1 is already defined.}%
  \fi\fi}%
%    \end{macrocode}
%
% Is the proposed definer of new definitions itself not new?  Well,
% we'd like a warning, but go ahead and define it anyway. All
% \cs{newdef} does is check whether the macro being defined is already
% defined, raise a warning (but \emph{not} an error) and define it
% anyway. We do something similar with \cs{let}.
%    \begin{macrocode}
\mfp@testdef\newdef
\def\newdef#1{\mfp@testdef#1\def#1}%
\newdef\newlet#1{\mfp@testdef#1\let#1}%
%    \end{macrocode}
%
% \subsection{Error messages and warnings}
%
% If one tries to switch on \MP{} support after the output file has been
% set up, we issue this error message.
%    \begin{macrocode}
\newdef\mfp@useMP@error{%
  \mfp@errmsg {Command \mfp@b usemetapost too late}%
   {It is too late to select the metapost option.^^J%
    It must be selected before the \opengraphsfile command.^^J%
    If you proceed, the metafont option will be assumed.}}%
%    \end{macrocode}
%
% This one is for macros that need an output file to write to, but are
% called before one has been opened.
%    \begin{macrocode}
\def\mfp@nooutput@error#1{%
  \mfp@errmsg {No output file has been opened}%
   {You have tried to used a command, #1, that requires an output^^J%
    file to be opened with the \opengraphsfile command, which^^J%
    was either not issued or was not successful.}}%
%    \end{macrocode}
%
% Some options and commands require the \opt{metapost} option be in
% effect. We define an error message for the case where it is not in
% effect. Rarely, we need a similar warning for the \opt{metafont}
% option.
%    \begin{macrocode}
\newdef\mfp@noMP@error#1{%
  \mfp@errmsg {Metafont does not support #1, use MetaPost}%
   {Metafont doesn't support #1. Perhaps you forgot to turn on^^J%
    MetaPost support by using the metapost option or issuing the^^J%
    command \usemetapost. For now, I will ignore it.}}%
\newdef\mfp@noMF@warn#1{%
  \Mfpic@warn
    {Metapost does not support \string#1, it will be ignored.}}%
%    \end{macrocode}
%
% This next is like \cs{mfp@useMP@error}, but it is not so specific.
% It is for other options that also need to be issued before
% \cs{opengraphsfile}.
%    \begin{macrocode}
\def\mfp@afteropen@error#1{%
  \mfp@errmsg{Improper use of command \string#1\on@line}%
   {You must issue the command #1 prior to \opengraphsfile.
    It will be ignored now.}}%
%    \end{macrocode}
%
% \cs{mfp@end} is defined to be an error message, but that is for
% debugging purposes. It's actual use is to mark the end when we need to
% process a list of tokens. The code should simply detect and remove it,
% and it should never be expanded, so seeing the error message indicates
% a coding error by me, or incorrect syntax by a user.
%    \begin{macrocode}
\newdef\mfp@end{%
  \mfp@errmsg {Unexpected token \string\mfp@end}%
   {If you get this message but did not misuse the command^^J%
    \mfp@end, it could mean you have unbalanced braces.}}%
%    \end{macrocode}
%
% The next two are error messages for missing or empty data files.
%    \begin{macrocode}
\newdef\mfp@nofile@error#1{%
  \mfp@errmsg{No data file: #1}%
  {The data file you tried to plot was not found.}}%
\newdef\mfp@nodata@error#1{%
  \mfp@errmsg{Empty data file: #1}%
  {The data file contained only empty lines and comments.}}%
%    \end{macrocode}
%
% This message is issued when the \cs{tlabeljustify} command (see
% section~\ref{labelsettings}) is issued with an invalid parameter.
%    \begin{macrocode}
\newdef\mfp@justify@error{%
    \mfp@errmsg{Invalid justification parameter for text label}%
     {The optional argument for an mfpic text label must be^^J%
      one of B, b, c or t, followed by^^J%
      one of l, r or c, optionally followed by an angle.}}%
%    \end{macrocode}
%
% This is the default meaning assigned to \cs{@nountil} at the
% beginning of \cs{mfploop}. Use of \cs{mfpuntil} cancels the
% warning, which is otherwise issued by \cs{mfpendloop}.
%    \begin{macrocode}
\newdef\mfp@untilwarn{%
  \Mfpic@warn{\mfp@b mfploop without \string\mfpuntil!}}%
%    \end{macrocode}
%
%
% \section{Configuring \mfpic{} behavior}\label{configuring}
%
% \subsection{Options}\label{options}
%
% \DescribeMacro{\ifmfpmpost}
% I have decided to make this a user-level macro so that a user can
% write code that behaves one way for \MP{} and another for \MF. However
% the commands to change the setting are private.
%
% Our switch to turn \MP{} support on or off needs to be global, so it
% can't be a normal \cs{newif}.
%    \begin{macrocode}
\newlet\ifmfpmpost\iffalse
\newdef\mfp@mposttrue {\global\let\ifmfpmpost\iftrue}%
\newdef\mfp@mpostfalse{\global\let\ifmfpmpost\iffalse}%
\newdef\mfp@ifmpost{%
  \ifmfpmpost\@xp\@firstoftwo\else\@xp\@secondoftwo\fi}%
%    \end{macrocode}
%
% \DescribeMacro{\usemetafont}
% We make user-level commands for switching to the appropriate drawing
% program. This is necessary for plain\TeX, but also used internally by
% \mfpic. \CMF{} is the default. This command needs to not only clear the
% boolean \cs{ifmfpmpost}, but also restore the default graphics inclusion
% commands. Actually, it doesn't \emph{need} to unless \cs{usemetapost}
% was previously issued to change the default. This would normally not
% happen unless the user wanted to close the current graph file and open a
% new one for \MF. For similar reasons, we clear the \opt{mplabels}
% option.
%
% \MP{} support requires macros for including EPS graphics. What works
% best depends on the format, so we delay the definition of
% \cs{usemetapost} until the \LaTeX{} options section.
%
% Since \cs{mfpicllx} and \cs{mfpiclly} are globally defined by graphic
% inclusion, we reset then to 0, in case \opt{metafont} and \opt{metapost}
% options are mixed in one file.
%    \begin{macrocode}
\newdef\usemetafont{\mfp@mpostfalse
  \nomplabels
  \def\preparemfpicgraphic##1{}%
  \def\setmfpicgraphic##1{\mfp@graphfont\char\mfp@count}%
  \def\getmfpicoffset##1{\gdef\mfpicllx{0}\gdef\mfpiclly{0}}}%
%    \end{macrocode}
%
% Some options need an open \file{.mf} or \file{.mp} file before they
% can do anything. This means the \cs{opengraphsfile} command must have
% been issued but not \cs{closegraphsfile}. Since those commands define and
% undefine \cs{mfp@filename}, we use that as our test.
%    \begin{macrocode}
\newdef\mfp@ifopengraphsfile{\mfp@ifdefined\mfp@filename}%
%    \end{macrocode}
%
% \DescribeMacro{\mfmode}
% For use with the \opt{metafont} option, we allow the user to set the
% \MF{} mode. Example: \verb$\mfmode{ljfour}$
%
% \DescribeMacro{\mfresolution}
% If modes are too esoteric, the user can at least set the resolution.
% This should be a pure number representing dots per inch. Example:
% \verb$\mfresolution{600}$
%    \begin{macrocode}
\newdef\mfmode#1{\edef\mfp@mode{#1}%
  \mfp@ifopengraphsfile%
  {\mfp@afteropen@error\mfmode}%
  {\mfp@ifmpost{\mfp@noMF@warn\mfmode}{}}}%
\newdef\mfresolution#1{\edef\mfp@resolution{#1}%
  \mfp@ifopengraphsfile%
  {\mfp@afteropen@error\mfresolution}%
  {\mfp@ifmpost{\mfp@noMF@warn\mfresolution}{}}}%
%    \end{macrocode}
%
% \DescribeMacro{\setmfvariable}
% A useful abbreviation for a common requirement: declaring and setting
% a \MF{} variable. I have decided to change it to a user-level macro for
% power users.
% \DescribeMacro{\setmpvariable}
% For consistency, \cs{setmpvariable} is an alternative name for it. It
% takes three arguments: the type of variable, the variable itself, and
% its value. Example:\\
% \indent \cs{setmfvariable}\marg{numeric}\marg{shadewd}\marg{.7pt}.\\
% Since the \MF{} code \mfc{save}\,s the variable, there must be no
% suffix. This is not a big problem since mostly it is for internal use.
% We document that fact for power users and advise ordinary users on the
% naming of \MF{} variables.
%
% Since \MP{} has three (or four) data types for color, we have to write
% the command `\gbc{setcolor}' to the output file instead of
% `\gbc{setvariable (color)}' so that the datatype can be determined
% before declaring the variable. (Unlike the other data types the
% \grafbase{} command \gbc{setcolor} is more complicated than
% \gbc{setvariable(color)}.) For simplicity, we do this with all data
% types. For example \cs{setmfvariable}\marg{numeric} writes
% `\gbc{setnumeric}'. This makes spaces significant in the first argument,
% so we strip them off the ends with \cs{MFP@sp@def} (defined in
% section~\ref{optional}).
%
% We have abbreviations for the most common internal uses. For example
% \SpecialUsageIndex{\setmfboolean}\cs{setmfboolean} is the equivalent of
% \cs{setmfvariable} with type \mfc{boolean}. A similar statement is true
% For \SpecialUsageIndex{\setmfnumeric}\cs{setmfnumeric},
% \SpecialUsageIndex{\setmfpair}\cs{setmfpair}, and
% \SpecialUsageIndex{\setmfcolor}\cs{setmfcolor}.
%
% \DescribeMacro{\globalsetmfvariable}
% This is like \cs{setmfvariable}, except it doesn't perform a
% \mfc{save} and so the variable is globally defined. Also,
% suffixed variables are permitted (but not numeric suffixes).
% Here, too, we have to write a different command for setting color.
% Thus, me need to test whether the first argument is `color'. Here again,
% spaces are significant.
%    \begin{macrocode}
\newdef\setmfvariable#1{%
  \MFP@sp@def\mfp@tempa{#1}\@setmfvariable\mfp@tempa}%
\newdef\@setmfvariable#1#2#3{%
  \mfp@ifopengraphsfile%
    {\mfcmd{set#1 (#2) #3}}%
    {\mfp@nooutput@error\setmfvariable}}%
\newdef\setmfboolean{\@setmfvariable{boolean}}%
\newdef\setmfnumeric{\@setmfvariable{numeric}}%
\newdef\setmfpair   {\@setmfvariable{pair}}%
\newdef\setmfcolor  {\@setmfvariable{color}}%
\newdef\globalsetmfvariable#1#2#3{%
  \MFP@sp@def\mfp@tempa{#1}%
  \mfp@ifopengraphsfile
  {\mfcmd{\ifx\mfp@tempa\mfp@C gsetcolor \else gsetvariable (#1) \fi
    (#2) #3}}%
  {\mfp@nooutput@error\globalsetmfvariable}}%
\newlet\setmpvariable\setmfvariable
\newlet\globalsetmpvariable\globalsetmfvariable
%    \end{macrocode}
%
% The command \cs{setmfvariable} arranges for the value of
% that variable to be localized to each figure if set inside one, but
% it is global otherwise. We have to be careful that \TeX{} and \MF{}
% stay in synchrony, as they have different understandings as to what is
% global and what is not. So we define a switch that will be set at the
% start of an \env{mfpic} environment to test if a command is issued
% inside one. The command \cs{mfp@local} tests this switch and makes the
% following assignment global if it fails. Then we have two shortcuts for
% the more commonly occuring cases.
%
% We also define here \texttt{true}, \texttt{false} and \texttt{color} as
% macros. These are strings we need to write to the output frequently.
%    \begin{macrocode}
\newlet\ifin@mfpicenv\iffalse
\newdef\mfp@local{\relax\ifin@mfpicenv\else\global\fi}%
\newdef\mfp@let{\mfp@local\let}%
\newdef\mfp@def{\mfp@local\def}%
\newdef\mfp@T{true}%
\newdef\mfp@F{false}%
\newdef\mfp@C{color}%
%    \end{macrocode}
%
% \DescribeMacro{\usecenteredcaptions}
% This (\opt{centeredcaptions}) is the simplest option. Other options
% follow a similar pattern: a user-level command \cs{usecenteredcaptions}
% is defined for turning it on and another,
% \DescribeMacro{\nocenteredcaptions}
% \cs{nocenteredcaptions}, is defined for turning it off. Selection of
% centered captions can be turned on or off at will throughout a document.
%    \begin{macrocode}
\newdef\usecenteredcaptions{\mfp@let\ifmfp@centcapt\iftrue}%
\newdef\nocenteredcaptions {\mfp@let\ifmfp@centcapt\iffalse}%
\nocenteredcaptions
%    \end{macrocode}
%
% \DescribeMacro{\useraggedcaptions}
% Here we define the settings for justified and ragged captions.
% Justified captions are the default. Ragged captions are normally
% raggedright, but are ragged on both sides if \opt{centeredcaptions} is
% in effect.
% \DescribeMacro{\noraggedcaptions}
% For justified captions, lines are justified on both sides, except the
% last is centered under \opt{centeredcaptions}.
%    \begin{macrocode}
\newdef\useraggedcaptions{\mfp@let\mfp@capsettings\mfp@raggedcap}%
\newdef\noraggedcaptions{\mfp@let\mfp@capsettings\mfp@justifiedcap}%
\newdef\mfp@raggedcap{%
  \ifmfp@latex
    \ifmfp@centcapt \centering \else \raggedright \fi
  \else
    \rightskip 0pt plus 1fil\relax
    \ifmfp@centcapt
      \leftskip 0pt plus 1fil
      \parfillskip 0pt plus 1fil\relax
    \fi
    \def\\{\unskip\hbox{}\penalty-\@M\ignorespaces}%
  \fi}%
\def\mfp@justifiedcap{%
  \ifmfp@centcapt
    \leftskip 0pt plus 0.5fil
    \rightskip 0pt plus -0.5fil
    \parfillskip 0pt plus 1fil\relax
  \fi
  \def\\{\unskip\hbox{}\hfil\penalty-\@M\ignorespaces}}%
\noraggedcaptions
%    \end{macrocode}
%
% This common code is repeated almost verbatim four times, so we define
% the following abbreviation. The first two arguments are the commands
% to turn the option on and off. The third and fourth are the \MF{} and
% \TeX{} booleans to switch. In all cases, the default for the option is
% \emph{off}, so we issue the second command after it is defined.
%
% Since the output file has not been opened while \mfpic{} is loading, the
% \MF{} boolean is not set, but the \cs{opengraphsfile} code will check
% the \TeX{} boolean and write the appropriate \MF{} code.
%    \begin{macrocode}
\newdef\mfp@makeoption#1#2#3#4{%
  \newdef#1{\mfp@let#4\iftrue
    \mfp@ifopengraphsfile{\setmfboolean{#3}\mfp@T}{}}%
  \newdef#2{\mfp@let#4\iffalse
    \mfp@ifopengraphsfile{\setmfboolean{#3}\mfp@F}{}}%
  #2}%
%    \end{macrocode}
%
% \DescribeMacro{\clipmfpic}
% The \opt{clip} option shows only what's inside the rectangle given in
% the \cs{mfpic} command. It can be turned on or off for each figure
% independently.
% \DescribeMacro{\noclipmfpic}
% The default is the old behavior: no clipping.
%    \begin{macrocode}
\mfp@makeoption\clipmfpic\noclipmfpic{clipall}\ifmfp@clip
%    \end{macrocode}
%
% \DescribeMacro{\usetruebbox}
% The \opt{truebbox} option lets \MP{} set the true bounding box (which
% may differ from the numbers defined through \cs{mfpic}).
% \DescribeMacro{\notruebbox}
% The default is the old behavior, \cs{notruebbox}.
%
% We don't need to be too careful with the scope of these option
% commands. As currently written, \TeX{} never needs to know the setting
% except to pass the information on to \cs{opengraphsfile} if the option
% is set before then. However, we treat it like most other settings,
% turning on or off an appropriate \TeX{} boolean, in case it ever becomes
% necessary to know the setting. It is local to any \env{mfpic}, global
% otherwise. The default is to have \opt{truebbox} turned off.
%    \begin{macrocode}
\mfp@makeoption\usetruebbox\notruebbox{truebbox}\ifmfp@truebbox
%    \end{macrocode}
%
% \DescribeMacro{\usemplabels}
% An option to let \MP{} create labels, \opt{mplabels} mostly just
% switches between two versions of \cs{tlabel} so no \MP{} booleans
% are set and so synchronization of scope is not an issue.
% \DescribeMacro{\nomplabels}
% The default is the old behavior: labels are placed by \TeX. The actual
% setting is delayed until \cs{opengraphsfile} so the order of these
% commands and \cs{usemetapost} is not significant (before
% \cs{opengraphsfile}).
%
% Because of the frequent need to check this setting, we define
% \cs{@ifmplabels} to execute one of two alternatives based on it.
% When writing \TeX{} code to the file we need to make sure \texttt\#
% is not doubled. We do this by issuing \cs{mp@mksharpother} before
% reading the argument that will be written.
%    \begin{macrocode}
\newdef\usemplabels{\mfp@let\ifmfp@mplabels\iftrue
  \mfp@ifopengraphsfile
    {\mfp@ifmpost{}%
     {\mfp@noMP@error{mplabels}\global\let\ifmfp@mplabels\iffalse}}{}}%
\newdef\nomplabels{\mfp@let\ifmfp@mplabels\iffalse}%
\newdef\@ifmplabels{%
  \ifmfp@mplabels\@xp\@firstoftwo\else\@xp\@secondoftwo\fi}%
\nomplabels
\newdef\mp@mksharpother{\@ifmplabels{\@makeother\#}{}}%
%    \end{macrocode}
%
% \DescribeMacro{\overlaylabels}
% The option \opt{overlaylabels} instructs \MP{} to defer adding labels
% until the end of the picture. That means they don't get clipped or
% covered up by any drawing elements.
% \DescribeMacro{\nooverlaylabels}
% The default is the old behavior, \cs{nooverlaylabels}. Neither of these
% commands affect \MF, but they write to the output file anyway if issued
% after \cs{opengraphsfile}.
%    \begin{macrocode}
\mfp@makeoption%
  \overlaylabels\nooverlaylabels{overlaylabels}\ifmfp@overlabels
%    \end{macrocode}
%
% \DescribeMacro{\clearsymbols}
% The option \opt{clearsymbols} causes the symbols drawn by
% \cs{plotsymbol} and \cs{plotnodes} to have their interiors erased before
% being drawn.
% \DescribeMacro{\noclearsymbols}
% The default is the old behavior: \cs{noclearsymbols}.
%    \begin{macrocode}
\mfp@makeoption%
  \clearsymbols\noclearsymbols{clearsymbols}\ifmfp@clearsym
%    \end{macrocode}
%
% \DescribeMacro{\stopshipping}
% This is to turn off character shipping for duration of innermost
% enclosing \MF{} group (eg, \env{mfpic} environment).  As far as I know
% it has never been tested with \MP. (It hasn't been tested recently even
% in \MF.) The \MF{} code prevents the figure from being added to the font,
% the \TeX{} switch \cs{ifmfp@noship} is checked before \cs{endmfpic}
% attempts to add the (nonexistent) figure to the document.
% \DescribeMacro{\resumeshipping}
% The macro \cs{resumeshipping} restores character shipping.
%
% \DescribeMacro{\noship}
% The macro \cs{noship} is the older name for \cs{stopshipping}. Its name
% indicated that it was intended for use in one picture. This is not
% actually an option (that is, there is no corresponding
% \cs{DeclareOption} in \LaTeX), but it is coded the same.
%    \begin{macrocode}
\mfp@makeoption\stopshipping\resumeshipping{noship}\ifmfp@noship
\newlet\noship\stopshipping
%    \end{macrocode}
%
% \DescribeMacro{\mfpreadlog}
% This sets the boolean governing the option to examine the \MF{} or
% \MP{} log file for certain information.
%    \begin{macrocode}
\newlet\ifmfp@readlog\iffalse
\newdef\mfpreadlog{%
  \mfp@ifopengraphsfile
    {\mfp@afteropen@error\mfpreadlog}{\global\let\ifmfp@readlog\iftrue}}%
%    \end{macrocode}
%
% \subsection{Graphic inclusion}\label{graphic}
%
% \DescribeMacro{\mfpicllx}
% The code to include a figure has been divided into three parts. Under
% \opt{metapost} we need to both include the figure and save the
% \DescribeMacro{\mfpiclly}
% bounding box coordinates of the lower left corner. Here we initialize
% the macros that hold these coordinates.
%    \begin{macrocode}
\newdef\mfpicllx{0}%
\newdef\mfpiclly{0}%
%    \end{macrocode}
%
% \DescribeMacro{\preparemfpicgraphic}
% Most EPS inclusion macros make the bounding box information available,
% and so after the inclusion command we just save it in the above two
% macros. However, \LaTeX's \cs{includegraphics} does not, so we have to
% issue a command before the inclusion to force it to become available.
% That command is \cs{preparemfpicgraphic}. Usually it does nothing,
% but in the \LaTeXe{} case it locally redefines one of the graphics
% packages internal macros.
%
% \DescribeMacro{\setmfpicgraphic}
% This command includes the graphic. The \mfpic{} default (for the
% \opt{metafont} option) is set by running \cs{usemetafont}.
%
% \DescribeMacro{\getmfpicoffset}
% This one saves the lower left corner in the macros \cs{mfpicllx} and
% \cs{mfpiclly}. In the case described above, that is accomplished by
% the redefined internal command, so this command does nothing.
%
% The command \cs{@setmfpicgraphic} is a wrapper around the inclusion
% code. It takes the name of the graphic file and passes it along to the
% above three commands. Those three commands can be redefined by the
% user for special circumstances. The user is then responsible to make
% sure \cs{mfpicllx} and \cs{mfpiclly} are properly set when necessary.
% Redefining one may necessitate redefining one or both of the others.
%
% The definition of these three is delayed to the option processing
% section, except under the \MF{} default: \cs{usemetafont} defines them.
%
% We actually define two alternative versions of \cs{@setmfpicgraphic}.
% The normal one is as described above, and a `nofile' alternative for
% when the graphic file somehow doesn't exist. Then we just print the
% filename.
%    \begin{macrocode}
\newdef\normal@setmfpgraphic#1{%
  \preparemfpicgraphic{#1}\setmfpicgraphic{#1}\getmfpicoffset{#1}}%
\newdef\nofile@setmfpgraphic#1{%
 {\edef\mfp@tempa{#1}%
  \vbox to 0pt{\vss
     \rlap{\kern2pt \mfpdraftfont \mfp@sanitized\mfp@tempa}\kern 2pt}}}%
\mfp@ifdefined\strip@prefix{}{\def\strip@prefix#1>{}}%
\newdef\mfp@sanitized{\@xp\strip@prefix\meaning}%
\newlet\@setmfpicgraphic\normal@setmfpgraphic
\usemetafont
%    \end{macrocode}
%
% \DescribeMacro{\setfilename}
% The user can also change \cs{setfilename} to modify the assumed
% filenames of the graphics output by \MP. The default is the output
% file's basename (\arg1) with the picture number as the extension.
%
% \DescribeMacro{\setfilenametemplate}
% The user can also tell \MP{} what kind of filename he wishes it to
% produce. one uses \verb$\_$ in the template as a placeholder for the
% \file{.mp} filename (the name used in \cs{opengraphsfile}) and \verb$\#$
% for the figure number.
%    \begin{macrocode}
\newdef\setfilename#1#2{#1.#2}%
\newdef\setfilenametemplate#1{%
  \begingroup
    \def\_{\mfp@p j}%
    \def\#{\mfp@p c}%
    \let\@nl\relax
    \xdef\mfp@settemplate{\@nl setoutputtemplate "#1";\@nl}%
    \let\number\relax
    \let\mfp@count\relax
    \let\mfp@filename\relax
    \def\_{\mfp@filename}%
    \def\#{\number\mfp@count}%
    \xdef\setfilename##1##2{#1}%
  \endgroup
}%
%    \end{macrocode}
%
% The \opt{draft}, \opt{final} and \opt{nowrite} options override
% \mfpic's attempts to automatically detect whether the pictures should
% be included. They also work under the \opt{metafont} option, but are
% less important then (even unnecessary).
%
% \DescribeMacro{\mfpicdraft}
% The \opt{draft} option (\cs{mfpicdraft} command) causes the pictures
% created by \mfpic{} to be omitted.
%
% \DescribeMacro{\mfpicnowrite}
% The \opt{nowrite} option (\cs{mfpicnowrite} command) turns off creation
% of the output \file{.mp} file. It is intended to help speed things up
% after all figures are completed, so it permits the insertion of pictures.
%
% \DescribeMacro{\mfpicfinal}
% The \opt{final} option (\cs{mfpicfinal} command) can be used to
% override a global draft option. It forces \mfpic{} to attempt to
% insert the pictures. Under the \opt{metapost} option, missing figures
% may cause serious slow-downs as a large number of directories may be
% searched.
%
% Each of these sets the user level if-command
% \SpecialUsageIndex{\ifmfpicdraft}\cs{ifmfpicdraft}, which is retained
% for backward compatibility. These settings are global since they are
% intended to be set for the whole document. The four commands
% \cs{mfp@\{draft\|final\}\{true\|false\}} are used to communicate with
% the \cs{opengraphsfile} command, in case the user-level commands occur
% before then.
%    \begin{macrocode}
\newif\ifmfpicdraft
\newlet\ifmfp@draft\iffalse
\newlet\ifmfp@final\iffalse
\newlet\ifmfp@nowrite\iffalse
\newdef\mfpicdraft{%
  \mfp@ifopengraphsfile{\global\mfpicdrafttrue}%
   {\global\let\ifmfp@draft\iftrue}}%
\newdef\mfpicfinal{%
  \mfp@ifopengraphsfile{\global\mfpicdraftfalse}%
    {\global\let\ifmfp@final\iftrue}}%
\newdef\mfpicnowrite{%
  \mfp@ifopengraphsfile{\mfp@afteropen@error\mfpicnowrite}%
    {\global\let\ifmfp@nowrite\iftrue}}%
%</tex>
%    \end{macrocode}
%
% \subsection{\LaTeX{} options and \MP{} graphics inclusion}\label{latex}
%
% Code dependent on \LaTeXe. Mostly this is the option processing
% facilities. The declaration of options is in the file
% \file{mfpic.sty}, which will input \file{mfpic.tex}.
%    \begin{macrocode}
%<*sty>
\DeclareOption{draft}{\mfpicdraft}%
\DeclareOption{final}{%
  \mfpicfinal\PassOptionsToPackage{final}{graphics}}%
\DeclareOption{nowrite}{\mfpicnowrite}%
\DeclareOption{metapost}{\mfp@mposttrue}%
\DeclareOption{metafont}{\usemetafont}%
\DeclareOption{centeredcaptions}{\usecenteredcaptions}%
\DeclareOption{justifiedcaptions}{\noraggedcaptions}%
\DeclareOption{raggedcaptions}{\useraggedcaptions}%
\DeclareOption{clip}{\clipmfpic}%
\DeclareOption{truebbox}{\usetruebbox}%
\DeclareOption{mplabels}{\usemplabels}%
\DeclareOption{overlaylabels}{\overlaylabels}%
\DeclareOption{clearsymbols}{\clearsymbols}%
\DeclareOption{debug}{\mfpicdebugtrue}%
\DeclareOption{mfpreadlog}{\mfp@readlogtrue}%
\DeclareOption*{%
  \@ifpackageloaded{graphics}%
   {\Mfpic@warn{Unrecognized option \CurrentOption.}}%
   {\Mfpic@msg{Passing option \CurrentOption\space to %
    graphics package.}%
    \PassOptionsToPackage{\CurrentOption}{graphics}}}%
\newcommand*\mfpdraftfont{\normalfont\ttfamily}%
%    \end{macrocode}
%
% Now we define one of three versions of \cs{@usemetapost}. This command
% will be issued by the user level command \cs{usemetapost}, and consists
% of the format dependent code. The one here is, of course, for \LaTeX{}
% and will be in \file{mfpic.sty}.
%
% Unlike all the other EPS inclusion macros, \cs{includegraphics} does
% not make the bounding box coordinates available: \cs{Gin@llx} and the
% others are defined, but are local to a group surrounding the internals
% of \cs{includegraphics}. We locally modify one graphics package internal
% macro to globally save the information we need. Here we save the
% original definition and define our replacement. For this, we definitely
% need to make sure the \prog{graphics} package is loaded.
%    \begin{macrocode}
\def\@usemetapost{%
  \mfp@ifdefined\includegraphics{}{\RequirePackage{graphics}}%
  \let\mfp@save@parse@bb\Gread@parse@bb
  \newdef\mfp@parse@bb##1 ##2 ##3 ##4 ##5\\{%
    \mfp@save@parse@bb##1 ##2 ##3 ##4 ##5\\%
    \xdef\mfpicllx{\Gin@llx}\xdef\mfpiclly{\Gin@lly}}%
%    \end{macrocode}
% The \prog{graphics} package makes decisions about graphic files based on
% the files' extensions. Since we don't want to force our users to rename
% all the graphics output by \MP, we add code to \cs{preparemfpicgraphic}
% to force \cs{includegraphics} to treat the current extension (some
% number) as if it were `{\tt eps}' or `{\tt mps}' according to the
% context. We also use this command to substitute the above BoundingBox
% parsing code for the \prog{graphics} package version.
%    \begin{macrocode}
  \ifmfp@pdf \gdef\mfp@Gtype{mps}%
  \else      \gdef\mfp@Gtype{eps}%
  \fi
  \gdef\preparemfpicgraphic##1{%
    \@namedef{Gin@rule@.\number\mfp@count}####1{{\mfp@Gtype}%
      {.\number\mfp@count}{####1}}%
    \let\Gread@parse@bb\mfp@parse@bb}%
  \global\let\setmfpicgraphic\includegraphics
  \gdef\getmfpicoffset##1{}}%
%    \end{macrocode}
%
% The \LaTeX{} wrapper ends by inputing \file{mfpic.tex}.
%    \begin{macrocode}
\input mfpic.tex\relax
%</sty>
%    \end{macrocode}
%
% \DescribeMacro{\usemetapost}
% The user level command \cs{usemetapost} starts with a few actions common
% to all formats, then calls \cs{@usemetapost} which is defined
% differently for different formats.
%    \begin{macrocode}
%<*tex>
\newdef\usemetapost{%
  \mfp@ifopengraphsfile{\mfp@mpostfalse\mfp@useMP@error}%
   {\mfp@mposttrue \@usemetapost}}%
%    \end{macrocode}
%
% Under \LaTeX, if \file{mfpic.cfg} exists, it will be input at this
% point. Then, we \cs{ProcessOptions}, using the star-form because it allows
% package options to take precedence over global options. Thus \mfpic's
% \opt{final} option can counteract the \mfpic-specific side effects of a
% global \opt{draft} option.
%    \begin{macrocode}
\ifmfp@latexe
  \InputIfFileExists{mfpic.cfg}{}{}%
  \ProcessOptions*\relax
%    \end{macrocode}
%
% \cs{ProcessOptions} doesn't allow \cs{RequirePackage}\marg{graphics},
% so the above and the following were not simply put inside
% \cs{DeclareOption}\marg{metapost}. The \cs{AtEndDocument} command will
% close the output file if the user forgot.
%    \begin{macrocode}
  \mfp@ifmpost{\usemetapost}{}%
  \AtEndDocument{\mfp@closegraphsfile}%
%    \end{macrocode}
%
% Now those cases outside \LaTeXe{} that we try to support.
%    \begin{macrocode}
\else
  \mfp@msg{}\Mfpic@msg{\mfpfiledate\space v\mfpfileversion.\@nl}%
%    \end{macrocode}
%
% The definition of \cs{@usemetapost} in plain \TeX{} depends on the
% setting of \cs{ifmfp@pdf}. However both cases are so similar that we
% define a helper macro \cs{mfp@useMP} that just needs to have the names
% of three commands and two files fed to it.
%    \begin{macrocode}
  \newdef\mfp@useMP#1#2#3#4#5{%
    \mfp@ifdefined#1{}{%
      \InputIfFileExists{#2}{}{%
        \InputIfFileExists{#3}{}{%
          \mfp@errmsg{Files not found: #1, #2}%
            {One of the two named files is necessary
             for mfpic, but neither was found.}}}}%
    \global\let\setmfpicgraphic\mfp@includeMPS
    \gdef\getmfpicoffset##1{\xdef\mfpicllx{#4}\xdef\mfpiclly{#5}}}%
%    \end{macrocode}
%
% Under \pdfTeX{}, the graphics inclusion command is \cs{convertMPtoPDF},
% defined in \file{supp-pdf.tex}. This command parses the file's PS
% contents to PDF code, and leaves the bounding box info in macros
% \cs{MPllx} and \cs{MPlly}.
%    \begin{macrocode}
  \ifmfp@pdf
    \newdef\mfp@includeMPS#1{\convertMPtoPDF{#1}{1}{1}}%
    \newdef\@usemetapost{%
      \mfp@useMP\convertMPtoPDF{supp-pdf.mkii}{supp-pdf.tex}%
        \MPllx\MPlly}%
%    \end{macrocode}
%
% Under plain\TeX, eplain (still need to test this after recent eplain
% changes), \AmSTeX, or \LaTeX2.09, the graphics inclusion command is
% \cs{epsfbox}, defined in \file{epsf.tex}. This command writes a
% \cs{special} for \prog{dvips} (and other DVI driver programs), and
% leaves the bounding box info in macros \cs{epsfllx} and \cs{epsflly}.
%    \begin{macrocode}
  \else
    \newdef\mfp@includeMPS#1{\epsfbox{#1}}%
    \newdef\@usemetapost{%
      \mfp@useMP\epsfbox{epsf.tex}{epsf.sty}\epsfllx\epsflly}%
  \fi
\fi
%    \end{macrocode}
%
%
% \section{Optional parameter handling}\label{optional}
%
% We borrow \LaTeX's \cs{@ifnextchar}. The first argument is the token
% being checked. It doesn't have to be a character and we sometimes use
% \cs{@ifnextchar} to check whether a certain command follows.
% The next argument is the code to run if that character is present, the
% last is code to use if the character is not present.
%    \begin{macrocode}
\mfp@DBlog{Handlers for optional parameters.}%
\mfp@ifundefined\@ifnextchar
  \long\def\@ifnextchar#1#2#3{%
    \let\reserved@d#1%
    \def\reserved@a{#2}%
    \def\reserved@b{#3}%
    \futurelet\@let@token\@ifnch}%
  \def\@ifnch{%
    \ifx\@let@token\@sptoken
      \let\reserved@c\@xifnch
    \else
      \ifx\@let@token\reserved@d
        \let\reserved@c\reserved@a
      \else
        \let\reserved@c\reserved@b
      \fi
    \fi
    \reserved@c}%
  {%
    \def\:{\global\let\@sptoken= }\: % this makes \@sptoken a space token
    \def\:{\@xifnch}\@xp\gdef\: {\futurelet\@let@token\@ifnch}%
  }%
\mfp@enddef
%    \end{macrocode}
%
% Here we borrow from \file{keyval.sty}. We need a command that strips
% spaces off ends of an argument and stores the result in a macro. In
% \file{keyval}, that is \cs{KV@@sp@def}; we copy it here with name
% changes. Defining \cs{mfp@tempa}, and then calling it with a space as
% argument, ensures there will be an actual space token where needed in
% the definition of \cs{MFP@sp@def}.
%    \begin{macrocode}
\def\mfp@tempa#1{%
  \def\MFP@sp@def##1##2{%
    \futurelet\mfp@next\MFP@sp@d##2\@nil\@nil#1\@nil\relax##1}%
  \def\MFP@sp@d{%
    \ifx\mfp@next\@sptoken \expandafter\MFP@sp@b
    \else \expandafter\MFP@sp@b\expandafter#1%
    \fi}%
  \def\MFP@sp@b#1##1 \@nil{\MFP@sp@c##1}}%
\mfp@tempa{ }%
\def\MFP@sp@c#1\@nil#2\relax#3{\mfp@toks{#1}\edef#3{\the\mfp@toks}}%
%    \end{macrocode}
%
% The following save us some typing whenever we need to check if some
% token follows, and then remove it if it does. That's what
% \cs{mfp@iftoken} does, being just a generalized form of \LaTeX{}'s
% \cs{@ifstar}. Almost all our star-form commands differ only in what
% parameter is passed to some other command. Thus \cs{mfp@ifstar} passes
% either \arg{2} or \arg{3} to command \arg{1}.
%
% The \cs{mfp@ifend} is for use in processing lists, which all end with
% the token \cs{mfp@end}. \cs{mfp@ifendorcomma} is useful for processing
% comma-separated lists. If \cs{mfp@end} follows, it is removed and \arg1
% is executed. Otherwise, if a comma follows, it is removed and \arg2 is
% executed. When neither follows, nothing is removed and \arg3 is
% executed. Normally, this last is the main command being applied to each
% element of the list.
%
% We also define \LaTeX's \cs{@ifstar} for the few cases that require it.
