%% $Id: pstricks-add.tex 705 2023-04-17 18:32:58Z herbert $ %% %% This is file `pstricks-add.tex', %% %% IMPORTANT NOTICE: %% %% Package `pstricks-add.tex' %% %% Dominique Rodriguez %% Herbert Voss %% Michael Sharpe %% %% This program can be redistributed and/or modified under the terms %% of the LaTeX Project Public License Distributed from CTAN archives %% in directory macros/latex/base/lppl.txt. %% %% DESCRIPTION: %% `pstricks-add' is a PSTricks package for additionals to the standard %% pstricks package %% \csname PSTricksAddLoaded\endcsname \let\PSTricksAddLoaded\endinput % % Requires some packages \ifx\PSTricksLoaded\endinput\else \input pstricks \fi \ifx\PSTplotLoaded\endinput\else \input pst-plot \fi \ifx\PSTnodesLoaded\endinput\else \input pst-node \fi \ifx\PSTarrowLoaded\endinput\else \input pst-arrow \fi \ifx\PSTthreeDLoaded\endinput\else\input pst-3d \fi \ifx\MultidoLoaded\endinput\else \input multido \fi \ifx\PSTXKeyLoaded\endinput\else \input pst-xkey \fi \ifx\PSTmathLoaded\endinput\else \input pst-math \fi % \def\fileversion{3.94} \def\filedate{2023/04/17} \let\pstricksaddFV\fileversion \message{`pstricks-add' v\fileversion, \filedate\space (dr,hv)} % \edef\PstAtCode{\the\catcode`\@} \catcode`\@=11\relax \SpecialCoor \pst@addfams{pstricks-add} % %% prologue for postcript \pstheader{pstricks-add.pro}% % \def\psGetSlope(#1,#2)(#3,#4)#5{% 4 values without a dimen! #5 is a macro \pst@dimm=#1pt% \advance\pst@dimm by -#3pt% \pst@dimn=#2pt% \advance\pst@dimn by -#4pt \pst@divide{\pst@dimn}{\pst@dimm}#5} % \def\psGetDistance{\@ifnextchar[\psGetDistance@i{\psGetDistance@ii}} \def\psGetDistance@i[#1](#2,#3)(#4,#5)#6{% 4 values without a dimen! #6 is a macro \if@pstLaTeX \edef#6{\pscalculate{round(sqrt((#4-#2)^2+(#5-#3)^2),#1)}}% \else \pst@dimm=#1pt \advance\pst@dimm by -#3pt \pst@dimn=#2pt \advance\pst@dimn by -#4pt \pst@pyth\pst@dimm\pst@dimn\pst@dimo \edef#5{\strip@pt\pst@dimo}% \fi }% \def\psGetDistance@ii(#1,#2)(#3,#4)#5{% 4 values without a dimen! #6 is a macro \if@pstLaTeX \edef#5{\pscalculate{sqrt((#3-#1)^2+(#4-#2)^2)}}% \else \pst@dimm=#1pt \advance\pst@dimm by -#3pt \pst@dimn=#2pt \advance\pst@dimn by -#4pt \pst@pyth\pst@dimm\pst@dimn\pst@dimo \edef#5{\strip@pt\pst@dimo}% \fi }% %--------------------------------------- small stuff ------------------------------- \define@boolkey[psset]{pstricks-add}[Pst@]{CMYK}[true]{} \psset[pstricks-add]{CMYK=true} % \def\defineTColor{\@ifnextchar[{\defineTColor@i}{\defineTColor@i[]}} \def\defineTColor@i[#1]#2#3{% "semi transparency colors" \def\pst@tempA{#1}% \newpsstyle{#2}{% fillstyle=vlines,hatchwidth=0.1\pslinewidth, hatchsep=1\pslinewidth,hatchcolor=#3}% \ifx\pst@tempA\@empty\else\psset{#1}\fi% } \defineTColor{TRed}{red} \defineTColor{TGreen}{green} \defineTColor{TBlue}{blue} % \def\rmultiput{\pst@object{rmultiput}} \def\rmultiput@i#1{% \pst@killglue% \begingroup% \use@par% \@ifnextchar({\rmultiput@ii{#1}}{\rmultiput@ii{#1}(\z@,\z@)}} \def\rmultiput@ii#1(#2){% \if@star\rput*(#2){#1}\else\rput(#2){#1}\fi \@ifnextchar({\rmultiput@ii{#1}}{\endgroup}} % #1: (x,y) #2: rotAngle #3: object \def\psrotate{\pst@object{psrotate}} \def\psrotate@i(#1)#2{% \pst@killglue \begingroup% \use@par\pst@makebox{\psrotate@ii(#1){#2}}} \def\psrotate@ii(#1)#2{% \pst@getcoor{#1}\pst@tempA \pst@getangle{#2}\pst@tempB \leavevmode \pst@Verb{ gsave { \pst@tempA /yRot ED /xRot ED \pst@tempB dup cos /cosA ED sin /sinA ED /ax cosA def /by sinA def /cx sinA neg def /dy cosA def /ex xRot cosA mul neg xRot add yRot sinA mul add def /fy xRot sinA mul neg yRot add yRot cosA mul sub def [ax by cx dy ex fy] concat } \tx@TMChange }% \box\pst@hbox \pst@Verb{ \tx@TMRestore grestore }\endgroup \ignorespaces} % % [#1]: obtargs; (#2,#3): center; {#4}: factor; {#5}: object \def\psHomothetie{\def\pst@par{}\pst@object{psHomothetie}} \def\psHomothetie@i(#1)#2{% \begin@SpecialObj% \pst@getcoor{#1}\pst@tempA% converts the coordinates without a unit into pt \pst@makebox{\psHomothetie@ii{#2}}}% put the contents into a box \def\psHomothetie@ii#1{% \pst@Verb{% { \pst@tempA /yH ED /xH ED [#1 0 0 #1 #1 xH mul neg xH add #1 yH mul neg yH add] concat } \tx@TMChange }% \box\pst@hbox% \pst@Verb{ \tx@TMRestore }% \end@SpecialObj} % \define@key[psset]{pstricks-add}{intSeparator}{\def\psk@intSeparator{#1}} \psset{intSeparator={,}} % \def\psFormatInt{\def\pst@par{}\pst@object{psFormatInt}} \def\psFormatInt@i#1{{% \pst@killglue \use@par \count1=#1\count2=\count1 \ifnum\count1=0 0\else \ifnum\count1>999999 \count3=\count1 \divide\count3 by 1000000 \the\count3\psk@intSeparator\relax \multiply\count3 by 1000000 \advance\count1 by -\count3 % modulo 1000000 \fi% \ifnum\count2>999 \count3=\count1 \divide\count3 by 1000 \ifnum\count2>99999 \ifnum\count3<100 0\fi \ifnum\count3<10 0\fi \fi% \the\count3\psk@intSeparator\relax \multiply\count3 by 1000 \advance\count1 by -\count3 %modulo 1000 \fi% \ifnum\count2>999 \ifnum\count1<100 0\fi \ifnum\count1<10 0\fi \fi% \the\count1 \fi% }\ignorespaces} % \define@key[psset]{pstricks-add}{braceWidth}{\pst@getlength{#1}\psk@braceWidth} \define@key[psset]{pstricks-add}{bracePos}{\pst@checknum{#1}\psk@bracePos} \define@key[psset]{pstricks-add}{braceWidthInner}{\pst@getlength{#1}\psk@braceWidthInner} \define@key[psset]{pstricks-add}{braceWidthOuter}{\pst@getlength{#1}\psk@braceWidthOuter} % \define@boolkey[psset]{pstricks-add}[PST@]{singleline}[true]{}%use \ifPST@metricFunction \psset{singleline=false} \def\psbrace{\def\pst@par{}\pst@object{psbrace}} \def\psbrace@i(#1)(#2)#3{% \addbefore@par{ref=lb,linewidth=0.01pt,fillstyle=solid,fillcolor=black}% default setting \begin@SpecialObj \if@star\def\pst@tempC{true }\else\def\pst@tempC{false }\fi \ifx\psk@rot\empty\def\psk@@rot{0}\else\let\psk@@rot\psk@rot\fi \def\psk@rot{Alpha \psk@@rot\space add 90 sub}% \pst@getcoor{#1}\pst@tempA \pst@getcoor{#2}\pst@tempB \rput(! /ifStar \pst@tempC def /radius1 \psk@braceWidthOuter def /radius2 \psk@braceWidthInner def /Alpha \pst@tempA \pst@tempB 3 -1 roll sub 3 1 roll exch sub atan def gsave STV CP T /ps@rot \psk@rot\space def grestore /Length \pst@tempA \pst@tempB Pyth2 def /Left { Length \psk@bracePos\space mul } bind def /Right { Length Left sub } bind def /Width \psk@braceWidth def /pop4 { pop pop pop pop } def gsave [ Alpha cos Alpha sin Alpha sin neg Alpha cos \pst@tempA ] concat 0 0 moveto 0 radius2 neg radius2 radius2 neg radius2 arcto pop4 Left radius2 sub radius1 sub 0 rlineto Left radius2 neg Left radius2 radius1 add neg radius1 arcto pop4 currentpoint /y@Label ED /x@Label ED Left radius2 neg Left radius1 add radius2 neg radius1 arcto pop4 Right radius2 sub radius1 sub 0 rlineto Length radius2 neg Length 0 radius2 arcto pop4 \ifPST@singleline\else % 0 Width neg rlineto Length radius2 Width add neg Length radius2 sub radius2 Width add neg radius2 arcto pop4 Right radius2 sub radius1 sub neg 0 rlineto Left radius1 add Width radius1 add radius2 add neg radius1 90 180 arc Left radius1 sub Width radius1 add radius2 add neg radius1 0 90 arc Left radius2 sub radius1 sub neg 0 rlineto radius2 Width neg radius2 270 180 arcn 0 0 lineto \ifx\psk@fillstyle\relax\else gsave ifStar { \pst@usecolor\pslinecolor }{ \pst@usecolor\psfillcolor } ifelse fill grestore \fi \fi % \pst@number\pslinewidth setlinewidth \pst@usecolor\pslinecolor stroke \ifx\pslinestyle\@none\else \pst@number\pslinewidth SLW \pst@usecolor\pslinecolor \@nameuse{psls@\pslinestyle} \tx@setStrokeTransparency \fi stroke 0 0 moveto grestore % now calculate the label pos /Dh radius1 radius2 add Width add def \pst@tempA \pst@tempB 3 -1 roll sub 3 1 roll exch sub % dy dx \psk@bracePos\space mul exch \psk@bracePos\space mul % d'x d'y \pst@tempA 3 -1 roll add Dh Alpha cos mul sub % d'x x yA \psk@nodesepB sub % use minus sign to shidt right 3 1 roll add Dh Alpha sin mul add \psk@nodesepA add exch \tx@UserCoor ){#3} \end@SpecialObj} % \def\psBrace{\def\pst@par{}\pst@object{psBrace}} \def\psBrace@i(#1)(#2){% \begin@ClosedObj \if@star\def\pst@tempC{true }\else\def\pst@tempC{false }\fi % \ifx\psk@rot\empty\def\psk@@rot{0}\else\let\psk@@rot\psk@rot\fi % \def\psk@rot{Alpha \psk@@rot\space add 90 sub}% \pst@getcoor{#1}\pst@tempA \pst@getcoor{#2}\pst@tempB \addto@pscode{ /ifStar \pst@tempC def /radius1 \psk@braceWidthOuter def /radius2 \psk@braceWidthInner def /Alpha \pst@tempA \pst@tempB 3 -1 roll sub 3 1 roll exch sub atan def % gsave STV CP T /ps@rot \psk@rot\space def grestore /Length \pst@tempA \pst@tempB Pyth2 def /Left { Length \psk@bracePos\space mul } bind def /Right { Length Left sub } bind def /Width \psk@braceWidth def /pop4 { pop pop pop pop } def [ Alpha cos Alpha sin Alpha sin neg Alpha cos \pst@tempA ] concat 0 0 moveto 0 radius2 neg radius2 radius2 neg radius2 arcto pop4 Left radius2 sub radius1 sub 0 rlineto Left radius2 neg Left radius2 radius1 add neg radius1 arcto pop4 currentpoint /y@Label ED /x@Label ED Left radius2 neg Left radius1 add radius2 neg radius1 arcto pop4 Right radius2 sub radius1 sub 0 rlineto Length radius2 neg Length 0 radius2 arcto pop4 % 0 Width neg rlineto Length radius2 Width add neg Length radius2 sub radius2 Width add neg radius2 arcto pop4 Right radius2 sub radius1 sub neg 0 rlineto Left radius1 add Width radius1 add radius2 add neg radius1 90 180 arc Left radius1 sub Width radius1 add radius2 add neg radius1 0 90 arc Left radius2 sub radius1 sub neg 0 rlineto radius2 Width neg radius2 270 180 arcn 0 0 lineto } \end@ClosedObj \ignorespaces} % \newdimen\psparallelogramsep \define@key[psset]{pstricks-add}{parallelogramsep}[3mm]{\pssetlength\psparallelogramsep{#1}} \psset[pstricks-add]{parallelogramsep=3mm} % \def\psparallelogrambox{\pst@object{psparallelogrambox}} \def\psparallelogrambox@i{\pst@makebox\psparallelogrambox@ii} \def\psparallelogrambox@ii{% \begingroup \pst@useboxpar \pst@dima=\pslinewidth \advance\pst@dima by \psframesep \pst@dimc=\wd\pst@hbox\advance\pst@dimc by \pst@dima \pst@dimb=\dp\pst@hbox\advance\pst@dimb by \pst@dima \pst@dimd=\ht\pst@hbox\advance\pst@dimd by \pst@dima % Dirk Osburg modification begin - Jul. 16, 2011 \divide\psparallelogramsep by 2 \advance\pst@dima by \psparallelogramsep \advance\pst@dimc by \psparallelogramsep % Dirk Osburg modification end \setbox\pst@hbox=\hbox{% \ifpsboxsep\kern\pst@dima\fi \begin@ClosedObj \addto@pscode{% \psk@cornersize \pst@number\pst@dima neg % left \pst@number\pst@dimb neg % lower \pst@number\pst@dimc % right \pst@number\pst@dimd % upper .5 % D.G. modification begin - Nov. 28, 2001 %\tx@Frame}% \pst@number\psparallelogramsep \tx@Parallelogram}% % D.G. modification end \def\pst@linetype{2}% \showpointsfalse \end@ClosedObj \box\pst@hbox \ifpsboxsep\kern\pst@dima\fi% }% \ifpsboxsep\dp\pst@hbox=\pst@dimb\ht\pst@hbox=\pst@dimd\fi \leavevmode\box\pst@hbox \endgroup% } % From the Frame and Rect PostScript macros \pst@def{Parallelogram}<{% /ParallelogramA { % Dirk Osburg modification begin - Jul. 16, 2011 %%%% old stuff: %%% %x1 pgs sub y1 moveto %x1 y2 lineto %x2 pgs add y2 lineto %x2 y1 lineto %x1 pgs sub y1 lineto %%%% replaced by: %%% x1 pgs sub y1 moveto x1 pgs add y2 lineto x2 pgs add y2 lineto x2 pgs sub y1 lineto x1 pgs sub y1 lineto % Dirk Osburg modification end closepath} def % /pgs ED CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add /y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq {pop pop ParallelogramA } { OvalFrame } ifelse}> % \def\parseRP#1;#2;#3\@nil{%check whether arg of refpt contains ; \def\arg@A{#1}\def\arg@B{#2}} % \def\Put{\pst@object{Put}}% \def\Put@i{\@ifnextchar({\Put@ii{}}{\Put@ii}}% \def\Put@ii#1(#2)#3{{% \pst@killglue \use@par \expandafter\parseRP#1;;\@nil%sets \arg@A, \arg@B \ifx\arg@B\@empty% use \rput \edef\arg@A{\if@star*\fi\ifx\arg@A\@empty\else[\arg@A]\fi}% \expandafter\rput\arg@A(>#2){#3} \else% use \uput \edef\arg@A{\if@star*\fi% \ifx\arg@A\@empty\else{\arg@A}\fi% \ifx\arg@B\@empty[0]\else[\arg@B]\fi}% \expandafter\uput\arg@A(>#2){#3} \fi}\ignorespaces}% % Modify pst@rot so that a rotation may be specified with a node or ps code % \define@key[psset]{pstricks-add}{Os}[0]{\def\PST@Os{#1}} \psset{Os=0}% \define@key[psset]{pstricks-add}{Ds}[1]{\def\PST@Ds{#1}} \psset{Ds=1}% \define@key[psset]{pstricks-add}{metricInitValue}[0]{\def\PST@metricInitValue{#1}} \psset{metricInitValue=0}% \define@boolkey[psset]{pstricks-add}[PST@]{metricFunction}[true]{}%use \ifPST@metricFunction \psset{metricFunction=false}% \def\pscurvepoints{\pst@object{pscurvepoints}}% \def\pscurvepoints@i#1#2#3#4{{%optional [plotpoints=xx] % #1=tmin,#2=tmax,#3=function (of t),#4=array root name, \pst@killglue \use@par \edef\my@tempA{#3}% x(t) y(t) expanded \expandafter\testAlg\my@tempA|\@nil% \pst@Verb{ % so we can use definitions from tx@Dict /unitratio \pst@number\psyunit \pst@number\psxunit div def /unitratiosq unitratio dup mul def /t0 #1 def /t1 #2 def t1 t0 sub \psk@plotpoints\space div /dt exch def }% \pst@cntc=\psk@plotpoints\relax%\psk@plotpoints=plotpoints-1 \pst@cntb=\pst@cntc\relax%\psk@plotpoints=plotpoints-1 \advance\pst@cntc by \@ne\relax%=plotpoints \ifx\my@tempD\@empty\pst@Verb{ /Func (#3) cvx def }% \else\pst@Verb{ /Func (#3 ) AlgParser cvx def }% \fi% \pst@Verb{ /#4.X \the\pst@cntc\space array def /#4.Y \the\pst@cntc\space array def % /#4Delta.X \the\pst@cntc\space array def % /#4Delta.Y \the\pst@cntc\space array def % /#4Normal.X \the\pst@cntc\space array def % /#4Normal.Y \the\pst@cntc\space array def % /t #1 def Func 2 copy /priory ED /priorx ED #4.Y 0 3 -1 roll put #4.X 0 3 -1 roll put % 1 1 \the\pst@cntb\space { dup /j ED dt mul #1 add /t ED Func %x y on stack 2 copy priory sub dup #4Delta.Y j 3 -1 roll put % x y x y-priory unitratiosq mul neg #4Normal.X j 3 -1 roll put % x y x priorx sub dup #4Delta.X j 3 -1 roll put % x y x-priorx #4Normal.Y j 3 -1 roll put % x y 2 copy /priory ED /priorx ED % x y #4.Y j 3 -1 roll put #4.X j 3 -1 roll put } for % }% \expandafter\xdef \csname #4pointcount\endcsname {\psk@plotpoints}% % \typeout{Created points #40 .. #4\psk@plotpoints}% }\ignorespaces}% % %code to place ticks along polyline \def\pspolylineticks{\pst@object{pspolylineticks}}% \def\pspolylineticks@i#1{\@ifnextchar[{\pspolylineticks@ii{#1}}{\pspolylineticks@ii{#1}[]}}% \newcount\pst@cntC% \def\pspolylineticks@ii#1[#2]#3#4#5{{% %#1= root name,#2=pscode (optional),#3=metric function,#4=first tick,#5=tick count % Metric function may be a function of x, y (keyword metricFunction) % or a function of x, y, dx, dy, ds requiring incremental build \addbefore@par{arrows=-,linewidth=\psk@ytickwidth\pslinewidth}% \use@par% \pst@killglue%there's a leak that can occur here with ticksize--fixed in recent pstricks.tex \pst@cntC=\expandafter\csname #1pointcount\endcsname\relax% \pst@cntb=\pst@cntC\advance\pst@cntb\m@ne\relax% \pst@cntd=\pst@cntC\advance\pst@cntd\@ne\relax% \pst@Verb{ % so we can use definitions from tx@Dict in pstricks.pro /TDict 20 dict def TDict begin % /Func (#3) cvx def /sarray \the\pst@cntd\space array def % #2 \ifPST@metricFunction 0 1 #1.X length 1 sub { /j ED sarray j % #1.X j get /x ED #1.Y j get /y ED Func put } for % \else %build by increments sarray 0 \PST@metricInitValue\space put % 1 1 #1.X length 1 sub { /j ED sarray j % #1.X j 1 sub get /x ED #1.Y j 1 sub get /y ED #1Delta.X j get /dx ED #1Delta.Y j get /dy ED /ds dx dup mul dy dup mul add sqrt def % Func sarray j 1 sub get add put } for % \fi %\ifPSTfunctionMetric \ifnum\Pst@Debug>0 /str 10 string def /tmpar [(Metric range: [) () (, ) () (])] def % tmpar 1 sarray 0 get str cvs put /str 10 string def tmpar 3 sarray \the\pst@cntC\space get str cvs put tmpar tx@NodeDict begin concatstringarray = end % \fi % end debug %compute ticks /nl 0 def /nu \the\pst@cntC\space def /smin sarray 0 get def /smax sarray nu get def /Os \ifx\PST@Os\@empty smin \else \PST@Os\space \fi def % /Ds \ifx\PST@Ds\@empty smax Os sub 10 div \else \PST@Ds\space \fi def % /scount smax Os sub Ds div cvi def % /tarray scount 1 add array def % /#1Tick.X scount 1 add array def % /#1Tick.Y scount 1 add array def % /#1TickN.X scount 1 add array def % /#1TickN.Y scount 1 add array def % 0 1 scount { dup Ds mul Os add tarray 3 1 roll put } for %tick positions in tarray % find the corresponding s values using binary search 0 1 scount { dup tarray exch get /s exch def /j exch def %sought metric value,index /m nl def /n nu def /k nl nu add 2 div cvi def 20 { s sarray k get lt { % /n k def /k k m add 2 div cvi def }{ /m k def /nl k def /k k n add 2 div cvi def } ifelse % n 1 sub m le { /nl m def exit } if } repeat % sarray n get sarray m get dup 3 1 roll % sm sn sm sub dup 0 le { pop pop 0 }{%sm sn-sm exch %sn-sm sm s sub neg exch div } ifelse % s->(s-sm)/(sn-sm) dup #1Delta.X m 1 add get mul #1.X m get add #1Tick.X j 3 -1 roll put % s on stack #1Delta.Y m 1 add get mul #1.Y m get add #1Tick.Y j 3 -1 roll put % #1TickN.X j #1Normal.X m 1 add get put #1TickN.Y j #1Normal.Y m 1 add get put % } for % \ifnum\Pst@Debug>0 /tmpar 2 array def /str 4 string def tmpar 0 (Created data for points #1Tick0..#1Tick) put tmpar 1 scount str cvs put tmpar tx@NodeDict begin concatstringarray = end \fi% end }% end pst@Verb %Draw ticks \multido{\iA=#4+1}{#5}{% \pnode(! TDict begin \iA\space scount gt { 1 0 /VV ED /UU ED 0 0 } { #1TickN.X \iA\space get #1TickN.Y \iA\space get /VV ED /UU ED #1Tick.X \iA\space get #1Tick.Y \iA\space get } ifelse 2 copy /YY ED /XX ED end){#1Tick\iA}% \pnode(! TDict begin UU VV end ){#1Normal\iA}% \pnode(! TDict begin VV UU neg unitratiosq div end ){#1Tangent\iA}% \edef\cmd{\noexpand\psline(\the\pst@yticksizeA;{(! TDict begin UU VV end )})(\the\pst@yticksizeB;{(! TDict begin UU VV end )})}% \pscustom{\translate(! TDict begin XX YY end)\cmd}}% }\ignorespaces}% % \define@key[psset]{pstricks-add}{randomPoints}[1000]{\def\psk@randomPoints{#1}} \define@key[psset]{pstricks-add}{randInit}[rrand]{\def\psk@randInit{#1 }} \define@boolkey[psset]{pstricks-add}[Pst@]{color}[true]{} \psset{randomPoints=1000,color=false,randInit} % \def\psRandom{\def\pst@par{}\pst@object{psRandom}}% hv 2004-11-12 \def\psRandom@i{\@ifnextchar({\psRandom@ii}{\psRandom@iii(0,0)(1,1)}} \def\psRandom@ii(#1){\@ifnextchar({\psRandom@iii(#1)}{\psRandom@iii(0,0)(#1)}} \def\psRandom@iii(#1)(#2)#3{% \def\pst@tempA{#3}% \ifx\pst@tempA\pst@empty\psclip{\psframe(#2)}\else\psclip{#3}\fi \pst@getcoor{#1}\pst@tempA \pst@getcoor{#2}\pst@tempB \begin@SpecialObj \addto@pscode{ \pst@tempA\space /yMin exch def /xMin exch def \pst@tempB\space /yMax exch def /xMax exch def /dy yMax yMin sub def /dx xMax xMin sub def \psk@randInit srand % initializes the random generator /getRandReal { rand 2147483647 div } def \psk@dotsize % defines /DS ... def \@nameuse{psds@\psk@dotstyle} \psk@randomPoints { \ifPst@color getRandReal getRandReal getRandReal setrgbcolor \fi getRandReal dx mul xMin add getRandReal dy mul yMin add Dot \ifx\psk@fillstyle\psfs@solid fill \fi stroke } repeat }% \end@SpecialObj \endpsclip \ignorespaces } % \define@key[psset]{pstricks-add}{fillcolorA}[blue]{\pst@getcolor{#1}\psk@fillcolorA} \define@key[psset]{pstricks-add}{fillcolorB}[red]{\pst@getcolor{#1}\psk@fillcolorB} \define@boolkey[psset]{pstricks-add}[Pst@]{countDots}[true]{} \psset[pstricks-add]{countDots=false,fillcolorA=blue,fillcolorB=red} % \def\psRandomPointArea{\pst@object{psRandomPointArea}} \def\psRandomPointArea@i#1#2{% \pst@killglue \addbefore@par{radius=2pt,fillcolorA=blue,fillcolorB=red}% \begin@SpecialObj \pssetlength\pst@dimc{\psk@radius} \addto@pscode{ realtime srand Rand pop 4 dict begin /Func \ifPst@algebraic (#2) tx@addDict begin AlgParser end cvx \else { #2 } \fi def 1 1 #1 { /i ED Rand /x ED Func /f ED % function value Rand /y ED gsave x y \tx@ScreenCoor \pst@number\pst@dimc 0 360 arc y f lt { \pst@usecolor\psk@fillcolorA }{ \pst@usecolor\psk@fillcolorB } ifelse fill grestore \ifPst@countDots x y \tx@ScreenCoor moveto i 4 string cvs \ifpst@psfonts /Helvetica \else /NimbusSanL-Regu \fi findfont 5 scalefont setfont show \fi } for end }% \end@SpecialObj \ignorespaces } % \def\psComment{\def\pst@par{}\pst@object{psComment}} \def\psComment@i{\pst@getarrows\psComment@ii} \def\psComment@ii(#1)(#2)#3{\@ifnextchar[ {\psComment@iii(#1)(#2){#3}} {\psComment@iii(#1)(#2){#3}[\ncline]}} \def\psComment@iii(#1)(#2)#3[#4]{\@ifnextchar[ {\psComment@iv(#1)(#2){#3}[#4]} {\psComment@iv(#1)(#2){#3}[#4][\rput]}} \def\psComment@iv(#1)(#2)#3[#4][#5]{% \pnode(#1){comment@1} \pnode(#2){comment@2} \ifx\relax#4\relax\let\pst@ConnectionCommand\ncline \else\let\pst@ConnectionCommand#4\fi \ifx\relax#5\relax\let\pst@PutCommand\rput \else\let\pst@PutCommand#5\fi \addbefore@par{npos=0}% \begin@SpecialObj% \pst@ConnectionCommand{comment@1}{comment@2} \if@star\pst@PutCommand*(#1){#3}\else\pst@PutCommand(#1){#3}\fi \end@SpecialObj% \ignorespaces% } % \define@key[psset]{pstricks-add}{tipAngle}[60]{\pst@getangle{#1}\psk@tipAngle} \define@key[psset]{pstricks-add}{tipLength}[5mm]{\pst@getlength{#1}\psk@tipLength} \define@key[psset]{pstricks-add}{tipWidth}[2mm]{\pst@getlength{#1}\psk@tipWidth} \define@key[psset]{pstricks-add}{tipPos}[0.2]{\def\psk@tipPos{#1 }} \psset[pstricks-add]{tipAngle=60,tipLength=5mm,tipWidth=2mm,tipPos=0.2}% % \def\psCallout{\def\pst@par{}\pst@object{psCallout}} \def\psCallout@i(#1)#2{% \setbox\pst@hbox=\hbox{#2}% \begingroup \addbefore@par{linewidth=0.1pt,framesep=6pt}% \use@par \pstVerb{ /boxsepX { \pst@number\psframesep\space \pst@number\psxunit div } bind def /boxsepY { \pst@number\psframesep\space \pst@number\psyunit div } bind def /tipEnd { \psk@tipLength\space \pst@number\psxunit div \psk@tipAngle\space PtoC } bind def /boxW { \pst@number\wd\pst@hbox\space \pst@number\psxunit div boxsepX 2 mul add } bind def /boxH { \pst@number\ht\pst@hbox\space \pst@number\psyunit div boxsepY 2 mul add } bind def }% \rput(#1){% \psline[linearc=0,linejoin=2]% (! tipEnd exch \psk@tipWidth\space 2 div \pst@number\psxunit div sub exch)% (0,0) (! tipEnd exch \psk@tipWidth\space 2 div \pst@number\psxunit div add exch)% \psline[linejoin=2]% (! tipEnd exch \psk@tipWidth\space 2 div \pst@number\psxunit div sub exch)% (! tipEnd exch \psk@tipPos boxW mul sub exch)% lower left (! tipEnd exch \psk@tipPos boxW mul sub exch boxH add )% upper left (! tipEnd exch 1 \psk@tipPos sub boxW mul add exch boxH add)% upper right (! tipEnd exch 1 \psk@tipPos sub boxW mul add exch) (! tipEnd exch \psk@tipWidth\space 2 div \pst@number\psxunit div add exch)% \rput[lb](! tipEnd boxsepY add exch \psk@tipPos boxW mul sub boxsepX add exch){#2}% }% \endgroup \ignorespaces } % \def\tx@MovetoByHand{ tx@addDict begin MovetoByHand end } \def\tx@LinetoByHand{ tx@addDict begin LinetoByHand end } %/amplHand {.8} def %/dtHand 2 def \def\pslineByHand{\def\pst@par{}\pst@object{pslineByHand}} \def\pslineByHand@i{% \addbefore@par{VarStepEpsilon=2,varsteptol=0.8} \pst@getarrows{% \begin@OpenObj \pst@getcoors[\pslineByHand@ii}} \def\pslineByHand@ii{% \addto@pscode{ tx@addDict begin /dtHand \psk@VarStepEpsilon\space def /amplHand \psk@varsteptol\space def % \pst@cp % current point \tx@setlinejoin % hv 2007-10-13 MovetoByHand counttomark 2 div /maxLines ED 1 1 maxLines { pop LinetoByHand } for end }% \end@OpenObj% } % \def\psRelLine{\def\pst@par{}\pst@object{psRelLine}} \def\psRelLine@i{\@ifnextchar({\psRelLine@iii}{\psRelLine@ii}} \def\psRelLine@ii#1{% \addto@par{arrows=#1}% \psRelLine@iii% } \def\psRelLine@iii(#1)(#2)#3#4{{ \pst@killglue \use@par \psRelNode(#1)(#2){#3}{#4} \pcline(#1)(#4)%%%% \psline->\pcline 20140722 }\ignorespaces} % % #1 options % draw a parallel line to #2 #3 % #2---------#3 % #4----------#5(new node) % #5 length of the line % #6 node name \def\psParallelLine{\def\pst@par{}\pst@object{psParallelLine}} \def\psParallelLine@i{\@ifnextchar({\psParallelLine@iii}{\psParallelLine@ii}} \def\psParallelLine@ii#1{\addto@par{arrows=#1}\psParallelLine@iii} \def\psParallelLine@iii(#1)(#2)(#3)#4#5{{ \pst@killglue \use@par \pst@getcoor{#1}\pst@tempA \pst@getcoor{#2}\pst@tempB \pst@getcoor{#3}\pst@tempC % \pst@getlength{#4}\pst@dima \pnode(!% \pst@tempA /YA exch \pst@number\psyunit div def /XA exch \pst@number\psxunit div def \pst@tempB /YB exch \pst@number\psyunit div def /XB exch \pst@number\psxunit div def \pst@tempC /YC exch \pst@number\psyunit div def /XC exch \pst@number\psxunit div def % /dx XB XA sub def /dy YB YA sub def /laenge dy dup mul dx dup mul add sqrt #4 mul def /Alpha dy dx atan def laenge Alpha cos mul XC add laenge Alpha sin mul YC add ){#5}% \pcline(#3)(#5)%%%% \psline->\pcline 20140722 }\ignorespaces } % \define@key[psset]{pstricks-add}{startColor}[black]{\colorlet{tempcolor}[rgb]{#1}% we need rgb \pst@getcolor{tempcolor}\ps@startColor} \define@key[psset]{pstricks-add}{endColor}[white]{\colorlet{tempcolor}[rgb]{#1}% \pst@getcolor{tempcolor}\ps@endColor} \define@key[psset]{pstricks-add}{colorsteps}[256]{\pst@getint{#1}\pst@colorsteps}% hv 20211224 \psset[pstricks-add]{startColor=black,endColor=white,colorsteps=256} % \def\psColorLine{\def\pst@par{}\pst@object{psColorLine}} \def\psColorLine@i{% \pst@getarrows{% \begin@OpenObj \psColorLine@ii}% } \def\psColorLine@ii(#1){\@ifnextchar({\psColorLine@iii(#1)}{\psColorLine@iii(0,0)(#1)}}% \def\psColorLine@iii(#1,#2)(#3,#4){% % \use@par \ifx\psk@arrowA\@empty\else\psline[linecolor=\ps@startColor]{->}(!#3 0.5 mul #4 0.5 mul)(#1,#2)\fi \ifx\psk@arrowB\@empty\else\psline[linecolor=\ps@endColor]{->}(!#1 0.5 mul #2 0.5 mul)(#3,#4)\fi \pst@getcoor{#1,#2}\pst@tempA \pst@getcoor{#3,#4}\pst@tempB \addto@pscode{ 20 dict begin [ \psgetRGBColorValues{\ps@startColor} ] aload length 1 eq { dup dup } if 3 copy 3 array astore /startColor ED [ \psgetRGBColorValues{\ps@endColor} ] aload length 1 eq { dup dup } if 3 copy 3 array astore /endColor ED % on stack R1 G1 B1 R2 G2 B2 4 -1 roll % R1 G1 R2 G2 B2 B1 sub \pst@colorsteps\space div /dB ED % R1 G1 R2 G2 3 -1 roll % R1 R2 G2 G1 sub \pst@colorsteps\space div /dG ED % R1 R2 exch sub \pst@colorsteps\space div /dR ED \pst@tempB /Y2 ED /X2 ED \pst@tempA /Y1 ED /X1 ED Y2 Y1 sub X2 X1 sub atan /Angle ED Y2 Y1 sub Angle sin dup 0 eq { pop }{ div } ifelse /L_line ED % line length \ifx\psk@arrowA\@empty\else X2 X1 sub L_line div \psk@arrowlength\space mul \pst@number\psxunit mul X1 add /X1 ED Y2 Y1 sub L_line div \psk@arrowlength\space mul \pst@number\psyunit mul Y1 add /Y1 ED \fi \ifx\psk@arrowB\@empty\else X2 X1 sub L_line div \psk@arrowlength\space mul \pst@number\psxunit mul X2 exch sub /X2 ED Y2 Y1 sub L_line div \psk@arrowlength\space mul \pst@number\psyunit mul Y2 exch sub /Y2 ED \fi Y2 Y1 sub \pst@colorsteps\space 1 add div /dY ED X2 X1 sub \pst@colorsteps\space 1 add div /dX ED % dR dG dB == == == %startColor == endColor == \ifPst@noCurrentPoint\else\pst@cp\fi % current point? 0 1 \pst@colorsteps { /dIndex ED %startColor == X1 Y1 moveto X1 dX add Y1 dY add % start for coordinate array % gsave lineto CP /Y1 ED /X1 ED \pst@number\pslinewidth SLW startColor aload pop 3 copy setrgbcolor % on stack r g b dB add 3 1 roll % b+dB r g dG add 3 1 roll % b+dB g+dG r dR add 3 1 roll % b+dB g+dG r+dR 3 array astore /startColor ED \tx@setStrokeTransparency stroke % grestore } for end % of local part }% \end@OpenObj \ignorespaces } % \def\psIntersectionPoint(#1)(#2)(#3)(#4)#5{% \pst@getcoor{#1}\pst@tempA \pst@getcoor{#2}\pst@tempB \pst@getcoor{#3}\pst@tempC \pst@getcoor{#4}\pst@tempd \pnode(!% \pst@tempA /YA exch \pst@number\psyunit div def /XA exch \pst@number\psxunit div def \pst@tempB /YB exch \pst@number\psyunit div def /XB exch \pst@number\psxunit div def \pst@tempC /YC exch \pst@number\psyunit div def /XC exch \pst@number\psxunit div def \pst@tempd /YD exch \pst@number\psyunit div def /XD exch \pst@number\psxunit div def /dY1 YB YA sub def /dX1 XB XA sub def /dY2 YD YC sub def /dX2 XD XC sub def dX1 abs 0.01 lt { /m2 dY2 dX2 div def XA dup XC sub m2 mul YC add }{ dX2 abs 0.01 lt { /m1 dY1 dX1 div def XC dup XA sub m1 mul YA add }{% /m1 dY1 dX1 div def /m2 dY2 dX2 div def m1 XA mul m2 XC mul sub YA sub YC add m1 m2 sub div dup XA sub m1 mul YA add } ifelse } ifelse ){#5}% } % \def\psRiemannSum(#1,#2)#3#4{% (x0,x1) n f(#1) \def\psFunction@##1{#4}% \edef\ps@@dx{\pscalculate{(#2-#1)/#3}}% \edef\ps@@dxHalf{\pscalculate{\ps@@dx/2}}% % \typeout{dx=\ps@dx}% \def\psRightSumValue{0}% \def\psLeftSumValue{0}% \def\psMiddleSumValue{0}% \def\psDiffSumValue{0}% \Multido{\rA=#1+\ps@@dx,\rB=\ps@@dx+\ps@@dx,\rC=\ps@@dxHalf+\ps@@dx}{#3}{% \def\ps@rightY{\pscalculate{\psFunction@{\rB}}}% \def\ps@leftY{\pscalculate{\psFunction@{\rA}}}% \def\ps@middleY{\pscalculate{\psFunction@{\rC}}}% % \typeout{\ps@leftY, \ps@rightY }% \edef\psLeftSumValue{\pscalculate{\psLeftSumValue+\ps@@dx*\ps@leftY}}% \edef\psRightSumValue{\pscalculate{\psRightSumValue+\ps@@dx*\ps@rightY}}% \edef\psMiddleSumValue{\pscalculate{\psMiddleSumValue+\ps@@dx*\ps@middleY}}% \edef\psDiffSumValue{\pscalculate{\psDiffSumValue+abs(\ps@@dx*(\ps@rightY-\ps@leftY))}}% % \typeout{\psLeftSumValue , \psRightSumValue }% }% end \Multido } %\define@key[psset]{pstricks-add}{method}{\def\psk@method{#1}}% defined in pst-plot \define@key[psset]{pstricks-add}{whichabs}{\def\psk@whichabs{#1}}% \define@key[psset]{pstricks-add}{whichord}{\def\psk@whichord{#1}}% \define@key[psset]{pstricks-add}{plotfuncx}{\def\psk@plotfuncx{#1}}% \define@key[psset]{pstricks-add}{plotfuncy}{\def\psk@plotfuncy{#1}}% \define@key[psset]{pstricks-add}{expression}{\def\psk@expression{#1}}% \define@boolkey[psset]{pstricks-add}[Pst@]{buildvector}[true]{}% % \define@key[psset]{pstricks-add}{varsteptol}{\def\psk@varsteptol{#1}}% \define@key[psset]{pstricks-add}{adamsorder}{\def\psk@adamsorder{#1}}% %\define@key[psset]{pstricks-add}{varstepincrease}{\def\psk@varstepincrease{#1}}% varrk4 % \define@boolkey[psset]{pstricks-add}[Pst@]{saveSumValue}[true]{} \psset[pstricks-add]{saveSumValue=false} \define@key[psset]{pstricks-add}{StepType}{\pst@expandafter\psset@@StepType{#1}\@nil}% \def\psset@@StepType#1#2\@nil{% \ifx#1u\let\psk@StepType\@ne \else\ifx#1l\let\psk@StepType\z@ \else\ifx#1i\let\psk@StepType\thr@@ \else\ifx#1s\let\psk@StepType\f@ur \else\let\psk@StepType\tw@\fi\fi\fi\fi} \psset{StepType=lower} % alternative StepType=upper/inf/sup/Riemann \define@boolkey[psset]{pstricks-add}[Pst@]{noVerticalLines}[true]{}% \psset{noVerticalLines=false} \define@boolkey[psset]{pstricks-add}[Pst@]{drawLines}[true]{}% \psset{drawLines=true} % \newcount\pst@stepcount \pst@stepcount=1 \def\get@Letter#1;{% \ifcase#1\or A\or B\or C\or D\or E\or F\or G\or H\or I\or J\or K\or L\or M\or N\or O\or P\or Q\or R\or S\or T\or U\or V\or W\or X\or Y\or Z\else0\fi} \def\psStep{\def\pst@par{}\pst@object{psStep}} \def\psStep@i(#1,#2)#3#4{% \expandafter\xdef\csname pstArea\get@Letter\the\pst@stepcount;\endcsname{undef}% \IfFileExists{\jobname-area\the\pst@stepcount.tex}{\input{\jobname-area\the\pst@stepcount.tex}}{}% \begin@ClosedObj \addto@pscode{ \ifPst@saveSumValue /AreaFile (\jobname-area\the\pst@stepcount.tex) (w) file def AreaFile (\string\% Created by \string\\psStep\string\n ) writestring \fi /Func \ifPst@algebraic (#4) tx@addDict begin AlgParser end cvx \else {#4} \fi def /x #1 def /dx #2 #1 sub #3 div def /scx { \pst@number\psxunit mul } def /scy { \pst@number\psyunit mul } def /Area 0 def % \ifcase\psk@StepType % 0->lower, height is always f(x) \ifPst@drawLines x scx 0 moveto \fi #3 { Func dup dx mul Area add /Area ED \ifPst@drawLines scy dup x scx exch \ifPst@noVerticalLines moveto \else lineto \fi \else pop \fi /x x dx add def \ifPst@drawLines x scx exch lineto x scx 0 \ifPst@noVerticalLines moveto \else lineto \fi \fi } repeat \or % 1-> upper, height is always f(x+dx) \ifPst@drawLines x scx 0 moveto \fi #3 { /x x dx add def Func \ifPst@saveSumValue dup dx mul Area add /Area ED \fi \ifPst@drawLines scy dup x dx sub scx exch \ifPst@noVerticalLines moveto \else lineto \fi x scx exch lineto x scx 0 \ifPst@noVerticalLines moveto \else lineto \fi \else pop \fi } repeat \ifPst@saveSumValue \fi \or % 2-> Riemann /eps3 500 def %% increased from 100 to 500 20140507 /xMinMax [] def /AMax [] def /AMin [] def /dt dx eps3 div def #3 { /Max Func def /Min Max def /t x def % save x value eps3 { Func \ifPst@saveSumValue dup dx mul Area add /Area ED \fi dup Max lt { /Max exch def } { dup Min gt { /Min exch def }{ pop } ifelse } ifelse /x x dt add def } repeat /x t def % restore x scx Min scy Max scy xMinMax aload length 3 add array astore /xMinMax exch def /x x dx add def closepath } repeat /dx dx scx def \ifPst@drawLines xMinMax aload length 3 div cvi { /yMax ED /yMin ED /x ED x yMin moveto dx 0 \ifPst@noVerticalLines rmoveto \else rlineto \fi x dx add yMax lineto dx neg 0 \ifPst@noVerticalLines rmoveto \else rlineto \fi x yMin \ifPst@noVerticalLines moveto \else lineto \fi closepath \fi } repeat \or % 3->inf(imum) % \ifPst@drawLines x scx 0 moveto % \fi #3 { \ifPst@algebraic Func \else #4 \fi \ifPst@saveSumValue dup dx mul Area add /Area ED \fi /yMin ED % Max value f(x) /xStart x def /xEnd xStart dx add def /DX dx 100 div def xStart DX xEnd { /x ED \ifPst@algebraic Func \else #4 \fi /yVal ED yVal yMin lt { /yMin yVal def } if } for % y0 y1 gt { y0 }{ y1 } ifelse % use supremum /x xEnd def yMin scy dup xStart scx exch \ifPst@noVerticalLines moveto \else lineto \fi x scx exch lineto x scx 0 \ifPst@noVerticalLines moveto \else lineto \fi closepath x scx 0 moveto } repeat \or % 4-> sup(remum) x scx 0 moveto #3 { \ifPst@algebraic Func \else #4 \fi \ifPst@saveSumValue dup dx mul Area add /Area ED \fi /yMax ED % Max value f(x) /xStart x def /xEnd xStart dx add def /DX dx 100 div def xStart DX xEnd { /x ED \ifPst@algebraic Func \else #4 \fi /yVal ED yVal yMax gt { /yMax yVal def } if } for % y0 y1 gt { y0 }{ y1 } ifelse % use supremum /x xEnd def yMax scy dup xStart scx exch \ifPst@noVerticalLines moveto \else lineto \fi x scx exch lineto x scx 0 \ifPst@noVerticalLines moveto \else lineto \fi closepath x scx 0 moveto } repeat \fi \ifPst@saveSumValue AreaFile (\string\\gdef\string\\pstArea\get@Letter\the\pst@stepcount;\string{) writestring Area 10 string cvs AreaFile exch writestring AreaFile (\string}\string\n) writestring AreaFile closefile \fi }% \global\advance\pst@stepcount by 1 \psk@fillstyle \pst@stroke \end@ClosedObj \ignorespaces } % \define@key[psset]{pstricks-add}{Derive}{\def\psk@Derive{#1}} %\define@key[psset]{pstricks-add}{Derive}{\expandafter\psk@@Derive#1,,\@nil}% %\def\psk@@Derive#1,#2,#3\@nil{% % \ifx\relax#2\relax % \ifPST@algebraic\def\psk@Derive{ (#1) tx@addDict begin AlgParser end cvx }\else \def\psk@Derive{ #1 }\fi % \else\def\psk@Derive{ (#1)(x) tx@Derive begin Derive end tx@addDict begin AlgParser end cvx } \fi %} \define@boolkey[psset]{pstricks-add}[PST@]{Tnormal}[true]{} \psset[pstricks-add]{CMYK=true} \def\@NOTEMPTY{NOT@EMPTY}%%dr 0606 % \def\psTangentLine{\def\pst@par{}\pst@object{psTangentLine}} \def\psTangentLine@i(#1,#2)(#3,#4)(#5,#6)#7#8{% \begin@OpenObj% \addto@pscode{ [[#1 dup dup mul exch 1 #2] [#3 dup dup mul exch 1 #4] [#5 dup dup mul exch 1 #6]] SolveLinEqSystem /abc ED abc aload pop % a b c on stack exch #7 % a c b x mul add exch % c+b*x a #7 dup mul mul add % a*x^2+b*x+c /y0 ED % save value abc aload pop pop exch % b a #7 mul 2 mul add % b+2*a*x0=mTan \ifPST@Tnormal neg 1 exch div % -1/mTan=mOrth #8 mul /dy ED % mOrth*dx=dy [ #7 #8 add y0 dy add \tx@ScreenCoor % x0+dx y0 +dy #7 y0 \tx@ScreenCoor % x0 y0 \else dup % mTan mTan #8 mul /dy1 ED % mTan*dx #8 neg mul /dy2 ED % mTan*-dx [ #7 #8 add y0 dy1 add \tx@ScreenCoor % x0+dx y0 +dy1 #7 #8 sub y0 dy2 add \tx@ScreenCoor % x0-dx y0 +dy2 \fi /Lineto /lineto load def \ifshowpoints true \else false \fi \tx@setlinejoin % \tx@Line }% \end@OpenObj% \pnode(! [[#1 dup dup mul exch 1 #2][#3 dup dup mul exch 1 #4][#5 dup dup mul exch 1 #6]] SolveLinEqSystem /abc ED abc aload pop % a b c on stack exch #7 % a c b x mul add exch % c+b*x a #7 dup mul mul add % a*x^2+b*x+c /y0 ED % save value #7 y0 ){OCurve}% \pnode(! [[#1 dup dup mul exch 1 #2][#3 dup dup mul exch 1 #4][#5 dup dup mul exch 1 #6]] SolveLinEqSystem /abc ED abc aload pop % a b c on stack exch #7 % a c b x mul add exch % c+b*x a #7 dup mul mul add % a*x^2+b*x+c /y0 ED % save value abc aload pop pop exch % b a #7 mul 2 mul add % b+2*a*x0=mTan neg 1 exch div % -1/mTan=mOrth #8 mul /dy ED % mOrth*dx=dy #7 #8 add y0 dy add % x0+dx y0 +dy ){ENormal}% \pnode(! [[#1 dup dup mul exch 1 #2][#3 dup dup mul exch 1 #4][#5 dup dup mul exch 1 #6]] SolveLinEqSystem /abc ED abc aload pop % a b c on stack exch #7 % a c b x mul add exch % c+b*x a #7 dup mul mul add % a*x^2+b*x+c /y0 ED % save value abc aload pop pop exch % b a #7 mul 2 mul add % b+2*a*x0=mTan #8 mul /dy1 ED % mTan*dx #7 #8 add y0 dy1 add ){ETangent}% \ignorespaces} \def\psplotTangent@x#1,#2,#3\@nil{% \def\pst@tempLeft{#1}% \def\pst@tempRight{#2}} %% #1 : x value %% #2 : delta x or x0,x1 %% #3 : function \def\psplotTangent{\@ifnextchar*{\@startrue\psplotTangent@i}{\@starfalse\psplotTangent@i*}} \def\psplotTangent@i*{\@ifnextchar[{\psplotTangent@ii}{\psplotTangent@ii[]}} \def\psplotTangent@ii[#1]#2#3#4{% \pst@killglue \expandafter\psplotTangent@x#3,,\@nil\relax \begingroup \ifx\relax#1\relax\else\psset{linestyle=solid,#1}\fi \ifx\psk@Derive\@empty\ifPst@algebraic\def\psk@Derive{NOT@EMPTY}\fi\fi %%dr 0606 hv 1003 \pst@addarrowdef \addto@pscode{ /F@pstplot \ifPst@algebraic (#4) tx@addDict begin AlgParser end cvx \else { #4 } \fi def % define function \ifx\psk@Derive\@empty\else \ifx\psk@Derive\@NOTEMPTY\else %%dr 0606 /FDer@pstplot % do we have a derivation defined? \ifPst@algebraic (\psk@Derive) tx@addDict begin AlgParser end cvx \else { \psk@Derive } \fi def % define derivation \fi %%dr 0606 \fi% /@parametric false def %%dr 0606 % first we calculate the origin #2 dup /x ED /t ED tx@addDict begin mark F@pstplot end counttomark 1 gt % test, if we have parametricplot { /y ED /x ED /@parametric true def } % if yes, then we have 2 values %%dr 0606 { \ifPst@polarplot x \ifPst@algebraic RadtoDeg \fi PtoC /y ED /x ED \else /y ED \fi } ifelse cleartomark \ifx\psk@Derive\@NOTEMPTY %%begin dr 0606 % %% algebraic we can use the derivative machine /FDer@pstplot (#4) @parametric { (t) } { (x) } ifelse tx@Derive begin Derive end tx@addDict begin AlgParser end cvx def \fi %%end dr 0606 x \pst@number\psxunit mul y \pst@number\psyunit mul translate % define the temporary origin % now we calculate the slope of the tangent \ifx\psk@Derive\@empty % de we have a derivation defined? #2 abs 1.0e-6 lt % no, we choose secant for the tangent { #2 0.0005 add dup /x ED /t ED tx@addDict begin mark F@pstplot end counttomark 1 gt % test, if we have parametricplot { /y2 ED /x2 ED } % we have 2 values { \ifPst@polarplot dup x \ifPst@algebraic RadtoDeg \fi cos mul /x2 ED x \ifPst@algebraic RadtoDeg \fi sin mul \else /x2 x def \fi /y2 ED } ifelse cleartomark % delete the mark #2 0.0005 sub dup /x ED /t ED tx@addDict begin mark F@pstplot end counttomark 1 gt % test, if we have parametricplot { /y1 ED /x1 ED } { \ifPst@polarplot dup x \ifPst@algebraic RadtoDeg \fi cos mul /x1 ED x \ifPst@algebraic RadtoDeg \fi sin mul \else /x1 x def \fi /y1 ED } ifelse cleartomark y2 y1 sub x2 x1 sub } % dy dx { % > 1.0e-06 #2 1.0005 mul dup /x ED /t ED tx@addDict begin mark F@pstplot end counttomark 1 gt % test, if we have parametricplot { /y2 ED /x2 ED } % we have 2 values { \ifPst@polarplot dup x \ifPst@algebraic RadtoDeg \fi cos mul /x2 ED x \ifPst@algebraic RadtoDeg \fi sin mul \else /x2 x def \fi /y2 ED } ifelse cleartomark #2 .9995 mul dup /x ED /t ED tx@addDict begin mark F@pstplot end counttomark 1 gt % test, if we have parametricplot { /y1 ED /x1 ED } % we have 2 values { \ifPst@polarplot dup x \ifPst@algebraic RadtoDeg \fi cos mul /x1 ED x \ifPst@algebraic RadtoDeg \fi sin mul \else /x1 x def \fi /y1 ED } ifelse cleartomark y2 y1 sub \pst@number\psyunit mul x2 x1 sub \pst@number\psxunit mul } ifelse atan % atan(dy dx), we have the slope angle of the secant \ifPST@Tnormal 90 add \fi \else % there is a derivation defined #2 dup /x ED /t ED tx@addDict begin mark FDer@pstplot end counttomark 1 gt % test, if we have parametricplot { /y ED /x ED } { \ifPst@polarplot /Fphi ED % the value F'(phi) tx@addDict begin F@pstplot end x \ifPst@algebraic RadtoDeg \fi PtoC /y0 ED /x0 ED % the x y values x \ifPst@algebraic RadtoDeg \fi sin Fphi mul x0 add /y ED x \ifPst@algebraic RadtoDeg \fi cos Fphi mul y0 sub /x ED \else /y ED /x 1 def \fi } ifelse cleartomark y \pst@number\psyunit mul x \pst@number\psxunit mul Atan \ifPST@Tnormal 90 add \fi % y ATAN1 % we have the slope angle of the tangent. ATAN is defined int the pstricks.pro, patch 6 \fi dup % to prevent rounding errors use original value cvi 180 mod 90 gt { 180 sub } if % -90 <= angle <= 90 rotate % rotate, depending to the origin /Lineto /lineto load def % the pro file needs /Lineto \pst@cp % kill the currentpoint, if any [ % start array of points \ifPST@Tnormal 0 \psk@nodesepA add 0 % moveto #3 \pst@number\psxunit mul \psk@nodesepB sub 0 % y \pst@number\psyunit mul x \pst@number\psxunit mul Atan cos div \pst@number\psxunit mul 0 % lineto \else % points are in reverse order ... \ifx\pst@tempRight\@empty #3 \psk@nodesepA \pst@number\psxunit div sub \else \pst@tempRight\space \fi \pst@number\psxunit mul 0 % moveto \if@star 0 \else \ifx\pst@tempRight\@empty #3 \psk@nodesepB \pst@number\psxunit div sub neg \else \pst@tempLeft\space \fi \pst@number\psxunit mul \fi 0 % lineto \fi \pst@usecolor\pslinecolor false % don't show the points \tx@Line \ifx\pslinestyle\@none\else \pst@number\pslinewidth SLW \tx@setStrokeTransparency \@nameuse{psls@\pslinestyle} \fi \ifshowpoints % show the points? gsave \psk@dotsize \@nameuse{psds@\psk@dotstyle} 0 0 Dot grestore \fi }% \use@pscode %% ---- only for algebraic: 3 Nodes for Origin, Tangent-End and Normal-End --- 31.05.2014 TS \iffalse \ifPst@algebraic \pst@Verb{ #2 /x ED % x-Wert wird definiert /Function (#4) tx@AlgToPs begin AlgToPs end cvx def /mt (#4) (x) tx@Derive begin Derive end tx@addDict begin AlgParser end cvx def % mt ist die Steigung an der Stelle x = #2 x Function /y ED % y = f(x=#2) ist der Funktionswert an der Stelle x = #2 #3 mt 1 Atan cos dup mul mt 1 Atan sin \pst@number\psyunit mul \pst@number\psxunit div dup mul add sqrt div /ldt ED mt 0 ge { ldt mt 1 Atan cos mul /Dx ED ldt mt 1 Atan sin mul /Dy ED } {ldt mt 1 Atan cos mul neg /Dx ED ldt mt 1 Atan sin mul neg /Dy ED } ifelse x Dx add /xt ED y Dy add /yt ED x Dy \pst@number\psyunit mul \pst@number\psxunit div add /xn ED y Dx \pst@number\psxunit mul \pst@number\psyunit div sub /yn ED }% \pnode(! x y){OCurve}% \pnode(! xt yt){ETangent}% \pnode(! xn yn){ENormal}% \psLNode(ENormal)(OCurve){2}{ENormalE}% \psLNode(ETangent)(OCurve){2}{ETangentE}% \fi \fi \endgroup \@starfalse \ignorespaces} % %% #1-#2 x range %% #3 initial value of y (which is a vector) y(0) y'(0) y''(0) ... %% #4 value of the derivative (y and t can be used) % \define@boolkey[psset]{pstricks-add}[Pst@]{GetFinalState}[true]{} \define@key[psset]{pstricks-add}{filename}{\def\psk@filename{#1}}% \define@boolkey[psset]{pstricks-add}[Pst@]{saveData}[true]{} % \ifPst@saveData \psset[pstricks-add]{GetFinalState=false,saveData=false,filename=PSTdata} % \def\Begin@SaveFinalState{ end /PST@beginspecial /@beginspecial load def /PST@endspecial /@endspecial load def /PST@setspecial /@setspecial load def /@beginspecial {} def /@endspecial{} def /@setspecial {} def tx@Dict begin } \newif\ifPst@BeginSaveFinalState \Pst@BeginSaveFinalStatefalse \def\BeginSaveFinalState{\Pst@BeginSaveFinalStatetrue} \def\End@SaveFinalState{ /@beginspecial /PST@beginspecial load def /@endspecial /PST@endspecial load def /@setspecial /PST@setspecial load def } \def\EndSaveFinalState{\pstverb{\End@SaveFinalState}} \def\psplotDiffEqn{\def\pst@par{}\pst@object{psplotDiffEqn}}% initial code by Dominique 2005-05-21 \def\psplotDiffEqn@i#1#2#3#4{% \addbefore@par{xStart=#1}% \pst@killglue% \begingroup% \use@par% \@nameuse{beginplot@\psplotstyle}% \addto@pscode{% \ifPst@BeginSaveFinalState \Begin@SaveFinalState \fi \ifPst@saveData /Pst@data (\psk@filename) (w) file def \fi /x #1 def % first value /x1 #2 def % last value \ifPst@GetFinalState \Begin@SaveFinalState /y FinalState def \else /y [ #3 ] def \fi % values for t=0 /ylength y length def % number of elements in #3 /addvect { 1 1 ylength { /i exch def ylength i sub 2 add -1 roll add ylength 2 mul i sub 1 roll } for } def /dx x1 x sub \psk@plotpoints\space div def /mulvect { ylength exch 1 index { dup 4 -1 roll mul 2 index 2 add 1 roll } repeat pop pop } def /divvect { ylength exch 1 index { dup 4 -1 roll exch div 2 index 2 add 1 roll } repeat pop pop } def /k0 0 def /k1 0 def /k2 0 def /k3 0 def \ifPst@algebraic /F@pstplot (#4) tx@addDict begin AlgParser end cvx def \fi /Func { \ifPst@algebraic F@pstplot ylength array astore \else \ifPst@buildvector\else y aload pop \fi #4 \ifPst@buildvector\else ylength array astore \fi \fi } def \ifx\psk@method\@adams /F1 0 def /F2 0 def /F3 0 def /F4 0 def /F5 0 def /F6 0 def /INIT 1 def \fi \ifx\psk@method\@empty\else \ifx\psk@method\@varrkiv %% RUNGE-KUTTA method with var step algorithm /VarStep false def /VarStepRatio 1 def /RK { /k0 Func { dx mul } forall ylength array astore def %% y dup aload pop k0 { 2 div } forall addvect ylength array astore /y exch def % x dup dx 2 div add /x exch def %% y x /k1 Func { dx mul } forall ylength array astore def %% y x exch dup aload pop k1 { 2 div } forall addvect y astore pop %% x y /k2 Func { dx mul } forall ylength array astore def %% x y dup aload pop k2 aload pop addvect y astore pop exch dup dx add /x exch def %% y x /k3 Func { dx mul } forall ylength array astore def %% y x /x exch def %% y dup aload pop k0 aload pop k1 aload pop k2 aload pop addvect 2 mulvect addvect k3 aload pop addvect 6 divvect addvect y astore } def /VARRK { VarStep %{ /dx dx \psk@varstepincrease\space mul def /VarStep false def } if { /dx dx VarStepRatio mul def /VarStep false def } if x dx add x1 gt { /dx x1 x sub def } if %{ /dx dx \psk@varstepdecrease\space div def } ifelse %% we compute y(x+dx) from y(x) using RK4 RK %% y(x) y(x+dx) exch /y exch def /dx dx 2 div def { %% we compute y(x+dx/2) from y(x) using RK4 y RK %% y(x+dx) y(x+dx/2) %% then y(x+dx) from y(x+dx/2) using RK4 /y exch def y RK %% y(x+dx) y(x) y(x+dx/2) y(x+dx) dup aload pop 4 ylength add -1 roll { -1 mul } forall addvect 0 ylength { exch abs 2 copy lt { exch } if pop } repeat 0 3 -1 roll {abs 2 copy lt { exch } if pop } forall dup 1e-6 lt { pop } { div } ifelse /dx dx 2 mul def dup \psk@varsteptol\space lt %{ \psk@varsteptol\space div .1 lt { /VarStep true def } if pop exit } if %pop /dx dx 4 div def exch /y exch def } loop { .001 div dup .1 lt { dup 1e-6 lt { pop 3 } { log neg } ifelse /VarStepRatio exch def /VarStep true def } { pop } ifelse pop exit } if pop /dx dx 4 div def exch /y exch def } loop } def \else %% RUNGE-KUTTA & ADAMS methods /RK { /k0 Func { dx mul } forall ylength array astore def %% y dup aload pop k0 { 2 div } forall addvect ylength array astore /y exch def % x dup dx 2 div add /x exch def %% y x /k1 Func { dx mul } forall ylength array astore def %% y x exch dup aload pop k1 { 2 div } forall addvect y astore pop %% x y /k2 Func { dx mul } forall ylength array astore def %% x y dup aload pop k2 aload pop addvect y astore pop exch dup dx add /x exch def %% y x /k3 Func { dx mul } forall ylength array astore def %% y x /x exch def %% y dup aload pop k0 aload pop k1 aload pop k2 aload pop addvect 2 mulvect addvect k3 aload pop addvect 6 divvect addvect y astore pop } def \ifx\psk@method\@adams /ADAMS { \ifcase\psk@adamsorder \errmessage{pstricks-add error: no order 0th for adams method (see user's manual)} \or\errmessage{pstricks-add error: no order 1st for adams method (see user's manual)} \or\errmessage{pstricks-add error: no order 2nd for adams method (see user's manual)} \or\errmessage{pstricks-add error: no order 3rd for adams method (see user's manual)} \or %% ORDRE 4 F4 aload pop 55 mulvect F3 aload pop -59 mulvect addvect F2 aload pop 37 mulvect addvect F1 aload pop -9 mulvect addvect dx mulvect 24 divvect \or %% ORDRE 5 F5 aload pop 1901 mulvect F4 aload pop -2774 mulvect addvect F3 aload pop 2616 mulvect addvect F2 aload pop -1274 mulvect addvect F1 aload pop 251 mulvect addvect dx mulvect 720 divvect \or %% ORDRE 6 F6 aload pop 4277 mulvect F5 aload pop -7923 mulvect addvect F4 aload pop 9982 mulvect addvect F3 aload pop -7298 mulvect addvect F2 aload pop 2877 mulvect addvect F1 aload pop -475 mulvect addvect dx mulvect 1440 divvect \fi y aload pop addvect ylength array astore /y exch def } def \fi \fi \fi /xy { \ifx\psk@plotfuncx\@empty \ifx\psk@whichabs\@empty x \else y \psk@whichabs\space get \fi \else \psk@plotfuncx\space \fi \pst@number\psxunit mul y \ifx\psk@method\@empty %% EULER method /y Func { dx mul } forall y aload pop addvect ylength array astore def \else% \ifx\psk@method\@varrkiv %% RUNGE-KUTTA method VARRK \else\ifx\psk@method\@rkiv %% RUNGE-KUTTA method RK \else /F1 F2 def /F2 F3 def /F3 F4 def /F4 %% ADAMS method \ifcase\psk@adamsorder\or\or\or\or %% ORDRE 4 Func def \or %% ORDRE 5 F5 def /F5 Func def \or %% ORDRE 6 F5 def /F5 F6 def /F6 Func def \fi INIT \psk@adamsorder\space lt { RK /INIT INIT 1 add def } { ADAMS } ifelse \fi\fi \fi \ifx\psk@plotfuncy\@empty \ifx\psk@whichord\@empty 0 \else \psk@whichord\space \fi get % \else \psk@plotfuncy\space \fi \pst@number\psyunit mul % Pst@data (\string\[) writestring \ifPst@saveData 2 copy \pst@number\psyunit div exch \pst@number\psxunit div 20 string cvs Pst@data exch writestring Pst@data (\space) writestring 20 string cvs Pst@data exch writestring Pst@data (\string\n) writestring \fi } def }% \gdef\psplot@init{}% \@pstfalse \@nameuse{testqp@\psplotstyle}% \if@pst\psplot@ii\else\psplot@iii\fi % \addto@pscode{\ifPst@saveData Pst@data closefile \fi} \endgroup% \ignorespaces% } % % \def\psGTriangle{\def\pst@par{}\pst@object{psGTriangle}} \def\psGTriangle@i(#1)(#2)(#3)#4#5#6{{% \begin@ClosedObj \pst@getcoor{#1}\pst@tempA % A: "rgb xr xg xb" or "gray xg" \pst@getcoor{#2}\pst@tempB % B \pst@getcoor{#3}\pst@tempC % C \pst@getcolor{#4}\pst@colorA \pst@getcolor{#5}\pst@colorB \pst@getcolor{#6}\pst@colorC \addto@pscode{% \pst@tempC % C \pst@tempB % B \psk@gangle % rotating angle \pst@tempA % A, temporary origin % /rgb {} def % /gray {} def % /rg /setrgbcolor load def % /RG /setrgbcolor load def % we use RGB [ \psgetRGBColorValues{\pst@colorC} ] aload length 1 eq { dup dup } if 3 array astore % gray -> rgb [ \psgetRGBColorValues{\pst@colorB} ] aload length 1 eq { dup dup } if 3 array astore [ \psgetRGBColorValues{\pst@colorA} ] aload length 1 eq { dup dup } if 3 array astore tx@addDict begin GTriangle end % PS part }% \if@star\pspolygon[fillstyle=none](#1)(#2)(#3)\fi% draw borderline \def\pst@linetype{2}% \end@ClosedObj% }\ignorespaces} % \def\psdice{\def\pst@par{}\pst@object{psdice}} \def\psdice@i#1{{% \pst@killglue% \addbefore@par{framearc=0.3,linewidth=1pt}% \use@par% \psframe(-0.5,-0.5)(0.5,0.5)% \ifodd#1 \qdisk(0,0){0.1\psunit}\else\qdisk(-0.3,-0.3){0.1\psunit}\qdisk(0.3,0.3){0.1\psunit}\fi \ifcase#1% \or\or\or\qdisk(-0.3,-0.3){0.1\psunit}\qdisk(0.3,0.3){0.1\psunit}% 3 \or\qdisk(-0.3,0.3){0.1\psunit}\qdisk(0.3,-0.3){0.1\psunit}% 4 \or\qdisk(-0.3,-0.3){0.1\psunit}\qdisk(0.3,0.3){0.1\psunit}% 5 \qdisk(-0.3,0.3){0.1\psunit}\qdisk(0.3,-0.3){0.1\psunit} \or\qdisk(-0.3,0.3){0.1\psunit}\qdisk(0.3,-0.3){0.1\psunit}% 6 \qdisk(-0.3,0){0.1\psunit}\qdisk(0.3,0){0.1\psunit}% \fi% \ignorespaces% }} % % the datafile must be a matrix with % /dotmatrix [ % ..... % ..... % ] def % \def\pswavelengthToGRAY{ tx@addDict begin wavelengthToGRAY end } \def\pswavelengthToRGB{ tx@addDict begin wavelengthToRGB Red Green Blue end } % \define@key[psset]{pstricks-add}{Xoffset}[0pt]{\pst@getlength{#1}\psk@Xoffset} \define@key[psset]{pstricks-add}{Yoffset}[0pt]{\pst@getlength{#1}\psk@Yoffset} \define@key[psset]{pstricks-add}{XYoffset}[0pt]{\pst@getlength{#1}\psk@Xoffset\let\psk@Yoffset\psk@Xoffset} \psset[pstricks-add]{XYoffset=0pt} \define@boolkey[psset]{pstricks-add}[Pst@]{PixelPlot}[true]{} % \ifPst@saveData \define@key[psset]{pstricks-add}{colorType}[0]{\def\psk@colorType{#1}} \define@key[psset]{pstricks-add}{colorTypeDef}[{}]{\def\psk@colorTypeDef{#1\space}} \psset[pstricks-add]{PixelPlot=false,colorType=0,colorTypeDef={}} % 0-> two color mode 1->wavelength mode (400..700nm) % 0-> two color mode % 1-> wavelength mode (400..700nm) % 2-> wavelength mode inverse % 3-> gray color mode % 4-> gray color mode invers % 5-> own color definition % \def\psMatrixPlot{\def\pst@par{}\pst@object{psMatrixPlot}} \def\psMatrixPlot@i#1#2#3{% \pst@killglue% \addbefore@par{xStep=1,yStep=1}% \begin@SpecialObj% \addto@pscode{ 20 dict begin (#3) run % load the data file /Min 0 def /Max 0 def dotmatrix { dup Min lt { /Min ED } { dup Max gt { /Max ED } { pop } ifelse } ifelse } forall /dMaxMin Max Min sub def \psk@dotsize % defines /DS ... def \psk@Xoffset\space \psk@Yoffset\space translate \ifPst@PixelPlot\else\@nameuse{psds@\psk@dotstyle}\fi /n 0 def % index for element 1 1 #1 { % the y loop (outer one) /y exch def % save y 1 1 #2 { % the x loop (inner one) /x exch def % save x dotmatrix n get % get value from matrix \ifcase\psk@colorType dup 0 gt { % test if > 0 \or Min sub dMaxMin div 300 mul 400 add \pswavelengthToRGB setrgbcolor \or Min sub dMaxMin div neg 1 add 300 mul 400 add \pswavelengthToRGB setrgbcolor \or Min sub dMaxMin div neg 1 add 300 mul 400 add \pswavelengthToGRAY setgray \or Min sub dMaxMin div neg 1 add 300 mul 400 add \pswavelengthToGRAY neg 1 add setgray \or currentdict /colorTypeDef known { colorTypeDef } { \psk@colorTypeDef } ifelse \fi x \psk@xStep\space mul \pst@number\psxunit mul \ifPst@ChangeOrder #1 y sub 1 add \else y \fi \psk@yStep\space mul \pst@number\psyunit mul \ifPst@PixelPlot 1 DS mul 0 360 arc fill \else Dot \fi \ifcase\psk@colorType } { pop } ifelse \fi /n n 1 add def } for } for end }% \end@SpecialObj% \ignorespaces% } % \newdimen\chart@ColorIndex \newdimen\chart@ColorStep \newdimen\pst@chartHeight \newdimen\pst@chartStackDepth \newdimen\pst@chartStackWidth \newcount\chart@Toggle \newif\if@chartSep \newif\if@chartUserColor % \define@key[psset]{pstricks-add}{chartStyle}{\def\psk@chartStyle{#1}} \psset[pstricks-add]{chartStyle=pie}% p)ie P)ie-3d-view h)istogram H)istogram-3dview % \define@key[psset]{pstricks-add}{chartColor}{\pst@expandafter\psk@@chartColor{#1}\@nil} \def\psk@@chartColor#1#2\@nil{% \ifx#1r\def\psk@chartColor{2}\else% \ifx#1c\def\psk@chartColor{380}\else\def\psk@chartColor{0}\fi\fi} \psset[pstricks-add]{chartColor=gray}% gray, color, randomColor % \define@key[psset]{pstricks-add}{chartSep}{\pst@getlength{#1}\psk@chartSep} \define@key[psset]{pstricks-add}{chartStack}{\pst@getint{#1}\psk@chartStack} \define@key[psset]{pstricks-add}{chartStackDepth}{\pssetylength\pst@chartStackDepth{#1}} \define@key[psset]{pstricks-add}{chartStackWidth}{\pssetxlength\pst@chartStackWidth{#1}} \define@key[psset]{pstricks-add}{chartHeight}{\pssetylength\pst@chartHeight{#1}} \psset[pstricks-add]{chartSep=10pt,chartStack=0,chartStackDepth=2cm,chartStackWidth=2cm,% chartHeight=5mm} % \define@boolkey[psset]{pstricks-add}[Pst@]{uselinecolor}[true]{} \psset[pstricks-add]{uselinecolor=false} % \define@key[psset]{pstricks-add}{userColor}{% \chart@Toggle=0\relax% \def\chart@option{#1}% \ifx\chart@option\@empty\@chartUserColorfalse% \else% \@chartUserColortrue% \expandafter\psk@@chartUserColor#1,,\@nil% \fi} \def\psk@@chartUserColor#1,#2,#3\@nil{% \advance\chart@Toggle by \@ne% \xglobal\colorlet{chartFillColor\the\chart@Toggle}{#1}% \def\chart@option{#2}% \ifx\chart@option\@empty\else\psk@@chartUserColor#2,#3,\@nil\fi}% \psset[pstricks-add]{userColor={}} \define@key[psset]{pstricks-add}{chartNodeI}{\def\psk@chartNodeI{#1}} \define@key[psset]{pstricks-add}{chartNodeO}{\def\psk@chartNodeO{#1}} \psset[pstricks-add]{chartNodeI=0.75,chartNodeO=1.5} % \def\psChart{\pst@object{psChart}} \def\psChart@i#1#2#3{% % #1:values #2:separated charts % #3 radius->pie; max height->histogram \pst@killglue% \global\pssetylength\pst@chartHeight{#3}% \global\let\pst@chartRadius\pst@chartHeight% \begingroup \edef\psk@chartValues{#1}% \def\psk@chartSepValues{#2}% only valid for a pie chart \pst@dimm=\z@% sum of all entries (for a pie) \pst@cnta=1\relax% number of entries \pst@dimn=\z@% greatest entry \psforeach{\chart@tempA}{#1}{% \global\advance\pst@cnta by \@ne% % no of entries \global\advance\pst@dimm by \chart@tempA\p@% % sum of all entries \pst@dima=\chart@tempA\p@% \ifdim\pst@dima>\pst@dimn\global\pst@dimn=\pst@dima\fi% }% \addbefore@par{linejoin=2,dimen=outer}% \begin@SpecialObj% \ifnum\psk@chartColor>0\relax% \chart@ColorStep=400\p@\else\chart@ColorStep=\p@\fi % the "numerical color" \divide\chart@ColorStep by \pst@cnta% % step =1/no or 400/no \chart@ColorIndex=\psk@chartColor\p@% % the start color (gray or wave) \@nameuse{pscs@\psk@chartStyle}% \end@SpecialObj% \endgroup% \ignorespaces% } % \def\pscs@pie{% \degrees[\pst@number\pst@dimm]% % instead of 360 degrees \def\chart@alpha{0}% \pst@dimm=\z@\pst@dimn=\z@\pst@dimo=\z@\pst@cnta=0\relax% \global\chart@Toggle=1\relax% \ifpsshadow% create shadow first \psforeach{\chart@tempA}{\psk@chartValues}{% \global\advance\pst@dimm by \chart@tempA\p@% \global\advance\pst@dimn by \chart@alpha\p@% \global\advance\pst@cnta by \@ne% \pst@dimo=0.5\pst@dimn\advance\pst@dimo by 0.5\pst@dimm% half angle of the chart \global\@chartSepfalse% \if$\psk@chartSepValues$\else% \psforeach{\chart@tempC}{\psk@chartSepValues}{\ifnum\chart@tempC=\the\pst@cnta\relax\global\@chartSeptrue\fi}% \fi% \if@chartSep% \pswedge(\psk@chartSep\p@;\pst@number\pst@dimo){\pst@chartRadius}{\pst@number\pst@dimn}{\pst@number\pst@dimm}% \else% \pswedge(0,0){\pst@chartRadius}{\pst@number\pst@dimn}{\pst@number\pst@dimm}% \fi% \global\let\chart@alpha\chart@tempA% }% \psshadowfalse% \fi% \def\chart@alpha{0}% \pst@dimm=0pt\pst@dimn=0pt\pst@dimo=0pt\pst@cnta=0\relax% \psForeach{\chart@tempA}{\psk@chartValues}{% \global\advance\pst@dimm by \chart@tempA\p@% \global\advance\pst@dimn by \chart@alpha\p@% \def\pst@tempB{\pst@number\chart@ColorIndex}% % \psDEBUG[psChart:wave:color]{\pst@tempB}% \global\advance\pst@cnta by \@ne% \if@chartUserColor\else% \def\chart@FillColor{chartFillColor\the\pst@cnta}% \ifnum\psk@chartColor>0\relax% \xglobal\definecolor{\chart@FillColor}{wave}{\pst@tempB}% \else\xglobal\definecolor{\chart@FillColor}{gray}{\pst@tempB}\fi% \fi% \pst@dimo=0.5\pst@dimn\advance\pst@dimo by 0.5\pst@dimm% half