%%%
%%%  File: mfpic.tex
%%%
% Preliminary version of macros.
%%%
%%%
\immediate\write16
  {mfpic version 0.2.10.9 alfa  Sat 9 November 1996}
%%%
%%% Major contributions by Daniel H. Luecking (DHL),
%%% 19 June 1995 and 28 Feb 1996.
%%%
\immediate\write16
  {Transforms may now be used among figure modifiers.}
\wlog {}
%%%
%%%
\wlog {mfpic: check whether mfpic.tex already loaded}
\expandafter\ifx\csname mfpic-package\endcsname\relax  % DHL:
\else
  \immediate\write16 {}
  \immediate\write16
    {You have loaded  mfpic  more than once!  Please load it only once!}%
  \immediate\write16 {}
  \expandafter \endinput  % DHL:
\fi
\expandafter\xdef\csname mfpic-package\endcsname  % DHL: (use load check)
  {\catcode`\string @=\the\catcode`\@ }  % DHL:  (to save @'s catcode)
%%%
%%%
% DHL:  This lets one keep multiple versions around with minimal changes:
\def \grafbasename {grafbase}  % DHL:
%%%
%%%
\wlog {mfpic: local catcode change for `at' character}
\catcode`@=11
%%%
%%%
%
% Let TeX read mfpic.tex without accidentally introducing
% spurious spaces into the DVI file produced from a TeX document
% that uses mfpic.
%
\wlog {mfpic: font changed to nullfont while loading mfpic.tex}
% Save old font.
\global \font\@tcurr=\fontname\font\relax
% Change to null font.
\nullfont
%
%%%
%%%
% Test for (any release of) LaTeX.
\wlog {mfpic: test for LaTeX}
\newif\ifin@latex
%  GT:  \UndEfInEd  introduced by  D.H. Luecking.
\ifx \documentstyle\UndEfInEd
  \in@latexfalse
\else
  \in@latextrue
\fi
%%%
%%%
\wlog {mfpic: defining test for previous definitions of macros}
% (Cannot use \testdef to pre-test \testdef, without circular definition.)
\ifx \testdef\UndEfInEd
\else
  \immediate\write16
    {Hey!  How can  testdef  already be defined?  I'll define it, anyway!}
\fi
%
% Define the test for whether a macro name is already defined.
\def\testdef#1{%
  \ifx #1\UndEfInEd
  \else
    \immediate\write16 {mfpic: BEWARE:  \noexpand #1 is already defined!}%
  \fi}
% Warn if macro defined, but `let' it anyway.
\testdef\newlet
\def\newlet#1=#2{\testdef#1\let#1=#2}
% Simple definitions.
\newlet\sim@def=\def
\newlet\sim@gdef=\gdef
% Is the proposed definer of new definitions itself not new?
\testdef\newdef
% Warn if macro previously defined, but still redefine it.
\sim@def\newdef#1{\testdef#1\sim@def#1}
\sim@def\newgdef#1{\testdef#1\sim@gdef#1}
% Redefine macro.
\newlet\redef=\sim@def
%%%
%%% Handle Optional Parameters in TeX macros:
%%%
\wlog {mfpic: handlers for optional parameters}
\newdef\do@ptparam#1#2%
{%
  \redef\@ptparami[##1]{\csname#1\endcsname[##1]}%
  \redef\@ptparamii{\csname#1\endcsname[#2]}%
  \redef\@ptparamiii
  {%
    \ifx [\nchr
      \expandafter\@ptparami
    \else
      \expandafter\@ptparamii
    \fi
  }%
  \futurelet\nchr\@ptparamiii
}%
%%%
%%% End of Optional Parameters code.
%%%
%
%%%
%%%
\wlog {mfpic: direct output to METAFONT file}
%
{\catcode`\^^M\active %
  \newgdef\mfpicobeylines{\catcode`\^^M=\active \let^^M=\endgraf}%
  \global\let^^M=\endgraf%
} %
%
\newdef\preservelines{%
  \mfpicobeylines
  \newlinechar=`\^^M}
%
\newdef\mfsrc#1{%
  {\immediate\write\@outx{#1}}%
  \ignorespaces
}
%%%
%%% Percent, Sharp and Backslash signs for METAFONT file:
%%%
\newdef\mf@gobble#1{}
\newdef\mf@p{\expandafter\mf@gobble\string\%}
\newdef\mf@s{\expandafter\mf@gobble\string\#}
%
% Works but conflicts with LaTeX:
% \chardef\\=`\\
% \newdef\mf@bsl{\expandafter\mf@gobble\string\\}
%
% Doesn't work:
% \chardef\my@bsl=`\\
% \newdef\mf@bsl{\expandafter\mf@gobble\string\my@bsl}
%%%
\wlog {mfpic: three local declarations used with graphs files}
\newwrite\@outx
\newread\@graphx
\newcount\@gcode
%%%
%%% Open and Close METAFONT Graphs file:
%%%
%%% Use command names:  \@gcode, \@outx, \@graphx, \@graphfont.
