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% Pictures (a subset of \LaTeX's conventions, plus squines)
\catcode`@=11 % enable private control sequences
\def\wlog#1{} % don't put allocation info into the log
\newskip\hsssglue \hsssglue=0pt plus 1fill minus 1fill \def\hsss{\hskip\hsssglue}
\newdimen\unitlength \newdimen\linethickness
\newdimen\@picheight \newdimen\@xdim \newdimen\@ydim \newdimen\@len \newdimen\@save
\newcount\@multicount \newcount\@xarg \newcount\@yarg
\newbox\@picbox \newbox\@mpbox
\font\tenln=line10 \font\tenlnw=linew10
\font\tencirc=lcircle10 \font\tencircw=lcirclew10
\def\thinlines{\let\linefont=\tenln \let\circlefont=\tencirc
\linethickness=\fontdimen8\linefont}
\def\thicklines{\let\linefont=\tenlnw \let\circlefont=\tencircw
\linethickness=\fontdimen8\linefont}
\thinlines
\def\beginpicture(#1,#2)(#3,#4){\@picheight=#2\unitlength
\setbox\@picbox=\hbox to#1\unitlength\bgroup \let\line=\@line
\kern-#3\unitlength \lower#4\unitlength\hbox\bgroup\ignorespaces}
\def\endpicture{\egroup\hss\egroup
\ht\@picbox=\@picheight \dp\@picbox=\z@
\leavevmode\box\@picbox}
\def\put(#1,#2)#3{\raise#2\unitlength\rlap{\kern#1\unitlength #3}\ignorespaces}
\def\multiput(#1,#2)(#3,#4)#5#6{\@multicount=#5\relax
\@xdim=#1\unitlength \@ydim=#2\unitlength \setbox\@mpbox=\hbox{#6}%
\loop\ifnum\@multicount>0
\raise\@ydim\rlap{\kern\@xdim \unhcopy\@mpbox}%
\advance\@xdim#3\unitlength \advance\@ydim#4\unitlength
\advance\@multicount\m@ne \repeat\ignorespaces}
\def\makebox(#1,#2)#3{\setbox\@picbox=\hbox to#1\unitlength{\hss#3\hss}%
\@ydim=\ht\@picbox \advance\@ydim-\dp\@picbox
\ht\@picbox=#2\unitlength \dp\@picbox=\z@
\leavevmode\lower.5\@ydim\box\@picbox}
\newif\ifneg
\def\@line(#1,#2)#3{\@xarg=#1 \@yarg=#2 \@len=#3\unitlength \leavevmode
\ifnum\@xarg<0 \reverseline \else \negfalse \@ydim=\z@\fi
\ifnum\@xarg=0 \@vline
\else\ifnum\@yarg=0 \@hline \else\@sline\fi\fi
\ifneg\kern-\@len\else\@save=\@ydim\fi}
\def\reverseline{\negtrue \kern-\@len \@xarg=-\@xarg
\@ydim=\@len \multiply\@ydim\@yarg \divide\@ydim\@xarg \@yarg=-\@yarg}
\def\@hline{\vrule height.5\linethickness depth.5\linethickness width\@len}
\def\@vline{\kern-.5\linethickness\vrule width\linethickness
\ifnum\@yarg<0 height\z@ depth\else depth\z@ height\fi\@len
\kern-.5\linethickness}
\def\@sline{\setbox\@picbox=\hbox{\linefont \count@=\@xarg \multiply\count@ 8
\ifnum\@yarg>0 \advance\count@\@yarg \advance\count@-9
\else \advance\count@-\@yarg \advance\count@ 55 \fi \char\count@}%
\ifnum\@yarg<0 \@picheight=-\ht\@picbox \advance\@ydim\@picheight
\else \@picheight=\ht\@picbox \fi
\@xdim=\wd\@picbox \@save=\@ydim
\loop\ifdim\@xdim<\@len \raise\@ydim\copy\@picbox
\advance\@xdim\wd\@picbox \advance\@ydim\@picheight \repeat
