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piclatex.sty
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1988-10-16
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\catcode`@=11 \catcode`!=11
\expandafter\ifx\csname fiverm\endcsname\relax
\let\fiverm\fivrm
\fi
\let\!latexendpicture=\endpicture
\let\!latexframe=\frame
\let\!latexlinethickness=\linethickness
\let\!latexmultiput=\multiput
\let\!latexput=\put
\def\@picture(#1,#2)(#3,#4){%
\@picht #2\unitlength
\setbox\@picbox\hbox to #1\unitlength\bgroup
\let\endpicture=\!latexendpicture
\let\frame=\!latexframe
\let\linethickness=\!latexlinethickness
\let\multiput=\!latexmultiput
\let\put=\!latexput
\hskip -#3\unitlength \lower #4\unitlength \hbox\bgroup}
\catcode`@=12 \catcode`!=12
\catcode`!=11 % ***** THIS MUST NEVER BE OMITTED
\def\PiC{P\kern-.12em\lower.5ex\hbox{I}\kern-.075emC}
\def\PiCTeX{\PiC\kern-.11em\TeX}
\def\!ifnextchar#1#2#3{%
\let\!testchar=#1%
\def\!first{#2}%
\def\!second{#3}%
\futurelet\!nextchar\!testnext}
\def\!testnext{%
\ifx \!nextchar \!spacetoken
\let\!next=\!skipspacetestagain
\else
\ifx \!nextchar \!testchar
\let\!next=\!first
\else
\let\!next=\!second
\fi
\fi
\!next}
\def\\{\!skipspacetestagain}
\expandafter\def\\ {\futurelet\!nextchar\!testnext}
\def\\{\let\!spacetoken= } \\ % ** set \spacetoken to a space token
\def\!tfor#1:=#2\do#3{%
\edef\!fortemp{#2}%
\ifx\!fortemp\!empty
\else
\!tforloop#2\!nil\!nil\!!#1{#3}%
\fi}
\def\!tforloop#1#2\!!#3#4{%
\def#3{#1}%
\ifx #3\!nnil
\let\!nextwhile=\!fornoop
\else
#4\relax
\let\!nextwhile=\!tforloop
\fi
\!nextwhile#2\!!#3{#4}}
\def\!etfor#1:=#2\do#3{%
\def\!!tfor{\!tfor#1:=}%
\edef\!!!tfor{#2}%
\expandafter\!!tfor\!!!tfor\do{#3}}
\def\!cfor#1:=#2\do#3{%
\edef\!fortemp{#2}%
\ifx\!fortemp\!empty
\else
\!cforloop#2,\!nil,\!nil\!!#1{#3}%
\fi}
\def\!cforloop#1,#2\!!#3#4{%
\def#3{#1}%
\ifx #3\!nnil
\let\!nextwhile=\!fornoop
\else
#4\relax
\let\!nextwhile=\!cforloop
\fi
\!nextwhile#2\!!#3{#4}}
\def\!ecfor#1:=#2\do#3{%
\def\!!cfor{\!cfor#1:=}%
\edef\!!!cfor{#2}%
\expandafter\!!cfor\!!!cfor\do{#3}}
\def\!empty{}
\def\!nnil{\!nil}
\def\!fornoop#1\!!#2#3{}
\def\!ifempty#1#2#3{%
\edef\!emptyarg{#1}%
\ifx\!emptyarg\!empty
#2%
\else
#3%
\fi}
\def\!getnext#1\from#2{%
\expandafter\!gnext#2\!#1#2}%
\def\!gnext\\#1#2\!#3#4{%
\def#3{#1}%
\def#4{#2\\{#1}}%
\ignorespaces}
\def\!getnextvalueof#1\from#2{%
\expandafter\!gnextv#2\!#1#2}%
\def\!gnextv\\#1#2\!#3#4{%
#3=#1%
\def#4{#2\\{#1}}%
\ignorespaces}
\def\!copylist#1\to#2{%
\expandafter\!!copylist#1\!#2}
\def\!!copylist#1\!#2{%
\def#2{#1}\ignorespaces}
\def\!wlet#1=#2{%
\let#1=#2
\wlog{\string#1=\string#2}}
\def\!listaddon#1#2{%
\expandafter\!!listaddon#2\!{#1}#2}
\def\!!listaddon#1\!#2#3{%
\def#3{#1\\#2}}
\def\!rightappend#1\withCS#2\to#3{\expandafter\!!rightappend#3\!#2{#1}#3}
\def\!!rightappend#1\!#2#3#4{\def#4{#1#2{#3}}}
\def\!leftappend#1\withCS#2\to#3{\expandafter\!!leftappend#3\!#2{#1}#3}
\def\!!leftappend#1\!#2#3#4{\def#4{#2{#3}#1}}
\def\!lop#1\to#2{\expandafter\!!lop#1\!#1#2}
\def\!!lop\\#1#2\!#3#4{\def#4{#1}\def#3{#2}}
\def\!loop#1\repeat{\def\!body{#1}\!iterate}
\def\!iterate{\!body\let\!next=\!iterate\else\let\!next=\relax\fi\!next}
\def\!!loop#1\repeat{\def\!!body{#1}\!!iterate}
\def\!!iterate{\!!body\let\!!next=\!!iterate\else\let\!!next=\relax\fi\!!next}
\def\!removept#1#2{\edef#2{\expandafter\!!removePT\the#1}}
{\catcode`p=12 \catcode`t=12 \gdef\!!removePT#1pt{#1}}
\def\placevalueinpts of <#1> in #2 {%
\!removept{#1}{#2}}
\def\!mlap#1{\hbox to 0pt{\hss#1\hss}}
\def\!vmlap#1{\vbox to 0pt{\vss#1\vss}}
\def\!not#1{%
#1\relax
\!switchfalse
\else
\!switchtrue
\fi
\if!switch
\ignorespaces}
\let\!!!wlog=\wlog % "\wlog" is defined in plain TeX
\def\wlog#1{}
\newdimen\headingtoplotskip %.A.................
\newdimen\linethickness %.A..X....U........T
\newdimen\longticklength %.A................T
\newdimen\plotsymbolspacing %......D...L....Q...
\newdimen\shortticklength %.A................T
\newdimen\stackleading %.A..........P......
\newdimen\tickstovaluesleading %.A................T
\newdimen\totalarclength %......D...L....Q...
\newdimen\valuestolabelleading %.A.................
\newbox\!boxA %.AW...............T
\newbox\!boxB %..W................
\newbox\!picbox %............P......
\newbox\!plotsymbol %..........L..O.....
\newbox\!putobject %............PO...S.
\newbox\!shadesymbol %.................S.
\newcount\!countA %.A....D..UL....Q.ST
\newcount\!countB %......D..U.....Q.ST
\newcount\!countC %...............Q..T
\newcount\!countD %...................
\newcount\!countE %.............O....T
\newcount\!countF %.............O....T
\newcount\!countG %..................T
\newcount\!fiftypt %.........U.........
\newcount\!intervalno %..........L....Q...
\newcount\!npoints %..........L........
\newcount\!nsegments %.........U.........
\newcount\!ntemp %............P......
\newcount\!parity %.................S.
\newcount\!scalefactor %..................T
\newcount\!tfs %.......V...........
\newcount\!tickcase %..................T
\newdimen\!Xleft %............P......
\newdimen\!Xright %............P......
\newdimen\!Xsave %.A................T
\newdimen\!Ybot %............P......
\newdimen\!Ysave %.A................T
\newdimen\!Ytop %............P......
\newdimen\!angle %........E..........
\newdimen\!arclength %..W......UL....Q...
\newdimen\!areabloc %.A........L........
\newdimen\!arealloc %.A........L........
\newdimen\!arearloc %.A........L........
\newdimen\!areatloc %.A........L........
\newdimen\!bshrinkage %.................S.
\newdimen\!checkbot %..........L........
\newdimen\!checkleft %..........L........
\newdimen\!checkright %..........L........
\newdimen\!checktop %..........L........
\newdimen\!dimenA %.AW.X.DVEUL..OYQRST
\newdimen\!dimenB %....X.DVEU...O.QRS.
\newdimen\!dimenC %..W.X.DVEU......RS.
\newdimen\!dimenD %..W.X.DVEU....Y.RS.
\newdimen\!dimenE %..W........G..YQ.S.
\newdimen\!dimenF %...........G..YQ.S.
\newdimen\!dimenG %...........G..YQ.S.
\newdimen\!dimenH %...........G..Y..S.
\newdimen\!dimenI %...BX.........Y....
\newdimen\!distacross %..........L....Q...
\newdimen\!downlength %..........L........
\newdimen\!dp %.A..X.......P....S.
\newdimen\!dshade %.................S.
\newdimen\!dxpos %..W......U..P....S.
\newdimen\!dxprime %...............Q...
\newdimen\!dypos %..WB.....U..P......
\newdimen\!dyprime %...............Q...
\newdimen\!ht %.A..X.......P....S.
\newdimen\!leaderlength %......D..U.........
\newdimen\!lshrinkage %.................S.
\newdimen\!midarclength %...............Q...
\newdimen\!offset %.A................T
\newdimen\!plotheadingoffset %.A.................
\newdimen\!plotsymbolxshift %..........L..O.....
\newdimen\!plotsymbolyshift %..........L..O.....
\newdimen\!plotxorigin %..........L..O.....
\newdimen\!plotyorigin %..........L..O.....
\newdimen\!rootten %...........G.......
\newdimen\!rshrinkage %.................S.
\newdimen\!shadesymbolxshift %.................S.
\newdimen\!shadesymbolyshift %.................S.
\newdimen\!tenAa %...........G.......
\newdimen\!tenAc %...........G.......
\newdimen\!tenAe %...........G.......
\newdimen\!tshrinkage %.................S.
\newdimen\!uplength %..........L........
\newdimen\!wd %....X.......P....S.
\newdimen\!wmax %...............Q...
\newdimen\!wmin %...............Q...
\newdimen\!xB %...............Q...
\newdimen\!xC %...............Q...
\newdimen\!xE %..W.....E.L....Q.S.
\newdimen\!xM %..W.....E......Q.S.
\newdimen\!xS %..W.....E.L....Q.S.
\newdimen\!xaxislength %.A................T
\newdimen\!xdiff %..........L........
\newdimen\!xleft %............P......
\newdimen\!xloc %..WB.....U.......S.
\newdimen\!xorigin %.A........L.P....S.
\newdimen\!xpivot %................R..
\newdimen\!xpos %..........L.P..Q.ST
\newdimen\!xprime %...............Q...
\newdimen\!xright %............P......
\newdimen\!xshade %.................S.
\newdimen\!xshift %..W.........PO...S.
\newdimen\!xtemp %............P......
\newdimen\!xunit %.AWBX...EUL.P..QRS.
\newdimen\!xxE %........E..........
\newdimen\!xxM %........E..........
\newdimen\!xxS %........E..........
\newdimen\!xxloc %..WB....EU.........
\newdimen\!yB %...............Q...
\newdimen\!yC %...............Q...
\newdimen\!yE %..W.....E.L....Q...
\newdimen\!yM %..W.....E......Q...
\newdimen\!yS %..W.....E.L....Q...
\newdimen\!yaxislength %.A................T
\newdimen\!ybot %............P......
\newdimen\!ydiff %..........L........
\newdimen\!yloc %..WB.....U.......S.
\newdimen\!yorigin %.A........L.P....S.
\newdimen\!ypivot %................R..
\newdimen\!ypos %..........L.P..Q.ST
\newdimen\!yprime %...............Q...
\newdimen\!yshade %.................S.
\newdimen\!yshift %..W.........PO...S.
\newdimen\!ytemp %............P......
\newdimen\!ytop %............P......
\newdimen\!yunit %.AWBX...EUL.P..QRS.
\newdimen\!yyE %........E..........
\newdimen\!yyM %........E..........
\newdimen\!yyS %........E..........
\newdimen\!yyloc %..WB....EU.........
\newdimen\!zpt %.AWBX.DVEULGP.YQ.ST
\newif\if!axisvisible %.A.................
\newif\if!gridlinestoo %..................T
\newif\if!keepPO %...................
\newif\if!placeaxislabel %.A.................
\newif\if!switch %H..................
\newif\if!xswitch %.A................T
\newtoks\!axisLaBeL %.A.................
\newtoks\!keywordtoks %.A.................
\newwrite\!replotfile %.............O.....
\newhelp\!keywordhelp{The keyword mentioned in the error message in unknown.
Replace NEW KEYWORD in the indicated response by the keyword that
should have been specified.} %.A.................
\!wlet\!!origin=\!xM %.A................T
\!wlet\!!unit=\!uplength %.A................T
\!wlet\!Lresiduallength=\!dimenG %.........U.........
\!wlet\!Rresiduallength=\!dimenF %.........U.........
