--- /dev/null
+\documentclass{article}
+\usepackage[a4paper,margin=2cm]{geometry}
+\usepackage[latin1]{inputenc}
+\usepackage{pstricks-add,pst-eqdf,pst-func}
+\usepackage{array,amsmath}
+%\usepackage{listings}
+\newpsstyle{vecteurA}{arrowinset=0.05,arrowsize=0.125,linecolor={[rgb]{1 0.5 0}}}
+\newpsstyle{vecteurB}{arrowinset=0.05,arrowsize=0.1,linecolor={[rgb]{0 0.5 1}}}
+\newpsstyle{vecteurC}{arrowinset=0.1,arrowsize=0.2,linecolor={[rgb]{1 0.5 0}}}
+%%%%%%%%%%%%%%%%%%
+\def\datRoot{C:/Users/J\"{u}rgen/Desktop/gravitation/}
+\title{Interaction gravitationnelle avec PSTricks}
+\date{19 juin 2\,012}
+\begin{document}
+\maketitle
+\def\eqsatellite{%
+y[2]|y[3]|-GM*y[0]/((sqrt(y[0]^2+y[1]^2))^3)|-GM*y[1]/((sqrt(y[0]^2+y[1]^2))^3)}%
+\section{Mise en orbite d'un satellite}
+\begin{figure}[htbp]
+ \begin{center}
+\psset{unit=2}
+\begin{pspicture}(-6,-2)(2,5)
+\pstVerb{
+ /GM 1 def
+ /theta0 -35 def
+ /r0 1 def
+ /x0 r0 theta0 cos mul def
+ /y0 r0 theta0 sin mul def
+ /v0 1.3 def
+ /v0x v0 theta0 sin mul neg def
+ /v0y v0 theta0 cos mul def
+ /Lc r0 v0 mul def % moment cinetique
+ /par Lc dup mul GM div def % param\`{e}tre de l'ellipse
+% excentricit\'{e}
+ /exc 1 0.5 v0 4 exp mul r0 dup mul mul GM r0 mul v0 dup mul mul sub GM dup mul div 2 mul add sqrt def
+%%%%%%%%%%%%%%
+ /a_2 par 1 exc dup mul sub div def % demi-grand axe
+ /b_2 par 1 exc dup mul sub sqrt div def % demi-petit axe
+ /periode 2 3.1416 mul a_2 3 exp GM div sqrt mul def
+% vitesse \`{a} l'apog\'{e}e
+ /vA GM par div sqrt 1 exc sub mul def
+% vitesse au p\'{e}rig\'{e}e
+ /vP GM par div sqrt 1 exc add mul def
+% coordonn\'{e}es de vA
+ /vAx vA theta0 90 add cos mul neg def
+ /vAy vA theta0 90 add sin mul neg def
+% coordonn\'{e}es de vP
+ /vPx vP theta0 90 add cos mul def
+ /vPy vP theta0 90 add sin mul def
+% Apog\'{e}e
+ /xA par 1 exc sub div theta0 cos mul neg def
+ /yA par 1 exc sub div theta0 sin mul neg def
+% P\'{e}rig\'{e}e
+ /xP par 1 exc add div theta0 cos mul def
+ /yP par 1 exc add div theta0 sin mul def
+% Centre
+ /xO xP xA add 2 div def
+ /yO yP yA add 2 div def
+}%
+\pscircle[fillcolor=gray!70,fillstyle=solid](0,0){0.3}
+\psdot[dotstyle=+](0,0)
+\uput[d](0,0){O}
+\psgrid[subgriddiv=2,gridcolor=lightgray,gridlabels=8pt](-6,-2)(2,5)
+\rput(1,4){\psframebox[linestyle=none,fillstyle=solid,fillcolor=white]{T=\psPrintValue[decimals=2]{periode}\hphantom{0000}s}}
+\parametricplot[linecolor=red,plotpoints=360]{0}{360}{/radius par 1 exc t theta0 sub cos mul add div def
+ radius t cos mul
+ radius t sin mul}
+\pscircle*(!x0 y0){0.05}
+\pnode(!xP yP){P} % p\'{e}rig\'{e}e
+\pnode(!xA yA){A} % Apog\'{e}e
+\pnode(!xO yO){O} % centre
+\rput(!x0 y0){\psline[style=vecteurB]{->}(!v0x v0y)\uput[ur](!v0x v0y){$\overrightarrow{v_0}$}}
+\psline[linestyle=dashed](A)(P)
+\pscircle*(A){0.05}
+\uput[ul](A){$A$}
+\uput[dr](P){$P$}
+% position du satellite \`{a} un instant quelconque
+\pstVerb{/theta_i 170 def
+ /radius par 1 exc theta_i theta0 sub cos mul add div def
+ /xS radius theta_i cos mul def
+ /yS radius theta_i sin mul def
+ /ux theta_i cos 1 mul def
+ /uy theta_i sin 1 mul def
+ /xi xS ux sub def
+ /yi yS uy sub def
+ /xi2 xS ux 2 div sub def
+ /yi2 yS uy 2 div sub def}%
+\pnode(!xi2 yi2){Mi2}
+\pnode(!xi yi){Mi}
+\pnode(!xS yS){S}
+\pscircle*(S){0.05}
+\psline[linestyle=dotted](S)(0,0)
+\psline[style=vecteurA]{->}(S)(Mi)
+\uput[l](S){S}
+\uput[u](Mi2){$\overrightarrow{F}$}
+\psarcn{->}(0,0){0.4}{0}{!theta0}
+\uput{0.5}[!theta0 2 div](0,0){$\theta_0$}
+\rput(A){\psline[style=vecteurB]{->}(!vAx vAy)}
+%\rput(P){\psline[style=vecteurB]{->}(!vPx vPy)}
+\psline[arrowinset=0.05,arrowsize=0.1]{<->}(2,0)(0,0)(0,5)
+\uput[r](0,4.9){$y$}\uput[u](1.9,0){$x$}
+\psdot(O)\uput[r](O){$\Omega$}
+\rput{!90 theta0 add}(O){\psline[linestyle=dashed](!b_2 neg 0)(!b_2 0)}
+\end{pspicture}
+\caption{Mouvement d'un satellite}
+ \end{center}
+\end{figure}
+Soit (M) la masse de l'astre et (m) celle du satellite avec $m\ll M$. Le centre de masse du syst\`{e}me \{M,m\} est confondu avec le centre de l'astre attracteur. La mise en orbite s'effectue \`{a} partir du point $M_0(x_0,y_0)$ avec une vitesse $\overrightarrow{v_0}(v_{0_x},v_{0_x})$. $\theta_0$ est l'angle que fait $\overrightarrow{Ox}$ avec $\overrightarrow{OM_0}$. Le satellite (S), suppos\'{e} ponctuel, subit de la part de l'astre une force d'attraction gravitationnelle :
+\[
+\overrightarrow{F}=-\mathcal{G}\frac{Mm}{r^2}\overrightarrow{u}\qquad \text{avec}\quad \overrightarrow{u}=\frac{\overrightarrow{r}}{r}\quad \text{et}\quad \overrightarrow{r}=\overrightarrow{OS}
+\]
+Tous les \textit{bons} livres de m\'{e}canique\footnote{Comme celui, par exemple, de Jos\'{e}-Philippe P\'{e}rez, aux \'{e}ditions Masson.} \'{e}tablissent les relations suivantes :
+\[
+r=\frac{p}{1+\mathrm{e}\cos(\theta-\theta_0)}
+\]
+Param\`{e}tres et excentricit\'{e} ont pour expressions respectives, avec les notations suivantes : $K=\mathcal{G}Mm$, $\mathcal{E}$ l'\'{e}nergie du syst\`{e}me et $L$ le moment cin\'{e}tique.
