new latex package diagmac2 (20apr09)

git-svn-id: svn://tug.org/texlive/trunk@12792 c570f23f-e606-0410-a88d-b1316a301751

1 files changed, 976 insertions, 0 deletions

diff --git a/Master/texmf-dist/tex/latex/diagmac2/diagmac2.sty b/Master/texmf-dist/tex/latex/diagmac2/diagmac2.sty
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+%MACROS FOR DIAGRAMS - J. C. Reynolds - December 1987
+
+% Modified to use pict2e.sty by Bob Tennent, February 2004
+% Changes indicated thusly:  %%%pict2e
+
+\AtBeginDocument{\RequirePackage{pict2e}} %%%pict2e
+\def\slopemax{1000}  %%%pict2e slope factor maximum 
+
+%This file contains general-purpose macros for drawing diagrams in LATEX,
+%followed by additional macros especially for category-theory diagrams.
+%A user's manual is given in the file diagmac.doc, and a test program is
+%given in the file diagmactest.tex.
+
+%GENERAL-PURPOSE MACROS
+
+%The following control symbols may need to be redefined by the user.
+\def\diagramunit{1pt}%Redefine only in main program or at the beginning
+%      of \diagram or \ctdiagram.
+\def\centerheight{3pt}
+\def\edgeheaddisp{4pt}
+\def\circleheaddisp{2pt}
+\def\diameterlist{1pt,2pt,3pt,4pt,5pt,6pt,7pt,8pt,9pt,10pt,11pt,%
+12pt,13pt,14pt,15pt,16pt,20pt,24pt,28pt,32pt,36pt,40pt,}
+%Redefine if circle fonts are different.
+
+%The following registers store the representation of diagram and/or
+%expression programs:
+\newdimen\texpr\newdimen\bexpr\newdimen\lexpr\newdimen\rexpr%current rectangle
+\newdimen\xcenter\newdimen\ycenter%center point
+\newcount\xslope\newcount\yslope%slope of current edge
+\newdimen\xstart\newdimen\ystart%start point of current edge
+\newdimen\xend\newdimen\yend%end point of current edge
+\newdimen\dcircle%diameter of current circle
+\newdimen\xcircle\newdimen\ycircle%center of current circle
+\newcount\zzisedge%1 if current edge is defined, 0 otherwise
+\newcount\zziscircle%1 if current circle is defined, 0 otherwise
+\newbox\zzdiagbox%printable material in state
+\newdimen\zztotlwidth\newdimen\zztotrwidth%horizontal extent of box material
+\newdimen\zztotheight\newdimen\zztotdepth%vertical extent of box material
+
+%The following registers are assigned globally to communicate information
+%across group boundaries:
+\newdimen\zzglobaltotlwidth\newdimen\zzglobaltotrwidth
+\newdimen\zzglobaltotheight\newdimen\zzglobaltotdepth
+\newdimen\zzglobalxcenter\newdimen\zzglobalycenter
+\newcount\zzglobalcnA
+
+%The following registers are used locally for various purposes:
+\newdimen\zzdmA\newdimen\zzdmB\newdimen\zzdmC\newdimen\zzdmD\newdimen\zzdmE
+\newdimen\zzdmF\newdimen\zzdmG\newdimen\zzdmH\newdimen\zzdmI
+\newcount\zzcnA\newcount\zzcnB\newcount\zzcnC
+\newcount\zzcnD\newcount\zzcnE\newcount\zzcnF
+\newcount\zzcnG\newcount\zzcnH\newcount\zzcnI
+
+%Hidden macros and other defined control symbols:
+%    generally used macros: \zzsetupbox\zznoshadow\zzissue\zzrecordwidth
+%        \zzrecordheight\zzmultdiagramunit\zzmakepicture\zzsqroot\zzdistance
+%        \zzreduceterms
+%    error-checking macros: \zzisnegside\zzcheckedge\zzcheckslope\zzcheckslopea
+%        \zzcheckcircle\zzcheckbool\zzcheckposdimen\zzchecknonnegnum
+%    used by \vertex: \zzconsvertexlist\zzconsvertexlista\zzconsvertexlistb
+%    used by \rect: \zzprocrect
+%    used by \hexagon: \zzprochexagon
+%    used by \octagon and \rorect: \zzprococtagon
+%    used by \diamond: \zzprocdiamond
+%    used by \rorect: \zzprocrorecta\zzsearchdiameterlist\zzsearchdiameterlista
+%        \zzsearchdiameterlistb
+%    used by \outline: \zzoutlinepoly\zzoutlinepolya\zzoutlinepolyb
+%        \zzoutlinepolyc
+%    used by \outline with \rorect: \zzoutlinerorect
+%    used by \setedge: \zzsearchvertexlist\zzsearchvertexlista
+%        \zzsearchvertexlistb
+%    used by \shadeedge: \zzcastpoly\zzcastpolya\zzcastpolyb
+%        \zzcastpolyc\zzcastpolye\zzcastpolyf\zzcastpolyg
+%    used by \drawdashedge, \drawdotedge, and \drawsolidedge: \zzdrawedge
+%    used by \drawedgehead: \zzdrawedgeheada
+%    used by all abutment macros: \zzslidehoriz\zzslidevert\zzclosestpoly
+%        \zzclosestpolya\zzclosestpolyb\zzclosestpolyc\zzclosestpolyd
+%    used by edge abutment macros: \zzabut
+%    used by circle abutment macros: \zzabutcircle\zzabutcirclea\zzrotate
+%    used by \shadeedge and all abutment macros: \zzcastpolyd
+%    used by \drawcircle: \zzdrawcirclea
+%    multiply defined control symbols: \zzvertexlist\zzshadow\zzglobalshadow
+%        \zztesta\zztestb\zzvertexitem\zzprocpoly\zzprocrorect\zznext
+%        \zzstartshadow\zzendshadow\zzlocalshadow
+
+%\diagram creates a box, initializes \zztotlwidth, \zztotrwidth, and
+%\zzvertexlist, sets \zzisedge to 0, executes #1, which must be a diagram
+%program, and then issues the resulting box, surrounded by kerns so that
+%there are no horizontal overhangs.
+
+\def\diagram#1{{\setbox\zzdiagbox=\hbox{$\mathsurround=0pt
+\zztotlwidth=0pt\zztotrwidth=0pt\def\zzvertexlist{\end}\zzisedge=0\relax
+#1\relax\kern\zztotrwidth\global\zzglobaltotlwidth=\zztotlwidth $}
+\kern-\zzglobaltotlwidth\box\zzdiagbox}}
+
+%\zzsetupbox sets \zzdiagbox to the expression #1 modified by the program #2.
+%It also sets \zzglobalxcenter and \zzglobalycenter to the coordinates of
+%the center relative to the reference point, \zzglobaltotlwidth to the
+%negative of the left overhang width of the expression, and \zzglobalshadow
+%to the shadow established by the program, relative to the reference point.
+%Before executing #2, it initializes \texpr, \bexpr, \lexpr, \rexpr,
+%\xcenter, and \ycenter appropriately, and sets \zziscircle to 0.
+
+\def\zzsetupbox#1#2{\setbox\zzdiagbox=\hbox{$\mathsurround=0pt
+\setbox\zzdiagbox=\hbox{$\mathsurround=0pt{{#1}}$}
+\texpr=\ht\zzdiagbox\bexpr=-\dp\zzdiagbox\rexpr=\wd\zzdiagbox\lexpr=0pt
+\xcenter=\rexpr\divide\xcenter by 2\ycenter=\centerheight
+\zztotlwidth=0pt\zztotrwidth=\rexpr\def\zzshadow{\zznoshadow0pt,0pt:;}
+\zziscircle=0
+\box\zzdiagbox\kern-\rexpr
+#2\relax
+\global\zzglobalxcenter=\xcenter\global\zzglobalycenter=\ycenter
+\global\zzglobaltotlwidth=\zztotlwidth\kern\zztotrwidth
+\global\let\zzglobalshadow=\zzshadow
+$}}
+
+%\zznoshadow is a dummy shadowing routine that gives an error when executed.
+
+\def\zznoshadow#1,#2:;{\errmessage{ATTEMPT TO OUTLINE OR ABUT AN EXPRESSION
+WITH NO SHADOW}}
+
+%\leftghost (\rightghost) sets \xcenter to \lexpr plus (\rexpr minus)
+%half of the width of its argument.