\!wlet\!axisLength=\!distacross %.A................T
\!wlet\!axisend=\!ydiff %.A................T
\!wlet\!axisstart=\!xdiff %.A................T
\!wlet\!axisxlevel=\!arclength %.A................T
\!wlet\!axisylevel=\!downlength %.A................T
\!wlet\!beta=\!dimenE %...............Q...
\!wlet\!gamma=\!dimenF %...............Q...
\!wlet\!shadexorigin=\!plotxorigin %.................S.
\!wlet\!shadeyorigin=\!plotyorigin %.................S.
\!wlet\!ticklength=\!xS %..................T
\!wlet\!ticklocation=\!xE %..................T
\!wlet\!ticklocationincr=\!yE %..................T
\!wlet\!tickwidth=\!yS %..................T
\!wlet\!totalleaderlength=\!dimenE %.........U.........
\!wlet\!xone=\!xprime %....X..............
\!wlet\!xtwo=\!dxprime %....X..............
\!wlet\!ySsave=\!yM %...................
\!wlet\!ybB=\!yB %.................S.
\!wlet\!ybC=\!yC %.................S.
\!wlet\!ybE=\!yE %.................S.
\!wlet\!ybM=\!yM %.................S.
\!wlet\!ybS=\!yS %.................S.
\!wlet\!ybpos=\!yyloc %.................S.
\!wlet\!yone=\!yprime %....X..............
\!wlet\!ytB=\!xB %.................S.
\!wlet\!ytC=\!xC %.................S.
\!wlet\!ytE=\!downlength %.................S.
\!wlet\!ytM=\!arclength %.................S.
\!wlet\!ytS=\!distacross %.................S.
\!wlet\!ytpos=\!xxloc %.................S.
\!wlet\!ytwo=\!dyprime %....X..............
\!zpt=0pt % static
\!xunit=1pt
\!yunit=1pt
\!arearloc=\!xunit
\!areatloc=\!yunit
\!dshade=5pt
\!leaderlength=24in
\!tfs=256 % static
\!wmax=5.3pt % static
\!wmin=2.7pt % static
\!xaxislength=\!xunit
\!xpivot=\!zpt
\!yaxislength=\!yunit
\!ypivot=\!zpt
\plotsymbolspacing=.4pt
\!dimenA=50pt \!fiftypt=\!dimenA % static
\!rootten=3.162278pt % static
\!tenAa=8.690286pt % static (A5)
\!tenAc=2.773839pt % static (A3)
\!tenAe=2.543275pt % static (A1)
\def\!cosrotationangle{1} %................R..
\def\!sinrotationangle{0} %................R..
\def\!xpivotcoord{0} %................R..
\def\!xref{0} %............P......
\def\!xshadesave{0} %.................S.
\def\!ypivotcoord{0} %................R..
\def\!yref{0} %............P......
\def\!yshadesave{0} %.................S.
\def\!zero{0} %..................T
\let\wlog=\!!!wlog
\def\normalgraphs{%
\longticklength=.4\baselineskip
\shortticklength=.25\baselineskip
\tickstovaluesleading=.25\baselineskip
\valuestolabelleading=.8\baselineskip
\linethickness=.4pt
\stackleading=.17\baselineskip
\headingtoplotskip=1.5\baselineskip
\visibleaxes
\ticksout
\nogridlines
\unloggedticks}
\def\setplotarea x from #1 to #2, y from #3 to #4 {%
\!arealloc=\!M{#1}\!xunit \advance \!arealloc -\!xorigin
\!areabloc=\!M{#3}\!yunit \advance \!areabloc -\!yorigin
\!arearloc=\!M{#2}\!xunit \advance \!arearloc -\!xorigin
\!areatloc=\!M{#4}\!yunit \advance \!areatloc -\!yorigin
\!initinboundscheck
\!xaxislength=\!arearloc \advance\!xaxislength -\!arealloc
\!yaxislength=\!areatloc \advance\!yaxislength -\!areabloc
\!plotheadingoffset=\!zpt
\!dimenput {{\setbox0=\hbox{}\wd0=\!xaxislength\ht0=\!yaxislength\box0}}
[bl] (\!arealloc,\!areabloc)}
\def\visibleaxes{%
\def\!axisvisibility{\!axisvisibletrue}}
\def\invisibleaxes{%
\def\!axisvisibility{\!axisvisiblefalse}}
\def\!fixkeyword#1{%
\errhelp=\!keywordhelp
\errmessage{Unrecognized keyword `#1': \the\!keywordtoks{NEW KEYWORD}'}}
\!keywordtoks={enter `i\fixkeyword}
\def\fixkeyword#1{%
\!nextkeyword#1 }
\def\axis {%
\def\!nextkeyword##1 {%
\expandafter\ifx\csname !axis##1\endcsname \relax
\def\!next{\!fixkeyword{##1}}%
\else
\def\!next{\csname !axis##1\endcsname}%
\fi
\!next}%
\!offset=\!zpt
\!axisvisibility
\!placeaxislabelfalse
\!nextkeyword}
\def\!axisbottom{%
\!axisylevel=\!areabloc
\def\!tickxsign{0}%
\def\!tickysign{-}%
\def\!axissetup{\!axisxsetup}%
\def\!axislabeltbrl{t}%
\!nextkeyword}
\def\!axistop{%
\!axisylevel=\!areatloc
\def\!tickxsign{0}%
\def\!tickysign{+}%
\def\!axissetup{\!axisxsetup}%
\def\!axislabeltbrl{b}%
\!nextkeyword}
\def\!axisleft{%
\!axisxlevel=\!arealloc
\def\!tickxsign{-}%
\def\!tickysign{0}%
\def\!axissetup{\!axisysetup}%
\def\!axislabeltbrl{r}%
\!nextkeyword}
\def\!axisright{%
\!axisxlevel=\!arearloc
\def\!tickxsign{+}%
\def\!tickysign{0}%
\def\!axissetup{\!axisysetup}%
\def\!axislabeltbrl{l}%
\!nextkeyword}
\def\!axisshiftedto#1=#2 {%
\if 0\!tickxsign
\!axisylevel=\!M{#2}\!yunit
\advance\!axisylevel -\!yorigin
\else
\!axisxlevel=\!M{#2}\!xunit
\advance\!axisxlevel -\!xorigin
\fi
\!nextkeyword}
\def\!axisvisible{%
\!axisvisibletrue
\!nextkeyword}
\def\!axisinvisible{%
\!axisvisiblefalse
\!nextkeyword}
\def\!axislabel#1 {%
\!axisLaBeL={#1}%
\!placeaxislabeltrue
\!nextkeyword}
\expandafter\def\csname !axis/\endcsname{%
\!axissetup % This could done already by "ticks"; if so, now \relax
\if!placeaxislabel
\!placeaxislabel
\fi
\if +\!tickysign % ** (A "top" axis)
\!dimenA=\!axisylevel
\advance\!dimenA \!offset % ** dimA = top of the axis structure
\advance\!dimenA -\!areatloc % ** dimA = excess over the plot area
\ifdim \!dimenA>\!plotheadingoffset
\!plotheadingoffset=\!dimenA % ** Greatest excess over the plot area
\fi
\fi}
\def\grid #1 #2 {%
\!countA=#1\advance\!countA 1
\axis bottom invisible ticks length <\!zpt> andacross quantity {\!countA} /
\!countA=#2\advance\!countA 1
\axis left invisible ticks length <\!zpt> andacross quantity {\!countA} / }
\def\plotheading#1 {%
\advance\!plotheadingoffset \headingtoplotskip
\!dimenput {#1} [B] <.5\!xaxislength,\!plotheadingoffset>
(\!arealloc,\!areatloc)}
\def\!axisxsetup{%
\!axisxlevel=\!arealloc
\!axisstart=\!arealloc
\!axisend=\!arearloc
\!axisLength=\!xaxislength
\!!origin=\!xorigin
\!!unit=\!xunit
\!xswitchtrue
\if!axisvisible
\!makeaxis
\fi}
\def\!axisysetup{%
\!axisylevel=\!areabloc
\!axisstart=\!areabloc
\!axisend=\!areatloc
\!axisLength=\!yaxislength
\!!origin=\!yorigin
\!!unit=\!yunit
\!xswitchfalse
\if!axisvisible
\!makeaxis
\fi}
\def\!makeaxis{%
\setbox\!boxA=\hbox{% (Make a pseudo-y[x] tick for an x[y]-axis)
\beginpicture
\!setdimenmode
\setcoordinatesystem point at {\!zpt} {\!zpt}
\putrule from {\!zpt} {\!zpt} to
{\!tickysign\!tickysign\!axisLength}
{\!tickxsign\!tickxsign\!axisLength}
\endpicturesave <\!Xsave,\!Ysave>}%
\wd\!boxA=\!zpt
\!placetick\!axisstart}
\def\!placeaxislabel{%
\advance\!offset \valuestolabelleading
\if!xswitch
\!dimenput {\the\!axisLaBeL} [\!axislabeltbrl]
<.5\!axisLength,\!tickysign\!offset> (\!axisxlevel,\!axisylevel)
\advance\!offset \!dp % ** advance offset by the "tallness"
\advance\!offset \!ht % ** of the label
\else
\!dimenput {\the\!axisLaBeL} [\!axislabeltbrl]
<\!tickxsign\!offset,.5\!axisLength> (\!axisxlevel,\!axisylevel)
\fi
\!axisLaBeL={}}
\def\arrow <#1> [#2,#3]{%
\!ifnextchar<{\!arrow{#1}{#2}{#3}}{\!arrow{#1}{#2}{#3}<\!zpt,\!zpt> }}
\def\!arrow#1#2#3<#4,#5> from #6 #7 to #8 #9 {%
\!xloc=\!M{#8}\!xunit
\!yloc=\!M{#9}\!yunit
\!dxpos=\!xloc \!dimenA=\!M{#6}\!xunit \advance \!dxpos -\!dimenA
\!dypos=\!yloc \!dimenA=\!M{#7}\!yunit \advance \!dypos -\!dimenA
\let\!MAH=\!M% ** save current c/d mode
\!setdimenmode% ** go into dimension mode
\!xshift=#4\relax \!yshift=#5\relax% ** pick up shift
\!reverserotateonly\!xshift\!yshift% ** back rotate shift
\advance\!xshift\!xloc \advance\!yshift\!yloc
\!xS=-\!dxpos \advance\!xS\!xshift
\!yS=-\!dypos \advance\!yS\!yshift
\!start (\!xS,\!yS)
\!ljoin (\!xshift,\!yshift)
\!Pythag\!dxpos\!dypos\!arclength
\!divide\!dxpos\!arclength\!dxpos
\!dxpos=32\!dxpos \!removept\!dxpos\!!cos
\!divide\!dypos\!arclength\!dypos
\!dypos=32\!dypos \!removept\!dypos\!!sin
\!halfhead{#1}{#2}{#3}% ** draw half of arrow head
\!halfhead{#1}{-#2}{-#3}% ** draw other half
\let\!M=\!MAH% ** restore old c/d mode
\ignorespaces}
\def\!halfhead#1#2#3{%
\!dimenC=-#1%
\divide \!dimenC 2 % ** half way back
\!dimenD=#2\!dimenC% ** half the mid width
\!rotate(\!dimenC,\!dimenD)by(\!!cos,\!!sin)to(\!xM,\!yM)
\!dimenC=-#1% ** all the way back
\!dimenD=#3\!dimenC
\!dimenD=.5\!dimenD% ** half the full width
\!rotate(\!dimenC,\!dimenD)by(\!!cos,\!!sin)to(\!xE,\!yE)
\!start (\!xshift,\!yshift)
\advance\!xM\!xshift \advance\!yM\!yshift
\advance\!xE\!xshift \advance\!yE\!yshift
\!qjoin (\!xM,\!yM) (\!xE,\!yE)
\ignorespaces}
\def\betweenarrows #1#2 from #3 #4 to #5 #6 {%
\!xloc=\!M{#3}\!xunit \!xxloc=\!M{#5}\!xunit%
\!yloc=\!M{#4}\!yunit \!yyloc=\!M{#6}\!yunit%
\!dxpos=\!xxloc \advance\!dxpos by -\!xloc
\!dypos=\!yyloc \advance\!dypos by -\!yloc
\advance\!xloc .5\!dxpos
\advance\!yloc .5\!dypos
\let\!MBA=\!M% ** save current coord\dimen mode