%    \begin{macrocode}
\def\mfp@iftoken#1#2{\@ifnextchar#1{\@firstoftwo{#2}}}%
\def\mfp@ifstar#1#2#3{\mfp@iftoken*{#1{#2}}{#1{#3}}}%
\def\mfp@ifend{\mfp@iftoken\mfp@end}%
\def\mfp@ifendorcomma#1#2#3{\mfp@ifend{#1}{\mfp@iftoken,{#2}{#3}}}%
\mfp@ifundefined\@ifstar
  \def\@ifstar#1{\@ifnextchar*{\@firstoftwo{#1}}}%
\mfp@enddef
%    \end{macrocode}
%
% I've taken to making an empty optional argument the default for a lot
% of commands. I wanted to make it possible to have the same result for
% empty brackets (i.e., \texttt{[\,]}) as for omitted brackets.
% \cs{mfp@ifempty} helps check for emptyness. It uses a simple \cs{if} so
% that \arg{1} will be expanded. I use a non-active \texttt\textasciitilde
% (so it won't expand) to test for emptiness because, even if
% a tilde should accidentally occur in a user's \arg1, it will most
% likely be the usual active version which expands to something else.
%
% The shorthand \cs{mfp@ifexist} executes some code if \arg1 is not
% empty, otherwise it does nothing. And \cs{mfp@emptysub} expands to
% \arg1 if it isn't empty, otherwise \arg2.
%
% The \cs{@ifmtarg} macro is borrowed from \file{ifmtarg.sty}.
% It is used when a space should count as empty, but expansion isn't
% needed. It would be nice to have one that counts both as empty, but
% that seems impossible (or impossibly hard).
%    \begin{macrocode}
{%
  \catcode`Q3 \catcode`\~12
  \gdef\mfp@ifempty#1{\if~#1~\@xp\@firstoftwo\else\@xp\@secondoftwo\fi}%
  \gdef\mfp@ifexist#1{\if~#1~\@xp\@gobble\else\@xp\@firstofone\fi}%
  \gdef\mfp@emptysub#1#2{\if~#1~#2\else#1\fi}%
  \long\gdef\@ifmtarg#1{\@xifmtarg#1QQ\@secondoftwo\@firstoftwo\@nil}%
  \long\gdef\@xifmtarg#1#2Q#3#4#5\@nil{#4}%
}%
%    \end{macrocode}
%
% These are the two most common methods to parse optional arguments. In
% \cs{mfp@defaultopt}, if an optional argument is present, we use
% \cs{mfp@ifemptyopt} to see if it is empty and substitute a default
% (\arg{2}) if it is. Argument \arg{1} is the command to run
% on the resulting argument after this check. It needn't be a single
% command token, but can (and often will) be a series of commands, or a
% command with additional arguments.
%
% \cs{mfp@nullopt} is a convenient abbreviation for a common case: the
% default option is empty. We could define it in terms of
% \cs{mfp@defaultopt}, but then we'd have the redundant step of checking
% for an empty optional argument, only to replace it by an empty argument.
% That might not make a significant difference, but it just feels wrong.
%
% Both commands turn the delimited argument, if present, into an ordinary
% one. This extra step permits us to avoid many bracket pairs in later
% code.
%    \begin{macrocode}
\newdef\mfp@defaultopt#1#2{%
  \@ifnextchar[{\mfp@ifemptyopt{#1}{#2}}{#1{#2}}}%
\newdef\mfp@ifemptyopt#1#2[#3]{\mfp@ifempty{#3}{#1{#2}}{#1{#3}}}%
\newdef\mfp@nullopt#1{\@ifnextchar[{\mfp@getopt{#1}}{#1{}}}%
\newdef\mfp@getopt#1[#2]{#1{#2}}%
%    \end{macrocode}
%
% Why do we bother to check for an empty optional argument? Because
% quite a few \mfpic{} commands stuff several parameters into a
% single optional argument. All but the last are processed as undelimited
% arguments and the last one as delimited by the right bracket. If only
% the last parameter is missing, TeX{} takes that as an empty argument and
% we can proceed gracefully (substituting a default). However, if more
% than that are missing, \TeX{} takes the closing bracket as the
% \emph{undelimited} argument and produces pretty inscrutable error
% mesages. This decision to add extra information in one optional argument
% was, in retrospect, a bad one. It was made for backward compatibility
% and (originally) to minimize the changes in existing commands.
% Unfortunately we are stuck with it for at least the near future.
%
% Another reason is that multiple optional arguments generally mean that
% the to specify a later one, all the previous ones need to be specified.
% But with the above code, the user can always use an empty bracket pair
% to indicate the default, minimizing the extra typing.
%
%
% \section{Writing to the \file{.mf} or \file{.mp} file}\label{writing}
%
% \subsection{Preserving linebreaks}\label{linebreaks}
%
% Some macros (the ones we call list macros) can take quite long
% arguments, especially if they are automatically generated by some
% program. While the output file need not ever be looked at, there can be
% a problem with lines too long for the \MF{} executable's line buffer.
% Plus, for debugging, we might want to examine the file \mfpic{} writes.
% We therefore try to get at least the list macros to preserve linebreaks
% on output.
%
% We make use of the \TeX{} property that expandable commands are expanded
% inside \cs{write} commands, but unexpandable commands and characters are
% written verbatim (almost). If this were the only consideration, nothing
% would need to be done. But characters with catagory code 5 (end-of-line)
% are converted to spaces upon reading, so we have to change the category
% of the \cs{endlinechar}, or we have change the \cs{endlinechar} to a
% character of a different category. We do the former, because the line a
% macro starts on will already have the end-of-line character added, but
% it will not yet have been tokenized, so its category can be changed. We
% need a category that \TeX{} will not \emph{ignore}, but that
% nevertheless has no (or minimal) side effects if encountered in a \TeX{}
% file. We therefore make it active, but \cs{let} it equal to \cs{relax}.
% This makes the end-line-character unexpandable since \cs{relax} is not
% expandable.
%    \begin{macrocode}
\mfp@DBlog{Direct output to Metafont/Post file.}%
{%
  \catcode\mfp@ctrlM\active%
  \gdef\@activectrlM{^^M}%
  \gdef\mfp@obeylines{\catcode\mfp@ctrlM\active\let^^M\relax}%
}%
%    \end{macrocode}
%
% The choice \cs{relax} seems to be actually a slightly better choice
% than \cs{endgraf} (which we used to use, and which equals the
% unexpandable primative \cs{par}) because \cs{relax} is permitted before
% the opening brace in the syntax of \meta{general text} (for token
% variable assignments, \cs{write}, \cs{message}, and the like).
%
% The character assigned to \cs{endlinechar} is added to the end of all
% lines read in by \TeX. The character assigned to \cs{newlinechar}
% will produce a newline when it occurs in a \cs{write}. Our
% \cs{mfp@keeplines} ensures these are the same and makes the above
% changes in category. This will fail in the following case:
% \cs{endlinechar} is not \verb$^^M$ and the data starts on the same line
% as the command that issued \cs{mfp@keeplines}. But then the output will
% lack only that first linebreak.
%    \begin{macrocode}
\newdef\mfp@keeplines{\newlinechar\mfp@ctrlM
  \endlinechar\newlinechar \mfp@obeylines}%
%    \end{macrocode}
%
% We want our file writes to issue \cs{mfp@keeplines} before the text is
% read (and category codes assigned). Also we often want to add a few
% items to the argument (figure macros append a semi-colon, list macros
% surround with parentheses), so we isolate the common starting code in
% \cs{mfp@write}, and then invoke the appropriate continuation command.
%
% \DescribeMacro{\mfsrc}
% The macro \cs{mfsrc} is the most basic, merely writing its contents. For
% figure macros, we ultimately call
% \DescribeMacro{\mfcmd}
% \cs{mfcmd}, which appends a semicolon, terminating any pending \MF{}
% command. For macros which take a comma separated list of values as their
% arguments, we call
% \DescribeMacro{\mflist}
% \cs{mflist} which surrounds the list in parentheses and appends a
% semicolon
%
% The ending code is in \cs{mfp@src}. The \cs{begingroup} in
% \cs{mfp@write} matches the \cs{endgroup} in \cs{mfp@src}. The group
% isolates the changes to EOLs. We also define \cs{@nl} to expand to an
% active control-M so that it can be used for line breaks in cases where
% it is inconvenient to make EOLs active (in the replacement text of
% \cs{opengraphsfile} and \cs{@mfpic}, for example).
%    \begin{macrocode}
\newdef\mfsrc {\mfp@write\mfp@src\mfsrc}%
\newdef\mfcmd {\mfp@write\mfp@cmd}%
\newdef\mflist{\mfp@write\mfp@wlist}%
\newdef\mfp@write{\begingroup\mfp@keeplines \let\@nl\@activectrlM}%
%    \end{macrocode}
%
% The macro \cs{mfp@src} does the job of writing to files. The output
% stream \cs{mfp@out} is declared later. The other two commands invoke
% \cs{mfp@src} on a slightly modified argument. The first argument to
% \cs{mfp@src} is the command that called it (for the error message), the
% second is the code to write.
%    \begin{macrocode}
\newdef\mfp@src#1#2{%
  \mfp@ifopengraphsfile{\immediate\write\mfp@out{#2}}%
    {\mfp@nooutput@error{#1}}\endgroup}%
\newdef\mfp@cmd#1{\mfp@src\mfcmd{#1;}}%
\newdef\mfp@wlist#1{\mfp@src\mflist{(#1);}}%
%    \end{macrocode}
%
% If \prog{babel} is loaded with some options, certain punctuation will
% be made active. These will then be expanded when written to the graph
% file. \prog{Babel} provides a way to turn this off, but it would be an
% error to run those commands if \prog{babel} is not loaded. Rather than
% try to detect \prog{babel}, we run these commands only if they are
% defined.
%    \begin{macrocode}
\def\mfp@safe@activestrue{%
  \mfp@ifdefined\@safe@activestrue\@safe@activestrue{}}%
\def\mfp@safe@activesfalse{%
  \mfp@ifdefined\@safe@activesfalse\@safe@activesfalse{}}%
%    \end{macrocode}
%
% \subsection{Initializing the output file}\label{output}
%
% Category 12 characters percent, sharp and backslash signs for the
% \file{.mf} file. The command \cs{mfp@d} is used to write a line of
% dashes above and below each figure to make them stand out when debugging
% the file.
%    \begin{macrocode}
\edef\mfp@p{\@xp\@gobble\string\%}%   percent (%)
\edef\mfp@s{\@xp\@gobble\string\#}%   sharp (#)
\edef\mfp@b{\@xp\@gobble\string\\}%   backslash (\)
\newdef\mfp@d{--------------}%
%    \end{macrocode}
%
% The current date and time stamp will be written to the \file{.mf} file.
% We calculate it here and store the result in these macros. The commands
% \cs{normalyear} and \cs{normalmonth} are part of \ConTeXt, where they
% have been equated to the primitive commands \cs{year} and \cs{month}
% (which are then redefined).
%    \begin{macrocode}
\mfp@ifdefined\two@digits{}%
  {\def\two@digits#1{\ifnum#1<10 0\fi\number#1}}%
{%
  \mfp@ifdefined\normalmonth
  {\let\month\normalmonth\let\year\normalyear}{}%
  \count@\time \divide\count@ by 60
  \xdef\mfp@now{\number\year/\two@digits\month/\two@digits\day
    \space at \two@digits\count@:}%
  \multiply\count@ by -60 \advance\count@\time
  \xdef\mfp@now{\mfp@now\two@digits\count@}%
}%
%    \end{macrocode}
%
% These registers are allocated:
% \begin{itemize}
% \item \cs{mfp@out} Write stream for the \file{.mf} or \file{.mp} file.
% \item \cs{mfp@graph} Read stream used to test existence of files and
%       for reading datafiles.
% \item \cs{mfp@count} Number for next \env{mfpic} environment.
% \item \cs{mfp@linetype} Number indexing current line style in
%       multi-curve data plots.
% \item \cs{mfp@sequence} Counter incremented with every datapoint written
%       from a file to implement the feature that a list of numeric data
%       can be plotted against its sequence position.
% \item \cs{mfp@toks} Temporary token register.
% \item \cs{mfp@verbtex} A temporary token list used by \cs{mfpverbtex}.
% \item \cs{mfp@commonverbatimtex} Tokens written at the start of every
%       output file inside a \mfc{verbatimtex} group.
% \item \cs{ifmfp@switch} Not exactly a register, but a temporary
%       switch for passing information from one macro to another.
% \end{itemize}
%    \begin{macrocode}
\mfp@DBlog{Declarations used with data and graphs files.}%
\newwrite\mfp@out
\newread\mfp@graph
\newlet\mfp@data\mfp@graph
\newcount\mfp@count
\newcount\mfp@linetype
\newcount\mfp@sequence
\newtoks\mfp@toks
\newtoks\mfp@verbtex
\newtoks\mfp@commonverbatimtex
\newif\ifmfp@switch
%    \end{macrocode}
%
% We store most of the \mfc{verbatimtex} block that \mfpic{} relies on in
% the token register \cs{mfp@commonverbatimtex}. We do that because it
% relies on a couple of catcode changes and we want to be in a situation
% where we have that under control. Each line will end with an active
% ctrl-M, which is transformed by \cs{mfsrc} into a newline.
%
% The \cs{mpxshipout} is to cover all three cases of the output of
% `\texttt{mpto -tex}'. In public versions of \MP{} prior to 0.9 there was
% no such command in that output file. In 0.9 and 0.901 that command is
% defined at the start of the file, prior to any verbatimtex, but it is
% buggy. This code overwrites it and fixes the bugs. In later versions a
% good definition is used, but it appears only just before the first
% \mfc{btex} and so will overwrite my definition. Thus all cases are
% served.
%    \begin{macrocode}
\begingroup
  \mfp@keeplines\@makeother\#%
  \@makeother\%\global\mfp@commonverbatimtex
  {\gdef\mpxshipout{\afterassignment\middlempxshipout\setbox0=\hbox}%
   \gdef\middlempxshipout{\aftergroup\finishmpxshipout}%
   \gdef\finishmpxshipout{\dimen1=\ht0 \dimen2=\dp0
     \dimen0=\dimen1 \advance\dimen0\dimen2
     \setbox0=\hbox{\hbox{\box0
       \ifnum\dimen0>0 \vrule width1sp height\dimen1 depth\dimen2
       \else \vrule width1sp height1sp depth0sp\relax
       \fi}}%
     \ht0=0pt \dp0=0pt \shipout\hbox{\box0}}%
   \def\MFPtext#1{\vbox{\def\\{\cr}\MFPcfont\everylabel
        \halign{##\hfil\cr#1\crcr}}}%
    }\endgroup%
%    \end{macrocode}
%
% We store the first several lines that will be written to the output
% file in a few internal macros, so that changing them will be easier.
%
% The first two lines of the output file are comments identifying the
% file, the \mfpic{} version, the tex source file, and the timestamp.
% These are stored in \cs{mfp@versioninfo}. We also let \grafbase{} know
% the \mfpic{} version creating the file. This could catch version
% mismatches. But since older \grafbase{} didn't test this, some
% mismatches will be missed.
%
% After that (\cs{mfp@init@outfile}) we set the \mfc{mode} and the
% \mfc{mag} if not known (both ignored by \MP), and arrange for
% \grafbase{} macros to be loaded.
%    \begin{macrocode}
\newdef\mfp@versioninfo{%
  \mfp@p\space\mfp@filename.m\mfp@ifmpost{p}{f}, %
    generated by Mfpic, v\mfpfileversion\space\mfpfiledate,\@nl
  \mfp@p\space from TeX source "\jobname" on \mfp@now\@nl
  numeric mfpicversion; mfpicversion := \mfpicversion;\@nl}%
\newdef\mfp@init@outfile{%
  if unknown mode: mode := localfont; fi\@nl
  if unknown mag: mag := \number\mag/1000; fi\@nl
  if unknown grafbase: input grafbase; fi\@nl\@nl}%
%    \end{macrocode}
% Then a comparison of the version of this file, stored in
% \cs{mfpicversion} with the version stored in the \grafbase{} variable
% \mfc{grafbaseversion}. This should catch a mismatch caused by an old
% \grafbase{} with a current \mfpic.
%    \begin{macrocode}
\newdef\mfp@versioncheck{%
  if unknown grafbaseversion: grafbaseversion := 0; fi\@nl
  if grafbaseversion <> mfpicversion :\@nl
     GBmsg "Bad mfpic installation: mfpic and grafbase %
       versions do not match.";\@nl
  fi\@nl}%
%    \end{macrocode}
%
% This opens the output file and prints a reminder to the user to run
% \MF{} or \MP{}.
%    \begin{macrocode}
\newdef\mfp@openfile{%
  \ifmfp@nowrite \else \mfp@msg{}%
    \Mfpic@msg{Initializing \mfp@filename\mfp@ext.}%
    \immediate\openout\mfp@out=\mfp@filename\mfp@ext\relax
    \Mfpic@msg{Don't forget to process \mfp@filename\mfp@ext!}%
    \Mfpic@msg{Apply \mfp@progname\space to \mfp@filename\mfp@ext%
      \mfp@ifmpost{}{, then gftopk to the resulting gf file}.}%
    \Mfpic@msg{Then reprocess this file "\jobname".\@nl}%
  \fi}%
%    \end{macrocode}
%
% A little bit of \LaTeX{} for checking file existence.
%    \begin{macrocode}
\mfp@ifundefined\IfFileExists
  \def\IfFileExists#1{\openin\mfp@graph=#1\relax
    \ifeof\mfp@graph \@xp\@secondoftwo
    \else \immediate\closein\mfp@graph \@xp\@firstoftwo
    \fi}%
  \def\InputIfFileExists#1#2{\IfFileExists{#1}{#2\input #1\relax}}%
\mfp@enddef
%    \end{macrocode}
%
% The following is the code involved in opening the output file and
% checking for the existence of already created figures.
% \cs{mfp@checkoutput} checks if the output file of \MP{} or \MF{} exists.
% The first argument is the extension of that output file (\file{tfm} for
% \MF{}, the starting value of the figure counter for \MP{}). We use the
% existence of that output as a signal that there are graphics to be
% included.
%
% Based on the file existence, we set the values of the draft switch, and
% issue a message. Any other actions needed are passed as \arg2 (it
% exists) and \arg3 (it doesn't). These are nonempty only under the
% \opt{metafont} option: we load the font only if the \file{.tfm} exists,
% otherwise we use a the \texttt{dummy} font.
%
% We do not try to load a nonexistent font because that might trigger some
% \prog{maketfm} script which could be disastrous at this point, when the
% \file{.mf} file is in an uncertain state.
%    \begin{macrocode}
\newdef\mfp@checkoutput#1#2#3{%
  \IfFileExists{\setfilename\mfp@filename{#1}}%
   {\global\mfpicdraftfalse #2}%
   {\global\mfpicdrafttrue #3\mfp@msg{}%
    \Mfpic@msg{No file \setfilename\mfp@filename{#1}.}%
   }}%
\newdef\mfp@checkMPoutput{\mfp@checkoutput{\number\mfp@count}{}{}}%
\newdef\mfp@checkMFoutput{\mfp@checkoutput{tfm}%
  {\global\font\mfp@graphfont\mfp@filename\relax}%
  {\global\let\mfp@graphfont\mfp@dummy}}%
%    \end{macrocode}
%
% For \opt{metapost} the output file needs to load some color macros, and
% write some setup for text labels (even if \cs{nomplabels}, because
% \cs{usemplabels could be turned on later}). \MF{} now can also handle
% the definitions in \file{dvipsnam.mp} but it seems a waste to load all
% those definitions just to get more names for grayscales (even given
% that \MF{} can find that file).
%    \begin{macrocode}
\newdef\mfp@MPextras{\mfp@toks\@xp{\every@tlabel}%
  \mfsrc{%
    if unknown Apricot: input dvipsnam.mp; fi\@nl
    verbatimtex\@nl
    \ifmfp@verbtex \the\mfp@verbtex\@nl \fi
    \relax\@nl
    \the\mfp@commonverbatimtex
    \def\noexpand\everylabel{\the\mfp@toks}\@nl
    etex;\@nl
    \mfp@ifdefined\mfp@settemplate\mfp@settemplate{}%
  }%
  \global\mfp@verbtexfalse \global\mfp@verbtex{}%
%    \end{macrocode}
% Finally, we process the \MP{}-specific options as they are currently
% known. The \cs{usemplabels} was delayed until now so that the order of
% it and \cs{usemetapost} before now would not matter.
%    \begin{macrocode}
  \@ifmplabels\usemplabels{}%
  \ifmfp@truebbox \usetruebbox \fi
  \ifmfp@overlabels \overlaylabels \fi}%
%    \end{macrocode}
%
% There are a couple of extras that are only needed by \MF{}, the mode
% and resolution. Unlike the `MPextras' this does not write code, but
% rather \emph{is} code to write. It will occur inside a \cs{write}
% command.
%    \begin{macrocode}
\def\mfp@MFextras{%
    \mfp@ifdefined\mfp@resolution%
    {GBresolution := \mfp@resolution;\@nl}{}%
    \mfp@ifdefined\mfp@mode{mode := \mfp@mode;\@nl}{}}%
%    \end{macrocode}
%
% All the characters likely to cause problems in a filename are rendered
% harmless with this command. We want to allow macros so backslashes,
% braces and spaces aren't touched.
%    \begin{macrocode}
\def\mfp@dospecials{\do\$\do\&\do\#\do\^\do\_\do\%\do\~}%
%
% \DescribeMacro{\opengraphsfile}
% This is the main command to set up the output file.
% The name of the output file is its only parameter, and it appends
% the extension \file{.mf} or \file{.mp} depending on the whether option
% \opt{metafont} or \opt{metapost} was chosen. We first nullify \TeX{}
% special characters, then read the graphfile name, then store an
% expanded version.
%    \begin{macrocode}
\mfp@DBlog{Macros to open and close graphs files.}%
\newdef\opengraphsfile{\@bsphack
  \begingroup
    \let\do\@makeother
    \mfp@dospecials\@opengraphsfile}%
\newdef\@opengraphsfile#1{%
    \xdef\mfp@tempa{#1}%
  \endgroup
%    \end{macrocode}
%
% With the graphfile name safely stored, we check if a previous one had
% been opened and close it if so. Then we store in \cs{mfp@filename}
% a sanitized version of the name.
%
% A command can determine if it occurs after \cs{opengraphsfile} but
% before \cs{closegraphsfile} by testing whether \cs{mfp@filename} is
% defined. We also save the name of the processing program (\MF{} or \MP)
% and the file extension (\file{.mf} of \file{.mp}) in macros for use in
% messages.
%    \begin{macrocode}
  \mfp@ifopengraphsfile%
   {\Mfpic@warn
     {\@nl An attempt has been made to open a graph file, %
      \mfp@sanitized\mfp@tempa\@msgbreak
      while another, \mfp@filename, is still open. \@msgbreak
      Closing \mfp@filename.}\mfp@closegraphsfile}%
   {}%
  \xdef\mfp@filename{\mfp@sanitized\mfp@tempa}%
  \xdef\mfp@progname{meta\mfp@ifmpost{pos}{fon}t}%
  \xdef\mfp@ext{.m\mfp@ifmpost{p}{f}}%
%    \end{macrocode}
%
% These commands test for the existence of the graphics (\file{.tfm} file
% or first EPS file) and provisionally set \cs{ifmfpicdraft} based on the
% result. Then the \file{.mf} or \file{.mp} file is opened, and the
% automatic settings of \cs{ifmfpicdraft}, etc., are overridden if the
% user has explicitly chosen the \opt{draft} or \opt{final} option. The
% \opt{nowrite} option merely disables the \cs{mfp@src} command, called
% by all the commands that write to the file.
%    \begin{macrocode}
  \mfp@ifmpost\mfp@checkMPoutput\mfp@checkMFoutput
  \mfp@openfile
  \ifmfp@draft \global\mfpicdrafttrue  \fi
  \ifmfp@final \global\mfpicdraftfalse \fi
  \ifmfp@nowrite \gdef\mfp@src##1##2{\endgroup}\fi
%    \end{macrocode}
%
% Now we set up the header and preamble of the output file, writing
% version info, initializations, version checking code and extra code
% for \MP{}, if required.
%
% Finally, we process options as they are currently known. These were
% delayed until now because they might require a write to the output file.
% Finally, we read the \prog{meta*o*t} log file, if the option to do that
% is in effect.
%    \begin{macrocode}
  \mfsrc{\mfp@versioninfo \mfp@ifmpost{}\mfp@MFextras
    \mfp@init@outfile \mfp@versioncheck}%
  \mfp@ifmpost\mfp@MPextras{}%
  \ifmfp@clip     \clipmfpic       \fi
  \ifmfp@clearsym \clearsymbols    \fi
  \ifmfp@noship   \stopshipping    \fi
  \ifmfp@readlog  \mfp@readlogfile \fi
  \@esphack}%
%    \end{macrocode}
%
% \DescribeMacro{\closegraphsfile}
% This command finishes off the output file and undefines \cs{mfp@filename}.
% We define an error message free version \cs{mfp@closegraphsfile} for
% internal use. We unconditionally undefine \cs{mfp@filename} just in
% case.
%    \begin{macrocode}
\newdef\closegraphsfile{%
  \mfp@ifopengraphsfile{}{\mfp@nooutput@error\closegraphsfile}%
  \mfp@closegraphsfile}%
\newdef\mfp@closegraphsfile{%
  \mfp@ifopengraphsfile
   {\ifmfp@nowrite \else
      \mfsrc{\@nl end.}\immediate\closeout\mfp@out
    \fi \global\let\mfp@filename\UndEfInEd}{}}%
%    \end{macrocode}
%
% \subsection{Information from \MF: reading its log file}
%
% \DescribeMacro{\assignmfvalue}\SpecialUsageIndex{\globalassignmfvalue}
% This macro was suggested by Werner Lemberg, who also supplied working
% code. I have made modifications, so I am to blame if it has bugs. It
% writes code to the \file{.mf} file that causes \MF{} to write
% information to its \file{.log} file. If the option \opt{mfpreadlog} has
% been set, that log file will be examined for that information. The
% result, for example, of
% \begin{verbatim}
%   \setmfvariable{numeric}{s}{10}
%   \assignmfvalue\foo{s+2}
% \end{verbatim}
% is that \cs{foo} will be a macro that expands to `\texttt{12}' (during
% the \TeX{} run following the \MF{} pass). Under \opt{mplabels} a label
% containing \cs{foo} will only be correct in the \file{.mp} file after
% the second \MP{} pass, and so a third \TeX{} run may be required to
% insert the correct figure. To implement localization, the code causes
% the internal command \cs{mfpic-\meta{N}-foo} to be defined to the value,
% where \meta{N} is the number of the current figure. The \cs{foo} is then
% defined to the value of that internal command. Outside any \env{mfpic}
% environment, the internal command is \cs{mfpic--foo}. If the \file{.log}
% file doesn't exist or doesn't yet contain the information, \cs{foo} is
% defined to `???'.
%
% While \cs{mfpicvalue} is merely a signal and doesn't need a
% definition, we give it a useful definition for debugging: its own name.
% It could be accidentally redefined by a user, but that will be harmless;
% the debugging is mainly for me.
%
% It is possible to put \cs{global} in front of \cs{assignmfvalue} and
% its macro will be defined globally in the \TeX{} run, but I could find
% no way to make it global in the \file{.mp} file under \opt{mplabels}.
% Thus, I've created a \cs{globalassignmfvalue}.
%    \begin{macrocode}
\edef\mfpicvalue{\string\mfpicvalue}%
\newdef\mfp@cmdname{%
  mfpic-\ifin@mfpicenv\number\mfp@count\fi-\@xp\@gobble\string}%
\newdef\assignmfvalue{\mfp@assign\@empty}%
\newdef\globalassignmfvalue{\mfp@assign\global}%
\newdef\mfp@assign#1#2#3{%
  #1\edef#2{%
    \@ifundefined{\mfp@cmdname#2}{???}{\@nameuse{\mfp@cmdname#2}}}%
  \@ifundefined{\mfp@cmdname#2}%
    {\mfp@msg{}\Mfpic@msg{No value for \string#2\ifin@mfpicenv\space
    in mfpic figure \number\mfp@count\fi.\@nl}}%
    {}%
  \mfsrc{\@ifmplabels{\@nl verbatimtex #1\def\string#2{#2} etex;\@nl}{}%
    message "\string\mfpicvalue";\@nl
    message "\mfp@cmdname#2";\@nl
    show #3;\@nl
    message "";}}%
\newlet\assignmpvalue\assignmfvalue
\newlet\globalassignmpvalue\globalassignmfvalue
%    \end{macrocode}
%
% The following code is what really makes \cs{assignmfvalue} work. It is
% similar to code in the \prog{metatex} package, adapted by Werner Lemberg
% and then modified by me. It steps through the \mfpic{} output file looking
% for this signal: a line containing only `\verb$\mfpicvalue$'. It then
% reads the next line, creates a macro name from it, and assigns to that
% macro the value it reads on the next line. This is repeated to the end
% of the file.
%    \begin{macrocode}
\newdef\strip@gtgt>> #1\mfp@end{#1}%
\newdef\mfp@readlogfile{%
  \openin\mfp@data=\mfp@filename.log\relax
  \ifeof\mfp@data \Mfpic@msg{No file \mfp@filename.log.}%
  \else
    {%
      \mfp@resetwhitespace \endlinechar -1
      \catcode`\>12
      \def\@mfpicvalue{\mfpicvalue}%
      \message{< Mfpic: Reading \mfp@filename.log}%
      \mfp@readloglines
      \message{>}%
    }%
  \fi  \closein\mfp@data}%
\newdef\mfp@readloglines{%
  \read\mfp@data to \mfp@tempa
  \ifeof\mfp@data
  \else
    \ifx\mfp@tempa\@mfpicvalue
      \read\mfp@data to \mfp@tempa
      \read\mfp@data to \mfp@tempb
      \@XP\xdef\@nameuse\mfp@tempa{\@xp\strip@gtgt\mfp@tempb\mfp@end}%
    \fi
    \@xp\mfp@readloglines
  \fi}%
%    \end{macrocode}
%
%
% \section{\Mfpic{} dimensions}\label{dimensions}
%
% A number of packages, especially figure drawing packages, allocate a
% great many dimension registers. The most familiar example is \PiCTeX{}
% which is at least partially responsible for most ``No room for a new
% \cs{dimen}'' error messages. \Mfpic{} also needs many dimension
% values, but some are set by macros that simply write the value to the
% \file{.mf} file and do not use any registers. A few are stored in
% \TeX{} registers, but most are stored using a trick with font
% dimensions.
%    \begin{macrocode}
\mfp@DBlog{Using dummy font's dimensions, to spare TeX registers.}%
%    \end{macrocode}
%
% While most fonts have relatively few font dimensions (twenty-two is a
% common number), it turns out that if one loads a font and immediately
% assigns a value to \cs{fontdimen}~$n$, Then \TeX{} acts as if the font
% has \cs{fontdimen}\,s 0 through $n$ available. They can be assigned
% dimension values just like \TeX{} dimension registers.
%
% Virtually all \TeX{} systems have a \file{dummy.tfm}, which contains
% no characters (it is used for syntax checking by some packages and
% classes). Since this trick will only work if we are the first to
% load the font (the \AmSTeX{} document style \file{amsppt.sty} loads
% the dummy font), we use another trick, which is to load it scaled to
% some unlikely value, which \TeX{} treats as a new font.
%    \begin{macrocode}
\font\mfp@dummy=dummy scaled 1042
\fontdimen100\mfp@dummy0pt
%    \end{macrocode}
%
% Some versions of \file{dummy.tfm} have values already assigned to font
% dimensions 0 through 22. It would probably not hurt to use those, but
% we'll be cautious and use only font dimensions 23 and up, making 78
% available.
%
% We use an auxiliary count register to keep track of new font dimens.
%    \begin{macrocode}
\newcount\mfp@fdc
\mfp@fdc22
%    \end{macrocode}
%
% We define a macros that mimics the behavior of \cs{newdimen}, for
% allocating font dimension numbers. It increments \cs{mfp@fdc} and
% defines its argument \arg{1} to expand to a reference to the
% \cs{fontdimen} with that number. The syntax it produces is valid as
% the left side of a dimension assignment and also as a dimension
% that may follow a real factor and \cs{the}. For example, later we say
% \cs{newfdim}\cs{pointsize} and give it the value \texttt{2pt}. Then
% \verb$\the\pointsize$ prints this value and
% \verb$\pointsize = 0.5\pointsize$ is a valid assignment.
%    \begin{macrocode}
\newdef\newfdim#1{%
  \global\advance\mfp@fdc1
  \xdef#1{\fontdimen\number\mfp@fdc\mfp@dummy}%
  \wlog{\string#1=\fontdimen\number\mfp@fdc\mfp@dummy}}%
%    \end{macrocode}
% \TeX{} will not accept font dimensions in its syntax for the dimension
% arithmetic commands \cs{advance}, \cs{multiply} and \cs{divide}. In the
% rare cases where we need to do this we assign the value to a temporary
% register and calculate with it.
%
% We allocate a couple of boxes. At the end of an \mfpic{}
% environment, \cs{@wholegraph} is loaded with the picture (possibly
% null) as it exists then. Inside the environment, when text labels are
% processed, \cs{@textbox} holds this text temporarily so it can be
% measured, moved about, etc. We also define abbreviations for the
% frequent commands that specify the dimensions of \cs{@textbox}
%    \begin{macrocode}
\mfp@DBlog{A box register for whole labeled graph, %
    and a temporary one.}%
\newbox\@wholegraph
\newbox\@textbox
\newdef\tb@ht{\ht\@textbox}%
\newdef\tb@dp{\dp\@textbox}%
\newdef\tb@wd{\wd\@textbox}%
%    \end{macrocode}
%
% When labels are processed, they are accumulated in the box
% \cs{@alltlabels}. We allocate it, and four \cs{newfdim}\,s for the
% location of three of the sides (We don't need the fourth). The box
% \cs{@backtext} holds `background text', that is, text accumulated
% between \cs{startbacktext} and \cs{stopbacktext}.
%    \begin{macrocode}
\newbox\@alltlabels
\newbox\@backtext
\newfdim\@tlabelstop
\newfdim\@tlabelsbot
\newfdim\@tlabelsleft
%    \end{macrocode}
%
% The following fontdims record the dimensions of the box containing the
% picture. We need to adjust them when the text labels are added to the
% picture, because \TeX{} doesn't do it automatically. For example,
% kerning left outside the picture will not change the picture box's
% reference point.
%    \begin{macrocode}
\mfp@DBlog{Internal dimension parameters for graph dimensions...}%
\newfdim\@graphright
\newfdim\@graphleft
\newfdim\@graphtop
\newfdim\@graphbot
\mfp@DBlog{...and dimension parameters for tlabel positioning.}%
\newfdim\tb@raise
\newfdim\tb@moveright
\newfdim\tb@totalht
%    \end{macrocode}
%
% The following are for label adjustments. The first two are used to
% implement the feature that all labels can be simultaneously shifted an
% equal amount. The third is for the feature that the label can be a
% certain distance separated from the point where it is placed. And the
% last establishes the distance between a label and a path surrounding it.
%    \begin{macrocode}
\newfdim\tlabel@hadj
\newfdim\tlabel@vadj
\newfdim\tlabel@sep
\newfdim\tlpath@sep
\tlabel@hadj0pt
\tlabel@vadj0pt
\tlabel@sep0pt
\tlpath@sep0pt
%    \end{macrocode}
%
% It can be argued that dimensions not needed by \TeX{} should be stored
% in the output file rather than allocating (font) dimensions. These are
% everything below from \cs{pointsize} through \cs{symbolspace},
% inclusive. This would make synchrony between \TeX{} and \MF{} easier
% to maintain. Those that are needed by \TeX{} are then few enough to be
% regular \cs{dimen} registers, making them automatically local to each
% \env{mfpic} environment. Unfortunately, changing to such a scheme could
% break some past \mfpic{} files. It would also require recoding every
% command that now writes one of these dimensions to the output.
%
% The following are default parameters for various graphics commands that
% take an optional argument for the size of something.
% \begin{itemize}
% \item\cs{mfpicunit}\SpecialUsageIndex{mfpicunit},  the unit of length in
%       a picture. \cs{@mfpicunit} is used internally.
% \item\cs{pointsize}\SpecialUsageIndex{pointsize},  the diameter of a
%       \cs{point}.
% \item\cs{shadespace}\SpecialUsageIndex{shadespace}, the spacing of dots
%       in \cs{shade}.
% \item\cs{polkadotspace}\SpecialUsageIndex{polkadotspace}, the spacing of
%       polkadots.
% \item\cs{hatchspace}\SpecialUsageIndex{hatchspace}, the spacing of hatch
%       lines.
% \item\cs{headlen}\SpecialUsageIndex{headlen}, the size of arrowheads
%       (except on axes).
% \item\cs{axisheadlen}\SpecialUsageIndex{axisheadlen}, the size of the
%       arrowhead for $x$- and $y$-axes.
% \item\cs{sideheadlen}\SpecialUsageIndex{sideheadlen}, the size of the
%       arrowhead for border axes.
% \item\cs{hashlen}\SpecialUsageIndex{hashlen}, the length of tic marks on
%       axes.