%%%
\wlog {mfpic: macros to open and close graphs files}
%
\newdef\opengraphsfile#1%
{%
  \immediate\write16{}%
  \@gcode=0
  \immediate\openout\@outx=#1.mf
  \openin\@graphx=#1.tfm
  \ifeof \@graphx
    \immediate\write16
      {mfpic: No file #1.tfm.}%
    \font\@graphfont=dummy\relax
  \else
    \font\@graphfont=#1\relax
  \fi
  \closein\@graphx
  \immediate\write16
    {mfpic: Don't forget to process #1.mf!}%
  \immediate\write16
    {mfpic: (Apply metafont to #1.mf, then gftopk to the #1 gf file.)}%
  \immediate\write16
    {mfpic: Then reprocess this file (\jobname.tex).}%
  \immediate\write16{}%
  \mfsrc {if unknown mode: mode:= localfont; fi}%
  \mfsrc {if unknown mag: mag:=\number\mag/1000; fi}%
  % DHL: See \def of \grafbasename:
  \mfsrc {if unknown grafbase: input \grafbasename; fi}%
  \mfsrc {gcode:=\number\@gcode;}%
  \mfsrc {}%
}
\newdef\closegraphsfile
{%
  \mfsrc {}%
  \mfsrc {end.}%
  \immediate\closeout\@outx
}
%%%
%%%
\wlog {mfpic: using dummy font's dimensions, to spare TeX registers}
% TRICK:  Use font dimensions to spare TeX's dimension registers.
%
% Load dummy.tfm : most systems should have this,
% but other fonts (such as cmr10) may suffice.
%
\font\@dummy=dummy
\fontdimen100\@dummy=0pt
%
% Use an auxiliary count register:
%
\newcount\@fdc
% 
% In the web2c METAFONT 2.71 implementation I use on unix,
% each font initially has 22 dimensions.
% This number can be increased only by using a higher font
% dimension number immediately after the font is loaded.
% Most fonts use only font dimensions 1 to 22; start new font
% dimensions from number 23 to avoid mangling the font's typesetting.
% (For dummy.tfm, this may not matter, as it has no characters.)
%
\@fdc=23
%
% Rough equivalent of \newdimen, only for font dimensions.
% Note:  \newfdim defines a dimension globally, like \newdimen.
% Must define carefully, to use the current font dimension number.
%
\newdef\newfdim#1{\xdef#1{\fontdimen\the\@fdc\@dummy}%
                   \global \advance\@fdc by 1\relax}
%
% Now we can use \newfdim like this:
%
% \newfdim\bdim
% \newfdim\cdim
% \bdim=3pt
% \cdim=\bdim
% \show\the\cdim
%
% Drawback 1:  Font dimension assignments seem always to have global
% scope.
% Drawback 2:  Font dimensions cannot directly use \advance, \multiply
% or \divide.  One must copy to and from a temporary TeX dimension
% register.
%
%%%
%%%
\wlog {mfpic: a box for whole labeled graph, and a temporary box}
\newbox\@wholegraph
\newbox\@textbox
%
\wlog {mfpic: internal dimension parameters for graph dimensions}
\newfdim\@graphwd
\newfdim\@graphright
\newfdim\@graphleft
\newfdim\@graphht
\newfdim\@graphdp
%
\wlog {mfpic: user's dimension parameters, with default settings}
\newfdim\mfpicunit \mfpicunit=1pt
\newfdim\pointsize \pointsize=2pt
\newfdim\shadespace \shadespace=1pt
\newfdim\hatchspace \hatchspace=3pt
\newfdim\headlen \headlen=3pt
\newfdim\axisheadlen \axisheadlen=5pt
\newfdim\hashlen \hashlen=4pt
\newfdim\dashlen \dashlen=4pt
\newfdim\dashspace \dashspace=4pt
\newfdim\dotsize \dotsize=0.5pt
\newfdim\dotspace \dotspace=3pt
%
% Note: Prof. D.E.~Knuth recommends dimension register 255 be reserved
% as a scratch register.
%
% Advance a font dimension f (#1) by Dimension x (#2) :
\newdef\d@adv#1#2{{%
  \dimen255 = #1\relax
  \advance\dimen255 by #2\relax
  \global #1 = \dimen255
}}
% Multiply a font dimension f (#1) by Integer n (#2) :
\newdef\i@mul#1#2{{%
  \dimen255 = #1\relax
  \multiply\dimen255 by #2\relax
  \global #1 = \dimen255
}}
% Divide a font dimension f (#1) by Integer d (#2) :
\newdef\i@div#1#2{{%
  \dimen255 = #1\relax
  \divide\dimen255 by #2\relax
  \global #1 = \dimen255
}}
% Multiply a font dimension f (#1) by Rational q = n/d (#2 / #3) :
\newdef\q@mul#1#2#3{{%
  \dimen255 = #1\relax
  \multiply\dimen255 by #2\relax
  \divide\dimen255 by #3\relax
  \global #1 = \dimen255
}}
%%%
%%%
\wlog {mfpic: graphics macros}
%
% Standard shade setting macros:
\newdef\darkershade{%
  \q@mul{\shadespace}{5}{6}%
}
\newdef\lightershade{%
  \q@mul{\shadespace}{6}{5}%
}
% Note:  \dashlineset is same as initial setting:
\newdef\dashlineset{%
  \dashlen=4pt
  \dashspace=4pt}
\newdef\dotlineset{%
  \dashlen=1pt
  \dashspace=2pt}
% User can choose subsequent points to be either filled or open:
\newif\ifpointfill \pointfilltrue
%%%
%%%
\wlog {mfpic: tests to control multiple prefix commands}
%
% Start of a complex drawing command (one that includes prefixes).