\!setdimenmode% ** express locations in dimens
\ifdim\!dypos=\!zpt
\ifdim\!dxpos<\!zpt \!dxpos=-\!dxpos \fi
\put {\!lrarrows{\!dxpos}{#1}}#2{} at {\!xloc} {\!yloc}
\else
\ifdim\!dxpos=\!zpt
\ifdim\!dypos<\!zpt \!dypos=-\!zpt \fi
\put {\!udarrows{\!dypos}{#1}}#2{} at {\!xloc} {\!yloc}
\fi
\fi
\let\!M=\!MBA% ** restore previous c/d mode
\ignorespaces}
\def\!lrarrows#1#2{% #1=width, #2=text
{\setbox\!boxA=\hbox{$\mkern-2mu\mathord-\mkern-2mu$}%
\setbox\!boxB=\hbox{$\leftarrow$}\!dimenE=\ht\!boxB
\setbox\!boxB=\hbox{}\ht\!boxB=2\!dimenE
\hbox to #1{$\mathord\leftarrow\mkern-6mu
\cleaders\copy\!boxA\hfil
\mkern-6mu\mathord-$%
\kern.4em $\vcenter{\box\!boxB}$$\vcenter{\hbox{#2}}$\kern.4em
$\mathord-\mkern-6mu
\cleaders\copy\!boxA\hfil
\mkern-6mu\mathord\rightarrow$}}}
\def\!udarrows#1#2{% #1=width, #2=text
{\setbox\!boxB=\hbox{#2}%
\setbox\!boxA=\hbox to \wd\!boxB{\hss$\vert$\hss}%
\!dimenE=\ht\!boxA \advance\!dimenE \dp\!boxA \divide\!dimenE 2
\vbox to #1{\offinterlineskip
\vskip .05556\!dimenE
\hbox to \wd\!boxB{\hss$\mkern.4mu\uparrow$\hss}\vskip-\!dimenE
\cleaders\copy\!boxA\vfil
\vskip-\!dimenE\copy\!boxA
\vskip\!dimenE\copy\!boxB\vskip.4em
\copy\!boxA\vskip-\!dimenE
\cleaders\copy\!boxA\vfil
\vskip-\!dimenE \hbox to \wd\!boxB{\hss$\mkern.4mu\downarrow$\hss}
\vskip .05556\!dimenE}}}
\def\putbar#1breadth <#2> from #3 #4 to #5 #6 {%
\!xloc=\!M{#3}\!xunit \!xxloc=\!M{#5}\!xunit%
\!yloc=\!M{#4}\!yunit \!yyloc=\!M{#6}\!yunit%
\!dypos=\!yyloc \advance\!dypos by -\!yloc
\!dimenI=#2
\ifdim \!dimenI=\!zpt % ** If 0 breadth
\putrule#1from {#3} {#4} to {#5} {#6} % ** Then draw line
\else % ** Else, put in a rectangle
\let\!MBar=\!M% ** save current c/d mode
\!setdimenmode % ** go into dimension mode
\divide\!dimenI 2
\ifdim \!dypos=\!zpt
\advance \!yloc -\!dimenI % ** Equal y coordinates
\advance \!yyloc \!dimenI
\else
\advance \!xloc -\!dimenI % ** Equal x coordinates
\advance \!xxloc \!dimenI
\fi
\putrectangle#1corners at {\!xloc} {\!yloc} and {\!xxloc} {\!yyloc}
\let\!M=\!MBar % ** restore c/d mode
\fi
\ignorespaces}
\def\setbars#1breadth <#2> baseline at #3 = #4 {%
\edef\!barshift{#1}%
\edef\!barbreadth{#2}%
\edef\!barorientation{#3}%
\edef\!barbaseline{#4}%
\def\!bardobaselabel{\!bardoendlabel}%
\def\!bardoendlabel{\!barfinish}%
\let\!drawcurve=\!barcurve
\!setbars}
\def\!setbars{%
\futurelet\!nextchar\!!setbars}
\def\!!setbars{%
\if b\!nextchar
\def\!!!setbars{\!setbarsbget}%
\else
\if e\!nextchar
\def\!!!setbars{\!setbarseget}%
\else
\def\!!!setbars{\relax}%
\fi
\fi
\!!!setbars}
\def\!setbarsbget baselabels (#1) {%
\def\!barbaselabelorientation{#1}%
\def\!bardobaselabel{\!!bardobaselabel}%
\!setbars}
\def\!setbarseget endlabels (#1) {%
\edef\!barendlabelorientation{#1}%
\def\!bardoendlabel{\!!bardoendlabel}%
\!setbars}
\def\!barcurve #1 #2 {%
\if y\!barorientation
\def\!basexarg{#1}%
\def\!baseyarg{\!barbaseline}%
\else
\def\!basexarg{\!barbaseline}%
\def\!baseyarg{#2}%
\fi
\expandafter\putbar\!barshift breadth <\!barbreadth> from {\!basexarg}
{\!baseyarg} to {#1} {#2}
\def\!endxarg{#1}%
\def\!endyarg{#2}%
\!bardobaselabel}
\def\!!bardobaselabel "#1" {%
\put {#1}\!barbaselabelorientation{} at {\!basexarg} {\!baseyarg}
\!bardoendlabel}
\def\!!bardoendlabel "#1" {%
\put {#1}\!barendlabelorientation{} at {\!endxarg} {\!endyarg}
\!barfinish}
\def\!barfinish{%
\!ifnextchar/{\!finish}{\!barcurve}}
\def\putrectangle{%
\!ifnextchar<{\!putrectangle}{\!putrectangle<\!zpt,\!zpt> }}
\def\!putrectangle<#1,#2> corners at #3 #4 and #5 #6 {%
\!xone=\!M{#3}\!xunit \!xtwo=\!M{#5}\!xunit%
\!yone=\!M{#4}\!yunit \!ytwo=\!M{#6}\!yunit%
\ifdim \!xtwo<\!xone
\!dimenI=\!xone \!xone=\!xtwo \!xtwo=\!dimenI
\fi
\ifdim \!ytwo<\!yone
\!dimenI=\!yone \!yone=\!ytwo \!ytwo=\!dimenI
\fi
\!dimenI=#1\relax \advance\!xone\!dimenI \advance\!xtwo\!dimenI
\!dimenI=#2\relax \advance\!yone\!dimenI \advance\!ytwo\!dimenI
\let\!MRect=\!M% ** save current coord/dimen mode
\!setdimenmode
\!shaderectangle
\!dimenI=.5\linethickness
\advance \!xone -\!dimenI% ** adjust x-location to overlap corners
\advance \!xtwo \!dimenI% ** ditto
\putrule from {\!xone} {\!yone} to {\!xtwo} {\!yone}
\putrule from {\!xone} {\!ytwo} to {\!xtwo} {\!ytwo}
\advance \!xone \!dimenI% ** restore original x-values
\advance \!xtwo -\!dimenI%
\advance \!yone -\!dimenI% ** adjust y-location to overlap corners
\advance \!ytwo \!dimenI% ** ditto
\putrule from {\!xone} {\!yone} to {\!xone} {\!ytwo}
\putrule from {\!xtwo} {\!yone} to {\!xtwo} {\!ytwo}
\let\!M=\!MRect% ** restore coord/dimen mode
\ignorespaces}
\def\shaderectangleson{%
\def\!shaderectangle{\!!shaderectangle}%
\ignorespaces}
\def\shaderectanglesoff{%
\def\!shaderectangle{}%
\ignorespaces}
\shaderectanglesoff
\def\!!shaderectangle{%
\!dimenA=\!xtwo \advance \!dimenA -\!xone
\!dimenB=\!ytwo \advance \!dimenB -\!yone
\ifdim \!dimenA<\!dimenB
\!startvshade (\!xone,\!yone,\!ytwo)
\!lshade (\!xtwo,\!yone,\!ytwo)
\else
\!starthshade (\!yone,\!xone,\!xtwo)
\!lshade (\!ytwo,\!xone,\!xtwo)
\fi
\ignorespaces}
\def\frame{%
\!ifnextchar<{\!frame}{\!frame<\!zpt> }}
\long\def\!frame<#1> #2{%
\beginpicture
\setcoordinatesystem units <1pt,1pt> point at 0 0
\put {#2} [Bl] at 0 0
\!dimenA=#1\relax
\!dimenB=\!wd \advance \!dimenB \!dimenA
\!dimenC=\!ht \advance \!dimenC \!dimenA
\!dimenD=\!dp \advance \!dimenD \!dimenA
\let\!MFr=\!M
\!setdimenmode
\putrectangle corners at {-\!dimenA} {-\!dimenD} and {\!dimenB} {\!dimenC}
\!setcoordmode
\let\!M=\!MFr
\endpicture
\ignorespaces}
\def\rectangle <#1> <#2> {%
\setbox0=\hbox{}\wd0=#1\ht0=#2\frame {\box0}}
\def\plot{%
\!ifnextchar"{\!plotfromfile}{\!drawcurve}}
\def\!plotfromfile"#1"{%
\expandafter\!drawcurve \input #1 /}
\def\setquadratic{%
\let\!drawcurve=\!qcurve
\let\!!Shade=\!!qShade
\let\!!!Shade=\!!!qShade}
\def\setlinear{%
\let\!drawcurve=\!lcurve
\let\!!Shade=\!!lShade
\let\!!!Shade=\!!!lShade}
\def\sethistograms{%
\let\!drawcurve=\!hcurve}
\def\!qcurve #1 #2 {%
\!start (#1,#2)
\!Qjoin}
\def\!Qjoin#1 #2 #3 #4 {%
\!qjoin (#1,#2) (#3,#4) % \!qjoin is defined in QUADRATIC
\!ifnextchar/{\!finish}{\!Qjoin}}
\def\!lcurve #1 #2 {%
\!start (#1,#2)
\!Ljoin}
\def\!Ljoin#1 #2 {%
\!ljoin (#1,#2) % \!ljoin is defined in LINEAR
\!ifnextchar/{\!finish}{\!Ljoin}}
\def\!finish/{\ignorespaces}
\def\!hcurve #1 #2 {%
\edef\!hxS{#1}%
\edef\!hyS{#2}%
\!hjoin}
\def\!hjoin#1 #2 {%
\putrectangle corners at {\!hxS} {\!hyS} and {#1} {#2}
\edef\!hxS{#1}%
\!ifnextchar/{\!finish}{\!hjoin}}
\def\vshade #1 #2 #3 {%
\!startvshade (#1,#2,#3)
\!Shadewhat}
\def\hshade #1 #2 #3 {%
\!starthshade (#1,#2,#3)
\!Shadewhat}
\def\!Shadewhat{%
\futurelet\!nextchar\!Shade}
\def\!Shade{%
\if <\!nextchar
\def\!nextShade{\!!Shade}%
\else
\if /\!nextchar
\def\!nextShade{\!finish}%
\else
\def\!nextShade{\!!!Shade}%
\fi
\fi
\!nextShade}
\def\!!lShade<#1> #2 #3 #4 {%
\!lshade <#1> (#2,#3,#4) % \!lshade is defined in SHADING
\!Shadewhat}
\def\!!!lShade#1 #2 #3 {%
\!lshade (#1,#2,#3)
\!Shadewhat}
\def\!!qShade<#1> #2 #3 #4 #5 #6 #7 {%
\!qshade <#1> (#2,#3,#4) (#5,#6,#7) % \!qshade is defined in SHADING
\!Shadewhat}
\def\!!!qShade#1 #2 #3 #4 #5 #6 {%
\!qshade (#1,#2,#3) (#4,#5,#6)
\!Shadewhat}
\setlinear
\def\setdashpattern <#1>{%
\def\!Flist{}\def\!Blist{}\def\!UDlist{}%
\!countA=0
\!ecfor\!item:=#1\do{%
\!dimenA=\!item\relax
\expandafter\!rightappend\the\!dimenA\withCS{\\}\to\!UDlist%
\advance\!countA 1
\ifodd\!countA
\expandafter\!rightappend\the\!dimenA\withCS{\!Rule}\to\!Flist%
\expandafter\!leftappend\the\!dimenA\withCS{\!Rule}\to\!Blist%
\else
\expandafter\!rightappend\the\!dimenA\withCS{\!Skip}\to\!Flist%
\expandafter\!leftappend\the\!dimenA\withCS{\!Skip}\to\!Blist%
\fi}%
\!leaderlength=\!zpt
\def\!Rule##1{\advance\!leaderlength ##1}%
\def\!Skip##1{\advance\!leaderlength ##1}%
\!Flist%
\ifdim\!leaderlength>\!zpt
\else
\def\!Flist{\!Skip{24in}}\def\!Blist{\!Skip{24in}}\ignorespaces
\def\!UDlist{\\{\!zpt}\\{24in}}\ignorespaces
\!leaderlength=24in
\fi
\!dashingon}
\def\!dashingon{%
\def\!advancedashing{\!!advancedashing}%
\def\!drawlinearsegment{\!lineardashed}%
\def\!puthline{\!putdashedhline}%
\def\!putvline{\!putdashedvline}%
\ignorespaces}%
\def\!dashingoff{%
\def\!advancedashing{\relax}%
\def\!drawlinearsegment{\!linearsolid}%
\def\!puthline{\!putsolidhline}%
\def\!putvline{\!putsolidvline}%
\ignorespaces}
\def\setdots{%
\!ifnextchar<{\!setdots}{\!setdots<5pt>}}
\def\!setdots<#1>{%
\!dimenB=#1\advance\!dimenB -\plotsymbolspacing
\ifdim\!dimenB<\!zpt
\!dimenB=\!zpt
\fi
\setdashpattern <\plotsymbolspacing,\!dimenB>}