% \item\cs{dashlen}\SpecialUsageIndex{dashlen}, the length of dashes in
%       \cs{dashed}.
% \item\cs{dashspace}\SpecialUsageIndex{dashspace}, the space between such
%       dashes.
% \item\cs{dotsize}\SpecialUsageIndex{dotsize}, the size of dots for
%       \cs{dotted}.
% \item\cs{griddotsize}\SpecialUsageIndex{griddotsize}, the size of dots
%       for \cs{grid} and \cs{plrgridpoints}.
% \item\cs{dotspace}\SpecialUsageIndex{dotspace}, the space between such
%       dots.
% \item\cs{symbolspace}\SpecialUsageIndex{symbolspace}, the space between
%       symbols used in a \cs{plot} command.
% \end{itemize}
% We allocate them, and then initialize them.
%    \begin{macrocode}
\mfp@DBlog{User level dimension parameters, with default settings.}%
\newfdim\mfpicunit
\newfdim\@mfpicunit % internal version
\newfdim\pointsize
\newfdim\shadespace
\newfdim\polkadotspace
\newfdim\hatchspace
\newfdim\headlen
\newfdim\axisheadlen
\newfdim\sideheadlen
\newfdim\hashlen
\newfdim\dashlen
\newfdim\dashspace
\newfdim\dotsize
\newfdim\griddotsize
\newfdim\dotspace
\newfdim\symbolspace
\mfpicunit1pt
\pointsize2pt
\shadespace1pt
\polkadotspace10pt
\hatchspace3pt
\headlen3pt
\axisheadlen5pt
\sideheadlen0pt
\hashlen4pt
\dashlen4pt
\dashspace4pt
\dotsize0.5pt
\griddotsize0.5pt
\dotspace3pt
\symbolspace5pt
%    \end{macrocode}
%
% Font dimensions are global, and so not restricted to an \env{mfpic}
% environment even when assigned inside one. This would require the
% user to restore a value every time one picture needed a different
% value from the rest. To avoid requiring this, the following macro is
% used to save all values of these dimensions at the start of a picture,
% and to restore the saved values at the end. Some internal dimensions
% (all the \cs{@graph...}, \cs{@tlabels...} and \cs{tb@...}) don't need
% saving since they are reset with each picture.
%    \begin{macrocode}
\newdef\save@mfpicdimens{%
  \edef\restore@mfpicdimens{%
    \mfpicunit \the\mfpicunit
    \pointsize \the\pointsize
    \shadespace \the\shadespace
    \polkadotspace \the\polkadotspace
    \hatchspace \the\hatchspace
    \headlen \the\headlen
    \axisheadlen \the\axisheadlen
    \sideheadlen \the\sideheadlen
    \hashlen \the\hashlen
    \dashlen \the\dashlen
    \dashspace \the\dashspace
    \dotsize \the\dotsize
    \griddotsize \the\griddotsize
    \dotspace \the\dotspace
    \symbolspace \the\symbolspace
    \tlabel@hadj \the\tlabel@hadj
    \tlabel@vadj \the\tlabel@vadj
    \tlabel@sep \the\tlabel@sep
    \tlpath@sep \the\tlpath@sep}}%
%    \end{macrocode}
%
% Here are the few dimension registers we do allocate:
% \SpecialUsageIndex{\mfpframesep}\cs{mfpframesep}, and
% \SpecialUsageIndex{\mfpframethickness}\cs{mfpframethickness}
% govern frames.
% \SpecialUsageIndex{\mfpicheight}\cs{mfpicheight} and
% \SpecialUsageIndex{\mfpicwidth}\cs{mfpicwidth} are set
% after each picture to that picture's size. A \cs{vskip} of
% \SpecialUsageIndex{\mfpiccaptionskip}\cs{mfpiccaptionskip} is placed
% between figure and caption by \cs{tcaption}. We also allocate a
% frequently used scratch register
%    \begin{macrocode}
\newdimen\mfp@scratch
\newdimen\mfpframesep
\newdimen\mfpframethickness
\newdimen\mfpicheight
\newdimen\mfpicwidth
\newskip\mfpiccaptionskip
\mfpframethickness0.4pt
\mfpframesep2pt
\mfpiccaptionskip\medskipamount
%    \end{macrocode}
%
%
% \section{Helper macros}\label{helper}
%
% \DescribeMacro{\mfpicnumber}
% We make a user-level macro for setting the number of the next graph.
% The original purpose of this is so that the font file could have
% characters in the positions of printable characters. Then creating a
% composite figure is as easy as changing fonts: \marg{\cs{pic} ABABAAB}.
% The motivation came from a discussion on \texttt{comp.text.tex} started
% by someone who wanted to input a sequence of 0's and 1's and get a
% sequence of black and white squares. For \MP{} users it is not very
% important.
%    \begin{macrocode}
\def\mfpicnumber#1{\global\mfp@count#1\relax}%
%    \end{macrocode}
%
% \DescribeMacro{\mfpaddto}
% When placing text at intervals on an axis, we need to automatically
% calculate coordinates to feed to the \cs{tlabel} command. The
% following is a utility macro to add two real numbers. It is currently
% used only in the \cs{axislabels} command, so it needn't be globally
% defined, but it might be handy in the future.
% \begin{itemize}
% \item[] \arg{1} is a \emph{macro} that expands to some number.
% \item[] \arg{2} is a number to add to it.
% \end{itemize}
% The result is stored again in \arg{1}, overwriting the old value.
%
% \DescribeMacro{\mfpmultiply}
% This is the multiplicative version, with the same syntax and behavior.
% It is not used anywhere yet.
%    \begin{macrocode}
\newdef\mfpaddto#1#2{\mfp@scratch#1pt \advance\mfp@scratch#2pt
  \edef#1{\strip@pt\mfp@scratch}}%
\newdef\mfpmultiply#1#2{\mfp@scratch#1pt \mfp@scratch#2\mfp@scratch
  \edef#1{\strip@pt\mfp@scratch}}%
\mfp@ifundefined\strip@pt
  \begingroup
    \lccode`\/`\p
    \lccode`\?`\t
    \lowercase{%
  \endgroup
  \def\rem@pt#1.#2/?}{#1\ifnum#2>\z@.#2\fi}%
  \def\strip@pt{\@xp\rem@pt\the}%
\mfp@enddef
%    \end{macrocode}
%
% \DescribeMacro{\pointdef}
% A point defining macro, suggested by a user.
% \begin{itemize}
%   \item[] \arg{1} is a symbolic name for a point, only letters.
%   \item[] \arg{2} and \arg{3} are the coordinates.
%   \item[] Usage: \cs{pointdef}\marg{A}\parg{2,5} makes \cs{A} expand
%           to \texttt{(2,5)}, \cs{Ax} to \texttt{2}, and \cs{Ay} to
%           \texttt{5}.
% \end{itemize}
%    \begin{macrocode}
\newdef\pointdef#1(#2,#3){%
  \@ifundefined{#1} {}{\Mfpic@warn{\mfp@b#1  already defined.}}%
  \@ifundefined{#1x}{}{\Mfpic@warn{\mfp@b#1x already defined.}}%
  \@ifundefined{#1y}{}{\Mfpic@warn{\mfp@b#1y already defined.}}%
  \@namedef{#1}{(#2,#3)}\@namedef{#1x}{#2}\@namedef{#1y}{#3}}%
%    \end{macrocode}
%
% \DescribeMacro{\setmfarray}
% This enables the simultaneous definition of \MF{} (or \MP) variables
% such as \mfc{A1}, \mfc{A2}, etc., by writing
% \cs{setmfarray}\marg{\meta{type}}\marg{\meta{name}}\marg{\meta{list}},
% the \meta{name} being any \MF{} variable without a suffix, the list being
% a comma separated list of items of the appropriate \meta{type}.
% For example, \cs{setmfarray}\marg{pair} would require a list of
% pairs.
%
% \SpecialUsageIndex{\numericarray}
% As with \cs{setmfvariable}, we provide a few abbreviations.
% \cs{numericarray} is for arrays of numeric variables,
% \SpecialUsageIndex{\pairarray} \cs{pairarray} for arrays of pair
% variables and \SpecialUsageIndex{\colorarray}\cs{colorarray} is for
% arrays of color variables. Finally, to set arrays globally, there is
% \SpecialUsageIndex{\globalsetmfarray}\cs{globalsetmfarray}.
%    \begin{macrocode}
\newdef\setmfarray#1#2{\mfsrc{setarray (#1) (#2)}\mfp@writedata}%
\newlet\setmparray\setmfarray
\newdef\pairarray{\setmfarray{pair}}%
\newdef\numericarray{\setmfarray{numeric}}%
\newdef\colorarray{\setmfarray{color}}%
\newdef\rgbcolorarray{\setmfarray{rgbcolor}}%
\newdef\cmykcolorarray{\setmfarray{cmykcolor}}%
\newdef\globalsetmfarray#1#2{\mfsrc{gsetarray (#1) (#2)}\mfp@writedata}%
\newlet\globalsetmparray\globalsetmfarray
%    \end{macrocode}
%
% \DescribeMacro{\lightershade}
% Shade adjustment macros. \cs{lightershade} just multiplies
% \cs{shadespace} by $1.2$.
% \DescribeMacro{\darkershade}
% While \cs{darkershade} divides by $1.2$ (actually, multiplies by
% $1/1.2$)
%    \begin{macrocode}
\newdef\lightershade{\shadespace1.2\shadespace}%
\newdef\darkershade{\shadespace.83333\shadespace}%
%    \end{macrocode}
%
% \DescribeMacro{\dashlineset}
% The following arrange for contrastive dashed lines. \cs{dashlineset}
% just resets the default parameters that the \cs{dashed} macro uses,
% \DescribeMacro{\dotlineset}
% \cs{dotlineset} sets these parameters so that \cs{dashed} produces
% something almost dotted.
%    \begin{macrocode}
\newdef\dashlineset{\dashlen4pt \dashspace4pt }%
\newdef\dotlineset{\dashlen1pt \dashspace2pt }%
%    \end{macrocode}
%
% \DescribeMacro{\pointfilltrue}
% With the commands \cs{pointfilltrue} or \cs{pointfillfalse} the user
% can specify points drawn with the \cs{point} command to be either
% filled in or
% \DescribeMacro{\pointfillfalse}
% not.
%    \begin{macrocode}
\let\ifpointfill\iftrue
\newdef\pointfilltrue{\mfp@let\ifpointfill\iftrue}%
\newdef\pointfillfalse{\mfp@let\ifpointfill\iffalse}%
%    \end{macrocode}
%
% \CMF{} has very flexible looping capabilities. Before version 0.8 there
% was no \mfpic{} interface because it seemed that \cs{mfsrc} was the
% simplest way to access this capability. Anything else would have to
% be either a clone of \cs{mfsrc} or limit the possibilities. However, I
% now believe it might be a good thing to have a structured way to perform
% repetitive actions at the \MF{} level.
%
% As of version 0.9, \mfpic{} will allow loops outside \env{mfpic}
% environments. It seems like a reasonable thing to be allowed to do.
% Fortunately, the macro names are already unique.
%
% \DescribeMacro{\mfpfor}
% This is the simplest: it writes the word \mfc{for} plus the contents of
% its only mandatory argument, followed by a colon. The loop is ended by
% \DescribeMacro{\endmfpfor}
% \cs{endmfpfor} which merely writes the text \mfc{endfor}.
%    \begin{macrocode}
\newdef\mfpfor#1{\begingroup\mfsrc{for #1:}}%
\newdef\endmfpfor{\mfsrc{endfor}\endgroup}%
%    \end{macrocode}
%
% \DescribeMacro{\mfploop}
% The macro \cs{mfploop} starts a loop with \mfc{forever}. The user is
% expected to provide an escape condition with
% \DescribeMacro{\mfpuntil}
% \cs{mfpuntil}, which can be placed anywhere among the commands contained
% in the \env{mfploop} environment.
% \DescribeMacro{\endmfploop}
% The macro \cs{endmfploop} is a clone of \cs{endmfpfor} except for the
% warning. Grouping keeps the warning from being turned off if
% \cs{mfpuntil} occurs in a nested loop.
%    \begin{macrocode}
\newdef\mfploop{%
  \begingroup\mfsrc{forever:}\let\@nountil\mfp@untilwarn}%
\newdef\mfpuntil#1{\mfcmd{exitif #1}\let\@nountil\@empty}%
\newdef\endmfploop{\@nountil\endmfpfor}%
%    \end{macrocode}
%
% \DescribeMacro{\mfpwhile}
% This emulates a while-loop, the condition being given in the mandatory
% argument. It has the same behavior, and writes almost the same code as
% \cs{mfploop} with an immediate \cs{mfpuntil} using the negative of the
% condition.
% \DescribeMacro{\endmfpwhile}
% The closing, \cs{endmfpwhile}, is again the same as \cs{endmfpfor}.
%    \begin{macrocode}
\newdef\mfpwhile#1{\begingroup\mfcmd{forever: exitif not(#1)}}%
\newlet\endmfpwhile\endmfpfor
%    \end{macrocode}
%
% \DescribeMacro{\plr}
% A little utility to convert a list of pairs into another list of
% pairs, where the given list are assumed to be polar coordinates and the
% results are their Cartesian counterparts. This is guaranteed to work as
% expected only in macros with a list argument, or for a single pair.
% \DescribeMacro{\midpoint}
% And one to calculate the midpoint, given two points separated by a comma.
% Can be used in graphics macros where a point is required.
%    \begin{macrocode}
\newdef\plr#1{map (polar) (#1)}%
\newdef\midpoint#1{(0.5[#1])}%
%    \end{macrocode}
%
%
% \section{Macros to implement prefix commands}\label{prefix}
%
% Some \mfpic{} macros, like \cs{circle} create a path. When used without
% a prefix, they also draw the path. At the \MF{} level, every figure
% macro is syntactically a path expression. Other macros are prefix macros
% and operate on a figure macro that follows. Every prefix accepts a path
% expression as input and has a path as its return value, so a combination
% prefix + path expression is again a path expression.
%
% Prefixes may also have side effects, such as adding some ink to the
% current picture. Such prefixes are called \emph{rendering} macros.
%
% Rendering macros normally return the same path as their argument, but
% there are macros that modify the path. Some apply a linear transform,
% some close an open path, some return a subpath. These we call
% \emph{modification} macros.
%
% This scheme is quite simple, but unfortunately too simple. To avoid
% having to explicitly type a rendering prefix every time, a figure
% macro needs to know if a rendering prefix has occured, so prefix macros
% need to pass information to the figure macro (and to later prefixes).
%
% Moreover, \MF{} abhors an `isolated expression', so the first prefix
% has to write something with a different syntax, and pass the info that
% it has already done so on to later prefixes, who need to test that
% info. Thus, every prefix macro needs to know if it is the first or a
% later one. They test this \cs{if} command and also set it to false. The
% figure macros, which are last in the chain, close by resetting it true.
%    \begin{macrocode}
\mfp@DBlog{Tests to control multiple prefix commands.}%
\newif\if@mfpstart\@mfpstarttrue
%    \end{macrocode}
%
% If a prefix is a rendering prefix, it writes its rendering code and sets
% the following switch to false, letting the figure macro know it needn't
% invoke the default rendering. Figure macros close by resetting it true.
% Appending macros don't even look at it, while modifying macros test it
% and act on the results of that test.
%    \begin{macrocode}
\newif\if@mfprend\@mfprendtrue
%    \end{macrocode}
%
% The following macro is always (and only) invoked by the first prefix
% macro (or the figure macro, if there are no prefixes). It writes the
% code that prevents an isolated expression. It stores the following path
% expression in the variable \gbc{curpath}. Thus every combination of
% prefixes followed by a figure macro is syntactically a \MF{} variable
% assignment command.
%    \begin{macrocode}
\newdef\mfp@storepath{\mfsrc{\@nl store (curpath)}}%
%    \end{macrocode}
%
% Every prefix and figure macro has to invoke \cs{mfp@first}, since each
% is potentially the first in the sequence. If \cs{@mfpstart} is true, it
% writes the storing command, sets \cs{@mfpstartfalse}, and says that
% rendering is needed. (The rendering macros immediately cancel that
% switch.)
%    \begin{macrocode}
\newdef\mfp@first{\relax
  \if@mfpstart \mfp@storepath \@mfprendtrue \@mfpstartfalse\fi}%
%    \end{macrocode}
%
% Every rendering macro invokes this next command. After the first-stage
% code it writes its rendering command (via \cs{mfsrc}) and passes on the
% info that rendering is no longer required of the figure macro.
%    \begin{macrocode}
\newdef\mfp@rendmac{\mfp@first \@mfprendfalse \mfsrc}%
%    \end{macrocode}
%
% The \emph{figure} macros proceed as follows: (i)~they invoke the
% \cs{mfp@first} code, then (ii)~write a rendering macro if necessary
% (\cs{mfp@autorend}), (iii)~then make \cs{@mfpstarttrue} (for the next
% figure) and write \MF{} code that defines the path. The \cs{mfp@modmac}
% macros do only the first two, then write their modification code,
% counting on the following figure macro to do (iii). The idea is that
% [modifier + figure] should act the same as if the path it defines were
% encoded as a single figure command.
%    \begin{macrocode}
\newdef\mfp@modmac{\mfp@first\mfp@autorend\mfsrc}%
\newdef\mfp@autorend{\if@mfprend\@xp\mfp@render\fi}%
%    \end{macrocode}
%
% Only axis and arrow commands (plus \cs{reverse}) use \cs{mfp@addmac}.
% As the name suggests, something is added onto an existing figure. That
% is, it is designed to ignore the rendering state and not invoke implicit
% rendering. If no explicit rendering occurs, the figure macro that
% follows invokes a rendering. For arrows, this causes the arrowhead to be
% drawn on top of the drawing of the shaft.
%
% It would seem \cs{reverse} doesn't fit this name, but it also needs to
% be transparent to the rendering state so that it will work in
% combination with arrows.
%
% \cs{mfp@addmac} simply invokes the common first-stage code and writes
% its \MF{} code.
%    \begin{macrocode}
\newdef\mfp@addmac{\mfp@first \mfsrc}%
%    \end{macrocode}
%
% The \cs{mfp@addmac} and \cs{mfp@modmac} macros differ when there are no
% preceeding rendering macros. In that case it is as if \cs{draw} (or
% more generally \cs{mfp@render}) precedes the \cs{mfp@modmac} macro. That
% drawing happens \emph{in addition to} any rendering macros that follow.
% This implicitly added \cs{draw} is not present for \cs{mfp@addmac}
% macros; it is added by the following figure macro. The effect of this is
% the \cs{mfp@addmac} macros perform their additions on top of an already
% rendered figure.
%
% \DescribeMacro{\setrender}
% As mentioned above, when a figure macro is invoked without a rendering
% prefix, it will invoke some default. That default is stored in a macro
% and can be changed for special effects. Initially we define it as
% \cs{draw} (with empty optional argument) to draw solid paths in the
% default color, but we provide a command for the user to change it.
%    \begin{macrocode}
\newdef\mfp@render{\draw[]}%
\newdef\setrender#1{\mfp@def\mfp@render{#1}}%
%    \end{macrocode}
%
% A figure macro will invoke the common first-stage code and the rendering
% check. It also resets the \cs{@mfpstart} switch. Because a figure macro
% completes an assignment command in \MF, it writes its code with
% \cs{mfcmd}, which places a semicolon at the end. We define the first
% part (all but the writing) as a separate command because there are a few
% cases where we need to delay that writing.
%    \begin{macrocode}
\newdef\mfp@figmacbase{\mfp@first \mfp@autorend \@mfpstarttrue}%
\newdef\mfp@figmac{\mfp@figmacbase\mfcmd}%
%    \end{macrocode}
%
% The list macros take as their last argument a list of $(x,y)$ pairs (or
% occasionally a list of numbers). That list can either be typed directly
% into the \TeX{} source file (inside braces, separated by commas) or be
% present in an external datafile. Either way, the data is written as a
% list within an enclosing pair of parentheses. Since these are all
% figure macros, \cs{mfp@listmac} starts out just like \cs{mfp@figmac},
% but it writes only part of its arguments, the last one (the data list)
% being handled by \cs{mfp@writedata}.
%
% \cs{mfp@writedata} looks ahead to see if the token \cs{datafile}
% follows, if it does \cs{mfp@writefile} is invoked, which gobbles
% the \cs{datafile} token and processes the filename that should follow it.
% Otherwise, \cs{mflist} is invoked to write the list in braces
% that should follow.
%
% \cs{mfp@writedata} is also used by non-figure macros such as the axis
% marks macros, plus \cs{piechart} and \cs{barchart}.
%    \begin{macrocode}
\newdef\mfp@listmac#1{\mfp@figmacbase\mfsrc{#1}\mfp@writedata}%
\newdef\mfp@writedata{\mfp@iftoken\datafile{\mfp@writefile}{\mflist}}%
\newdef\mfp@writefile{%
  \mfp@ifopengraphsfile
    {\mfp@processfile{\mfp@rwdata}}{\mfp@nooutput@error\datafile}}%
%    \end{macrocode}
%
% \DescribeMacro{\mftitle}
% This is mainly for debugging the example files. \cs{mfp@title} takes
% two arguments: the command that called it (for the error message of
% \cs{mfp@src}), and some \TeX{} code. That code is written into the string
% argument of the \grafbase{} command \gbc{mftitle} and ends up in the
% \MF{} \file{.log} file and as a comment in the GF file. \cs{mftitle}
% merely calls \cs{mfp@title}, while
% \DescribeMacro{\tmtitle}
% \cs{tmtitle} also writes the argument to the \TeX{} \file{.log} file and
% typesets it in the document.
%
% We write the argument as a token list because that is the the easiest
% verbatim-like way to do it.
%    \begin{macrocode}
\newdef\mftitle#1{\@bsphack\mfp@title\mftitle{#1}\@esphack}%
\newdef\tmtitle#1{\mfp@title\tmtitle{#1}\wlog{\the\mfp@toks}{#1}}%
\newdef\mfp@title#1#2{\mfp@toks{#2}%
    \mfp@write\mfp@src#1{mftitle "\the\mfp@toks";}}%
%    \end{macrocode}
%
%
% \section{Macros for getting data from files}\label{rwdata}
%
% The following command contains the common code to open a data file for
% reading. The second parameter is the filename, the first is what to do
% if it exists and is nonempty. We first try to \cs{openin} the file and
% issue an error message if that fails. Then we skip any initial blank
% lines and comments and complain if that takes us to the end of the
% file. Otherwise we execute the command specified. Afterwards, since
% each \cs{plotdata} command in a given \env{mfpic} environment
% starts with the linetype at which the previous one ended, we allow the
% value of \cs{mfp@linetype} to survive this group but not any enclosing
% group.
%    \begin{macrocode}
\newdef\mfp@processfile#1#2{%
  \openin\mfp@data=#2\relax
  \ifeof\mfp@data \mfp@nofile@error{#2}%
  \else
    \mfp@DBlog{Opening file #2 for data.}%
    {%
      \mfp@resetwhitespace  \mfp@setcomment
      \mfp@skipblanklines
      \ifeof\mfp@data
        \mfp@nodata@error{#2}%
      \else
        \message{< Mfpic: Reading #2}%
        #1%
        \message{>}%
      \fi
      \@xp
    }\@xp\mfp@linetype\number\mfp@linetype\relax
    \mfp@DBlog{Closing file #2.}%
  \fi
  \closein\mfp@data}%
%    \end{macrocode}
%
% When reading files it is important that white space in the files
% always have the same meaning for \TeX{}. This utility resets spaces,
% tabs and EOLs to the standard categories.
%    \begin{macrocode}
\newdef\mfp@resetwhitespace{\mfp@restorepar
  \endlinechar`\^^M \catcode`\^^M5 \catcode`\ 10 \catcode`\^^I10 }%
%    \end{macrocode}
%
% \cs{mfp@skipcomments}
% does what it says, skipping comments in a data file. It reads a
% line from a previously opened file (input stream \cs{mfp@data}) and
% compares it to \cs{@empty}. It calls itself when they are equal (a
% comment line, a blank line would put a \cs{par} token in \cs{mfp@data}).
% When this macro finishes, \cs{mfp@temp} contains either \cs{par} (blank
% line or EOF) or real data.
%    \begin{macrocode}
\newdef\mfp@skipcomments{\read\mfp@data to \mfp@temp
  \ifx\mfp@temp\@empty \@xp\mfp@skipcomments\fi}%
%    \end{macrocode}
%
% \cs{mfp@skipblanklines}
% first skips comments. After that \cs{mfp@temp} can contain \cs{par},
% indicating either EOF or a blank line, or something else. In the first
% case (EOF) the macro terminates, in the second case (blank) it calls
% itself again, in the other case (something else) it also terminates,
% having presumably found real data.
%
% When this is called, a file should already be open using the handle
% \cs{mfp@data}.
%    \begin{macrocode}
\newdef\mfp@skipblanklines{\mfp@skipcomments
  \ifeof\mfp@data
  \else\ifx\mfp@temp\mfp@par \@XP\mfp@skipblanklines
  \fi\fi}%
%    \end{macrocode}
%
% The following two commands, \cs{mfp@rwdata} and \cs{mfp@rwdataloop}
% perform the work of writing the file (read stream \cs{mfp@data} opened
% by \cs{mfp@processfile}).
%
% The figure counter \cs{mfp@count} is reused (this should all be inside
% a group) to keep track of how many lines of the data file have been
% written to one line of the output. The token \cs{sequence} in a
% \cs{using} specification will expand to the value of the counter
% \cs{mfp@sequence}.
%
% When \cs{mfp@rwdata} is called, a non-blank line has been read to the
% macro \cs{mfp@temp}, to which we now add a space. The macro
% \cs{mfp@buffer} is what will be written to the output file as soon as it
% is long enough. We initialize it by defining it to be an open
% parenthesis followed by the result of applying \cs{parse@data} to the
% contents of \cs{mfp@temp}. Then we call \cs{mfp@rwdataloop}, which does
% the remaining reading and all the writing.
%    \begin{macrocode}
\newdef\mfp@nextdatum{\@xp\parse@data\mfp@temp\mfp@end}%
\newdef\mfp@rwdata{\mfp@count1 \mfp@sequence1
  \def\sequence{\number\mfp@sequence}%
  \edef\mfp@temp{\mfp@temp\space}%
  \edef\mfp@buffer{(\mfp@nextdatum}\mfp@rwdataloop}%
%    \end{macrocode}
%
% At this point, the buffer has been started with the first datum, so we
% read another line. If that is blank, we write the buffer (and the closing
% parenthesis and a semicolon) and terminate the loop. Otherwise we have
% read another datum and then we:
% \begin{enumerate}
%   \item increment the sequence counter,
%   \item add a comma to the buffer,
%   \item test whether the buffer is `full', and if so, write the buffer
%       to the output and clear it, then
%   \item add the datum to the buffer.
% \end{enumerate}
% The buffer is `full' when \cs{mfp@count} (the number of data in the
% buffer) exceeds \cs{mfp@dataperline}.
%
% \cs{mfp@rwdataloop} loops by calling itself at the end. Whenever
% \cs{mfp@temp} is empty (comment line read), (1)--(4) are skipped and
% another line read.
%    \begin{macrocode}
\newdef\mfp@rwdataloop{%
  \read\mfp@data to \mfp@temp
  \ifx\mfp@temp\mfp@par
    \mfcmd{\mfp@buffer)}%
  \else
    \ifx\mfp@temp\@empty
    \else
      \edef\mfp@temp{\mfp@temp\space}%
      \advance\mfp@sequence1
      \edef\mfp@buffer{\mfp@buffer\mfp@join}%
      \ifnum\mfp@count<\mfpdataperline\relax \advance\mfp@count1
      \else \mfsrc{\mfp@buffer}\mfp@count1 \def\mfp@buffer{}%
      \fi
      \edef\mfp@buffer{\mfp@buffer\mfp@nextdatum}%
    \fi
    \@xp\mfp@rwdataloop
  \fi}%
%    \end{macrocode}
%
%
% \section{Various \CMF{} Settings.}\label{MFsettings}
%
% \DescribeMacro{\penwd}
% Macros that write changes in default \grafbase{} variables now use the
% construct ``\gbc{save x; <type> x; x := <value>;}'' (via a call to
% \cs{setmfvariable}). This makes changes local if inside a given \env{mfpic}
% environment, global if outside. An exception is \gbc{penwd} which, as an
% internal variable uses `\gbc{interim}' instead (via the \grafbase{}
% command \gbc{resizedrawpen}).
%
% \SpecialUsageIndex{\drawpen}
% \cs{drawpen} was the original command used to set the pen diameter
% (prior to version 0.2.13). At some point it was replaced by
% \SpecialUsageIndex{\pen}\cs{pen}. However \cs{penwd} seems to be more
% consistent with other commands (e.g., \cs{shadewd}), and we keep all three.
%    \begin{macrocode}
\newdef\pen#1{\mfcmd{\@nl resizedrawpen (#1)}}%
\newlet\penwd\pen \newlet\drawpen\pen
%    \end{macrocode}
%
% \DescribeMacro{\shadewd}
% The \cs{shade} macro works in \MF{} by adding many copies of the small
% picture \gbc{shadedot} to the figure, in \MP{} the parameters
% \gbc{shadewd} and \cs{shadespace} are simply used to calculate a level
% of gray and a color fill is used.
%
% \DescribeMacro{\polkadotwd}
% However, both \MF{} and \MP{} handle polkadots the same. The only
% difference is \MF's need for fitting to a pixel grid. But that is
% handled in \grafbase.
%    \begin{macrocode}
\newdef\shadewd#1{\setmfnumeric{shadewd}{#1}}%
\newdef\polkadotwd#1{\setmfnumeric{polkadotwd}{#1}}%
%    \end{macrocode}
%
% \DescribeMacro{\hatchwd}
% The thickness of lines in the hatching fill is set by \cs{hatchwd}.
%    \begin{macrocode}
\newdef\hatchwd#1{\setmfnumeric{hatchwd}{#1}%
  \setmfvariable{pen}{hatchpen}{pencircle scaled hatchwd}}%
%    \end{macrocode}
%
% \DescribeMacro{\dashpattern}
% A dash pattern consists (internal to \MF) of an array of lengths. The
% \grafbase{} command \gbc{dashpat} accepts a name, and a sequence of
% numbers representing the sizes of dashes and spaces, and builds this
% array. It differs from \cs{numericarray} in that a little additional
% checking is done (at the \grafbase{} level).
%    \begin{macrocode}
\newdef\dashpattern#1{\mfsrc{save #1; dashpat (#1)}\mfp@writedata}%
%    \end{macrocode}
%
% \DescribeMacro{\settension}
% This sets the default tension for any command (for example, \cs{curve})
% that takes an optional argument that contains a tension value. This
% includes also \cs{function}, \cs{plrfcn}, \cs{fcncurve}, \cs{datafile},
% \cs{plotdata}. It also sets the default tension for \cs{sclosed} and
% \cs{bclosed}. The value should be at least $3/4$.
%    \begin{macrocode}
\newdef\settension#1{\setmfnumeric{default_tension}{#1}}%
%    \end{macrocode}
%
%
% \section{Settings for text label placement in figures}\label{labelsettings}
%
% \cs{tlabel}\,s are `justified' by placing a particular point of the
% text at the location specified. The \cs{tlabel} command accepts an
% optional argument containing two letters. There are 4 possibilities
% for the first and three for the second. It turns out to be easier to
% process these if we have a command that converts these to numbers, and
% then \cs{ifcase} can be used. There is a third part of the optional
% argument usable only in \MP{}: a number indicating degrees of rotation.
%
% \DescribeMacro{\tlabeljustify}
% The multi-part definition of \cs{tlabeljustify} is to guard
% against confusing error messages if some part of this optional argument
% is empty. The code assumes that if there are only 2, 1 or no parts, then
% later parts should be left unchanged. The rotation part is empty by
% default (rather than 0), because some commands will emit a warning if
% a nonempty rotation exists without \opt{mplabels}.
%
% The result of \cs{tlabeljustify} is that \cs{tl@vpos} is set equal to
% $-1$ if the first letter is (default) \texttt{B} (for Baseline), and
% 0--2 if it is \texttt{b} (bottom), \texttt{c} (center) or \texttt{t}
% (top). Similarly, \cs{tl@hpos} is set equal to $-1$ if the second
% letter is (default) \texttt{l} (for left), and 0 or 1 if it is
% \texttt{c} (center) or \texttt{r} (right). Making the defaults
% negative means they must be handled by the \cs{else} portion of any
% \cs{ifcase}.
%
% The rotation part is just saved in \cs{tl@rot}. This is true even
% without \opt{mplabels}, in case it is turned on later. It is ignored by
% \cs{tlabel} without \opt{mplabels}, but a warning is issued here anyway.
%    \begin{macrocode}
\newcount\tl@vpos \newcount\tl@hpos
\newdef\mfp@tlh@l{-1}%
\newdef\mfp@tlh@c{0}%
\newdef\mfp@tlh@r{1}%
\newdef\mfp@tlv@B{-1}%
\newdef\mfp@tlv@b{0}%
\newdef\mfp@tlv@c{1}%
\newdef\mfp@tlv@t{2}%
\newdef\tl@rot{}\tl@vpos-1 \tl@hpos-1
\newdef\tlabeljustify#1{\mfp@ifexist{#1}{\mfp@justify#1\mfp@end}}%
\newdef\mfp@justify#1#2\mfp@end{\mfp@local\mfp@vconv{#1}%
  \mfp@ifexist{#2}{\mfp@@justify#2\mfp@end}}%
\newdef\mfp@@justify#1#2\mfp@end{\mfp@local\mfp@hconv{#1}%
  \mfp@local\edef\tl@rot{#2}%
  \@ifmplabels{}%
   {\mfp@ifexist{#2}%
     {\Mfpic@warn{Rotation of labels is not supported without the %
        mplabels\@msgbreak option. Rotation setting\on@line\space
        may be ignored.}}%
   }}%
\newdef\mfp@vconv#1{%
  \@ifundefined{mfp@tlv@#1}%
   {\tl@vpos-1 \mfp@justify@error}%
   {\tl@vpos\@nameuse{mfp@tlv@#1}\relax}}%
\newdef\mfp@hconv#1{%
  \@ifundefined{mfp@tlh@#1}%
   {\tl@hpos-1 \mfp@justify@error}%
   {\tl@hpos\@nameuse{mfp@tlh@#1}\relax}}%
%    \end{macrocode}
%
% \DescribeMacro{\tlpathjustify}
% This acts just like \cs{tlabeljustify} from the user's point of view.
% Since it is only for users, and not used internally, it merely defines
% three macros that are passed to \cs{tlabeljustify} when no justification
% parameter is present for a \cs{tlabel}-path command.
%    \begin{macrocode}
\newdef\tlpathjustify#1{%
  \mfp@ifexist{#1}{\tlp@justify#1\mfp@end}}%
\newdef\tlp@justify#1#2\mfp@end{\mfp@def\tlpath@v{#1}%
  \mfp@ifexist{#2}{\tlp@@justify#2\mfp@end}}%
\newdef\tlp@@justify#1#2\mfp@end{%
  \mfp@def\tlpath@h{#1}\mfp@def\tlpath@r{#2}}%
\tlpathjustify{cc}%
%    \end{macrocode}
%
% \DescribeMacro{\tlpointsep}
% This takes an absolute length as its argument and sets parameters that
% determine by how much a tlabel is separated from the point it is placed
% at. This is in case something is drawn at that point, such as a dot or
% a hash mark on an axis.
%
% \DescribeMacro{\tlpathsep}
% This takes an absolute length and sets parameters that determine by how
% much a path created by one of the \cs{tlabel\meta{path}} macros is
% separated from the label it surrounds.
%
% \DescribeMacro{\tlabelsep}
% This simply issues both the above commands. This is for compatibility
% with \mfpic{} versions 0.7 or earlier, where both these separations were
% determined by the same parameters.
%
% \DescribeMacro{\tlabeloffset}
% \cs{tlabeloffset}, on the other hand, takes two arguments: dimensions,
% representing offsets of labels from their point of placement. This is
% mainly so that, if labels seem to be off, they can all be shifted with
% one command.
%
% Both these values are written to the \MF{} file for the sake of the
% commands that draw rectangles or ovals around labels.
%    \begin{macrocode}
\newdef\tlpointsep#1{\mfp@local\tlabel@sep#1\relax
  \setmfnumeric{label_sep}{\the\tlabel@sep}}%
\newdef\tlpathsep#1{\mfp@local\tlpath@sep#1\relax
  \setmfnumeric{labelpath_sep}{\the\tlpath@sep}}%
\newdef\tlabelsep#1{\tlpointsep{#1}\tlpathsep{#1}}%
\newdef\tlabeloffset#1#2{%
  \mfp@local\tlabel@hadj#1\relax \mfp@local\tlabel@vadj#2\relax
  \setmfpair{label_adjust}%
    {(\the\tlabel@hadj,\the\tlabel@vadj)}}%
%    \end{macrocode}
%
% \DescribeMacro{\everytlabel}
% Every line of a multiline label is written inside a group, so
% adjustments to baselineskip and other things are difficult or
% impossible. Therefore, \cs{everytlabel} is provided to define code to be
% inserted before the label code, outside these groups. The messing around
% with the token register \cs{mfp@toks} is so one can put definitions in
% the code without having to double \arg{} characters.