+\[
+\mathrm{e}=\sqrt{1+\frac{2\mathcal{E}L^2}{mK^2}}\qquad p=\frac{L^2}{mK}
+\]
+On choisit une vitesse initiale $\overrightarrow{v_0}$ perpendiculaire \`{a} $\overrightarrow{OM_0}$, dans ces conditions le moment cin\'{e}tique et l'\'{e}nergie, qui restent constants, valent :
+\[
+L=mr_0v_0\qquad \mathcal{E}=-\frac{K}{r_0}+\frac{1}{2}mv_0^2
+\]
+En rempla\c{c}ant $L$ et $\mathcal{E}$, on obtient pour l'excentricit\'{e} et le param\`{e}tre les expressions suivantes :
+\[
+\mathrm{e}=\sqrt{1+\frac{1}{\mathcal{G}^2M^2}\Big(\frac{1}{2}v_0^4r_0^2-\mathcal{G}Mr_0v_0^2\Big)}
+\]
+\[
+p=\frac{v_0^2r_0^2}{\mathcal{G}M}
+\]
+On se limite au cas du mouvement elliptique, avec, en cons\'{e}quence, la condition :
+\[
+\mathcal{E}=-\frac{K}{r_0}+\frac{1}{2}mv_0^2 < 0
+\]
+Le demi-grand axe $a$, le demi-petit axe $b$ sont :
+\[
+a=\frac{p}{1-\mathrm{e}^2}\qquad b=\frac{p}{\sqrt{1-\mathrm{e}^2}}
+\]
+La p\'{e}riode $T$ qui ob\'{e}it \`{a} la troisi\`{e}me loi de K\'{e}pler :
+\[
+T^2=\frac{4\pi^2a^3}{\mathcal{G}M}
+\]
+La vitesse, en un point de l'ellipse, se calcule par :
+\[
+v^2=\mathcal{G}M\Big( \frac{2}{r}-\frac{1}{a}\Big)
+\]
+Sachant que $r_p=\dfrac{p}{1+\mathrm{e}}$ et $r_A=\dfrac{p}{1-\mathrm{e}}$, on en d\'{e}duit les vitesses au p\'{e}rig\'{e}e et \`{a} l'apog\'{e}e :
+\[
+v_P=\sqrt{\frac{\mathcal{G}M}{p}}(1+\mathrm{e})\qquad v_A=\sqrt{\frac{\mathcal{G}M}{p}}(1-\mathrm{e})
+\]
+
+\section{L'\'{e}tude avec PSTricks}
+\subsection{La trajectoire}
+\def\parametres{
+ /GM 1 def % 4e14 def % GxM
+ /x0 6.5e6 def % position initiale
+ /y0 0 def
+ /vx0 0 def % vitesse initiale
+ /vy0 1e4 def
+}
+% x0 y0 x'0 y'0
+% y[0] y[1] y[2] y[3]
+\[
+\left\{
+\begin{array}{rcl}
+\ddot{x}&=&-\dfrac{GM}{r^3}x\\[1em]
+\ddot{y}&=&-\dfrac{GM}{r^3}y\\
+\end{array}
+\right.
+\label{eq1}
+\qquad r=\sqrt{x^2+y^2}
+\]
+
+On peut dessiner la trajectoire du satellite et de ses caract\'{e}ristiques de deux fa\c{c}ons :
+\begin{itemize}
+ \item par l'utilisation de \verb+\parametricplot+ ;
+ \item ou celle de \verb+\psplotDiffEqn+.
+\end{itemize}
+\verb+\parametricplot+ utilise l'expression exacte de l'\'{e}quation de la trajectoire en coordonn\'{e}es polaires :
+\begin{verbatim}
+ \parametricplot[linecolor=red,unit=2,plotpoints=360]{0}{360}{%
+ /radius par 1 exc t theta0 sub cos mul add div def
+ radius t cos mul
+ radius t sin mul}
+\end{verbatim}
+L'excentricit\'{e}, la p\'{e}riode, demi-grand axe et demi-petit axe sont calcul\'{e}s par quelques lignes de code \textsf{postscript}. Il faut s'assurer que les conditions initiales choisies v\'{e}rifient bien la condition d'une trajectoire elliptique, pour cela il faut que l'\'{e}nergie initiale $\mathcal{E}_0<0$, sinon cela entra\^{\i}nera une erreur lors du passage \`{a} l'interpr\'{e}teur \textsf{postscript}.
+\begin{verbatim}
+\pstVerb{
+ /GM 1 def
+ /theta0 -45 def
+ /r0 0.5 def
+ /x0 r0 theta0 cos mul def
+ /y0 r0 theta0 sin mul def
+ /v0 1.92 def
+ /v0x v0 theta0 sin mul neg def
+ /v0y v0 theta0 cos mul def
+ /Lc r0 v0 mul def % moment cinetique
+ /par Lc dup mul GM div def % param\`{e}tre de l'ellipse
+% excentricit\'{e}
+ /exc 1 0.5 v0 4 exp mul r0 dup mul mul GM r0 mul
+ v0 dup mul mul sub GM dup mul div 2 mul add sqrt def
+%demi-grand axe
+ /a_2 par 1 exc dup mul sub div def % demi-grand axe
+%demi-petit axe
+ /b_2 par 1 exc dup mul sub sqrt div def % demi-petit axe
+% p\'{e}riode
+ /periode 2 3.1416 dup mul a_2 3 exp mul GM div sqrt mul def
+}%
+\end{verbatim}
+\verb+\psplotDiffEqn+ utilise les \'{e}quations diff\'{e}rentielles du mouvement, en notation alg\'{e}brique :
+\begin{verbatim}
+% x0 y0 x'0 y'0
+% y[0] y[1] y[2] y[3]
+\def\eqsatellite{%
+y[2]|y[3]|-GM*y[0]/((sqrt(y[0]^2+y[1]^2))^3)|-GM*y[1]/((sqrt(y[0]^2+y[1]^2))^3)}
+ \psplotDiffEqn[unit=2,whichabs=0,whichord=1,%
+ linecolor=blue,linewidth=0.1,%
+ method=rk4,plotpoints=1000,%
+ algebraic]{0}{37.8}{x0 y0 v0x v0y}{\eqsatellite}%
+\end{verbatim}
+Ce qui permet, par ailleurs de v\'{e}rifier la qualit\'{e} du trac\'{e} par la m\'{e}thode num\'{e}rique, en bleu, tandis que le trac\'{e} \`{a} partir de l'expression exacte est en trait fin en rouge.