\def\setdotsnear <#1> for <#2>{%
\!dimenB=#2\relax \advance\!dimenB -.05pt
\!dimenC=#1\relax \!countA=\!dimenC
\!dimenD=\!dimenB \advance\!dimenD .5\!dimenC \!countB=\!dimenD
\divide \!countB \!countA
\ifnum 1>\!countB
\!countB=1
\fi
\divide\!dimenB \!countB
\setdots <\!dimenB>}
\def\setdashes{%
\!ifnextchar<{\!setdashes}{\!setdashes<5pt>}}
\def\!setdashes<#1>{\setdashpattern <#1,#1>}
\def\setdashesnear <#1> for <#2>{%
\!dimenB=#2\relax
\!dimenC=#1\relax \!countA=\!dimenC
\!dimenD=\!dimenB \advance\!dimenD .5\!dimenC \!countB=\!dimenD
\divide \!countB \!countA
\ifodd \!countB
\else
\advance \!countB 1
\fi
\divide\!dimenB \!countB
\setdashes <\!dimenB>}
\def\setsolid{%
\def\!Flist{\!Rule{24in}}\def\!Blist{\!Rule{24in}}%
\def\!UDlist{\\{24in}\\{\!zpt}}%
\!dashingoff}
\setsolid
\def\findlength#1{%
\begingroup
\setdashpattern <0pt, \maxdimen>
\setplotsymbol ({})
\dontsavelinesandcurves
#1%
\endgroup
\ignorespaces}
\def\!divide#1#2#3{%
\!dimenB=#1% ** dimB holds current remainder (r)
\!dimenC=#2% ** dimC holds divisor (d)
\!dimenD=\!dimenB% ** dimD holds quotient q=r/d for this
\divide \!dimenD \!dimenC% ** step, in units of scaled pts
\!dimenA=\!dimenD% ** dimA eventually holds answer (a)
\multiply\!dimenD \!dimenC% ** r <-- r - dq
\advance\!dimenB -\!dimenD% ** First step complete. Have integer part
\!dimenD=\!dimenC% ** Temporarily use dimD to hold |d|
\ifdim\!dimenD<\!zpt \!dimenD=-\!dimenD
\fi
\ifdim\!dimenD<64pt% ** Branch on the magnitude of |d|
\!divstep[\!tfs]\!divstep[\!tfs]%
\else
\!!divide
\fi
#3=\!dimenA\ignorespaces}
\def\!!divide{%
\ifdim\!dimenD<256pt
\!divstep[64]\!divstep[32]\!divstep[32]%
\else
\!divstep[8]\!divstep[8]\!divstep[8]\!divstep[8]\!divstep[8]%
\!dimenA=2\!dimenA
\fi}
\def\!divstep[#1]{% ** #1 = "B"
\!dimenB=#1\!dimenB% ** r <-- B*r
\!dimenD=\!dimenB% ** dimD holds quotient q=r/d for this
\divide \!dimenD by \!dimenC% ** step, in units of scaled pts
\!dimenA=#1\!dimenA% ** a <-- B*a + q
\advance\!dimenA by \!dimenD%
\multiply\!dimenD by \!dimenC% ** r <-- r - dq
\advance\!dimenB by -\!dimenD}
\def\Divide <#1> by <#2> forming <#3> {%
\!divide{#1}{#2}{#3}}
\def\circulararc{%
\ellipticalarc axes ratio 1:1 }
\def\ellipticalarc axes ratio #1:#2 #3 degrees from #4 #5 center at #6 #7 {%
\!angle=#3pt\relax% ** get angle
\ifdim\!angle>\!zpt
\def\!sign{}% ** counterclockwise
\else
\def\!sign{-}\!angle=-\!angle% ** clockwise
\fi
\!xxloc=\!M{#6}\!xunit% ** convert CENTER to dimension
\!yyloc=\!M{#7}\!yunit
\!xxS=\!M{#4}\!xunit% ** get STARTing point on rim of ellipse
\!yyS=\!M{#5}\!yunit
\advance\!xxS -\!xxloc% ** make center of ellipse (0,0)
\advance\!yyS -\!yyloc
\!divide\!xxS{#1pt}\!xxS % ** scale point on ellipse to point on
\!divide\!yyS{#2pt}\!yyS % corresponding circle
\let\!MC=\!M% ** save current c/d mode
\!setdimenmode% ** go into dimension mode
\!xS=#1\!xxS \advance\!xS\!xxloc
\!yS=#2\!yyS \advance\!yS\!yyloc
\!start (\!xS,\!yS)%
\!loop\ifdim\!angle>14.9999pt% ** draw in major portion of ellipse
\!rotate(\!xxS,\!yyS)by(\!cos,\!sign\!sin)to(\!xxM,\!yyM)
\!rotate(\!xxM,\!yyM)by(\!cos,\!sign\!sin)to(\!xxE,\!yyE)
\!xM=#1\!xxM \advance\!xM\!xxloc \!yM=#2\!yyM \advance\!yM\!yyloc
\!xE=#1\!xxE \advance\!xE\!xxloc \!yE=#2\!yyE \advance\!yE\!yyloc
\!qjoin (\!xM,\!yM) (\!xE,\!yE)
\!xxS=\!xxE \!yyS=\!yyE
\advance \!angle -15pt
\repeat
\ifdim\!angle>\!zpt% ** complete remaining arc, if any
\!angle=100.53096\!angle% ** convert angle to radians, divide
\divide \!angle 360 % ** by 2, and multiply by 32
\!sinandcos\!angle\!!sin\!!cos% ** get 32*sin & 32*cos
\!rotate(\!xxS,\!yyS)by(\!!cos,\!sign\!!sin)to(\!xxM,\!yyM)
\!rotate(\!xxM,\!yyM)by(\!!cos,\!sign\!!sin)to(\!xxE,\!yyE)
\!xM=#1\!xxM \advance\!xM\!xxloc \!yM=#2\!yyM \advance\!yM\!yyloc
\!xE=#1\!xxE \advance\!xE\!xxloc \!yE=#2\!yyE \advance\!yE\!yyloc
\!qjoin (\!xM,\!yM) (\!xE,\!yE)
\fi
\let\!M=\!MC% ** restore c/d mode
\ignorespaces}% ** if appropriate
\def\!rotate(#1,#2)by(#3,#4)to(#5,#6){%
\!dimenA=#3#1\advance \!dimenA -#4#2% ** Rcos(x+t)=Rcosx*cost - Rsinx*sint
\!dimenB=#3#2\advance \!dimenB #4#1% ** Rsin(x+t)=Rsinx*cost + Rcosx*sint
\divide \!dimenA 32 \divide \!dimenB 32
#5=\!dimenA #6=\!dimenB
\ignorespaces}
\def\!sin{4.17684}% ** 32*sin(pi/24) (pi/24=7.5deg)
\def\!cos{31.72624}% ** 32*cos(pi/24)
\def\!sinandcos#1#2#3{%
\!dimenD=#1% ** angle is expressed in radians/32: 1pt = 1/32rad
\!dimenA=\!dimenD% ** dimA will eventually contain 32sin(angle)in pts
\!dimenB=32pt% ** dimB will eventually contain 32cos(angle)in pts
\!removept\!dimenD\!value% ** get value of 32*angle, without "pt"
\!dimenC=\!dimenD% ** holds 32*angle**i/i! in pts
\!dimenC=\!value\!dimenC \divide\!dimenC by 64 % ** now 32*angle**2/2
\advance\!dimenB by -\!dimenC% ** 32-32*angle**2/2
\!dimenC=\!value\!dimenC \divide\!dimenC by 96 % ** now 32*angle**3/3!
\advance\!dimenA by -\!dimenC% ** now 32*(angle-angle**3/6)
\!dimenC=\!value\!dimenC \divide\!dimenC by 128 % ** now 32*angle**4/4!
\advance\!dimenB by \!dimenC%
\!removept\!dimenA#2% ** set 32*sin(angle)
\!removept\!dimenB#3% ** set 32*cos(angle)
\ignorespaces}
\def\putrule#1from #2 #3 to #4 #5 {%
\!xloc=\!M{#2}\!xunit \!xxloc=\!M{#4}\!xunit%
\!yloc=\!M{#3}\!yunit \!yyloc=\!M{#5}\!yunit%
\!dxpos=\!xxloc \advance\!dxpos by -\!xloc
\!dypos=\!yyloc \advance\!dypos by -\!yloc
\ifdim\!dypos=\!zpt
\def\!!Line{\!puthline{#1}}\ignorespaces
\else
\ifdim\!dxpos=\!zpt
\def\!!Line{\!putvline{#1}}\ignorespaces
\else
\def\!!Line{}
\fi
\fi
\let\!ML=\!M% ** save current coord\dimen mode
\!setdimenmode% ** express locations in dimens
\!!Line%
\let\!M=\!ML% ** restore previous c/d mode
\ignorespaces}
\def\!putsolidhline#1{%
\ifdim\!dxpos>\!zpt
\put{\!hline\!dxpos}#1[l] at {\!xloc} {\!yloc}
\else
\put{\!hline{-\!dxpos}}#1[l] at {\!xxloc} {\!yyloc}
\fi
\ignorespaces}
\def\!putsolidvline#1{%
\ifdim\!dypos>\!zpt
\put{\!vline\!dypos}#1[b] at {\!xloc} {\!yloc}
\else
\put{\!vline{-\!dypos}}#1[b] at {\!xxloc} {\!yyloc}
\fi
\ignorespaces}
\def\!hline#1{\hbox to #1{\leaders \hrule height\linethickness\hfill}}
\def\!vline#1{\vbox to #1{\leaders \vrule width\linethickness\vfill}}
\def\!putdashedhline#1{%
\ifdim\!dxpos>\!zpt
\!DLsetup\!Flist\!dxpos
\put{\hbox to \!totalleaderlength{\!hleaders}\!hpartialpattern\!Rtrunc}
#1[l] at {\!xloc} {\!yloc}
\else
\!DLsetup\!Blist{-\!dxpos}
\put{\!hpartialpattern\!Ltrunc\hbox to \!totalleaderlength{\!hleaders}}
#1[r] at {\!xloc} {\!yloc}
\fi
\ignorespaces}
\def\!putdashedvline#1{%
\!dypos=-\!dypos% ** vertical leaders go from top to bottom
\ifdim\!dypos>\!zpt
\!DLsetup\!Flist\!dypos
\put{\vbox{\vbox to \!totalleaderlength{\!vleaders}
\!vpartialpattern\!Rtrunc}}#1[t] at {\!xloc} {\!yloc}
\else
\!DLsetup\!Blist{-\!dypos}
\put{\vbox{\!vpartialpattern\!Ltrunc
\vbox to \!totalleaderlength{\!vleaders}}}#1[b] at {\!xloc} {\!yloc}
\fi
\ignorespaces}
\def\!DLsetup#1#2{% ** Dashed-Line set up
\let\!RSlist=#1% ** set !Rule-Skip list
\!countB=#2% ** convert rule length to integer (number of sps)
\!countA=\!leaderlength% ** ditto, leaderlength
\divide\!countB by \!countA% ** number of complete leader units
\!totalleaderlength=\!countB\!leaderlength
\!Rresiduallength=#2%
\advance \!Rresiduallength by -\!totalleaderlength% \** excess length
\!Lresiduallength=\!leaderlength
\advance \!Lresiduallength by -\!Rresiduallength
\ignorespaces}
\def\!hleaders{%
\def\!Rule##1{\vrule height\linethickness width##1}%
\def\!Skip##1{\hskip##1}%
\leaders\hbox{\!RSlist}\hfill}
\def\!hpartialpattern#1{%
\!dimenA=\!zpt \!dimenB=\!zpt
\def\!Rule##1{#1{##1}\vrule height\linethickness width\!dimenD}%
\def\!Skip##1{#1{##1}\hskip\!dimenD}%
\!RSlist}
\def\!vleaders{%
\def\!Rule##1{\hrule width\linethickness height##1}%
\def\!Skip##1{\vskip##1}%
\leaders\vbox{\!RSlist}\vfill}
\def\!vpartialpattern#1{%
\!dimenA=\!zpt \!dimenB=\!zpt
\def\!Rule##1{#1{##1}\hrule width\linethickness height\!dimenD}%
\def\!Skip##1{#1{##1}\vskip\!dimenD}%
\!RSlist}
\def\!Rtrunc#1{\!trunc{#1}>\!Rresiduallength}
\def\!Ltrunc#1{\!trunc{#1}<\!Lresiduallength}
\def\!trunc#1#2#3{%
\!dimenA=\!dimenB
\advance\!dimenB by #1%
\!dimenD=\!dimenB \ifdim\!dimenD#2#3\!dimenD=#3\fi
\!dimenC=\!dimenA \ifdim\!dimenC#2#3\!dimenC=#3\fi
\advance \!dimenD by -\!dimenC}
\def\!start (#1,#2){%
\!plotxorigin=\!xorigin \advance \!plotxorigin by \!plotsymbolxshift
\!plotyorigin=\!yorigin \advance \!plotyorigin by \!plotsymbolyshift
\!xS=\!M{#1}\!xunit \!yS=\!M{#2}\!yunit
\!rotateaboutpivot\!xS\!yS
\!copylist\!UDlist\to\!!UDlist% **\!UDlist has the form \\{dimen1}\\{dimen2}..