% Figure macros close by setting it true;
% Rendering and other prefix macros close by setting this false.
%
\newif\if@startfig \@startfigtrue
%
% Implicit Rendering:
% Rendering macros close by setting this false;
% Figure macros close by setting it true;
% Other prefix macros (eg, \closed and \reverse) do not touch it.
%
\newif\if@imrend \@imrendtrue
%
% Storage of a path.
\newdef\store@path{%
  \mfsrc {}%
  \mfsrc {store (curpath)}%
}
%
% First stage of (rendering and path modification) prefix macros.
%
\newdef\@firststage
{%
  \if@startfig
    \store@path
    \@imrendtrue
    \@startfigfalse
  \fi
}
%
% Rendering macro specification.
%
\newdef\@rendmac#1{%
  \@firststage
  \mfsrc {#1}%
  \@imrendfalse
}
%
% Path modification (eg, path reversal) macro specification.
%
\newdef\@modmac#1{%
  \@firststage
  \mfsrc {#1}%
}
%
% Path closure macro specification.
%
\newdef\@closmac#1{%
  \@firststage
  \if@imrend
    \@render
  \fi
  \mfsrc {#1}%
}
%
%
% (Implicitly) Render current figure.
% Initial default is to draw solid paths.
%
\newdef\@render{\draw}
%
% Redefine (implicit) Render command.
%
\newdef\setrender#1{\redef\@render{#1}}
%
% Figure macro specification.
%
\newdef\@figmac#1{%
  \@firststage
  \if@imrend
    \@render
  \fi
  \mfsrc {#1;}%
  \@startfigtrue
  \@imrendtrue
}
%
% METAFONT title:
\newdef\mftitle#1{\mfsrc {mftitle "#1";}}%
% TeX text and METAFONT title:
\newdef\tmtitle#1{#1\wlog {#1}\mftitle {#1}}%
%
% To turn off character shipping for duration of innermost
% enclosing group (eg, mfpic environment) :
\newdef\noship{%
  \mfsrc {save shipit; let shipit = relax;}%
  \advance\@gcode -1 \mfsrc {decr gcode;}}
%
% Pen size settings for drawing, shading and hatching:
%
% Drawing pen's width:
\newdef\drawpen#1{%
  \mfsrc {}%
  \mfsrc {penwd := #1;}%
  \mfsrc {drawpen := pencircle scaled penwd yscaled aspect_ratio;}}
\newlet\pen=\drawpen
%
% Shading dot's diameter:
\newdef\shadewd#1{%
  \mfsrc {shadewd := ceiling (#1);}%
  \mfsrc {setdotpath (fullcircle, shadewd);}}
%
% Hatch line's thickness:
\newdef\hatchwd#1{%
  \mfsrc {hatchwd := #1;}%
  \mfsrc {hatchpen := pencircle scaled hatchwd yscaled aspect_ratio;}}
%
% Arrowhead shape setting:
\newdef\headshape#1#2#3{\mfsrc {headshape (#1, #2, #3);}}
%%%
%%%
% Define mfpic graphics macros.
\newdef\@mfpic@graf@macs
{%
  %%
  %% The (METAFONT based) drawing macros:
  %%
  % Tiling environment:
  \newdef\tile##1{\mfsrc {tile (##1);}}%
  \newdef\endtile{\mfsrc {endtile;}}%
  %
  % Store all enclosed paths in METAFONT path array ##1.
  % The grouping is to localise the redefinition of \store@path.