%
% The command \cs{extra@endtlabel} is called at the end of every
% \cs{tlabel}. Normally it does nothing, but the \cs{tlabels} command
% defines it to repeat the start of a loop.
%    \begin{macrocode}
\newdef\everytlabel{\afterassignment\mfp@everytlabel\mfp@toks}%
\newdef\mfp@everytlabel{\mfp@local\edef\every@tlabel{\the\mfp@toks}%
  \mfp@ifmpost
   {\mfp@ifopengraphsfile
     {\mfcmd{verbatimtex\@nl
        \def\noexpand\everylabel{\the\mfp@toks} etex}}%
     {}}%
   {}}%
\newdef\every@tlabel{}%
\newdef\extra@endtlabel{}%
%    \end{macrocode}
%
% Without \opt{mplabels} it is impossible to use \MP{} variables in
% a text label placement parameter. I have occasionally found it useful
% to have a \TeX{} version of the numeric variable \gbc{pi}.
%    \begin{macrocode}
\newdef\pinumber{3.14159}%
%    \end{macrocode}
%
%
% \section{Other settings}\label{othersettings}
%
% \DescribeMacro{\headshape}
% This sets the arrowhead shape. The parameters are: the ratio of width
% to length, the tension (see \file{grafbase.dtx}) and a boolean
% (\gbc{true} or \gbc{false}) to say whether the the head is filled, or
% only the barbs are drawn. It would be more consistent with other
% commands to have one \TeX{} parameter with commas separating the
% components, but this is legacy code.
%    \begin{macrocode}
\newdef\headshape#1#2#3{\mfcmd{\@nl headshape (#1, #2, #3)}}%
%    \end{macrocode}
%
% There are up to 4 optional arguments to any given \cs{arrow} command,
% and these can take any one of 6 special indicators ({\mytt b}, {\mytt c},
% {\mytt f}, {\mytt l}, {\mytt r} or {\mytt s}). Here we define macros
% to handle these options. Each macro is fed a \emph{value}. For example,
% the indicator {\mytt b} must be followed by a length, and that length is
% the argument of \cs{mfp@arr@b}.
%    \begin{macrocode}
\newdef\mfp@arr@b#1{\edef\mfp@hlocate{#1}}%
\newdef\mfp@arr@c#1{\edef\mfp@hcolour{#1}}%
\newdef\mfp@arr@l#1{\edef\mfp@hlength{#1}}%
\newdef\mfp@arr@r#1{\edef\mfp@hrotate{#1}}%
\newlet\mfp@arr@f\mfp@arr@b
\newlet\mfp@arr@s\mfp@arr@l
%    \end{macrocode}
%
% The \cs{arc} and \cs{circle} commands take an optional argument that
% indicates how the arc or circle is defined (and therefore the format of
% the non-optional argument). These are passed to different \grafbase{}
% commands whose names start with \gbc{arc} or \gbc{circle}. The commands
% below store the rest of that name. The switch is set true by the
% \cs{arc} command and false by \cs{circle}.
%    \begin{macrocode}
\newdef\mfp@arc@s{pps}%
\newdef\mfp@arc@t{ppp}%
\newdef\mfp@arc@p{\ifmfp@switch plr\fi}%
\newdef\mfp@arc@a{\ifmfp@switch alt\fi}%
\newdef\mfp@arc@c{cp\ifmfp@switch s\fi}%
\newdef\mfp@arc@r{pp (\mfp@T)}%
\newdef\mfp@arc@q{pp (\mfp@F)}%
%    \end{macrocode}
%
% \DescribeMacro{\mfpdefinecolor}
% \prog{Mfpic} supports color under \MP{} by writing all color
% definitions to the output \file{.mp} file. In order to support a
% \LaTeX-like color syntax, all the color models allowed by the color
% package correspond to a \grafbase{} function that returns a \MP{}
% color value. For example, \gbc{cmyk(.3,.3,0,.7)} returns \gbc{(0,0,.3)},
% a very dark blue. This can be set by
% \cs{mfpdefinecolor}\marg{vdblue}\marg{cmyk}\marg{.3,.3,0,.7}.
%
% Several commands are provided to set certain special colors. Currently
% we have the following commands, setting the color of the same name as
% the command (except \cs{backgroundcolor} which sets a color named
% \gbc{background}):
% \cs{drawcolor}\SpecialUsageIndex{\drawcolor},\\
% \cs{fillcolor}\SpecialUsageIndex{\fillcolor},
% \cs{hatchcolor}\SpecialUsageIndex{\hatchcolor},
% \cs{headcolor}\SpecialUsageIndex{\headcolor},
% \cs{pointcolor}\SpecialUsageIndex{\pointcolor},
% \cs{tlabelcolor}\SpecialUsageIndex{\tlabelcolor}, and\\
% \cs{backgroundcolor}\SpecialUsageIndex{\backgroundcolor}.
%
% These commands support the \LaTeX-like syntax:\\
% \indent\cs{fillcolor}\oarg{\meta{model}}\marg{\meta{parameters}}.\\
% The code for \cs{backgroundcolor} has to be spelled out since the
% command name has the string `\texttt{color}', but the color does not.
%    \begin{macrocode}
\newdef\mfpdefinecolor#1#2#3{\setmfcolor{#1}{#2(#3)}}%
\newdef\mfp@defclr#1#2#3{\setmfcolor{#1}{\mfp@ifempty{#2}{#3}{#2(#3)}}}%
\newdef\mfp@newcolorcmd#1{%
  \@namedef{#1\mfp@C}{\mfp@nullopt{\mfp@defclr{#1\mfp@C}}}}%
\mfp@newcolorcmd{draw}\mfp@newcolorcmd{fill}\mfp@newcolorcmd{tlabel}%
\mfp@newcolorcmd{hatch}\mfp@newcolorcmd{head}\mfp@newcolorcmd{point}%
\def\backgroundcolor{\mfp@nullopt{\mfp@defclr{background}}}%
%    \end{macrocode}
%
% When \cs{plotdata} is used to draw several graphs from one file, each
% sequence of non-blank lines corresponds to a different curve with a
% different style of rendering. The user has the option to cycle through
% different dashing patterns, different colors, or different symbols.
%
% Internally, \cs{plotdata} issues the command \cs{mfp@setstyle} (which
% can be defined to be any rendering macro), followed by a path defining
% command such as \cs{curve} or \cs{polyline}, followed by a command
% that reads the data and writes it in a suitable format. The following
% commands essentially allow the user to select the rendering macro.
% They start by resetting \cs{mfp@linetype}, the count register that keeps
% track of how many curves have been drawn, then they define
% \cs{mfp@setstyle}.
%
% \DescribeMacro{\dashedlines}
% \cs{dashedlines} uses the rendering prefix \cs{gendashed} with 6
% different dashing patterns \gbc{dashtype0} through \gbc{dashtype5}.
% These are actually selected in \MF{} through the command
% \gbc{getdashpat}. This takes care of cycling back to
% \gbc{dashtype0} when the number of available dash patterns is exceeded.
% Dashed lines is the default.
%    \begin{macrocode}
\newdef\dashedlines{\mfp@local\mfp@linetype0
  \mfp@def\mfp@setstyle{\gendashed{getdashpat \number\mfp@linetype}}}%
\dashedlines
%    \end{macrocode}
%
% \DescribeMacro{\coloredlines}
% This uses \cs{draw} with an optional color parameter set to
% \gbc{colortype0} through (by default) \gbc{colortype7}. These are color
% variables defined by \grafbase{}. It also issues a warning if \MF{} is
% being used. As with \cs{dashedlines}, a \MP{} command \gbc{getcolor}
% selects these colors.
%    \begin{macrocode}
\newdef\coloredlines{%
  \mfp@ifmpost
   {\mfp@local\mfp@linetype0
    \mfp@def\mfp@setstyle{\draw[getcolor \number\mfp@linetype]}}%
   {\Mfpic@warn{You can't use \mfp@b coloredlines in %
      Metafont.\@msgbreak Using \dashedlines instead}%
    \dashedlines}}%
%    \end{macrocode}
%
% \DescribeMacro{\pointedlines}
% This makes a sort of dotted line, except the dots are actually different
% symbols. It uses the rendering macro \cs{plot} with a parameter cycling
% through 9 different symbols.
%    \begin{macrocode}
\newdef\pointedlines{\mfp@local\mfp@linetype0
  \mfp@def\mfp@setstyle{\plot{getsymbol \number\mfp@linetype}}}%
%    \end{macrocode}
%
% \DescribeMacro{\datapointsonly}
% \cs{datapointsonly} uses symbols like \cs{pointedlines}, but places
% them only at the data points from the file. It uses the rendering macro
% \cs{plotnodes} with a parameter cycling through the same 9 symbols.
%    \begin{macrocode}
\newdef\datapointsonly{\mfp@local\mfp@linetype0
  \mfp@def\mfp@setstyle{\relax
    \plotnodes{getsymbol \number\mfp@linetype}}}%
%    \end{macrocode}
%
% \DescribeMacro{\reconfigureplot}
% This command allows the user to set the dashes, colors and symbols used
% by the \cs{plotdata} command. The first argument is the plotting method
% to be changed (\texttt{dashes}, \texttt{colors}, or \texttt{symbols})
% and the second argument is a comma separated list of appropriate type
% variables for \cs{plotdata} to cycle through. For example,
% \cs{reconfigureplot}\marg{dashes} takes a list of dashing patterns
% (previously defined by the \cs{dashpattern} command) separated by
% commas. It writes a command instructing \MF{} to redefine the arrays
% \mfc{dashtype0}, \mfc{dashtype1}, etc., used with \cs{gendashed} when
% \cs{dashedlines} is in effect. The number of patterns is counted by \MF,
% which also handles the mod-ing operation now.
%
% \cs{reconfigureplot}\marg{colors} takes a list of colors (expressions or
% color names previously defined) separated by commas. It redefines
% \gbc{colortype0}, etc., used with \cs{plotdata} when \cs{coloredlines}
% is in effect.
%
% \cs{reconfigureplot}\marg{symbols} takes a list of symbols (\MF{} path
% expressions, one of the symbols available to \cs{plotsymbol}, or path
% names defined by \cs{store}) separated by commas. It redefines
% \gbc{pointtype0}, etc., used by \cs{plotdata} when \cs{pointedlines} or
% \cs{datapointsonly} is in effect.
%
% \DescribeMacro{\defaultplot}
% This restores \mfpic's predefined defaults for dash patterns, colors and
% symbols in \cs{plotdata}. The one argument is one of the words
% \texttt{dashes}, \texttt{colors}, or \texttt{symbols}, indicating which
% plotting method is to be restored.
%    \begin{macrocode}
\newdef\reconfigureplot#1{\mfsrc{setdata#1}\mfp@writedata}%
\newdef\defaultplot#1{\mfcmd{default#1}}%
%    \end{macrocode}
%
% \DescribeMacro{\mfplinetype}
% The user-level command \cs{mfplinetype} allows the user to set the
% starting value of \cs{mfp@linetype}. The default is to start at $0$.
% \DescribeMacro{\mfplinestyle}
% The macro \cs{mfplinestyle} is an alias for this same command. The names
% `linestyle' and `linetype' come from an analogous system of changing
% rendering in \prog{gnuplot}. (The reason for two names is that
% \prog{gnuplot} documentation was not consistent in its terminology.)
%    \begin{macrocode}
\newdef\mfplinetype#1{\mfp@local\mfp@linetype#1\relax}%
\newlet\mfplinestyle\mfplinetype
\mfplinetype{0}%
%    \end{macrocode}
%
% \prog{Mfpic} has 6 possible axes, the $x$- and $y$-axes pass through the
% origin, $(0,0)$, the four border axes are at the edges of the graph
% space, possibly offset from it by some amount. These four commands hold
% the amount of that offset in graph units, the default being 0.
%    \begin{macrocode}
\newdef\mfp@lshift{0}\newdef\mfp@bshift{0}%
\newdef\mfp@rshift{0}\newdef\mfp@tshift{0}%
%    \end{macrocode}
%
% \DescribeMacro{\axismargin}
% The main user-level command for setting the above offsets is
% \cs{axismargin}. Its first argument is one of the letters l, b, r, or t
% to select the axis and the second is the offset in graph units. A
% positive offset represents an inward shift, which is why we call them
% \emph{margins}.
% \DescribeMacro{\setaxismargins}
% The arguments of \cs{setaxismargins} are four offsets for the axes (in
% the above order, which is anticlockwise, starting with the left).
% \DescribeMacro{\setallaxismargins}
% \cs{setallaxismargins} takes one offset and applies it to all axes.
%
% The values are passed on to \MF{} in the variables \gbc{laxis},
% \gbc{baxis}, \gbc{raxis}, and \gbc{taxis}. They are also needed by the
% \cs{axislabels} command so they are saved in macros.
%    \begin{macrocode}
\newdef\axismargin#1#2{\setmfnumeric{#1axis}{#2}%
  \mfp@local\@namedef{mfp@#1shift}{#2}}%
\newdef\setaxismargins#1#2#3#4{\axismargin l{#1}\axismargin b{#2}%
  \axismargin r{#3}\axismargin t{#4}}%
\newdef\setallaxismargins#1{\setaxismargins{#1}{#1}{#1}{#1}}%
%    \end{macrocode}
%
% The following converts axis letters to a numeric, making conditionals for
% axes simpler to code (\cs{ifcase} versus six nested \cs{if}\,s).
% Plus we get to define the error message only once. The first argument
% of \cs{mfp@getaxis} is the letter and the third argument is the calling
% command (for the error message). We allow the letter to be instead a word,
% using only the first letter and discarding the rest (\arg2).
%    \begin{macrocode}
\def\mfp@axis@x{0}%
\def\mfp@axis@y{1}%
\def\mfp@axis@l{2}%
\def\mfp@axis@b{3}%
\def\mfp@axis@r{4}%
\def\mfp@axis@t{5}%
\def\mfp@getaxis#1#2\mfp@end#3{%
  \@ifundefined{mfp@axis@#1}%
   {\mfp@errmsg {Invalid axis letter "#1"}%
    {The command #3 requires an axis to be designated by one of^^J%
     the following letters: x, y, l, b, r, or t. If you proceed, ^^J%
     x will be assumed.}\def\mfp@axisnum{0}\def\mfp@axisletter{x}}%
   {\edef\mfp@axisnum{\@nameuse{mfp@axis@#1}}\def\mfp@axisletter{#1}}%
  \edef\mfp@defheadlen{%
    \the\ifnum\mfp@axisnum>1 \sideheadlen\else \axisheadlen\fi}}%
%    \end{macrocode}
%
% The tick marks (or hash marks) on the axes can be in three possible
% positions: centered on the axes, on one side, or on the other side.
% The default for the $x$- and $y$-axes is centered, for the border axes it
% is inside.
% \DescribeMacro{\setaxismarks}
% For changing this we provide the \cs{setaxismarks} command, whose first
% argument is the axis letter, and whose second argument is one of the
% words \texttt{inside}, \texttt{outside}, \texttt{centered},
% \texttt{ontop}, \texttt{onbottom}, \texttt{onleft}, or \texttt{onright}.
%
% \DescribeMacro{\setxmarks}
% \cs{setxmarks} takes one argument and sets the position for the $x$ axis
% only, while
% \DescribeMacro{\setymarks}
% \cs{setymarks} does the same for the $y$ axis. For the border axes we
% provide
% \DescribeMacro{\setbordermarks}
% \cs{setbordermarks}, which takes four arguments: the positions for the
% left, bottom, right and top axis (in that order).
% \DescribeMacro{\setallbordermarks}
% The abbreviation \cs{setallbordermarks} takes one argument and sets the
% position for all border axis marks to that.
%    \begin{macrocode}
\newdef\setaxismarks#1#2{\setmfnumeric{#1tick}{#2}}%
\newdef\setxmarks#1{\setaxismarks x{#1}}%
\newdef\setymarks#1{\setaxismarks y{#1}}%
\newdef\setbordermarks#1#2#3#4{\setaxismarks l{#1}\setaxismarks b{#2}%
  \setaxismarks r{#3}\setaxismarks t{#4}}%
\newdef\setallbordermarks#1{\setbordermarks{#1}{#1}{#1}{#1}}%
%    \end{macrocode}
%
% The \cs{datafile} and \cs{plotdata} commands originally just created
% polygonal paths, but users requested the ability to draw smooth ones.
% Originally only the commands below (\cs{smoothdata} and
% \cs{unsmoothdata}) were written to do this. Later, these file
% manipulation commands were given optional arguments to achieve the same
% effect, so now the commands below just set the defaults for the optional
% parameter, storing them in the macros \cs{mfp@smoothness} and
% \cs{mfp@tension}. The latter can be used to adjust the tension of the
% \MF{} path if smoothness is `\texttt{s}'.
%
% \DescribeMacro{\smoothdata}
% This takes an option tension argument. It defines \cs{mfp@smoothness} to
% be `\texttt{s}' and \cs{mfp@tension} to be the optional argument.
% Default tension is empty rather than 1 so we can implement a scheme to
% change the actual default used.
% \DescribeMacro{\unsmoothdata}
% The macro \cs{unsmoothdata} defines \cs{mfp@smoothness} to be
% `\texttt{p}' and \cs{mfp@tension} to be empty. The latter might not be
% necessary.
%    \begin{macrocode}
\newdef\mfp@smdata#1{\mfp@def\mfp@smoothness{#1}%
  \mfp@nullopt{\mfp@def\mfp@tension}}%
\newdef\smoothdata{\mfp@smdata{s}}%
\newdef\unsmoothdata{\mfp@smdata{p}\@empty}%
\unsmoothdata% default
%    \end{macrocode}
%
% \DescribeMacro{\using}
% The command \cs{using} is named after a keyword in \prog{gnuplot}. It
% controls which datum is plotted against which by \cs{plotdata} and
% \cs{datafile}.
%
% \DescribeMacro{\usingpairdefault}
% The macro \cs{usingpairdefault} sets the default, which is to read the
% first two space separated words on a line as the $x$ and $y$ coordinate
% of a point. To allow that there might be more data on a line, it is also
% assumed that the second word is followed by a space and the rest of the
% line is read as a third parameter that is not used. In case there are
% only two words, \mfpic{} will always add a space on the end and then the
% third parameter will be empty.
%
% \DescribeMacro{\usingnumericdefault}
% For the occasional command that needs numeric data,
% \cs{usingnumericdefault} sets \cs{using} so that the first
% space-separated word on a line is selected and the remainder of the line
% discarded.
%
% The \cs{parse@data} command reads its argument as delimited
% parameters, and the \cs{using} command tells what those delimiters are.
% For example, in the first part of
% \cs{using}\marg{\#1 \#2 \#3}\marg{(\#1,\#2)}, we are telling
% \cs{parse@data} that everything on a line up to the first space is the
% first parameter, and everything up to the second space is the second
% parameter and the rest of the line is the third parameter. In the second
% part we are telling it that what we write to the output is a pair in
% parentheses with the first two parameters separated by a comma. This
% example is the default as we see here in \cs{usingpairdefault}. This
% command can be issued by a user to return to that default. The user can
% also issue \cs{usingnumericdefault} to write the first word as a single
% numeric for commands like \cs{piechart}.
%
% \DescribeMacro{\mfpdataperline}
% \cs{mfpdataperline} is a user level macro that controls the maximum
% number of points that will be written to a single line in the output.
%    \begin{macrocode}
\newdef\using#1#2{\mfp@def\parse@data#1\mfp@end{#2}}%
\newdef\usingpairdefault{\using{##1 ##2 ##3}{(##1,##2)}}%
\newdef\usingnumericdefault{\using{##1 ##2}{##1}}%
\usingpairdefault
\newdef\mfpdataperline{5}%
%    \end{macrocode}
%
% The following macros are used internally by \cs{datafile} and
% \cs{plotdata}. A blank line is read as \cs{par} (not the primitive
% \cs{par}, but the literal token \cs{par}, so it tests as equal to
% \cs{mfp@par}. Early versions of \cs{plotdata} wrote a literal \MF{} path
% expression to the output file and \cs{mfp@join} created the \mfc{--}
% between points. Now we write one of the \grafbase{} list-to-path
% commands followed by a comma separated list of points, so \cs{mfp@join}
% has morphed into a comma.
%    \begin{macrocode}
\newdef\mfp@par{\par}\newdef\mfp@join{,}%
%    \end{macrocode}
%
% \DescribeMacro{\mfpdatacomment}
% The user can change the comment character for data files with
% something like \cs{mfpdatacomment}\marg{\cs{\#}}. This also changes the
% percent character to category `other'. We can also use the percent sign
% as part of the numeric data by placing
% \DescribeMacro{\makepercentother}
% \cs{makepercentother} before the \cs{using} command to turn `\texttt\%'
% into an ordinary character.
% \DescribeMacro{\makepercentcomment}
% \cs{makepercentcomment} returns it to its usual role as a comment. Every
% file reading command issues \cs{mfp@setcomment} before reading. The
% count register \cs{mfp@commentchar} holds the ASCII code of the current
% comment character, the default being the percent sign.
%    \begin{macrocode}
\newcount\mfp@commentchar \mfp@commentchar`\%%
\newdef\makepercentother{\@makeother\%}%
\newdef\makepercentcomment{\catcode`\%14 }%
\newdef\mfpdatacomment#1{\mfp@local\mfp@commentchar`#1}%
\newdef\mfp@setcomment{\makepercentother\catcode\mfp@commentchar14 }%
%    \end{macrocode}
%
% \DescribeMacro{\fdef}
% The following is for defining functions to be used in \cs{function}
% through \cs{plrregion}. The first argument is the name of the function,
% the second is its variable, the last is the \MF{} code. Obviously its
% use requires a knowledge of the \MF{} language. The function produced is
% a \mfc{vardef}, and can contain almost arbitrary \MF{} code, but must
% end with an expression. Normally it must be a numerical expression, to
% be use in \cs{function}, or a pair expression so it can be used alone in
% the last argument of \cs{parafcn}.
%
% We apply \cs{@makeother} to \arg{} so it doesn't get doubled. The
% \arg{} is frequent in vardefs among the \MF{} gurus.
%    \begin{macrocode}
\newdef\fdef{\begingroup\@makeother\#\mfp@keeplines\mfp@fdef}%
\newdef\mfp@fdef#1#2#3{\mfcmd{\@nl save #1;\@nl
  vardef #1 (expr #2) = \@nl #3\@nl enddef}\endgroup}%
%    \end{macrocode}
%
% The following is executed right after \cs{mfp@grafmacs}. It is a hook
% for adding new definitions inside and \env{mfpic} environment. It is
% initialized to empty, and add-on packages can add to it.
%    \begin{macrocode}
\newdef\mfp@additions{}%
%    \end{macrocode}
%
% \section{The user level graphics macros}
%
% This is the start of the definition of \cs{mfp@grafmacs}. It contains
% the definition of every user command that has no purpose outside an
% \env{mfpic} environment. It will be expanded inside every \env{mfpic}
% environment, localizing all these definitions. We do this so we can
% avoid name clashes without giving them all names beginning with \cs{mfp}.
%    \begin{macrocode}
\newdef\mfp@grafmacs{%
%    \end{macrocode}
%
% \subsection{Figure macros}\label{figure}
%
% These are the figure macros. These are implemented as \MF{} paths that
% can be variously rendered, transformed, etc., with the prefix macros of
% subsection~\ref{prefixcommands}.
%
% Most of the \mfpic{} graphic commands take optional arguments. Most of
% them follow the scheme \cs{mfp@command} takes mandatory arguments
% enclosed in braces, and does the work. \cs{command} is simply defined to
% test for an optional argument (with \cs{mfp@defaultopt}) and pass it or a
% default to \cs{mfp@command}. A typical example is \cs{ellipse} defined
% to be \verb$\mfp@defaultopt\mfp@ellipse0$. In some cases, the default
% option is signaled by passing an empty argument via \cs{mfp@nullopt}.
%
% Of the commands that have no optional argument, most simply write
% the appropriate commands to the output file, and require no
% \cs{mfp@} version.
%
% This section contains a description of the behavior of each command and
% its syntax in use. For those that call an \cs{mfp@} version, the
% implementation is in the next section.
%
% \subsubsection{Common geometric objects}\label{geometric}
%
% The first few (\cs{rect} through \cs{sector}) are closed paths and
% need not be prefixed with a closing macro before filling, etc.
%
% \DescribeMacro{\rect}
% This takes one mandatory argument, the two diagonally opposite
% corners of the rectangle separated by a comma, and draws the rectangle
% with horizontal and vertical sides having these as two corners. The
% direction of the path (which seldom makes a difference) is such that it
% starts at the first specified point and moves horizontally first.
%
% This is an example of a command that requires no further processing.
% The \cs{mfp@figmac} command sets the appropriate switches and writes its
% argument to the output file, followed by a semicolon.
%    \begin{macrocode}
  \newdef\rect##1{\mfp@figmac{rect (##1)}}%
%    \end{macrocode}
%
% \DescribeMacro{\regpolygon}
% There are four arguments. The first is the number of sides. The second
% is the name of a variable to represent the vertices. The other
% two should be equations locating two vertices or the center and one
% vertex. If the name used is \gbc{Ver}, then the vertices will be
% \gbc{Ver1}, \gbc{Ver2}, etc., numbering anticlockwise. The center is
% \gbc{Ver0}. Case is significant. After the command, the points can be
% referred to in other \mfpic{} commands (except text label commands
% when \opt{mplabels} is not in effect).
%    \begin{macrocode}
  \newdef\regpolygon##1##2##3##4{%
    \mfp@figmac{regularpolygon (##1) (##2) (##3; ##4;)}}%
%    \end{macrocode}
%
% \DescribeMacro{\circle}
% This has one optional argument containing one of the letters
% \texttt{t}, \texttt{p} (the default), \texttt{c}, \texttt{s},
% \texttt{r}, or \texttt{q}. Its purpose is to specify what kind of data
% is in the single mandatory argument. These are a subset of the optional
% arguments that the \cs{arc} commad (below) takes, and have almost the
% same meaning:
% \begin{itemize}
% \item \oarg{t}, the three point form needs three points (of course).
% \item \oarg{p}, the polar form needs the center point and the radius.
%       This is the default when the optional argument is absent.
% \item \oarg{c}, the center/point form needs the center and one point on
%       the circle.
% \item \oarg{s}, the point-sweep form requires two points and the angle of
%       arc between them. The angle may be positive or negative. A
%       positive angle indicates the number of degrees anticlockwise from
%       the first point to the second. Negative means clockwise.
% \item \oarg{r}, the point-radius form requires two points and the
%       radius of the circle. Of the two possible circles, it produces the
%       one where the anticlockwise arc from the first point to the second
%       is not more than 180 degrees.
% \item \oarg{q}, an alternative point-radius with the same parameters.
%       It produces the circle
%       where the anticlockwise arc from the first point to the second
%       is not less than 180 degrees.
% \end{itemize}
%
% Supplying \cs{arc} with the same parameters, or the appropriate superset
% in the case of \oarg{p} and \oarg{c}, would produce a sub-arc of the
% circle that \cs{circle} produces. This is the reason for giving
% \cs{circle} these options: to make diagrams which show a circle and an
% arc on it.
%
% We use \cs{def} instead of \cs{newdef} because we know \LaTeX{} has
% already defined a \cs{circle} command. We now use the same command,
% \cs{mfp@arccircle}, for arcs and circles, setting a switch to tell it
% which to produce.
%    \begin{macrocode}
  \def\circle{\mfp@switchfalse\mfp@defaultopt\mfp@arccircle{p}}%
%    \end{macrocode}
%
% \DescribeMacro{\ellipse}
% \cs{ellipse} has one optional argument, an angle of rotation and one
% mandatory argument, containing the center, the horizontal and vertical
% radii (before rotation), separated by commas.
%    \begin{macrocode}
  \newdef\ellipse{\mfp@defaultopt\mfp@ellipse{0}}%
%    \end{macrocode}
%
% \DescribeMacro{\sector}
% This is the closed curve starting at the center of a circle, out
% along a radius to the circumference of the circle, along an arc of the
% circle,  then back to the center. It has one mandatory argument
% containing the center, the radius, and the two angles, separated by
% commas.
%    \begin{macrocode}
  \newdef\sector##1{\mfp@figmac{sector (##1)}}%
%    \end{macrocode}
%
% \DescribeMacro{\arc}
% We have seven (actually 14) ways to specify a circular arc. \cs{arc}
% takes an optional argument: a letter to indicate which of the 7
% specifications. It has one mandatory argument containing the data for
% that specification, separated by commas. It also has a star-form,
% which produces the complementary arc. That is, instead of the arc that
% is specified (as described below) it produces the rest of the circle
% from the end of the specified arc to its start.
%
% The available letters and the corresponding required data are listed
% below. The default optional argument is \oarg{s}.
% \begin{itemize}
% \item \oarg{t}, the three point form needs three ordered pairs.
% \item \oarg{p}, the polar form needs the center point, two angles and
%       the radius (in that order).
% \item \oarg{a}, the alternative polar form needs the center, the radius
%       and two angles (in that order).
% \item \oarg{c}, the center-point-sweep form needs the center, the
%       starting point, and the angle.
% \item \oarg{s}, the points-sweep form requires the starting point, the
%       ending point and the angle.
% \item \oarg{r}, the points-radius form requires the starting point, the
%       ending point and the radius of the arc. There are two circles with
%       the given radius that pass through the given points, and hence
%       four possible arcs. One arc on each circle is anticlockwise from
%       the first point to the second. Of those two arcs, only one  is
%       less than $180$ degrees. That one is produced.
% \item \oarg{q} Same as \oarg{r}, except the arc is the larger of two
%       anticlockwise arcs.
% \end{itemize}
%    \begin{macrocode}
  \newdef\arc{\mfp@iftoken*{\arccomplement\mfp@arc}{\mfp@arc}}%
%    \end{macrocode}
%
% This final circle is for we complex function theorists. It makes a
% `pseudohyperbolic circle'. This requires a point $z$ inside the circle
% with center $(0,0)$ and radius $1$, and a radius $R < 1$. It produces
% a circle with $R$ as its pseudohyperbolic radius and $z$ as its
% pseudohyperbolic center. The star form switches contexts to the upper
% half-plane.
%    \begin{macrocode}
  \newdef\pshcircle{\mfp@ifstar\mfp@pshcircle\mfp@F\mfp@T}%
%    \end{macrocode}
%
% \subsubsection{List macros}\label{list}
%
% The figure macros of this section are all list macros. They produce a
% path from a list of ordered pairs. The list can be explicitly given as a
% mandatory argument containing a comma-separated list of pair
% expressions, or it can be taken from an external datafile. This is true
% for \cs{polyline} through \cs{turtle}. These macros differ only in how
% the data determine the path. (Some of the splines don't connect given
% points, but rather use the points in a different way to determine a
% curve.) The list of pairs is not an argument of any of these. It should
% follow, and is ultimately written to output by the ending code of
% \cs{mfp@listmac}. This is basic to list macros, and will not be repeated
% for each one.
%
% Commands in this section are grouped by the argument structure of the
% command written to the output file. The first twelve come in pairs
% that are distinguished by a boolean parameter, which usually determines
% whether the path produced is closed, followed by the list.
%
% \DescribeMacro{\polyline}
% The most basic, a polyline or polygonal path, \cs{polyline} draws line
% segments from each point to the next.
% \DescribeMacro{\lines}
% \cs{lines} is an alias.
%
% \DescribeMacro{\closedpolyline}
% The macro \cs{closedpolyline} does the same, except it produces a closed
% path, connecting the last point to the first.
% \DescribeMacro{polygon}
% \cs{polygon} is an alias.
%
% \DescribeMacro{\computedspline}
% The \cs{computedspline} command takes a list of points and computes the
% controls of a cubic spline that connects the points. Adjacent segments
% have matching first and second derivatives at the common endpoint. It is
% limited to what is called a \emph{relaxed} spline, which has zero
% curvature at the beginning and ending points.
%
% \DescribeMacro{\closedcomputedspline}
% This is similar, but computes the unique \emph{closed} cubic spline that
% connects a list of points.
%
% The next four commands also produce types of splines. The list of pairs
% is not, however, the points passed through but rather are control points,
% of a sort.
%
% \DescribeMacro{\qspline}
% This produces quadratic splines. The points create the path as follows:
% for successive points $p\sb i, p\sb {i+1}$ in the list, the path passes
% through the midpoint of the line segment connecting $p\sb i$ and
% $p\sb {i+1}$, tangent to that line segment. This causes adjacent
% B\'ezier segments to have matching derivatives at their common
% endpoint. Each three successive data points determines one segment of
% the path.
%
% \DescribeMacro{\closedqspline}
% The closed variant works by creating two additional segments, viewing
% the triples $p\sb{n-1}, p\sb{n}, p\sb1$ and $p\sb{n}, p\sb1, p\sb2$ as
% being `successive'.
%
% \DescribeMacro{\cspline}
% The macro \cs{cspline} produces cubic splines. The points determine the
% curve as follows: for successive points $p\sb i, p\sb {i+1}$ in the
% list, the line segment connecting them is divided into thirds with two
% points $q\sb i$ and $q\sb i'$. The curve then passes through the
% midpoint of the segment from $q\sb {i-1}'$ to $q\sb i$ and tangent to
% that segment. This causes adjacent B\'ezier segments to have matching
% first and second derivatives at their common endpoint. Each four
% successive data points determines one segment of the path.
%
% \DescribeMacro{\closedcspline}
% The closed variant works by viewing the first point as a succesor of the
% last point, creating three additional path segments.
%
% \DescribeMacro{\qbeziers}
% This produces the equivalent of a sequence of \LaTeX{} \cs{qbezier}
% commands. The mandatory argument will be a list of points alternating
% between nodes and control points, ending with the last node.
% \DescribeMacro{\closedqbeziers}
% The closed version ends with the control point between the last node and
% the first. Therefore, the \cs{qbeziers} command needs an odd number of
% points in the list, while \cs{closedqbeziers} needs an even number. If
% this is not the case, the last point in the list is repeated, causing
% the final segment to be a straight line (closed case) or trivial.
%
% Note that quadratic B\'eziers need not be smooth at the nodes unless
% the control points line up. Our plural name distinguishes it from the
% \LaTeX{} command.
%
% \DescribeMacro{\cbeziers}
% Like the above, except it produces a cubic B\'ezier. It requires a
% list of $3n+1$ points in the pattern node-control-control, ending with
% an extra node.
% \DescribeMacro{closedcbeziers}
% The closed version requires only $3n$ points, taking the first for the
% final node.
%
% \DescribeMacro{\fcnspline}
% The above splines are two dimensional splines, that is, functions of
% $t$ with pair values $(x,y)$. One dimensional splines are functions of
% $x$ with numeric values $y$. This command produces the \emph{graph} of
% such a function computed from a supplied list of points. It is required
% that the $x$-values of the points are in increasing order, although it
% will produce some sort of curve as long as adjacet $x$-values are
% distinct. It produces the graph of a \emph{relaxed} spline, in the sense
% that the second derivative $d^2y/dx^2$ is zero at the beginning and end.
%
% \DescribeMacro{\periodicfcnspline}
% This is the same, but instead of requiring the second derivative to be
% zero at both ends, it produces a graph such that the first and second
% derivatives at the end match the ones at the beginning. If a copy of the
% graph is placed with its starting point at the original graph's ending
% point, then there is a smooth join. If the $y$-values of the
% beginning and ending points match, a periodic graph is obtained. For
% these last two commands the paths cannot be closed, and the boolean
% determines the behavior at the endpoints.
%
% The command \cs{mfp@listi} that implements these writes the command
% name and the argument and ends with code to write the list of pairs.
%    \begin{macrocode}
  \newdef\lines{\mfp@listi{polyline}\mfp@F}%
  \newdef\polygon{\mfp@listi{polyline}\mfp@T}%
  \newdef\computedspline{\mfp@listi{dospline}\mfp@F}%
  \newdef\closedcomputedspline{\mfp@listi{dospline}\mfp@T}%
  \newdef\qspline{\mfp@listi{qspline}\mfp@F}%
  \newdef\closedqspline{\mfp@listi{qspline}\mfp@T}%
  \newdef\cspline{\mfp@listi{cspline}\mfp@F}%
  \newdef\closedcspline{\mfp@listi{cspline}\mfp@T}%
  \newdef\qbeziers{\mfp@listi{qbezier}\mfp@F}%
  \newdef\closedqbeziers{\mfp@listi{qbezier}\mfp@T}%
  \newdef\cbeziers{\mfp@listi{cbezier}\mfp@F}%
  \newdef\closedcbeziers{\mfp@listi{cbezier}\mfp@T}%
  \newdef\fcnspline{\mfp@listi{fcnspline}\mfp@F}%
  \newdef\periodicfcnspline{\mfp@listi{fcnspline}\mfp@T}%
  \newlet\closedpolyline\polygon
  \newlet\polyline\lines
%    \end{macrocode}
%
% The next six macros have an optional argument called `tension', a
% numerical value that controls how tightly the path turns at each point
% in the list. If the optional argument is absent (or empty), the
% \grafbase{} command that is written takes only a boolean argument
% (closed or not closed) followed by the list of points. If the tension
% argument is present, a different comamnd is written that also has a tension
% argument. The command name is almost the same, but has a `\gbc{t}'
% prepended. The default tension is the \cs{grafbase}{} variable
% \gbc{default_tension}, set with \cs{settension}, initialized to 1.