+
+\def\leftghost#1{\setbox\zzdiagbox=\hbox{$\mathsurround=0pt{{#1}}$}
+\xcenter=\wd\zzdiagbox\divide\xcenter by 2\advance\xcenter by \lexpr}
+
+\def\rightghost#1{\setbox\zzdiagbox=\hbox{$\mathsurround=0pt{{#1}}$}
+\xcenter=\wd\zzdiagbox\divide\xcenter by -2\advance\xcenter by \rexpr}
+
+%\zzissue should be executed after \zzsetupbox.  It issues the contents of
+%\zzdiagbox with its center placed at \zzdmA, \zzdmB (which are modified),
+%and adjusts \zztotlwidth and \zztotrwidth appropriately.
+
+\def\zzissue{\advance\zzdmA by -\zzglobalxcenter
+\advance\zzdmB by -\zzglobalycenter
+\zzdmC=\zzdmA\advance\zzdmC by \wd\zzdiagbox
+\zzdmD=\zzdmA\advance\zzdmD by \zzglobaltotlwidth
+\zzrecordwidth\zzdmD\zzdmC
+\kern\zzdmA\raise\zzdmB\box\zzdiagbox\kern-\zzdmC}
+
+%\zzrecordwidth adjusts \zztotlwidth to be the minimum of its previous value
+%and #1, and adjusts \zztotrwidth to be the maximum of its previous value
+%and #2.
+
+\def\zzrecordwidth#1#2{\relax\ifdim#1<\zztotlwidth\relax\zztotlwidth=#1\fi
+\ifdim\zztotrwidth<#2\relax\zztotrwidth=#2\fi}
+
+%\zzrecordheight adjusts \zztotheight to be the maximum of its previous value
+%and #1, and adjusts \zztotdepth to be the minimum of its previous value
+%and #2.
+
+\def\zzrecordheight#1#2{\relax\ifdim\zztotheight<#1\relax\zztotheight=#1\fi
+\ifdim#2<\zztotdepth\relax\zztotdepth=#2\fi}
+
+%\placed executes \zzsetupbox{#3}{#4} and issues the contents of the resulting
+%\zzdiagbox with its center placed at #1, #2 (which must be dimensions).
+%\place is similar except that #1, #2 must be integer multiples of
+%\diagramunit.
+
+\def\placed#1#2#3#4{\zzsetupbox{#3}{#4}\zzdmA=#1\zzdmB=#2\zzissue}
+
+\def\place#1,#2:#3#4{\zzsetupbox{#3}{#4}\zzmultdiagramunit\zzdmA{#1}
+\zzmultdiagramunit\zzdmB{#2}\zzissue}
+
+%\zzmultdiagramunit sets #1 to #2 times \diagramunit.
+
+\def\zzmultdiagramunit#1#2{#1=\diagramunit\multiply#1 by #2\relax}
+
+%\vertex#1,#2:#3#4 executes \zzsetupbox{#3}{#4}, issues the contents of the
+%resulting \zzdiagbox with its center placed at #1, #2 times \diagramunit,
+%adjusts \zztotlwidth and \zztotrwidth appropriately, and adds \zzglobalshadow
+%to the beginning of \zzvertexlist (unless \zzglobalshadow is a call of
+%\zznoshadow) after readjusting the shadow to be relative
+%to the coordinates of the enclosing box.
+
+\def\vertex#1,#2:#3#4{\place{#1},{#2}:{#3}{#4}\zzcnA=#1\zzcnB=#2\relax
+\expandafter\zzconsvertexlist\zzglobalshadow}
+
+\def\zzconsvertexlist#1#2,#3:#4;{\def\zztesta{#1}\def\zztestb{\zznoshadow}
+\ifx\zztesta\zztestb\else
+\advance\zzdmA by #2\advance\zzdmB by #3\relax
+\edef\zzvertexitem{\the\zzcnA,\the\zzcnB:\noexpand #1\the\zzdmA,\the\zzdmB:#4;}
+\expandafter\zzconsvertexlista\zzvertexlist\fi}
+
+\def\zzconsvertexlista{\expandafter\zzconsvertexlistb\zzvertexitem}
+
+\def\zzconsvertexlistb#1\end{\def\zzvertexlist{#1\end}}
+
+%\rect, \hexagon, \octagon, and \diamond (and, roughly speaking, \rorect)
+%are polygon descriptors.  A polygon descriptor defines \zzshadow to have
+% the form \somecontrolsymbol #1,#2:#3; such that executing
+%\zzshadow causes a call \zzprocpoly{#1}{#2}{<edgelist>}, where <edgelist>
+%depends only upon the parameter #3.  Here #1, #2 are the
+%coordinates of a vertex of a convex polygon, and <edgelist> is a list of
+%triples describing the edges of the polygon in clockwise order.  If an
+%edge is x = xs.t + x0, y = ys.t + y0 for 0 < t < tend (with the start at
+%t = 0 and the end at t = tend when the edge is traversed in clockwise
+%order) the the trip describing the edge is {xs}{ys}{tend}, where xs and
+%ys are numbers (the brackets may be omitted for single-digit numbers)
+%and tend is a dimension. xs and ys must have a least common divisor of one.
+
+\def\rect{\zzdmC=\rexpr\advance\zzdmC by -\lexpr
+\zzdmD=\texpr\advance\zzdmD by -\bexpr
+\zzisnegside{\zzdmC}{RECT}\zzisnegside{\zzdmD}{RECT}
+\edef\zzshadow{\noexpand\zzprocrect
+\the\lexpr,\the\texpr:\the\zzdmC,\the\zzdmD;}}
+
+\def\zzprocrect#1,#2:#3,#4;{\zzprocpoly
+{#1}{#2}{10{#3}0{-1}{#4}{-1}0{#3}01{#4}}}
+
+\def\zzisnegside#1#2{\relax\ifdim#1<0pt\errmessage
+{#2 WITH NEGATIVE SIDE}\fi}
+
+\def\hexagon{\zzdmC=\rexpr\advance\zzdmC by -\lexpr
+\zzdmD=\texpr\advance\zzdmD by -\bexpr\divide\zzdmD by 4
+\zzisnegside{\zzdmC}{HEXAGON}\zzisnegside{\zzdmD}{HEXAGON}
+\edef\zzshadow{\noexpand\zzprochexagon
+\the\lexpr,\the\texpr:\the\zzdmC,\the\zzdmD;}}
+
+\def\zzprochexagon#1,#2:#3,#4;{\zzprocpoly{#1}{#2}
+{10{#3}1{-2}{#4}{-1}{-2}{#4}{-1}0{#3}{-1}2{#4}12{#4}}}
+
+\def\octagon#1{\zzdmC=#1\zzdmD=\zzdmC\multiply\zzdmD by -2\zzdmE=\zzdmD
+\advance\zzdmD by \rexpr\advance\zzdmD by -\lexpr
+\advance\zzdmE by \texpr\advance\zzdmE by -\bexpr
+\zzdmF=\lexpr\advance\zzdmF by \zzdmC
+\zzisnegside{\zzdmC}{OCTAGON}\zzisnegside{\zzdmD}{OCTAGON}
+\zzisnegside{\zzdmE}{OCTAGON}
+\edef\zzshadow{\noexpand\zzprococtagon
+\the\zzdmF,\the\texpr:\the\zzdmC,\the\zzdmD,\the\zzdmE;}}
+
+\def\zzprococtagon#1,#2:#3,#4,#5;{\zzprocpoly{#1}{#2}
+{10{#4}1{-1}{#3}0{-1}{#5}{-1}{-1}{#3}{-1}0{#4}{-1}1{#3}01{#5}11{#3}}}
+
+\def\diamond{\zzdmC=\texpr\advance\zzdmC by -\bexpr
+\advance\zzdmC by \rexpr\advance\zzdmC by -\lexpr\divide\zzdmC by 2
+\zzdmD=\lexpr\advance\zzdmD by \rexpr\divide\zzdmD by 2
+\zzdmE=\texpr\advance\zzdmE by \bexpr\divide\zzdmE by 2\advance\zzdmE by \zzdmC
+\zzisnegside{\zzdmC}{DIAMOND}
+\edef\zzshadow{\noexpand\zzprocdiamond
+\the\zzdmD,\the\zzdmE:\the\zzdmC;}}
+
+\def\zzprocdiamond#1,#2:#3;{\zzprocpoly{#1}{#2}
+{1{-1}{#3}{-1}{-1}{#3}{-1}1{#3}11{#3}}}
+
+\def\rorect#1#2#3{\zzcheckposdimen{#1}{FIRST}{RORECT}
+\zzcheckbool{#2}{SECOND}{RORECT}\zzcheckbool{#3}{THIRD}{RORECT}
+\zzdmD=\rexpr\advance\zzdmD by -\lexpr\zzdmE=\texpr\advance\zzdmE by -\bexpr
+\zzdmC=#1\relax
+\ifnum#2=1\relax\ifdim\zzdmD>\zzdmC\relax\zzdmC=\zzdmD\fi\fi
+\ifnum#3=1\relax\ifdim\zzdmE>\zzdmC\relax\zzdmC=\zzdmE\fi\fi
+%\expandafter\zzsearchdiameterlist\diameterlist\end\zzdmC=\zzdmF\relax %%%pict2e
+\ifdim\zzdmC>\zzdmD\relax\zzdmD=\zzdmC\fi
+\ifdim\zzdmC>\zzdmE\relax\zzdmE=\zzdmC\fi
+\zzdmF=\lexpr\advance\zzdmF by \rexpr\divide\zzdmF by 2
+\zzdmG=\bexpr\advance\zzdmG by \texpr\divide\zzdmG by 2
+\edef\zzshadow{\noexpand\zzprocrorect
+\the\zzdmF,\the\zzdmG:\the\zzdmC,\the\zzdmD,\the\zzdmE;}}
+
+\def\zzsearchdiameterlist#1{\def\zztesta{#1}\def\zztestb{\end}
+\ifx\zztesta\zztestb\let\zznext=\zzsearchdiameterlista
+\else\let\zznext=\zzsearchdiameterlistb\fi\zznext #1}
+
+\def\zzsearchdiameterlista#1\end{}
+
+\def\zzsearchdiameterlistb#1,{\zzdmF=#1\relax
+\ifdim\zzdmF<\zzdmC\relax\let\zznext=\zzsearchdiameterlist
+\else\let\zznext=\zzsearchdiameterlista\fi\zznext}
+
+%\outline uses \zzoutlinepoly and \zzoutlinerorect to issue an outline of
+%the shadow.