+%
+\begin{center}
+\begin{pspicture}(-12,-2)(4,10)
+\pstVerb{
+ /GM 1 def
+ /theta0 -45 def
+ /r0 0.5 def
+ /x0 r0 theta0 cos mul def
+ /y0 r0 theta0 sin mul def
+ /v0 1.92 def
+ /v0x v0 theta0 sin mul neg def
+ /v0y v0 theta0 cos mul def
+ /Lc r0 v0 mul def % moment cinetique
+ /par Lc dup mul GM div def % param\`{e}tre de l'ellipse
+% excentricit\'{e}
+ /exc 1 0.5 v0 4 exp mul r0 dup mul mul GM r0 mul v0 dup mul mul sub GM dup mul div 2 mul add sqrt def
+%%%%%%%%%%%%%%
+ /a_2 par 1 exc dup mul sub div def % demi-grand axe
+ /b_2 par 1 exc dup mul sub sqrt div def % demi-petit axe
+ /periode 2 3.1416 dup mul a_2 3 exp mul GM div sqrt mul def
+}%
+\psframe*[linecolor=white](-3,-0.2)(0,0.2)
+\pscircle[fillcolor=blue!50,fillstyle=solid](0,0){0.5}
+\psgrid[unit=2,subgriddiv=2,gridcolor=lightgray,gridlabels=8pt](-6,-1)(2,5)
+\rput(-2,0){T=\psPrintValue[decimals=2]{periode}\hphantom{00000}s}
+ \psplotDiffEqn[unit=2,whichabs=0,whichord=1,linecolor=blue,linewidth=0.1,method=rk4,plotpoints=1000,algebraic]{0}{37.8}{x0 y0 v0x v0y}{\eqsatellite}%
+\parametricplot[linecolor=red,unit=2,plotpoints=360]{0}{360}{/radius par 1 exc t theta0 sub cos mul add div def
+ radius t cos mul
+ radius t sin mul}
+\psdot[unit=2,dotsize=0.12](!x0 y0)
+\rput(!x0 2 mul y0 2 mul){\psline[style=vecteurC]{->}(!v0x v0y)}
+\end{pspicture}
+\end{center}
+\subsection{La vitesse}
+\verb+\psplotDiffEqn+ permet de voir comment varie la vitesse sur l'ellipse :
+\begin{verbatim}
+% x0 y0 x'0 y'0
+% y[0] y[1] y[2] y[3]
+ \psplotDiffEqn[xunit=0.2,yunit=5,%
+ plotfuncy=dup 2 get dup mul exch 3 get dup mul add sqrt,
+ linecolor=red,method=rk4,plotpoints=1000,
+ algebraic]{0}{50}{x0 y0 v0x v0y}{\eqsatellite}%
+\end{verbatim}
+\begin{center}
+\begin{pspicture}(0,-1)(10,7)
+\psgrid[subgriddiv=0,gridcolor=lightgray,griddots=10,gridlabels=0pt]
+\pstVerb{/GM 1 def
+ /theta0 -35 def
+ /r0 1 def
+ /x0 r0 theta0 cos mul def
+ /y0 r0 theta0 sin mul def
+ /v0 1.3 def
+ /v0x v0 theta0 sin mul neg def
+ /v0y v0 theta0 cos mul def}%
+\psplotDiffEqn[xunit=0.2,yunit=5,
+ plotfuncy=dup 2 get dup mul exch 3 get dup mul add sqrt,
+ ,linecolor=red,method=rk4,plotpoints=1000,algebraic]{0}{50}{x0 y0 v0x v0y}{\eqsatellite}%
+ \multido{\i=1+1,\I=5+5}{9}{\uput[u](\i,0){\I}}
+\pnode(! 36.4 5 div 0){P}
+\psdot(P)\uput[d](P){P\'{e}rig\'{e}e}
+\psline[linestyle=dashed](P)(! 36.4 5 div 7)
+\pnode(! 36.4 10 div 0){A}
+\psdot(A)\uput[d](A){Apog\'{e}e}
+\psline[linestyle=dashed](A)(! 36.4 10 div 7)
+\uput[l](0,6.5){$v$}
+\psline[arrowinset=0.1,arrowsize=0.2]{<->}(10,0)(0,0)(0,7)
+\uput[u](10,0){$t$(s)}
+\uput[ul](0,0){0}
+\end{pspicture}
+\end{center}
+On peut obtenir les caract\'{e}ristiques de la vitesse en un point quelconque, car le moment cin\'{e}tique $L=mr\dot{\theta}$ \'{e}tant constant, pour chaque valeur de $\theta$, on en d\'{e}duit $r$ puis $\dot{\theta}$. En coordonn\'{e}es polaires, la vitesse s'exprime par :
+\[
+\overrightarrow{v}=\dot{r}\overrightarrow{u_r}+r\dot{\theta}\overrightarrow{u_{\theta}}
+\]
+$\dot{\theta}$ et $\dot{r}$ s'obtiennent par les relations suivantes :
+\[
+\dot{\theta}=\frac{r_0v_0}{r^2}
+\]
+\[
+\dot{r}=-\frac{p(-\dot{\theta}\sin(\theta-\theta_0)}{(1+\mathrm{e}\cos(\theta-\theta_0))^2}=\frac{r_0v_0}{p}\sin(\theta-\theta_0)
+\]
+La cha\^{\i}ne de calculs est la suivante : $\theta\Longrightarrow r\Longrightarrow \dot{\theta}\Longrightarrow \dot{r}\Longrightarrow \overrightarrow{v}$.
+
+Le package `\textsf{pst-eqdf}' comprend la commande \verb+\psequadiff+ qui est une version simplifi\'{e}e de \verb+\psplotDiffEqn+, dont elle ne reprend que la m\'{e}thode Runge-Kutta~4. Elle permet de sauvegarder sous forme de tableaux et/ou de fichiers toutes les variables et les d\'{e}riv\'{e}es de la fonction \'{e}tudi\'{e}e, cette possibilit\'{e} est int\'{e}ressante pour d\'{e}terminer les caract\'{e}ristiques de la vitesse au cours du temps et elle est particuli\`{e}rement utile pour cr\'{e}er une animation. Nous allons l'utiliser pour dessiner le vecteur-vitesse \`{a} quelques instants.
+
+On sauve successivement le tableau des positions et celui des vitesses.
+\begin{verbatim}
+\psequadiff[method=rk4,plotpoints=1000,
+ algebraic,
+ whichabs=0,whichord=1,
+ tabname=XiYi]{0}{43}{x0 y0 v0x v0y}{\eqsatellite}%
+\end{verbatim}
+\begin{verbatim}
+\psequadiff[method=rk4,plotpoints=1000,
+ algebraic,
+ whichabs=2,whichord=3,
+ tabname=vxvy]{0}{43}{x0 y0 v0x v0y}{\eqsatellite}%
+\end{verbatim}
+
+Pour ensuite dessiner la trajectoire et les vecteurs-vitesse.