% Tension of 0 is ignored (ultimately tension is divided by) and may
% produce error messages from \MF{}.
%
% \DescribeMacro{\curve}
% \cs{curve} draws a smooth curve connecting a list of points. it arranges
% for the curve, at point $p\sb n$ to be traveling parallel to the direction
% from $p\sb {n-1}$ to $p\sb {n+1}$ (except at the first and last point).
%
% \DescribeMacro{\closedcurve}
% The closed version \cs{closedcurve} treats the
% first point and last point the same as the rest. It has the alias
% \DescribeMacro{\cyclic}
% \cs{cyclic}.
%
% \DescribeMacro{\convexcurve}
% This convex version produces a smooth curve that is convex in those
% places where \cs{polyline} (with the same list of points) would produce
% a convex shape.
% \DescribeMacro{\closedconvexcurve}
% It also comes in a closed version, with the alias
% \DescribeMacro{\convexcyclic}
% \cs{convexcyclic}.
%
% \DescribeMacro{\mfbezier}
% This produces the standard \MF{} cubic B\'ezier using the \MF{} path
% join operator (\mfc{..}) with tension given by an optional argument.
% \DescribeMacro{\closedmfbezier}
% The closed version connects the last point to the first in the same way.
%
% The command \cs{mfp@curve} examines the optional argument and writes
% the command name (first argument, possibly modified) with the
% appropriate arguments (the boolean or tension plus boolean).
%    \begin{macrocode}
  \newdef\curve{\mfp@curve{curve}\mfp@F}%
  \newdef\cyclic{\mfp@curve{curve}\mfp@T}%
  \newdef\convexcurve{\mfp@curve{ccurve}\mfp@F}%
  \newdef\convexcyclic{\mfp@curve{ccurve}\mfp@T}%
  \newdef\mfbezier{\mfp@curve{bezier}\mfp@F}%
  \newdef\closedmfbezier{\mfp@curve{bezier}\mfp@T}%
  \newlet\closedcurve\cyclic
  \newlet\closedconvexcurve\convexcyclic
%    \end{macrocode}
%
% \DescribeMacro{\fcncurve}
% A `function curve' is the graph of a function of $x$. It should always
% travel left to right. This is not guaranteed by the \cs{curve} macro,
% above, even if the $x$ coordinates are listed in order. \cs{fcncurve} is
% guaranteed to do this if the list of points has the $x$ coordinates so
% ordered.
%
% While the optional argument is called tension, it is not quite the
% same as the tension argument to \cs{curve}, but it has a similar effect.
% The default value is the sane as for \cs{curve}. The above guarantee is
% voided if the value used is ${}\le1/3$.
%    \begin{macrocode}
  \newdef\fcncurve{\mfp@nullopt\mfp@fcncurve}%
%    \end{macrocode}
%
% \DescribeMacro{\turtle}
% Many years ago there was a tool for teaching programming concepts to
% young children. They could draw a figure on a screen by programming a
% `turtle' with a sequence of turns and distances. The following is
% similar. It has a mandatory argument containing a list of ordered pairs.
% The first is the coordinates of the starting point, and each of the rest
% is interpreted as a displacement from the current position, along which
% a line segment is to be drawn. The terminal point of that segment is the
% new current position
%    \begin{macrocode}
  \newdef\turtle{\mfp@listmac{turtle}}%
%    \end{macrocode}
%
% \DescribeMacro{\brownianmotion}
% Used by me once to ilustrate Brownian motion. The argument consists of
% a starting point, the number of steps, and a scale factor, separated
% by commas. It draws a polyline starting with the starting point moving
% in a random direction a random distance, then repeating that from the
% new point, etc., for the number of steps given. The size of each step is
% random, but the scale factor gives the average size.
%    \begin{macrocode}
  \newdef\brownianmotion##1{\mfp@figmac{brownianpath (##1)}}%
%    \end{macrocode}
%
% \subsubsection{Graphing functions}\label{functions}
%
% \DescribeMacro{\function}
% \prog{Mfpic} provides the ability to plot the graph of any function that
% can be defined in \MF. This is done with the \cs{function} command, a
% figure macro which takes one optional parameter that selects
% the smoothness of the \MF{} path produced. It can be \oarg{p}, which
% draws a polyline path through selected points (much like \cs{polyline}),
% or \oarg{s\meta{tension}} which selects a smooth path (much like
% \cs{curve}\oarg{\meta{tension}}). The tension may be omitted and then
% will be 1 (or the value set by \cs{settension}). The default optional
% argument is \oarg{s}, a smooth curve with the default tension.
%
% There are two mandatory arguments. The second is the function, which
% must be written as a formula (strictly speaking, a \MF{} numerical
% expression) containing only one variable, \texttt{x}. The first
% mandatory argument contains three numbers separated by commas. They are,
% in order, the starting value of \texttt{x}, the ending value, and the
% step size.
%
% \DescribeMacro{\parafcn}
% \cs{parafcn} is similar, except its formula must be an ordered pair of
% formulas (strictly speaking, a \MF{} pair expression) in which
% \texttt{t} is the only variable.
%
% \DescribeMacro{\plrfcn}
% \cs{plrfcn} is similar, except its argument is a formula (a \MF{}
% numeric expression) representing the radius, in which \texttt{t} is the
% only variable, interpreted as the angle coordinate, $\theta$, in degrees.
%
% These three commands are so alike that they call the same macro
% with the name to be written as the first argument and the default
% optional argument as the second. The latter is so that we can reuse it
% for two other commands where the default is different.
%    \begin{macrocode}
  \newdef\function{\mfp@fcn{function}s}%
  \newdef\parafcn{\mfp@fcn{parafcn}s}%
  \newdef\plrfcn{\mfp@fcn{plrfcn}s}%
%    \end{macrocode}
%
% \DescribeMacro{\btwnfcn}
% The region between two functions \cs{btwnfcn} is a figure macro. It is
% mostly intended for shading or other filling operations so it is already
% closed and, by default, it is not `smooth'. Its parameters are the
% same as those of \cs{function} (above), with two exceptions: the default
% optional argument is \oarg{p} and it has an additional mandatory
% argument, the other function. The resulting \MF{} path travels along the
% graph of the first function from the starting $x$ to the ending $x$,
% thence vertically to the graph of the second function, along it (in
% reverse) to the starting $x$ and finally, vertically to the start of the
% first function's graph.
%
% \DescribeMacro{\btwnplrfcn}
% We also have the polar function version, where the two function
% arguments are as in \cs{plrfcn}. The default option is also \oarg{p}.
% As with \cs{function}, these are implemented by calling a common
% command with the basename of the \grafbase{} command as argument.
%
% \DescribeMacro{\plrregion}
% This is like \cs{btwnplrfcn} with 0 as the first function, but it
% is more efficient. It takes only the other function as an argument.
% Again, the default option is \oarg{p}.
%
% \DescribeMacro{\belowfcn}
% This is like \cs{btwnfcn} with 0 as the first function, but it
% is more efficient. It takes only the other function as an argument.
% The default option is \oarg{p}.
%    \begin{macrocode}
  \newdef\btwnfcn{\mfp@btwn{btwnfcn}}%
  \newdef\btwnplrfcn{\mfp@btwn{btwnplrfcn}}%
  \newdef\belowfcn{\mfp@fcn{belowfcn}p}%
  \newdef\plrregion{\mfp@fcn{plrregion}p}%
%    \end{macrocode}
%
% \DescribeMacro{\levelcurve}
% One way to graph a function of two variables is to draw level curves.
% The figure macro \cs{levelcurve} takes an optional smoothness
% argument (\texttt{[s\meta{tension}]} or \texttt{[p]} with \texttt{p}
% being the default), and two mandatory arguments. The first
% mandatory argument is a `seed' point which is known to lie inside the
% level curve, followed by a comma and a step size. The second is an
% inequality between the function and the level value that is true inside
% the level curve. Strictly speaking, the last argument can be any \MF{}
% boolean valued expression with variables \mfc{x} and \mfc{y}. The simple
% example,\\
%    \indent\verb$\levelcurve[p]{(0,0),0.1}{x*x + y*y < 3}$\\
% will draw approximately the circle with radius $\sqrt3$ as a sequence of
% line segments with length $0.1$. That will require about 108 segments.
% Its parameters are similar enough to those of \cs{function} that we
% can use the same interface.
%    \begin{macrocode}
  \def\levelcurve{\mfp@fcn{levelset}p}%
%    \end{macrocode}
%
% We now define two macros for depicting the solution of an
% ordinary differential equation. THe first of these, \cs{DEgraph},
% produces the graph of solutions of equations of the form
% $$
%  \frac{dy}{dx} = f(x,y),\quad y(x_0) = y_0.
% $$
% The data required are the \emph{initial values} (the two numbers $x_0$
% and $y_0$), the formula $f(x,y)$ (an explicit \MF{} numerical expression
% with literal variables \mfc{x} and \mfc{y} as the only unknowns. Since
% the \MF{} and only handle paths connecting discrete points, also
% required is a step size which, roughly speaking, is the distance between
% points in graph coordinates, and the number of steps $N$ to use. The \MF{}
% macros then calculate $N$ additional points (the first is $(x_0,y_0)$) and join
% them together to produce the graph.
%
% The second macro, \cs{DEtrajectory}, draws the trajectory of a
% two-dimentional differential equation of the form
% $$
%   \left( \frac{dx}{dt}, \frac{dy}{dt}\right) = (f(x,y,t),g(x,y,t)\,,
%        \quad (x(0),y(0)) = (x\sb0,y\sb0)
% $$
% This is not, strictly speaking, a \emph{graph} since that would
% require three dimensions to indicate the relation between $x$, $y$, and
% $t$. Mathematicians call it a trajectory, and it only shows the
% two-dimensional path followed by the moving object. The required data
% are an initial point $(x_0,y_0)$, the formula for the right-hand side
% (an explicit \MF{} pair-valued expression or a pair of numerical
% expressions in parentheses, with literal variables \mfc{x}, \mfc{y} and
% \mfc{t} as the only unknowns. Also required are a step size and the
% number of steps, as in \cs{DEgraph}.
%
% The method used to calculate the points to connect is a modified version
% of the four-step Runge-Kutta method. The modifications are intended to
% avoid numerical overflow. That is, infinite blow-up in finite time. An
% example is the simple equation
% $$
%    \frac{dy}{dx} = y^2 \quad y(0) = 1,
% $$
% whose solution is $y = 1/(1-x)$. The usual definition of
% Runge-Kutta-IV would have one process equally spaced $x$-values. If a
% user had no idea of the character of the solution, and asked for $N$
% $x$-values with separation $h$ to get a graph on $0\le x \le Nh$, and if
% $Nh > 1$, then the result would be either quite different from the actual
% solution (especially around $x=1$), or would reach a point of numerical
% overflow.
%
% Thus our macros require the user to supply a parameter that will be
% interpreted as a distance step: if $h$ is this parameter, instead of
% finding values of $y$ at $x_0$, $x_0+h$, $x_0+2h$, etc., it finds points
% $(x_n,y_n)$ on the graph so that the two-dimensional distance from $(x_0,y_0)$
% to $(x_1,y_1)$ is $h$, then the distance from $(x_1,y_1)$ to $(x_2,y_2)$
% is also $h$, etc. The resulting graph therefore simply follow the graph
% of $y = 1/(1-x)$ a distance roughly $Nh$ and numerical overflow is
% impossible unless the value of $Nh$ exceeds \MF{}'s size limits.
%
% There is an optional smoothness parameter as in \cs{function}.
%    \begin{macrocode}
  \newdef\DEgraph{\mfp@fcn{odeRKIV}s}%
  \newdef\DEtrajectory{\mfp@fcn{xyRKIV}s}%
%    \end{macrocode}
%
%
% \subsection{Plotting data from files}\label{datafiles}
%
% \DescribeMacro{\plotdata}
% The optional parameter is the smoothness, which may be
% \oarg{s\meta{tension}} for a smooth path or \oarg{p} for a polygonal
% path, or empty to select the default. The default is \oarg{p} when
% \mfpic{} is loaded, but can be changed with \cs{smoothdata} and restored
% with \cs{unsmoothdata}.
%    \begin{macrocode}
  \newdef\plotdata{\mfp@nullopt\mfp@plotdata}%
%    \end{macrocode}
%
% \DescribeMacro{\datafile}
% \cs{datafile} defines a path connecting the points in a datafile. It has
% an optional parameter for the smoothness, as in \cs{plotdata}.
%    \begin{macrocode}
  \newdef\datafile{\mfp@nullopt\mfp@datafile}%
%    \end{macrocode}
%
% \subsection{The prefix commands}\label{prefixcommands}
%
% \subsubsection{Storing and reusing a figure}\label{storing}
%
% \DescribeMacro{\store}
% This stores an \mfpic{} path in a \MF{} path variable. The argument is
% the variable name. It should be followed by an \mfpic{} figure macro
% (such as \cs{rect}\marg{...}). The stored path can be reused via the
% \cs{mfobj} command. This command is written as a \cs{mfp@rendmac} even
% though it does no rendering. This is so (1)~it will turn off implicit
% rendering (any rendering must be explicitly written) and (2) it can be
% placed anywhere within the prefix area. This is new behavior with
% version 0.7. Prior to this it was required to place the path to be
% stored as a second argument. Though that argument could contain other
% prefixes in addition to the path, it was required that no other prefixes
% precede \cs{store}. Note that \cs{store} takes a second argument but
% it merely puts it back. This is so that the old syntax (with the figure
% macro in braces) will continue to work.
%
% \DescribeMacro{\norender}
% Occasionally it is useful to turn off rendering (say we want to add an
% arrowhead to a subpath of a path that is already rendered). One could
% put \cs{store} at the start with an unused name, but as every path is
% already stored in \gbc{curpath}, that seems redundant. So here is a
% prefix macro with null rendering and no side effects. It is exactly
% like \cs{mfp@rendmac}, except it does not end with \cs{mfsrc}.
%    \begin{macrocode}
  \newdef\store##1##2{\mfp@rendmac{stored (##1)}##2}%
  \newdef\norender{\mfp@first\@mfprendfalse}%
%    \end{macrocode}
%
% \DescribeMacro{\mfobj}
% This is the interface to use a \cs{store}-d object.
% \cs{mfobj}\marg{\meta{name}} is a figure macro, and should act exactly
% the same as if the figure macro that had been stored in the variable
% were typed in its place. Its one argument is the variable name.
% \DescribeMacro{\mpobj}
% The macro \cs{mpobj} is just another name for the same command.
%    \begin{macrocode}
  \newlet\mfobj\mfp@figmac \newlet\mpobj\mfobj
%    \end{macrocode}
%
% \DescribeMacro{\mfpimage}
% The command \cs{mfpimage} starts a group in which drawing commands
% work just as usual, except they draw in a picture variable, whose name
% is the only mandatory argument to \cs{mfpimage}.
% \DescribeMacro{\endmfpimage}
% The command \cs{endmfpimage} ends that group. There is an optional
% argument to set the reference point of the created picture, the default
% being \gbc{(0,0)}. The resulting picture can then be placed using
% \cs{putmfpimage}.
%    \begin{macrocode}
  \newdef\mfpimage{\mfp@defaultopt\mfp@image{(0,0)}}%
  \newdef\endmfpimage{\mfcmd{\@nl concludeimage}}%
%    \end{macrocode}
%
% \DescribeMacro{\putmfpimage}
% This takes the name of a picture variable created with the
% \cs{mfpimage} environment (or even with the \cs{tile} environment), and
% places it with its reference point at the points in a list.
%    \begin{macrocode}
  \newdef\putmfpimage##1{\mfsrc{\@nl putimage (##1)}\mfp@writedata}%
%    \end{macrocode}
%
% \subsubsection{Subpaths}
%
% \DescribeMacro{\cutoffbefore}
% This macro take one mandatory argument which is an object stored with
% \cs{store}. It modifies the path it is prefixed to so that it starts
% at its first point of intersection with the object, cutting off any
% earlier part of the path.
%
% \DescribeMacro{\cutoffafter}
% This is similar, except the modified path ends at the last point of
% intersection between the following path and the object, cutting off
% any later part of the path.  It is internally the same as applying
% \cs{cutoffbefore} to the reversed path and reversing the result.
%
% \DescribeMacro{\trimpath}
% This trims off the specified absolute amounts from the start and end of
% the path. The amounts can be specified as two absolute dimensions
% separated by a comma, or a single dimension. In the second case, that
% dimension is used at both the start and end.
%
% The implementation uses \cs{mfp@modi} which simply reads the argument
% and writes it (via \cs{mfp@modmac}) as a set of parameters to the
% appropriate \grafbase{} command. With \cs{trimpath}, however, we have to
% parse that argument with \cs{mfp@getdimens}.
%    \begin{macrocode}
  \newdef\cutoffafter {\mfp@modi{cutoffafter}}%
  \newdef\cutoffbefore{\mfp@modi{cutoffbefore}}%
  \newdef\trimpath##1{\mfp@getdimens##1,,\mfp@end
    \mfp@modi{trimmedpath}\mfp@thedimens}%
%    \end{macrocode}
%
% \DescribeMacro{\partpath}
% This produces a subpath of the following path. Its mandatory argument
% contains two numbers separated by a comma. The numbers should be between
% 0 and 1 and produce a fraction of the following path.
% \DescribeMacro{\subpath}
% The macro \cs{subpath} has a similar argument, but the numbers are
% between $0$ and the number of segments in the path, and it produces the
% equivalent of \MF's \mfc{subpath} primitive.
%    \begin{macrocode}
  \newdef\partpath{\mfp@modi{partialpath}}%
  \newdef\subpath{\mfp@modi{gsubpath}}%
%    \end{macrocode}
%
% \subsubsection{Drawing a curve}\label{drawing}
%
% These are rendering macros that draw the curve in some fashion: solid,
% dashed, colored, etc.
%
% \DescribeMacro{\draw}
% \cs{draw} takes one optional argument, a color. In \MF{}, where the
% color commands return a numeric, if it is ${}\ge 1$ (representing white)
% the path is subtracted from the picture, otherwise it is drawn in black
% (the default). The default in \MP{} is \gbc{drawcolor}.
%
% We signal the use of the default color by passing a null optional
% argument. Because several commands handle color the same way, and all
% are rendering macros, we have a common macro that only needs the name of
% the \grafbase{} command.
%    \begin{macrocode}
  \newdef\draw{\mfp@nullopt{\mfp@clroptrend{drawn}}}%
%    \end{macrocode}
%
% \DescribeMacro{\doubledraw}
% Behaves something like \cs{draw}, except it draws a  double line. It
% takes two optional arguments; the first is the distance between the
% centers of the two lines (default \gbc{2penwd}) and the second is a
% color.
%    \begin{macrocode}
  \newdef\doubledraw{\mfp@defaultopt\mfp@doubledraw{2penwd}}%
%    \end{macrocode}
%
% \DescribeMacro{\dashed}
% \cs{dashed} and \cs{dotted} take one optional argument, which should
% contain the length of the dashes (diameter of
% \DescribeMacro{\dotted}
% dots) and the length of the spaces between, separated by a comma.
%
% Several rendering macros take an optional argument which is written as
% the first parameter of a \grafbase{} command. Thus all are handled with
% a single macro whose arguments are the name of the command and the
% default for the optional argument.
%    \begin{macrocode}
  \newdef\dashed{\mfp@optrendi{DASHED}{\the\dashlen,\the\dashspace}}%
  \newdef\dotted{\mfp@optrendi{dotted}{\the\dotsize,\the\dotspace}}%
%    \end{macrocode}
%
% \cs{gendashed} takes one mandatory argument, the name of a dash pattern
% previously defined by \cs{dashpattern}. The implementing macro,
% \cs{mfp@rendi}, is like the above, except it doesn't need to perform the
% option processing.
%    \begin{macrocode}
  \newdef\gendashed{\mfp@rendi{gendashed}}%
%    \end{macrocode}
%
% \DescribeMacro{\zigzag}
% This draws a zigzag, crossing from one side of the following path to
% the other. It has one required argument containing four dimensions,
% \meta{dim$\sb1$} through \meta{dim$\sb4$}, separated by commas. What is
% drawn depends on whether the path is closed or open. For an open path,
% this draws the start of the path for a distance \meta{dim$\sb1$},
% followed by zigzags, followed by the end of the path for a distance
% \meta{dim$\sb2$}. For a closed path the first two dimensions are
% ignored and the zigzags follow the entire path.
%
% The last two dimensions define the size and slant of each `zig'. If we
% think of the zigzags as representing a periodic wave, \meta{dim$\sb3$}
% is the wavelength and \meta{dim$\sb4$} is the amplitude (distance from
% the true path to the sharp points).
%
% \DescribeMacro{\sinewave}
% This is similar, but the result is a smooth sinewave shaped rendering.
%
% \DescribeMacro{\coil}
% This creates a coil, or corkscrew-shaped rendering. In this case
% \meta{dim$\sb3$} is the distance from one loop to the next and
% \meta{dim$\sb4$} is the maximum distance to each side of the path.
% An alias,
% \DescribeMacro{\corkscrew}
% \cs{corkscrew}, is provided.
%
% Both \cs{sinewave} and \cs{corkscrew} take an optional `tension'
% argument that affects the smoothness of the result. The default is $1$
% and the higher the value the closer they become to a zigzag.
%    \begin{macrocode}
  \newdef\zigzag{\mfp@rendi{zigzag}}%
  \newdef\sinewave {\mfp@defaultopt{\mfp@wiggle{sinewave}}1}%
  \newdef\coil{\mfp@defaultopt{\mfp@wiggle{corkscrew}}1}%
  \newlet\corkscrew\coil
%    \end{macrocode}
%
% \cs{plot} is like \cs{dotted}, except the dots are variously shaped
% symbols. It takes one optional argument containing the size of the
% symbol and the spacing, separated by a comma, and one mandatory
% argument, the name of the symbol. This can in principal be any
% expression of type \mfc{picture} or \mfc{path}. (In \MP, type
% \mfc{string} is also permitted). For the size parameter to work
% correctly, the symbol should be a path, and it should have 1
% as it's natural size. \Mfpic{} provides the predefined paths
% \texttt{Triangle}, \texttt{Square}, \texttt{Circle}, \texttt{Star},
% \texttt{Diamond}, \texttt{Plus}, \texttt{Cross} and \texttt{Asterisk}.
% The first 5 have filled-in versions: \texttt{SolidTriangle}, etc.
%
% The utility \cs{mfp@optrendii} is similar \cs{mfp@optrendi} except it
% takes an additional argument, in this case, the first mandatory argument
% of \cs{plot}.
%    \begin{macrocode}
  \newdef\plot{\mfp@optrendii{doplot}{\the\pointsize,\the\symbolspace}}%
%    \end{macrocode}
%
% \DescribeMacro{\plotnodes}
% Sometimes, rather than equally spaced dots or symbols, we would rather
% have a symbol at each `node' of the following path. If the path is
% created by a list macro, then usually each point in the list is a node
% (but some of the spline paths are exceptions). For other figures, the
% nodes can seem pretty random. For example, a \cs{circle} command without
% optional argument produces a curve with 8 equally spaced nodes, but with
% optional argument the nodes depend on how it is drawn and the size of
% any angle parameter.
%
% \cs{plotnodes} has almost the same syntax as \cs{plot}, but since it
% places the symbols only at the nodes of the path, there is no spacing
% parameter in the optional argument.
%    \begin{macrocode}
  \newdef\plotnodes{\mfp@optrendii{plotnodes}{\the\pointsize}}%
%    \end{macrocode}
%
% \DescribeMacro{\showcontrols}
% Mainly for debugging, this places a symbol at the precontrol and
% postcontrol of each node, and draws a line segment from each symbol to
% the node. The names of two symbols are given in a mandatory argument,
% separated by commas. As a special case, if either symbol is just the
% number `\mfc{0}', it is not drawn. There is an optional argument for
% the size of these symbols. If the size is zero, neither symbol is drawn.
% That is useful if one only wants to see the line segments.
%    \begin{macrocode}
  \newdef\showcontrols{\mfp@optrendii{showcontrols}{\the\pointsize}}%
%    \end{macrocode}
%
% \subsubsection{Closing a curve}\label{closing}
%
% There are several commands used to close paths (by prefixing them to
% figure macros). The \grafbase{} commands that implement closing have a
% common naming pattern. They all contain the string `\texttt{closed},
% to which is added a distinguishing prefix. If the command takes a
% tension argument, the letter `\texttt{t}' is appended. The corresponding
% command without the `\texttt{t}' calls it with a default tension value.
%
% These macros all call \cs{mfp@close}, feeding it the proper prefix and
% the tension value (empty if there is no tension option).
%
% \DescribeMacro{\sclosed}
% The first, \cs{sclosed}, closes smoothly in the same manner that
% \cs{curve} creates a smooth path.
% \DescribeMacro{\bclosed}
% The second, \cs{bclosed}, uses an ordinary \MF{} B\'ezier. These two
% have an optional argument: the amount of tension to put in the
% connecting link. This makes no sense with the rest.
%
% \DescribeMacro{\lclosed}
% The macro \cs{lclosed} always draws a straight line from the end of a
% path to its start.
%
% \DescribeMacro{\cbclosed}
% The macro \cs{cbclosed} computes a closure by calculating cubic B-spline
% control points from the path data and then generating a connecting
% spline (see \cs{cspline}).
% \DescribeMacro{\qbclosed}
% The macro \cs{qbclosed} is similar, but quadratic B-splines are used.
%
% \DescribeMacro{\uclosed}
% At one time \cs{uclosed} was defined in a more complicated manner than
% necessary, but actually produced exactly the same path as \cs{bclosed}.
% So now they are just made to be equal.
%    \begin{macrocode}
  \newdef\bclosed{\mfp@nullopt{\mfp@close b}}%
  \newdef\sclosed{\mfp@nullopt{\mfp@close s}}%
  \newdef\lclosed{\mfp@close l{}}%
  \newdef\cbclosed{\mfp@close{cb}{}}%
  \newdef\qbclosed{\mfp@close{qb}{}}%
  \newlet\uclosed\bclosed
%    \end{macrocode}
%
% \DescribeMacro{\makesector}
% Takes a following arc and draws the sector (even if the center point
% is not known). It really only works if prefixed to one of the
% \cs{arc} commands, but it will attempt to create something even for
% other paths. It calculates the center of the circle containing the arc
% and connects that to the endpoints with two straight lines.
%    \begin{macrocode}
  \newdef\makesector{\mfp@modmac{makesector}}%
%    \end{macrocode}
%
% \subsubsection{Filling a closed curve}\label{filling}
%
% The next few prefix macros fill the interior of the closed path that
% follows with some sort of pattern. The path must be closed; if not,
% the path will simply be drawn with a solid line.
%
% \DescribeMacro{\tess}
% \cs{tess} takes one mandatory argument, the name of a previously defined
% tile (see subsection~\ref{composite}), and fills with shifted copies of
% the tile.
%    \begin{macrocode}
  \newdef\tess{\mfp@rendi{tess}}%
%    \end{macrocode}
%
% \DescribeMacro{\shade}
% \cs{shade} is implemented in \MF{} by filling a region with a pattern
% of dots, simulating gray. It take one optional parameter, the separation
% between dots, defaulting to \cs{shadespace}. The size of the dots is
% set by issuing the command \cs{shadewd}. In \MP{} a gray fill is
% used but the syntax is the same. It would be better to just use
% \cs{gfill} instead (described later).
%
% \DescribeMacro{\polkadot}
% This command is actually meant to fill with a pattern of large dots.
% It also takes the separation between dots (default \cs{polkadotspace})
% as an optional argument. The command \cs{polkadotwd} sets the size of
% the dots.
%    \begin{macrocode}
  \newdef\shade{\mfp@optrendi{shade}{\the\shadespace}}%
  \newdef\polkadot{\mfp@optrendi{polkadot}{\the\polkadotspace}}%
%    \end{macrocode}
%
% \DescribeMacro{\thatch}
% The hatching macros mostly take two optional parameters, the
% separation of the hatching lines (default \cs{hatchspace}) and their
% color. One slight exception is \cs{thatch}, which is called by all the
% others. Its first optional argument is the separation \emph{and} the
% angle (default $0$) of the lines, separated by a comma. The other
% hatching macros have a fixed angle.
% \DescribeMacro{\lhatch}
% The macro \cs{lhatch} has lines at a $-45$ degree angle (upper left to
% lower right),
% \DescribeMacro{\rhatch}
% \cs{rhatch} produces the opposite diagonal (angle $45$ degrees), and
% \DescribeMacro{\xhatch}
% \cs{xhatch} does both sets of lines (cross hatching).
%    \begin{macrocode}
  \newdef\thatch{\mfp@defaultopt\mfp@thatch{\the\hatchspace,0}}%
  \newdef\lhatch{\mfp@defaultopt\mfp@lhatch{\the\hatchspace}}%
  \newdef\rhatch{\mfp@defaultopt\mfp@rhatch{\the\hatchspace}}%
  \newdef\xhatch{\mfp@defaultopt\mfp@xhatch{\the\hatchspace}}%
  \newlet\hatch\xhatch
%    \end{macrocode}
%
% \DescribeMacro{\gfill}
% \cs{gfill} take one optional argument, the color with which to fill.
% Under \MF{} the color must be a numeric (representing a level of gray)
% or one of the color functions, which are defined in \file{grafbase.mf}
% to return numeric values.
%
% \DescribeMacro{\gclear}
% \cs{gclear} will actually fill with the color \texttt{background} in \MP.
% This merely covers what originally was there.
%
% \DescribeMacro{\gclip}
% \cs{gclip} clears the outside of a region, but it is a true clip
% operation, completely different from \cs{gclear}.
%    \begin{macrocode}
  \newdef\gfill{\mfp@nullopt{\mfp@clroptrend{filled}}}%
  \newdef\gclear{\mfp@rendmac{unfilled}}%
  \newdef\gclip{\mfp@rendmac{Clip}}%
%    \end{macrocode}
%
% \subsubsection{Modifying a curve}\label{transforming}
%
% The following are transformation prefixes. They are all (except
% \cs{reverse}, for reasons covered in section~\ref{prefix}) implemented
% with \cs{mfp@modmac}. Most have a mandatory argument, the parameters of
% the transformation. Because of the implementation, one can insert
% rendering macros between a transformation macro and the path being
% transformed, and they will apply to the untransformed path.
%
% If the \env{mfpic} environment has different $x$ and $y$ scales, the
% \cs{rotatepath} and \cs{reflectpath} compensates so that the result is
% congruent to the original. This is what users seem to expect. The rest
% do not compensate and users don't seem to mind.
% \begin{itemize}
% \item \cs{reverse} and \cs{xyswappath} have no argument.
% \item \cs{rotatepath} takes  \marg{\meta{point},\meta{angle}}.
% \item \cs{shiftpath} takes  \marg{\meta{pair}}.
% \item \cs{scalepath} takes  \marg{\meta{center of scaling},\meta{factor}}.
% \item \cs{xscalepath} takes  \marg{\meta{x-center},\meta{factor}}.
% \item \cs{yscalepath} takes  \marg{\meta{y-center},\meta{factor}}.
% \item \cs{slantpath} takes  \marg{\meta{y-pivot},\meta{factor}}.
% \item \cs{xslantpath} = \cs{slantpath}.
% \item \cs{yslantpath} takes  \marg{\meta{x-pivot},\meta{factor}}.
% \item \cs{reflectpath} takes \marg{\meta{point1},\meta{point2}}, the
% endpoints of a `mirror'.
% \item \cs{transformpath} takes \marg{\meta{transformer}}, a \MF{}
%       `transformer' (see ``The \MF book'', page~212).
% \end{itemize}
%
% All of them simply write the \grafbase{} command of nearly the same
% name, with the same arguments, via
% \cs{mfp@modi}.\SpecialUsageIndex{\reverse}
% \SpecialUsageIndex{\xyswappath}\SpecialUsageIndex{\rotatepath}
% \SpecialUsageIndex{\shiftpath}\SpecialUsageIndex{\scalepath}
% \SpecialUsageIndex{\xscalepath}\SpecialUsageIndex{\yscalepath}
% \SpecialUsageIndex{\slantpath}\SpecialUsageIndex{\xslantpath}
% \SpecialUsageIndex{\yslantpath}\SpecialUsageIndex{\reflectpath}
% \SpecialUsageIndex{\transformpath}
%
%    \begin{macrocode}
  \newdef\reverse{\mfp@addmac{reverse}}%
  \newdef\xyswappath{\mfp@modmac{xyswappedpath}}%
  \newdef\rotatepath{\mfp@modi{rotatedpath}}%
  \newdef\shiftpath{\mfp@modi{shiftedpath}}%
  \newdef\scalepath{\mfp@modi{scaledpath}}%
  \newdef\xscalepath{\mfp@modi{xscaledpath}}%
  \newdef\yscalepath{\mfp@modi{yscaledpath}}%
  \newdef\slantpath{\mfp@modi{xslantedpath}}%
  \newlet\xslantpath\slantpath
  \newdef\yslantpath{\mfp@modi{yslantedpath}}%
  \newdef\reflectpath{\mfp@modi{reflectedpath}}%
  \newdef\transformpath{\mfp@modi{transformedpath}}%
%    \end{macrocode}
%
% \DescribeMacro{\parallelpath}
% This is not an affine transformation, but is a transformation of sorts.
% It tries to define a curve that parallels the following curve at a fixed
% distance. The mandatory argument is the separation, in graph units. It
% is sort of experimental and  will probably fail if the path that follows
% is too wild. Since \cs{doubledraw} shares code with \cs{parallelpath},
% that too will probably fail in similar circumstances.
%    \begin{macrocode}
  \newdef\parallelpath{\mfp@modi{parapath}}%
%    \end{macrocode}
%
% \DescribeMacro{\randomizepath}
% This, too, is a nonaffine transformation. It tries to define a curve
% that remains smooth if the original is, but applies random shifts to the
% nodes and random changes to the direction at each node.
%
% The only argument is mandatory and consists of a maximum shift (in graph
% units) and a `weirdness' (a pure number) separated by a comma.
%
% The maximum shift can be a number, in which case it is the maximum
% possible distance and there is no preferred direction, or it can be an
% ordered pair, in which case it gives maximum horizontal and vertical
% shift amounts.
%
% The `weirdness' is applied to path directions. If it is 0, there is no
% change in directions of the path at nodes. If it is a positive number
% $w$, a random angle of up to $\pm 30 w$ is added to the directions at
% each node. Also a random scaling between $2^{-w}$ and $2^w$ is applied
% to the control vectors. Also, if a path has a corner, the angle between
% the two sides is randomly adjusted to be between $2^{-w}$ and $2^w$
% times its original size.
%
% \DescribeMacro{\randomlines}
% This is a simpler version whose mandatory argument contains only the
% maximum shift parameter. It shifts the nodes and connects the results
% with straight lines.
%    \begin{macrocode}
  \newdef\randomizepath{\mfp@modi{randompath}}%
  \newdef\randomlines{\mfp@modi{randomlines}}%
%    \end{macrocode}
%
% \DescribeMacro{\arccomplement}
% This can precede an arc and then returns its complement. It starts at
% the last point of the following arc and ends at the beginning of that
% arc. The sense of the resulting arc (clockwise or anticlockwise) is the
% same as the arc it is applied to. If the following path is not an arc,
% the result is an arc that connects the end of the path to the beginning,
% but may bear no obvious relation to that path.
%    \begin{macrocode}
  \newdef\arccomplement{\mfp@modmac{arccomplement}}%
%    \end{macrocode}
%
% \subsubsection{Adding arrowheads (and tails)}\label{arrows}
%
% Paths can now have heads and tails and something placed in the
% middle. Also the head, tail or the `something' can be any symbol. In
% addition to the \cs{plotsymbol} possibilities, there is \gbc{Arrowhead},
% which is the arrowhead of previous \mfpic{} versions, as well as
% \gbc{Leftharpoon} and \gbc{Rightharpoon}, which are the left and right
% halves.
%
% Intended for middle or tail of an arrow are \gbc{Crossbar}, \gbc{Leftbar}
% and \gbc{Rightbar}, and for the tail there are \gbc{Lefthook} and
% \gbc{Righthook}. \gbc{Crossbar} cuts right across the shaft
% (perpendicular unless a rotation option is present) while \gbc{Leftbar}
% extends to the left (from the point of view of someone facing in the
% direction of the path. Similarly \gbc{Lefthook} curls to the left of the
% arrow's shaft.
%
% All the new arrow commands take one mandatory argument, the name of the
% symbol, followed by up to four optional arguments. Three of the optional
% arguments are the same for all commands: these set the color, the size
% and the amount of rotation of the symbol. Normally the symbol is
% adjusted to `point' in the direction of the path (\gbc{Crossbar} is
% actually perpendicular to it); with the rotation option it can be
% adjusted.
%
% For example, \oarg{c red} makes the symbol red, \oarg{l 5pt} or \oarg{s
% 5pt} scales the symbol so its nominal size or length is 5 points,
% \oarg{r 10} rotates the symbol 10 degrees (anticlockwise) from its
% default position.