+
+\def\outline{\def\zzprocpoly{\zzoutlinepoly}
+\def\zzprocrorect{\zzoutlinerorect}\zzshadow}
+
+%\zzmakepicture encapsulates all usage of the LATEX picture facility.
+
+\def\zzmakepicture#1{{\setlength{\unitlength}{1sp}\begin{picture}(0,0)
+#1\relax
+\global\zzglobaltotlwidth=\zztotlwidth\global\zzglobaltotrwidth=\zztotrwidth
+\global\zzglobaltotheight=\zztotheight\global\zzglobaltotdepth=\zztotdepth
+\end{picture}\vrule height\zzglobaltotheight depth-\zzglobaltotdepth width0pt}
+\zztotlwidth=\zzglobaltotlwidth\zztotrwidth=\zzglobaltotrwidth}
+
+\def\zzoutlinepoly#1#2#3{\zzmakepicture{\zzdmA=#1\zzdmB=#2\relax
+\zztotheight=\zzdmB\zztotdepth=\zzdmB\zzoutlinepolya #3\end}}
+
+\def\zzoutlinepolya#1{\def\zztesta{#1}\def\zztestb{\end}
+\ifx\zztesta\zztestb\let\zznext=\zzoutlinepolyb
+\else\let\zznext=\zzoutlinepolyc\fi\zznext {#1}}
+
+\def\zzoutlinepolyb#1{}
+
+\def\zzoutlinepolyc#1#2#3{\zzrecordwidth\zzdmA\zzdmA\zzrecordheight\zzdmB\zzdmB
+\zzdmE=#3\multiply\zzdmE by #1\zzdmF=#3\multiply\zzdmF by #2\relax
+\zzcnA=\zzdmA\zzcnB=\zzdmB\relax
+\ifnum #1=0\relax\zzcnC=\zzdmF\else\zzcnC=\zzdmE\fi
+\ifnum\zzcnC<0\relax\zzcnC=-\zzcnC\fi
+\put(\zzcnA,\zzcnB){\line(#1,#2){\zzcnC}}
+\advance\zzdmA by \zzdmE\advance\zzdmB by \zzdmF
+\zzoutlinepolya}
+
+\def\zzoutlinerorect#1,#2:#3,#4,#5;{\zzmakepicture{
+\zzdmA=#1\zzdmB=#2\zzdmC=#3\zzdmD=#4\zzdmE=#5
+\zzcnA=\zzdmA\zzcnB=\zzdmB\zzcnC=\zzdmC\zzcnD=\zzdmD\zzcnE=\zzdmE
+\ifnum\zzcnD=\zzcnC\relax\put(\zzcnA,\zzcnB){\oval(\zzcnD,\zzcnE)}
+\else\ifnum\zzcnE=\zzcnC\relax\put(\zzcnA,\zzcnB){\oval(\zzcnD,\zzcnE)}
+\else\advance\zzcnE by -\zzcnC
+\zzcnF=\zzcnE\divide\zzcnF by 2\advance\zzcnF by \zzcnB
+\put(\zzcnA,\zzcnF){\oval(\zzcnD,\zzcnC)[t]}
+\advance\zzcnF by -\zzcnE
+\put(\zzcnA,\zzcnF){\oval(\zzcnD,\zzcnC)[b]}
+\zzcnC=\zzcnD\divide\zzcnC by 2\advance\zzcnA by \zzcnC
+\put(\zzcnA,\zzcnF){\line(0,1){\zzcnE}}
+\advance\zzcnA by -\zzcnD
+\put(\zzcnA,\zzcnF){\line(0,1){\zzcnE}}\fi\fi
+\zztotheight=\zzdmE\divide\zztotheight by 2\advance\zztotheight by \zzdmB
+\zztotdepth=\zztotheight\advance\zztotdepth by -\zzdmE
+\zzdmC=\zzdmD\divide\zzdmC by -2\advance\zzdmC by \zzdmA
+\advance\zzdmD by \zzdmC\zzrecordwidth\zzdmC\zzdmD}}
+
+%\border, \borderto, and \symmetrize adjust the current rectangle.
+
+\def\border#1#2{\advance\texpr by #2\advance\bexpr by -#2
+\advance\lexpr by -#1\advance\rexpr by #1}
+
+\def\borderto#1#2{\zzdmA=\rexpr\advance\zzdmA by -\lexpr\relax
+\ifdim#1>\zzdmA\relax\advance\zzdmA by -#1\divide\zzdmA by 2
+\advance\rexpr by -\zzdmA\advance\lexpr by \zzdmA\fi
+\zzdmA=\texpr\advance\zzdmA by -\bexpr\relax
+\ifdim#2>\zzdmA\relax\advance\zzdmA by -#2\divide\zzdmA by 2
+\advance\texpr by -\zzdmA\advance\bexpr by \zzdmA\fi}
+
+\def\symmetrize{\zzdmA=\texpr\advance\zzdmA by -\ycenter
+\zzdmB=\ycenter\advance\zzdmB by -\bexpr\relax
+\ifdim\zzdmA<\zzdmB\relax\zzdmA=\zzdmB\fi
+\texpr=\ycenter\advance\texpr by \zzdmA
+\bexpr=\ycenter\advance\bexpr by -\zzdmA}
+
+%\setedge#1,#2,#3,#4: accepts four numbers (giving dimensions as multiples of
+%\diagramunit).  It sets \xstart, \ystart, \xend, \yend to #1, #2, #3,
+%#4, each multiplied by \diagramunit, and \xslope, \yslope to numbers
+% giving the slope of the line from \xstart, \ystart to \xend, \yend,
+%reduced to have a least common divisor.  It uses \zzsearchvertexlist to set
+%\zzstartshadow (\zzendshadow) to the \zzshadow stored on \zzvertexlist with
+%coordinates #1, #2 (#3, #4).  It sets \zzisedge to 1.
+
+\def\setedge#1,#2,#3,#4:{\zzcnA=#1\zzcnB=#2
+\zzmultdiagramunit\xstart\zzcnA\zzmultdiagramunit\ystart\zzcnB
+\expandafter\zzsearchvertexlist\zzvertexlist
+\let\zzstartshadow=\zzshadow
+\zzcnA=#3\zzcnB=#4
+\zzmultdiagramunit\xend\zzcnA\zzmultdiagramunit\yend\zzcnB
+\expandafter\zzsearchvertexlist\zzvertexlist
+\let\zzendshadow=\zzshadow
+\xslope=#3\advance\xslope by -#1\relax
+\yslope=#4\advance\yslope by -#2\relax
+\zzreduceterms\xslope\yslope{START AND END OF EDGE ARE BOTH THE SAME}
+\xslope=\zzcnC\yslope=\zzcnD\zzisedge=1}
+
+%\zzreduceterms sets \zzcnC and \zzcnD to the results of dividing the numbers
+% #1 and #2 by their greatest common divisor.  The error message #3 is given
+%if #1 and #2 are both zero.