\!getnextvalueof\!downlength\from\!!UDlist
\!distacross=\!zpt% ** 1st point goes at start of curve
\!intervalno=0 % ** initialize interval counter
\global\totalarclength=\!zpt% ** initialize distance traveled along curve
\ignorespaces}
\def\!ljoin (#1,#2){%
\advance\!intervalno by 1
\!xE=\!M{#1}\!xunit \!yE=\!M{#2}\!yunit
\!rotateaboutpivot\!xE\!yE
\!xdiff=\!xE \advance \!xdiff by -\!xS%** xdiff = xE - xS
\!ydiff=\!yE \advance \!ydiff by -\!yS%** ydiff = yE - yS
\!Pythag\!xdiff\!ydiff\!arclength% ** arclength = sqrt(xdiff**2+ydiff**2)
\global\advance \totalarclength by \!arclength%
\!drawlinearsegment% ** set by dashpat to \!linearsolid or \!lineardashed
\!xS=\!xE \!yS=\!yE% ** shift ending points to starting points
\ignorespaces}
\def\!linearsolid{%
\!npoints=\!arclength
\!countA=\plotsymbolspacing
\divide\!npoints by \!countA% ** now #pts =. arclength/plotsymbolspacing
\ifnum \!npoints<1
\!npoints=1
\fi
\divide\!xdiff by \!npoints
\divide\!ydiff by \!npoints
\!xpos=\!xS \!ypos=\!yS
\loop\ifnum\!npoints>-1
\!plotifinbounds
\advance \!xpos by \!xdiff
\advance \!ypos by \!ydiff
\advance \!npoints by -1
\repeat
\ignorespaces}
\def\!lineardashed{%
\ifdim\!distacross>\!arclength
\advance \!distacross by -\!arclength %nothing to plot in this interval
\else
\loop\ifdim\!distacross<\!arclength
\!divide\!distacross\!arclength\!dimenA% ** dimA = across/arclength
\!removept\!dimenA\!t% ** \!t holds value in dimA, without the "pt"
\!xpos=\!t\!xdiff \advance \!xpos by \!xS
\!ypos=\!t\!ydiff \advance \!ypos by \!yS
\!plotifinbounds
\advance\!distacross by \plotsymbolspacing
\!advancedashing
\repeat
\advance \!distacross by -\!arclength% ** prepare for next interval
\fi
\ignorespaces}
\def\!!advancedashing{%
\advance\!downlength by -\plotsymbolspacing
\ifdim \!downlength>\!zpt
\else
\advance\!distacross by \!downlength
\!getnextvalueof\!uplength\from\!!UDlist
\advance\!distacross by \!uplength
\!getnextvalueof\!downlength\from\!!UDlist
\fi}
\def\inboundscheckoff{%
\def\!plotifinbounds{\!plot(\!xpos,\!ypos)}%
\def\!initinboundscheck{\relax}\ignorespaces}
\def\inboundscheckon{%
\def\!plotifinbounds{\!!plotifinbounds}%
\def\!initinboundscheck{\!!initinboundscheck}%
\!initinboundscheck\ignorespaces}
\inboundscheckoff
\def\!!plotifinbounds{%
\ifdim \!xpos<\!checkleft
\else
\ifdim \!xpos>\!checkright
\else
\ifdim \!ypos<\!checkbot
\else
\ifdim \!ypos>\!checktop
\else
\!plot(\!xpos,\!ypos)
\fi
\fi
\fi
\fi}
\def\!!initinboundscheck{%
\!checkleft=\!arealloc \advance\!checkleft by \!xorigin
\!checkright=\!arearloc \advance\!checkright by \!xorigin
\!checkbot=\!areabloc \advance\!checkbot by \!yorigin
\!checktop=\!areatloc \advance\!checktop by \!yorigin}
\def\!logten#1#2{%
\expandafter\!!logten#1\!nil
\!removept\!dimenF#2%
\ignorespaces}
\def\!!logten#1#2\!nil{%
\if -#1%
\!dimenF=\!zpt
\def\!next{\ignorespaces}%
\else
\if +#1%
\def\!next{\!!logten#2\!nil}%
\else
\if .#1%
\def\!next{\!!logten0.#2\!nil}%
\else
\def\!next{\!!!logten#1#2..\!nil}%
\fi
\fi
\fi
\!next}
\def\!!!logten#1#2.#3.#4\!nil{%
\!dimenF=1pt % ** DimF holds log10 original argument
\if 0#1%
\!!logshift#3pt % ** Argument < 1
\else % ** Argument >= 1
\!logshift#2/% ** Shift decimal pt as many places
\!dimenE=#1.#2#3pt % ** as there are figures in #2
\fi % ** Now dimE holds revised X want log10 of
\ifdim \!dimenE<\!rootten% ** Transform X to XX between sqrt(10)
\multiply \!dimenE 10 % ** and 10*sqrt(10)
\advance \!dimenF -1pt
\fi
\!dimenG=\!dimenE% ** dimG <- (XX + 10)
\advance\!dimenG 10pt
\advance\!dimenE -10pt % ** dimE <- (XX - 10)
\multiply\!dimenE 10 % ** dimE = 10*(XX-10)
\!divide\!dimenE\!dimenG\!dimenE% ** Now dimE=10t==10*(XX-10)/(XX+10)
\!removept\!dimenE\!t% ** !t=10t, with "pt" removed
\!dimenG=\!t\!dimenE% ** dimG=100t**2
\!removept\!dimenG\!tt% ** !tt=100t**2, with "pt" removed
\!dimenH=\!tt\!tenAe% ** dimH=10*a5*(10t)**2 /100
\divide\!dimenH 100
\advance\!dimenH \!tenAc% ** ditto + 10*a3
\!dimenH=\!tt\!dimenH% ** ditto * (10t)**2 /100
\divide\!dimenH 100
\advance\!dimenH \!tenAa% ** ditto + 10*a1
\!dimenH=\!t\!dimenH% ** ditto * 10t / 100
\divide\!dimenH 100 % ** Now dimH = log10(XX) - 1
\advance\!dimenF \!dimenH}% ** dimF = log10(X)
\def\!logshift#1{%
\if #1/%
\def\!next{\ignorespaces}%
\else
\advance\!dimenF 1pt
\def\!next{\!logshift}%
\fi
\!next}
\def\!!logshift#1{%
\advance\!dimenF -1pt
\if 0#1%
\def\!next{\!!logshift}%
\else
\if p#1%
\!dimenF=1pt
\def\!next{\!dimenE=1p}%
\else
\def\!next{\!dimenE=#1.}%
\fi
\fi
\!next}
\def\beginpicture{%
\setbox\!picbox=\hbox\bgroup%
\!xleft=\maxdimen
\!xright=-\maxdimen
\!ybot=\maxdimen
\!ytop=-\maxdimen}
\def\endpicture{%
\ifdim\!xleft=\maxdimen% ** check if nothing was put in picbox
\!xleft=\!zpt \!xright=\!zpt \!ybot=\!zpt \!ytop=\!zpt
\fi
\global\!Xleft=\!xleft \global\!Xright=\!xright
\global\!Ybot=\!ybot \global\!Ytop=\!ytop
\egroup%
\ht\!picbox=\!Ytop \dp\!picbox=-\!Ybot
\ifdim\!Ybot>\!zpt
\else
\ifdim\!Ytop<\!zpt
\!Ybot=\!Ytop
\else
\!Ybot=\!zpt
\fi
\fi
\hbox{\kern-\!Xleft\lower\!Ybot\box\!picbox\kern\!Xright}}
\def\endpicturesave <#1,#2>{%
\endpicture \global #1=\!Xleft \global #2=\!Ybot \ignorespaces}
\def\setcoordinatesystem{%
\!ifnextchar{u}{\!getlengths }
{\!getlengths units <\!xunit,\!yunit>}}
\def\!getlengths units <#1,#2>{%
\!xunit=#1\relax
\!yunit=#2\relax
\!ifcoordmode
\let\!SCnext=\!SCccheckforRP
\else
\let\!SCnext=\!SCdcheckforRP
\fi
\!SCnext}
\def\!SCccheckforRP{%
\!ifnextchar{p}{\!cgetreference }
{\!cgetreference point at {\!xref} {\!yref} }}
\def\!cgetreference point at #1 #2 {%
\edef\!xref{#1}\edef\!yref{#2}%
\!xorigin=\!xref\!xunit \!yorigin=\!yref\!yunit
\!initinboundscheck % ** See linear.tex
\ignorespaces}
\def\!SCdcheckforRP{%
\!ifnextchar{p}{\!dgetreference}%
{\ignorespaces}}
\def\!dgetreference point at #1 #2 {%
\!xorigin=#1\relax \!yorigin=#2\relax
\ignorespaces}
\long\def\put#1#2 at #3 #4 {%
\!setputobject{#1}{#2}%
\!xpos=\!M{#3}\!xunit \!ypos=\!M{#4}\!yunit
\!rotateaboutpivot\!xpos\!ypos%
\advance\!xpos -\!xorigin \advance\!xpos -\!xshift
\advance\!ypos -\!yorigin \advance\!ypos -\!yshift
\kern\!xpos\raise\!ypos\box\!putobject\kern-\!xpos%
\!doaccounting\ignorespaces}
\long\def\multiput #1#2 at {%
\!setputobject{#1}{#2}%
\!ifnextchar"{\!putfromfile}{\!multiput}}
\def\!putfromfile"#1"{%
\expandafter\!multiput \input #1 /}
\def\!multiput{%
\futurelet\!nextchar\!!multiput}
\def\!!multiput{%
\if *\!nextchar
\def\!nextput{\!alsoby}%
\else
\if /\!nextchar
\def\!nextput{\!finishmultiput}%
\else
\def\!nextput{\!alsoat}%
\fi
\fi
\!nextput}
\def\!finishmultiput/{%
\setbox\!putobject=\hbox{}%
\ignorespaces}
\def\!alsoat#1 #2 {%
\!xpos=\!M{#1}\!xunit \!ypos=\!M{#2}\!yunit
\!rotateaboutpivot\!xpos\!ypos%
\advance\!xpos -\!xorigin \advance\!xpos -\!xshift
\advance\!ypos -\!yorigin \advance\!ypos -\!yshift
\kern\!xpos\raise\!ypos\copy\!putobject\kern-\!xpos%
\!doaccounting
\!multiput}
\def\!alsoby*#1 #2 #3 {%
\!dxpos=\!M{#2}\!xunit \!dypos=\!M{#3}\!yunit
\!rotateonly\!dxpos\!dypos
\!ntemp=#1%
\!!loop\ifnum\!ntemp>0
\advance\!xpos by \!dxpos \advance\!ypos by \!dypos
\kern\!xpos\raise\!ypos\copy\!putobject\kern-\!xpos%
\advance\!ntemp by -1
\repeat
\!doaccounting
\!multiput}
\def\accountingon{\def\!doaccounting{\!!doaccounting}\ignorespaces}
\def\accountingoff{\def\!doaccounting{}\ignorespaces}
\accountingon
\def\!!doaccounting{%
\!xtemp=\!xpos
\!ytemp=\!ypos
\ifdim\!xtemp<\!xleft
\!xleft=\!xtemp
\fi
\advance\!xtemp by \!wd
\ifdim\!xright<\!xtemp
\!xright=\!xtemp
\fi
\advance\!ytemp by -\!dp
\ifdim\!ytemp<\!ybot
\!ybot=\!ytemp
\fi
\advance\!ytemp by \!dp
\advance\!ytemp by \!ht
\ifdim\!ytemp>\!ytop
\!ytop=\!ytemp
\fi}
\long\def\!setputobject#1#2{%
\setbox\!putobject=\hbox{#1}%
\!ht=\ht\!putobject \!dp=\dp\!putobject \!wd=\wd\!putobject
\wd\!putobject=\!zpt
\!xshift=.5\!wd \!yshift=.5\!ht \advance\!yshift by -.5\!dp
\edef\!putorientation{#2}%
\expandafter\!SPOreadA\!putorientation[]\!nil%
\expandafter\!SPOreadB\!putorientation<\!zpt,\!zpt>\!nil\ignorespaces}
\def\!SPOreadA#1[#2]#3\!nil{\!etfor\!orientation:=#2\do\!SPOreviseshift}
\def\!SPOreadB#1<#2,#3>#4\!nil{\advance\!xshift by -#2\advance\!yshift by -#3}
\def\!SPOreviseshift{%
\if l\!orientation
\!xshift=\!zpt
\else