  %
  \newdef\patharr##1{%
    \begingroup
      \mfsrc {hide (numeric ##1; path ##1[]; ##1 = 0;)}%
      \redef\store@path{\mfsrc {store (##1[incr ##1])}}}%
  \newdef\endpatharr{%
      \redef\store@path{\mfsrc {store (curpath)}}%
    \endgroup}%
  %
  % Prefix commands:
  %
  % Store following mfpic path in METAFONT path variable ##1:
  \newdef\store##1##2{\mfsrc {store (##1)}%
    \@startfigfalse
    \@imrendfalse
      ##2%
    \@imrendtrue
    \@startfigtrue}%
  % Allow METAFONT path ##1 to be shaded, connected, etc:
  \newdef\mfobj##1{\@figmac {##1}}%
  % Tesselation (tiling):
  \newdef\tess##1{\@rendmac {tess (##1)}}%
  % Shading:
  \newdef\@shade[##1]{\@rendmac {shade (##1)}}%
  \newdef\shade{\do@ptparam{@shade}{\the\shadespace}}%
  % Hatching:
  \newdef\@thatch[##1,##2]{\@rendmac {thatch (##1, ##2)}}%
  \newdef\thatch{\do@ptparam{@thatch}{\the\hatchspace, 0 deg}}%
  % Extra hatch macros, for convenience:
  \newdef\@lhatch[##1]{\@rendmac {thatch (##1, -45 deg)}}%
  \newdef\lhatch{\do@ptparam{@lhatch}{\the\hatchspace}}%
  \newdef\@rhatch[##1]{\@rendmac {thatch (##1, 45 deg)}}%
  \newdef\rhatch{\do@ptparam{@rhatch}{\the\hatchspace}}%
  \newdef\@xhatch[##1]{\@rendmac {thatch (##1, 45 deg) thatch (##1, -45 deg)}}%
  \newdef\xhatch{\do@ptparam{@xhatch}{\the\hatchspace}}%
  \newlet\hatch=\xhatch
  % Filling and Erasing:
  \newdef\gfill {\@rendmac {filled}}%
  \newdef\gclear{\@rendmac {unfilled}}%
  % Arrowhead:
  \newdef\@arrowoption##1##2%
  {%
    \ifx ##1l\gdef\@hlength{##2}\else
    \ifx ##1r\gdef\@hrotate{##2}\else
    \ifx ##1b\gdef\@hbackset{##2}\fi\fi\fi
  }%
  \newdef\@arrowthree[##1##2]%
  {%
    \@arrowoption{##1}{##2}%
    \@modmac {headpath (\@hlength, \@hrotate, \@hbackset)}%
  }%
  \newdef\@arrowtwo[##1##2]{%
    \@arrowoption{##1}{##2}%
    \do@ptparam{@arrowthree}{WW}}%
  \newdef\@arrowone[##1##2]%
  {%
    \gdef\@hlength{\the\headlen}%
    \gdef\@hrotate{0 deg}%
    \gdef\@hbackset{0pt}%
    \@arrowoption{##1}{##2}%
    \do@ptparam{@arrowtwo}{ZZ}%
  }%
  \newdef\arrow{\do@ptparam{@arrowone}{YY}}%
  % Solid path:
  \newdef\draw {\@rendmac {drawn}}%
  % Dashed path:
  \newdef\@dashed[##1,##2]{%
    \@rendmac {dashed (##1,##2)}}%
  \newdef\dashed{%
    \do@ptparam{@dashed}%
      {\the\dashlen,\the\dashspace}}%
  % Dotted path:
  \newdef\@dotted[##1,##2]{%
    \@rendmac {dotted (##1,##2)}}%
  \newdef\dotted{%
    \do@ptparam{@dotted}%
      {\the\dotsize,\the\dotspace}}%
  % Closed path:
  \newdef\lclosed{\@closmac {lclosed}}%
  \newdef\bclosed{\@closmac {bclosed}}%
  \newdef\sclosed{\@closmac {sclosed}}%
  \newdef\cbclosed{\@closmac {cbclosed}}%
  %
  % Reversing orientation of path:
  \newdef\reverse {\@modmac {reverse}}%
  %
  % Rotating a path:
  \newdef\rotatepath##1{\@modmac {rotatedpath (##1)}}%
  %
  %
  % Connecting two or more open figures:
  \newdef\connect{%
    \@figmac {begingroup}%
    \patharr {nexus}%
  }%
  \newdef\endconnect{%
    \endpatharr
    \mfsrc {mkpoly (false, nexus)}%
    \mfsrc {endgroup}%
  }%
  %
  %
  % Affine transforms of the METAFONT _coordinate system_ :
  % Grouping macros that enable nested coordinate systems:
  \newdef\coords{\mfsrc {}\mfsrc {bcoords}\mfsrc {}}%
  \newdef\endcoords{\mfsrc {}\mfsrc {ecoords}\mfsrc {}}%
  % Macro that applies a nominated METAFONT affine transformer:
  \newdef\applyT##1{\mfsrc {hide (apply_t (##1);)}}%
  % Specific transform macros for METAFONT coordinates;
  % See _The METAFONTbook_ for most of these.
  \newdef\rotate##1{\applyT {rotated ##1}}%  degrees.
  \newdef\rotatearound##1##2{\applyT {rotatedaround (##1, ##2)}}%  point, degrees.
  \newdef\@turn[##1]##2{\rotatearound{##1}{##2}}%  point, degrees.
  \newdef\turn{\do@ptparam{@turn}{(0,0)}}%
  \newdef\reflectabout##1##2{\applyT {reflectedabout (##1,##2)}}%  line ##1 -- ##2.