+
+\def\zzreduceterms#1#2#3{{
+\ifnum#1<0\relax\zzcnA=-#1\else\zzcnA=#1\fi
+\ifnum#2<0\relax\zzcnB=-#2\else\zzcnB=#2\fi
+\loop\ifnum\zzcnB>0\relax
+\zzcnC=\zzcnA\divide\zzcnC by \zzcnB\multiply\zzcnC by -\zzcnB
+\advance\zzcnC by \zzcnA\zzcnA=\zzcnB\zzcnB=\zzcnC
+\repeat\relax
+\ifnum\zzcnA=0\errmessage{#3}\fi
+\global\zzglobalcnA=\zzcnA}
+\zzcnC=#1\divide\zzcnC by \zzglobalcnA\zzcnD=#2\divide\zzcnD by \zzglobalcnA}
+
+%\zzsearchvertexlist\zzvertexlist searches \zzvertexlist for an entry of the
+%form #1,#2:#3; for which #1 = \zzcnA and #2 = \zzcnB.  If such an entry is
+%found, \zzshadow is defined to be #3;.  Otherwise, \zzshadow is defined to be
+%\zzdmE=\zzdmA\zzdmF=\zzdmB.
+
+\def\zzsearchvertexlist#1{\def\zztesta{#1}\def\zztestb{\end}
+\ifx\zztesta\zztestb\def\zzshadow{\zzdmE=\zzdmA\zzdmF=\zzdmB}
+\let\zznext=\zzsearchvertexlista
+\else\let\zznext=\zzsearchvertexlistb\fi\zznext #1}
+
+\def\zzsearchvertexlista#1\end{}
+
+\def\zzsearchvertexlistb#1,#2:#3;{\relax
+\ifnum\zzcnA=#1\relax\ifnum\zzcnB=#2\relax
+\def\zzshadow{#3;}\let\zznext=\zzsearchvertexlista
+\else\let\zznext=\zzsearchvertexlist\fi
+\else\let\zznext=\zzsearchvertexlist\fi\zznext}
+
+%\shadeedge shades the start and end of the current edge, changing \xstart,
+%\ystart, \xend, \yend.
+
+\def\shadeedge{\zzcheckedge{SHADE}
+\def\zzprocpoly{\zzcastpoly}\def\zzprocrorect{\zzprocrorecta}
+\zzdmA=\xstart\zzdmB=\ystart\zzcnA=\xslope\zzcnB=\yslope
+\zzstartshadow\xstart=\zzdmE\ystart=\zzdmF
+\zzdmA=\xend\zzdmB=\yend\zzcnA=-\xslope\zzcnB=-\yslope
+\zzendshadow\xend=\zzdmE\yend=\zzdmF}
+
+\def\zzcheckedge#1{\relax\ifnum\zzisedge=0\relax\errmessage
+{ATTEMPT TO #1 NONEXISTENT EDGE}\fi}
+
+%\zzprocrorecta is used as the definition of \zzprocrorect within \shadeedge
+%and \zzabut.  It causes a rounded rectangle to be treated as the
+%circumscribed octagon for purposes of shadowing or abutment.
+
+\def\zzprocrorecta#1,#2:#3,#4,#5;{\zzdmC=#3
+\multiply\zzdmC by 53\divide\zzdmC by 181
+\zzdmD=\zzdmC\multiply\zzdmD by -2\zzdmE=\zzdmD
+\advance\zzdmD by #4\advance\zzdmE by #5
+\zzdmF=#4\divide\zzdmF by -2\advance\zzdmF by #1\advance\zzdmF by \zzdmC
+\zzdmG=#5\divide\zzdmG by 2\advance\zzdmG by #2
+\edef\zzlocalshadow{\noexpand\zzprococtagon
+\the\zzdmF,\the\zzdmG:\the\zzdmC,\the\zzdmD,\the\zzdmE;}
+\zzlocalshadow}
+
+%\zzcastpoly computes the outgoing intersection of a directed line,
+%x = xs.t+x0, y = ys.t+y0 with a convex polygon.  It is called
+%by defining \zzprocpoly to be \zzcastpoly, setting \zzdmA, \zzdmB, \zzcnA,
+%\zzcnB to x0, y0, xs, ys, and executing \zzshadow, which must have been
+%defined by a polygon descriptor.  The result is left in \zzdmE, \zzdmF.
+%If the directed line does not intersect the polygon, the result is the
+%point on the line that is closest to the polygon.
+
+\def\zzcastpoly#1#2#3{\zzdmC=#1\zzdmD=#2\zzcnC=0
+\zzcastpolya #3\end}
+
+\def\zzcastpolya#1{\def\zztesta{#1}\def\zztestb{\end}
+\ifx\zztesta\zztestb\let\zznext=\zzcastpolyg
+\else\let\zznext=\zzcastpolyc\fi\zznext {#1}}
+
+\def\zzcastpolyb#1\end{\zzcnC=\zzcnA\multiply\zzcnC by \zzcnA
+\zzcnD=\zzcnB\multiply\zzcnD by \zzcnB\advance\zzcnC by \zzcnD
+\zzdmE=\zzdmC\advance\zzdmE by -\zzdmA\multiply\zzdmE by \zzcnA
+\zzdmF=\zzdmD\advance\zzdmF by -\zzdmB\multiply\zzdmF by \zzcnB
+\advance\zzdmE by \zzdmF\divide\zzdmE by \zzcnC\zzdmF=\zzdmE
+\multiply\zzdmE by \zzcnA\advance\zzdmE by \zzdmA
+\multiply\zzdmF by \zzcnB\advance\zzdmF by \zzdmB}
+
+
+\def\zzcastpolyc#1#2#3{\zzcnD=\zzcnB\multiply\zzcnD by #1\relax
+\zzcnE=\zzcnA\multiply\zzcnE by #2\relax\advance\zzcnD by -\zzcnE\relax
+\ifnum\zzcnD>0\relax
+\ifnum\zzcnC=2\zzcastpolyd{#1}{#2}{#3}\let\zznext=\zzcastpolya\else
+\zzdmE=\zzdmA\advance\zzdmE by -\zzdmC\multiply\zzdmE by \zzcnB
+\zzdmF=\zzdmB\advance\zzdmF by -\zzdmD\multiply\zzdmF by \zzcnA
+\advance\zzdmE by -\zzdmF\divide\zzdmE by \zzcnD\relax
+\ifdim\zzdmE>#3\relax\zzcnC=3\zzcastpolyd{#1}{#2}{#3}\let\zznext=\zzcastpolya
+\else\ifnum\zzcnC=3\zzcastpolyf{#1}{#2}\let\zznext=\zzcastpolye\else
+\ifdim\zzdmE<0pt\relax
+\ifnum\zzcnC=1\let\zznext=\zzcastpolyb\else
+\zzcnC=2\zzcastpolyd{#1}{#2}{#3}\let\zznext=\zzcastpolya\fi
+\else\zzcastpolyf{#1}{#2}\let\zznext=\zzcastpolye\fi\fi\fi\fi
+\else\ifnum\zzcnC=3\let\zznext=\zzcastpolyb
+\else\zzcnC=1\zzcastpolyd{#1}{#2}{#3}\let\zznext=\zzcastpolya\fi\fi
+\zznext}
+
+\def\zzcastpolyd#1#2#3{
+\zzdmE=#3\multiply\zzdmE by #1\advance\zzdmC by \zzdmE
+\zzdmE=#3\multiply\zzdmE by #2\advance\zzdmD by \zzdmE}
+
+\def\zzcastpolye#1\end{}
+
+\def\zzcastpolyf#1#2{\zzdmF=\zzdmE
+\multiply\zzdmE by #1\relax\advance\zzdmE by \zzdmC
+\multiply\zzdmF by #2\relax\advance\zzdmF by \zzdmD}
+
+\def\zzcastpolyg#1{\zzcastpolyb\end}
+
+%\shiftedge changes \xstart, \ystart, \xend, \yend so as to displace
+%the edge from \xstart, \ystart to \xend, \yend by a vector of length
+%#1 (a dimension) that is rotated 90 degrees counterclockwise from the edge.