\if r\!orientation
\!xshift=\!wd
\else
\if b\!orientation
\!yshift=-\!dp
\else
\if B\!orientation
\!yshift=\!zpt
\else
\if t\!orientation
\!yshift=\!ht
\fi
\fi
\fi
\fi
\fi}
\long\def\!dimenput#1#2(#3,#4){%
\!setputobject{#1}{#2}%
\!xpos=#3\advance\!xpos by -\!xshift
\!ypos=#4\advance\!ypos by -\!yshift
\kern\!xpos\raise\!ypos\box\!putobject\kern-\!xpos%
\!doaccounting\ignorespaces}
\def\!setdimenmode{%
\let\!M=\!M!!\ignorespaces}
\def\!setcoordmode{%
\let\!M=\!M!\ignorespaces}
\def\!ifcoordmode{%
\ifx \!M \!M!}
\def\!ifdimenmode{%
\ifx \!M \!M!!}
\def\!M!#1#2{#1#2}
\def\!M!!#1#2{#1}
\!setcoordmode
\let\setdimensionmode=\!setdimenmode
\let\setcoordinatemode=\!setcoordmode
\def\Xdistance#1{%
\!M{#1}\!xunit
\ignorespaces}
\def\Ydistance#1{%
\!M{#1}\!yunit
\ignorespaces}
\def\stack{%
\!ifnextchar[{\!stack}{\!stack[c]}}
\def\!stack[#1]{%
\let\!lglue=\hfill \let\!rglue=\hfill
\expandafter\let\csname !#1glue\endcsname=\relax
\!ifnextchar<{\!!stack}{\!!stack<\stackleading>}}
\def\!!stack<#1>#2{%
\vbox{\def\!valueslist{}\!ecfor\!value:=#2\do{%
\expandafter\!rightappend\!value\withCS{\\}\to\!valueslist}%
\!lop\!valueslist\to\!value
\let\\=\cr\lineskiplimit=\maxdimen\lineskip=#1%
\baselineskip=-1000pt\halign{\!lglue##\!rglue\cr \!value\!valueslist\cr}}%
\ignorespaces}
\def\lines{%
\!ifnextchar[{\!lines}{\!lines[c]}}
\def\!lines[#1]#2{%
\let\!lglue=\hfill \let\!rglue=\hfill
\expandafter\let\csname !#1glue\endcsname=\relax
\vbox{\halign{\!lglue##\!rglue\cr #2\crcr}}%
\ignorespaces}
\def\Lines{%
\!ifnextchar[{\!Lines}{\!Lines[c]}}
\def\!Lines[#1]#2{%
\let\!lglue=\hfill \let\!rglue=\hfill
\expandafter\let\csname !#1glue\endcsname=\relax
\vtop{\halign{\!lglue##\!rglue\cr #2\crcr}}%
\ignorespaces}
\def\setplotsymbol(#1#2){%
\!setputobject{#1}{#2}
\setbox\!plotsymbol=\box\!putobject%
\!plotsymbolxshift=\!xshift
\!plotsymbolyshift=\!yshift
\ignorespaces}
\setplotsymbol({\fiverm .})% ** initialize plotsymbol
\def\!!plot(#1,#2){%
\!dimenA=-\!plotxorigin \advance \!dimenA by #1% ** over
\!dimenB=-\!plotyorigin \advance \!dimenB by #2% ** up
\kern\!dimenA\raise\!dimenB\copy\!plotsymbol\kern-\!dimenA%
\ignorespaces}
\def\!!!plot(#1,#2){%
\!dimenA=-\!plotxorigin \advance \!dimenA by #1% ** over
\!dimenB=-\!plotyorigin \advance \!dimenB by #2% ** up
\kern\!dimenA\raise\!dimenB\copy\!plotsymbol\kern-\!dimenA%
\!countE=\!dimenA
\!countF=\!dimenB
\immediate\write\!replotfile{\the\!countE,\the\!countF.}%
\ignorespaces}
\def\savelinesandcurves on "#1" {%
\immediate\closeout\!replotfile
\immediate\openout\!replotfile=#1%
\let\!plot=\!!!plot}
\def\dontsavelinesandcurves {%
\let\!plot=\!!plot}
\dontsavelinesandcurves
{\catcode`\%=11\xdef\!Commentsignal{%}}
\def\writesavefile#1 {%
\immediate\write\!replotfile{\!Commentsignal #1}%
\ignorespaces}
\def\replot"#1" {%
\expandafter\!replot\input #1 /}
\def\!replot#1,#2. {%
\!dimenA=#1sp
\kern\!dimenA\raise#2sp\copy\!plotsymbol\kern-\!dimenA
\futurelet\!nextchar\!!replot}
\def\!!replot{%
\if /\!nextchar
\def\!next{\!finish}%
\else
\def\!next{\!replot}%
\fi
\!next}
\def\!Pythag#1#2#3{%
\!dimenE=#1\relax
\ifdim\!dimenE<\!zpt
\!dimenE=-\!dimenE
\fi% ** dimE = |x|
\!dimenF=#2\relax
\ifdim\!dimenF<\!zpt
\!dimenF=-\!dimenF
\fi% ** dimF = |y|
\advance \!dimenF by \!dimenE% ** dimF = s = |x|+|y|
\ifdim\!dimenF=\!zpt
\!dimenG=\!zpt% ** dimG = z = sqrt(x**2+y**2)
\else
\!divide{8\!dimenE}\!dimenF\!dimenE% ** now dimE = 8t = (8|x|)/s
\advance\!dimenE by -4pt% ** 8tau = (8t-4)*2
\!dimenE=2\!dimenE% ** (tau = 2*t - 1)
\!removept\!dimenE\!!t% ** 8tau, without "pt"
\!dimenE=\!!t\!dimenE% ** (8tau)**2, in pts
\advance\!dimenE by 64pt% ** u = [64 + (8tau)**2]/2
\divide \!dimenE by 2% ** [u = (8f)**2]
\!dimenH=7pt% ** initial guess g at sqrt(u)
\!!Pythag\!!Pythag\!!Pythag% ** 3 iterations give sqrt(u)
\!removept\!dimenH\!!t% ** 8f=sqrt(u), without "pt"
\!dimenG=\!!t\!dimenF% ** z = (8f)*s/8
\divide\!dimenG by 8
\fi
#3=\!dimenG
\ignorespaces}
\def\!!Pythag{% ** Newton-Raphson for sqrt
\!divide\!dimenE\!dimenH\!dimenI% ** v = u/g
\advance\!dimenH by \!dimenI% ** g <-- (g + u/g)/2
\divide\!dimenH by 2}
\def\placehypotenuse for <#1> and <#2> in <#3> {%
\!Pythag{#1}{#2}{#3}}
\def\!qjoin (#1,#2) (#3,#4){%
\advance\!intervalno by 1
\!ifcoordmode
\edef\!xmidpt{#1}\edef\!ymidpt{#2}%
\else
\!dimenA=#1\relax \edef\!xmidpt{\the\!dimenA}%
\!dimenA=#2\relax \edef\!ymidpt{\the\!dimenA}%
\fi
\!xM=\!M{#1}\!xunit \!yM=\!M{#2}\!yunit \!rotateaboutpivot\!xM\!yM
\!xE=\!M{#3}\!xunit \!yE=\!M{#4}\!yunit \!rotateaboutpivot\!xE\!yE
\!dimenA=\!xM \advance \!dimenA by -\!xS% ** dimA = I = xM - xS
\!dimenB=\!xE \advance \!dimenB by -\!xM% ** dimB = II = xE-xM
\!xB=3\!dimenA \advance \!xB by -\!dimenB% ** b=3I-II
\!xC=2\!dimenB \advance \!xC by -2\!dimenA% ** c=2(II-I)
\!dimenA=\!yM \advance \!dimenA by -\!yS%
\!dimenB=\!yE \advance \!dimenB by -\!yM%
\!yB=3\!dimenA \advance \!yB by -\!dimenB%
\!yC=2\!dimenB \advance \!yC by -2\!dimenA%
\!xprime=\!xB \!yprime=\!yB% ** x'(t) = b + 2ct
\!dxprime=.5\!xC \!dyprime=.5\!yC% ** dt=1/4 ==> dx'(t) = c/2
\!getf \!midarclength=\!dimenA
\!getf \advance \!midarclength by 4\!dimenA
\!getf \advance \!midarclength by \!dimenA
\divide \!midarclength by 12
\!arclength=\!dimenA
\!getf \advance \!arclength by 4\!dimenA
\!getf \advance \!arclength by \!dimenA
\divide \!arclength by 12% ** Now have arc length over [1/2,1]
\advance \!arclength by \!midarclength
\global\advance \totalarclength by \!arclength
\ifdim\!distacross>\!arclength
\advance \!distacross by -\!arclength% ** nothing
\else
\!initinverseinterp% ** initialize for inverse interpolation on arc length
\loop\ifdim\!distacross<\!arclength% ** loop over points on arc
\!inverseinterp% ** find t such that arc length[0,t] = distacross,
\!xpos=\!t\!xC \advance\!xpos by \!xB
\!xpos=\!t\!xpos \advance \!xpos by \!xS
\!ypos=\!t\!yC \advance\!ypos by \!yB
\!ypos=\!t\!ypos \advance \!ypos by \!yS
\!plotifinbounds% ** plot point if in bounds
\advance\!distacross \plotsymbolspacing%** advance arc length for next pt
\!advancedashing% ** see "linear"
\repeat
\advance \!distacross by -\!arclength% ** prepare for next interval
\fi
\!xS=\!xE% ** shift ending points to starting points
\!yS=\!yE
\ignorespaces}
\def\!getf{\!Pythag\!xprime\!yprime\!dimenA%
\advance\!xprime by \!dxprime
\advance\!yprime by \!dyprime}
\def\!initinverseinterp{%
\ifdim\!arclength>\!zpt
\!divide{8\!midarclength}\!arclength\!dimenE% ** dimE=8w=8r/s, where r
\ifdim\!dimenE<\!wmin \!setinverselinear
\else
\ifdim\!dimenE>\!wmax \!setinverselinear
\else% ** w in range: initialize
\def\!inverseinterp{\!inversequad}\ignorespaces
\!removept\!dimenE\!Ew% ** 8w, without "pt"
\!dimenF=-\!Ew\!dimenE% ** -(8w)**2
\advance\!dimenF by 32pt% ** 32 - (8w)**2
\!dimenG=8pt
\advance\!dimenG by -\!dimenE% ** 8 - 8w
\!dimenG=\!Ew\!dimenG% ** (8w)*(8-8w)
\!divide\!dimenF\!dimenG\!beta% ** beta = (32-(8w)**2)/(8w(8-8w))
\!gamma=1pt
\advance \!gamma by -\!beta% ** gamma = 1-beta
\fi% ** end of the \ifdim\!dimenE>\!wmax
\fi% ** end of the \ifdim\!dimenE<\!wmin
\fi% ** end of the \ifdim\!arclength>\!zpt
\ignorespaces}
\def\!inversequad{%
\!divide\!distacross\!arclength\!dimenG% ** dimG = v = distacross/arclength
\!removept\!dimenG\!v% ** v, without "pt"
\!dimenG=\!v\!gamma% ** gamma*v
\advance\!dimenG by \!beta% ** beta + gamma*v
\!dimenG=\!v\!dimenG% ** t = v*(beta + gamma*v)
\!removept\!dimenG\!t}% ** t, without "pt"
\def\!setinverselinear{%
\def\!inverseinterp{\!inverselinear}%
\divide\!dimenE by 8 \!removept\!dimenE\!t
\!countC=\!intervalno \multiply \!countC 2
\!countB=\!countC \advance \!countB -1
\!countA=\!countB \advance \!countA -1
\wlog{\the\!countB th point (\!xmidpt,\!ymidpt) being plotted
doesn't lie in the}%
\wlog{ middle third of the arc between the \the\!countA th
and \the\!countC th points:}%
\wlog{ [arc length \the\!countA\space to \the\!countB]/[arc length
\the \!countA\space to \the\!countC]=\!t.}%
\ignorespaces}
\def\!inverselinear{%
\!divide\!distacross\!arclength\!dimenG
\!removept\!dimenG\!t}
\def\startrotation{%
\let\!rotateaboutpivot=\!!rotateaboutpivot
\let\!rotateonly=\!!rotateonly
\!ifnextchar{b}{\!getsincos }%
{\!getsincos by {\!cosrotationangle} {\!sinrotationangle} }}