+\begin{verbatim}
+%\listplot[unit=1]{vxvy aload pop}
+% on dessine la vitesse un point sur 100
+\pscircle[fillcolor=gray!70,fillstyle=solid](0,0){0.3}
+\multido{\i=0+100}{20}{%
+\pstVerb{/vX vxvy \i\space get def
+ /vY vxvy \i\space 1 add get def
+ /xi XiYi \i\space get def
+ /yi XiYi \i\space 1 add get def}%
+\rput(!xi yi){\psline[style=vecteurA]{->}(! vX 2 mul vY 2 mul)}}
+\end{verbatim}
+\begin{center}
+\begin{pspicture}(-10,-10)(6,7)
+\psset{unit=2}%
+\pstVerb{/GM 1 def
+ /theta0 30 def
+ /r0 2 def
+ /x0 r0 theta0 cos mul def
+ /y0 r0 theta0 sin mul def
+ /v0 0.85 def
+ /v0x v0 theta0 sin mul neg def
+ /v0y v0 theta0 cos mul def
+ /Lc r0 v0 mul def % moment cinetique
+ /par Lc dup mul GM div def % param\`{e}tre de l'ellipse
+% excentricit\'{e}
+ /exc 1 0.5 v0 4 exp mul r0 dup mul mul GM r0 mul v0 dup mul mul sub GM dup mul div 2 mul add sqrt def
+%%%%%%%%%%%%%%
+ /a_2 par 1 exc dup mul sub div def % demi-grand axe
+ /b_2 par 1 exc dup mul sub sqrt div def % demi-petit axe
+ /periode 2 3.1416 dup mul a_2 3 exp mul GM div sqrt mul def}%
+\rput(-2,0){T=\psPrintValue[decimals=2]{periode}\hphantom{00000}s}
+\psequadiff[method=rk4,
+ plotpoints=1000,
+ algebraic,
+ whichabs=0,
+ whichord=1,
+ tabname=XiYi
+% ,saveData,filename=XiYi.dat
+]{0}{43}{x0 y0 v0x v0y}{\eqsatellite}%
+\listplot{XiYi aload pop}
+\psequadiff[method=rk4,
+ plotpoints=1000,
+ algebraic,
+ whichabs=2,
+ whichord=3,
+ tabname=vxvy
+% ,saveData,filename=vxvy.dat
+]{0}{43}{x0 y0 v0x v0y}{\eqsatellite}%
+%\listplot[unit=1]{vxvy aload pop}
+% on dessine la vitesse un point sur 100
+\pscircle[fillcolor=gray!70,fillstyle=solid](0,0){0.3}
+\multido{\i=0+100}{20}{%
+\pstVerb{/vX vxvy \i\space get def
+ /vY vxvy \i\space 1 add get def
+ /xi XiYi \i\space get def
+ /yi XiYi \i\space 1 add get def}%
+\rput(!xi yi){\psline[style=vecteurA]{->}(! vX 2 mul vY 2 mul)}}
+\psgrid[subgriddiv=2,gridcolor=lightgray,gridlabels=8pt](-5,-5)(3,3)
+\end{pspicture}
+\end{center}
+
+
+
+\section{Mouvement circulaire}
+ \begin{center}
+\psset{unit=1}
+\begin{pspicture}(-5,-5.5)(5,5.5)
+\pstVerb{
+ /GM 1 def
+ /theta0 60 def
+ /r0 5 def
+ /x0 r0 theta0 cos mul def
+ /y0 r0 theta0 sin mul def
+ /v0 GM r0 div sqrt def
+ /v0x v0 theta0 sin mul neg def
+ /v0y v0 theta0 cos mul def
+ /Lc r0 v0 mul def % moment cinetique
+ /par Lc dup mul GM div def % param\`{e}tre de l'ellipse
+% excentricit\'{e}
+ /exc 1 0.5 v0 4 exp mul r0 dup mul mul GM r0 mul v0 dup mul mul sub GM dup mul div 2 mul add sqrt def
+%%%%%%%%%%%%%%
+ /a_2 par 1 exc dup mul sub div def % demi-grand axe
+ /b_2 par 1 exc dup mul sub sqrt div def % demi-petit axe
+ /periode 2 3.1416 mul a_2 3 exp GM div sqrt mul def
+% vitesse \`{a} l'apog\'{e}e
+ /vA GM par div sqrt 1 exc sub mul def
+% vitesse au p\'{e}rig\'{e}e
+ /vP GM par div sqrt 1 exc add mul def
+% coordonn\'{e}es de vA
+ /vAx vA theta0 90 add cos mul neg def
+ /vAy vA theta0 90 add sin mul neg def
+% coordonn\'{e}es de vP
+ /vPx vP theta0 90 add cos mul def
+ /vPy vP theta0 90 add sin mul def
+}%
+\pscircle[fillcolor=gray!70,fillstyle=solid](0,0){0.75}
+\psdot[dotstyle=+](0,0)
+\uput[d](0,0){O}
+\psgrid[subgriddiv=2,gridcolor=lightgray,gridlabels=8pt](-5,-5)(5,5)
+\rput(0,-2){\psframebox[linestyle=none,fillstyle=solid,fillcolor=white]{T=\psPrintValue[decimals=2]{periode}\hphantom{000000}s}}
+\parametricplot[linecolor=red,plotpoints=360]{0}{360}{/radius par 1 exc t theta0 sub cos mul add div def
+ radius t cos mul
+ radius t sin mul}
+\pscircle*(!x0 y0){0.1}
+%\pnode(!par 1 exc add div theta0 cos mul par 1 exc add div theta0 sin mul){P} % p\'{e}rig\'{e}e
+%\pnode(!par 1 exc sub div theta0 cos mul neg par 1 exc sub div theta0 sin mul neg){A} % Apog\'{e}e
+\rput(!x0 y0){\psline[arrowinset=0.1,arrowsize=0.2,linecolor={[rgb]{0 0.5 1}},unit=4]{->}(!v0x v0y)\uput[ur](!v0x 2 mul v0y 2 mul){$\overrightarrow{v_0}$}}
+\uput[ur](!x0 y0){$M_0$}
+\psline[linestyle=dashed](0,0)(!x0 y0)
+% position du satellite \`{a} un instant quelconque
+\pstVerb{/theta_i 170 def
+ /radius par 1 exc theta_i theta0 sub cos mul add div def
+ /xS radius theta_i cos mul def
+ /yS radius theta_i sin mul def
+ /ux theta_i cos 1 mul def
+ /uy theta_i sin 1 mul def
+ /xi xS ux sub def
+ /yi yS uy sub def
+ /xi2 xS ux 2 div sub def
+ /yi2 yS uy 2 div sub def}%
+\pnode(!xi2 yi2){Mi2}
+\pnode(!xi yi){Mi}
+\pnode(!xS yS){S}
+\pscircle*(S){0.1}
+\psline[linestyle=dotted](S)(0,0)
+\psline[style=vecteurC]{->}(S)(Mi)
+\uput[l](S){S}
+\uput[u](Mi2){$\overrightarrow{F}$}
+\psarc{->}(0,0){1}{0}{!theta0}
+\uput{1.1}[!theta0 2 div](0,0){$\theta_0$}
+\psline[arrowinset=0.1,arrowsize=0.2]{<->}(5,0)(0,0)(0,5)
+\psline[arrowinset=0.05,arrowsize=0.1]{<->}(5,0)(0,0)(0,5)
+\uput[u](0,5){$y$}\uput[r](5,0){$x$}
+\end{pspicture}
+ \end{center}
+Il s'obtient tr\`{e}s facilement \`{a} partir de l'\'{e}tude pr\'{e}c\'{e}dente si on sait que dans ce cas :
+\[
+v_0=\sqrt{\frac{\mathcal{G}M}{r_0}}
+\]
+\begin{verbatim}
+\pstVerb{
+ /GM 1 def
+ /theta0 60 def
+ /r0 5 def
+ /x0 r0 theta0 cos mul def
+ /y0 r0 theta0 sin mul def
+ /v0 GM r0 div sqrt def
+ /v0x v0 theta0 sin mul neg def
+ /v0y v0 theta0 cos mul def }%
+\end{verbatim}
+
+\end{document}
--- /dev/null
+%% $Id: pstricks-add.tex 692 2012-06-04 06:47:40Z herbert $
+%%
+%%
+%% This is file `pstricks-add.tex',
+%%
+%% IMPORTANT NOTICE:
+%%
+%% Package `pstricks-add.tex'
+%%
+%% Dominique Rodriguez
+%% Herbert Voss <hvoss@tug.org>
+%% Michael Sharpe <msharpe@ucsd.edu>
+%%
+%% 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\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{3.58}
+\def\filedate{2012/06/04}