+
+\def\shiftedge#1{\zzcheckedge{SHIFT}
+\zzdistance\xslope\yslope
+\zzdmA=#1\multiply\zzdmA by 100\divide\zzdmA by \zzglobalcnA\zzdmB=\zzdmA
+\multiply\zzdmA by -\yslope\multiply\zzdmB by \xslope
+\advance\xstart by \zzdmA \advance\xend by \zzdmA
+\advance\ystart by \zzdmB \advance\yend by \zzdmB}
+
+%\zzsqroot#1 accepts an integer and sets \zzglobalcnA to the integer part
+%of its square root.  It works for numbers up to at least 1,000,000,000.
+
+\def\zzsqroot#1{{\zzcnA=#1
+%x is \zzcnA, y is \zzcnB, n is \zzcnC, z is \zzcnD
+\zzcnC=0\zzcnD=1
+\loop\zzcnE=\zzcnA\divide\zzcnE by \zzcnD\advance\zzcnE by 1
+\relax\ifnum\zzcnD<\zzcnE\relax
+\advance \zzcnC by 1\multiply\zzcnD by 2
+\repeat
+\zzcnB=0
+\loop\ifnum\zzcnC>0\relax
+\advance\zzcnC by -1\divide\zzcnD by 2
+\zzcnE=\zzcnB\advance\zzcnE by \zzcnD\multiply\zzcnE by \zzcnE\relax
+\ifnum\zzcnA<\zzcnE\relax\else\advance\zzcnB by \zzcnD\fi
+\repeat
+\global\zzglobalcnA=\zzcnB}}
+
+%\zzdistance#1#2 accepts two integers and sets \zzglobalcnA to 100 times
+%the square root of the sum of their squares.
+
+\def\zzdistance#1#2{{\zzcnA=#1\multiply\zzcnA by \zzcnA
+\zzcnB=#2\multiply\zzcnB by \zzcnB
+\advance\zzcnA by \zzcnB\multiply\zzcnA by 10000
+\zzsqroot\zzcnA}}
+
+%\drawdashedge, \drawdotedge, or \drawsolidedge draws a dashed, dotted, or
+%solid line along the current edge.
+
+\def\drawdashedge#1#2#3#4{\zzcnA=1\zzdmA=#1\zzdmB=#2
+\zzcheckposdimen\zzdmA{FIRST}{DRAWDASHEDGE}
+\zzcheckposdimen\zzdmB{SECOND}{DRAWDASHEDGE}
+\zzchecknonnegnum{#3}{THIRD}{DRAWDASHEDGE}
+\zzchecknonnegnum{#4}{FOURTH}{DRAWDASHEDGE}
+\zzcnI=#3\relax\advance\zzcnI by #4\relax
+\ifnum\zzcnI>0\else\errmessage
+{SUM OF THIRD AND FOURTH PARAMETERS OF DRAWDASHEDGE MUST BE POSITIVE}\fi
+\advance\zzdmB by \zzdmA
+\zzdrawedge{\advance\zzcnC by -\zzcnD
+\zzcnG=\zzcnC\divide\zzcnG by \zzcnE\relax
+\ifnum\zzcnG>0\relax
+\zzcnH=\zzcnG\multiply\zzcnH by \zzcnE\advance\zzcnC by -\zzcnH
+\zzcnH=\zzcnI\multiply\zzcnH by \zzcnG
+\advance\zzcnH by #3\divide\zzcnC by \zzcnH
+\zzcnH=#3\multiply\zzcnH by \zzcnC\advance\zzcnD by \zzcnH
+\multiply\zzcnC by \zzcnI\advance\zzcnE by \zzcnC
+\else\advance\zzcnD by \zzcnC\fi}
+{\line(\xslope,\yslope){\zzcnD}}}
+
+\def\zzcheckposdimen#1#2#3{\relax\ifdim#1>0pt\else\errmessage{
+#2 PARAMETER OF #3 MUST BE POSITIVE}\fi}
+
+\def\zzchecknonnegnum#1#2#3{\relax\ifnum#1<0\relax\errmessage{
+#2 PARAMETER OF #3 MUST BE NONNEGATIVE}\fi}
+
+\def\drawdotedge#1#2{\zzcnA=0\zzdmA=0pt\zzdmB=#1
+\zzcheckposdimen\zzdmB{}{DRAWDOTEDGE}\zzcheckbool{#2}{SECOND}{DRAWDOTEDGE}
+\zzdrawedge{\zzcnG=\zzcnC\divide\zzcnG by \zzcnE\relax
+\ifnum\zzcnG<1\relax\zzcnG=1\fi\zzcnE=\zzcnC\divide\zzcnE by \zzcnG\relax
+\ifnum#2=0\relax\advance\zzcnG by -1\fi}
+{\kern-1.39pt\raise-.76pt\hbox{.}}}
+
+\def\drawsolidedge{\zzcnA=1\zzdmA=0pt\zzdmB=0pt
+\zzdrawedge{\zzcnG=0\zzcnD=\zzcnC}
+{\line(\xslope,\yslope){\zzcnD}}}
+
+\def\zzdrawedge#1#2{\zzcheckedge{DRAW}\relax
+\ifnum\zzcnA=1\relax\zzcheckslope\xslope\yslope\slopemax{SOLID OR DASHED EDGE}\fi%%%pict2e
+\zzcnA=\xstart\zzcnB=\ystart\zzcnD=\zzdmA\zzcnE=\zzdmB\relax
+\ifnum\xslope=0\relax\zzcnC=\yend\advance\zzcnC by -\zzcnB\zzcnF=\yslope
+\else\zzcnC=\xend\advance\zzcnC by -\zzcnA\zzcnF=\xslope
+\zzdistance\xslope\yslope\relax
+\ifnum\xslope<0\relax\global\zzglobalcnA=-\zzglobalcnA\fi
+\multiply\zzcnD by 100\divide\zzcnD by \zzglobalcnA\multiply\zzcnD by \xslope
+\multiply\zzcnE by 100\divide\zzcnE by \zzglobalcnA\multiply\zzcnE by \xslope
+\fi
+\ifnum\zzcnF<0\relax\zzcnC=-\zzcnC\fi
+\ifnum\zzcnC>0\relax #1\relax
+\ifnum\zzcnF<0\relax\zzcnE=-\zzcnE\fi\zzcnF=\zzcnE\relax
+\ifnum\xslope=0\relax\zzcnE=0
+\else\multiply\zzcnF by \yslope\divide\zzcnF by \xslope\fi
+\zzmakepicture{\loop\put(\zzcnA,\zzcnB){#2}
+\ifnum\zzcnG>0\relax\advance\zzcnG by -1
+\advance\zzcnA by \zzcnE\advance\zzcnB by \zzcnF\repeat
+\zzrecordwidth\xstart\xstart\zzrecordwidth\xend\xend
+\zztotheight=\ystart\zztotdepth=\ystart\zzrecordheight\yend\yend}\fi}
+
+%\drawedgehead draws an arrowhead along the current edge.
+
+\def\drawedgehead#1#2#3{\zzcheckbool{#2}{SECOND}{DRAWEDGEHEAD}
+\zzcheckbool{#3}{THIRD}{DRAWEDGEHEAD}\zzcnB=#3
+\relax\ifnum#2=1\relax\zzcnA=#1\relax
+\zzdrawedgeheada\xstart\ystart\xend\yend\xslope\yslope
+\else\zzcnA=100\advance\zzcnA by -#1\relax
+\zzdrawedgeheada\xend\yend\xstart\ystart{-\xslope}{-\yslope}\fi}
+
+%\zzcheckbool gives an error message unless its first argument is 1 or 0.
+
+\def\zzcheckbool#1#2#3{
+\ifnum#1<0\errmessage{#2 PARAMETER OF #3 MUST BE 1 OR 0}\fi
+\ifnum#1>1\errmessage{#2 PARAMETER OF #3 MUST BE 1 OR 0}\fi}
+
+\def\zzdrawedgeheada#1#2#3#4#5#6{\zzcheckedge{DRAW ARROWHEAD FOR}
+\zzcheckslope{#5}{#6}\slopemax{ARROWHEAD}%%%pict2e
+\zzdmA=#3\advance\zzdmA by -#1
+\divide\zzdmA by 10\multiply\zzdmA by \zzcnA\divide\zzdmA by 10
+\zzdmB=#4\advance\zzdmB by -#2
+\divide\zzdmB by 10\multiply\zzdmB by \zzcnA\divide\zzdmB by 10
+\relax\ifnum\zzcnB=1\relax
+\zzdistance{#5}{#6}\zzdmC=\edgeheaddisp
+\multiply\zzdmC by 100\divide\zzdmC by \zzglobalcnA\zzdmD=\zzdmC
+\multiply\zzdmC by #5\multiply\zzdmD by #6
+\advance\zzdmA by \zzdmC\advance\zzdmB by \zzdmD\fi
+\advance\zzdmA by #1\zzcnA=\zzdmA\advance\zzdmB by #2\zzcnB=\zzdmB
+\zzmakepicture{\put(\zzcnA,\zzcnB){\vector(#5,#6){0}}
+\zzrecordwidth\zzdmA\zzdmA\zztotheight=\zzdmB\zztotdepth=\zzdmB}}
+
+%\zzcheckslope gives an errormessage if the absolute value of #1 or #2
+%is greater than #3.