  \newlet\mirror=\reflectabout
  \newdef\shift##1{\applyT {shifted ##1}}%  pair.
  \newdef\scale##1{\applyT {scaled ##1}}%  same scaling in X and Y directions.
  \newdef\xscale##1{\applyT {xscaled ##1}}%  scale only X.
  \newdef\yscale##1{\applyT {yscaled ##1}}%  scale only Y.
  \newdef\zscale##1{\applyT {zscaled ##1}}%  complex multiplication of points.
  \newdef\xslant##1{\applyT {xslant ##1}}%  skew in X direction by a multiple of Y coord.
  \newdef\yslant##1{\applyT {yslant ##1}}%  skew in Y direction by a multiple of X coord.
  \newdef\zslant##1{\applyT {zslant ##1}}%  see `grafbase.mf'.
  \newdef\boost##1{\applyT {boost ##1}}%  special relativity boost.
  \newdef\xyswap{\applyT {xyswap}}%  reflect in line Y=X.
  %
  % End of Prefix commands.
  %
  % Axes and axis Marks:
  \newdef\@axes[##1]{%
    \mfsrc {axes (##1);}}%
  \newdef\axes{\do@ptparam{@axes}{\the\axisheadlen}}%
  \newdef\@xmarks[##1]##2{%
    \mfsrc {xmarks (##1,##2);}}%
  \newdef\xmarks{\do@ptparam{@xmarks}{\the\hashlen}}%
  \newdef\@ymarks[##1]##2{%
    \mfsrc {ymarks (##1,##2);}}%
  \newdef\ymarks{\do@ptparam{@ymarks}{\the\hashlen}}%
  % Points (filled disks of a given size) :
  \newdef\grid##1{%
    \mfsrc {grid (##1);}}%
  \newdef\@point[##1]##2{%
    \mfsrc {}%
    \mfsrc {pointd (##1, \ifpointfill true\else false\fi) (##2);}}%
  \newdef\point{\do@ptparam{@point}{\the\pointsize}}%
  % Polyline (open) :
  \newdef\polyline##1{%
    \@figmac {polyline (false) (##1)}}%
  \newlet\lines=\polyline
  % Polygon (closed) :
  \newdef\polygon##1{%
    \@figmac {polyline (true) (##1)}}%
  % Upright rectangle:
  \newdef\rect##1{%
    \@figmac {rect (##1)}}%
  % Curve (open) :
  \newdef\curve##1{%
    \@figmac {curve (false) (##1)}}%
  % Cyclic curve (closed) :
  \newdef\cyclic##1{%
% BEGIN TEST:
%    \message {CYCLIC argument = ``##1''}%
% END TEST.
    \@figmac {curve (true) (##1)}}%
  % Open Quadratic B-splines
  \newdef\qspline##1{%
    \@figmac {openqbs (##1)}}%
  % Closed Quadratic B-splines
  \newdef\closedqspline##1{%
    \@figmac {closedqbs (##1)}}%
  % Open Cubic B-splines
  \newdef\cspline##1{%
    \@figmac {opencbs (##1)}}%
  % Closed Cubic B-splines
  \newdef\closedcspline##1{%
    \@figmac {closedcbs (##1)}}%
  % Circle and Ellipse:
  \newdef\circle##1{\@figmac {circle (##1)}}%
  \newdef\@ellipse[##1]##2{%
    \@figmac {ellipse (##2, ##1)}}%
  \newdef\ellipse{\do@ptparam{@ellipse}{0 deg}}%
  % Circular Arc:
  \newdef\@arc[##1]##2{%
    \if ##1s\@figmac {arcpps (##2)}\else
    \if ##1p\@figmac {arcplr (##2)}\else
    \if ##1c\@figmac {arccps (##2)}\else
           \@figmac {arcppp (##2)}\fi\fi\fi}%
  \newdef\arc{\do@ptparam{@arc}{s}}%
  % Polar coordinates:
  \newdef\plr##1{map (polar) (##1)}%
  % `Turtle graphics':
  \newdef\turtle##1{%
    \@figmac {turtle (##1)}}%
  % Sector of a circular region:
  \newdef\sector##1{%
    \@figmac {sector (##1)}}%
  % Function Plots:
  \newdef\@function[##1]##2##3{%
    \@figmac {function (%
      \if ##1s true\else false\fi) (##2) (##3)}}%
  \newdef\function{\do@ptparam{@function}{s}}%
  \newdef\@parafcn[##1]##2##3{%
    \@figmac {parafcn (%
      \if ##1s true\else false\fi) (##2) (##3)}}%
  \newdef\parafcn{\do@ptparam{@parafcn}{s}}%
  \newdef\@plrfcn[##1]##2##3{%
    \@figmac {plrfcn (%
      \if ##1s true\else false\fi) (##2) (##3)}}%
  \newdef\plrfcn{\do@ptparam{@plrfcn}{s}}%
  \newdef\@btwnfcn[##1]##2##3##4{%
    \@figmac {((function (
      \if ##1s true\else false\fi) (##2) (##3))
      --(reverse function (
      \if ##1s true\else false\fi) (##2) (##4))
      --cycle)}}%
  \newdef\btwnfcn{\do@ptparam{@btwnfcn}{p}}%
  \newdef\@plrregion[##1]##2##3{%
    \@figmac {(plrfcn (\if ##1s true\else false\fi) (##2) (##3)
             --(0,0)--cycle)}}%
  \newdef\plrregion{\do@ptparam{@plrregion}{p}}%
  %%
  %% End of the (METAFONT based) drawing macros.
