% G"andertes PiCTeX.TEX mit weniger Dimensionsregistern %
% von Andreas Schrell, ohne Gew"ahr!!!!!!!
% Version 0.0 vom 31.03.1994
% FEHLERMELDUNGEN an [email protected]
% This is PiCTeXWD, 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
% *******************************
% *** 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{}
\newskip\headingtoplotskip %.A................. %-as-%
\newskip\linethickness %.A..X....U........T
\newskip\longticklength %.A................T %-as-%
\newskip\plotsymbolspacing %......D...L....Q...
\newskip\shortticklength %.A................T %-as-%
\newskip\stackleading %.A..........P...... %-as-%
\newskip\tickstovaluesleading %.A................T %-as-%
\newskip\totalarclength %......D...L....Q...
\newskip\valuestolabelleading %.A................. %-as-%
\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\!tickcase %..................T
\newskip\!Xleft %............P......
\newskip\!Xright %............P......
\newskip\!Xsave %.A................T
\newskip\!Ybot %............P......
\newskip\!Ysave %.A................T
\newskip\!Ytop %............P......
\newskip\!angle %........E..........
\newskip\!arclength %..W......UL....Q...
\newskip\!areabloc %.A........L........
\newskip\!arealloc %.A........L........
\newskip\!arearloc %.A........L........
\newskip\!areatloc %.A........L........
\newskip\!bshrinkage %.................S.
\newskip\!checkbot %..........L........
\newskip\!checkleft %..........L........
\newskip\!checkright %..........L........
\newskip\!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\!rshrinkage %.................S.
\newdimen\!shadesymbolxshift %.................S.
\newdimen\!shadesymbolyshift %.................S.
\newdimen\!tshrinkage %.................S.
\newdimen\!uplength %..........L........
\newdimen\!wd %....X.......P....S.
\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.........
\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
\def\!zpt{0pt} % static
\!xunit=1pt
\!yunit=1pt
\!arearloc=\!xunit
\!areatloc=\!yunit
\!dshade=5pt
\!leaderlength=24in
\def\!tfs{256} % static
\def\!wmax{5.3pt} % static
\def\!wmin{2.7pt} % static
\!xaxislength=\!xunit
\!xpivot=\!zpt
\!yaxislength=\!yunit
\!ypivot=\!zpt
\plotsymbolspacing=.4pt
\!dimenA=50pt \def\!fiftypt{\the\!dimenA} % static
\def\!rootten{3.162278pt} % static
\def\!tenAa{8.690286pt} % static (A5)
\def\!tenAc{2.773839pt} % static (A3)
\def\!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}
\font\fiverm=cmr5
\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\!ymidpt{\the\!dimenA}%
\fi
\!xM=\!M{#1}\!xunit \!yM=\!M{#2}\!yunit \!rotateaboutpivot\!xM\!yM
\!xE=\!M{#3}\!xunit \!yE=\!M{#4}\!yunit \!rotateaboutpivot\!xE\!yE
%
% ** 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
|