+
+\def\zzcheckslope#1#2#3#4{\relax
+\ifnum#1>#3\zzcheckslopea{#1}{#2}{#4}\fi
+\ifnum#1<-#3\zzcheckslopea{#1}{#2}{#4}\fi
+\ifnum#2>#3\zzcheckslopea{#1}{#2}{#4}\fi
+\ifnum#2<-#3\zzcheckslopea{#1}{#2}{#4}\fi}
+
+\def\zzcheckslopea#1#2#3{\errmessage{\the#1,\the#2 IS ILLEGAL SLOPE FOR #3}}
+
+%The following macros each call \zzsetupbox{#2}{#3} and then issue the
+%resulting expression so that its shadow touches the edge x = \xslope.t
+%+\xstart, y = \yslope.t+\ystart. \abutX places the expression to the X
+%of the edge. For \abutleft and \abutright, #1 gives the y-coordinate
+%of the expression as an integer multiple of \diagramunit.  For \abutbelow
+%and \abutabove, #1 gives the x-coordinate similarly.  The macros \abutXd
+%are similar, except that #1 should be a dimension.
+
+\def\abutleft#1:#2#3{\zzabut{#1}{#2}{#3}{-\yslope}{\zzslidehoriz}{1}}
+\def\abutright#1:#2#3{\zzabut{#1}{#2}{#3}{\yslope}{\zzslidehoriz}{1}}
+\def\abutbelow#1:#2#3{\zzabut{#1}{#2}{#3}{\xslope}{\zzslidevert}{1}}
+\def\abutabove#1:#2#3{\zzabut{#1}{#2}{#3}{-\xslope}{\zzslidevert}{1}}
+
+\def\abutleftd#1#2#3{\zzabut{#1}{#2}{#3}{-\yslope}{\zzslidehoriz}{0}}
+\def\abutrightd#1#2#3{\zzabut{#1}{#2}{#3}{\yslope}{\zzslidehoriz}{0}}
+\def\abutbelowd#1#2#3{\zzabut{#1}{#2}{#3}{\xslope}{\zzslidevert}{0}}
+\def\abutaboved#1#2#3{\zzabut{#1}{#2}{#3}{-\xslope}{\zzslidevert}{0}}
+
+\def\zzabut#1#2#3#4#5#6{\zzcheckedge{ABUT TO}
+\zzsetupbox{#2}{#3}\zzcnA=\xslope\zzcnB=\yslope
+\relax\ifnum#4<0\relax\zzcnA=-\zzcnA\zzcnB=-\zzcnB\fi
+\def\zzprocpoly{\zzclosestpoly}\def\zzprocrorect{\zzprocrorecta}
+\zzglobalshadow
+\advance\zzdmC by -\zzglobalxcenter\advance\zzdmD by -\zzglobalycenter
+\relax\ifnum#6=1\relax\zzmultdiagramunit\zzdmA{#1}\else\zzdmA=#1\fi
+\zzdmB=\zzdmA#5\relax\zzissue}
+
+\def\zzslidehoriz{\relax\ifnum\yslope=0\errmessage
+{ABUTLEFT OR ABUTRIGHT ATTEMPTED FOR HORIZONTAL EDGE}\fi
+\advance\zzdmA by \zzdmD\advance\zzdmA by -\ystart
+\multiply\zzdmA by \xslope\divide\zzdmA by \yslope
+\advance\zzdmA by \xstart\advance\zzdmA by -\zzdmC}
+
+\def\zzslidevert{\relax\ifnum\xslope=0\errmessage
+{ABUTBELOW OR ABUTABOVE ATTEMPTED FOR VERTICAL EDGE}\fi
+\advance\zzdmB by \zzdmC\advance\zzdmB by -\xstart
+\multiply\zzdmB by \yslope\divide\zzdmB by \xslope
+\advance\zzdmB by \ystart\advance\zzdmB by -\zzdmD}
+
+%\zzclosestpoly finds the vertex of a convex polygon that is closest to a
+%directed line, x = xs.t+x0, y = ys.t+y0, assuming that the directed line
+%is to the left (right) of the polygon if ys is positive (negative)
+%and above (below) the polygon if xs is positive (negative).
+%It is called by defining \zzprocpoly to be \zzclosestpoly, setting \zzcnA,
+%\zzcnB to xs, ys, and executing \zzglobalshadow, which must have been
+%defined by a polygon descriptor.  The output is left in \zzdmC, \zzdmD.
+
+\def\zzclosestpoly#1#2#3{\zzdmC=#1\zzdmD=#2\zzcnC=0\zzclosestpolya #3\end}
+
+\def\zzclosestpolya#1{\def\zztesta{#1}\def\zztestb{\end}
+\ifx\zztesta\zztestb\let\zznext=\zzclosestpolyb
+\else\let\zznext=\zzclosestpolyc\fi\zznext {#1}}
+
+\def\zzclosestpolyb#1{}
+
+\def\zzclosestpolyc#1#2#3{\zzcnD=\zzcnB\multiply\zzcnD by #1\relax
+\zzcnE=\zzcnA\multiply\zzcnE by #2\relax\advance\zzcnD by -\zzcnE\relax
+\ifnum\zzcnD>0\relax
+\ifnum\zzcnC=1\let\zznext=\zzclosestpolyd
+\else\zzcnC=0\zzcastpolyd{#1}{#2}{#3}\let\zznext=\zzclosestpolya\fi
+\else\zzcnC=1\zzcastpolyd{#1}{#2}{#3}\let\zznext=\zzclosestpolya\fi
+\zznext}
+
+\def\zzclosestpolyd#1\end{}
+
+%\setcircle initializes \dcircle, \xcircle, and \ycircle to its first
+%three parameters, and sets \zziscircle to 1.
+
+\def\setcircle#1#2#3{\dcircle=#1\xcircle=#2\ycircle=#3\zziscircle=1}
+
+%\shiftcircle#1#2 displaces \xcircle, \ycircle by #1, #2.
+
+\def\shiftcircle#1#2{\zzcheckcircle{SHIFT}
+\advance\xcircle by #1\advance\ycircle by #2}
+
+\def\zzcheckcircle#1{\relax\ifnum\zziscircle=0\errmessage
+{ATTEMPT TO #1 NONEXISTENT CIRCLE}\fi}
+
+%\drawcircle draws quadrants of the current circle.
+
+\def\drawcircle#1#2#3#4{\zzcheckcircle{DRAW}\zzdmA=\dcircle\divide\zzdmA by 2
+\zzmakepicture{\zzcnA=\dcircle\zzcnB=\xcircle\zzcnC=\ycircle
+\zztotheight=\ycircle\zztotdepth=\ycircle
+\zzrecordwidth\xcircle\xcircle\relax
+\zzdrawcirclea{#1}{tr}{\zzdmA}{\zzdmA}\zzdrawcirclea{#2}{br}{\zzdmA}{-\zzdmA}
+\zzdrawcirclea{#3}{bl}{-\zzdmA}{-\zzdmA}
+\zzdrawcirclea{#4}{tl}{-\zzdmA}{\zzdmA}}}
+
+\def\zzdrawcirclea#1#2#3#4{\zzcheckbool{#1}{}{DRAWCIRCLE}\ifnum#1=1\relax
+\put(\zzcnB,\zzcnC){\oval(\zzcnA,\zzcnA)[#2]}
+\zzdmB=\xcircle\advance\zzdmB by #3\zzrecordwidth\zzdmB\zzdmB
+\zzdmB=\ycircle\advance\zzdmB by #4\zzrecordheight\zzdmB\zzdmB\fi}
+
+%\drawcirclehead issues an arrowhead placed on the current circle.