  %%
}%
%%%
%%% End of \@mfpic@graf@macs Definition.
%%%
%
%%%
%%% Beginning mfpic environment:
%%%
\newdef\@mfpic#1#2#3#4#5#6%
{%
%%%
%%%
 % Set up TeX
 % Must enter horizontal mode for LaTeX center environment to work.
% \leavevmode
 \begingroup
  % Change to null font for duration of mfpic environment.
  % Advantage:  Prevents errant spaces from spoiling the typesetting
  % of the graph.
  % Disadvantage:  Also disallows typesetting of normal text,
  % unless one restricts that text to confined environments
  % such as those of mfpic's captions and labels.
  \nullfont
  % Plain TeX setting for paragraph's `finishing glue' (TeXbook, p 100).
  \parfillskip0pt plus1fil\relax
  % Define mfpic graphics macros.
  \@mfpic@graf@macs
  % Local conversion of a dimension control sequence ##1 :
  % (TeX won't \advance a font dimension,
  %  so use dimen255 as local temporary.)
  \newdef\@xconv##1%
  {%
    {%
      \dimen255 = ##1\relax
      \advance\dimen255 by -#3\mfpicunit
      \dimen255 = #1\dimen255
      \global ##1 = \dimen255
    }%
  }%
  \newdef\@yconv##1%
  {%
    {%
      \dimen255=##1\relax
      \advance\dimen255 by -#5\mfpicunit
      \dimen255 = -#2\dimen255
      \global ##1 = \dimen255
    }%
  }%
  % Set up Graph Box:
  \global \advance\@gcode1
  \@graphright=#4\mfpicunit \@xconv\@graphright
  \@graphht=#6\mfpicunit \@yconv\@graphht
  \@graphleft=0pt \@xconv\@graphleft
  \@graphdp=0pt \@yconv\@graphdp
  \global \@graphwd=\@graphright
  %
  % 
  %%% Only Here Is \@graphfont Used. %%%
  % If the graphics font is undefined (ie, if user has forgotten to
  % open a graphs file) then COMPLAIN!
  {%
    \chardef\\=`\\%
    \newdef\mf@bsl{\expandafter\mf@gobble\string\\}%
    \ifx \@graphfont\UndEfInEd
      \immediate\write16 {}
      \immediate\write16
        {mfpic: You must open a graphs file, using \mf@bsl opengraphsfile}%
      \immediate\write16
        {mfpic: (and match that with a \mf@bsl closegraphsfile),}%
      \immediate\write16
        {mfpic: otherwise this happens:}%
    \fi
  }%
  % Typeset METAFONT picture.
  \global \setbox\@wholegraph=
    \vtop to \@graphht  % NOTE: was \vtop then \vbox.
    {%
      \hbox to \@graphwd
        {\noindent\@graphfont\char\@gcode\hss}% End hbox.
     \vss
    }% End vtop.
  % Set up METAFONT file:
  \mfsrc {}%
  \mfsrc {unitlen:=\the\mfpicunit\mf@s;}%
  \mfsrc {xscale:=#1; yscale:=#2;}%
  \mfsrc {xneg:=#3; xpos:=#4;}%
  \mfsrc {yneg:=#5; ypos:=#6;}%
  \mfsrc {beginmfpic (incr gcode);}%
  %
  % (TeX based) labels and caption:
  %
  % Label:
  %
  % Arg 1 literals: t c b
  % Arg 2 literals: t c r
  % Arg 3 meaning: x position.
  % Arg 4 meaning: y position.
  % Arg 5 meaning: label's text; must be horizontal material.
  %
  \newdef\@tlabel[##1##2](##3,##4)##5{%
    % Compute width of graph with label (arg 5),
    % and reset size if necessary:
    %
    \setbox\@textbox=
      \vbox{% DHL:
        \def\\{\egroup\hbox\bgroup\ignorespaces}% DHL:
        \hbox\bgroup\@tcurr ##5\egroup  % End hbox.