angle of the chart \global\@chartSepfalse% \if$\psk@chartSepValues$\else% \psForeach{\chart@tempC}{\psk@chartSepValues}{\ifnum\chart@tempC=\the\pst@cnta\relax\global\@chartSeptrue\fi}% \fi% \if@chartSep \ifPst@uselinecolor \pswedge[linecolor=\pslinecolor,fillstyle=solid,fillcolor={chartFillColor\the\pst@cnta}]% (\psk@chartSep\p@;\pst@number\pst@dimo){\pst@chartRadius}{\pst@number\pst@dimn}{\pst@number\pst@dimm}% \else \pswedge*[linecolor={chartFillColor\the\pst@cnta}]% (\psk@chartSep\p@;\pst@number\pst@dimo){\pst@chartRadius}{\pst@number\pst@dimn}{\pst@number\pst@dimm}% \fi \pst@dima=\pst@chartRadius\advance\pst@dima by \psk@chartSep\p@% \pnode(\pst@dima;\pst@number\pst@dimo){psChart\the\pst@cnta}% \pst@dimb=\psk@chartNodeI\pst@dima% \pst@dimc=\psk@chartNodeO\pst@dima% \pnode(\pst@dimb;\pst@number\pst@dimo){psChartI\the\pst@cnta}% \pnode(\pst@dimc;\pst@number\pst@dimo){psChartO\the\pst@cnta}% \else% \ifPst@uselinecolor \pswedge[linecolor=\pslinecolor,fillstyle=solid,fillcolor={chartFillColor\the\pst@cnta}](0,0)% {\pst@chartRadius}{\pst@number\pst@dimn}{\pst@number\pst@dimm}% \else \pswedge*[linecolor={chartFillColor\the\pst@cnta}](0,0)% {\pst@chartRadius}{\pst@number\pst@dimn}{\pst@number\pst@dimm}% \fi \pnode(\pst@chartRadius;\pst@number\pst@dimo){psChart\the\pst@cnta}% \pst@dima=\pst@chartRadius% \pst@dimb=\psk@chartNodeI\pst@dima% \pst@dimc=\psk@chartNodeO\pst@dima% \pnode(\pst@dimb;\pst@number\pst@dimo){psChartI\the\pst@cnta}% \pnode(\pst@dimc;\pst@number\pst@dimo){psChartO\the\pst@cnta}% \fi% \global\let\chart@alpha\chart@tempA% \global\advance\chart@Toggle by \@ne% \ifnum\chart@Toggle<3\relax% \global\advance\chart@ColorIndex by 2\chart@ColorStep% \else% \global\chart@Toggle=0% \global\advance\chart@ColorIndex by -\chart@ColorStep% \fi% }% end foreach \ignorespaces% } % \def\pscs@histogram{% \def\chart@maxValue{\pst@number\pst@dimn}% max of the data \pst@@divide\pst@dimn\pst@chartHeight% maxValue/maxHeight \psDEBUG[pscs@histogram]{chart@maxValue=\chart@maxValue} \psDEBUG[pscs@histogram]{(maxValue/maxHeight)pst@dimg=\pst@number\pst@dimg} \psDEBUG[pscs@histogram]{pst@chartHeight=\the\pst@chartHeight} \pst@dimo=28.46\pst@dimg \edef\pst@chartUnit{\pst@number\pst@dimo} % \psaxes[axesstyle=frame, % dy=1cm,Dy=\pst@number\pst@dimo](\the\pst@cnta,\the\pst@chartHeight) \pst@dimm=0pt\pst@dimn=0pt\pst@dimo=0pt\pst@cnta=0% \global\chart@Toggle=1 \psforeach{\chart@tempA}{\psk@chartValues}{% \global\advance\pst@dimm by \chart@tempA pt% \def\pst@tempB{\pst@number\chart@ColorIndex}% \psDEBUG[psChart:wave:color]{\pst@tempB}% \global\advance\pst@cnta by \@ne% \if@chartUserColor\else \def\chart@FillColor{chartFillColor\the\pst@cnta} \ifnum\psk@chartColor>0 \xglobal\definecolor{\chart@FillColor}{wave}{\pst@tempB}% \else\xglobal\definecolor{\chart@FillColor}{gray}{\pst@tempB}\fi% \fi \psframe[linecolor={chartFillColor\the\pst@cnta},fillstyle=solid,fillcolor={chartFillColor\the\pst@cnta}]% (!\the\pst@cnta\space \psk@chartSep\space 28.46 div sub 0) (!\the\pst@cnta\space \psk@chartSep\space 28.46 div add \chart@tempA\space \pst@chartUnit\space div) \pnode(!\the\pst@cnta\space 0){psChart\the\pst@cnta}% \pnode(!\the\pst@cnta\space \chart@tempA\space 2 div \pst@chartUnit\space div){psChartM\the\pst@cnta}% \pnode(!\the\pst@cnta\space \chart@tempA\space \pst@chartUnit\space div){psChartT\the\pst@cnta}% \global\advance\chart@Toggle by \@ne \ifnum\chart@Toggle<3 \global\advance\chart@ColorIndex by 2\chart@ColorStep \else \global\chart@Toggle=0 \global\advance\chart@ColorIndex by -\chart@ColorStep% \fi% }% end foreach } % \def\pst@stackList{} \def\addbefore@stackList#1{% \ifx\pst@stackList\@empty \xdef\pst@stackList{#1}% \else \toks@{#1}% \pst@toks\expandafter{\pst@stackList}% \xdef\pst@stackList{\the\toks@,\the\pst@toks}% \fi% } % \def\pscs@Histogram{% \psDEBUG[pscs@Histogram]{psk@chartStack=\psk@chartStack}% \def\chart@maxValue{\pst@number\pst@dimn}% max of the data \pst@@divide\pst@dimn\pst@chartHeight% maxValue/maxHeight \psDEBUG[pscs@Histogram]{chart@maxValue=\chart@maxValue}% \psDEBUG[pscs@Histogram]{(maxValue/maxHeight)pst@dimg=\pst@number\pst@dimg}% \psDEBUG[pscs@Histogram]{pst@chartHeight=\the\pst@chartHeight}% \pst@dimo=28.46\pst@dimg% \edef\pst@chartUnit{\pst@number\pst@dimo}% % \psaxes[axesstyle=frame, % dy=1cm,Dy=\pst@number\pst@dimo](\the\pst@cnta,\the\pst@chartHeight) \pst@dimm=0pt\pst@dimn=0pt\pst@dimo=0pt\pst@cnta=0% \global\chart@Toggle=1 % for color toggling \pst@cntn=0 % stacked step \pst@cnto=0 % for a stacked view \pst@cntp=\psk@chartStack % for a stacked view \def\pst@stackList{} \psDEBUG[pscs@Histogram]{psk@chartStack=\the\pst@cntp}% \psforeach{\chart@tempA}{\psk@chartValues}{% the loop \ifnum\pst@cntp>0 % stacked version? \advance\pst@cnto by \@ne % increase \psDEBUG[pscs@Histogram]{chart@tempA=\chart@tempA}% \expandafter\addbefore@stackList\expandafter{\chart@tempA}% \psDEBUG[pscs@Histogram]{stack list=\pst@stackList}% \ifnum\pst@cnto=\pst@cntp % draw? \pst@cnto=\psk@chartStack\advance\pst@cnto by \m@ne \psforeach{\chart@tempB}{\pst@stackList}{% the stack loop \global\pst@cnta=\pst@cntn % we do not need the value \psDEBUG[pscs@Histogram]{pst@cnto=\the\pst@cnto}% \psDEBUG[pscs@Histogram]{pst@chartStackDepth=\the\pst@chartStackDepth}% \psDEBUG[pscs@Histogram]{pst@chartStackWidth=\the\pst@chartStackWidth}% \edef\pst@tempA{\the\pst@cnto}% \psDEBUG[pscs@Histogram]{pst@tempA=\pst@tempA}% \ifnum\pst@cnto>0 \pst@dima=\pst@chartStackDepth% \pst@dimb=\pst@chartStackWidth% \divide \pst@dima by \pst@tempA% \divide \pst@dimb by \pst@tempA% \else\pst@dima=\z@ \pst@dimb=\z@% \fi% \rput(\the\pst@dima, \the\pst@dimb){\pscs@Histogram@i{\chart@tempB}} \advance\pst@cnto by \m@ne % decrease stack counter }% \advance\pst@cntn by \tw@ % increase \def\pst@stackList{}% reset stack list \pst@cnto=0 % reset stack counter \fi% \else% \pscs@Histogram@i{\chart@tempA}% non stacked version \fi% }% end foreach } % \def\pscs@Histogram@i#1{% draw the 3d-like bar \def\pst@tempB{\pst@number\chart@ColorIndex}% \global\advance\pst@cnta by \@ne% \if@chartUserColor\else \def\chart@FillColor{chartFillColor\the\pst@cnta} \ifnum\psk@chartColor>0 \xglobal\definecolor{\chart@FillColor}{wave}{\pst@tempB}% \else\xglobal\definecolor{\chart@FillColor}{gray}{\pst@tempB}\fi% \fi \pspolygon[fillstyle=solid,fillcolor={chartFillColor\the\pst@cnta}]% (!\the\pst@cnta\space \psk@chartSep\space 28.46 div sub 0)% ll (!\the\pst@cnta\space \psk@chartSep\space 28.46 div add 0)% lr (!\the\pst@cnta\space \psk@chartSep\space 28.46 div 1.5 mul add \psk@chartSep\space 56.92 div)% 'lr (!\the\pst@cnta\space \psk@chartSep\space 28.46 div 1.5 mul add \psk@chartSep\space 56.92 div #1 \pst@chartUnit\space div add )% 'ur (!\the\pst@cnta\space \psk@chartSep\space 56.92 div sub \psk@chartSep\space 56.92 div #1 \pst@chartUnit\space div add )% 'ul (!\the\pst@cnta\space \psk@chartSep\space 28.46 div sub #1 \pst@chartUnit\space div)%ul \psline% (!\the\pst@cnta\space \psk@chartSep\space 28.46 div add 0)% lr (!\the\pst@cnta\space \psk@chartSep\space 28.46 div add #1 \pst@chartUnit\space div) (!\the\pst@cnta\space \psk@chartSep\space 28.46 div sub #1 \pst@chartUnit\space div)%ul \psline% (!\the\pst@cnta\space \psk@chartSep\space 28.46 div add #1 \pst@chartUnit\space div) (!\the\pst@cnta\space \psk@chartSep\space 28.46 div 1.5 mul add \psk@chartSep\space 56.92 div #1 \pst@chartUnit\space div add )% 'ur \pnode(!\the\pst@cnta\space 0){psChart\the\pst@cnta}% \pnode(!\the\pst@cnta\space #1 2 div \pst@chartUnit\space div){psChartM\the\pst@cnta}% \pnode(!\the\pst@cnta\space #1 \pst@chartUnit\space div){psChartT\the\pst@cnta}% \global\advance\chart@Toggle by \@ne \ifnum\chart@Toggle<3 \global\advance\chart@ColorIndex by 2\chart@ColorStep \else \global\chart@Toggle=0 \global\advance\chart@ColorIndex by -\chart@ColorStep% \fi% \global\advance\chart@ColorIndex by 1pt } % \define@key[psset]{pstricks-add}{cancelType}{\pst@expandafter\psk@@cancelType{#1xx}\@nil} \def\psk@@cancelType#1#2\@nil{% \ifx\relax#1\relax\def\psk@cancelType{2}\else% x \ifx#1B\def\psk@cancelType{5}\else% \ new option B \ifx#1S\def\psk@cancelType{4}\else% \ new option S \ifx#1X\def\psk@cancelType{3}\else% \ new option X \ifx#1b\def\psk@cancelType{2}\else% \ \ifx#1s\def\psk@cancelType{1}\else% / \def\psk@cancelType{0}\fi\fi\fi\fi\fi\fi}% x every other \psset[pstricks-add]{cancelType=}% x, crossing \def\psCancel{\def\pst@par{}\pst@object{psCancel}}% by Stefano Baroni 2008-06-21 \def\psCancel@i{\pst@makebox\psCancel@iii} \def\psCancel@iii{% \begingroup \solid@star \use@par \ifnum\psk@cancelType>\tw@ % check if \psk@cancelType > 2 % here: option cancelType with small letter X, S, B \pst@dimc=\wd\pst@hbox \pst@dimb=\dp\pst@hbox \pst@dimd=\ht\pst@hbox \pst@dima=\z@ \edef\psk@cancelType{\the\numexpr\psk@cancelType-3\relax} \else % here: option cancelType with capital letter x, s, b set \pst@diam as before \pst@dima=\pslinewidth \advance\pst@dima by \psframesep \pst@dimc=\wd\pst@hbox\advance\pst@dimc by \pst@dima \pst@dimb=\dp\pst@hbox\advance\pst@dimb by \pst@dima \pst@dimd=\ht\pst@hbox\advance\pst@dimd by \pst@dima \fi \setbox\pst@hbox=\hbox{% \ifpsboxsep\kern\pst@dima\fi \begin@ClosedObj \addto@pscode{ \psk@cornersize % arcradius boolean \pst@number\pst@dima neg \pst@number\pst@dimb neg \pst@number\pst@dimc \pst@number\pst@dimd .5 \if@star \tx@Frame \else CLW mul /a ED % the middle of the line 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add /y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED pop pop % delete arc values \ifnum\psk@cancelType<\tw@ % / or x (1 oder 0) x1 y1 moveto x2 y2 lineto \fi \ifnum\psk@cancelType=\@ne\else % \ or x (2 oder 0) x2 y1 moveto x1 y2 lineto \fi \fi }% \def\pst@linetype{2}% \showpointsfalse \end@ClosedObj \box\pst@hbox \ifpsboxsep\kern\pst@dima\fi }% \ifpsboxsep\dp\pst@hbox=\pst@dimb\ht\pst@hbox=\pst@dimd\fi \leavevmode\box\pst@hbox \endgroup% } \iffalse \define@key[psset]{pstricks-add}{cancelType}{\pst@expandafter\psk@@cancelType{#1xx}\@nil} \def\psk@@cancelType#1#2\@nil{% \ifx\relax#1\relax\def\psk@cancelType{2}\else% x \ifx#1b\def\psk@cancelType{2}\else% \ \ifx#1s\def\psk@cancelType{1}\else% / \def\psk@cancelType{0}\fi\fi\fi}% x every other \psset[pstricks-add]{cancelType=}% x, crossing \def\psCancel{\def\pst@par{}\pst@object{psCancel}}% by Stefano Baroni 2008-06-21 \def\psCancel@i{\pst@makebox\psCancel@iii} \def\psCancel@iii{% \begingroup \solid@star \use@par \pst@dima=\pslinewidth \advance\pst@dima by \psframesep \pst@dimc=\wd\pst@hbox\advance\pst@dimc by \pst@dima \pst@dimb=\dp\pst@hbox\advance\pst@dimb by \pst@dima \pst@dimd=\ht\pst@hbox\advance\pst@dimd by \pst@dima \setbox\pst@hbox=\hbox{% \ifpsboxsep\kern\pst@dima\fi \begin@ClosedObj \addto@pscode{ \psk@cornersize % arcradius boolean \pst@number\pst@dima neg \pst@number\pst@dimb neg \pst@number\pst@dimc \pst@number\pst@dimd .5 \if@star \tx@Frame \else CLW mul /a ED % the middle of the line 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add /y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED pop pop % delete arc values \ifnum\psk@cancelType<\tw@ % / or x x1 y1 moveto x2 y2 lineto \fi% \ifnum\psk@cancelType=\@ne\else % \ or x x2 y1 moveto x1 y2 lineto \fi \fi }% \def\pst@linetype{2}% \showpointsfalse \end@ClosedObj \box\pst@hbox \ifpsboxsep\kern\pst@dima\fi% }% \ifpsboxsep\dp\pst@hbox=\pst@dimb\ht\pst@hbox=\pst@dimd\fi \leavevmode\box\pst@hbox \endgroup% } \fi % \newcount\psVectorCtr \define@boolkey[psset]{pstricks-add}[Pst@]{markAngle}[true]{} \psset[pstricks-add]{markAngle=false} % \newpsstyle{psMarkAngleStyle}{arrows=->,arrowsize=4pt} \newpsstyle{psMarkAngleLineStyle}{linestyle=dotted,arrows=-} % \def\psStartPoint{\@ifnextchar[{\psStartPoint@i}{\psStartPoint@i[Vector]}} \def\psStartPoint@i[#1](#2){% \global\psVectorCtr=\@ne \gdef\psVectorName{#1}% \pnode(#2){#10}% % \pst@getcoor{#2}\pst@vector@cp \pstVerb{ gsave tx@Dict begin STV CP T \psGetNodeCenter{#10} /cp.X #10.x def /cp.Y #10.y def % \pst@vector@cp % \pst@number\psyunit mul /cp.Y exch def % \pst@number\psxunit mul /cp.X exch def end grestore }% \ignorespaces} % \def\psVector{\pst@object{psVector}} \def\psVector@i{% \pst@killglue \addbefore@par{arrows=->,arrowsize=6pt}% % \addto@par{showpoints=false}% \psVector@ii} \def\psVector@ii{\@ifnextchar<\psVector@iii\psVector@iv}% \def\psVector@iii<#1>{\psStartPoint(#1)\psVector@iv} \def\psVector@iv(#1){% \pst@getcoor{#1}\pst@tempCoor \begingroup \use@keep@par \pst@cntm=\the\psVectorCtr \advance\pst@cntm by \m@ne \rput(\psVectorName\the\pst@cntm){% \else cp.X cp.Y \fi){% \pnode(0,0){@@@A}\pnode(#1){@@@B} \ifPst@markAngle \psarc[style=psMarkAngleStyle](0,0){1}{0}{!\pst@tempCoor exch atan}% \psline[style=psMarkAngleLineStyle](1.5,0)% \fi}% \ncline[nodesep=0pt]{@@@A}{@@@B} \pnode(! \pst@tempCoor \pst@number\psyunit div cp.Y add exch \pst@number\psxunit div cp.X add exch ){\psVectorName\the\psVectorCtr}% \global\advance\psVectorCtr by \@ne% \endgroup \pst@Verb{ \pst@tempCoor \pst@number\psyunit div cp.Y add /cp.Y exch def \pst@number\psxunit div cp.X add /cp.X exch def }% \@ifnextchar(\psVector@iv\ignorespaces} % \define@key[psset]{pstricks-add}{basename}{\def\psk@basename{#1}}% \psset[pstricks-add]{basename=}% % \def\psCircleTangents{\pst@object{psCircleTangents}} \def\psCircleTangents@i(#1){\@ifnextchar({\psCircleTangents@ii(#1)}{\psCircleTangents@iii(#1)}}% \def\psCircleTangents@ii(#1)(#2)#3{% (viewpoint) (circle) {radius} \pst@killglue \begingroup \pst@getlength{#3}\pst@LengthA \addbefore@par{basename=CircleT}% \use@par % \edef\@cmd{\noexpand\psEllipseTangentsN(#2)(! \pst@LengthA dup % \pst@number\psxunit div exch \pst@number\psyunit div )(#1){\psk@basename}}% % \@cmd \psEllipseTangentsN(#2)(!\pst@LengthA dup \pst@number\psxunit div exch \pst@number\psyunit div )(#1){\psk@basename}% \endgroup \ignorespaces }% \def\psCircleTangents@iii(#1)#2(#3)#4{% two circles--- (Cntr1){radius1}(Cntr2){radius2} \pst@killglue \begingroup \pst@getlength{#2}\pst@LengthA% radius1 \pst@getlength{#4}\pst@LengthB% radius2 \addbefore@par{basename=CircleT}% \use@par \psLCNodeVar(#1)(#3)(! \pst@LengthA \pst@number\psrunit div dup \pst@LengthB \pst@number\psrunit div % r1 r1 r2 on stack 3 copy add div /tti ED sub dup 0 eq % r1 r1-r2 on stack { pop pop /ttx 1000 def }{ div dup abs 1000 gt % r1/(r1-r2) on stack { 0 gt { ttx 1000 def }{ ttx -1000 def } ifelse}{ /ttx ED } ifelse } ifelse 1 tti sub tti )% 1-tti tti on stack {\psk@basename C1}% % tti=r1/(r1+r2), ttx=r1/(r1-r2) \psLCNodeVar(#1)(#3)(! 1 ttx sub ttx ){\psk@basename C2}% outside crossing pt \expandafter\psCircleTangents@ii\expandafter(\psk@basename C1)(#1){#2}% \pnode(CircleT1){\psk@basename I1}\pnode(CircleT2){\psk@basename I3}% \expandafter\psCircleTangents@ii\expandafter(\psk@basename C1)(#3){#4}% \pnode(CircleT1){\psk@basename I2}\pnode(CircleT2){\psk@basename I4}% % external tangents \expandafter\psCircleTangents@ii\expandafter(\psk@basename C2)(#1){#2}% \pnode(CircleT1){\psk@basename O2}\pnode(CircleT2){\psk@basename O4}% \expandafter\psCircleTangents@ii\expandafter(\psk@basename C2)(#3){#4}% \pnode(CircleT1){\psk@basename O1}\pnode(CircleT2){\psk@basename O3}% \endgroup% \ignorespaces% }% % \def\psEllipseTangents{\pst@object{psEllipseTangents}} \def\psEllipseTangents@i(#1)(#2)(#3){% (Center)(axes)(viewpoint) \pst@killglue{% \use@par% only one parameter matters---psk@basename \ifx\psk@basename\@empty \def\psk@basename{EllipseT}\fi % \edef\@cmd{\noexpand\psEllipseTangentsN(#1)(#2)(#3){\psk@basename}}% \@cmd}\ignorespaces}% % \def\psEllipseTangentsN(#1)(#2)(#3)#4{% (xe,ye)(a,b)(xP,yP){basename} % no optional arguments \pst@killglue % \pst@getcoor{#1}\pst@tempA \pnode(#1){E@Cntr}% \pnode(#2){@@TMP}% \pnode(#3){@@@TMP}% (center)(semimajor, semiminor)(viewpt) \pst@getcoor{#3}\my@tempC% external viewpoint \AtoB(E@Cntr)(@@@TMP){@TMP}% center to viewpoint \ifnum\Pst@Debug>0 \shownode(E@Cntr)% \shownode(@TMP)% \shownode(@@@TMP)% \fi \pnode(! \psGetNodeCenter{E@Cntr}\space /Xc E@Cntr.x def /Yc E@Cntr.y def \psGetNodeCenter{@@TMP}\space /B @@TMP.y def % semiminor /A @@TMP.x def % semimajor \psGetNodeCenter{@TMP}\space /Xp @TMP.x def /Yp @TMP.y def % center to viewpoint % /A2 A dup mul def /B2 B dup mul def /C2 B A div dup mul def /Xp2 Xp dup mul def /Yp2 Yp dup mul def /R Xp2 A2 sub C2 mul Yp2 add Sqrt def % R=Sqrt{(Xp2-A2) C2 + Yp2} /Q C2 Xp2 mul Yp2 add def % C2 Xp2 + Yp2 /Xta B2 Xp mul A Yp R mul mul sub Q div def /Yta Yp Xp R mul A div add B2 mul Q div def /Xtb B2 Xp mul A Yp R mul mul add Q div def /Ytb Yp Xp R mul A div sub B2 mul Q div def 0 Xta Yp mul Yta Xp mul sub gt % swap a, b { /A Xta def /B Yta def /Xta Xtb def /Yta Ytb def /Xtb A def /Ytb B def } if Xta Xc add %/xTemp ED Yta Yc add %/yTemp ED % xTemp Xc yTemp Yc Pyth2 /Length ED % xTemp Xc sub yTemp Yc sub exch atan 0 add Length exch PtoC % Yc add exch Xc add exch ) {#42}% \pnode(! Xtb Xc add Ytb Yc add ) {#41}% \ignorespaces}% % \define@key[psset]{pstricks-add}{rotate}{\def\psk@rotate{#1 }} \psset[pstricks-add]{rotate=0} \def\pst@saveDegrees{} \def\psKiviat{\pst@object{psKiviat}} \def\psKiviat@i#1#2{% #1: number of edges #2 radius \gdef\pst@saveDegrees{#1} \begingroup% \degrees[#1]% \SpecialCoor% \addbefore@par{rotate=0} \use@par% \global\let\psk@@rotate\psk@rotate \def\pst@Coordinates{} \psLoop{#1}{\xdef\pst@Coordinates{\pst@Coordinates(#2;\the\psLoopIndex)}} \rput{\psk@rotate}(0,0){\expandafter\pspolygon\pst@Coordinates \multido{\nA=0+1}{#1}{\uput{\pslabelsep}[\nA]{*0}(#2;\nA){\psPutYLabel{\nA}}}} \endgroup% \ignorespaces} % \def\psKiviatLine{\pst@object{psKiviatLine}} \def\psKiviatLine@i#1{{% \addbefore@par{showpoints}% \use@par% \degrees[\pst@saveDegrees]% \psKiviatLine@ii#1\@nil}}% \def\psKiviatLine@ii#1,#2\@nil{% \global\pst@cntm=0 \global\pst@cntn=1 \begingroup \xdef\pst@saveCoors{} \psKiviatLine@iii#1,#2,#1,,\@nil \rput{\psk@@rotate}(0,0){\expandafter\pspolygon\pst@saveCoors} } \def\psKiviatLine@iii#1,#2,#3\@nil{% \ifx\relax#2\relax\else%\psline(#1;\the\pst@cntm)(#2;\the\pst@cntn) \xdef\pst@saveCoors{\pst@saveCoors(#1;\the\pst@cntm)}\fi \advance\pst@cntm\@ne \advance\pst@cntn\@ne \ifx\relax#3\relax\endgroup\else\psKiviatLine@iii#2,#3\@nil\fi} % \def\psKiviatTicklines{\pst@object{psKiviatTicklines}} \def\psKiviatTicklines@i#1#2{{% n, radius \degrees[#1]% \use@par% \pstFPDiv\pst@tempN{#2}{\psk@Dx}% \pst@cntm=\pst@tempN \advance\pst@cntm by \m@ne \multido{\rA=\psk@Dx+\psk@Dx}{\the\pst@cntm}{% \def\pst@Coordinates{}% \psLoop{#1}{\xdef\pst@Coordinates{\pst@Coordinates(\rA;\the\psLoopIndex)}}% \rput{\psk@@rotate}(0,0){\expandafter\pspolygon\pst@Coordinates}% }% }\ignorespaces}% % \def\psKiviatAxes{\pst@object{psKiviatAxes}} \def\psKiviatAxes@i#1#2{{% \degrees[#1] \use@par% \multido{\iA=0+1}{#1}{\rput{\psk@@rotate}(0,0){\psline(0,0)(#2;\iA)}}% }\ignorespaces}% % \define@key[psset]{pstricks-add}{colSteps}{\def\psk@colSteps{#1 }} \define@boolkey[psset]{pstricks-add}[Pst@]{colored}[true]{} \define@key[psset]{pstricks-add}{colorOffset}[]{\def\psk@colorOffset{#1 }} \psset[pstricks-add]{colSteps=0,colored=false,colorOffset=}% continuing colors and grayscale % \def\pstContour{\pst@object{pstContour}} \def\pstContour@i#1{% \addbefore@par{radius=1pt} \begin@SpecialObj% \pssetlength\pst@dimb\psk@radius \addto@pscode{ (#1) run /zMax 0 def /zMin 0 def % lowest and highest value contourdata aload length /N_data ED % get the no of arrays N_data{ % inside contourdata /data ED % save first inner array data aload length 3 div round cvi { % get the records \psk@colorOffset dup zMin lt % z