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diff --git a/Master/texmf-dist/tex/context/base/thrd-pic.tex b/Master/texmf-dist/tex/context/base/thrd-pic.tex new file mode 100644 index 00000000000..3c6375cbd73 --- /dev/null +++ b/Master/texmf-dist/tex/context/base/thrd-pic.tex @@ -0,0 +1,3694 @@ +% Since this file is not available in every distribution, we +% have copied the original in this file. The manuals to +% Wichura's PiCTeX and TaBlE packages are not available on +% line and are distributed by respectively the TeX Users Group +% and Personal TeX Inc. + +% We've patched this file for catcode ! because in luatex we use +% catcode tables and using unprotect/protect is cleaner. + +% This is PiCTeX, Version 1.1 9/21/87 + +% CAVEAT: The PiCTeX manual often has a more lucid explanation +% of any given topic than you will find in the internal documentation +% of the macros. + +% PiCTeX's commands can be classified into two groups: (1) public (or +% external), and (2) private (or internal). The public macros are +% discussed at length in the manual. The only discussion of the private +% macros is the internal documentation. The private macros all have +% names beginning with an exclamation point (!) of category code 11. +% Since in normal usage "!" has category code 12, these macros can't +% be accessed or modified by the general user. + +% The macros are organized into thematically related groups. For example, +% the macros dealing with dots & dashes are all in the DASHPATTERN group. +% The table below shows which macros are in which groups. The table +% covers all public macros, and many (but not all) of PiCTeX's upper level +% private macros. Following the table, the various groups are listed +% in the order in which they appear in the table. + +% *********************** TABLE OF GROUPS OF MACROS ********************** + +% HACKS: Utility macros +% \PiC +% \PiCTeX +% \placevalueinpts +% \!!loop +% \!cfor +% \!copylist +% \!ecfor +% \!etfor +% \!getnext +% \!getnextvalueof +% \!ifempty +% \!ifnextchar +% \!leftappend +% \!listaddon +% \!loop +% \!lop +% \!mlap +% \!not +% \!removept +% \!rightappend +% \!tfor +% \!vmlap +% \!wlet + +% ALLOCATION: Allocates registers + +% AREAS: Deals with plot areas +% \axis +% \grid +% \invisibleaxes +% \normalgraphs +% \plotheading +% \setplotarea +% \visibleaxes + +% ARROWS: Draws arrows +% \arrow +% \betweenarrows + +% BARS: Draws bars +% \putbar +% \setbars + +% BOXES: Draws rectangles +% \frame +% \putrectangle +% \rectangle +% \shaderectangleson +% \shaderectanglesoff + +% CURVES: Upper level plot commands +% \hshade +% \plot +% \sethistograms +% \setlinear +% \setquadratic +% \vshade + +% DASHPATTERNS: Sets up dash patterns +% \findlength +% \setdashes +% \setdashesnear +% \setdashpattern +% \setdots +% \setdotsnear +% \setsolid +% \!dashingoff +% \!dashingon + +% DIVISION: Does long division of dimension registers +% \Divide +% \!divide + +% ELLIPSES: Draws ellipses and circles +% \circulararc +% \ellipticalarc + +% RULES: Draws rules, i.e., horizontal & vertical lines +% \putrule +% \!putdashedhline +% \!putdashedvline +% \!puthline +% \!putsolidhline +% \!putsolidvline +% \!putvline + +% LINEAR ARC: Draws straight lines -- solid and dashed +% \inboundscheckoff +% \inboundscheckon +% \!advancedashing +% \!drawlinearsegment +% \!initinboundscheck +% \!linearsolid +% \!lineardashed +% \!ljoin +% \!plotifinbounds +% \!start + +% LOGTEN: Log_10 function +% \!logten + +% PICTURES: Basic setups for PiCtures; \put commands +% \accountingoff +% \accountingon +% \beginpicture +% \endpicture +% \endpicturesave +% \lines +% \multiput +% \put +% \setcoordinatemode +% \setcoordinatesystem +% \setdimensionmode +% \stack +% \Lines +% \Xdistance +% \Ydistance +% \!dimenput +% \!ifcoordmode +% \!ifdimenmode +% \!setcoordmode +% \!setdimenmode +% \!setputobject + +% PLOTTING: Things to do with plotting +% \dontsavelinesandcurves +% \replot +% \savelinesandcurves +% \setplotsymbol +% \writesavefile +% \!plot + +% PYTHAGORAS: Euclidean distance function +% \placehypotenuse +% \!Pythag + +% QUADRATIC ARC: Draws a quadratic arc +% \!qjoin + +% ROTATIONS: Handles rotations +% \startrotation +% \stoprotation +% \!rotateaboutpivot +% \!rotateonly + +% SHADING: Handles shading +% \setshadegrid +% \setshadesymbol +% \!lshade +% \!qshade +% \!starthshade +% \!startvshade + +% TICKS: Draws ticks on graphs +% \gridlines +% \loggedticks +% \nogridlines +% \ticksin +% \ticksout +% \unloggesticks + +% ***************** END OF TABLE OF GROUPS OF MACROS ******************** + + +% \catcode`!=11 % ***** THIS MUST NEVER BE OMITTED + +\unprotect + +% ******************************* +% *** HACKS (Utility macros) *** +% ******************************* + +% ** User commands +% ** \PiC{P\kern-.12em\lower.5ex\hbox{I}\kern-.075emC} +% ** \PiCTeX{\PiC\kern-.11em\TeX} +% ** \placevalueinpts of <DIMENSION REGISTER> in {CONTROL SEQUENCE} + +% ** Internal commands +% ** \!ifnextchar{CHARACTER}{TRUE ACTION}{FALSE ACTION} +% ** \!tfor NAME := LIST \do {BODY} +% ** \!etfor NAME:= LIST \do {BODY} +% ** \!cfor NAME := LIST \do {BODY} +% ** \!ecfor NAME:= LIST \do {BODY} +% ** \!ifempty{MACRO}{TRUE ACTION}{FALSE ACTION} +% ** \!getnext\\ITEMfrom\LIST +% ** \!getnextvalueof\DIMEN\from\LIST +% ** \!copylist\LISTMACRO_A\to\LISTMACRO_B +% ** \!wlet\CONTROL_SEQUENCE_A=\CONTROL_SEQUENCE_B +% ** \!listaddon ITEM LIST +% ** \!rightappendITEM\withCS\to\LISTMACRO +% ** \!leftappendITEM\withCS\to\LISTMACRO +% ** \!lop\LISTMACRO\to\ITEM +% ** \!loop ... repeat +% ** \!!loop ... repeat +% ** \!removept{DIMENSION REGISTER}{CONTROL SEQUENCE} +% ** \!mlap{...} +% ** \!vmlap{...} +% ** \!not{TEK if-CONDITION} + +% ** First, here are the the PiCTeX logo, and the syllable PiC: +\def\PiC{P\kern-.12em\lower.5ex\hbox{I}\kern-.075emC} +\def\PiCTeX{\PiC\kern-.11em\TeX} + +% ** The following macro expands to parameter #2 or parameter #3 according to +% ** whether the next non-blank character following the macro is or is not #1. +% ** Blanks following the macro are gobbled. +\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 + + +% ** Borrow the "tfor" macro from Latex: +% ** \!tfor NAME := LIST \do {BODY} +% ** if, before expansion, LIST = T1 ... Tn, where each Ti is a token +% ** or {...}, then executes BODY n times, with NAME = Ti on the +% ** i-th iteration. Works for n=0. +\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}} + + +% ** \!etfor NAME:= LIST\do {BODY} +% ** This is like \!cfor, but LIST is any balanced token list whose complete +% ** expansion has the form T1 ... Tn +\def\!etfor#1:=#2\do#3{% + \def\!!tfor{\!tfor#1:=}% + \edef\!!!tfor{#2}% + \expandafter\!!tfor\!!!tfor\do{#3}} + + +% ** modify the Latex \tfor (token-for) loop to a \cfor (comma-for) loop. +% ** \!cfor NAME := LIST \do {BODY} +% ** if, before expansion, LIST = a1,a2,...an, then executes BODY n times, +% ** with NAME = ai on the i-th iteration. Works for n=0. +\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}} + + +% ** \!ecfor NAME:= LIST\do {BODY} +% ** This is like \!cfor, but LIST is any balanced token list whose complete +% ** expansion has the form a1,a2,...,an. +\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{} + + +% ** \!ifempty{ARG}{TRUE ACTION}{FALSE ACTION} +\def\!ifempty#1#2#3{% + \edef\!emptyarg{#1}% + \ifx\!emptyarg\!empty + #2% + \else + #3% + \fi} + +% ** \!getnext\\ITEMfrom\LIST +% ** \LIST has the form \\{item1}\\{item2}\\{item3}...\\{itemk} +% ** This routine sets \ITEM to item1, and cycles \LIST to +% ** \\{item2}\\{item3}...\\{itemk}\\{item1} +\def\!getnext#1\from#2{% + \expandafter\!gnext#2\!#1#2}% +\def\!gnext\\#1#2\!#3#4{% + \def#3{#1}% + \def#4{#2\\{#1}}% + \ignorespaces} + + +% ** \!getnextvalueof\DIMEN\from\LIST +% ** Similar to !getnext. +% ** \LIST has the form \\{dimen1}\\{dimen2}\\{dimen3} ... +% ** \DIMEN is a dimension register +% ** Works also for counts +% +\def\!getnextvalueof#1\from#2{% + \expandafter\!gnextv#2\!#1#2}% +\def\!gnextv\\#1#2\!