+
+\def\drawcirclehead#1#2#3{\zzcheckcircle{DRAW ARROWHEAD FOR}
+\zzreduceterms{#1}{#2}{0,0 ARE ILLEGAL PARAMETERS FOR DRAWCIRCLEHEAD}
+\zzdistance{\zzcnC}{\zzcnD}\zzcheckbool{#3}{THIRD}{DRAWCIRCLEHEAD}
+\ifnum#3=1\relax\zzcnA=\zzcnD\zzcnB=-\zzcnC\else\zzcnA=-\zzcnD\zzcnB=\zzcnC\fi
+\zzdmA=\dcircle\multiply\zzdmA by 50\divide\zzdmA by \zzglobalcnA
+\zzdmB=\circleheaddisp\multiply\zzdmB by 100\divide\zzdmB by \zzglobalcnA
+\zzdmE=\zzdmA\multiply\zzdmE by \zzcnC\zzdmC=\xcircle\advance\zzdmC by \zzdmE
+\zzdmE=\zzdmB\multiply\zzdmE by \zzcnA\advance\zzdmC by \zzdmE
+\zzdmE=\zzdmA\multiply\zzdmE by \zzcnD\zzdmD=\ycircle\advance\zzdmD by \zzdmE
+\zzdmE=\zzdmB\multiply\zzdmE by \zzcnB\advance\zzdmD by \zzdmE
+\zzcnC=\zzdmC\zzcnD=\zzdmD\zzcheckslope\zzcnA\zzcnB\slopemax{ARROWHEAD}%%%pict2e
+\zzmakepicture{\put(\zzcnC,\zzcnD){\vector(\zzcnA,\zzcnB){0}}
+\zzrecordwidth\zzdmC\zzdmC\zztotheight=\zzdmD\zztotdepth=\zzdmD}}
+
+%The next four macros cause an expression to be abutted to the current
+%circle.
+
+\def\abutcircleleft#1#2#3{\zzabutcircle{#1}{#2}{#3}{}
+\zzslidehoriz{\relax\ifdim\zzdmA>\zzdmH\relax\zzdmH=\zzdmA\fi}}
+
+\def\abutcircleright#1#2#3{\zzabutcircle{#1}{#2}{#3}{\zzrotate\zzrotate}
+\zzslidehoriz{\relax\ifdim\zzdmA<\zzdmH\relax\zzdmH=\zzdmA\fi}}
+
+\def\abutcirclebelow#1#2#3{\zzabutcircle{#1}{#2}{#3}{\zzrotate}
+\zzslidevert{\relax\ifdim\zzdmB>\zzdmI\relax\zzdmI=\zzdmB\fi}}
+
+\def\abutcircleabove#1#2#3{\zzabutcircle
+{#1}{#2}{#3}{\zzrotate\zzrotate\zzrotate}
+\zzslidevert{\relax\ifdim\zzdmB<\zzdmI\relax\zzdmI=\zzdmB\fi}}
+
+\def\zzabutcircle#1#2#3#4#5#6{\zzcheckcircle{ABUT TO}
+\zzsetupbox{#2}{#3}\def\zzprocpoly{\zzclosestpoly}
+\def\zzprocrorect{\zzprocrorecta}
+\zzdmF=\dcircle\divide\zzdmF by 2
+\zzdmG=\dcircle\multiply\zzdmG by 100\divide\zzdmG by 283
+\xstart=-\zzdmF\ystart=0pt\xslope=0\yslope=-1
+\zzabutcirclea{#1}{#4}{#5}\zzdmH=\zzdmA\zzdmI=\zzdmB
+\xstart=-\zzdmG\ystart=\zzdmG\xslope=-1\yslope=-1
+\zzabutcirclea{#1}{#4}{#5}#6\relax
+\xstart=-\zzdmG\ystart=-\zzdmG\xslope=1\yslope=-1
+\zzabutcirclea{#1}{#4}{#5}#6\relax
+\zzdmA=\zzdmH\advance\zzdmA by \xcircle
+\zzdmB=\zzdmI\advance\zzdmB by \ycircle
+\zzissue}
+
+\def\zzabutcirclea#1#2#3{#2\relax
+\zzcnA=\xslope\zzcnB=\yslope
+\zzglobalshadow
+\advance\zzdmC by -\zzglobalxcenter\advance\zzdmD by -\zzglobalycenter
+\zzdmA=#1\zzdmB=\zzdmA #3\relax}
+
+\def\zzrotate{\zzdmE=\xstart\xstart=-\ystart\ystart=\zzdmE
+\zzcnC=\xslope\xslope=-\yslope\yslope=\zzcnC}
+
+%MACROS FOR CATEGORY-THEORY DIAGRAMS
+
+%The following control symbols may be redefined by the user:
+\def\ctvertexstyle{\displaystyle}
+\def\ctabutstyle{\textstyle}
+\def\ctvertexborderlr{3pt}
+\def\ctvertexbordertb{4pt}
+\def\ctloopdiameter{20pt}
+\def\ctabutcircledisp{5pt}
+\def\ctabutborderlr{2pt}
+\def\ctabutbordertb{2pt}
+\def\ctabutborderinset{3pt}
+\def\ctabutborderinsetdouble{6pt}%Must be twice \ctabutborderinset
+\def\ctdoubleedgedisp{2pt}
+
+%The following registers are used locally:
+\newdimen\zzdmX\newdimen\zzdmY
+
+%Hidden macros and other defined control symbols:
+%    used by \ctdiagram: \diagram\ctsolid\cthead
+%    used by \ctv and \ctvg: \vertex\border\rect
+%    used by \ctgl: \leftghost
+%    used by \ctgr: \rightghost
+%    used by \ctlptl, \ctlptlcc, \ctlptr, \ctlptrcc, \ctlpbr, \ctlpbrcc,
+%    \ctlpbl, \ctlpblcc: \zzctlp\border\setcircle\shiftcircle\drawcircle
+%        \drawcirclehead\abutcircleleft\abutcircleright\zzctabutprog
+%        \octagon
+%    used by \cten, \ctet, \cteb, \ctel, \cter, \ctetg, \ctebg, \ctelg, \cterg,
+%    \ctetb, \ctelr, \ctetbg, \ctelrg: \setedge\zzctxmean\zzctymean
+%        \zzmultdiagramunit\zzcte\zzctee\shadeedge\abutaboved\abutbelowd
+%        \abutleftd\abutrightd\zzctabutprog\border\octagon\shiftedge
+%        \drawsolidedge\zzctdrawdashedge\drawdashedge\zzctdrawdotedge
+%        \drawdotedge\zzctdrawedgehead\drawedgehead\zzctnodrawedgehead
+%    multiply defined control symbols: \zzctdrawedge\zzctdrawhead
+%        \zzctxmeanadj\zzctymeanadj
+
+%\ctdiagram is similar to \diagram, except that it executes \ctsolid and
+%\cthead before the expression program #1.
+
+\def\ctdiagram#1{\diagram{\ctsolid\cthead\ctoutermid #1}}
+
+%\ctvg is similar to \vertex except that the expression #3 is printed in
+%\ctvertexstyle mode, and the expression program #4 is followed by a
+%standard program that borders the current rectangle by \ctvertexborderlr
+%on the sides and \ctvertexbordertb on the top and bottom, and then
+%creates a rectangular shadow.  \ctv is similar to \ctvg except that the
+%expression program is empty (except for the standard program).
+
+\def\ctvg#1,#2:#3#4{\vertex #1,#2:{\ctvertexstyle #3}{#4\relax
+\border\ctvertexborderlr\ctvertexbordertb\rect}}
+
+\def\ctv#1,#2:#3{\ctvg #1,#2:{#3}{}}
+
+%\ctgl and \ctgr are similar to \leftghost and \rightghost except that
+%the expression #1 is printed in \ctvertexstyle.
+
+\def\ctgl#1{\leftghost{\ctvertexstyle #1}}
+
+\def\ctgr#1{\rightghost{\ctvertexstyle #1}}
+
+%The following eight macros print a three-quarter-circle loop of diameter
+%\ctloopdiameter at one of the corners of an expanded current rectangle,
+%with an arrowhead at one end of the loop.