%
% The other optional argument depends on the command: for heads it is an
% amount to shift the head backward, for tails the amount to shift it
% forward, and for things placed in the middle, it is the fraction of the
% length of the path along which the symbol is placed.
%
% For example, \oarg{b 2pt} shifts a head two points backward, \oarg{f
% 2pt} shifts a tail 2 points forward and \oarg{f .5} puts the symbol
% right in the middle.
%
% The letters are mnemonics, being the initial letters of the words
% `color', `length' or `size', `rotate', `back', and `forward' or
% `fraction'. Actually, the letters \texttt{s} and \texttt{l} have
% identical effects since I couldn't decide which mnemonic was more
% natural. Oddly, \texttt{b} and \texttt{f} have identical effects also.
% So if you accidentally use \oarg{b 2pt} for a tail, it will still be
% shifted \emph{forward}! The reason for this is that these \mfpic{}
% commands all correspond to \grafbase{} commands that have the same
% argument structure. Both \texttt{b} and \texttt{f} simply cause the
% accompanying value to be written into the fourth argument, while the
% different commands use that argument differently. (You can shift a
% tail backwards with a negative argument, if you really need that.)
%
% \DescribeMacro{\arrowhead}\SpecialUsageIndex{\arrow}
% The \cs{arrowhead} command has a star-form which allows part of the
% path beyond the tip of the arrowhead to be erased. The presence of a
% star ultimately changes the \MF{} command passed on to later macros.
% It does so by passing to \cs{mfp@arrowhead} the word `\texttt{true}' for
% the star-form and `\texttt{false}' otherwise.
%
% The old \cs{arrow} command first checks for a star, and passes to
% \cs{mfp@arrow} either an `\texttt{x}' or an empty parameter. This is
% used to construct the \grafbase{} command name. We use \cs{def}
% because \prog{eplain} defines one also.
%    \begin{macrocode}
  \newdef\arrowhead{\mfp@ifstar\mfp@arrowhead\mfp@T\mfp@F}%
  \def\arrow{\mfp@ifstar\mfp@arrow{x}{}}%
%    \end{macrocode}
%
% \DescribeMacro{\arrowtail}
% Tails are just like heads except that there is no star-form and the
% \grafbase{} command name (second parameter of \cs{mfp@arr}) is
% different.
% \DescribeMacro{\arrowmid}
% And \cs{arrowmid} is just like \cs{arrowtail} except for the command
% name and the different default for the position optional argument.
%    \begin{macrocode}
  \newdef\arrowtail##1{\mfp@arr 0{tailpath (##1)}}%
  \newdef\arrowmid##1{\mfp@arr{0.5}{midpath (##1)}}%
%    \end{macrocode}
%
% This ends the prefix macros.
%
% \subsection{Transforming the coordinate system}\label{coordinate}
%
% \DescribeMacro{\coords}
% The following apply transforms to the \MF{} coordinate system, and
% these can be localized with the \env{coords} environment. In plain
% \TeX{} \cs{coords} starts the environment and
% \DescribeMacro{\endcoords}
% \cs{endcoords} closes it. The transforms apply when the curve is
% \emph{rendered} and do not affect what paths are defined. Thus, for
% example, \cs{store} will store the same path whatever the state of the
% coordinate system. In terms of \grafbase{} commands, only \gbc{vtr} and
% \gbc{ztr} are changed, and these are only applied when rendering.
%
% \DescribeMacro{\applyT}
% These are implemented by \cs{applyT} which takes as its argument a \MF{}
% `transformer'.
%
% These commands (except \cs{turn}, kept for backward compatibility) have
% no optional arguments, only mandatory arguments containing the
% parameters of the transformation. \cs{rotate} rotates around the origin,
% \cs{rotatearound} rotates around a given point, \cs{turn} takes the point
% as an optional argument, defaulting to $(0,0)$.
%
% Transformations are applied in reverse of the order they appear in the
% file (i.e., the most recent first). This applies even if \env{coords}
% environments are nested, except that at \cs{endcoords} the state at
% the matching \cs{coords} is restored.
%    \begin{macrocode}
  \newdef\coords{\mfsrc{\@nl bcoords\@nl}}%
  \newdef\endcoords{\mfsrc{\@nl ecoords\@nl}}%
  \newdef\applyT##1{\mfsrc{\@nl hide(apply_t (##1))}}%
  \def\rotate##1{\applyT{rotated ##1}}%
  \newdef\rotatearound##1##2{%
    \applyT{rotatedaround (##1, ##2)}}%
  \newdef\turn{\mfp@defaultopt\mfp@turn{(0,0)}}%
  \newdef\reflectabout##1##2{\applyT{reflectedabout (##1, ##2)}}%
  \let\mirror\reflectabout
  \newdef\shift##1{\applyT{shifted ##1}}% pair.
  \def\scale##1{\applyT{scaled ##1}}% same scaling
  \newdef\xscale##1{\applyT{xscaled ##1}}%
  \newdef\yscale##1{\applyT{yscaled ##1}}%
  \newdef\zscale##1{\applyT{zscaled ##1}}%
  \newdef\xslant##1{\applyT{xslant ##1}}%
  \newdef\yslant##1{\applyT{yslant ##1}}%
  \newdef\zslant##1{\applyT{zslant ##1}}%
  \newdef\boost##1{\applyT{boost ##1}}%
  \newdef\xyswap{\applyT{xyswap}}%
%    \end{macrocode}
%
% \subsection{Axes and grids}\label{axes}
%
% An axis would normally not be thought of as a figure macro, because one
% would not want to position them arbitrarily nor transform them. One
% would also not want the hassle of having always to specify the origin,
% etc. However, one would want to occasionally make them dotted or dashed
% or colored.
%
% \DescribeMacro{\axes}
% The original \cs{axes} was therefore not a figure macro. It always drew
% both axes with solid lines.
% \DescribeMacro{\xaxis}
% Later \cs{xaxis} and \cs{yaxis} were introduced, which mimicked the
% behavior of \cs{axes}. For backward
% \DescribeMacro{\yaxis}
% compatibility, the old behavior is supported with the old commands. The
% optional argument to \cs{axes}, \cs{xaxis} and \cs{yaxis} is the length
% of the arrowhead, defaulting to \cs{the}\cs{axisheadlen}.
%    \begin{macrocode}
  \newdef\xaxis{\mfp@defaultopt{\mfp@simple{xaxis}}{\the\axisheadlen}}%
  \newdef\yaxis{\mfp@defaultopt{\mfp@simple{yaxis}}{\the\axisheadlen}}%
  \newdef\axes{\mfp@defaultopt {\mfp@simple{axes}}{\the\axisheadlen}}%
%    \end{macrocode}
%
% \DescribeMacro{\axis}
% When border axes were added, all the code was revamped, and now we
% create axes as figure macros. It also became clear there was so
% much common code that it would be better to implement the syntax
% \cs{axis}\marg{l}, etc., rather than have separate commands \cs{laxis},
% etc. for all six possible axes. Therefore, only the $x$- and $y$-axes
% have their own commands. The \cs{axis} command has one optional argument
% (the arrowhead length) and one mandatory argument, a single letter
% designating the axis to draw.
%
% \DescribeMacro{\axisline}
% The \cs{axisline} command is provided for users who want more control.
% It is a figure macro that produces the corresponding line, and the user
% can use all the flexibility of the \cs{arrowhead} command if necessary.
%    \begin{macrocode}
  \newdef\axis{\mfp@nullopt\mfp@axis}%
  \newdef\axisline##1{\mfp@figmac{axisline.##1}}%
%    \end{macrocode}
%
% \DescribeMacro{\doaxes}
% \cs{doaxes} takes one optional argument, the arrowhead length, and one
% mandatory argument, all the axes to draw. These should be just letters
% with nothing separating them except optional spaces. \cs{doaxes} is
% implemented via the self-looping  macro \cs{mfp@doaxis}.
%
% \DescribeMacro{\border}
% The \cs{border} command is almost equivalent to \cs{doaxes}\marg{lbrt},
% except it is a figure macro. With it, the whole picture can be filled
% with a background color, or outlined in any available rendering.
%    \begin{macrocode}
  \newdef\doaxes{\mfp@nullopt\mfp@doaxes}%
  \newdef\border{\mfp@figmac{borderrect}}%
%    \end{macrocode}
%
% \DescribeMacro{\axismarks}
% Hash marks (or tick marks) on the axes are provided by the
% \cs{axismarks} command (\cs{marks} was the original choice, but that
% turned out to conflict with one of e\kern-.06em\TeX's primitives).
% For brevity, therefore, we also have separate commands
% \DescribeMacro{\xmarks}
% \cs{xmarks},
% \cs{ymarks}\SpecialUsageIndex\ymarks,
% \cs{lmarks}\SpecialUsageIndex\lmarks,
% \cs{bmarks}\SpecialUsageIndex\bmarks,
% \cs{rmarks}\SpecialUsageIndex\rmarks, and
% \cs{tmarks}\SpecialUsageIndex\tmarks.
%
% \cs{axismarks} has two mandatory arguments: the letter for the axis, and
% a comma separated list of numbers giving the positions on the axis. It
% functions as a list macro (see previous discussion of types of macros)
% and so the list of numbers can be prescribed by an external file
% \cs{datafile}\marg{\meta{file}}. One must be sure to issue an
% appropriate \cs{using} command to produce a numeric list in the output.
% This is the main reason for the \cs{usingnumericdefault} command.
%
% I had a change of heart after the \cs{axis} command, and I made things
% simpler to code here by putting the optional argument of \cs{axismarks}
% after the first mandatory argument. I could justify this because I
% expect most users will use the shorter versions that don't require the
% first argument (that is, the expectation that optional arguments come
% first is still satisfied). The optional argument is the length of the
% marks. The position of the marks is controlled separately by the
% \cs{setaxismarks} command, described in section~\ref{othersettings}.
%    \begin{macrocode}
  \newdef\axismarks##1{\mfp@defaultopt{\mfp@marks{##1}}{\the\hashlen}}%
  \newdef\xmarks{\axismarks x}%
  \newdef\ymarks{\axismarks y}%
  \newdef\lmarks{\axismarks l}%
  \newdef\bmarks{\axismarks b}%
  \newdef\rmarks{\axismarks r}%
  \newdef\tmarks{\axismarks t}%
%    \end{macrocode}
%
% \DescribeMacro{\grid}
% The command \cs{grid} is, I think, inaccurately named: the word `grid'
% suggests a set of lines, but this actually produces dots. Its function
% is to allow a visualization of the coordinates. The dots are located at
% the points whose coordinates are integer multiples of two numbers, which
% are given in the single mandatory argument separated by commas. The
% optional first argument is the diameter of the dots. This defaults to
% \cs{griddotsize}, initially \texttt{0.5pt}.
%
% Because of my concerns about the name, I have provided two aliases:
% \cs{gridpoints}\SpecialUsageIndex{\gridpoints} (for consistency with
% \cs{gridlines}, below) and \cs{lattice}\SpecialUsageIndex{\lattice}.
%
% \DescribeMacro{\gridlines}
% Macro \cs{gridlines} has no optional argument and takes the same
% mandatory argument as \cs{grid}. It draws horizontal and vertical lines
% intersecting at all the dots that \cs{grid} would draw. Some packages
% (and \ConTeXt) define a \cs{grid} command so we use \cs{def} here
% instead of \cs{newdef}.
%
% \DescribeMacro{\hgridlines}
% This draws only the horizontal lines and its argument is the separation
% (in graph units) between successive lines.
% \DescribeMacro{\vgridlines}
% \cs{vgridlines} is the vertical version.
%
% No arguments are shown because \cs{mfp@simple} or \cs{mfp@simpli} will
% read what it needs.
%    \begin{macrocode}
  \def\grid{\mfp@defaultopt{\mfp@simplei{vargrid}}{\the\griddotsize}}%
  \newlet\gridpoints\grid \newlet\lattice\grid
  \newdef\gridlines{\mfp@simple{gridlines}}%
  \newdef\vgridlines{\mfp@simple{vgridlines}}%
  \newdef\hgridlines{\mfp@simple{hgridlines}}%
%    \end{macrocode}
%
% \DescribeMacro{\plrgrid}
% The command \cs{plrgrid} takes one mandatory argument which contains two
% numbers separated by a comma. The first is a radius (in graph
% coordinates) and the second an angle. It draws circular arcs at integer
% multiples of the radius, and radial lines at integer multiples of the
% angle. It fills the picture rectangle and is clipped to that rectangle.
%
% \DescribeMacro{\plrgridpoints}
% \cs{plrgridpoints} is similar but places only dots at the intersections
% of these arcs and rays. It takes an optional argument for the size of
% the dots, default \cs{griddotsize}.
% \DescribeMacro{\gridarcs}
% The macro \cs{gridarcs} draws only the arcs. Its only parameter is the
% distance between them (in graph units).
% \DescribeMacro{\gridrays}
% The macro \cs{gridrays} draws only the rays and its parameter is the
% angle separating the rays.
%
% \DescribeMacro{\plrpatch}
% \cs{plrpatch} draws: a circular arc at a starting radius, then
% increments that radius by a step size and draws another arc, etc., and
% finally draws an arc at the ending radius. It does a similar thing for
% radial lines and angles. It takes one mandatory argument, which contains
% $6$ numbers separated by commas: starting radius, ending radius, radius
% step, starting angle, ending angle, angle step.
%    \begin{macrocode}
  \newdef\plrgrid{\mfp@simple{polargrid}}%
  \newdef\plrgridpoints{%
    \mfp@defaultopt{\mfp@simplei{polargridpoints}}{\the\griddotsize}}%
  \newdef\gridarcs{\mfp@simple{gridarcs}}%
  \newdef\gridrays{\mfp@simple{gridrays}}%
  \newdef\plrpatch{\mfp@simple{polarpatch}}%
%    \end{macrocode}
%
% \DescribeMacro{\vectorfield}The \cs{vectorfield} command draws arrows to
% represent a vector field. It takes one optional argument, the length of
% the arrowhead (default \cs{headlen}), and three mandatory arguments. The
% first is like \cs{grid}: it contains two numbers, separated by commas.
% The arrows are located at the points whose coordinates are integer
% multiples of two numbers. The second argument is the formula for the
% vector field. It should consist of a pair expression in which the only
% unknowns are the variables \texttt{x} and \texttt{y}. The last argument
% should contain a boolean expression in which the only unknowns are
% \texttt{x} and \texttt{y}. The macro steps through the relevant set of
% points and draws the vector only if the boolean is true at that point.
% The set of points considered includes only those inside the axis margins
% (set by \cs{axismargin} and related commands). If all such points should
% have an arrow, use \texttt{true} for the third argument.
%    \begin{macrocode}
  \newdef\vectorfield{%
    \mfp@defaultopt{\mfp@vectorfield{}}{\the\headlen}}%
  \newdef\plrvectorfield{%
    \mfp@defaultopt{\mfp@vectorfield{plr}}{\the\headlen}}%
%    \end{macrocode}
%
% \subsection{Visualizing points}\label{points}
%
% \DescribeMacro{\point}
% \cs{point} draws a dot or a small circle. It takes one optional
% argument, the diameter of the dot, and one mandatory argument, the ordered
% pair (or comma separated list of them) at which to draw a dot. After
% \cs{pointfillfalse}, the dots will be unfilled (i.e., small circles),
% after \cs{pointfilltrue} (the default), they will be solid. Like the
% grid macros, it is not a figure macro, but merely does its drawing and
% is not subject to any prefix macros.
%
% \DescribeMacro{\plotsymbol}
% In order to mark points with other than circles, we have the
% \cs{plotsymbol} command, so-called because it uses the same symbols as
% the \cs{plot} command (previously discussed). There is an optional
% argument that gives the size of the symbol, a mandatory argument with
% the name of the symbol, and a second mandatory argument which
% is a comma separated list of ordered pairs for the locations.
%
% For both these commands, the default optional argument is
% \cs{the}\cs{pointsize}. These are list macros: in place of a list of
% points in braces, one can use the \cs{datafile} construct.
%    \begin{macrocode}
  \newdef\point{\mfp@defaultopt\mfp@point{\the\pointsize}}%
  \newdef\plotsymbol{\mfp@defaultopt\mfp@plotsymbol{\the\pointsize}}%
%    \end{macrocode}
%
% \DescribeMacro{\plottext}
% We keep \cs{plottext} for backward compatability. It is equivalent
% to a \cs{tlabel} command with a different default for the justification
% (\oarg{cc}) and the arguments rearranged. The order for \cs{plottext}
% is: optional justification, then \TeX{} label, then list of points.
% Because of the complication involved in making it work, in this case we
% do not allow a datafile to replace the list of points. All this
% command now does is perform a simplified version of the start of the
% \cs{tlabel} command and jump to one of its internals, \cs{mfp@thelabel}.
%    \begin{macrocode}
  \newdef\plottext{\begingroup\mfp@resetwhitespace\mp@mksharpother
    \mfp@defaultopt\mfp@plottext{cc}}%
%    \end{macrocode}
%
% \subsection{Some composite objects}\label{composite}
%
% \DescribeMacro{\tile}
% A tile is syntactically a \MF{} picture variable. The commands between
% \cs{tile} and \cs{endtile} (or \cs{begin}\marg{tile} and
% \cs{end}\marg{tile}) should be any sequence of \mfpic{} figure macros
% with possible prefix macros. They will be drawn not on the main picture
% (\gbc{currentpicture}), but on the picture given by the name in the
% \cs{tile} command's argument.
%
% The argument has five parts separated by commas, the first is the
% name, the second is the unit of length (some absolute dimension like
% \mfc{1pt}), the next two are the width and height (pure numbers, the
% actual dimensions being these numbers times the unit of length), the
% last is one of the words \mfc{true} or \mfc{false}, indicating whether
% tile should be clipped to these dimensions (true) or allowed to extend
% beyond them (false).
%    \begin{macrocode}
  \newdef\tile{\mfp@simple{tile}}%
  \newdef\endtile{\mfcmd{\@nl endtile}}%
%    \end{macrocode}
%
% \DescribeMacro{\patharr}
% A path array is a set of \MF{} path variables each having the same base
% name followed by a different numeric suffix. This command turns off
% rendering and simply assigns these variables in order to the path
% expressions written by the figure macros between \cs{patharr} and
% \cs{endpatharr}. It works by redefining \cs{mfp@storepath}, issued by all
% the figure macros. These variables can be accessed in \mfpic{} by using
% the \cs{mfobj} command. The name of the path array \emph{without} a
% numeric suffix is a \MF{} numeric variable whose value is the number of
% array elements.
%
% \emph{Explicit} rendering commands will work in the sense that the
% affected path will be rendered in addition to being assigned to the
% variable. The only parameter is the common base name of the variables.
%    \begin{macrocode}
  \newdef\patharr##1{\begingroup
    \mfsrc{hide(numeric ##1; path ##1[]; ##1 = 0)}%
    \def\mfp@storepath{\mfsrc{\@nl store (##1[incr ##1])}}%
    \setrender{}}%
  \newdef\endpatharr{\endgroup}%
%    \end{macrocode}
%
% \DescribeMacro{\connect}
% This starts an environment that can contain any sequence of figure
% macros. The environment functions as a single large \cs{mfp@figmac}, the
% figure being the path obtained by connecting all the paths
% \DescribeMacro{\endconnect}
% (up to the following \cs{endconnect} command) by straight lines from the
% end of one to the beginning of the next. It is implemented via a path
% array, so the individual figures within the environment have implicit
% rendering turned off. Explicit rendering commands within the
% environment will have the expected effect.
%
% The \cs{mfp@checklatexenv} at the end allows \cs{connect} to be used as
% a \LaTeX{} environment.
%    \begin{macrocode}
  \newdef\connect{\mfp@figmac{begingroup; save mfpicnexus}%
    \patharr{mfpicnexus}}%
  \newdef\endconnect{\endpatharr
    \mfcmd{\@nl mkpoly (\mfp@F, mfpicnexus)\@nl endgroup}%
    \mfp@checklatexenv{connect}{\aftergroup\@mfpstarttrue}{}}%
%    \end{macrocode}
%
% \subsection{Other graphical features}\label{otherfeatures}
%
% And now for something completely different: pie charts and bar charts
% (or bar graphs, or histograms).
%
% \DescribeMacro{\piechart}
% Actually, nothing is drawn by the \cs{piechart} command; it only defines
% a path array and a few other internal variables.  Since nothing is
% drawn by this command, it makes sense to allow it outside the drawing
% environment, so it has been made available outside \env{mfpic}
% environments with the command name \cs{mfppiechart}(page
% \pageref{charts}).
%
% The \cs{piechart} command takes one optional argument and two mandatory
% argument. The first mandatory argument contains the center and radius of
% the chart separated by a comma; the second is the list of data. The
% optional argument contains a letter and an optional angle. The letter
% can be `\texttt{c}' for clockwise or `\texttt{a}' for anticlockwise and
% determines the direction around the pie the different wedges will be drawn.
% The angle determines the angle of the first edge (in the given
% direction) of the first wedge. The default letter is \texttt{c} and the
% default angle is $90$ degrees, which starts the first wedge at
% 12~o'clock and proceeds from there either clockwise or anticlockwise..
%
% \cs{piechart} acts like a list macro in that the above arguments should
% be followed by either a list of numbers in braces or a \cs{datafile}
% command (with numbers in a datafile). If this feature is used, an
% appropriate \cs{using} command is needed. If the numbers are listed one
% per line, then \cs{usingnumericdefault} should work.
%
% \DescribeMacro{\piewedge}
% Each individual wedge (elements of the above mentioned path array) may
% be drawn using the \cs{piewedge} command, which is a figure macro. That
% command takes one optional argument that determines how the wedge is
% drawn (described below) and one mandatory argument, the number of the
% wedge. Without the optional argument, \cs{piewedge}\marg{1} draws the
% first wedge in the position given by the arguments of the \cs{piechart}
% command, as described above.
%
% The optional arguments can be:
% \begin{itemize}
%   \item \oarg{x\meta{distance}}, the wedge is `exploded': drawn
%     shifted radially outward from the center of the pie chart by
%     \meta{distance} (in graph units).
%   \item \oarg{s(\meta{dx},\meta{dy})}, the wedge is shifted from its
%     position by \meta{dx} horizontally and \meta{dy} vertically (in
%     graph units).
%   \item \oarg{m(\meta{x},\meta{y})}, the wedge is moved so that its
%     point is at coordinates \parg{\meta{x},\meta{y}}.
% \end{itemize}
%    \begin{macrocode}
  \newlet\piechart\mfppiechart
  \newdef\piewedge{\mfp@defaultopt\mfp@piewedge{d}}%
%    \end{macrocode}
%
% \DescribeMacro{\barchart}
% As with \cs{piechart}, the \cs{barchart} command does not actually draw
% anything, but defines a path array, so we make available a version for
% use outside \cs{mfpic} environments: \cs{mfpbarchart} (page
% \pageref{charts}).
%
% The \cs{barchart} command takes one optional and a mandatory
% arguments. The data follow the mandatory argument. Like \cs{piechart},
% the data can be a list in braces or an external file. The data determine
% the length of the bars in graph units. Since version 0.7, the data can
% be a list of numbers or pairs or both. It is difficult to give a
% \cs{using} specification that allows both in an external file, but a
% list in braces is simply written as is and \MF{} has no problems mixing
% them.
%
% Pairs are interpreted as giving the start and end of a bar. Numbers are
% interpreted as giving only the end, with the start at $0$. If a datafile
% is used, an appropriate \cs{using} command should be issued beforehand.
% In that case probably all the data should be pairs or all numeric.
%
% The optional argument determines the position and width of the bars and
% the first mandatory argument determines the orientation. The mandatory
% argument can be \marg{v} for vertical bars with base on the $x$ axis, or
% \marg{h} for horizontal bars with base on the $y$ axis.
% The optional argument contains three numbers separated by commas. The
% first is the coordinate of the leading edge of the first bar, the second
% is the distance (in graph coordinates) between the leading edge of one
% bar and that of the next, and the third is the fraction of that distance
% that is occupied by the bar. The default is \oarg{0,1,1}.
%
% We provide the aliases \cs{bargraph}, \cs{histogram} and \cs{gantt}.
%
% \DescribeMacro{\chartbar}
% The \cs{chartbar} command can then be used to draw a bar (one of the
% members of the just mentioned array). It is a figure macro and take the
% number of the bar as its mandatory argument. Aliases \cs{graphbar},
% \cs{histobar} and \cs{ganttbar} are provided. We avoid \cs{bar} because
% it is already a math accent command. This ends \cs{mfp@grafmacs}.
%    \begin{macrocode}
  \newlet\barchart\mfpbarchart
  \newlet\bargraph\barchart
  \newlet\histogram\barchart
  \newlet\gantt\barchart
  \newdef\chartbar##1{\mfp@figmac{chartbar[##1]}}%
  \newlet\graphbar\chartbar
  \newlet\histobar\chartbar
  \newlet\ganttbar\chartbar
}% end \mfp@grafmacs
%    \end{macrocode}
%\toks0={^^A What's this?
\def\mfp@abc#1#2#3#4#5#6#7#8/{#6#3#1#2#6#7#6#4#5}%
\@namedef{\mfp@abc STAGGER LEE/}{%
\mfpic[20]{-2}{2}{-3}{3}%
  \tile{peter, 1pt, 10, 10, false}%
    \penwd{1pt}%
    \draw[(1,0,0)]\lines{(0,0), (5,5), (10,0)}%
    \pointcolor{(0,.8,0)}%
    \point[3pt]{(2.5,7.5)}%
  \endtile
  \draw\tess{peter}\gfill[(1,1,0)]\ellipse{(0,0),2,3}%
\endmfpic}%
%}
%
% \DescribeMacro{\mfppiechart}
% We make \cs{mfppiechart} and \cs{mfpbarchart}\label{charts} global,
% since all they do is define variables
% \DescribeMacro{\mfpbarchart}
% and arrays.
%    \begin{macrocode}
\newdef\mfppiechart{\mfp@defaultopt\mfp@piechart{c}}%
\newdef\mfpbarchart{\mfp@defaultopt\mfp@barchart{0,1,1}}%
\newlet\mfpbargraph\mfpbarchart
\newlet\mfphistogram\mfpbarchart
\newlet\mfpgantt\mfpbarchart
%    \end{macrocode}
%
% \section{Implementing the graphics macros}
%
% To keep \cs{mfp@grafmacs} from becoming unweildy, we define here all the
% internal commands that are called by the user level macros. We've
% given most of them names that begin \cs{mfp} to keep from overwriting
% other package commands
%
% \cs{arc} and \cs{circle} are defined identically except that the first
% sets a switch to true, the second to false. This selects the spelling of
% the corresponding \grafbase{} command and the value of the first
% argument of \gbc{fallbackpath}. Both \cs{arc} and \cs{circle} then
% call \cs{mfp@arccircle} which takes the optional argument as \arg1,
% and the data required for that option as \arg2. Actually, \cs{arc}
% first checks for a * and then calls \cs{mfp@arc}, which follows the
% above description.
%
% The \gbc{fallbackpath} is a $0$-length path at whatever point is listed
% first in \arg2, it is cyclic in the case of a circle (not that it
% matters for a one-point path).
%    \begin{macrocode}
\newdef\mfp@arc{\mfp@switchtrue\mfp@defaultopt\mfp@arccircle{s}}%
\newdef\arc@or@circle{\ifmfp@switch arc\else circle\fi}%
\newdef\mfp@arccircle#1#2{%
  \@ifundefined{mfp@arc@#1}%
   {\Mfpic@warn{Invalid option; ignoring \mfp@b\arc@or@circle\space
      command.}%
    \mfp@figmac{fallbackpath(\ifmfp@switch\mfp@F\else\mfp@T\fi) (#2)}}%
   {\mfp@figmac{\arc@or@circle\@nameuse{mfp@arc@#1} (#2)}}}%
\newdef\mfp@ellipse#1#2{\mfp@figmac{ellipse (#2, #1)}}%
%    \end{macrocode}
%
% The first argument of \cs{mfp@pshcircle} is a boolean: \texttt{true}
% in the disk case, \texttt{false} for the half-plane. The second argument
% should be \marg{\meta{center},\meta{radius}}.
%    \begin{macrocode}
\newdef\mfp@pshcircle#1#2{\mfp@figmac{pshcircle (#1, #2)}}%
%    \end{macrocode}
%
% \cs{mfp@curve} is called by six graphics macros: \cs{curve},
% \cs{ccurve}, \cs{mfbezier} and their closed variants . Its two arguments
% are the name of a \grafbase{} command, and \mfc{true} or \mfc{false}.
% This works for any \grafbase{} command that creates a smooth path from a
% list of points, provided the command has two versions: one that begins
% with \texttt{t} and takes a tension as the first argument and the other
% without a \texttt{t} that takes the same arguments \emph{except} the
% tension. The second argument of \cs{mfp@curve} determines whether the
% curve is to be closed. These are passed along to \cs{mfp@@curve}, which
% gets the tension as the third argument.
%    \begin{macrocode}
\newdef\mfp@curve#1#2{\mfp@nullopt{\mfp@@curve{#1}{#2}}}%
\newdef\mfp@@curve#1#2#3{%
  \mfp@listmac{\mfp@ifempty{#3}{#1}{t#1 (#3)} (#2)}}%
%    \end{macrocode}
%
% The argument of \cs{mfp@fcncurve} is the optional argument of
% \cs{fcncurve} (the tension).
%    \begin{macrocode}
\newdef\mfp@fcncurve#1{%
  \mfp@listmac{\mfp@ifempty{#1}{fcncurve}{functioncurve (#1)}}}%
%    \end{macrocode}
%
% \cs{mfp@fcn} is called by eight commands: \cs{levelcurve},
% \cs{plrregion}, \cs{belowfcn}, \cs{function}, \cs{plrfcn},
% \cs{parafcn}, \cs{DEgraph} and \cs{DEtrajectory}. They have a common
% argument structure for both the \mfpic{} and \grafbase{} command.
% \cs{mfp@fcn} calls \cs{mfp@dotension} to parse the optional tension
% argument (the second argument) leaving the results in the macros
% \cs{mfp@t} (a \texttt{t} for command name if a tension value was
% present) and \cs{mfp@sval} (\texttt{true} or \texttt{false} and the
% tension value if it was present). The first argument is the base name of
% a \grafbase{} command.
%
% Ultimately, \cs{mfp@@fcn} is called, and only then the two mandatory
% arguments of the calling command are read.
%    \begin{macrocode}
\newdef\mfp@fcn#1#2{%
  \mfp@defaultopt{\mfp@dotension{\mfp@@fcn{#1}}}{#2}}%
\newdef\mfp@@fcn#1#2#3{%
  \mfp@figmac{\mfp@t#1 (\mfp@sval) (#2) (#3)}}%
%    \end{macrocode}
%
% \cs{mfp@btwn} is called by \cs{btwnfcn} and \cs{btwnplrfcn}, with the
% name of a \grafbase{} command as its argument. It does the same tension
% processing as \cs{mfp@fcn} and calls \cs{mfp@@btwn}, which reads the
% three mandatory arguments of the calling command.
%    \begin{macrocode}
\newdef\mfp@btwn#1{%
  \mfp@defaultopt{\mfp@dotension{\mfp@@btwn{#1}}}p}%
\newdef\mfp@@btwn#1#2#3#4{%
  \mfp@figmac{\mfp@t#1 (\mfp@sval) (#2) (#3) (#4)}}%
%    \end{macrocode}
%
% The tension parsing is done by \cs{mfp@@dotension}. It causes
% \cs{mfp@t} to be empty or \texttt{t} depending on the existence of
% the tension parameter, and causes \cs{mfp@sval} to contain either the
% smoothness boolean alone or the boolean followed by the tension value,
% separated by a comma. After this, \cs{mfp@dotension} calls the code it
% is passed in its first argument.
%    \begin{macrocode}
\newdef\mfp@dotension#1#2{\mfp@@dotension#2\mfp@end#1}%
\newdef\mfp@@dotension#1#2\mfp@end{\def\mfp@t{}%
  \if p#1\relax \let\mfp@sval\mfp@F
  \else \let\mfp@sval\mfp@T
    \mfp@ifexist{#2}{\def\mfp@t{t}\edef\mfp@sval{\mfp@sval, #2}}%
  \fi}%
%    \end{macrocode}
%
% \cs{mfp@plotdata} is called by \cs{plotdata}. I follows the scheme of
% most of the data file processing commands: it passes another command (in
% this case \cs{mfp@doplots}) to \cs{mfp@processfile}, which reads the
% filename as its second argument. The argument of \cs{mfp@plotdata},
% which is passed to \cs{mfp@doplots}, is the original optional parameter
% of \cs{plotdata}.
%    \begin{macrocode}
\newdef\mfp@plotdata#1{\mfp@processfile{\mfp@doplots{#1}}}%
%    \end{macrocode}
%
% \cs{mfp@doplots} is a self-looping macro. It issues the rendering
% prefix (in \cs{mfp@setstyle}), increments the linetype, and writes the
% path expression defined by the first set of data in the file (via
% \cs{mfp@@datafile}, which stops at a blank line). That part, when prefixed
% by \cs{mfp@figmacbase}, functions as a \cs{mfp@figmac}. When finished with
% one figure, \cs{mfp@ifenddata} checks if there is another set of data in
% the file. If so, \cs{mfp@doplots} calls itself again.
%
% The argument is the smoothness parameter(s), which it merely passes on.
% There is no filename argument: \cs{mfp@plotdata} has already opened
% the input stream \cs{mfp@data} and subsequent macros will read from it.
%    \begin{macrocode}
\newdef\mfp@doplots#1{\mfp@setstyle
  \advance\mfp@linetype1 \mfp@figmacbase
  \mfp@@datafile{#1}\mfp@ifenddata{}{\mfp@doplots{#1}}}%
%    \end{macrocode}
%
% When two blank lines occur in succession, \cs{plotdata} is suppose to
% stop. \cs{mfp@ifenddata} is called when \cs{mfp@@datafile} ends (one blank
% line was found), it checks for another blank line (or end-of-file)
% and, if it finds one, selects the first of the two alternatives that
% follow.
%    \begin{macrocode}
\newdef\mfp@ifenddata{%
  \ifeof\mfp@data \@xp\@firstoftwo
  \else \mfp@skipcomments
    \ifx\mfp@temp\mfp@par \@XP\@firstoftwo
    \else \@XP\@secondoftwo
    \fi
  \fi}%
%    \end{macrocode}
%
% The \cs{datafile} command, which calls \cs{mfp@datafile} is really
% obsolete, as one can now use \cs{curve} or \cs{polyline} (or any other
% list-to-path command) followed by the \cs{datafile} construct.
% However, it requires only two extra commands and then calls a link in
% the \cs{plotdata} chain of commands, so we keep it.
%
% \cs{mfp@datafile} is called by \cs{datafile}, which passes the optional
% smoothness argument. It does the figure macro stuff, then calls
% \cs{mfp@processfile} to open the data file and run \cs{mfp@@datafile}.
%    \begin{macrocode}
\newdef\mfp@datafile#1{%
  \mfp@figmacbase\mfp@processfile{\mfp@@datafile{#1}}}%
%    \end{macrocode}
%
% \cs{mfp@@datafile} checks for an empty optional parameter and then calls
% \cs{mfp@dodatafile}. We could handle the options earlier in the chain,
% but we would have to do that for both \cs{plotdata} and \cs{datafile}
% since both call on it. It is somewhat more efficient to reproduce a bit
% of the internals of \cs{mfp@defaultopt} just once.
%    \begin{macrocode}
\newdef\mfp@@datafile#1{%
  \mfp@ifempty{#1}%
    {\mfp@dodatafile\mfp@smoothness\mfp@tension}%
    {\mfp@dodatafile#1}\mfp@end}%
%    \end{macrocode}
%
% And \cs{mfp@dodatafile} is mainly just a wrapper, processing the optional
% parameter (passed by either \cs{plotdata} or \cs{datafile}) which
% selects what figure making code should be written. For
% \oarg{s\meta{tension}} a \gbc{curve} command is used. For \oarg{p}, a
% \gbc{polyline}. (The `\cs{mfp@F}' means the curve is not closed).
%
% After that, \cs{mfp@rwdata} is called, which initiates the reading and
% writing of the the data.
%    \begin{macrocode}
\newdef\mfp@dodatafile#1#2\mfp@end{%
  \mfsrc{%
    \if s#1 \mfp@ifempty{#2}{curve }{tcurve (#2) }%
    \else polyline
    \fi (\mfp@F)}\mfp@rwdata}%
%    \end{macrocode}
%
% \cs{mfp@image} is called by \cs{mfpimage} with the optional argument in
% \arg1 and the mandatory argument in \arg2.
%    \begin{macrocode}
\newdef\mfp@image#1#2{\mfsrc{\@nl makeimage (#2, #1)}}%
%    \end{macrocode}
%
% The command \cs{mfp@getdimens} is only called by \cs{trimpath}. Its
% first argument is the comma separated pair of dimensions from that
% command. It defines \cs{mfp@thedimens} to expand to exactly that,
% except: if there is only one dimension and no comma (empty \arg2 and
% \arg3), the result is a pair of dimensions both equal to it; if there is
% a comma, but nothing on one side, it returns \texttt{0pt} for the empty
% side. If a \TeX{} dimension command is used in either position, its
% value is returned.
