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author | Norbert Preining <norbert@preining.info> | 2019-09-02 13:46:59 +0900 |
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committer | Norbert Preining <norbert@preining.info> | 2019-09-02 13:46:59 +0900 |
commit | e0c6872cf40896c7be36b11dcc744620f10adf1d (patch) | |
tree | 60335e10d2f4354b0674ec22d7b53f0f8abee672 /macros/latex/contrib/diagmac/diagmac.sty |
Initial commit
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-rw-r--r-- | macros/latex/contrib/diagmac/diagmac.sty | 971 |
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diff --git a/macros/latex/contrib/diagmac/diagmac.sty b/macros/latex/contrib/diagmac/diagmac.sty new file mode 100644 index 0000000000..adc96b1aa5 --- /dev/null +++ b/macros/latex/contrib/diagmac/diagmac.sty @@ -0,0 +1,971 @@ +%LaTeX style +%MACROS FOR DIAGRAMS - J. C. Reynolds - December 1987 + +%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 +\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 6{SOLID OR DASHED EDGE}\fi +\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}4{ARROWHEAD} +\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\zzcnB4{ARROWHEAD} +\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}} |