#3#4{% + #3=#1% + \def#4{#2\\{#1}}% + \ignorespaces} + + +% ** \!copylist\LISTMACROA\to\LISTMACROB +% ** makes the replacement text of LISTMACRO B identical to that of +% ** list macro A. +\def\!copylist#1\to#2{% + \expandafter\!!copylist#1\!#2} +\def\!!copylist#1\!#2{% + \def#2{#1}\ignorespaces} + + +% ** \!wlet\CSA=\CSB +% ** lets control sequence \CSB = control sequence \CSA, and writes a +% ** message to that effect in the log file using plain TEK's \wlog +\def\!wlet#1=#2{% + \let#1=#2 + \wlog{\string#1=\string#2}} + +% ** \!listaddon ITEM LIST +% ** LIST <-- LIST \\ ITEM +\def\!listaddon#1#2{% + \expandafter\!!listaddon#2\!{#1}#2} +\def\!!listaddon#1\!#2#3{% + \def#3{#1\\#2}} + +% ** \!rightappendITEM\to\LISTMACRO +% ** \LISTMACRO --> \LISTMACRO\\{ITEM} +%\def\!rightappend#1\to#2{\expandafter\!!rightappend#2\!{#1}#2} +%\def\!!rightappend#1\!#2#3{\def#3{#1\\{#2}}} + + +% ** \!rightappendITEM\withCS\to\LISTMACRO +% ** \LISTMACRO --> \LISTMACRO||CS||{ITEM} +\def\!rightappend#1\withCS#2\to#3{\expandafter\!!rightappend#3\!#2{#1}#3} +\def\!!rightappend#1\!#2#3#4{\def#4{#1#2{#3}}} + + +% ** \!leftappendITEM\withCS\to\LISTMACRO +% ** \LISTMACRO --> CS||{ITEM}||\LISTMACRO +\def\!leftappend#1\withCS#2\to#3{\expandafter\!!leftappend#3\!#2{#1}#3} +\def\!!leftappend#1\!#2#3#4{\def#4{#2{#3}#1}} + + +% ** \!lop\LISTMACRO\to\ITEM +% ** \\{item1}\\{item2}\\{item3} ... --> \\{item2}\\{item3} ... +% ** item1 --> \ITEM +\def\!lop#1\to#2{\expandafter\!!lop#1\!#1#2} +\def\!!lop\\#1#2\!#3#4{\def#4{#1}\def#3{#2}} + + +% ** \!placeNUMBER\of\LISTMACRO\in\ITEM +% ** the NUMBERth item of \LISTMACRO --> replacement text of \ITEM +%\def\!place#1\of#2\in#3{\def#3{\outofrange}% +%{\count0=#1\def\\##1{\advance\count0-1 \ifnum\count0=0 \gdef#3{##1}\fi}#2}} + + +% ** Following code converts a commalist to a list macro, with all items +% ** fully expanded. +%\!ecfor\item:=\commalist\do{\expandafter\!rightappend\item\to\list} + + +% ** \!loop ... repeat +% ** This is exactly like TEX's \loop ... repeat. It can be used in nesting +% ** two loops, without puting the inner one inside a group. +\def\!loop#1\repeat{\def\!body{#1}\!iterate} +\def\!iterate{\!body\let\!next=\!iterate\else\let\!next=\relax\fi\!next} + +% ** \!!loop ... repeat +% ** This is exactly like TEX's \loop ... repeat. It can be used in nesting +% ** two loops, without puting the inner one inside a group. +\def\!!loop#1\repeat{\def\!!body{#1}\!!iterate} +\def\!!iterate{\!!body\let\!!next=\!!iterate\else\let\!!next=\relax\fi\!!next} +% (\multiput uses \!!loop) + +% ** \!removept{DIMENREG}{\CS} +% ** Defines the control sequence CS to be the value (in points) in the +% ** dimension register DIMENREG (but without the "pt" TEK usually adds) +% ** E.g., after \dimen0=12.3pt \!removept\dimen0\A, \A expands to 12.3 +\def\!removept#1#2{\edef#2{\expandafter\!!removePT\the#1}} +{\catcode`p=12 \catcode`t=12 \gdef\!!removePT#1pt{#1}} + +% ** \pladevalueinpts of <DIMENSION REGISTER> in {CONTROL SEQUENCE} +\def\placevalueinpts of <#1> in #2 {% + \!removept{#1}{#2}} + +% ** \!mlap{...} \!vmlap{...} +% ** Center ... in a box of width 0. +\def\!mlap#1{\hbox to 0pt{\hss#1\hss}} +\def\!vmlap#1{\vbox to 0pt{\vss#1\vss}} + +% ** \!not{TEK if-CONDITION} +% ** By a TEK if-CONDITION is meant something like +% ** \ifnum\N<0, or \ifdim\A>\B +% ** \!not produces an if-condition which is false if the original condition +% ** is true, and true if the original condition is false. +\def\!not#1{% + #1\relax + \!switchfalse + \else + \!switchtrue + \fi + \if!switch + \ignorespaces} + + +% ******************* +% *** ALLOCATIONS *** +% ******************* + +% This section allocates all the registers PiCTeX uses. Following +% each allocation is a string of the form ....N.D...L......... ; +% the various letters show which sections of PiCTeX make explicit +% reference to that register, according to the following code: + +% H Hacks +% A Areas +% W arroWs +% B Bars +% X boXes +% C Curves +% D Dashpattterns +% V diVision +% E Ellipses +% U rUles +% L Linear arc +% G loGten +% P Pictures +% O plOtting +% Y pYthagoras +% Q Quadratic arc +% R Rotations +% S Shading +% T Ticks + +% Turn off messages from TeX's allocation macros +\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................. + +% The following commands assign alternate names to some of the +% above registers. "\!wlet" is defined in Hacks. +\!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.............. + + +% Initial values for registers +\!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) + +% Initial values for control sequences +\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 + +% Reset TeX to report allocations +\let\wlog=\!!!wlog +% ************************************* +% *** AREAS: Deals with plot areas *** +% ************************************* +% +% ** User commands +% ** \setplotarea x from LEFT XCOORD to RIGTH XCOORD, y from BOTTOM YCOORD +% ** to TOP YCOORD +% ** \axis BOTTOM-LEFT-TOP-RIGHT [SHIFTEDTO xy=COORD] [VISIBLE-INVISIBLE] +% ** [LABEL {label}] [TICKS] / +% ** \visibleaxes +% ** \invisibleaxes +% ** \plotheading {HEADING} +% ** \grid {# of columns} {# of rows} +% ** \normalgraphs + +% ** \normalgraphs +% ** Sets defaults for graph setup. See Subsection 3.4 of manual. +\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} +% +% ** \setplotarea x from LEFT XCOORD to RIGTH XCOORD, y from BOTTOM YCOORD +% ** to TOP YCOORD +% ** Reserves space in PICBOX for a rectangular box with the indicated +% ** coordinates. Must be specified before calls to \axis, +% ** \grid, \plotheading. +% ** See Subsection 3.1 of the manual. +\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)} +% +% ** \visibleaxes, \invisibleaxes +% ** Switches for setting visibility of subsequent axes. +% ** See Subsection 3.2 of the manual. +\def\visibleaxes{% + \def\!axisvisibility{\!axisvisibletrue}} +\def\invisibleaxes{% + \def\!axisvisibility{\!axisvisiblefalse}} +% +% ** The next few macros enable the user to fix up an erroneous keyword +% ** in the \axis command. +% \newhelp is in ALLOCATIONS +% \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.} + +\def\!fixkeyword#1{% + \errhelp=\!keywordhelp + \errmessage{Unrecognized keyword `#1': \the\!keywordtoks{NEW KEYWORD}'}} + +% \newtoks\!keywordtoks In ALLOCATIONS. +\!keywordtoks={enter `i\fixkeyword} + +\def\fixkeyword#1{% + \!nextkeyword#1 } + +% ** \axis BOTTOM-LEFT-TOP-RIGHT [SHIFTEDTO xy=COORD] [VISIBLE-INVISIBLE] +% ** [LABEL {label}] [TICKS] / +% ** Exactly one of the keywords BOTTOM, LEFT, TOP, RIGHT must be +% ** specified. Axis is drawn along the indicated edge of the current +% ** plot area, shifted if the SHIFTEDTO option is used, visible or +% ** invisible according the selected option, with an optional LABEL, +% ** and optional TICKS (see ticks.tex for the options avialabel with +% ** TICKS). The TICKS option must be the last one specified. The \axis +% ** MUST be terminated with a / followed by a space. +% ** See Subsection 3.2 of the manual for more information. + +% ** The various options of the \axis command are processed by the +% ** \!nextkeyword macro defined below. For example, +% ** `\!nextkeyword shiftedto ' expands to `\!axisshiftedto'. +\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} + +% ** This and the various macros that follow handle the keyword +% ** specifications on the \axis command +% ** See Subsection 3.2 of the manual. +\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} + +% ** \grid {c} {r} +% ** Partitions the plot area into c columns and r rows; see Subsection 3.3 +% ** of the manual. +% ** (Other grid patterns can be drawn with the TICKS option of the \axis +% ** command. +\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} / } + +% ** \plotheading{HEADING} +% ** Places HEADING centered above the top of the plotarea (and above +% ** any top axis ticks marks, tick labels, and axis label); see +% ** Subsection 3.3 of the manual. +\def\plotheading#1 {% + \advance\!plotheadingoffset \headingtoplotskip + \!dimenput {#1} [B] <.5\!xaxislength,\!plotheadingoffset> + (\!arealloc,\!areatloc)} + +% ** From here on, the routines are internal. +\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={}} + + +% ******************************* +% *** ARROWS (Draws arrows) *** +% ******************************* +% +% ** User commands +% ** \arrow <ARROW HEAD LENGTH> [MID FRACTION, BASE FRACTION] +% ** [<XSHIFT,YSHIFT>] from XFROM YFROM to XTO YTO +% ** \betweenarrows {TEXT} [orientation & shift] from XFROM YFROM to XTO YTO + +% ** \arrow <ARROW HEAD LENGTH> [MID FRACTION, BASE FRACTION] +% ** [<XSHIFT,YSHIFT>] from XFROM YFROM to XTO YTO +% ** Draws an arrow from (XFROM,YFROM) to (XTO,YTO). The arrow head +% ** is constructed two quadratic arcs, which extend back a distance +% ** ARROW HEAD LENGTH (a dimension) on both sides of the arrow shaft. +% ** All the way back the arcs are a distance BASE FRACTION*ARROW HEAD +% ** LENGTH apart, while half-way back they are a distance MID FRACTION* +% ** ARROW HEAD LENGTH apart. <XSHIFT,YSHIFT> is optional, and has +% ** its usual interpreation. See Subsection 5.4 of the manual. + +\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 {% +% +% ** convert to dimensions + \!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 +% +% ** draw shaft of arrow + \!xS=-\!dxpos \advance\!xS\!xshift + \!yS=-\!dypos \advance\!yS\!yshift + \!start (\!xS,\!yS) + \!ljoin (\!xshift,\!yshift) +% +% ** find 32*cosine and 32*sine of angle of rotation + \!Pythag\!dxpos\!dypos\!arclength + \!divide\!dxpos\!arclength\!dxpos + \!dxpos=32\!dxpos \!removept\!dxpos\!!cos + \!divide\!dypos\!arclength\!dypos + \!dypos=32\!dypos \!removept\!dypos\!!sin +% +% ** construct arrowhead + \!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} +% +% ** draw half of arrow head + \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} + + +% ** \betweenarrows {TEXT} [orientation & shift] from XFROM YFROM to XTO YTO +% ** Makes things like <--- text --->, using arrow heads from TeX's fonts. +% ** See Subsection 5.4 of the manual. +\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} + +% ** Subroutine for left-right between arrows +\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 + $\mathord-\mkern-6mu + \cleaders\copy\!boxA\hfil + \mkern-6mu\mathord\rightarrow$}}} + +% ** Subroutine for up-down between arrows +\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}}} + + +% *************************** +% *** BARS (Draws bars) *** +% *************************** +% +% ** User commands: +% ** \putbar [<XSHIFT,YSHIFT>] breadth <BREADTH> from XSTART YSTART +% ** to XEND YEND +% ** \setbars [<XSHIFT,YSHIFT>] breadth <BREADTH> baseline at XY = COORD +% ** [baselabels ([B_ORIENTATION_x,B_ORIENTATION_y] <B_XSHIFT,B_YSHIFT>)] +% ** [endlabels ([E_ORIENTATION_x,E_ORIENTATION_y] <E_XSHIFT,E_YSHIFT>)] + + +% ** \putbar [<XSHIFT,YSHIFT>] breadth <BREADTH> from XSTART YSTART +% ** to XEND YEND +% ** Either XSTART=XEND or YSTART=YEND. Draws a rectangle between +% ** (XSTART,YSTART) & (XEND,YEND). The "depth" of the rectangle +% ** is determined by those two plot positions; its other +% ** dimension "breadth" is specified by the dimension BREADTH. +% ** See Subsection 4.2 of the manual. +\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} + + +% ** \setbars [<XSHIFT,YSHIFT>] breadth <BREADTH> baseline at XY = COORD +% ** [baselabels ([B_ORIENTATION_x,B_ORIENTATION_y] <B_XSHIFT,B_YSHIFT>)] +% ** [endlabels ([E_ORIENTATION_x,E_ORIENTATION_y] <E_XSHIFT,E_YSHIFT>)] +% ** This command puts PiCTeX into the bar graph drawing mode described +% ** in Subsection 4.4 of the manual. +\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} + +% ** \!barcurve +% ** Draws a bargraph with preset values of barshift, barbreadth, +% ** barorientation (x or y) and barbaseline (coordinate) +\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}} + + +% ******************************** +% *** BOXES (Draws rectangles) *** +% ******************************** +% +% ** User commands: +% ** \putrectangle [<XSHIFT,YSHIFT>] corners at XCOORD1 YCOORD1 +% ** and XCOORD2 YCOORD2 +% ** \shaderectangleson +% ** \shaderectanglesoff +% ** \frame [<SEPARATION>] {TEXT} +% ** \rectangle <WIDTH> <HEIGHT> +% +% +% ** \putrectangle [<XSHIFT,YSHIFT>] corners at XCOORD1 YCOORD1 +% ** and XCOORD2 YCOORD2 +% ** Draws a rectangle with corners at (X1,Y1), (X2,Y1), (X1,Y2), (X2,Y2) +% ** Lines have thickness \linethickness, and overlap at the corners. +% ** The optional field <XSHIFT,YSHIFT> functions as with a \put command. +% ** See Subsection 4.2 of the manual. +\def\putrectangle{% + \!ifnextchar<{\!putrectangle}{\!putrectangle<\!zpt,\!zpt> }} +\def\!putrectangle<#1,#2> corners at #3 #4 and #5 #6 {% +% +% ** get locations + \!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 +% +% ** shade rectangle if appropriate + \!shaderectangle +% +% ** draw horizontal edges + \!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} +% +% ** draw vertical edges + \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} + +% ** \shaderectangleson +% ** Subsequent rectangles will be shaded according to +% ** the current shading pattern. Affects \putrectangle, \putbar, +% ** \frame, \sethistograms, and \setbars. See Subsection 7.5 of the manual. +\def\shaderectangleson{% + \def\!shaderectangle{\!!shaderectangle}% + \ignorespaces} +% ** \shaderectanglesoff +% ** Suppresses \shaderectangleson. The default. +\def\shaderectanglesoff{% + \def\!shaderectangle{}% + \ignorespaces} + +\shaderectanglesoff + +% ** The following internal routine shades the current rectangle, when +% ** \!shaderectangle = \!!shaderectangle . +\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} + +% ** \frame [<SEPARATION>] {TEXT} +% ** Draws a frame of thickness linethickness about the box enclosing +% ** TEXT; the frame is separated from the box by a distance of +% ** SEPARATION. The result is an hbox with the same baseline as TEXT. +% ** If <SEPARATION> is omitted, you get the effect of <0pt>. +% ** See Subsection 4.2 of the manual. +\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} + +% ** \rectangle <WIDTH> <HEIGHT> +% ** Constructs a rectangle of width WIDTH and heigth HEIGHT. +% ** See Subsection 4.2 of the manual. +\def\rectangle <#1> <#2> {% + \setbox0=\hbox{}\wd0=#1\ht0=#2\frame {\box0}} + + +% ********************************************* +% *** CURVES (Upper level \plot commands) *** +% ********************************************* +% +% ** User commands +% ** \plot DATA / +% ** \plot "FILE NAME" +% ** \setquadratic +% ** \setlinear +% ** \sethistograms +% ** \vshade ... +% ** \hshade ... + +% \plot: multi-purpose command. Draws histograms, bar graphs, piecewise-linear +% or piecewise quadratic curves, depending on the setting of \!drawcurve. +% See Subsections 4.3-4.5, 5.1, 5.2 of the manual. +\def\plot{% + \!ifnextchar"{\!plotfromfile}{\!drawcurve}} +\def\!plotfromfile"#1"{% + \expandafter\!drawcurve \input #1 /} + +% Command to set piecewise quadratic mode +% See Subsections 5.1, 7.3, and 7.4 of the manual. +\def\setquadratic{% + \let\!drawcurve=\!qcurve + \let\!!Shade=\!!qShade + \let\!!!Shade=\!!!qShade} + +% Command to set piecewise linear mode +% See Subsections 5.1, 7.3, and 7.4 of the manual. +\def\setlinear{% + \let\!drawcurve=\!lcurve + \let\!!Shade=\!!lShade + \let\!!!Shade=\!!!lShade} + +% Command to set histogram mode +% See Subsection 4.3 of the manual. +\def\sethistograms{% + \let\!drawcurve=\!hcurve} + +% Commands to cycle through list of coordinates in piecewise quadratic +% interpolation mode +\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}} + +% Commands to cycle through list of coordinates in piecewise linear +% interpolation mode +\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} + +% Command to cycle through list of coordinates in histogram mode +\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}} + + +% \vshade: See Subsection 7.3 of the manual. +\def\vshade #1 #2 #3 {% + \!startvshade (#1,#2,#3) + \!Shadewhat} + +% \hshade: See Subsection 7.4 of the manual. +\def\hshade #1 #2 #3 {% + \!starthshade (#1,#2,#3) + \!Shadewhat} + +% Commands to cycle through coordinates and optional "edge effect" +% fields while shading. +\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} + +% ** Set default interpolation mode +\setlinear + + +% ******************************************** +% *** DASHPATTERNS (Sets up dash patterns) *** +% ******************************************** + +% ** User commands: +% ** \setdashpattern <DIMEN1,DIMEN2,DIMEN3,...