%
% The only time \arg3 is nonempty is when the original argument of
% \cs{trimpath} contains a comma (then \arg3 is a comma). In that case we
% let \cs{mfp@scratch} keep its previous value.
%    \begin{macrocode}
\newdef\mfp@getdimens#1,#2,#3\mfp@end{%
  \mfp@scratch \@ifmtarg{#1}{\z@}{#1}\relax
  \edef\mfp@thedimens{\the\mfp@scratch}%
  \@ifmtarg{#3}{}{\mfp@scratch \@ifmtarg{#2}{\z@}{#2}\relax}%
  \edef\mfp@thedimens{\mfp@thedimens,\the\mfp@scratch}}%
%    \end{macrocode}
%
% The argument of \cs{mfp@doubledraw} is the optional separation parameter
% passed by \cs{doubledraw}. Then the optional color is processed.
%    \begin{macrocode}
\newdef\mfp@doubledraw#1{%
  \mfp@nullopt{\mfp@clroptrendi{doubledraw}{#1}}}%
%    \end{macrocode}
%
% Parameter \arg1 of \cs{mfp@wiggle} is the name, \gbc{sinewave} or
% \gbc{corkscrew}, \arg2 is the optional argument (tension). The four
% dimension values should follow as the mandatory argument of the calling
% command.
%    \begin{macrocode}
\newdef\mfp@wiggle#1#2{\mfp@rendi{#1 (#2)}}%
%    \end{macrocode}
%
% The utility macros, \cs{mfp@rendi}, \cs{mfp@modi} and \cs{mfp@listi}
% write a command name and one set of parameters. They differ in the setup
% required. The first writes via \cs{mfp@rendmac}, the second via
% \cs{mfp@modmac} and the last via \cs{mfp@listmac}. \cs{mfp@rendii}
% writes two sets of parameters, reversing them. \cs{mfp@optrendi} runs
% \cs{mfp@rendi}, but feeds it the result of processing a optional
% argument. \cs{mfp@optrendii} is similar, running \cs{mfp@rendii}.
%    \begin{macrocode}
\newdef\mfp@rendi#1#2{\mfp@rendmac{#1 (#2)}}%
\newdef\mfp@rendii#1#2#3{\mfp@rendmac{#1 (#3, #2)}}%
\newdef\mfp@optrendi#1{\mfp@defaultopt{\mfp@rendi{#1}}}%
\newdef\mfp@optrendii#1{\mfp@defaultopt{\mfp@rendii{#1}}}%
\newdef\mfp@modi#1#2{\mfp@modmac{#1 (#2)}}%
\newdef\mfp@listi#1#2{\mfp@listmac{#1 (#2)}}%
%    \end{macrocode}
%
% A great many \grafbase{} rendering commands come in two parts: one
% command takes a color argument and the other command simply calls the
% color version with a default color. In all these commands, the name of
% the first is just the second with `\texttt{color}' prepended. This means
% that the corresponding \mfpic{} rendering commands can share a common
% macro, \cs{mfp@clropt}, which is passed the optional color and the name of
% the second command.
%
% To simplify the output file, if a command's color option is empty
% (signaling the default color) the `\texttt{color}'-free \grafbase{}
% command name is written, otherwise the command name beginning with
% `\texttt{color}' is written along with the color parameter.
% \cs{mfp@clropt} makes the test and writes the command. \arg1 is the
% color argument and \arg2 is the command's base name. The commands
% \cs{mfp@clroptrend} and \cs{mfp@clroptrendi} provide useful
% abbreviations when the command is a rendering command and the
% \grafbase{} command takes no argument or one argument beside the color.
%
% There are a number of commands that are not subject to prefixes. For
% this we have \cs{mfp@simple}. It reads a command name and its
% arguments and writes the command, followed by the arguments wrapped in
% parentheses, followed by a semicolon. We also have \cs{mfp@simplei}
% which reads an additional argument.
%    \begin{macrocode}
\newdef\mfp@clropt#1#2{\mfp@ifempty{#1}{#2}{\mfp@C#2 (#1)}}%
\newdef\mfp@clroptrend#1#2{\mfp@rendmac{\mfp@clropt{#2}{#1}}}%
\newdef\mfp@clroptrendi#1#2#3{\mfp@rendmac{\mfp@clropt{#3}{#1} (#2)}}%
\newdef\mfp@simple#1#2{\mfcmd{\@nl #1 (#2)}}%
\newdef\mfp@simplei#1#2#3{\mfcmd{\@nl #1 (#2, #3)}}%
%    \end{macrocode}
%
% All the path closing commands are implemented with \cs{mfp@close}. It
% writes the closing command determined by the first argument, with a
% `\texttt{t}' plus the second argument as a parameter, if that is not
% empty.
%    \begin{macrocode}
\newdef\mfp@close#1#2{\mfp@modmac{#1closed\mfp@ifexist{#2}{t (#2)}}}%
%    \end{macrocode}
%
% These next implement hatching. Except for \cs{mfp@xhatch}, they all call
% \cs{mfp@thatch}. The argument of these is the optional argument of the
% calling command. The second optional argument of that command (the
% color) is processed by \cs{mfp@clroptrendi}.
%    \begin{macrocode}
\newdef\mfp@thatch#1{\mfp@nullopt{\mfp@clroptrendi{thatch}{#1}}}%
\newdef\mfp@lhatch#1{\mfp@thatch{#1,-45}}%
\newdef\mfp@rhatch#1{\mfp@thatch{#1,45}}%
\newdef\mfp@xhatch#1{\mfp@nullopt{\mfp@clroptrendi{xhatch}{#1}}}%
%    \end{macrocode}
%
% The all-purpose \cs{mfp@arr} sets the default values for the
% \cs{mfp@h...} commands (two of which are passed as parameters). This
% is accomplished by the \cs{mfp@arr@\meta{x}} commands. The
% next two commands constitute a loop that ends when no more options
% follow. Each turn through the loop the initial letter is checked and the
% value that follows it is stored in one of those macro (possibly
% replacing some default). Ultimately, \cs{mfp@doarrow} writes the
% code to the output file.
%    \begin{macrocode}
\newdef\mfp@arrowhead#1#2{\mfp@arr 0{Gheadpath (#1) (#2)}}%
\newdef\mfp@arrow#1{\mfp@arr 0{headpath#1}}%
\newdef\mfp@arr#1#2{\mfp@arr@c{}\mfp@arr@l{\the\headlen}%
  \mfp@arr@b{#1}\edef\mfp@hcommand{#2}\mfp@arr@r{0}\mfp@@arr}%
\newdef\mfp@@arr{\@ifnextchar[{\mfp@arropt}{\mfp@doarrow}}%
\newdef\mfp@arropt[#1]{%
  \mfp@ifexist{#1}{\mfp@@arropt#1\mfp@end}\mfp@@arr}%
\newdef\mfp@@arropt#1#2\mfp@end{%
  \mfp@ifempty{#2}%
   {\Mfpic@warn{Arrow option #1 has no value\on@line; %
      it will be ignored.}}%
   {\@ifundefined{mfp@arr@#1}%
     {\Mfpic@warn{Arrow option #1 invalid \on@line; %
        it will be ignored}}%
     {\@nameuse{mfp@arr@#1}{#2}}%
   }}%
\newdef\mfp@doarrow{%
  \mfp@addmac{\mfp@clropt{\mfp@hcolour}{\mfp@hcommand} (\mfp@hlength, %
    \mfp@hrotate, \mfp@hlocate)}}%
%    \end{macrocode}
%
% Implement the optional argument of \cs{turn} with \cs{mfp@turn}.
%    \begin{macrocode}
\newdef\mfp@turn#1#2{\rotatearound{#1}{#2}}%
%    \end{macrocode}
%
% The first argument of \cs{mfp@axis} is the optional argument of
% \cs{axis}. Unfortunately, the $x$ and $y$ axis have one default head
% length, \cs{axisheadlen} (initially \texttt{5pt}), while the side
% axes have a different default, \cs{sideheadlen} (initially \texttt{0pt}).
% Therefore we don't know which default to use until the mandatory argument
% is read. In retrospect, it would have been better to put the optional
% argument after the mandatory one. So if there is no optional argument,
% the first argument of \cs{mfp@axis} is empty rather than a default.
%
% We use \cs{mfp@getaxis} to check the mandatory argument and return the
% default head length in \cs{mfp@defheadlen}. It also stores the
% letter in \cs{mfp@axisletter}, but returns `\texttt{x}' for an invalid
% one.
%
% The letter argument \arg{2} is permitted to be a word, provided it
% begins with one of the allowed letters. The `\marg{(none)}' is there to
% provide an argument (and an informative error message) in the unlikely
% case that this argument is empty.
%
% The \cs{mfp@addmac} command is the internal code that \cs{arrow[l \#1]}
% would produce. This is slightly more efficient than calling \cs{arrow}.
%    \begin{macrocode}
\newdef\mfp@axis#1#2{\mfp@getaxis#2{(none)}\mfp@end\axis
  \mfp@addmac{headpath (\mfp@emptysub{#1}{\mfp@defheadlen}, 0, 0)}%
  \axisline{\mfp@axisletter}}%
\newdef\mfp@doaxes#1#2{\def\mfp@@axis##1{\mfp@axis{#1}{##1}\mfp@@doaxis}%
  \mfp@@doaxis#2\mfp@end}%
\newdef\mfp@@doaxis{\mfp@ifend{}\mfp@@axis}%
%    \end{macrocode}
%
% The six commands for putting hashmarks on an axis call \cs{mfp@marks}
% with the axis letter and the optional length of the marks. Note that
% the location of the marks is a list of numbers, so it is picked up by
% \cs{mfp@writedata} just as in \cs{mfp@listmac}. But it is not a figure
% macro, so we cannot use \cs{mfp@listmac} itself.
%    \begin{macrocode}
\newdef\mfp@marks#1#2{\mfsrc{\@nl #1marks (#2)}\mfp@writedata}%
%    \end{macrocode}
%
% Called by \cs{vectorfield} or \cs{plrvectorfield} after processing the
% optional argument, the following simply writes the appropriate
% \grafbase{} code. The first argument is either empty or the string
% `\texttt{plr}'.
%    \begin{macrocode}
\newdef\mfp@vectorfield#1#2#3#4#5{%
  \mfcmd{#1vectorfield (#2, #3) (#4) (#5)}}%
%    \end{macrocode}
%
% The first argument of both these is the optional size argument of the
% calling commands (\cs{point} and \cs{plotsymbol}). For
% \cs{mfp@plotsymbol} the second argument is the symbol name.
%    \begin{macrocode}
\newdef\mfp@point#1{%
  \mfsrc{\@nl pointd (#1, \ifpointfill\mfp@T\else\mfp@F\fi)}%
  \mfp@writedata}%
\newdef\mfp@plotsymbol#1#2{%
  \mfsrc{\@nl plotsymbol (#2, #1)}\mfp@writedata}%
%    \end{macrocode}
%
% \cs{mfp@plottext} now simply calls the \cs{tlabel} code, since that can
% now handle a list of points.
%    \begin{macrocode}
\newdef\mfp@plottext#1#2#3{\tlabeljustify{#1}%
  \def\tl@points{#3}\mfp@toks{#2}\mfp@thelabel\endgroup}%
%    \end{macrocode}
%
% The first argument of \cs{mfp@piechart} is the optional argument of
% \cs{piechart}. It comes in two parts: a letter and an optional angle,
% so \cs{mfp@@piechart} is used to parse it. A similar description
% applies to \cs{piewedge}.
%    \begin{macrocode}
\newdef\mfp@piechart#1{\mfp@@piechart#1\mfp@end}%
\newdef\mfp@@piechart#1#2\mfp@end#3{% #3 = center,radius
  \mfsrc{\@nl piechart(\if a#1 \else-\fi1, %
      \mfp@emptysub{#2}{90}, #3)}\mfp@writedata}%
\newdef\mfp@piewedge#1{\mfp@@piewedge#1\mfp@end}%
\newdef\mfp@@piewedge#1#2\mfp@end#3{% #3=number
  \mfp@figmac{(piewedge[#3]%
    \mfp@ifexist{#2}%
     {\if #1x shifted (#2*piedirection[#3])%
      \else\if #1s shifted (#2)%
      \else\if #1m shifted (#2 - piecenter)%
      \fi\fi\fi})}}%
%    \end{macrocode}
%
% The optional argument of \cs{barchart} becomes \arg{1} and the data is
% \arg{2}.
%    \begin{macrocode}
\newdef\mfp@barchart#1#2{%
  \mfsrc{\@nl barchart (#1, \if h#2\mfp@F\else\mfp@T\fi)}%
  \mfp@writedata}%
%    \end{macrocode}
%
%
% \section{The \env{mfpic} environment}\label{mfpicenv}
%
% \subsection{Initializing the environment}\label{mfpicinitializations}
%
%  For mostly historical reasons, the macros that create labels are
% redefined anew with each \env{mfpic} environment. These have gradually
% grown in number and size. We are still doing this, but the internal
% part of these commands have now been moved outside the environment,
% and only the user lever commands are localized.
%
% \DescribeMacro{\everymfpic}
% This takes a token list and saves it in \cs{every@mfpic} to be issued
% at the very end of the \cs{mfpic} command. There is a companion macro
% \DescribeMacro{\everyendmfpic}
% that is issued at the very beginning of \cs{endmfpic}. These are always
% global, otherwise they are defined much like \cs{everytlabel}.
%    \begin{macrocode}
\newdef\everymfpic{\afterassignment\@everymfpic\mfp@toks}%
\newdef\everyendmfpic{\afterassignment\@everyendmfpic\mfp@toks}%
\newdef\@everymfpic{\edef\every@mfpic{\the\mfp@toks}}%
\newdef\@everyendmfpic{\edef\every@endmfpic{\the\mfp@toks}}%
\everymfpic{}\everyendmfpic{}%
%    \end{macrocode}
%
% \DescribeMacro{\mfpic}
% This command (or the \LaTeX{} environment \cs{begin}\marg{mfpic}) takes
% two optional arguments: the xscale and the yscale. When both are
% omitted, they are both set to 1, if the yscale is omitted, it is set
% equal to the xscale.
%
% There are also 4 mandatory arguments: the first two give the minimum and
% maximum extent of the $x$ coordinates and the last two do the same for the
% $y$ coordinates. The coordinates used in the figure commands within an
% mfpic environment are multiplied by the corresponding scales, and that
% is the multiple of \cs{mfpicunit} used in positioning, drawing, etc.
%
% The optional arguments are converted by the option handling code to
% mandatory arguments for \cs{@mfpic}, which contains the actual
% definition.
%    \begin{macrocode}
\newdef\mfpic{\mfp@defaultopt\@mfpicA{1}}%
\newdef\@mfpicA#1{\mfp@defaultopt{\@mfpic{#1}}{#1}}%
\newdef\@mfpic#1#2#3#4#5#6{%
%    \end{macrocode}
%
% We start by saving \mfpic's extra fontdimen values. They will be
% restored by \cs{endmfpic}. This makes the values local (font dimensions
% are normally always global). Also, we save \cs{mfpicunit} using an
% internal name to prevent users from changing it midpicture.
%
% Then we begin a group to localize ordinary
% \TeX{} definitions and assignments, disable writes to the output if
% \cs{opengraphsfile} hasn't occurred yet (an error), save the current
% font in \cs{@tcurr} for restoration inside text labels and captions, set
% the switch that says we are in an \cs{mfpic} environment, disable
% \cs{par} so that blank lines have (little or) no effect, and switch to
% \cs{nullfont} so that stray characters (always an error) and spaces (not
% an error) have no effect. I don't know whether \cs{relax} is a better
% disabling definition for \cs{par} than \cs{@empty}.
%    \begin{macrocode}
  \save@mfpicdimens
  \begingroup % ended near end of \endmfpic
  \@mfpicunit\mfpicunit
  \mfp@safe@activestrue
  \mfp@ifopengraphsfile{}%
   {\ifmfp@nowrite\else \mfp@nooutput@error\mfpic
      \def\mfp@src##1##2{\endgroup}%
    \fi}%
  \mfp@DBlog{Starting mfpic \number\mfp@count \on@line.}%
  \@xp\let\@xp\@tcurr\the\font
  \let\ifin@mfpicenv\iftrue
  \let\par\@empty
  \nullfont
%    \end{macrocode}
%
% The graphics macros are undefined outside the \env{mfpic} environment.
% They are defined now by invoking \cs{mfp@grafmacs}.
%
% One can add to \cs{mfp@additions} to extend \mfpic. Currently it
% is empty.
%    \begin{macrocode}
  \mfp@grafmacs
  \mfp@additions
%    \end{macrocode}
%
% We also define the coordinate conversion macros \cs{@xconv} and
% \cs{@yconv} via \cs{mfp@setconv}. These are used to calculate the
% nominal dimensions of the picture and to position \TeX{} labels.
%
% We make all the arguments of \cs{@mfpic} available to the user. Macro
% \cs{mfp@setconv} now also makes use of them.
% \begin{itemize}
%   \item  the x-scaling factor.
% \DescribeMacro{\xfactor}
%   \item  the y-scaling factor.
% \DescribeMacro{\yfactor}
%   \item  the leftmost x-coordinate.
% \DescribeMacro{\xmin}
%   \item  the rightmost x-coordinate.
% \DescribeMacro{\xmax}
%   \item  the leftmost y-coordinate.
% \DescribeMacro{\ymin}
%   \item  the rightmost y-coordinate.
% \DescribeMacro{\ymax}
% \end{itemize}
%
% We are going to add all text labels to a box \cs{@alltlabels} and put
% that whole box on top of the graph during \cs{endmfpic}.
% We initialize the box here, as well as the dimensions \cs{@tlabelsbot},
% etc.
%    \begin{macrocode}
  \edef\xfactor{#1}\edef\yfactor{#2}%
  \edef\xmin{#3}\edef\xmax{#4}\edef\ymin{#5}\edef\ymax{#6}%
  \mfp@setconv
  \mfp@inittlabels
%    \end{macrocode}
%
% The graph is loaded into a box register at the end of the \env{mfpic}
% environment. The size of that box register may have to correspond to the
% arguments of the \cs{mfpic} command. Since \cs{endmfpic} doesn't receive
% these arguments we process them now.
%
% Dimensions \cs{@graphright}, etc., represent the extent of the graph
% box. We increase them when the text is added if it extends beyond the
% edges of the graph. These are all font dimensions, so they are global
% assignments.
%    \begin{macrocode}
  \@xconv\xmax\@graphright
  \@yconv\ymax\@graphtop
  \@graphleft 0pt
  \@graphbot  0pt
%    \end{macrocode}
%
%  \subsection{Initializing the \MF{} picture}
%  \label{current}
%
% Each \env{mfpic} environment produces a \gbc{beginmfpic...endmfpic}
% environment in the output file. Here we initialize the variables that
% correspond there to the 6 arguments and \cs{mfpicunit}, then begin the
% \MF{} environment. \gbc{beginmfpic} takes the number of the current
% figure as its only argument. For debugging purposes we write a \MF{}
% comment the contains the line number in the \TeX{} source file where the
% \cs{mfpic} command occurred. We also write a line of dashes
% (\cs{mfp@d}) to make it easier to find the start of the environment. This
% may be removed in the public release.
%
% When \opt{mplabels} is in effect we need to set the font for the labels
% to the saved \cs{@tcurr} by writing some \mfc{verbatimtex} code. Since
% \opt{mplabels} can be turned on at any time, we write this whenever the
% \opt{metapost} option is in effect. It is a common misconception that
% \mfc{verbatimtex} can be used only once at the start of a \MP{} file. In
% fact it can be used any number of times. It's purpose is to be at an
% outer level, while \mfc{btex} is localized inside a box
%    \begin{macrocode}
  \mfsrc{\@nl \mfp@p\mfp@d\mfp@d<\number\mfp@count>\@nl
    unitlen := \the\@mfpicunit\mfp@s;\@nl
    xscale := #1; yscale := #2;\@nl
    bounds (#3, #4, #5, #6);\@nl
    \@nl
    beginmfpic(\number\mfp@count); \mfp@p\space\mfp@lineno.
    \mfp@ifmpost
     {\@nl verbatimtex \relax
      \bgroup\font\noexpand\MFPcfont=\fontname\@tcurr\relax
      etex;}{}}%
%    \end{macrocode}
%
% \subsection{Placing text labels}\label{textlabels}
%
% All the rest of \cs{@mfpic} defines commands that in some way or another
% produce labels. The easiest part is defining \cs{tlabel} under
% \opt{mplabels} where most of the work takes place in \file{grafbase.mp}.
% The most involved is the definition of \cs{tlabel} without
% \opt{mplabels}. All the rest (except \cs{tcaption}) add labels by
% calling \cs{tlabel} or one of its internal commands. Some of those could
% be simpler under \opt{mplabels} but then we'd need two versions of each.
%
% \DescribeMacro{\tlabel}
% This is the common code, processing optional arguments, etc. for
% \cs{tlabel}. It, and the first several commands it calls, set switches
% and macros based on the arguments. The first argument is optional: the
% justification (the default is that set with the \cs{tlabeljustify}
% command), the second is a location or locations, and the last is the
% \TeX{} code that constitutes the label. All these are ultimately stored
% as macros and then either \cs{mp@tlabel} or \cs{tex@tlabel} is called
% without arguments.
%
% The location can be in the form \parg{\meta{x},\meta{y}}, but if \MP{}
% is processing labels we would like to be able to use \MP{} expressions,
% which can contain parentheses and commas. This would mess up \TeX's
% token matching for reading the two coordinates. Therefore we allow the
% whole point to be enclosed in braces. Under \opt{mplabels} the contents
% of the braces will be written to the output file without any further
% parsing. Without \opt{mplabels}, the braces should contain a comma
% separated list of locations in the previously described syntax.
%
% We start things off by calling \cs{mfp@label} to process the optional
% argument, feeding it an empty one if none is present.
%    \begin{macrocode}
  \newdef\tlabel{\mfp@nullopt\mfp@label}%
%    \end{macrocode}
%
% We allow some \cs{tlabels} to be placed behind the picture rather than
% on top. This is easy under \opt{mplabels}: just use \cs{tlabel} before
% any rendering commands (making sure \opt{overlaylabels} is turned off.)
% However, \MP{} labels can contain only fonts and one would often want
% to do this with an included graphic (as a background). After
% \DescribeMacro{\startbacktext}
% \cs{startbacktext}, labels are saved in a special place to be included
% behind the \mfpic{} graphic. This continues until
% \DescribeMacro{\stopbacktext}
% \cs{stopbacktext}.
%
% We simply turn off \gbc{overlaylabels} and turn on \gbc{backtextlabels}
% for \MP{}. We also save the box \cs{@alltlabels} in \cs{@wholegraph}
% (which will not be needed until \cs{endmfpic}) and then reinitialize it.
% At \cs{endbacktext} we copy the box \cs{@alltlables} into \cs{@backtext},
% and then restore what we changed. We let the values of \cs{@tlabelsleft},
% etc., be updated normally as labels are added to the backtext.
%    \begin{macrocode}
  \newdef\startbacktext{\let\mfp@restoreOL\@empty
    \mfp@ifmpost
     {\ifmfp@overlabels
        \let\mfp@restoreOL\overlaylabels\nooverlaylabels
      \fi \setmfboolean{underlaylabels}{\mfp@T}}{}%
    \setbox\@wholegraph \box\@alltlabels
    \setbox\@alltlabels \vbox{\hbox{}}}%
  \newdef\stopbacktext{%
    \setbox\@backtext  \box\@alltlabels
    \setbox\@alltlabels\box\@wholegraph
    \mfp@ifmpost{\setmfboolean{underlaylabels}{\mfp@F}}{}%
    \mfp@restoreOL}%
%    \end{macrocode}
%
% \subsection{Surrounding the label with a path}\label{surrounding}
%
% These next macros place labels, but also define a path surrounding the
% label. This allows one to clear a space for the label, create a
% background, draw a box around it, etc., all in one command (with the
% appropriate sequence of prefixes). They take two optional arguments.
% The first optional argument depends on the type of path being created.
% It is described below. The second one is the justification as in the
% \cs{tlabel} command. There are two mandatory arguments, the location
% (same syntax as for \cs{tlabel} except it cannot be a list) and the text.
% They also have star-forms, which create the path but don't place the
% label.
%
% All the curves are sized to just contain what I will call the
% \emph{label strip}. Imagine a rectangle that just fits around the text.
% Now extend it on all sides by the value defined with \cs{tlpathsep}.
% This rectangle is the label strip.
%
% \DescribeMacro{\tlabelrect}
% \cs{tlabelrect} creates the rectangular boundaries of the label strip by
% default. With the optional argument a rectangle with rounded corners is
% produced; the optional argument is the radius of the quarter circles used.
% These quarter circles pass through the corners of the label strip and are
% joined together with straight lines to create the rest of the rectangle.
% As a special case, the optional argument can contain the keyword
% `\texttt{roundends}' to produce a rectangle with the short sides
% replaced by a semicircle. If the radius is negative, the corners are
% concave.
%
% \DescribeMacro{\tlabeloval}
% \cs{tlabeloval} produces an ellipse which, by default has the same
% aspect ratio as the label strip. It's size just includes the label strip,
% and it passes through the four corners. The optional argument contains a
% numerical factor $m$ that changes the width and the height so that the
% width-to-height ratio is multiplied by $m$, but the ellipse still
% passes through those four corners. The default value of $m$ is 1.
% Negative $m$ has the same effect as $|m|$. If $m=0$ a rectangle is
% produced.
%
% \DescribeMacro{\tlabelellipse}
% \cs{tlabelellipse} produces an ellipse, where the optional argument $a$
% is the ratio of its width to its height. The default for $a$ is 1, which
% produces a circle. Negative $a$ has the same effect as $|a|$. If $a =
% 0$, a rectangle is produced.
%
% \DescribeMacro{\tlabelcircle}
% To get a circle one can use \cs{tlabelellipse} without the optional
% argument, or with argument \oarg{1}. However, it makes for a more
% readable source if the command reflects the shape. \cs{tlabelcircle} is
% defined to be essentially \cs{tlabelellipse}\oarg{1}, but it first
% checks for the \texttt{*} and passes it along in front of the \oarg{1}.
%
% We implement the other three by calling \cs{mfp@labelpath} with the name
% of the curve (\texttt{rect}, \texttt{oval}, or \texttt{ellipse}) and the
% default value of the optional argument (\texttt{0}, \texttt{1}, and
% \texttt{1}, respectively) as arguments.
%    \begin{macrocode}
  \newdef\tlabelrect{\mfp@labelpath{rect}{0}}%
  \newdef\tlabeloval{\mfp@labelpath{oval}{1}}%
  \newdef\tlabelellipse{\mfp@labelpath{ellipse}{1}}%
  \newdef\tlabelcircle{%
    \mfp@iftoken*{\tlabelellipse*[1]}{\tlabelellipse[1]}}%
%    \end{macrocode}
%
% \subsection{Placing multiple text labels}\label{multiple}
%
% One of the more onerous things about labels in \env{mfpic} environments
% used to be the shear amount of typing required. The following commands
% are intended to reduce the work by having to repeat only the arguments.
%
% \DescribeMacro{\tlabels}
% This command takes only one argument containing any sequence of valid
% arguments for the \cs{tlabel} command, optionally separated by
% whitespace (but not blank lines).
%
% We begin a group, reset whitespace to normal, and call the command that
% reads the argument.
%    \begin{macrocode}
  \newdef\tlabels{\begingroup
    \mfp@resetwhitespace\mp@mksharpother \mfp@labels}%
%    \end{macrocode}
%
% Labelling axes generates a lot of \cs{tlabel} commands, or a single
% \cs{tlabels} command with a lot of arguments. Given that such labels
% have much in common (e.g., for the $x$ axis the $y$ coordinate and the
% justification are usually the same for all the labels) we can do still
% better at abbreviating this task.
%
% \DescribeMacro{\axislabels}
% The \cs{axislabels} command takes a mandatory argument (the axis)
% followed by an optional argument (the justification, as in the
% \cs{tlabel} command), followed by another mandatory argument, a comma
% separated list of items of the form \marg{\meta{label}}\meta{coord}. The
% label is placed at that coordinate on the given axis.
%
% Here we call \cs{mfp@axislabel}, feeding it the arguments of the current
% \cs{@mfpic} command.
%    \begin{macrocode}
  \newlet\axislabels\mfp@axislabels
%    \end{macrocode}
%
% \subsection{Captions}\label{captions}
%
% Captions are not added immediately by the \cs{tcaption} command. That
% command redefines \cs{mfp@docaption} to add it, and \cs{endmfpic}
% executes \cs{mfp@docaption}. For now, \cs{mfp@docaption} does nothing.
%
% \DescribeMacro{\tcaption}
% \cs{tcaption} takes an optional argument that holds two numbers,
% separated by a comma. The first number determines the maximum width of a
% one line caption. Captions larger than that multiple of the width of the
% graphic will be reset as a paragraph, whose lines have length the second
% number times the width of the graph. The defaults are \oarg{1.2,1}.
%    \begin{macrocode}
  \let\mfp@docaption\@empty
  \newdef\tcaption{\mfp@defaultopt\mfp@caption{1.2,1.0}}%
%    \end{macrocode}
%
% Finally, invoke the \cs{everymfpic} tokens.
%    \begin{macrocode}
  \every@mfpic}% End of \@mfpic
%    \end{macrocode}
%
%  \section{Implementing the label and caption macros}
%
% \cs{mfp@setconv} uses the stored arguments of the surrounding
% \env{mfpic} environment: \cs{xfactor} and \cs{yfactor}
% are the scale factors; \cs{xmin} and \cs{ymin} are the coordinates of
% the lower left corner. It defines two macros used to convert graph
% coordinates into actual dimensions relative to the lower left corner of
% the picture. The second argument of \cs{@xconv} and \cs{@yconv} is a
% dimension register in which the converted result is returned. We make
% the final assignment global for consistency (font dimension assignments
% are always global). We don't really need to define \cs{mfp@setconv}
% and then call it. We could just define \cs{@xconv} and \cs{@yconv}.
% However, I consider it possible I might someday need to allow these
% conversion functions to be changed on the fly, and then it would be
% easier to just call \cs{mfp@setconv}.
%    \begin{macrocode}
\newdef\mfp@setconv{%
  \def\@xconv##1##2{% ##1 = coord. ##2 = dimension register or fdim
  {\mfp@scratch=##1\@mfpicunit \advance\mfp@scratch by -\xmin\@mfpicunit
    \mfp@scratch=\xfactor\mfp@scratch
    \global ##2=\mfp@scratch}}%
  \def\@yconv##1##2{% ditto
  {\mfp@scratch=##1\@mfpicunit \advance\mfp@scratch by -\ymin\@mfpicunit
    \mfp@scratch=\yfactor\mfp@scratch
    \global ##2=\mfp@scratch}}}%
\newdef\mfp@inittlabels{%
  \setbox\@alltlabels\vbox{\hbox{}}%
  \setbox\@backtext\vbox{\hbox{}}%
  \@tlabelsbot  \maxdimen
  \@tlabelstop -\maxdimen
  \@tlabelsleft \maxdimen}%
%    \end{macrocode}
%
% The first argument of \cs{mfp@label} is the justification option. After
% starting a group (it is ended in \cs{mfp@label@@}, we restore the
% meaning of whitespace and give \texttt\# a safe catcode for writing to the
% output, if necessary (\opt{mplabels}). Then we run \cs{tlabeljustify} on
% the optional argument. An empty argument means any previously set values
% won't be changed. Then we check for a left parenthesis and assume the
% \parg{\meta{x},\meta{y}} syntax in that case, calling \cs{mfp@label@}
% to process it. All it does is pack it in braces and call
% \cs{mfp@label@@}. If no parentheses we skip to \cs{mfp@label@@}.
%
% Then \cs{mfp@label@@} gets a point or list of points as its first argument
% and the label code as the second. It defines the macro \cs{tl@points} to
% equal the point (or list) and puts the label into a token register.
%
% After all the data are stored away, we call \cs{mfp@thelabel} with no
% parameters. Then the group (begun by \cs{mfp@label}) is ended, and the
% \cs{extra@endtlabel} command invoked.
%    \begin{macrocode}
\newdef\mfp@label#1{\begingroup\mfp@resetwhitespace\mp@mksharpother
  \tlabeljustify{#1}\@ifnextchar({\mfp@label@}{\mfp@label@@}}%
\newdef\mfp@label@(#1,#2){\mfp@label@@{(#1,#2)}}%
\newdef\mfp@label@@#1#2{\def\tl@points{#1}\mfp@toks{#2}\mfp@thelabel
  \endgroup\extra@endtlabel}%
%    \end{macrocode}
%
% At this point all the necessary information has been stored and
% \cs{mfp@thelabel} merely branches depending on \opt{mplabels}.
%
% Clearly we could have put this code at the end of \cs{mfp@label@@} instead
% of invoking this command. The point of doing things this way is so that
% other commands too can store away the necessary info while doing other
% things and simply call \cs{mfp@thelabel} to get the label placed.
%    \begin{macrocode}
\newdef\mfp@thelabel{\@ifmplabels\mp@tlabel\tex@tlabel}%
%    \end{macrocode}
%
% We now come to the main code under \opt{mplabels}, which should just
% arrange to write the correct commands to the output file. All labels are
% passed as \mfc{btex ... etex} structures via the command \cs{mfp@btex}
% below. The definition of \cs{MFPtext} will have been written earlier by
% \cs{opengraphsfile}.
%    \begin{macrocode}
\newdef\mfp@btex#1{btex \noexpand\MFPtext{#1} etex}%
%    \end{macrocode}
%
% The command \gbc{newgblabel}, defined in \file{graphbase.mp} for placing
% labels, uses three parameters to justify the text. If we didn't have to
% support the \texttt{B} vertical placement option, there would be only
% two. All the other options involve placement \emph{relative} to the
% bounding box. But the baseline is absolute: \MP{} always puts it at
% $y$ coordinate 0 in the picture returned by \gbc{btex}. The first two
% parameters are numerical and the third is boolean. The
% first represents the fraction of the text that lies left of given
% point. The second is the fraction of the text below the point. If the
% third parameter is \mfc{true}, this fraction ignores the depth of the
% text (so $0$ indicates baseline placement); if it is false, the depth
% is accounted for (so $0$ indicates the very bottom of the text).
%
% By this point the letters of the optional parameter have been converted
% to integer values for \cs{tl@hpos} and \cs{tl@vpos} by
% \cs{tlabeljustify}. The following converts these integers to comma
% separated parameters as described above using \cs{ifcase}.
%
% The fourth parameter of \gbc{newgblabel} is the angle of rotation. Empty
% rotation is converted to the angle 0, otherwise it is written as is.
% All four parameters are stored in \cs{mfp@MPpos} by the invocation of
% \cs{mfp@setMPpos}.
%    \begin{macrocode}
\newdef\mfp@setMPpos{%
  \edef\mfp@MPpos{%
    \ifcase\tl@hpos .5\or 1\else 0\fi, % horizontal
    \ifcase\tl@vpos0\or .5\or 1\else 0\fi, % vertical
    \ifnum \tl@vpos<0 \mfp@T\else\mfp@F\fi,  % true=Baseline
    \mfp@emptysub{\tl@rot}{0}}}%
%    \end{macrocode}
%
% \cs{mp@tlabel} is the code called by \cs{tlabel} when \opt{mplabels} is
% in effect. At this point all the data needed are stored in macros and
% we just have to put it together. Thus, it has no parameters and other
% commands can prepare the data and simply invoke it (or, more usually,
% invoke \cs{mfp@thelabel} which invokes \cs{tex@tlabel} or \cs{mp@tlabel} as
% appropriate). The \gbc{newgblabel} command is written with the
% justification and two more parameters: the label tokens, and the point
% (or list of points).
%    \begin{macrocode}
\newdef\mp@tlabel{\mfp@setMPpos
  \mfcmd{\@nl newgblabel(\mfp@MPpos)(\mfp@btex{\the\mfp@toks})\@nl
    (\tl@points)}}%
%    \end{macrocode}
%
% When \opt{mplabels} is not in effect, we use \TeX{} to position the
% label. We put the label in a box (\cs{@textbox}) so we can measure and
% position it. It is a \cs{vbox} so we can have multiline labels. This is
% effected by wrapping it in a simple, left-aligned, one column
% \cs{halign}, defining \cs{\bsl} to be \cs{cr}. We make this procedure a
% separate macro, since we need to do the identical thing in the
% \cs{tlabelpath} code.
%    \begin{macrocode}
\newdef\set@textbox#1{%
  \setbox\@textbox\vbox{\def\\{\cr}\mfp@restorepar
    \mfp@safe@activesfalse\@tcurr\every@tlabel
    \halign{##\hfil\cr#1\crcr}}}%
%    \end{macrocode}
%
% We call \cs{tex@tlabel} to perform the necessary positioning. Again, all
% the necessary data has been stored so \cs{tex@tlabel} takes no parameters.