+\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(#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@pyth\pst@dimm\pst@dimn\pst@dimo
+ \edef#5{\strip@pt\pst@dimo}
+}%
+%--------------------------------------- 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{%
+ { \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 }\endgroup}
+%
+% [#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}
+%
+\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
+% 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
+ \pst@number\pslinewidth setlinewidth \pst@usecolor\pslinecolor 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}
+%
+\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}>
+%
+%
+% -------------- the arrow part -------------
+% the original table
+% \def\pst@arrowtable{,<->,<<->>,>-<,>>-<<,(-),[-],)-(,]-[,|>-<|}
+%
+% v : Vee arrow (inside) v,V,f and F by Christophe FOUREY
+% V : Vee arrow (outside)
+% f : Filled vee arrow (inside)
+% F : Filled vee arrow (outside)
+\edef\pst@arrowtable{\pst@arrowtable,v-v,V-V,f-f,F-F,t-t,T-T}
+
+% Vee arrow
+\define@key[psset]{pstricks-add}{veearrowlength}[3mm]{\pst@getlength{#1}\psk@veearrowlength}
+\psset[pstricks-add]{veearrowlength=3mm} % default projected length
+\define@key[psset]{pstricks-add}{veearrowangle}[30]{\pst@getangle{#1}\psk@veearrowangle}
+\psset[pstricks-add]{veearrowangle=30} % default angle
+\define@key[psset]{pstricks-add}{veearrowlinewidth}[0.35mm]{\pst@getlength{#1}\psk@veearrowlinewidth}
+\psset[pstricks-add]{veearrowlinewidth=0.35mm} % default vee arrow line width
+
+% Filled vee arrow
+\define@key[psset]{pstricks-add}{filledveearrowlength}[3mm]{\pst@getlength{#1}\psk@filledveearrowlength}
+\psset[pstricks-add]{filledveearrowlength=3mm} % default projected length
+\define@key[psset]{pstricks-add}{filledveearrowangle}[15]{\pst@getangle{#1}\psk@filledveearrowangle}
+\psset[pstricks-add]{filledveearrowangle=15} % default angle
+\define@key[psset]{pstricks-add}{filledveearrowlinewidth}[0.35mm]{\pst@getlength{#1}\psk@filledveearrowlinewidth}
+\psset[pstricks-add]{filledveearrowlinewidth=0.35mm} % default vee arrow line width
+\define@key[psset]{pstricks-add}{arrowlinestyle}[solid]{%
+ \@ifundefined{psls@#1}%
+ {\@pstrickserr{Line style `#1' not defined}\@eha}%
+ {\def\psarrowlinestyle{#1}}}
+\psset[pstricks-add]{arrowlinestyle=solid} % default
+\pst@def{VeeArrow}<%
+ 1 setlinecap % round caps
+ 1 setlinejoin % round join
+ setlinewidth % vee arrow line width
+ /y ED % projected length
+ 2 div /a ED % angle (divide by 2)
+ /t ED % false = inside, true = outside
+ a sin a cos div y mul /x ED % perpendicular length : x=tan(a).y
+ t { 1 -1 scale } if % if outside : symmetry
+ x neg y moveto % point #1
+ 0 0 L % point #2
+ x y L % point #3
+ { closepath gsave fill grestore } if % if filled : close and fill
+ \@nameuse{psls@\psarrowlinestyle}
+ stroke % draw line
+ 0 t { y 2 mul } { 0 } ifelse moveto> % if outside : twice longer line
+
+% VeeArrow : filled? outside? (total) angle (projected) length (arrow) line width
+
+\@namedef{psas@v}{%
+ false false \psk@veearrowangle \psk@veearrowlength \psk@veearrowlinewidth \tx@VeeArrow}
+\@namedef{psas@V}{%
+ false true \psk@veearrowangle \psk@veearrowlength \psk@veearrowlinewidth \tx@VeeArrow}
+\@namedef{psas@f}{%
+ true false \psk@filledveearrowangle \psk@filledveearrowlength \psk@filledveearrowlinewidth \tx@VeeArrow}
+\@namedef{psas@F}{%
+ true true \psk@filledveearrowangle \psk@filledveearrowlength \psk@filledveearrowlinewidth \tx@VeeArrow}
+
+% And An another arrowhead
+% architectural tick / oblique arrow
+
+% Tick arrow
+\define@key[psset]{pstricks-add}{tickarrowlength}[1.5mm]{\pst@getlength{#1}\psk@tickarrowlength}
+\psset[pstricks-add]{tickarrowlength=1.5mm} % default projected length
+\define@key[psset]{pstricks-add}{tickarrowlinewidth}[0.35mm]{\pst@getlength{#1}\psk@tickarrowlinewidth}
+\psset[pstricks-add]{tickarrowlinewidth=0.35mm} % default tick arrow line width
+
+\pst@def{TickArrow}<%
+ 1 setlinecap % round caps
+ 1 setlinejoin % round join
+ setlinewidth % tick line width
+ /y ED % projected length
+ /t ED % false = normal, true = reversed
+ t { 1 -1 scale } if % if reversed : symmetry
+ y neg y moveto % point #1
+ y y neg L % point #2
+ \@nameuse{psls@\psarrowlinestyle}
+ stroke % draw line
+ 0 0 moveto> % origin
+
+\@namedef{psas@t}{ false \psk@tickarrowlength \psk@tickarrowlinewidth \tx@TickArrow }
+\@namedef{psas@T}{ true \psk@tickarrowlength \psk@tickarrowlinewidth \tx@TickArrow }
+%
+% HookLeft/RightArrow
+\newdimen\pshooklength
+\newdimen\pshookwidth
+\define@key[psset]{pstricks-add}{hooklength}[3mm]{\pssetlength\pshooklength{#1}}
+\define@key[psset]{pstricks-add}{hookwidth}[1mm]{\pssetlength\pshookwidth{#1}}
+%\psset{hooklength=3mm,hookwidth=1mm}
+%
+\edef\pst@arrowtable{\pst@arrowtable,H-H,h-h} % add new arrow
+\def\tx@RHook{RHook } % PostScript name
+\def\tx@Rhook{Rhook } % PostScript name
+\@namedef{psas@H}{%
+ /RHook {
+ /x ED % hook width
+ /y ED % hook length
+ /z CLW 2 div def % save it
+ x y moveto % goto first point
+ x 0 0 0 0 y
+ curveto % draw Bezier
+ stroke
+ 0 y moveto % define current point
+ } def
+ \pst@number\pshooklength
+ \pst@number\pshookwidth
+ \tx@RHook
+}
+\@namedef{psas@h}{%
+ /Rhook {
+ CLW mul % size * CLW
+ add dup % +length size*CLW+length size*CLW+length
+ 2 div /w ED % (size*CLW+length)/2 -> w
+ mul dup /h ED mul % (size*CLW+length)
+ /a ED
+ w neg h abs moveto 0 0 L
+ gsave
+ stroke grestore
+ } def
+ 0 \psk@arrowlength \psk@arrowsize \tx@Rhook
+}