> +% ** \setdots <INTRADOT_DISTANCE> +% ** \setdotsnear <INTRADOT_DISTANCE> for <ARC LENGTH> +% ** \setdashes <DASH/SKIP_DISTANCE> +% ** \setdashesnear <DASH/SKIP_DISTANCE> for <ARC LENGTH> +% ** \setsolid +% ** \findlength {CURVE CMDS} + +% ** Internal commands: +% ** \!dashingon +% ** \!dashingoff + +% ** Dash patterns are specified by a balanced token list whose complete +% ** expansion has the form: DIMEN1,DIMEN2,DIMEN3,DIMEN4,... ; this produces +% ** an arc of length DIMEN1, a skip of length DIMEN2, an arc of length +% ** DIMEN3, a skip of length DIMEN4, ... . Any number of DIMEN values may +% ** be given. The pattern is repeated as many times (perhaps fractional) +% ** as necessary to draw the curve. +% ** A dash pattern remains in effect until it is overridden by a call to +% ** \setdashpattern, or to \setdots, \setdotsnear ... , \setdashes, +% ** \setdashesnear ... , or \setsolid. +% ** Solid lines are the default. + + +% ** \def\setdashpattern <DIMEN1,DIMEN2,DIMEN3,...> +% ** The following routine converts a balanced list of tokens whose +% ** complete expansion has the form DIMEN1,DIMEN2, ... , DIMENk into +% ** three list macros that are used in drawing dashed rules and curves: +% ** !Flist: \!Rule{DIMEN1}\!Skip{DIMEN2}\!Rule{DIMEN3}\!Skip{DIMEN4} ... +% ** !Blist: ...\!Skip{DIMEN4}\!Rule{DIMEN3}\!Skip{DIMEN2}\!Rule{DIMEN1} +% ** !UDlist: \\{DIMEN1}\\{DIMEN2}\\{DIMEN3}\\{DIMEN4} ...; +% ** calculates \!leaderlength := DIMEN1 + ... + DIMENk; and +% ** sets the curve drawing routines to dash mode. +% ** Those lists are used by the curve drawing routines. +% ** Dimenj ... may be given as an explicit dimension (e.g., 5pt), or +% ** as an expression involving a dimension register (e.g., -2.5\dimen0). +% ** See Subsection 6.2 of the manual +\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} + + +% ** \!dashingon -- puts the curve drawing routines into dash mode +% ** \!dashingoff -- puts the curve drawing routines into solid mode +% ** These are internal commands, invoked by \setdashpattern and \setsolid +\def\!dashingon{% + \def\!advancedashing{\!!advancedashing}% + \def\!drawlinearsegment{\!lineardashed}% + \def\!puthline{\!putdashedhline}% + \def\!putvline{\!putdashedvline}% +% \def\!putsline{\!putdashedsline}% + \ignorespaces}% +\def\!dashingoff{% + \def\!advancedashing{\relax}% + \def\!drawlinearsegment{\!linearsolid}% + \def\!puthline{\!putsolidhline}% + \def\!putvline{\!putsolidvline}% +% \def\!putsline{\!putsolidsline}% + \ignorespaces} + + +% ** \setdots <LENGTH> -- sets up a dot/skip pattern where dot (actually +% ** the current plotsymbol) is plunked down once for every LENGTH +% ** traveled along the curve. LENGTH defaults to 5pt. +% ** See Subsection 6.1 of the manual. +\def\setdots{% + \!ifnextchar<{\!setdots}{\!setdots<5pt>}} +\def\!setdots<#1>{% + \!dimenB=#1\advance\!dimenB -\plotsymbolspacing + \ifdim\!dimenB<\!zpt + \!dimenB=\!zpt + \fi +\setdashpattern <\plotsymbolspacing,\!dimenB>} + +% ** \setdotsnear <LENGTH> for <ARC LENGTH> +% ** sets up a dot pattern where the dots are approximately LENGTH apart, +% ** the total length of the pattern is ARC LENGTH, and the pattern +% ** begins and ends with a dot. See Subsection 6.3 of the manual. +\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>} + +% ** \setdashes <LENGTH> -- sets up a dash/skip pattern where the dash +% ** and the skip are each of length LENGTH (the dash is formed by +% ** plunking down the current plotsymbol over an arc of length LENGTH +% ** and so may actually be longer than LENGTH. LENGTH defaults to 5pt. +% ** See Subsection 6.1 of the manual. +\def\setdashes{% + \!ifnextchar<{\!setdashes}{\!setdashes<5pt>}} +\def\!setdashes<#1>{\setdashpattern <#1,#1>} + +% ** \setdashesnear ... +% ** Like \setdotsnear; the pattern begins and ends with a dash. +% ** See Subsection 6.3 of the manual. +\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>} + +% ** \setsolid -- puts the curve drawing routines in "solid line" mode, +% ** the default mode. See Subsection 6.1 of the manual. +\def\setsolid{% + \def\!Flist{\!Rule{24in}}\def\!Blist{\!Rule{24in}}% + \def\!UDlist{\\{24in}\\{\!zpt}}% + \!dashingoff} +\setsolid + +% ** \findlength {CURVE CMDS} +% ** PiCTeX executes the \start, \ljoin, and \qjoin cmds comprising +% ** CURVE CMDS without plotting anything, but stashes the length +% ** of the phantom curve away in \totalarclength. +% ** See Subsection 6.3 of the manual. +\def\findlength#1{% + \begingroup + \setdashpattern <0pt, \maxdimen> + \setplotsymbol ({}) + \dontsavelinesandcurves + #1% + \endgroup + \ignorespaces} + + +% ************************************************************* +% *** DIVISION (Does long division of dimension registers) *** +% ************************************************************* + +% ** User command: +% ** \Divide {DIVIDEND} by {DIVISOR} forming {RESULT} + +% ** Internal command +% ** \!divide{DIVIDEND}{DIVISOR}{RESULT} + +% ** \!divide DIVIDEND [by] DIVISOR [to get] ANSWER +% ** Divides the dimension DIVIDEND by the dimension DIVISOR, placing the +% ** quotient in the dimension register ANSWER. Values are understood to +% ** be in points. E.g. 12.5pt/1.4pt=8.92857pt. +% ** Quotient is accurate to 1/65536pt=2**[-16]pt +% ** |DIVISOR| should be < 2048pt (about 28 inches). +\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 +% ** of a, and corresponding remainder. + \!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} + +% ** The following code handles divisors d with +% ** (1) .88in = 64pt <= d < 256pt = 3.54in +% ** (2) 3.54in = 256pt <= d < 2048pt = 28.34in +% ** Anything bigger than that may result in an overflow condition. +% ** For our purposes, we should never even see case (2). +\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} + + +% ** The following macro does the real long division work. +\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} + +% ** \Divide: See Subsection 9.3 of the manual. +\def\Divide <#1> by <#2> forming <#3> {% + \!divide{#1}{#2}{#3}} + + +% ********************************************* +% *** ELLIPSES (Draws ellipses and circles) *** +% ********************************************* + +% ** User commands +% ** \ellipticalarc axes ratio A:B DEGREES degrees from XSTART YSTART +% ** center at XCENTER YCENTER +% ** \circulararc DEGREES degrees from XSTART YSTART +% ** center at XCENTER YCENTER + +% ** Internal command +% ** \!sinandcos{32*ANGLE in radians}{32*SIN}{32*COS} + + +% ** \ellipticalarc axes ratio A:B DEGREES degrees from XSTART YSTART +% ** center at XCENTER YCENTER +% ** Draws a elliptical arc starting at the coordinate point (XSTART,YSTART). +% ** The center of the ellipse of which the arc is a segment is at +% ** (XCENTER,YCENTER). +% ** The arc extends through an angle of DEGREES degrees (may be + or -). +% ** A:B is the ratio of the length of the xaxis to the length of +% ** the yaxis of the ellipse +% ** Sqrt{[(XSTART-XCENTER)/A]**2 + [(YSTART-YCENTER)/B]**2} +% ** must be < 512pt (about 7in). +% ** Doesn't modify the dimensions (ht, dp, wd) of the PiCture under +% ** construction. + +% ** \circulararc -- See Subsection 5.3 of the manual. +\def\circulararc{% + \ellipticalarc axes ratio 1:1 } + +% ** \ellipticalarc -- See Subsection 5.3 of the manual. +\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 + + +% ** \!rotate(XREG,YREG)by(32cos,32sin)to(XXREG,YYREG) +% ** rotates (XREG,YREG) by angle with specfied scaled cos & sin to +% ** (XXREG,YYREG). Uses \!dimenA & \!dimenB as scratch registers. +\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) + + +% ** \!sinandcos{32*ANGLE in radians}{\SINCS}{\COSCS} +% ** Computes the 32*sine and 32*cosine of a small ANGLE expressed in +% ** radians/32 and puts these values in the replacement texts of +% ** \SINCS and \COSCS +\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} + + +% ***************************************************************** +% *** RULES (Draws rules, i.e., horizontal & vertical lines) *** +% ***************************************************************** + +% ** User command: +% ** \putrule [<XDIMEN,YDIMEN>] from XCOORD1 YCOORD1 +% ** to XCOORD2 YCOORD2 + +% ** Internal commands: +% ** \!puthline [<XDIMEN,YDIMEN>] (h = horizontal) +% ** Set by dashpat to either: \!putsolidhline or \!putdashedhline +% ** \!putvline [<XDIMEN,YDIMEN>] (v = vertical) +% ** Either: \!putsolidvline or \!putdashedvline + + +% ** \putrule [<XDIMEN,YDIMEN>] from XCOORD1 YCOORD1 +% ** to XCOORD2 YCOORD2 +% ** Draws a rule -- dashed or solid depending on the current dash pattern -- +% ** from (X1,Y1) to (X2,Y2). Uses TEK's \hrule & \vrule & \leaders +% ** constructions to handle horizontal & vertical lines efficiently both +% ** in terms of execution time and space in the DVI file. +% ** See Subsection 4.1 of the manual. +\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} + + +% ** \!putsolidhline [<XDIMEN,YDIMEN>] +% ** Place horizontal solid line +\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} + +% ** \!putsolidvline [shifted <XDIMEN,YDIMEN>] +% ** Place vertical solid line +\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}} + + +% ** \!putdashedhline [<XDIMEN,YDIMEN>] +% ** Place dashed horizontal line +\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} + +% ** \!putdashedhline [<XDIMEN,YDIMEN>] +% ** Place dashed vertical line +\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} + + +% ** The rest of the macros in this section are subroutines used by +% ** \!putdashedhline and \!putdashedvline. +\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} + + +% **************************************************************** +% *** LINEAR ARC (Draws straight lines -- solid and dashed) *** +% **************************************************************** + +% ** User commands +% ** \inboundscheckoff +% ** \inboundscheckon + +% ** Internal commands +% ** \!start (XCOORD,YCOORD) +% ** \!ljoin (XCOORD,YCOORD) +% ** \!drawlinearsegment -- set by \dashpat to either +% ** \!linearsolid or \!lineardashed +% ** \!advancedashing -- set by \dashpat to either +% ** \relax or \!!advancedashing +% ** \!plotifinbounds -- set by \inboundscheck off/on to either +% ** \!plot or \!!plotifinbounds +% ** \!initinboundscheck -- set by \inboundscheck off/on to either +% ** \relax or \!!initinboundscheck + + +% \plotsymbolspacing ** distance between consecutive plot positions +% \!xS ** starting x +% \!yS ** starting y +% \!xE ** ending x +% \!yE ** ending y +% \!xdiff ** x_end - x_start +% \!ydiff ** y_end - y_start +% \!distacross ** how far along curve next point to be plotted is +% \!arclength ** approximate length of arc for current interval +% \!downlength ** remaining length for "pen" to be down +% \!uplength ** length for "pen" to be down +% \!intervalno ** counts segments to curve +% \totalarclength ** cumulative distance along curve +% \!npoints ** approximately (arc length / plotsymbolspacing) + +% ** Calls -- \!Pythag, \!divide, \!plot + + +% ** \!start (XCOORD,YCOORD) +% ** Sets initial point for linearly (or quadratically) interpolated curve +\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}.. +% ** Routine will draw dashed line with pen +% ** down for dimen1, up for 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} + + +% ** \!ljoin (XCOORD,YCOORD) +% ** Draws a straight line starting at the last point specified +% ** by the most recent \!start, \!ljoin, or \!qjoin, and +% ** ending at (XCOORD,YCOORD). +\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} + + +% ** The following routine is used to draw a "solid" line between (xS,yS) +% ** and (xE,yE). Points are spaced nearly every \plotsymbolspacing length +% ** along the line. +\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} + + +% ** The following routine is used to draw a dashed line between (xS,yS) +% ** and (xE,yE). The dash pattern continues from the previous segment. +\def\!lineardashed{% +% ** + \ifdim\!distacross>\!arclength + \advance \!distacross by -\!arclength %nothing to plot in this interval +% + \else +% + \loop\ifdim\!distacross<\!arclength +% ** plot point, interpolating linearly in x and y + \!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} + + +% ** \inboundscheckoff & \inboundscheckon: See Subsection 5.5 of the manual. +\def\inboundscheckoff{% + \def\!plotifinbounds{\!plot(\!xpos,\!ypos)}% + \def\!initinboundscheck{\relax}\ignorespaces} +\def\inboundscheckon{% + \def\!plotifinbounds{\!!plotifinbounds}% + \def\!initinboundscheck{\!!initinboundscheck}% + \!initinboundscheck\ignorespaces} +\inboundscheckoff + +% ** The following code plots the current point only if it falls in the +% ** current plotarea. It doesn't matter if the coordinate system has +% ** changed since the plotarea was set up. However, shifts of the plot +% ** are ignored (how the plotsymbol stands relative to its plot position is +% ** unknown anyway). +\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} + + +% ********************************* +% *** LOGTEN (Log_10 function) *** +% ********************************* +% +% ** \!logten{X} +% ** Calculates log_10 of X. X and LOG10(X) are in fixed point notation. +% ** X must be positive; it may have an optional `+' sign; any number +% ** of digits may be specified for X. The absolute error in LOG10(X) is +% ** less than .0001 (probably < .00006). That's about as good as you +% ** hope for, since TEX only operates to 5 figures after the decimal +% ** point anyway. + +% \!rootten=3.162278pt **** These are values are set in ALLOCATIONS +% \!tenAe=2.543275pt (=A5) +% \!tenAc=2.773839pt (=A3) +% \!tenAa=8.690286pt (=A1) + +\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} + + +% *********************************************************** +% *** PICTURES (Basic setups for PiCtures; \put commands) *** +% *********************************************************** + +% ** User Commands: +% ** \beginpicture +% ** \endpicture +% ** \endpicturesave <XREG,YREG> +% ** \setcoordinatesystem units <XUNIT,YUNIT> point at XREF YREF +% ** \put {OBJECT} [ORIENTATION] <XSHIFT,YSHIFT> at XCOORD YCOORD +% ** \multiput {OJBECT} [ORIENTATION] <XSHIFT,YSHIFT>) at +% ** XCOORD YCOORD +% ** *NUMBER_OF_TIMES DXCOORD DYCOORD / +% ** \accountingon +% ** \accountingoff +% ** \stack [ORIENTATION] <LEADING> {LIST OF ITEMS} +% ** \lines [ORIENTATION] {LINES} +% ** \Lines [ORIENTATION] {LINES} +% ** \setdimensionmode +% ** \setcoordinatemode +% ** \Xdistance +% ** \Ydistance + +% ** Internal commands: +% ** \!setputobject{OBJECT}{[ORIENTATION]<XSHIFT,YSHIFT>} +% ** \!dimenput{OBJECT}[ORIENTATION]<XSHIFT,YSHIFT>(XDIMEN,YDIMEN) +% ** \!setdimenmode +% ** \!setcoordmode +% ** \!ifdimenmode +% ** \!ifcoordmode + + +% ** \beginpicture +% ** \endpicture +% ** \endpicturesave <XREG,YREG> +% ** \beginpicture ... \endpicture creates an hbox. Objects are +% ** placed in this box using the \put command and the like (see below). +% ** The location of an object is specified in terms of coordinate system(s) +% ** established by \setcoordinatesystem. Each coordinate system (there +% ** might be just one) specifies the length of 1 horizontal unit, the length +% ** of 1 vertical unit, and the coordinates of a "reference point". The +% ** reference points of various coordinate systems will be in the same +% ** physical location. The macros keep track of the