      }% DHL:
    %
    \dimendef\@labeldim=255 % scratch register
    %
    % Stretch Graph Rightward:
    %
    \@labeldim=##3\mfpicunit
    \@xconv\@labeldim
    \if ##2l\advance\@labeldim by \wd\@textbox \else
    \if ##2c\advance\@labeldim by 0.5\wd\@textbox \fi\fi
    \ifdim \@labeldim>\@graphright
      \global \@graphright=\@labeldim \fi
    %
    % Stretch Graph Leftward:
    %
    \@labeldim=##3\mfpicunit
    \@xconv\@labeldim
    \if ##2r\advance\@labeldim by -\wd\@textbox \else
    \if ##2c\advance\@labeldim by -0.5\wd\@textbox \fi\fi
    \ifdim \@labeldim<\@graphleft
      \global \@graphleft=\@labeldim
    \fi
    %
    % Stretch Graph Upward:
    %
    \@labeldim=##4\mfpicunit
    \@yconv\@labeldim
    \if ##1b\advance\@labeldim by \ht\@textbox \else
    \if ##1c\advance\@labeldim by 0.5\ht\@textbox \fi\fi
    \ifdim \@labeldim>\@graphht
      \global \@graphht=\@labeldim
    \fi
    %
    % Stretch Graph Downward:
    %
    \@labeldim=##4\mfpicunit
    \@yconv\@labeldim
    \if ##1t\advance\@labeldim by -\dp\@textbox \else
    \if ##1c\advance\@labeldim by -0.5\dp\@textbox \fi\fi
    \ifdim \@labeldim<\@graphdp
      \global \@graphdp=\@labeldim
    \fi
    %
    % Set label onto graph:
    %
    \global \setbox\@wholegraph =
      \vtop{\unvbox\@wholegraph  % NOTE: was \vtop then \vbox.
        \vbox to0pt{%
          \if ##1c\kern-0.5\ht\@textbox \else
          \if ##1b\kern-\ht\@textbox \fi\fi
          \@labeldim=##4\mfpicunit
          \@yconv\@labeldim
          \kern\@labeldim
          \hbox{%
            \@labeldim=##3\mfpicunit
            \@xconv\@labeldim
            \kern\@labeldim
            \if ##2c\kern-0.5\wd\@textbox \else
            \if ##2r\kern-\wd\@textbox \fi\fi
            \box\@textbox }% End hbox.
          \vss}% End vbox.
        \nointerlineskip}% End vtop.
    \ignorespaces
  }% -- End \@tlabel
  %
  % \tlabel[tr](x,y){text} :
  %
  \newdef\tlabel{\do@ptparam{@tlabel}{bl}}%
  %
  % Caption:
  %
  % \@docaption (called by \endmfpic) :
  \newdef\@docaption{\global \@graphleft=0pt \@xconv\@graphleft \relax}%
%  \newdef\@docaption{}%
  %
  % Arg 1 meaning:  maxwd; see mfpicdoc.tex.
  % Arg 2 meaning:  linewd; see mfpicdoc.tex.
  % Arg 3 meaning:  caption's text.
  %
  \newdef\@tcaption[##1,##2]##3%
  {%
    % Redefine \@docaption to Set Caption:
    \redef\@docaption
    {%
      % Compute Adjustments to Center:
      % 1.  Measure caption text.
      % GT:  What if the caption's not horizontal material?)
      % GT:  A long caption doesn't wrap inside an hbox!
      %
      \setbox\@textbox =%
        \hbox
        \bgroup
          \@tcurr
          \def\\{\hskip\@m pt\relax}% DHL: \\ forces width test to "true".
          ##3%
        \egroup % End hbox.
      % 2.  If caption text is so much wider than graph, then
      %     stretch graph box horizontally.
      \ifdim \wd\@textbox>##1\@graphwd
%
%      \ifdim \wd\@textbox>\@graphwd
%        \@graphwd=\wd\@textbox
%
        \@graphwd=##2\@graphwd
        \setbox\@textbox =
          \hbox
          \bgroup
%            \tolerance=500\relax
%            \hfuzz=100pt\relax
            \vbox{%
              % Prevent \leftskip and \rightskip from interfering with
              % caption:
              \leftskip=0pt
              \rightskip=0pt
              % 3. Here's where the graph box's width is adjusted.
%              \hsize=##2\@graphwd
%
              \hsize=\@graphwd
%
              % 4. Contribute the caption text,
              %    in a nonindented paragraph below the graph.
              \def\\{\hfil\break\ignorespaces}% DHL:
              \noindent \@tcurr \unhbox\@textbox \relax
            }% End vbox.
          \egroup % End hbox.
      \fi
      \dimendef\@centerskip=255 % Scratch Register
      \@centerskip=\@graphwd
      \advance\@centerskip -\wd\@textbox
      \divide\@centerskip by 2
      % Set Caption onto Picture:
      \global \setbox\@wholegraph =
        \vbox{%
          % Check whether Caption's Wider than Graph:
          \ifdim \@centerskip<0pt
            \global \@graphleft = -\@centerskip
            \moveright -\@centerskip
          \fi
          \vbox
          \bgroup
            \unvbox\@wholegraph
            \medskip
            \hbox
            {%
              \noindent
              \kern\@centerskip
              \box\@textbox
            }% End hbox.