+
+\def\ctlptl#1{\zzctlp{\lexpr\texpr}{{0pt}\circleheaddisp}{1011}{101}
+{\abutcircleleft\ctabutcircledisp}{#1}}
+
+\def\ctlptlcc#1{\zzctlp{\lexpr\texpr}{{-\circleheaddisp}{0pt}}{1011}{0{-1}0}
+{\abutcircleleft\ctabutcircledisp}{#1}}
+
+\def\ctlptr#1{\zzctlp{\rexpr\texpr}{\circleheaddisp{0pt}}{1101}{0{-1}1}
+{\abutcircleright\ctabutcircledisp}{#1}}
+
+\def\ctlptrcc#1{\zzctlp{\rexpr\texpr}{{0pt}\circleheaddisp}{1101}{{-1}00}
+{\abutcircleright\ctabutcircledisp}{#1}}
+
+\def\ctlpbr#1{\zzctlp{\rexpr\bexpr}{{0pt}{-\circleheaddisp}}{1110}{{-1}01}
+{\abutcircleright{-\ctabutcircledisp}}{#1}}
+
+\def\ctlpbrcc#1{\zzctlp{\rexpr\bexpr}{\circleheaddisp{0pt}}{1110}{010}
+{\abutcircleright{-\ctabutcircledisp}}{#1}}
+
+\def\ctlpbl#1{\zzctlp{\lexpr\bexpr}{{-\circleheaddisp}{0pt}}{0111}{011}
+{\abutcircleleft{-\ctabutcircledisp}}{#1}}
+
+\def\ctlpblcc#1{\zzctlp{\lexpr\bexpr}{{0pt}{-\circleheaddisp}}{0111}{100}
+{\abutcircleleft{-\ctabutcircledisp}}{#1}}
+
+\def\zzctlp#1#2#3#4#5#6{\border\ctvertexborderlr\ctvertexbordertb
+\setcircle\ctloopdiameter #1
+\border{-\ctvertexborderlr}{-\ctvertexbordertb}
+\shiftcircle #2\drawcircle #3\drawcirclehead #4
+#5{\ctabutstyle #6}\zzctabutprog}
+
+\def\zzctabutprog{\border\ctabutborderlr\ctabutbordertb
+\borderto{\ctabutborderinsetdouble}{\ctabutborderinsetdouble}
+\octagon\ctabutborderinset}
+
+%\cten#1,#2,#3,#4: draws a shaded edge from #1,#2 to #3,#4, possibly with
+%an arrowhead at its end.
+
+\def\cten#1:{\setedge#1:\shadeedge\zzctdrawedge\zzctdrawhead1}
+
+%The following four macros draw a shaded edge, possibly with an arrowhead
+%at the end, and abut an expression to the edge at its midpoint.
+
+\def\ctet#1:#2{\setedge#1:\zzctxmean\zzcte\abutaboved{#2}\zzctxmeanadj}
+
+\def\cteb#1:#2{\setedge#1:\zzctxmean\zzcte\abutbelowd{#2}\zzctxmeanadj}
+
+\def\ctel#1:#2{\setedge#1:\zzctymean\zzcte\abutleftd{#2}\zzctymeanadj}
+
+\def\cter#1:#2{\setedge#1:\zzctymean\zzcte\abutrightd{#2}\zzctymeanadj}
+
+\def\zzctxmean{\zzdmX=\xstart\advance\zzdmX by \xend\divide\zzdmX by 2}
+
+\def\zzctymean{\zzdmX=\ystart\advance\zzdmX by \yend\divide\zzdmX by 2}
+
+\def\zzcte#1#2#3{\shadeedge #3\zzctdrawedge\zzctdrawhead1
+#1\zzdmX{\ctabutstyle #2}\zzctabutprog}
+
+%The next four macros behave similarly to those above, but abut an
+%expression to a specified point on the edge.
+
+\def\ctetg#1;#2:#3{\setedge#1:\zzmultdiagramunit\zzdmX{#2}\zzcte
+\abutaboved{#3}\relax}
+
+\def\ctebg#1;#2:#3{\setedge#1:\zzmultdiagramunit\zzdmX{#2}\zzcte
+\abutbelowd{#3}\relax}
+
+\def\ctelg#1;#2:#3{\setedge#1:\zzmultdiagramunit\zzdmX{#2}\zzcte
+\abutleftd{#3}\relax}
+
+\def\cterg#1;#2:#3{\setedge#1:\zzmultdiagramunit\zzdmX{#2}\zzcte
+\abutrightd{#3}\relax}
+
+%\ctetb (\ctelr) draws a pair of shaded edges, with two expressions
+%abutted to the top and bottom (left and right) of the midpoint.
+%\ctetbg and \ctelrg are similar, but abut to a specified point on the edge.
+
+\def\ctetb#1:#2#3#4#5{\zzcheckbool{#2}{FIFTH}{CTETB}
+\zzcheckbool{#3}{SIXTH}{CTETB}
+\setedge#1:\zzctxmean\zzctee\xslope\abutaboved\abutbelowd
+{#2}{#3}{#4}{#5}\zzctxmeanadj}
+
+\def\ctelr#1:#2#3#4#5{\zzcheckbool{#2}{FIFTH}{CTELR}
+\zzcheckbool{#3}{SIXTH}{CTELR}
+\setedge#1:\zzctymean\zzctee\yslope\abutleftd\abutrightd
+{#2}{#3}{#4}{#5}\zzctymeanadj}
+
+\def\ctetbg#1;#2,#3:#4#5#6#7{\zzcheckbool{#4}{SEVENTH}{CTETBG}
+\zzcheckbool{#5}{EIGHTH}{CTETBG}\setedge#1:\zzmultdiagramunit\zzdmX{#2}
+\zzctee\xslope
+\abutaboved{\zzmultdiagramunit\zzdmX{#3}\abutbelowd}{#4}{#5}{#6}{#7}\relax}
+
+\def\ctelrg#1;#2,#3:#4#5#6#7{\zzcheckbool{#4}{SEVENTH}{CTELRG}
+\zzcheckbool{#5}{EIGHTH}{CTELRG}\setedge#1:\zzmultdiagramunit\zzdmX{#2}
+\zzctee\yslope
+\abutleftd{\zzmultdiagramunit\zzdmX{#3}\abutrightd}{#4}{#5}{#6}{#7}\relax}
+
+\def\zzctee#1#2#3#4#5#6#7#8{
+\ifnum#1>0\relax\zzdmY=\ctdoubleedgedisp\else\zzdmY=-\ctdoubleedgedisp\fi
+\shiftedge\zzdmY\shadeedge #8\zzctdrawedge\zzctdrawhead{#4}
+#2\zzdmX{\ctabutstyle #6}\zzctabutprog
+\multiply\zzdmY by -2\relax
+\shiftedge\zzdmY\shadeedge #8\zzctdrawedge\zzctdrawhead{#5}
+#3\zzdmX{\ctabutstyle #7}\zzctabutprog}
+
+%\ctinnermid defines \zzctxmeanadj and \zzctymeanadj so that \ctet, \cteb,
+%\ctel, \cter, \ctetb, and \ctelr recompute the midpoint of the current
+%edge after shading.  \ctoutermid defines these control symbols so that
+%these routines do not recompute the midpoint.
+
+\def\ctinnermid{\def\zzctxmeanadj{\zzctxmean}\def\zzctymeanadj{\zzctymean}}
+
+\def\ctoutermid{\def\zzctxmeanadj{\relax}\def\zzctymeanadj{\relax}}
+
+%\zzctdrawdashedge draws a dashed edge.
+
+\def\zzctdrawdashedge{\relax
+\ifnum\xslope=0\relax\drawdashedge{7pt}{7pt}11
+\else\ifnum\yslope=0\relax\drawdashedge{7pt}{7pt}11
+\else\drawdashedge{15pt}{7pt}01\fi\fi}
+
+%\zzctdrawdotedge draws a dotted edge.
+
+\def\zzctdrawdotedge{\drawdotedge{8pt}1}
+
+%\ctsolid (\ctdash,\ctdot) defines \zzctdrawedge to be \drawsolidedge
+%(\zzctdrawdashedge,\zzctdrawdotedge), so that edges will be solid
+%(dashed, dotted).
+
+\def\ctsolid{\def\zzctdrawedge{\drawsolidedge}}
+
+\def\ctdash{\def\zzctdrawedge{\zzctdrawdashedge}}
+
+\def\ctdot{\def\zzctdrawedge{\zzctdrawdotedge}}
+
+%\zzctdrawedgehead places a forward-pointing arrowhead at the end of an edge
+%if #1=1 or a backward-pointing arrowhead at the beginning if #1=0.
+%\zzctnodrawedgehead is called in the same way but does nothing.
+
+\def\zzctdrawedgehead#1{\relax\ifnum#1=1\relax
+\drawedgehead{100}10\else\drawedgehead{0}00\fi}
+
+\def\zzctnodrawedgehead#1{}
+
+%\cthead (\ctnohead) defines \zzctdrawhead to be \zzctdrawedgehead
+%(\zzctnodrawedgehead), so that edges will (will not) have arrowheads.
+
+\def\cthead{\def\zzctdrawhead{\zzctdrawedgehead}}
+
+\def\ctnohead{\def\zzctdrawhead{\zzctnodrawedgehead}}