size of the objects +% ** and their locations. The resulting hbox is the smallest hbox which +% ** encloses all the objects, and whose TEK reference point is the point +% ** on the left edge of the box closest vertically to the PICTEX reference +% ** point. Using \endpicturesave, you can (globally) save the distance TEK's +% ** reference point is to the right (respectively, up from) PICTEX's +% ** reference point in the dimension register \XREG (respectively \YREG). +% ** You can then \put the picture OBJECT into a larger picture so that its +% ** reference point is at (XCOORD,YCOORD) with the command +% ** \put {picture OBJECT} [Bl] <\XREG, \YREG> at XCOORD YCOORD + +% ** \beginpicture : See Subsection 1.1 of the manual. +\def\beginpicture{% + \setbox\!picbox=\hbox\bgroup% + \!xleft=\maxdimen + \!xright=-\maxdimen + \!ybot=\maxdimen + \!ytop=-\maxdimen} + +% ** \endpicture : See Subsection 1.1 of the manual. +\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}} + +% ** \endpicturesave : See Subsection 8.4 of the manual. +\def\endpicturesave <#1,#2>{% + \endpicture \global #1=\!Xleft \global #2=\!Ybot \ignorespaces} + + +% ** \setcoordinatesystem units <XUNIT,YUNIT> +% ** point at XREF YREF +% ** Each of `units <XUNIT,YUNIT>' and `point at XREF YREF' +% ** are optional. +% ** Unit lengths must be given in dimensions (e.g., <10pt,1in>). +% ** Default unit lengths are 1pt, 1pt, or previous unit lengths. +% ** Reference point is specified in current units (e.g., 3 5 ). +% ** Default reference point is 0 0 , or previous reference point. +% ** Unit lengths and reference points obey TEX's scoping rules. +% ** See Subsection 1.2 of the manual. +\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} + + +% ** \put {OBJECT} [XY] <XDIMEN,YDIMEN> at (XCOORD,YCOORD) +% ** `[XY]' and `<XDIMEN,YDIMEN>' are optional. +% ** First OBJECT is placed in an hbox (the "objectbox") and then a +% ** "reference point" is assigned to the objectbox as follows: +% ** [1] first, the reference point is taken to be the center of the box; +% ** [2] next, centering is overridden by the specifications +% ** X=l -- reference point along the left edge of the objectbox +% ** X=r -- reference point along the right edge of the objectbox +% ** Y=b -- reference point along the bottom edge of the objectbox +% ** Y=B -- reference point along the Baseline of the objectbox +% ** Y=t -- reference point along the top edge of the objectbox; +% ** [3] finally the reference point is shifted left by XDIMEN, down +% ** by YDIMEN (both default to 0pt). +% ** The objectbox is placed within PICBOX with its reference point at +% ** (XCOORD,YCOORD). +% ** If OBJECT is a saved box, say box0, you have to write +% ** \put{\box0}... or \put{\copy0}... +% ** The objectbox is void after the put. +% ** See Subsection 2.1 of the manual. +\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} + +% ** \multiput etc. Like \put. The objectbox is not voided until the +% ** termininating /, and is placed repeatedly with: +% ** XCOORD YCOORD -- the objectbox is put down with its reference point +% ** at (XCOORD,YCOORD); +% ** *N DXCOORD DYCOORD -- each of N times the current +% ** (xcoord,ycoord) is incremented by (DXCOORD,DYCOORD), and the +% ** objectbox is put down with its reference point at (xcoord,ycoord) +% ** (This specification has to follow an XCOORD YCOORD pair) +% ** See Subsection 2.2 of the manual. +\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} + +% ** \!alsoat XCOORD YCOORD +% ** The objectbox is put down with reference point at XCOORD,YCOORD +\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} + +% ** \!alsoby*N DXCOORD DYCOORD +% ** N times, the current (XCOORD,YCOORD) is advanced by (DXCOORD,DYCOORD), +% ** and the current (shifted, oriented) OBJECT is put down. +\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} + +% ** \accountingoff : Suspends PiCTeX's accounting of the aggregate +% ** size of the picture box. +% ** \accounting on : Reinstates accounting. +% ** See Subsection 8.2 of the manual. +\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} + + +% ** \!dimenput{OBJECT} <XDIMEN,YDIMEN> [XY] (XLOC,YLOC) +% ** This is an internal put routine, similar to \put, except that +% ** XLOC=distance right from reference point, YLOC=distance up from +% ** reference point. XLOC and YLOC are dimensions, so this routine +% ** is completely independent of the current coordinate system. +% ** This routine does NOT do ROTATIONS. +\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} + + +% ** The following macros permit the picture drawing routines to be used +% ** either in the default "coordinate mode", or in "dimension mode". +% ** In coordinate mode \!M(1.5,\!xunit) expands to 1.5\!xunit +% ** In dimension mode \!M(1.5pt,\!xunit) expands to 1.5pt +% ** Dimension mode is useful in coding macros. +% ** Any special purpose picture macro that sets dimension mode should +% ** reset coordinate mode before completion. +% ** See Subsection 9.2 of the manual. +\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 + +% ** \Xdistance{XCOORD}, \Ydistance{YCOORD} are the horizontal and +% ** vertical distances from the origin (0,0) to the point +% ** (XCOORD,YCOORD) in the current coordinate system. +% ** See Subsection 9.2 of the manual. +\def\Xdistance#1{% + \!M{#1}\!xunit + \ignorespaces} +\def\Ydistance#1{% + \!M{#1}\!yunit + \ignorespaces} + +% ** The following macros -- \stack, \line, and \Lines -- are useful for +% ** annotating PiCtures. They can be used outside the \beginpicture ... +% ** \endpicture environment. + +% ** \stack [POSITIONING] <LEADING> {VALUESLIST} +% ** Builds a vertical stack of the values in VALUESLIST. Values in +% ** VALUESLIST are separated by commas. In the resulting stack, values are +% ** centered by default, and positioned flush left (right) if +% ** POSITIONING = l (r). Values are separated vertically by LEADING, +% ** which defaults to \stackleading. +% ** See Subsection 2.3 of the manual. +\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} + +% ** \lines [POSITIONING] {LINES} +% ** Builds a vertical array of the lines in LINES. Each line in LINES +% ** is terminated by a \cr. In the resulting array, lines are +% ** centered by default, and positioned flush left (right) if +% ** POSITIONING = l (r). The lines in the array are subject to TeX's +% ** usual spacing rules: in particular the baselines are ordinarily an equal +% ** distance apart. The baseline of the array is the baseline of the +% ** the bottom line. +% ** See Subsection 2.3 of the manual. +\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} + +% ** \Lines [POSITIONING] {LINES} +% ** Like \lines, but the baseline of the array is the baseline of the +% ** top line. See Subsection 2.3 of the manual. +\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} + + +% ********************************************* +% *** PLOTTING (Things to do with plotting) *** +% ********************************************* + +% ** User commands +% ** \setplotsymbol ({PLOTSYMBOL} [ORIENTATION] <XSHIFT,YSHIFT>) +% ** \savelinesandcurves on "FILE_NAME" +% ** \dontsavelinesandcurves +% ** \writesavefile {MESSAGE} +% ** \replot {FILE_NAME} + +% ** Internal command +% ** \!plot(XDIMEN,YDIMEN) + +% ** \setplotsymbol ({PLOTSYMBOL} [ ] < , >) +% ** Save PLOTSYMBOL away in an hbox for use with curve plotting routines +% ** See Subsection 5.2 of the manual. +\def\setplotsymbol(#1#2){% + \!setputobject{#1}{#2} + \setbox\!plotsymbol=\box\!putobject% + \!plotsymbolxshift=\!xshift + \!plotsymbolyshift=\!yshift + \ignorespaces} + +\setplotsymbol({\fiverm .