+% New parameter "arrowfill", with default as "true"
+\define@boolkey[psset]{pstricks-add}[ps]{ArrowFill}[true]{}
+%
+% Modification of the PostScript macro Arrow to choose to fill or not the arrow
+% (it require to restore the current linewidth, despite of the scaling)
+\pst@def{Arrow}<{%
+ CLW mul add dup 2 div
+ /w ED mul dup
+ /h ED mul
+ /a ED { 0 h T 1 -1 scale } if
+ gsave
+ \ifpsArrowFill\else\pst@number\pslinewidth \pst@arrowscale\space div SLW \fi
+ w neg h moveto
+ 0 0 L w h L w neg a neg rlineto
+ \ifpsArrowFill gsave fill grestore \else gsave closepath stroke grestore \fi
+ grestore
+ 0 h a sub moveto
+}>
+%
+\define@key[psset]{pstricks-add}{nArrowsA}[2]{\def\psk@nArrowsA{#1}}
+\define@key[psset]{pstricks-add}{nArrowsB}[2]{\def\psk@nArrowsB{#1}}
+\define@key[psset]{pstricks-add}{nArrows}[2]{\def\psk@nArrowsA{#1}\def\psk@nArrowsB{#1}}
+\psset{nArrows=2}
+%
+\@namedef{psas@>>}{%
+ \psk@nArrowsA\space 1 sub {
+ false \psk@arrowinset \psk@arrowlength \psk@arrowsize \tx@Arrow
+ 0 h a sub T
+ } repeat
+ gsave
+ newpath
+ false \psk@arrowinset \psk@arrowlength \psk@arrowsize \tx@Arrow
+ CP
+ grestore
+ moveto
+}
+%
+\@namedef{psas@<<}{%
+ true \psk@arrowinset \psk@arrowlength \psk@arrowsize \tx@Arrow
+ 0 h neg a add T
+ \psk@nArrowsB\space 2 sub {
+ false \psk@arrowinset \psk@arrowlength \psk@arrowsize \tx@Arrow
+ 0 h neg a add T
+ } repeat
+ false \psk@arrowinset \psk@arrowlength \psk@arrowsize \tx@Arrow
+ 0 h a 5 mul 2 div sub moveto
+}
+%
+% DG addition begin - Dec. 18/19, 1997 and Oct. 11, 2002
+% Adapted from \psset@arrows
+\define@key[psset]{pstricks-add}{ArrowInside}{%
+ \def\pst@tempArrow{#1}%
+ \ifx\pst@tempArrow\@empty \def\psk@ArrowInside{} %
+ \else%
+ \begingroup%
+ \pst@activearrows%
+ \xdef\pst@tempg{<#1}%
+ \endgroup%
+ \expandafter\psset@@ArrowInside\pst@tempg\@empty-\@empty\@nil%
+ \if@pst\else\@pstrickserr{Bad intermediate arrow specification: #1}\@ehpa\fi%
+ \fi%
+}
+% Adapted from \psset@@arrows
+\def\psset@@ArrowInside#1-#2\@empty#3\@nil{%
+ \@psttrue
+ \def\next##1,#1-##2,##3\@nil{\def\pst@tempg{##2}}%
+ \expandafter\next\pst@arrowtable,#1-#1,\@nil
+ \@ifundefined{psas@#2}%
+ {\@pstfalse\def\psk@ArrowInside{}}%
+ {\def\psk@ArrowInside{#2}}%
+}
+% Default value empty
+\psset{ArrowInside={}}
+% Modified version of \pst@addarrowdef
+\def\pst@addarrowdef{%
+ \addto@pscode{%
+ /ArrowA {
+ \ifx\psk@arrowA\@empty
+ \pst@oplineto
+ \else
+ \pst@arrowdef{A}
+ moveto
+ \fi
+ } def
+ /ArrowB { \ifx\psk@arrowB\@empty \else \pst@arrowdef{B} \fi } def
+% DG addition
+ /ArrowInside {
+ \ifx\psk@ArrowInside\@empty \else \pst@arrowdefA{Inside} \fi
+ } def
+ }%
+}
+% Adapted from \pst@arrowdef
+\def\pst@arrowdefA#1{%
+ \ifnum\pst@repeatarrowsflag>\z@ /Arrow#1c [ 6 2 roll ] cvx def Arrow#1c\fi
+ \tx@BeginArrow
+ \psk@arrowscale
+ \@nameuse{psas@\@nameuse{psk@Arrow#1}}
+ \tx@EndArrow%
+}
+% ArrowInsidePos parameter (default value 0.5)
+\define@key[psset]{pstricks-add}{ArrowInsidePos}[0.5]{\pst@checknum{#1}\psk@ArrowInsidePos}%
+%\psset{ArrowInsidePos=0.5}
+%
+%
+% Redefinition of the PostScript /Line macro to print the intermediate
+% arrow on each segment of the line
+%
+\define@key[psset]{pstricks-add}{ArrowInsideNo}[1]{\pst@checknum{#1}\psk@ArrowInsideNo}% hv 20031001
+\define@key[psset]{pstricks-add}{ArrowInsideOffset}[0]{\pst@checknum{#1}\psk@ArrowInsideOffset}% hv 20031001
+%\psset{ArrowInsideNo=1,ArrowInsideOffset=0}
+%
+\def\arrowType@H{H}
+\pst@def{Line}<
+ NArray n 0 eq not { n 1 eq { 0 0 /n 2 def } if
+ (\psk@ArrowInside) length 0 gt {
+ \ifx\psk@arrowA\arrowType@H % do we have a Hook arrow at the beginning?
+ \pst@number\pshooklength % yes
+ \else
+ \psk@arrowsize\space CLW mul add dup \psk@arrowlength\space mul exch \psk@arrowinset mul neg add
+ \fi
+ /arrowlength exch def
+ 4 copy % copy all four values for the arrow line
+ /y1 ED /x1 ED /y2 ED /x2 ED % save them
+ /Alpha y2 y1 sub x2 x1 sub Atan def % the gradient of the line
+% 2 copy /y1 ED /x1 ED ArrowA x1 y1
+ ArrowA % draw arrowA
+ x1 Alpha cos arrowlength mul add % dx add
+ y1 Alpha sin arrowlength mul add % dy add, to get the current point at the end of the arrow tip
+ /n n 1 sub def
+ n {
+ 4 copy
+ /y1 ED /x1 ED /y2 ED /x2 ED
+ x1 y1
+ \psk@ArrowInsidePos\space 1 gt {
+ /Alpha y2 y1 sub x2 x1 sub Atan def
+ /ArrowPos \psk@ArrowInsideOffset\space def
+ /dArrowPos \psk@ArrowInsidePos\space abs def
+% /Length x2 x1 sub y2 y1 sub Pyth def
+ \psk@ArrowInsideNo\space cvi {
+ /ArrowPos ArrowPos dArrowPos add def
+% ArrowPos Length gt { exit } if
+ x1 Alpha cos ArrowPos mul add
+ y1 Alpha sin ArrowPos mul add
+ ArrowInside
+ pop pop
+ } repeat
+ }{
+ /ArrowPos \psk@ArrowInsideOffset\space def
+ /dArrowPos \psk@ArrowInsideNo 1 gt {%
+ 1.0 \psk@ArrowInsideNo 1.0 add div
+ }{\psk@ArrowInsidePos } ifelse def
+ \psk@ArrowInsideNo\space cvi {
+ /ArrowPos ArrowPos dArrowPos add def
+ x2 x1 sub ArrowPos mul x1 add
+ y2 y1 sub ArrowPos mul y1 add
+ ArrowInside
+ pop pop
+ } repeat
+ } ifelse
+ pop pop Lineto
+ } repeat
+ }{ ArrowA /n n 2 sub def n { Lineto } repeat } ifelse
+ CP 4 2 roll ArrowB L pop pop } if >
+%
+% Redefinition of the PostScript /Polygon macro to print the intermediate
+% arrow on each segment of the line
+\pst@def{Polygon}<{%
+ NArray n 2 eq { 0 0 /n 3 def } if
+ n 3 lt {
+ n { pop pop } repeat
+ }{
+ n 3 gt { CheckClosed } if
+ n 2 mul -2 roll
+ /y0 ED
+ /x0 ED
+ /y1 ED
+ /x1 ED
+ /xx1 x1 def
+ /yy1 y1 def
+ x1 y1
+ /x1 x0 x1 add 2 div def
+ /y1 y0 y1 add 2 div def
+ x1 y1 moveto
+ /n n 2 sub def
+ /drawArrows {
+ x11 y11
+ \psk@ArrowInsidePos\space 1 gt {
+ /Alpha y12 y11 sub x12 x11 sub atan def