\def\!getsincos by #1 #2 {%
\edef\!cosrotationangle{#1}%
\edef\!sinrotationangle{#2}%
\!ifcoordmode
\let\!ROnext=\!ccheckforpivot
\else
\let\!ROnext=\!dcheckforpivot
\fi
\!ROnext}
\def\!ccheckforpivot{%
\!ifnextchar{a}{\!cgetpivot}%
{\!cgetpivot about {\!xpivotcoord} {\!ypivotcoord} }}
\def\!cgetpivot about #1 #2 {%
\edef\!xpivotcoord{#1}%
\edef\!ypivotcoord{#2}%
\!xpivot=#1\!xunit \!ypivot=#2\!yunit
\ignorespaces}
\def\!dcheckforpivot{%
\!ifnextchar{a}{\!dgetpivot}{\ignorespaces}}
\def\!dgetpivot about #1 #2 {%
\!xpivot=#1\relax \!ypivot=#2\relax
\ignorespaces}
\def\stoprotation{%
\let\!rotateaboutpivot=\!!!rotateaboutpivot
\let\!rotateonly=\!!!rotateonly
\ignorespaces}
\def\!!rotateaboutpivot#1#2{%
\!dimenA=#1\relax \advance\!dimenA -\!xpivot
\!dimenB=#2\relax \advance\!dimenB -\!ypivot
\!dimenC=\!cosrotationangle\!dimenA
\advance \!dimenC -\!sinrotationangle\!dimenB
\!dimenD=\!cosrotationangle\!dimenB
\advance \!dimenD \!sinrotationangle\!dimenA
\advance\!dimenC \!xpivot \advance\!dimenD \!ypivot
#1=\!dimenC #2=\!dimenD
\ignorespaces}
\def\!!rotateonly#1#2{%
\!dimenA=#1\relax \!dimenB=#2\relax
\!dimenC=\!cosrotationangle\!dimenA
\advance \!dimenC -\!rotsign\!sinrotationangle\!dimenB
\!dimenD=\!cosrotationangle\!dimenB
\advance \!dimenD \!rotsign\!sinrotationangle\!dimenA
#1=\!dimenC #2=\!dimenD
\ignorespaces}
\def\!rotsign{}
\def\!!!rotateaboutpivot#1#2{\relax}
\def\!!!rotateonly#1#2{\relax}
\stoprotation
\def\!reverserotateonly#1#2{%
\def\!rotsign{-}%
\!rotateonly{#1}{#2}%
\def\!rotsign{}%
\ignorespaces}
\def\setshadegrid{%
\!ifnextchar{s}{\!getspan }
{\!getspan span <\!dshade>}}
\def\!getspan span <#1>{%
\!dshade=#1\relax
\!ifcoordmode
\let\!GRnext=\!GRccheckforAP
\else
\let\!GRnext=\!GRdcheckforAP
\fi
\!GRnext}
\def\!GRccheckforAP{%
\!ifnextchar{p}{\!cgetanchor }
{\!cgetanchor point at {\!xshadesave} {\!yshadesave} }}
\def\!cgetanchor point at #1 #2 {%
\edef\!xshadesave{#1}\edef\!yshadesave{#2}%
\!xshade=\!xshadesave\!xunit \!yshade=\!yshadesave\!yunit
\ignorespaces}
\def\!GRdcheckforAP{%
\!ifnextchar{p}{\!dgetanchor}%
{\ignorespaces}}
\def\!dgetanchor point at #1 #2 {%
\!xshade=#1\relax \!yshade=#2\relax
\ignorespaces}
\def\setshadesymbol{%
\!ifnextchar<{\!setshadesymbol}{\!setshadesymbol<,,,> }}
\def\!setshadesymbol <#1,#2,#3,#4> (#5#6){%
\!setputobject{#5}{#6}%
\setbox\!shadesymbol=\box\!putobject%
\!shadesymbolxshift=\!xshift \!shadesymbolyshift=\!yshift
\!dimenA=\!xshift \advance\!dimenA \!smidge% ** default LS = xshift - smidge
\!override\!dimenA{#1}\!lshrinkage%
\!dimenA=\!wd \advance \!dimenA -\!xshift% ** default RS = width - xshift
\advance\!dimenA \!smidge% - smidge
\!override\!dimenA{#2}\!rshrinkage
\!dimenA=\!dp \advance \!dimenA \!yshift% ** default BS = depth + yshift
\advance\!dimenA \!smidge% - smidge
\!override\!dimenA{#3}\!bshrinkage
\!dimenA=\!ht \advance \!dimenA -\!yshift% ** default TS = height - yshift
\advance\!dimenA \!smidge% - smidge
\!override\!dimenA{#4}\!tshrinkage
\ignorespaces}
\def\!smidge{-.2pt}%
\def\!override#1#2#3{%
\edef\!!override{#2}%
\ifx \!!override\empty
#3=#1\relax
\else
\if z\!!override
#3=\!zpt
\else
\ifx \!!override\!blankz
#3=\!zpt
\else
#3=#2\relax
\fi
\fi
\fi
\ignorespaces}
\def\!blankz{ z}
\setshadesymbol ({\fiverm .})% ** initialize plotsymbol
\def\!startvshade#1(#2,#3,#4){%
\let\!!xunit=\!xunit%
\let\!!yunit=\!yunit%
\let\!!xshade=\!xshade%
\let\!!yshade=\!yshade%
\def\!getshrinkages{\!vgetshrinkages}%
\let\!setshadelocation=\!vsetshadelocation%
\!xS=\!M{#2}\!!xunit
\!ybS=\!M{#3}\!!yunit
\!ytS=\!M{#4}\!!yunit
\!shadexorigin=\!xorigin \advance \!shadexorigin \!shadesymbolxshift
\!shadeyorigin=\!yorigin \advance \!shadeyorigin \!shadesymbolyshift
\ignorespaces}
\def\!starthshade#1(#2,#3,#4){%
\let\!!xunit=\!yunit%
\let\!!yunit=\!xunit%
\let\!!xshade=\!yshade%
\let\!!yshade=\!xshade%
\def\!getshrinkages{\!hgetshrinkages}%
\let\!setshadelocation=\!hsetshadelocation%
\!xS=\!M{#2}\!!xunit
\!ybS=\!M{#3}\!!yunit
\!ytS=\!M{#4}\!!yunit
\!shadexorigin=\!xorigin \advance \!shadexorigin \!shadesymbolxshift
\!shadeyorigin=\!yorigin \advance \!shadeyorigin \!shadesymbolyshift
\ignorespaces}
\def\!lattice#1#2#3#4#5{%
\!dimenA=#1% ** dimA = ANCHOR
\!dimenB=#2% ** dimB = SPAN (assumed > 0pt)
\!countB=\!dimenB% ** ctB = SPAN, as a count
\!dimenC=#3% ** dimC = LOCATION
\advance\!dimenC -\!dimenA% ** now dimC = LOCATION-ANCHOR
\!countA=\!dimenC% ** ctA = above, as a count
\divide\!countA \!countB% ** now ctA = desired index, if dimC <= 0
\ifdim\!dimenC>\!zpt
\!dimenD=\!countA\!dimenB% ** (tentative k)*span
\ifdim\!dimenD<\!dimenC% ** if this is false, ctA = desired index
\advance\!countA 1 % ** if true, have to add 1
\fi
\fi
\!dimenC=\!countA\!dimenB% ** lattice location = anchor + ctA*span
\advance\!dimenC \!dimenA
#4=\!countA% ** the desired index
#5=\!dimenC% ** corresponding lattice location
\ignorespaces}
\def\!qshade#1(#2,#3,#4)#5(#6,#7,#8){%
\!xM=\!M{#2}\!!xunit
\!ybM=\!M{#3}\!!yunit
\!ytM=\!M{#4}\!!yunit
\!xE=\!M{#6}\!!xunit
\!ybE=\!M{#7}\!!yunit
\!ytE=\!M{#8}\!!yunit
\!getcoeffs\!xS\!ybS\!xM\!ybM\!xE\!ybE\!ybB\!ybC%**Get coefficients B & C for
\!getcoeffs\!xS\!ytS\!xM\!ytM\!xE\!ytE\!ytB\!ytC%**y=y0 + B(x-X0) + C(x-X0)**2
\def\!getylimits{\!qgetylimits}%
\!shade{#1}\ignorespaces}
\def\!lshade#1(#2,#3,#4){%
\!xE=\!M{#2}\!!xunit
\!ybE=\!M{#3}\!!yunit
\!ytE=\!M{#4}\!!yunit
\!dimenE=\!xE \advance \!dimenE -\!xS% ** xE-xS
\!dimenC=\!ytE \advance \!dimenC -\!ytS% ** ytE-ytS
\!divide\!dimenC\!dimenE\!ytB% ** ytB = (ytE-ytS)/(xE-xS)
\!dimenC=\!ybE \advance \!dimenC -\!ybS% ** ybE-ybS
\!divide\!dimenC\!dimenE\!ybB% ** ybB = (ybE-ybS)/(xE-xS)
\def\!getylimits{\!lgetylimits}%
\!shade{#1}\ignorespaces}
\def\!getcoeffs#1#2#3#4#5#6#7#8{%
\!dimenC=#4\advance \!dimenC -#2% ** dimC=Y1-Y0
\!dimenE=#3\advance \!dimenE -#1% ** dimE=X1-X0
\!divide\!dimenC\!dimenE\!dimenF% ** dimF=S1
\!dimenC=#6\advance \!dimenC -#4% ** dimC=Y2-Y1
\!dimenH=#5\advance \!dimenH -#3% ** dimH=X2-X1
\!divide\!dimenC\!dimenH\!dimenG% ** dimG=S2
\advance\!dimenG -\!dimenF% ** dimG=S2-S1
\advance \!dimenH \!dimenE% ** dimH=X2-X0
\!divide\!dimenG\!dimenH#8% ** C=(S2-S1)/(X2-X0)
\!removept#8\!t% ** C, without "pt"
#7=-\!t\!dimenE% ** -C*(X1-X0)
\advance #7\!dimenF% ** B=S1-C*(X1-X0)
\ignorespaces}
\def\!shade#1{%
\!getshrinkages#1<,,,>\!nil% % ** now effective LS=dimE, RS=dimF,
\advance \!dimenE \!xS% ** now dimE=xS+LS
\!lattice\!!xshade\!dshade\!dimenE% ** set parity=index of left-mst x-lattice
\!parity\!xpos% ** point >= xS+LS, xpos=its location
\!dimenF=-\!dimenF% ** set dimF=xE-RS
\advance\!dimenF \!xE
\!loop\!not{\ifdim\!xpos>\!dimenF}% ** loop over x-lattice points <= xE-RS
\!shadecolumn%
\advance\!xpos \!dshade% ** move over to next column
\advance\!parity 1% ** increase index of x-point
\repeat
\!xS=\!xE% ** shift ending values to starting values
\!ybS=\!ybE
\!ytS=\!ytE
\ignorespaces}
\def\!vgetshrinkages#1<#2,#3,#4,#5>#6\!nil{%
\!override\!lshrinkage{#2}\!dimenE
\!override\!rshrinkage{#3}\!dimenF
\!override\!bshrinkage{#4}\!dimenG
\!override\!tshrinkage{#5}\!dimenH
\ignorespaces}
\def\!hgetshrinkages#1<#2,#3,#4,#5>#6\!nil{%
\!override\!lshrinkage{#2}\!dimenG
\!override\!rshrinkage{#3}\!dimenH
\!override\!bshrinkage{#4}\!dimenE
\!override\!tshrinkage{#5}\!dimenF
\ignorespaces}
\def\!shadecolumn{%
\!dxpos=\!xpos
\advance\!dxpos -\!xS% ** dx = x - xS
\!removept\!dxpos\!dx% ** ditto, without "pt"
\!getylimits% ** get top and bottom y-values
\advance\!ytpos -\!dimenH% ** less TS
\advance\!ybpos \!dimenG% ** plus BS
\!yloc=\!!yshade% ** get anchor point for this column
\ifodd\!parity
\advance\!yloc \!dshade
\fi
\!lattice\!yloc{2\!dshade}\!ybpos%
\!countA\!ypos% ** ypos=smallest y point for this column
\!dimenA=-\!shadexorigin \advance \!dimenA \!xpos% ** over
\loop\!not{\ifdim\!ypos>\!ytpos}% ** loop over ypos <= yt(t)
\!setshadelocation% ** vmode: xloc=xpos, yloc=ypos
\!rotateaboutpivot\!xloc\!yloc%
\!dimenA=-\!shadexorigin \advance \!dimenA \!xloc% ** over
\!dimenB=-\!shadeyorigin \advance \!dimenB \!yloc% ** up
\kern\!dimenA \raise\!dimenB\copy\!shadesymbol \kern-\!dimenA
\advance\!ypos 2\!dshade
\repeat
\ignorespaces}
\def\!qgetylimits{%
\!dimenA=\!dx\!ytC