})% ** initialize plotsymbol + + +% ** \!plot is either \!!plot (when no lines and curves are being saved) or +% ** \!!!plot (when lines and curves are being saved) + +% ** \!!plot(XDIMEN,YDIMEN) +% ** Places the current plotsymbol a horizontal distance=XDIMEN-xorigin +% ** and a vertical distance=YDIMEN-yorigin from the current +% ** reference point. +\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} + +% ** \!!!plot(XDIMEN,YDIMEN) +% ** Like \!!plot, but also saves the plot location in units of +% ** scaled point, on file `replotfile' +\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} + + +% ** \savelinesandcurves on "FILE_NAME" +% ** Switch to save locations used for plotting lines and curves +% ** (No advantage in saving locations for solid lines; however +% ** replotting curve locations speeds things up by a factor of about 4. +% ** \dontsavelinesandcurves +% ** Terminates \savelinesandcurves. The default. +% ** See Subsection 5.6 of the manual. +\def\savelinesandcurves on "#1" {% + \immediate\closeout\!replotfile + \immediate\openout\!replotfile=#1% + \let\!plot=\!!!plot} + +\def\dontsavelinesandcurves {% + \let\!plot=\!!plot} +\dontsavelinesandcurves + +% ** \writesavefile {MESSAGE} +% ** The message is preceded by a "%", so that it won't interfere +% ** with replotting. +% ** See Subsection 5.6 of the manual. +{\catcode`\%=11\xdef\!Commentsignal{%}} +\def\writesavefile#1 {% + \immediate\write\!replotfile{\!Commentsignal #1}% + \ignorespaces} + +% ** \replot "FILE_NAME" +% ** Replots the locations saved earlier under \savelinesandcurves +% ** on "FILE_NAME" +% ** See Subsection 5.6 of the manual. +\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} +% ************************************************** +% *** PYTHAGORAS (Euclidean distance function) *** +% ************************************************** + +% ** User command: +% ** \placehypotenuse for <dimension1> and <dimension2> in <register> + +% ** Internal command: +% ** \!Pythag{X}{Y}{Z} +% ** Input X,Y are dimensions, or dimension registers. +% ** Output Z == sqrt(X**2+Y**2) must be a dimension register. +% ** Assumes that |X|+|Y| < 2048pt (about 28in). + +% ** Without loss of generality, suppose x>0, y>0. Put s = x+y, +% ** z = sqrt(x**2+y**2). Then z = s*f, where f = sqrt(t**2 + (1-t)**2) +% ** = sqrt((1+tau**2)/2), where t = x/s and tau = 2(t-1/2) . + +% ** Uses the \!divide macro (which uses registers \!dimenA--\!dimenD. +% ** Uses the \!removept macro (e.g., 123.45pt --> 123.45) +% ** Uses registers \!dimenE--\!dimenI. +\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} + +% ** \placehypotenuse for <XI> and <ETA> in <ZETA> +% ** See Subsection 9.3 of the manual. +\def\placehypotenuse for <#1> and <#2> in <#3> {% + \!Pythag{#1}{#2}{#3}} + + +% ********************************************** +% *** QUADRATIC ARC (Draws a quadratic arc) *** +% ********************************************** + +% ** Internal command +% ** \!qjoin (XCOORD1,YCOORD1) (XCOORD2,YCOORD2) + +% ** \!qjoin (XCOORD1,YCOORD1) (XCOORD2,YCOORD2) +% ** Draws an arc starting at the (last) point specified by the most recent +% ** \!qjoin, or \!ljoin, or \!start and passing through (X_1,Y_1), (X_2,Y_2). +% ** Uses quadratic interpolation in both x and y: +% ** x(t), 0 <= t <= 1, interpolates x_0, x_1, x_2 at t=0, .5, 1 +% ** y(t), 0 <= t <= 1, interpolates y_0, y_1, y_2 at t=0, .5, 1 + +\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\!xmidpt{\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 +% +% ** Find coefficients for x(t)=a_x + b_x*t + c_x*t**2 + \!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) +% +% ** Find coefficients for y(t)=y_x + b_y*t + c_y*t**2 + \!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% +% +% ** Use Simpson's rule to calculate arc length over [0,1/2]: +% ** arc length = 1/2[1/6 f(0) + 4/6 f(1/4) + 1/6 f(1/2)] +% ** with f(t) = sqrt(x'(t)**2 + y'(t)**2). + \!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 +% +% ** Get arc length over [0,1]. + \!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 +% +% +% ** Check to see if there's anything to plot in this interval + \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, +% ** using inverse quadratic interpolation +% ** now evaluate x(t)=(c*t + b)*t + a + \!xpos=\!t\!xC \advance\!xpos by \!xB + \!xpos=\!t\!xpos \advance \!xpos by \!xS +% ** evaluate y(t) + \!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} + + +% ** \!getf -- Calculates sqrt(x'(t)**2 + y'(t)**2) and advances +% ** x'(t) and y'(t) +\def\!getf{\!Pythag\!xprime\!yprime\!dimenA% + \advance\!xprime by \!dxprime + \advance\!yprime by \!dyprime} + + +% ** \!initinverseinterp -- initializes for inverse quadratic interpolation +% ** of arc length provided 1/3 < midarclength/arclength < 2/3; otherwise +% ** initializes for inverse linear interpolation. +\def\!initinverseinterp{% + \ifdim\!arclength>\!zpt + \!divide{8\!midarclength}\!arclength\!dimenE% ** dimE=8w=8r/s, where r +% ** = midarclength, s=arclength +% ** Test for w out of range: w<1/3 or w>2/3 + \ifdim\!dimenE<\!wmin \!setinverselinear + \else + \ifdim\!dimenE>\!wmax \!setinverselinear + \else% ** w in range: initialize + \def\!inverseinterp{\!inversequad}\ignorespaces +% +% ** Calculate the coefficients \!beta and \!gamma of the quadratic +% ** t = \!beta*v + \!gamma*v**2 +% ** taking the values t=0, 1/2, 1 at v=0, w==r/s, 1 respectively: +% ** \!beta = (1/2 - w**2)/[w(1-w)] +% ** \!gamma = 1 - beta. +% + \!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)) +% ** = (1/2 - w**2)/(w(1-w)) + \!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} + + +% ** For 0 <= t <= 1, let AL(t) = arclength[0,t]/arclength[0,1]; note +% ** AL(0)=0, AL(1/2)=midarclength/arclength, AL(1)=1. This routine +% ** calculates an approximation to AL^{-1}(distance across/arclength), +% ** using the assumption that AL^{-1} is quadratic. Specifically, +% ** it finds t such that +% ** AL^{-1}(v) =. t = v*(\!beta + \!gamma*v) +% ** where \!beta and \!gamma are set by \!initinv, and where +% ** v=distance across/arclength +\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" + + +% ** When w <= 1/3 or w >= 2/3, the following routine writes (using +% ** plain TEK's \wlog command) a warning message on the user's log file, +% ** and initializes for inverse linear interpolation on arc length. +\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} + +% ** Inverse linear interpolation +\def\!inverselinear{% + \!divide\!distacross\!arclength\!dimenG + \!removept\!dimenG\!t} + + +% ************************************** +% ** ROTATIONS (Handles rotations) *** +% ************************************** + +% ** User commands +% ** \startrotation [by COS_OF_ANGLE SIN_OF_ANGLE] [about XPIVOT YPIVOT] +% ** \stoprotation + +% ** \startrotation [by COS_OF_ANGLE SIN_OF_ANGLE] [about XPIVOT YPIVOT] +% ** Future (XCOORD,YCOORD)'s will be rotated about (XPIVOT,YPIVOT) +% ** by the angle with the give COS and SIN. Both fields are optional. +% ** [COS,SIN] defaults to previous value, or (1,0). +% ** (XPIVOT,YPIVOT) defaults to previous value, or (0,0) +% ** You can't change the coordinate system in the scope of a rotation. +% ** See Subsection 9.1 of the manual. +\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} + + +% ** Following terminates rotation. +% ** See Subsection 9.1 of the manual. +\def\stoprotation{% + \let\!rotateaboutpivot=\!!!rotateaboutpivot + \let\!rotateonly=\!!!rotateonly + \ignorespaces} + +% ** !!rotateaboutpivot{XREG}{YREG} +% ** XREG <-- xpvt + cos(angle)*(XREG-xpvt) - sin(angle)*(YREG-ypvt) +% ** YREG <-- ypvt + cos(angle)*(YREG-ypvt) + sin(angle)*(XREG-xpvt) +% ** XREG,YREG are dimension registers. Can't be \!dimenA to \!dimenD +\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} + +% ** \!!rotateonly{XREG}{YREG} +% ** Like \!!rotateaboutpivot, but with a pivot of (0,0) +\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} + + +% ********************************** +% *** SHADING (Handles shading) *** +% ********************************** + +% ** User commands +% ** \setshadegrid [span <SPAN>] [point at XSHADE YSHADE] +% ** \setshadesymbol [<LS, RS, BS, TS>] ({SHADESYMBOL} +% ** <XDIMEN,YDIMEN> [ORIENTATION]) + +% ** Internal commands: +% ** \!startvshade (xS,ybS,ytS) +% ** \!starthshade (yS,xlS,xrS) +% ** \!lshade [<LS,RS,BS,TS>] +% ** ** when shading vertically: +% ** [the region from (xS,ybS,ytS) to] (xE,ybE,ytE) +% ** ** when shading horizontally: +% ** [the region from (yS,xlS,xrS) to] (yE,xlE,xrE) +% ** \!qshade [<LS,RS,BS,TS>] +% ** ** when shading vertically: +% ** [the region from (xS,ybS,ytS) to] (xM,ybM,ytM) (xE,ybE,ytE) +% ** ** when shading horizontally: +% ** [the region from (yS,xlS,xrS) to] (yM,xlM,xrM) (yE,xlE,xrE) +% ** \!lattice{ANCHOR}{SPAN}{LOCATION}{INDEX}{LATTICE LOCATION} +% ** \!override{NOMINAL DIMEN}{REPLACEMENT DIMEN}{DIMEN} + + +% ** The shading routine can operate either in a "vertical mode" or a +% ** "horizontal mode". In vertical mode, the region to be shaded is specified +% ** in the form +% ** {(x,y): xl <= x <= xr & yb(x) <= y <= yt(x)} +% ** where yb and yt are functions of x. In horizontal mode, the region +% ** is specified in the form +% ** {(x,y): yb <= y <= yt & xl(y) <= x <= xr(y)}. +% ** The functions yb and yt may be either both linear or both quadratic; +% ** similarly for xl and xr. A region with say, piecewise quadratic bottom +% ** and top boundaries, can be shaded by consecutive (vertical) \!qshades, +% ** proceeding from left to right. Similarly, a region with piecewise +% ** quadratic left and right boundaries can be shaded by consecutive +% ** (horizontal) \!qshades, proceeding from bottom to top. More complex +% ** regions can be shaded by partitioning them into appropriate subregions, +% ** and shading those. + +% ** Shading is accomplished by placing a user-selected shading symbol at +% ** those points of a regular grid which fall within the region to be +% ** shaded. This region can be "shrunk" so that a largish shading symbol +% ** will not extend outside it. Shrinking is accomplished by specifying +% ** shrinkages for the left, right, bottom, and top boundaries, in a manner +% ** discussed further below. + +% ** \shades and \!joins MUST NOT be intermingled. Finish drawing a curve +% ** before starting to shade a region, and finish shading a region before +% ** starting to draw a curve. + + +% ** \setshadegrid [span <SPAN>] [point at XSHADE YSHADE] +% ** The shading symbol is placed down on the points of a grid centered +% ** at the coordinate point (XSHADE,YSHADE). The grid points are of the +% ** form (j*SPAN,k*SPAN), with j+k even. SPAN is specified +% ** as a dimension. +% ** (XSHADE,YSHADE) defaults to previous (XSHADE,YSHADE) (or (0,0) if none) +% ** SPAN defaults to previous span (or 5pt if none) +% ** See Subsection 7.2 of the manual. +\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} + +% ** \setshadesymbol [<LS, RS, BS, TS>] ({SHADESYMBOL} +% ** <XDIMEN,YDIMEN> [ORIENTATION]) +% ** Saves SHADESYMBOL away in an hbox for use with shading routines. +% ** A shade symbol will not be plotted if its plot position comes within +% ** distance LS of the left boundary, RS of the right boundary, TS of the +% ** top boundary, BS of the bottom boundary. These parameters have +% ** default values that should work in most cases (see below). +% ** To override a default value, specify the replacement value +% ** in the appropriate subfield of the shrinkages field. +% ** 0pt may be coded as "z" (without the quotes). To accept a +% ** default value, leave the field empty. Thus +% ** [,z,,5pt] sets LS=default, RS=0pt, BS=default, TS=5pt . +% ** Skipping the shrinkages field accepts all the defaults. +% ** See Subsection 7.1 of the manual. +\def\setshadesymbol{% + \!ifnextchar<{\!setshadesymbol}{\!setshadesymbol<,,,> }} + +\def\!setshadesymbol <#1,#2,#3,#4> (#5#6){% +% ** set the shadesymbol + \!setputobject{#5}{#6}% + \setbox\!shadesymbol=\box\!putobject% + \!shadesymbolxshift=\!xshift \!shadesymbolyshift=\!yshift +% +% ** set the shrinkages + \!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}% + +% ** \!override{NOMINAL DIMEN}{REPLACEMENT DIMEN}{DIMEN} +% ** Overrides the NOMINAL DIMEN by the REPLACEMENT DIMEN to produce DIMEN, +% ** according to the following rules: +% ** REPLACEMENT DIMEN empty: DIMEN <-- NOMINAL DIMEN +% ** REPLACEMENT DIMEN z: DIMEN <-- 0pt +% ** otherwise: DIMEN <-- REPLACEMENT DIMEN +% ** DIMEN must be a dimension register +\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 +% ** \fivesy ^^B is a small cross + + +% ** \!startvshade [at] (xS,ybS,ytS) +% ** Initiates vertical shading mode +\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} + +% ** \!starthshade [at] (yS,xlS,xrS) +% ** Initiates horizontal shading mode +\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} + + +% ** \!lattice{ANCHOR}{SPAN}{LOCATION}{INDEX}{LATTICE LOCATION} +% ** Consider the lattice with points ANCHOR + j*SPAN. This routine determines +% ** the index k of the smallest lattice point >= LOCATION, and sets +% ** LATTICE LOCATION = ANCHOR + k*SPAN. +% ** INDEX is assumed to be a count register, LATTICE LOCATION a dimen reg. +\def\!lattice#1#2#3#4#5{% + \!dimenA=#1% ** dimA = ANCHOR + \!dimenB=#2% ** dimB = SPAN (assumed > 0pt) + \!countB=\!dimenB% ** ctB = SPAN, as a count +% +% ** Determine index of smallest lattice point >= LOCATION + \!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} + + +% ** \!qshade [with shrinkages] [[LS,RS,BS,TS]] +% ***** during vertical shading: +% ** [the region from (xS,ybS,ytS) to] (xM,ybM,ytM) [and] (xE,ybE,ytE) +% ** Shades the region {(x,y): xS <= x <= xE, yb(x) <= y <= yt(x)}, where +% ** yb is the quadratic thru (xS,ybS) & (xM,ybM) & (xE,ybE) +% ** yt is the quadratic thru (xS,ytS) & (xM,ybM) & (xE,ytE) +% ** xS,ybS,ytS are either given by \!startvshade or carried over +% ** as the ending values of the immediately preceding \!qshade. +% ** For the interpretation of LS, RS, BS, & TS, see \setshadesymbol. The +% ** values set there can be overridden, for the course of this \!qshade +% ** only, in the same manner as overrides are specified for +% ** \setshadesymbol. +% ***** during horizontal shading: +% ** [the region from (yS,xlS,xrS) to] (yM,xlM,xrM) [and] (yE,xlE,xrE) +\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} + +% ** \!lshade ... (xE,ybE,ytE) +% ** This is like \!qshade, but the top and bottom boundaries are linear, +% ** rather than quadratic. +\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} + +% ** \!getcoeffs{X0}{Y0}{X1}{Y1}{X2}{Y2}{B}{C} +% ** Finds B and C such that the quadratic y = Y0 + B(x-X0) + C(x-X0)**2 +% ** passes through (X1,Y1) and (X2,Y2): when X0=0=Y0, the formulas are: +% ** B = S1 - X1*C, C = (S2-S1)/X2 +% ** with +% ** S1 = Y1/X1, S2 = (Y2-Y1)/(X2-X1). +\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{% +% ** Get LS,RS,BS,TS for this panel + \!getshrinkages#1<,,,>\!nil% % ** now effective LS=dimE, RS=dimF, +% ** BS=dimG, TS=dimH + \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 +% ** hmode: xloc=ypos, yloc=xpos + \!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} + + +% ************************************** +% *** TICKS (Draws ticks on graphs) *** +% ************************************** + +% ** User commands +% ** \ticksout +% ** \ticksin +% ** \gridlines +% ** \nogridlines +% ** \loggedticks +% ** \unloggesticks +% ** See Subsection 3.4 of the manual + +% ** The following is an option of the \axis command +% ** ticks +% ** [in] [out] +% ** [long] [short] [length <LENGTH>] +% ** [width <WIDTH>] +% ** [andacross] [butnotacross] +% ** [logged] [unlogged] +% ** [unlabeled] [numbered] [withvalues VALUE1 VALUE2 ... VALUEk / ] +% ** [quantity Q] [at LOC1 LOC2 ... LOCk / ] [from LOC1 to LOC2 by +% ** LOC_INCREMENT] +% ** See Subsection 3.2 of the manual for the rules. + +% ** The various options of the tick field are processed by the +% ** \!nextkeyword command defined below. +% ** For example, `\!nextkeyword short ' expands to `\!ticksshort', +% ** while `\!nextkeyword withvalues' expands to `\!tickswithvalues'. + +\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 + +% ** \!ticks/ : terminates read of tick options +\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 + +\protect \endinput |