          \egroup % End vbox.
          % \vss
        }% End vbox.
    }% -- End \@docaption.
    \ignorespaces
  }% -- End \@tcaption.
  %
  % \tcaption[maxwd,linewd]{text} :
  %
  \newdef\tcaption{\do@ptparam{@tcaption}{1.2, 1.0}}%
  %
  % End of Object Macros.
  % Skip spaces in TeX document after \mfpic command.
  \ignorespaces
  % Retain line separations when writing METAFONT file.
  % ALAS!  \obeylines causes LaTeX center to write \@@par to MF file,
  % for each line break in \mfsrc calls.
  \preservelines
}%
%%%
%% End of \@mfpic Definition.
%%%
%%%
% Setting up optional arguments for \mfpic:
\newdef\@pici[#1]#2#3#4#5{\@mfpic{\@param}{#1}{#2}{#3}{#4}{#5}}
%%%
%%% Definition of \mfpic Command.
%%%
\wlog {mfpic: definition of mfpic command}
%
% \mfpic[xscale][yscale]{xneg}{xpos}{yneg}{ypos}
%
% One of xscale, yscale must be present;
% if only one is present, then xscale = yscale.
%
\newdef\mfpic[#1]{%
  \hbox{}%
  \redef\@param{#1}%
  \do@ptparam{@pici}{#1}}
%%%
%%% End of \mfpic Definition.
%%%
%%%
%%% Definition of Closure of mfpic Environment:
%%%
\wlog {mfpic: definition of closure of mfpic environment}
\newdef\endmfpic
{%
  \wlog {}%
  \wlog {mfpic: ENTERED endmfpic.}%
  \wlog {}%
  \global \@graphwd=\@graphright
%  \d@adv{\@graphwd}{-\@graphleft}%
%
  \wlog {mfpic: graphleft = \the\@graphleft}%
  \wlog {mfpic: graphright = \the\@graphright}%
  \wlog {mfpic: graphwd = \the\@graphwd}%
  \wlog {}%
%
%  \@docaption
  \global \setbox\@wholegraph =
    \vbox
    {%
      \hbox to \@graphwd
      {%
%        \kern-\@graphleft
        \box\@wholegraph
        \hss
      }% End hbox.
      % \vss
    }% End vbox.
%
  \@docaption
%
  \mfsrc {}%
  \mfsrc {endmfpic;}%
  \mfsrc {}%
%
  \wlog {mfpic: graphleft = \the\@graphleft}%
  \wlog {mfpic: graphright = \the\@graphright}%
  \wlog {mfpic: graphwd = \the\@graphwd}%
  \wlog {}%
  \wlog {mfpic: DONE endmfpic.}%
  \wlog {}%
%
  %
  % Typesetting the graph, including labels and caption.
  %
  % DHL: \s@vemfpic is only defined if \savepic{\foo} was issued since
  % DHL: the last \endmfpic (UndEfInEd is presumably always UndEfInEd)
  \ifx\s@vemfpic\UndEfInEd % DHL:
%    \leavevmode % DHL: moved from start of \mfpic
    \box\@wholegraph
  \else % DHL:
    % DHL: ... in which case \s@vemfpic expands to \b\foo
    \global\setbox\s@vemfpic=\box\@wholegraph
  \fi % DHL:
  %
  \endgroup
  \global\let\s@vemfpic\UndEfInEd
  % DHL: previous line requires a new "\savepic\bar"
  % DHL: to save the next pic in box \b\bar
  \ignorespaces
}%
%%%
%%% End of \endmfpic Definition.
%%%
%
% DHL: \onelevel\mumble expands \mumble one level in an \edef:
\newdef\onelevel#1{\expandafter\noexpand#1}  % DHL:
%
% DHL: \savepic{\foo} allocates a box \b\foo
% DHL: (the second \ is part of the name)
% DHL: and defines \foo to expand to \box\b\foo
\newdef\savepic#1{% DHL:
      % DHL: makes \s@vemfpic expand to \b\foo (which is one token!) :
  \xdef\s@vemfpic{\onelevel\csname b\string#1\endcsname}% DHL:
      % DHL: allocate the box
  \csname newbox\expandafter\endcsname\s@vemfpic  % DHL:
      % DHL: defines \foo to place the box
  \xdef#1{\box\s@vemfpic}%  DHL:
}  % DHL:
%
% DHL: \copypic\foo --> \copy\b\foo
\newdef\copypic#1{%  \leavevmode  % DHL: \leavevmode moved from start of \mfpic
  \copy\csname b\string#1\endcsname}  % DHL:
%%%
%%%
%
% Restore current Font after reading mfpic.tex file.
%
\@tcurr
%
%%%
%%%
% DHL use the loading check to restore \catcode (of @)
\csname mfpic-package\endcsname  % DHL:
\wlog {mfpic: `@' character has reverted to old catcode}
%
\endinput  % DHL:
%%%
%%%  EOF  mfpic.tex
%%%