\advance\!dimenA \!ytB% ** yt(t)=ytS + dx*(Bt + dx*Ct)
\!ytpos=\!dx\!dimenA
\advance\!ytpos \!ytS
\!dimenA=\!dx\!ybC
\advance\!dimenA \!ybB% ** yb(t)=ybS + dx*(Bb + dx*Cb)
\!ybpos=\!dx\!dimenA
\advance\!ybpos \!ybS}
\def\!lgetylimits{%
\!ytpos=\!dx\!ytB% ** yt(t)=ytS + dx*Bt
\advance\!ytpos \!ytS
\!ybpos=\!dx\!ybB% ** yb(t)=ybS + dx*Bb
\advance\!ybpos \!ybS}
\def\!vsetshadelocation{% ** vmode: xloc=xpos, yloc=ypos
\!xloc=\!xpos
\!yloc=\!ypos}
\def\!hsetshadelocation{% ** hmode: xloc=ypos, yloc=xpos
\!xloc=\!ypos
\!yloc=\!xpos}
\def\!axisticks {%
\def\!nextkeyword##1 {%
\expandafter\ifx\csname !ticks##1\endcsname \relax
\def\!next{\!fixkeyword{##1}}%
\else
\def\!next{\csname !ticks##1\endcsname}%
\fi
\!next}%
\!axissetup
\def\!axissetup{\relax}%
\edef\!ticksinoutsign{\!ticksinoutSign}%
\!ticklength=\longticklength
\!tickwidth=\linethickness
\!gridlinestatus
\!setticktransform
\!maketick
\!tickcase=0
\def\!LTlist{}%
\!nextkeyword}
\def\ticksout{%
\def\!ticksinoutSign{+}}
\def\ticksin{%
\def\!ticksinoutSign{-}}
\ticksout
\def\gridlines{%
\def\!gridlinestatus{\!gridlinestootrue}}
\def\nogridlines{%
\def\!gridlinestatus{\!gridlinestoofalse}}
\nogridlines
\def\loggedticks{%
\def\!setticktransform{\let\!ticktransform=\!logten}}
\def\unloggedticks{%
\def\!setticktransform{\let\!ticktransform=\!donothing}}
\def\!donothing#1#2{\def#2{#1}}
\unloggedticks
\expandafter\def\csname !ticks/\endcsname{%
\!not {\ifx \!LTlist\empty}
\!placetickvalues
\fi
\def\!tickvalueslist{}%
\def\!LTlist{}%
\expandafter\csname !axis/\endcsname}
\def\!maketick{%
\setbox\!boxA=\hbox{%
\beginpicture
\!setdimenmode
\setcoordinatesystem point at {\!zpt} {\!zpt}
\linethickness=\!tickwidth
\ifdim\!ticklength>\!zpt
\putrule from {\!zpt} {\!zpt} to
{\!ticksinoutsign\!tickxsign\!ticklength}
{\!ticksinoutsign\!tickysign\!ticklength}
\fi
\if!gridlinestoo
\putrule from {\!zpt} {\!zpt} to
{-\!tickxsign\!xaxislength} {-\!tickysign\!yaxislength}
\fi
\endpicturesave <\!Xsave,\!Ysave>}%
\wd\!boxA=\!zpt}
\def\!ticksin{%
\def\!ticksinoutsign{-}%
\!maketick
\!nextkeyword}
\def\!ticksout{%
\def\!ticksinoutsign{+}%
\!maketick
\!nextkeyword}
\def\!tickslength<#1> {%
\!ticklength=#1\relax
\!maketick
\!nextkeyword}
\def\!tickslong{%
\!tickslength<\longticklength> }
\def\!ticksshort{%
\!tickslength<\shortticklength> }
\def\!tickswidth<#1> {%
\!tickwidth=#1\relax
\!maketick
\!nextkeyword}
\def\!ticksandacross{%
\!gridlinestootrue
\!maketick
\!nextkeyword}
\def\!ticksbutnotacross{%
\!gridlinestoofalse
\!maketick
\!nextkeyword}
\def\!tickslogged{%
\let\!ticktransform=\!logten
\!nextkeyword}
\def\!ticksunlogged{%
\let\!ticktransform=\!donothing
\!nextkeyword}
\def\!ticksunlabeled{%
\!tickcase=0
\!nextkeyword}
\def\!ticksnumbered{%
\!tickcase=1
\!nextkeyword}
\def\!tickswithvalues#1/ {%
\edef\!tickvalueslist{#1! /}%
\!tickcase=2
\!nextkeyword}
\def\!ticksquantity#1 {%
\ifnum #1>1
\!updatetickoffset
\!countA=#1\relax
\advance \!countA -1
\!ticklocationincr=\!axisLength
\divide \!ticklocationincr \!countA
\!ticklocation=\!axisstart
\loop \!not{\ifdim \!ticklocation>\!axisend}
\!placetick\!ticklocation
\ifcase\!tickcase
\relax % Case 0: no labels
\or
\relax % Case 1: numbered -- not available here
\or
\expandafter\!gettickvaluefrom\!tickvalueslist
\edef\!tickfield{{\the\!ticklocation}{\!value}}%
\expandafter\!listaddon\expandafter{\!tickfield}\!LTlist%
\fi
\advance \!ticklocation \!ticklocationincr
\repeat
\fi
\!nextkeyword}
\def\!ticksat#1 {%
\!updatetickoffset
\edef\!Loc{#1}%
\if /\!Loc
\def\next{\!nextkeyword}%
\else
\!ticksincommon
\def\next{\!ticksat}%
\fi
\next}
\def\!ticksfrom#1 to #2 by #3 {%
\!updatetickoffset
\edef\!arg{#3}%
\expandafter\!separate\!arg\!nil
\!scalefactor=1
\expandafter\!countfigures\!arg/
\edef\!arg{#1}%
\!scaleup\!arg by\!scalefactor to\!countE
\edef\!arg{#2}%
\!scaleup\!arg by\!scalefactor to\!countF
\edef\!arg{#3}%
\!scaleup\!arg by\!scalefactor to\!countG
\loop \!not{\ifnum\!countE>\!countF}
\ifnum\!scalefactor=1
\edef\!Loc{\the\!countE}%
\else
\!scaledown\!countE by\!scalefactor to\!Loc
\fi
\!ticksincommon
\advance \!countE \!countG
\repeat
\!nextkeyword}
\def\!updatetickoffset{%
\!dimenA=\!ticksinoutsign\!ticklength
\ifdim \!dimenA>\!offset
\!offset=\!dimenA
\fi}
\def\!placetick#1{%
\if!xswitch
\!xpos=#1\relax
\!ypos=\!axisylevel
\else
\!xpos=\!axisxlevel
\!ypos=#1\relax
\fi
\advance\!xpos \!Xsave
\advance\!ypos \!Ysave
\kern\!xpos\raise\!ypos\copy\!boxA\kern-\!xpos
\ignorespaces}
\def\!gettickvaluefrom#1 #2 /{%
\edef\!value{#1}%
\edef\!tickvalueslist{#2 /}%
\ifx \!tickvalueslist\!endtickvaluelist
\!tickcase=0
\fi}
\def\!endtickvaluelist{! /}
\def\!ticksincommon{%
\!ticktransform\!Loc\!t
\!ticklocation=\!t\!!unit
\advance\!ticklocation -\!!origin
\!placetick\!ticklocation
\ifcase\!tickcase
\relax % Case 0: no labels
\or % Case 1: numbered
\ifdim\!ticklocation<-\!!origin
\edef\!Loc{$\!Loc$}%
\fi
\edef\!tickfield{{\the\!ticklocation}{\!Loc}}%
\expandafter\!listaddon\expandafter{\!tickfield}\!LTlist%
\or % Case 2: labeled
\expandafter\!gettickvaluefrom\!tickvalueslist
\edef\!tickfield{{\the\!ticklocation}{\!value}}%
\expandafter\!listaddon\expandafter{\!tickfield}\!LTlist%
\fi}
\def\!separate#1\!nil{%
\!ifnextchar{-}{\!!separate}{\!!!separate}#1\!nil}
\def\!!separate-#1\!nil{%
\def\!sign{-}%
\!!!!separate#1..\!nil}
\def\!!!separate#1\!nil{%
\def\!sign{+}%
\!!!!separate#1..\!nil}
\def\!!!!separate#1.#2.#3\!nil{%
\def\!arg{#1}%
\ifx\!arg\!empty
\!countA=0
\else
\!countA=\!arg
\fi
\def\!arg{#2}%
\ifx\!arg\!empty
\!countB=0
\else
\!countB=\!arg
\fi}
\def\!countfigures#1{%
\if #1/%
\def\!next{\ignorespaces}%
\else
\multiply\!scalefactor 10
\def\!next{\!countfigures}%
\fi
\!next}
\def\!scaleup#1by#2to#3{%
\expandafter\!separate#1\!nil
\multiply\!countA #2\relax
\advance\!countA \!countB
\if -\!sign
\!countA=-\!countA
\fi
#3=\!countA
\ignorespaces}
\def\!scaledown#1by#2to#3{%
\!countA=#1\relax% ** get original #
\ifnum \!countA<0 % ** take abs value,
\def\!sign{-}% ** remember sign
\!countA=-\!countA
\else
\def\!sign{}%
\fi
\!countB=\!countA% ** copy |#|
\divide\!countB #2\relax% ** integer part (|#|/sf)
\!countC=\!countB% ** get sf * (|#|/sf)
\multiply\!countC #2\relax
\advance \!countA -\!countC% ** ctA is now remainder
\edef#3{\!sign\the\!countB.}% ** +- integerpart.
\!countC=\!countA % ** Tack on proper number
\ifnum\!countC=0 % ** of zeros after .
\!countC=1
\fi
\multiply\!countC 10
\!loop \ifnum #2>\!countC
\edef#3{#3\!zero}%
\multiply\!countC 10
\repeat
\edef#3{#3\the\!countA}% ** Add on rest of remainder
\ignorespaces}
\def\!placetickvalues{%
\advance\!offset \tickstovaluesleading
\if!xswitch
\setbox\!boxA=\hbox{%
\def\\##1##2{%
\!dimenput {##2} [B] (##1,\!axisylevel)}%
\beginpicture
\!LTlist
\endpicturesave <\!Xsave,\!Ysave>}%
\!dimenA=\!axisylevel
\advance\!dimenA -\!Ysave
\advance\!dimenA \!tickysign\!offset
\if -\!tickysign
\advance\!dimenA -\ht\!boxA
\else
\advance\!dimenA \dp\!boxA
\fi
\advance\!offset \ht\!boxA
\advance\!offset \dp\!boxA
\!dimenput {\box\!boxA} [Bl] <\!Xsave,\!Ysave> (\!zpt,\!dimenA)
\else
\setbox\!boxA=\hbox{%
\def\\##1##2{%
\!dimenput {##2} [r] (\!axisxlevel,##1)}%
\beginpicture
\!LTlist
\endpicturesave <\!Xsave,\!Ysave>}%
\!dimenA=\!axisxlevel
\advance\!dimenA -\!Xsave
\advance\!dimenA \!tickxsign\!offset
\if -\!tickxsign
\advance\!dimenA -\wd\!boxA
\fi
\advance\!offset \wd\!boxA
\!dimenput {\box\!boxA} [Bl] <\!Xsave,\!Ysave> (\!dimenA,\!zpt)
\fi}
\normalgraphs
\catcode`!=12 % ***** THIS MUST NEVER BE OMITTED
\catcode`@=11 \catcode`!=11
\let\!pictexendpicture=\endpicture
\let\!pictexframe=\frame
\let\!pictexlinethickness=\linethickness
\let\!pictexmultiput=\multiput
\let\!pictexput=\put
\def\beginpicture{%
\setbox\!picbox=\hbox\bgroup%
\let\endpicture=\!pictexendpicture
\let\frame=\!pictexframe
\let\linethickness=\!pictexlinethickness
\let\multiput=\!pictexmultiput
\let\put=\!pictexput
\let\input=\@@input % \@@input is LaTeX's saved version of TeX's primitive
\!xleft=\maxdimen
\!xright=-\maxdimen
\!ybot=\maxdimen
\!ytop=-\maxdimen}
\let\frame=\!latexframe
\let\pictexframe=\!pictexframe
\let\linethickness=\!latexlinethickness
\let\pictexlinethickness=\!pictexlinethickness
\let\\=\@normalcr
\catcode`@=12 \catcode`!=12