+ /ArrowPos \psk@ArrowInsideOffset\space def
+ /Length x12 x11 sub y12 y11 sub Pyth def
+ /dArrowPos \psk@ArrowInsidePos\space abs def
+ {
+ /ArrowPos ArrowPos dArrowPos add def
+ ArrowPos Length gt { exit } if
+ x11 Alpha cos ArrowPos mul add
+ y11 Alpha sin ArrowPos mul add
+ currentdict /ArrowInside known { ArrowInside } if
+ pop pop
+ } loop
+ }{
+ /ArrowPos \psk@ArrowInsideOffset\space def
+ /dArrowPos \psk@ArrowInsideNo\space 1 gt {%
+ 1.0 \psk@ArrowInsideNo\space 1.0 add div
+ }{ \psk@ArrowInsidePos } ifelse def
+ \psk@ArrowInsideNo\space cvi {
+ /ArrowPos ArrowPos dArrowPos add def
+ x12 x11 sub ArrowPos mul x11 add
+ y12 y11 sub ArrowPos mul y11 add
+ currentdict /ArrowInside known { ArrowInside } if
+ pop pop
+ } repeat
+ } ifelse
+ pop pop Lineto
+ } def
+ n {
+ 4 copy
+ /y11 ED /x11 ED /y12 ED /x12 ED
+ drawArrows
+ } repeat
+ x1 y1 x0 y0
+ 6 4 roll
+ 2 copy
+ /y11 ED /x11 ED /y12 y0 def /x12 x0 def
+ drawArrows
+ /y11 y0 def /x11 x0 def /y12 yy1 def /x12 xx1 def
+ drawArrows
+ pop pop
+ closepath
+ } ifelse %
+}>
+%
+%
+% Redefinition of the PostScript /OpenBezier macro to print the intermediate
+% arrow
+\pst@def{OpenBezier}<{%
+ /dArrowPos \psk@ArrowInsideNo 1 gt {%
+ 1.0 \psk@ArrowInsideNo 1.0 add div
+ }{ \psk@ArrowInsidePos } ifelse def
+ BezierNArray
+ n 1 eq { pop pop
+ }{ 2 copy
+ /y0 ED /x0 ED
+ ArrowA
+ n 4 sub 3 idiv { 6 2 roll 4 2 roll curveto } repeat
+ 6 2 roll
+ 4 2 roll
+ ArrowB
+ /y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED
+ /cx x1 x0 sub 3 mul def
+ /cy y1 y0 sub 3 mul def
+ /bx x2 x1 sub 3 mul cx sub def
+ /by y2 y1 sub 3 mul cy sub def
+ /ax x3 x0 sub cx sub bx sub def
+ /ay y3 y0 sub cy sub by sub def
+ /getValues {
+ ax t0 3 exp mul bx t0 t0 mul mul add cx t0 mul add x0 add
+ ay t0 3 exp mul by t0 t0 mul mul add cy t0 mul add y0 add
+ ax t 3 exp mul bx t t mul mul add cx t mul add x0 add
+ ay t 3 exp mul by t t mul mul add cy t mul add y0 add
+ } def
+ /getdL {
+ getValues
+ 3 -1 roll sub 3 1 roll sub Pyth
+ } def
+ /CurveLength {
+ /u 0 def
+ /du 0.01 def
+ 0 100 {
+ /t0 u def
+ /u u du add def
+ /t u def
+ getdL add
+ } repeat } def
+ /GetArrowPos {
+ /ende \psk@ArrowInsidePos\space 1 gt
+ {ArrowPos}
+ {ArrowPos CurveLength mul} ifelse def
+ /u 0 def
+ /du 0.01 def
+ /sum 0 def
+ { /t0 u def
+ /u u du add def
+ /t u def
+ /sum getdL sum add def
+ sum ende gt {exit} if
+ } loop u
+ } def
+ /ArrowPos \psk@ArrowInsideOffset\space def
+ /loopNo \psk@ArrowInsidePos\space 1 gt {%
+ CurveLength \psk@ArrowInsidePos\space div cvi
+ }{ \psk@ArrowInsideNo } ifelse def
+ loopNo cvi {
+ /ArrowPos ArrowPos dArrowPos add def
+ /t GetArrowPos def
+ /t0 t 0.95 mul def
+ getValues
+ ArrowInside pop pop pop pop
+ } repeat
+ x1 y1 x2 y2 x3 y3 curveto
+ } ifelse
+}>
+%
+% Redefinition of the PostScript /NCLine macro to print the intermediate
+% arrow of the line
+\pst@def{NCLine}<{%
+ NCCoor
+ tx@Dict begin
+ ArrowA CP 4 2 roll ArrowB
+ 4 copy
+ /y2 ED /x2 ED /y1 ED /x1 ED
+ x1 y1
+ \psk@ArrowInsidePos\space 1 gt {
+ /Alpha y2 y1 sub x2 x1 sub atan def
+ /ArrowPos \psk@ArrowInsideOffset\space def
+ /Length x2 x1 sub y2 y1 sub Pyth def
+ /dArrowPos \psk@ArrowInsidePos\space abs def
+ {%
+ /ArrowPos ArrowPos dArrowPos add def
+ ArrowPos Length gt { exit } if
+ x1 Alpha cos ArrowPos mul add
+ y1 Alpha sin ArrowPos mul add
+ ArrowInside
+ pop pop
+ } loop
+ }{%
+ /ArrowPos \psk@ArrowInsideOffset\space def
+ /dArrowPos \psk@ArrowInsideNo 1 gt {%
+ 1.0 \psk@ArrowInsideNo 1.0 add div
+ }{ \psk@ArrowInsidePos } ifelse def
+ \psk@ArrowInsideNo\space cvi {
+ /ArrowPos ArrowPos dArrowPos add def
+ x2 x1 sub ArrowPos mul x1 add
+ y2 y1 sub ArrowPos mul y1 add
+ ArrowInside
+ pop pop
+ } repeat
+ } ifelse
+ pop pop lineto pop pop
+ end%
+}>
+%
+\pst@def{NCCurve}<{%
+ GetEdgeA GetEdgeB
+ xA1 xB1 sub yA1 yB1 sub
+ Pyth 2 div dup 3 -1 roll mul
+ /ArmA ED
+ mul
+ /ArmB ED
+ /ArmTypeA 0 def
+ /ArmTypeB 0 def
+ GetArmA GetArmB
+ xA2 yA2 xA1 yA1
+ 2 copy
+ /y0 ED /x0 ED
+ tx@Dict begin
+ ArrowA
+ end
+ xB2 yB2 xB1 yB1
+ tx@Dict begin
+ ArrowB
+ end
+ /y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED
+ /cx x1 x0 sub 3 mul def
+ /cy y1 y0 sub 3 mul def
+ /bx x2 x1 sub 3 mul cx sub def
+ /by y2 y1 sub 3 mul cy sub def
+ /ax x3 x0 sub cx sub bx sub def
+ /ay y3 y0 sub cy sub by sub def
+ /getValues {
+ ax t0 3 exp mul bx t0 t0 mul mul add cx t0 mul add x0 add
+ ay t0 3 exp mul by t0 t0 mul mul add cy t0 mul add y0 add
+ ax t 3 exp mul bx t t mul mul add cx t mul add x0 add
+ ay t 3 exp mul by t t mul mul add cy t mul add y0 add
+ } def
+ /getdL {
+ getValues
+ 3 -1 roll sub 3 1 roll sub Pyth
+ } def
+ /CurveLength {
+ /u 0 def
+ /du 0.01 def
+ 0 100 {
+ /t0 u def
+ /u u du add def
+ /t u def
+ getdL add
+ } repeat } def
+ /GetArrowPos {
+ /ende \psk@ArrowInsidePos\space 1 gt {ArrowPos}{ArrowPos CurveLength mul} ifelse def
+ /u 0 def
+ /du 0.01 def
+ /sum 0 def
+ {
+ /t0 u def
+ /u u du add def
+ /t u def
+ /sum getdL sum add def
+ sum ende gt {exit} if
+ } loop u
+ } def
+ /dArrowPos \psk@ArrowInsideNo 1 gt {%
+ 1.0 \psk@ArrowInsideNo 1.0 add div
+ }{ \psk@ArrowInsidePos } ifelse def
+ /ArrowPos \psk@ArrowInsideOffset\space def
+ /loopNo \psk@ArrowInsidePos\space 1 gt {%
+ CurveLength \psk@ArrowInsidePos\space div cvi
+ }{ \psk@ArrowInsideNo } ifelse def
+ loopNo cvi {
+ /ArrowPos ArrowPos dArrowPos add def
+ /t GetArrowPos def
+ /t0 t 0.95 mul def
+ getValues
+ ArrowInside pop pop pop pop
+ } repeat
+ x1 y1 x2 y2 x3 y3 curveto
+ /LPutVar [ xA1 yA1 xA2 yA2 xB2 yB2 xB1 yB1 ] cvx def
+ /LPutPos { t LPutVar BezierMidpoint } def