\advance\@xdim-\@len \kern-\@xdim
\multiply\@xdim\@yarg \divide\@xdim\@xarg \advance\@ydim-\@xdim
\raise\@ydim\box\@picbox}
\def\vector(#1,#2)#3{\@line(#1,#2){#3}%
\ifnum\@xarg=0 \@vvector \else\ifnum\@yarg=0 \@hvector \else\@svector\fi\fi}
\def\@hvector{\ifneg\rlap{\linefont\char27}\else
\smash{\llap{\linefont\char45}}\fi} % we have to smash because of font bug
\def\@vvector{\ifnum\@yarg<0 \raise-\@len\rlap{\linefont\char63}%
\else\setbox\@picbox=\rlap{\linefont\char54}\advance\@len-\ht\@picbox
\raise\@len\box\@picbox\fi}
\def\@svector{\setbox\@picbox=\hbox to\z@{\linefont
\ifnum\@yarg<0 \count@=55 \@yarg=-\@yarg \else\count@=-9 \fi
\ifneg\multiply\@xarg16 \multiply\@yarg2
\else\hss % \llap
\ifnum\@xarg>2 \multiply\@xarg9 \multiply\@yarg2 \advance\count@29
\else\ifnum\@yarg>2 \multiply\@xarg16 \multiply\@yarg9 \advance\count@-20
\else\multiply\@xarg24 \multiply\@yarg3 \fi\fi\fi
\advance\count@\@xarg \advance\count@\@yarg \char\count@
\ifneg\hss\fi}% \rlap
\raise\@save\box\@picbox}
\def\disk#1{\@len=#1\unitlength \count@='160 \@diskcirc}
\def\circle#1{\@len=#1\unitlength \count@='140 \@diskcirc}
\def\@diskcirc{\setbox\@picbox=\hbox{\circlefont\char\count@}\@xdim=\wd\@picbox
\leavevmode \ifdim\@len>15.499\@xdim \@bigdc \else \@smalldc\fi}
\def\@bigdc{\ifnum\count@<'160 \@bigcirc
\else \@len=15\@xdim \@diskcirc\fi}
\def\@smalldc{{\advance\@len-.5\@xdim
\loop\ifdim\@xdim<\@len \advance\count@\@ne \advance\@xdim\wd\@picbox\repeat
\hbox{\circlefont\char\count@}}}
\def\@bigcirc{{\circlefont\count@=15
\setbox\@picbox=\hbox{\char\count@}\@xdim=\wd\@picbox
\ifdim\@len>2.5\@xdim \@len=2.5\@xdim\fi
\advance\@len-.125\wd\@picbox
\loop\ifdim\@xdim<\@len \advance\count@ 4 \advance\@xdim.25\wd\@picbox\repeat
\@ydim=.5\@xdim \advance\@ydim.5\linethickness
\setbox\@picbox=\vbox{\hbox{\char\count@\advance\count@-3\char\count@}%
\nointerlineskip
\hbox{\advance\count@\m@ne\char\count@\advance\count@\m@ne\char\count@}}%
\kern-\@ydim\lower\@ydim\box\@picbox}}
\newif\ifovaltl \newif\ifovaltr \newif\ifovalbl \newif\ifovalbr
\ovaltltrue \ovaltrtrue \ovalbltrue \ovalbrtrue
\def\oval(#1,#2){\@xdim=#1\unitlength \@ydim=#2\unitlength
{\circlefont \setbox\@picbox=\hbox{\char0}
\ifdim\@xdim<\wd\@picbox \@xdim=\wd\@picbox\fi
\ifdim\@ydim<\wd\@picbox \@ydim=\wd\@picbox\fi
\@save=\@xdim \ifdim\@ydim<\@save \@save=\@ydim \fi
\count@=39
\loop \setbox\@picbox=\hbox{\char\count@}\ifdim\@save<\wd\@picbox
\advance\count@-4 \repeat
\setbox\strutbox=\hbox{\vrule height\ht\@picbox depth\dp\@picbox width\z@
\kern\wd\@picbox}%
\@save=.5\wd\@picbox \advance\@save-.5\linethickness
\setbox0=\hbox to\@xdim{\ifovaltl\char\count@\else\strut\fi
\kern-\@save\leaders\hrule height\ifovaltl\linethickness\else\z@\fi\hfil