% Before calling the (rather extensive) positioning code, we have to
% process the (possible) list of points into separate points. Spaces
% outside parentheses are consumed by \cs{@ifnextchar} and separating
% commas (even if there are too many) are gobbled by the
% \cs{mfp@ifendorcomma}. Oddly, this code works even if the separating commas
% are omitted, but the \opt{mplabels} code does not.
%    \begin{macrocode}
\newdef\tex@tlabel{\@xp\@textlabel\tl@points\mfp@end}%
\newdef\@textlabel{\mfp@ifendorcomma{}\@textlabel\@@textlabel}%
\newdef\@@textlabel(#1,#2){\tex@@tlabel{#1}{#2}\@textlabel}%
%    \end{macrocode}
%
% This is the code that sets and positions the label. We compute its total
% height to simplify later code. The macro \cs{tb@ht} expands to
% \cs{ht}\cs{@textbox} and \cs{tb@dp} to \cs{dp}\cs{@textbox}.
%    \begin{macrocode}
\newdef\tex@@tlabel#1#2{%
  \set@textbox{\the\mfp@toks}%
  \mfp@scratch\tb@ht \advance\mfp@scratch\tb@dp
  \tb@totalht\mfp@scratch
  \@xconv{#1}\mfp@scratch
%    \end{macrocode}
%
% The following computes whether the leftmost extent of the picture will
% be increased by the addition of the label. The macro \cs{tb@wd} expands
% to \cs{wd}\cs{@textbox}.
%
% We have convert the $x$ coordinate of the label's location to a distance
% from the left edge of the picture. We then subtract from that the amount
% of the label extending to the left of this location. Then we add or
% subtract the separation of the label from its location. Finally, we
% simply add the horizontal adjustment defined by the user with
% \cs{tlabeloffset}. The value of \cs{@tlabelsleft} is set equal to this
% if it was greater. We save the calculated value in \cs{tb@moveright},
% because it is exactly the amount we'll need to \cs{kern} later to
% position the label.
%    \begin{macrocode}
  \begingroup
    \ifcase\tl@hpos \advance\mfp@scratch -0.5\tb@wd % center
    \or \advance\mfp@scratch -\tb@wd                % right
        \advance\mfp@scratch -\tlabel@sep
    \else \advance\mfp@scratch \tlabel@sep          % left (default)
    \fi
    \advance\mfp@scratch \tlabel@hadj
    \ifdim \mfp@scratch<\@tlabelsleft
      \@tlabelsleft\mfp@scratch
    \fi
    \tb@moveright\mfp@scratch
  \endgroup
%    \end{macrocode}
%
% Now we base the calculations on the uppermost extent of picture and
% label. Otherwise the idea is the same, and we may increase
% \cs{@tlabelstop}.  Again we save the calculated result (in \cs{tb@raise})
% for later positioning of the label.
%    \begin{macrocode}
  \@yconv{#2}\mfp@scratch
  \begingroup
    \ifcase\tl@vpos \advance\mfp@scratch \tb@totalht % bottom
      \advance\mfp@scratch \tlabel@sep
    \or \advance\mfp@scratch 0.5\tb@totalht          % center
    \or \advance\mfp@scratch -\tlabel@sep            % top
    \else \advance\mfp@scratch \tb@ht                % baseline (default)
    \fi
    \advance\mfp@scratch \tlabel@vadj
    \ifdim \mfp@scratch>\@tlabelstop
      \@tlabelstop\mfp@scratch
    \fi
    \tb@raise\mfp@scratch
  \endgroup
%    \end{macrocode}
%
% Finally we compute the lowermost extent, and save it in \cs{@tlabelsbot}.
%    \begin{macrocode}
  \begingroup
    \ifcase\tl@vpos \advance\mfp@scratch \tlabel@sep % bottom
    \or \advance\mfp@scratch -0.5\tb@totalht         % center
    \or \advance\mfp@scratch -\tb@totalht            % top
        \advance\mfp@scratch -\tlabel@sep
    \else \advance\mfp@scratch -\tb@dp               % baseline (default)
    \fi
    \advance\mfp@scratch \tlabel@vadj
    \ifdim \mfp@scratch<\@tlabelsbot
      \@tlabelsbot\mfp@scratch
    \fi
  \endgroup
%    \end{macrocode}
%
% Now we've computed the new size of \cs{@alltlabels} and we put the
% new label on top of it with the above calculated kerns.
%    \begin{macrocode}
  \global \setbox\@alltlabels
    \vtop{\unvbox\@alltlabels
      \vbox to 0pt{\kern-\tb@raise
        \hbox{\kern\tb@moveright\box\@textbox}\vss}}%
}% End \tex@@tlabel
%    \end{macrocode}
%
% The argument of \cs{mfp@labels} is the ostensible argument of
% \cs{tlabels}. Looping is accomplished by defining \cs{extra@endtlabel}
% to repeat \cs{mfp@dolabel}.
%
% If \cs{mfp@dolabel} sees the end-of-loop delimiter it ends the group and
% gobbles the delimiter. Otherwise it calls \cs{tlabel}, which sees the
% next set of arguments, places the label, and repeats the loop.
%    \begin{macrocode}
\newdef\mfp@labels#1{\let\extra@endtlabel\mfp@dolabel
  \mfp@dolabel#1\mfp@end}%
\newdef\mfp@dolabel{\mfp@ifend\endgroup\tlabel}%
%    \end{macrocode}
%
% \cs{mfp@labelpath} stores the name of the path in \cs{mfp@name} and the
% default argument in \cs{mfp@param}, then check for a \texttt{*} and set
% a switch based on it before calling \cs{mfp@tlpath}. The
% \cs{mfp@figmacbase} must be outside the group so the switches it sets
% will survive for later commands to detect.
%    \begin{macrocode}
\newdef\mfp@labelpath#1#2{\mfp@figmacbase
  \begingroup % ended in \tlabelpath@
  \def\mfp@name{#1}\def\mfp@param{#2}%
    \mfp@ifstar\mfp@tlpath\mfp@switchtrue\mfp@switchfalse}%
%    \end{macrocode}
%
% Process the first optional argument, which has value of \cs{mfp@param}
% as default. The second one is a justification with a default set by the
% user with \cs{tlpathjustify} or the initial \texttt{[cc]} setting. Once
% these are processed, we check whether a parentheses follows, calling one
% of two different handlers for the location parameter(s).
%    \begin{macrocode}
\newdef\mfp@tlpath#1{#1\mfp@defaultopt\mfp@@tlpath\mfp@param}%
\newdef\mfp@@tlpath#1{\edef\mfp@param{#1}%
  \mfp@defaultopt\mfp@tlpath@{\tlpath@v\tlpath@h\tlpath@r}}%
\newdef\mfp@tlpath@#1{\mfp@resetwhitespace\mp@mksharpother
  \tlabeljustify{#1}\@ifnextchar({\@tlabelpath}{\@@tlabelpath}}%
%    \end{macrocode}
%
% These handlers just stuff the point into a macro and call the command
% that reads the label code. The name \cs{tl@points} is plural (even
% though only one point is supported) because the internal command that
% places the label expects this macro.
%    \begin{macrocode}
\newdef\@tlabelpath(#1,#2){\@@tlabelpath{(#1,#2)}}%
\newdef\@@tlabelpath#1#2{%
  \def\tl@points{#1}\mfp@toks{#2}\tlabelpath@}%
%    \end{macrocode}
%
% By this point, all the elements we need are gathered. For the purposes
% of the label we have \cs{mfp@toks} holding the label code,
% \cs{tl@points} holding the location, and \cs{tlabeljustify} encoding
% the adjustments. For the path, we have the type in \cs{mfp@name}, and the
% one optional parameter parameter in \cs{mfp@param}.
%
% Under \opt{mplabels} we expect \MP{} to measure the text. Otherwise we
% measure the text in \TeX{} and feed the bounding box corners to \MF{}
% for making the path. If \cs{ifmfp@switch} is false we place the text by
% calling \cs{mfp@thelabel}. All the data needed by \cs{mfp@thelabel} have
% already been stored in macros by previous commands in the chain. Then we
% complete the command by ending the group that \cs{mfp@labelpath}
% started.
%    \begin{macrocode}
\newdef\tlabelpath@{\@ifmplabels{}{\measure@textbox{\the\mfp@toks}}%
  \mfp@setMPpos
  \mfcmd{text\mfp@name x (\mfp@MPpos)\@nl
    (\@ifmplabels{origin, \mfp@btex{\the\mfp@toks}}{\tb@ll, \tb@ur}, %
      \mfp@param) (\tl@points)}%
  \ifmfp@switch\else \mfp@thelabel\fi \endgroup}%
%    \end{macrocode}
%
% Here we define the command that measures the text. It is almost a clone
% of a similar code sequence in \cs{tex@tlabel}, but it produces the \gbc{ll}
% and \gbc{ur} (corners of the boundingbox) that the \grafbase{} code
% needs.
%    \begin{macrocode}
\newdef\measure@textbox#1{\set@textbox{#1}%
  \mfp@scratch-\tb@dp
  \edef\tb@ll{(0, \the\mfp@scratch)}%
  \edef\tb@ur{(\the\tb@wd, \the\tb@ht)}}%
%    \end{macrocode}
%
% The argument of \cs{mfp@axislabels} is the axis letter.
%
% We start by determining the default justification. which is different
% for each axis (for example, for the left axis it is \oarg{cr} but for
% the bottom axis it is \oarg{tc}). For all of them, one of the parts is
% \texttt{c}, so after resetting whitespace we initialize them both to
% this and later change only the one that needs it.
%
% Also, one of the coordinates of a label will be given by the argument,
% while the other is the location of the axis. However, which coordinate
% is which is different for different axes. What we do is feed this
% position to \cs{mfp@xcoord} and \cs{mfp@ycoord}. Both are initialized to
% the identity macro, but one is changed to expand to just the axis
% position.  The axis position for $x$ and $y$ axis is 0. For border axes
% it is calculated by adding the border axis shift to the border
% coordinate.
%    \begin{macrocode}
\newdef\mfp@axislabels#1{%
    \begingroup % ended in \mfp@(@)doaxislabel
      \mfp@resetwhitespace
      \tl@vpos1 \tl@hpos0
      \let\mfp@xcoord\@firstofone \let\mfp@ycoord\@firstofone
      \mfp@getaxis#1\relax\mfp@end\axislabels
      \ifcase\mfp@axisnum\relax
        \tl@vpos2 \def\mfp@ycoord{0}\or
        \tl@hpos1 \def\mfp@xcoord{0}\or
        \tl@hpos1\edef\mfp@xcoord{\mfp@lshift}%
            \mfpaddto\mfp@xcoord\xmin\or
        \tl@vpos2\edef\mfp@ycoord{\mfp@bshift}%
            \mfpaddto\mfp@ycoord\ymin\or
        \tl@hpos-1 \edef\mfp@xcoord{-\mfp@rshift}%
            \mfpaddto\mfp@xcoord\xmax\or
        \tl@vpos0 \edef\mfp@ycoord{-\mfp@tshift}%
            \mfpaddto\mfp@ycoord\ymax
      \fi
%    \end{macrocode}
%
% Now one of \cs{mfp@xcoord} or \cs{mfp@ycoord} expands to the axis
% position. We change it so that it does this while gobbling the
% parameter, and then call \cs{mfp@@axislabels}, feeding it an empty
% argument as the default optional argument. We also give \texttt\# a safe
% catcode for writing to a \file{.mp} file.
%    \begin{macrocode}
      \ifx\@firstofone\mfp@xcoord
        \edef\mfp@ycoord##1{\mfp@ycoord}%
      \else
        \edef\mfp@xcoord##1{\mfp@xcoord}%
      \fi \mp@mksharpother\mfp@nullopt\mfp@@axislabels}%
%    \end{macrocode}
%
% \cs{mfp@@axislabels} processes the contents of the optional parameter
% and calls \cs{mfp@doaxislabel} on the list of labels.
%    \begin{macrocode}
\newdef\mfp@@axislabels#1#2{%
  \tlabeljustify{#1}\mfp@doaxislabel#2,\mfp@end}%
%    \end{macrocode}
%
% \cs{mfp@doaxislabel} checks for the end delimiter or a comma (the latter
% is an error). In the first case it ends all label processing, in the
% second it repeats itself, otherwise it continues with
% \cs{mfp@@doaxislabel}.
%
% The argument of \cs{mfp@@doaxislabel} should be the label. This command
% stores the label in \cs{mfp@toks}, then again checks for the delimiter
% or an comma (both are errors). In the first case it ends the process; in
% the second it goes back to \cs{mfp@doaxislabel} for another try. In both
% cases the label is discarded as we don't know where to put it. If
% neither the delimiter nor a comma occurs, \cs{mfp@mkaxislabel} is run.
%
% The argument of \cs{mfp@mkaxislabel} (everything to the next comma) is the
% location. The command \cs{mfp@mkaxislabel} does nothing if the location
% parameter is empty, otherwise it stores the location as a pair and calls
% \cs{mfp@thelabel} to place the label. Finally, it repeats
% \cs{mfp@doaxislabel} for the next iteration.
%    \begin{macrocode}
\newdef\mfp@doaxislabel{%
  \mfp@ifendorcomma\endgroup\mfp@doaxislabel\mfp@@doaxislabel}%
\newdef\mfp@@doaxislabel#1{\mfp@toks{#1}%
  \mfp@ifendorcomma\endgroup\mfp@doaxislabel\mfp@mkaxislabel}%
\newdef\mfp@mkaxislabel#1,{%
  \@ifmtarg{#1}{}%
    {\edef\tl@points{(\mfp@xcoord{#1},\mfp@ycoord{#1})}\mfp@thelabel}%
  \mfp@doaxislabel}%
%    \end{macrocode}
%
% \cs{mfp@caption} has one mandatory argument, the caption's text. In it, the
% \cs{\bsl} command forces line breaks. This works by forcing the width to
% be greater than any reasonable setting of the maximum line width. When
% this happens, the caption is reset in a \cs{vbox} and \cs{\bsl} is
% redefined like a normal line break.
%    \begin{macrocode}
\newdef\mfp@caption#1{\begingroup\mfp@resetwhitespace
  \mfp@@caption#1\mfp@end}%
\long\def\mfp@@caption#1,#2\mfp@end#3{\endgroup
  \def\mfp@docaption{%
    \setbox\@textbox
      \hbox{\def\\{\hskip\@M\p@\let\\\relax}\mfp@restorepar
       \mfp@safe@activesfalse\@tcurr#3}%
%    \end{macrocode}
%
% If the above \cs{hbox} is too wide, we re-assign \cs{@textbox} to a
% \cs{vbox} with \cs{hsize} determined by the second part of the optional
% argument. \cs{mfp@capsettings} implements the \opt{centeredcaptions}
% and \opt{raggedcaptions} options.
%    \begin{macrocode}
    \mfp@scratch\wd\@wholegraph
    \ifdim\tb@wd>#1\mfp@scratch
      \setbox\@textbox
      \hbox{%
        \vbox{%
          \hsize#2\mfp@scratch \mfp@restorepar
          \leftskip0pt \rightskip0pt\relax
          \mfp@capsettings
          \mfp@safe@activesfalse
          \noindent\@tcurr #3%
        }% End vbox.
      }% End hbox.
    \fi
%    \end{macrocode}
%
% Here we determine the wider of the graph or the caption, then put the
% graph and caption together by centering them in \cs{hbox}es with this
% width, stacked one atop the other with \cs{mfpiccaptionskip} (default:
% \cs{medskipamount}) in between.
%    \begin{macrocode}
    \ifdim \mfp@scratch<\tb@wd \mfp@scratch\tb@wd \fi
    \global\setbox\@wholegraph
    \vbox{\hbox to \mfp@scratch{\hss\box\@wholegraph\hss}%
      \nointerlineskip \vskip\mfpiccaptionskip
      \hbox to \mfp@scratch{\hss\box\@textbox\hss}}% End vbox.
  }% End \mfp@docaption.
}% End \mfp@@caption.
%    \end{macrocode}
%
% The following is used in \cs{endmfpic}. The first argument of
% \cs{mfp@adjustdim} is a border dimension of the box containing all the
% labels, the second is a comparison between that and the corresponding
% dimension of the graph box, which is the third argument. The last is the
% macro holding the adjustments needed when \opt{truebbox} is used. The
% first and last line compensate for the fact that the bbox need not start
% at $(0,0)$. The second line checks if the label box extends past the
% graph's edge and adjusts the graph's dimension is it does.
%    \begin{macrocode}
\def\mfp@adjustdim#1#2#3#4{%
  \mfp@scratch#1\relax \advance\mfp@scratch-#4 bp
  \ifdim\mfp@scratch#2#3\relax #3\mfp@scratch \fi
  #1\mfp@scratch}%
%    \end{macrocode}
%
% \section{Placing the picture: \cs{endmfpic}}\label{endmfpic}
%
% \DescribeMacro{\endmfpic}
% By the time \cs{endmfpic} is reached, the \MF{} code for the figure has
% all been written to the output file. The labels have all been
% accumulated and arrangements have been made to add the caption.
%
% Under \opt{metapost}, write a right brace to match the left written
% by \cs{mfpic} Then write the \cs{grafbase} command \gbc{endmfpic},
% followed by a comment telling which figure number it is, and the line
% number in the \TeX{} source where the \cs{endmfpic} occurred.
%    \begin{macrocode}
\mfp@DBlog{Definition of closure of mfpic environment.}%
\newdef\endmfpic{\every@endmfpic
  \mfsrc{%
    \mfp@ifmpost{\@nl verbatimtex \relax\egroup\space etex;}{}\@nl
    endmfpic; \mfp@p\space(\number\mfp@count) \mfp@lineno.\@nl
    \mfp@p\mfp@d\mfp@d\mfp@d\@nl}%
  \ifmfpicdebug\wlog{}\wlog{Mfpic: ENTERED endmfpic.}\wlog{}\fi
%    \end{macrocode}
%
% The code to load and place the box is skipped if figure shipping was
% turned off.
%    \begin{macrocode}
  \ifmfp@noship \else
%    \end{macrocode}
%
% \subsection{Loading and measuring the graphic}\label{loading}
%
% Now we load the graphic. It would be at this point that we could add a
% \cs{write18} to process the figure on-the-fly. Of course that would
% require re-initializing the output file with each graphic (i.e., the
% equivalent of issuing \cs{opengraphsfile} at every \cs{mfpic} and
% \cs{closegraphsfile} at every \cs{endmfpic}.)
%    \begin{macrocode}
    \global\setbox\@wholegraph
    \vbox{%
%    \end{macrocode}
%
% If draft mode has been detected or set by the user, we just make a box
% of the size specified with the figure number inside it.
%    \begin{macrocode}
      \ifmfpicdraft
        \vbox to \@graphtop{\vss
          \hbox to \@graphright{%
            \kern2pt \mfpdraftfont\#\number\mfp@count\hss}%
          \kern2pt}%
      \else
%    \end{macrocode}
%
% The \opt{truebbox} option works at the \MP{} level. Without it the
% height of the EPS bounding box will actually be the calculated value
% of \cs{@graphtop}. With it, the box will be its natural height. But
% in either case, the value will actually be increased by up to
% \texttt{2bp} because of rounding, so the bounding box height is what we
% use in the \MP{} case. For \MF{} we use the nominal height calculated in
% \cs{mfpic}.
%    \begin{macrocode}
        \mfp@ifmpost{\vbox}{\vbox to \@graphtop}%
         {\vss
%    \end{macrocode}
%
% \cs{@graphfilename} holds the name of the \MP{} output figure. (It will be
% ignored by the \opt{metafont} option.) We test if the file exists before
% doing the graphic inclusion because of the large number of confusing error
% messages many graphic inclusion packages generate otherwise. When absent
% we substitute the figure filename for \cs{@setmfpicgraphic}.
%    \begin{macrocode}
          \edef\@graphfilename{%
            \setfilename\mfp@filename{\number\mfp@count}}%
          \mfp@ifmpost
           {\IfFileExists{\@graphfilename}{}%
             {\Mfpic@msg{No graph file: \@graphfilename\space.}%
              \let\@setmfpicgraphic\nofile@setmfpgraphic}%
%    \end{macrocode}
%
% We put the graphic in an \cs{hbox} of the required width and close off
% the boxes.
%    \begin{macrocode}
            \hbox}%
           {\hbox to \@graphright}%
            {\@xp\@setmfpicgraphic\@xp{\@graphfilename}\hss}%
          \kern0pt
        }% End vbox
      \fi
    }%% End \setbox\@wholegraph \vbox
%    \end{macrocode}
%
% We change the horizontal and vertical dimensions under \opt{metapost} in
% case \opt{truebbox} was in effect, but also because they are almost always
% rounded up to whole numbers of \texttt{bp} and therefore, even without
% \opt{truebbox}, the calculated values needn't be correct.
%    \begin{macrocode}
    \mfp@ifmpost
     {\@graphright\wd\@wholegraph
      \@graphtop\ht\@wholegraph}{}%
    \ifmfpicdebug
      \wlog{Mfpic debug: Dimensions of wholegraph before labels %
        are added, and before truebbox adjustments:}%
      \wlog{Mfpic: graphleft  = \the\@graphleft}%
      \wlog{Mfpic: graphright = \the\@graphright}%
      \wlog{Mfpic: graphtop   = \the\@graphtop}%
      \wlog{Mfpic: graphbot   = \the\@graphbot}%
      \wlog{Mfpic: graphwd    = \the\wd\@wholegraph}%
      \wlog{Mfpic: graphht    = \the\ht\@wholegraph}%
      \wlog{Mfpic: graphdp    = \the\dp\@wholegraph}%
      \wlog{}%
    \fi
%    \end{macrocode}
%
% \subsection{Adding labels and caption}\label{addlabel}
%
% We now add the boxes \cs{@alltlabels} and \cs{@backtext} onto the graph
% box. But first we have to adjust for \cs{mfpicllx} and \cs{mfpiclly}
% which can only be known after the graphics inclusion. We reset those
% boxes so their contents are shifted by these values. We only need to do
% this if labels have have actually been added. The signal that this has
% happened is that the label dimensions are no longer $\pm$\cs{maxdimen}.
% This doesn't indicate whether it is \cs{@alltlabels} or \cs{@backtext}
% (or both) that is nonempty, so one of the box resets may be redundant.
%    \begin{macrocode}
    \ifmfpicdebug
      \wlog{Mfpic debug: Dimensions of alltlabels, before %
        truebbox adjustments:}%
      \mfp@scratch\mfpicllx bp\relax
      \wlog{Mfpic: mfpicllx     = \the\mfp@scratch}%
      \mfp@scratch\mfpiclly bp\relax
      \wlog{Mfpic: mfpiclly     = \the\mfp@scratch}%
      \wlog{Mfpic: tlabelsleft  = \the\@tlabelsleft}%
      \wlog{Mfpic: tlabelstop   = \the\@tlabelstop}%
      \wlog{Mfpic: tlabelsbot   = \the\@tlabelsbot}%
      \wlog{}%
    \fi
    \ifdim\@tlabelsleft < \maxdimen
      \setbox\@alltlabels\vtop to 0pt{%
        \kern \mfpiclly bp \moveleft \mfpicllx bp \box\@alltlabels\vss}%
      \setbox\@backtext  \vtop to 0pt{%
        \kern \mfpiclly bp \moveleft \mfpicllx bp \box\@backtext  \vss}%
%    \end{macrocode}
% Then we adjust \cs{@tlabelsleft}, etc. for the boundingbox offset.
% The graph dimensions are also adjusted if the tlabel dimensions extend
% past the edges.
%    \begin{macrocode}
      \mfp@adjustdim\@tlabelsleft <\@graphleft \mfpicllx
      \mfp@adjustdim\@tlabelstop  >\@graphtop  \mfpiclly
      \mfp@adjustdim\@tlabelsbot  <\@graphbot  \mfpiclly
      \ifmfpicdraft\else
        \setbox\@wholegraph
          \vtop{\offinterlineskip
            \box\@backtext\kern-\ht\@wholegraph
            \unvbox\@wholegraph\box\@alltlabels}%
      \fi
    \fi
%    \end{macrocode}
%
% The method for putting labels in \cs{@alltlabels} does not add any width
% on the left, nor any height to the top or depth to the bottom of that box
% (that \TeX{} can detect), but we have saved their values and now we can
% use them. For example, if \cs{@graphleft} is negative after the above,
% then a label sticks out to the left, but \TeX{} thinks it has no width.
% Therefore put \cs{kern}\texttt{-}\cs{@graphleft} to move the graph
% rightward. The height and depth are taken care of by putting it in
% \cs{vbox} with the calculated total height and moving the graph upward
% with \cs{kern}\texttt{-}\cs{@graphbot}. The rightward extensions do get
% detected by \TeX.
%    \begin{macrocode}
    \ifmfpicdebug
      \wlog{Mfpic debug: Dimensions of alltlabels after %
        truebbox adjustments:}%
      \wlog{Mfpic: tlabelsleft  = \the\@tlabelsleft}%
      \wlog{Mfpic: tlabelstop   = \the\@tlabelstop}%
      \wlog{Mfpic: tlabelsbot   = \the\@tlabelsbot}%
      \wlog{}%
    \fi
    \mfp@scratch\@graphtop
    \advance\mfp@scratch by -\@graphbot
    \global \setbox\@wholegraph
    \vbox to \mfp@scratch{\vss
      \hbox{\kern-\@graphleft\box\@wholegraph}%
      \kern-\@graphbot}% End vbox.
%    \end{macrocode}
%
% Now add the caption, then set the parameters \cs{mfpicheight} and
% \cs{mfpicwidth} for user to examine. The debug info now should show
% graphwd${}={}$graphright${}-{}$graphleft,
% graphht${}={}$graphtop${}-{}$graphbot, and graphdp${}= 0$.
%    \begin{macrocode}
    \ifmfpicdebug
      \wlog{Mfpic debug: Dimensions of wholegraph after %
        labels are added:}%
      \wlog{Mfpic: graphleft  = \the\@graphleft}%
      \wlog{Mfpic: graphright = \the\@graphright}%
      \wlog{Mfpic: graphtop   = \the\@graphtop}%
      \wlog{Mfpic: graphbot   = \the\@graphbot}%
      \wlog{Mfpic: graphwd    = \the\wd\@wholegraph}%
      \wlog{Mfpic: graphht    = \the\ht\@wholegraph}%
      \wlog{Mfpic: graphdp    = \the\dp\@wholegraph}%
      \wlog{}%
    \fi
    \mfp@docaption
    \ifmfpicdebug
      \wlog{Mfpic debug: Values after tcaption added:}%
      \wlog{Mfpic: graphleft  = \the\@graphleft}%
      \wlog{Mfpic: graphright = \the\@graphright}%
      \wlog{Mfpic: graphtop   = \the\@graphtop}%
      \wlog{Mfpic: graphbot   = \the\@graphbot}%
      \wlog{Mfpic: graphwd    = \the\wd\@wholegraph}%
      \wlog{Mfpic: graphht    = \the\ht\@wholegraph}%
      \wlog{Mfpic: graphdp    = \the\dp\@wholegraph}%
      \wlog{}%
    \fi
    \global\mfpicheight\ht\@wholegraph
    \global\mfpicwidth\wd\@wholegraph
%    \end{macrocode}
%
% \subsection{Placing the graphic}\label{placing}
%
% Add a frame around the box \cs{@wholegraph} in draft mode (so its size
% can be seen) since there is practically nothing in it except the picture
% number and perhaps some tlabels.
%    \begin{macrocode}
    \ifmfpicdraft
      \setbox\@wholegraph
      \hbox{\@mfpframed{-\mfpframethickness}{\box\@wholegraph}}%
    \fi
%    \end{macrocode}
% Now we save the graph globally, for placement after \cs{endgroup}. This
% is so that tokens placed by \cs{everypar} will be typeset in the current
% font (instead of \cs{nullfont}). Then we advance the figure count and
% end the group started by the \cs{mfpic} command.
%    \begin{macrocode}
    \global\setbox\@wholegraph\box\@wholegraph
    \global \advance\mfp@count1
  \fi % \ifmfp@noship
  \endgroup % Begun near start of \@mfpic
%    \end{macrocode}
% If the \cs{savepic} command occurred prior to this, then \cs{s@vemfpic}
% is defined and we save this picture in the box named in that command and
% stored in the macro \cs{s@vemfpic}. Otherwise, \cs{s@vemfpic} is
% undefined, and we place the picture (\cs{@wholegraph}) in the document.
% Afterward, we undefine \cs{s@vemfpic}. Note: if \opt{noship} is in
% force, it remains defined, so the next picture will be stored.
%    \begin{macrocode}
  \ifmfp@noship \else
    \mfp@ifdefined\s@vemfpic
      {\global\setbox\s@vemfpic\box\@wholegraph}%
      {\leavevmode\box\@wholegraph}%
    \global\let\s@vemfpic\UndEfInEd
  \fi
%    \end{macrocode}
% Then we  restore the values of extra font dimensions that were saved.
% Just in case, we unset the switch \cs{in@mfpicenv} and then arrange for
% spaces to be ignored in case this is a \LaTeX{} environment. (I think we
% shouldn't ignore spaces, but I was overruled. The argument was that
% \cs{end}\marg{mfpic} should behave like \cs{endmfpic}. I don't buy it,
% but I will keep things the way they were since version 0.4.)
%    \begin{macrocode}
  \restore@mfpicdimens
  \mfp@checklatexenv{mfpic}{\@ignoretrue}{}%
  \global\let\in@mfpicenv\iffalse
  \ignorespaces
}% endmfpic
%    \end{macrocode}
%
% The following is a little utility to run at \cs{foo} or \cs{endfoo} to
% see if was initiated as a \LaTeX{} environment or as a plain command.
% The first argument is the environment name, the second is what to do
% if that is the current environment, and the third is what to do
% otherwise. In the two cases we now use it, the third argument is
% empty.
%    \begin{macrocode}
\ifmfp@latex
  \newdef\mfp@checklatexenv#1#2#3{%
    \def\mfp@tempa{#1}\ifx\mfp@tempa\@currenvir #2\else #3\fi}%
\else
  \newdef\mfp@checklatexenv#1#2#3{#3}%
\fi
%    \end{macrocode}
%
%
% \section{Additional features}\label{additional}
%
% \subsection{Saving a copy of the picture}\label{saving}
%
% \DescribeMacro{\newsavepic}
% One saves a picture by first allocating a save box with
% \cs{newsavepic}\cs{mypic}, then saying \cs{savepic}\cs{mypic}
% beforehand. The \cs{endmfpic} code detects that this has been done and
% saves the picture in \cs{mypic}. It can be placed with
% \cs{usepic}\cs{mypic}.
%
% \cs{newsavepic} is just a clone of \LaTeX's \cs{newsavebox}. The one
% argument is a control sequence.
%    \begin{macrocode}
\ifmfp@latex
  \newlet\newsavepic\newsavebox
\else
  \newdef\newsavepic#1{%
    \mfp@ifdefined{#1}%
     {\mfp@errmsg{Command \string #1 already defined}%
       {You have used \newsavepic with an already defined or an^^J%
        improper control sequence. Replace #1 with another name.^^J%
        If you proceed, \newsavepic will be ignored.}}%
     {\@nameuse{newbox}#1}}%
\fi
\newlet\newpic\newsavepic
%    \end{macrocode}
%
% \DescribeMacro{\savepic}
% All \cs{savepic} really does is define \cs{s@vepic} to its argument,
% which should be a control sequence defined by \cs{newsavepic} (or
% \cs{newbox}).
%    \begin{macrocode}
\newdef\savepic#1{\relax
   \mfp@ifdefined{#1}{\gdef\s@vemfpic{#1}}%
   {\mfp@errmsg{Box \string#1 undefined}%
    {You tried to save a picture in a box which had not been^^J%
     previously allocated. Use \newsavepic to allocate a box.}}}%
%    \end{macrocode}
%
% \DescribeMacro{\usepic}
% \cs{usepic} takes one argument, a control sequence that should have
% been previously used in a \cs{savepic} comamnd. It just places the box
% with the primitive \cs{copy} command.
%    \begin{macrocode}
\newdef\usepic#1{\leavevmode \copy#1\relax}%
%    \end{macrocode}
%
% \subsection{Putting a frame around it}\label{frame}
%
% This is essentially code I wrote years ago to have a framing command
% that had two properties not enjoyed by some example `\cs{boxit}' commands
% for plain\TeX: It should have a baseline the same as the baseline of the
% contents, and it should work as an environment, not by reading an
% argument (so verbatim material could be included).
%
% \DescribeMacro{\mfpframed}
% \cs{mfpframed} takes an optional argument (the separation) and a
% mandatory argument, the contents.
% \DescribeMacro{\mfpframe}
% \cs{mfpframe}$\ldots$\cs{endmfpframe} is an environment and
% \cs{mfpframe} also takes the separation as an optional argument.
%
% \DescribeMacro{\framed}
% \cs{framed} is a common command (\ConTeXt{} has one, a few packages also
% define it), therefore we only define it if it is not already defined.
%    \begin{macrocode}
\newdef\mfpframed{\mfp@defaultopt\@mfpframed\mfpframesep}%
\newdef\mfpframe{\mfp@defaultopt\@mfpframe\mfpframesep}%
\newdef\@mfpframed#1#2{\@mfpframe{#1}#2\endmfpframe}%
\newdef\@mfpframe#1{%
  \leavevmode\hbox\bgroup
    \mfpframesep#1\relax
    \vrule width\mfpframethickness
    \vtop\bgroup
      \vbox\bgroup
        \hrule height\mfpframethickness
        \kern\mfpframesep
        \hbox\bgroup \kern\mfpframesep \ignorespaces}%
\newdef\endmfpframe{\unskip
          \kern\mfpframesep
        \egroup % end hbox
      \egroup % end vbox
      \kern\mfpframesep
      \hrule height\mfpframethickness
    \egroup % end vtop
    \vrule width\mfpframethickness
  \egroup}% end hbox
\mfp@ifdefined\framed{}{\let\framed\mfpframed}%
%    \end{macrocode}
%
% \subsection{Adding \mfc{verbatimtex} to the \file{.mp}
% file}\label{verbatimtex}
%
% \DescribeMacro{\mfpverbtex}
% This is a user level utility for putting some \mfc{verbatimtex} material
% in the output file for \MP. We allow the user to do this even before
% \cs{opengraphsfile} by appending it to a token register and setting a
% flag for that command to test.
%
% We now want \texttt\% signs to be written to the output, but also
% want to allow the construct
% \begin{verbatim}
%   \mfpverbtex% Comment
%   {<tex code>}\end{verbatim}
% to function as users might expect. We therefore perform a
% \cs{futurelet} (which should set \cs{mfp@next} equal to the opening
% brace) but we do it solely to get \TeX's scanning mechanism past the
% comment before we change the category of \texttt\%.
%    \begin{macrocode}
\def\mfpverbtex{\futurelet\mfp@next\@mfpverbtex}%
%    \end{macrocode}
%
% We start a group, change \texttt\% and \texttt\# to `other' so they
% can be written normally, then continue after loading the code into the
% token register \cs{mfp@toks}.
%    \begin{macrocode}
\def\@mfpverbtex{%
  \begingroup
    \@makeother\#\@makeother\%\mfp@keeplines
    \afterassignment\mfp@writetex\global\mfp@toks}%
%    \end{macrocode}
% We end the group and then either write it to the
% output, between the commands \gbc{verbatimtex} and \cs{etex},
% or append it to \cs{mfp@verbtex} and set the switch to tell
% \cs{opengraphsfile} that there is material to write when the output file
% is opened.
%    \begin{macrocode}
\newif\ifmfp@verbtex
\def\mfp@writetex{%
  \mfp@ifopengraphsfile
   {\mfp@ifmpost
      {\mfcmd{verbatimtex\@nl\the\mfp@toks\@nl\mfp@p\@nl etex}}%
      {\mfp@noMP@error\mfpverbtex}%
    \global\mfp@verbtexfalse\global\mfp@verbtex{}}%
   {\edef\mfp@tempa{\the\mfp@verbtex\the\mfp@toks}%
    \global\mfp@verbtex\@xp{\mfp@tempa}%
    \global\mfp@verbtextrue}%
  \endgroup
}%
%    \end{macrocode}
%
%
% \section{Finale}\label{finale}
%
% Set the default starting graphic number. We used to start at 0 and
% increment it at the start of each picture, but now we start at 1 and
% increment it at the end of each picture.
%    \begin{macrocode}
\mfpicnumber{1}%
%    \end{macrocode}
%
% Set the font for missing or draft mode figures (for the file name or
% figure number). This will already have been defined if \file{mfpic.sty}
% was used, so here we can probably assume \LaTeX{} wasn't used, and
% \cs{tt} ought to be available.
%    \begin{macrocode}
\mfp@ifdefined\mfpdraftfont{}{\newdef\mfpdraftfont{\tt}}%
%    \end{macrocode}
%
% Restore the meaning of \cs{+}, and execute the command that restores all
% the saved category codes and \cs{newlinechar}. Input user defaults in
% the file \file{mfpic.usr}.
%    \begin{macrocode}
\mfp@DBlog{Punctuation, etc., will revert to old catcodes now.}%
\let\+\mfpsaveplus
\mfp@restoreALL%
\InputIfFileExists{mfpic.usr}{}{}%
%</tex>
%    \end{macrocode}
%
%\clearpage
%\Finale