\leaders\hrule height\ifovaltr\linethickness\else\z@\fi\hfil\kern\@save
\ifovaltr\advance\count@-3\char\count@\else\strut\fi\kern-\wd\@picbox}%
\advance\count@\m@ne
\setbox2=\hbox to\@xdim{\ifovalbl\char\count@\else\strut\fi
\kern-\@save\leaders\hrule height\ifovalbl\linethickness\else\z@\fi\hfil
\leaders\hrule height\ifovalbr\linethickness\else\z@\fi\hfil\kern\@save
\ifovalbr\advance\count@\m@ne\char\count@\else\strut\fi\kern-\wd\@picbox}%
\@save=\@ydim \advance\@save-\wd\@picbox \divide\@save 2
\setbox\@picbox=\vbox{\box0\nointerlineskip
\hbox to\@xdim{\vrule height\@save width\ifovaltl\linethickness\else\z@\fi
\hfil\ifovaltr\vrule width\linethickness\kern-\linethickness\fi}%
\nointerlineskip
\hbox to\@xdim{\vrule height\@save width\ifovalbl\linethickness\else\z@\fi
\hfil\ifovalbr\vrule width\linethickness\kern-\linethickness\fi}%
\nointerlineskip\box2}%
\@save=.5\@ydim \advance\@save.5\linethickness \leavevmode
\kern-.5\@xdim \kern-.5\linethickness \lower\@save\box\@picbox}}
\def\cpic#1\endcpic{\vcenter{\hbox{\beginpicture#1\endpicture}}}
% Squines (quadratic splines)
% example of use: to plot f(x) between x0 and x1, you can say
% \put(0,0){\squine(x0,xm,x1,y0,ym,y1)}, where y0=f(x0), y1=f(x1)
% xm=(y0-y1+s1x1-s0x0)/(s1-s0), ym=(s0(s1x1-y1)-s1(s0x0-y0))/(s1-s0),
% s0=f'(x0), and s1=f'(x1).
\newdimen\@xi \newdimen\@xii \newdimen\@xiii \newdimen\@xiv
\newdimen\@xpt \newdimen\@xoldpt
\newdimen\@yi \newdimen\@yii \newdimen\@yiii \newdimen\@yiv
\newdimen\@ypt \newdimen\@yoldpt
\def\squine(#1,#2,#3,#4,#5,#6){\setbox\@picbox\hbox{\tencirc q}%
\global\@xoldpt=#1\unitlength \global\@yoldpt=#4\unitlength \kern\@xoldpt
\@xi=\@xoldpt \@xii=#2\unitlength \@xiii=#3\unitlength
\@yi=\@yoldpt \@yii=#5\unitlength \@yiii=#6\unitlength
\squinerec
\@xpt=#3\unitlength \@ypt=#6\unitlength \@addpoint
\raise\@ypt\copy\@picbox}
\newif\iffar
\def\squinerec{\farfalse \testnear\@xi\@xiii \testnear\@yi\@yiii
\iffar \decast \fi}
\def\testnear#1#2{\@save=#1\advance\@save-#2%
\ifdim\@save<\z@ \@save=-\@save\fi \ifdim\@save>\p@ \fartrue \fi}
\def\decast{\@xpt=\@xi \advance\@xpt\@xii \divide\@xpt2
\advance\@xii\@xiii \divide\@xii2
\@xiv=\@xpt \advance\@xiv\@xii \divide\@xiv2
\@ypt=\@yi \advance\@ypt\@yii \divide\@ypt2
\advance\@yii\@yiii \divide\@yii2
\@yiv=\@ypt \advance\@yiv\@yii \divide\@yiv2
\begingroup\@xii=\@xpt \@xiii=\@xiv
\@yii=\@ypt \@yiii=\@yiv \squinerec\endgroup
\@xpt=\@xiv \@ypt=\@yiv \@addpoint
\@xi=\@xiv \@yi=\@yiv \squinerec}
\def\@addpoint{%\message{(\the\@xpt,\the\@ypt)}%
\global\advance\@xoldpt-\@xpt \wd\@picbox=-\@xoldpt
\raise\@yoldpt\copy\@picbox \global\@xoldpt=\@xpt \global\@yoldpt=\@ypt}
\catcode`\@=12 % disable private control sequences
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