+ /HPutPos { { HPutLines } HPutCurve } def
+ /VPutPos { { VPutLines } HPutCurve } def
+}>
+%
+\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@boolkey[psset]{pstricks-add}[Pst@]{color}[true]{}
+\psset{randomPoints=1000,color=false}
+%
+\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
+ rrand 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
+}
+%
+\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%
+}
+%
+\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\psRelNode{\pst@object{psRelNode}}
+\def\psRelNode@i(#1)(#2)#3#4{{% A - B - factor - node name
+ \use@par
+ \pst@getcoor{#1}\pst@tempA%
+ \pst@getcoor{#2}\pst@tempB%
+ \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
+ /AlphaStrich \psk@angleA\space def
+ /unit \pst@number\psyunit \pst@number\psxunit div def % yunit/xunit
+%
+ /dx XB XA sub def
+ /dy YB YA sub \ifPst@trueAngle\space unit mul \fi\space def
+ /laenge dy dup mul dx dup mul add sqrt #3 mul def
+ /Alpha dy dx atan def
+ /beta Alpha AlphaStrich add def
+ laenge beta cos mul XA add
+ laenge beta sin mul \ifPst@trueAngle\space unit div \fi\space YA add ){#4}%
+}}
+%
+\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}
+ \psline(#1)(#4)%
+}\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}%
+ \psline(#3)(#5)
+}\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}%
+}
+%
+\define@cmdkeys[psset]{pstricks-add}[PSTPSPNk@]{% Christophe Jorssen 2007
+ blName,bcName,brName,
+ clName,ccName,crName,
+ tlName,tcName,trName}[]{}%
+\psset[pstricks-add]{%
+ blName=PSPbl,bcName=PSPbc,brName=PSPbr,
+ clName=PSPcl,ccName=PSPcc,crName=PSPcr,
+ tlName=PSPtl,tcName=PSPtc,trName=PSPtr}
+\def\psDefPSPNodes{\def\pst@par{}\pst@object{psDefPSPNodes}}
+\def\psDefPSPNodes@i{%
+ \pst@killglue
+ \begingroup
+ \use@par
+ \expandafter\psDefPSPNodes@ii\pic@coor}
+%
+\def\psDefPSPNodes@ii(#1)(#2)(#3){%
+% \pnode(#1){PSPN@temp}\pnode([nodesep=.75,angle=45]PSPN@temp){\PSTPSPNk@blName}
+% \pnode(#3){PSPN@temp}\pnode([nodesep=.75,angle=-135]PSPN@temp){\PSTPSPNk@trName}
+ \pnode(#1){PSPN@temp}\pnode([angle=45]PSPN@temp){\PSTPSPNk@blName}
+ \pnode(#3){PSPN@temp}\pnode([angle=-135]PSPN@temp){\PSTPSPNk@trName}
+ \pnode(\PSTPSPNk@blName|\PSTPSPNk@trName){\PSTPSPNk@tlName}
+ \pnode(\PSTPSPNk@trName|\PSTPSPNk@blName){\PSTPSPNk@brName}
+ \ncline[linestyle=none]{\PSTPSPNk@blName}{\PSTPSPNk@tlName}
+ \ncput[npos=.5]{\pnode{\PSTPSPNk@clName}}
+ \ncline[linestyle=none]{\PSTPSPNk@blName}{\PSTPSPNk@brName}
+ \ncput[npos=.5]{\pnode{\PSTPSPNk@bcName}}
+ \pnode(\PSTPSPNk@brName|\PSTPSPNk@clName){\PSTPSPNk@crName}
+ \pnode(\PSTPSPNk@bcName|\PSTPSPNk@trName){\PSTPSPNk@tcName}
+ \pnode(\PSTPSPNk@bcName|\PSTPSPNk@clName){\PSTPSPNk@ccName}
+ \endgroup
+ \ignorespaces}
+%
+%\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@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
+%
+\def\psStep{\def\pst@par{}\pst@object{psStep}}
+\def\psStep@i(#1,#2)#3#4{%
+ \begin@ClosedObj%
+ \addto@pscode{
+ \ifPst@algebraic /Func (#4) tx@addDict begin AlgParser end cvx def \fi
+ /x #1 def
+ /dx #2 #1 sub #3 div def
+ /scx { \pst@number\psxunit mul } def
+ /scy { \pst@number\psyunit mul } def
+ \ifcase\psk@StepType % 0->lower, height is always f(x)
+ x scx 0 moveto
+ #3 {
+ \ifPst@algebraic Func \else #4 \fi scy dup x scx exch lineto
+ /x x dx add def
+ x scx exch lineto x scx 0 lineto
+ } repeat
+ \or % 1-> upper, height is always f(x+dx)
+ x scx 0 moveto
+ #3 {
+ /x x dx add def
+ \ifPst@algebraic Func \else #4 \fi scy dup x dx sub scx exch lineto
+ x scx exch lineto x scx 0 lineto
+ } repeat
+ \or % 2-> Riemann
+ /eps3 100 def
+ /xMinMax [] def
+ /AMax [] def
+ /AMin [] def
+ /dt dx eps3 div def
+ #3 {
+ /Max \ifPst@algebraic Func \else #4 \fi def
+ /Min Max def
+ /t x def % save x value
+ eps3 {
+ \ifPst@algebraic Func \else #4 \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
+ } repeat
+ /dx dx scx def
+ xMinMax aload length 3 div cvi {
+ /yMax ED /yMin ED /x ED
+ x yMin moveto dx 0 rlineto x dx add yMax lineto
+ dx neg 0 rlineto x yMin lineto } repeat
+ \or % 3->inf(imum)
+ x scx 0 moveto
+ #3 {
+ \ifPst@algebraic Func \else #4 \fi /y0 ED % left value f(x)
+ /xOld x def
+ /x x dx add def
+ \ifPst@algebraic Func \else #4 \fi /y1 ED % right value f(x+dx)
+ y0 y1 lt { y0 }{ y1 } ifelse % use infimum
+ scy dup xOld scx exch lineto
+ x scx exch lineto x scx 0 lineto
+ } repeat
+ \or % 4-> sup(remum)
+ x scx 0 moveto
+ #3 {
+ \ifPst@algebraic Func \else #4 \fi /y0 ED % left value f(x)
+ /x x dx add def
+ \ifPst@algebraic Func \else #4 \fi /y1 ED % right value f(x+dx)
+ y0 y1 gt { y0 }{ y1 } ifelse % use supremum
+ scy dup x dx sub scx exch lineto
+ x scx exch lineto x scx 0 lineto
+ } repeat
+ \fi
+ }%
+ \psk@fillstyle
+ \pst@stroke
+ \end@ClosedObj%
+}
+%
+\define@key[psset]{pstricks-add}{Derive}{\def\psk@Derive{#1}}%
+\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 } % if yes, then we have 2 values
+ { /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
+ cvi 180 mod dup 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 0 % moveto
+ #3
+ 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 \else \pst@tempRight\space \fi \pst@number\psxunit mul 0 % moveto
+ \if@star 0
+ \else
+ \ifx\pst@tempRight\@empty #3 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
+ \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 SaveFinalState 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{{%
+ \def\solid@star{}%
+ \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
+ [ \pst@colorC ] aload length 1 eq { dup dup } if 3 array astore % gray -> rgb
+ [ \pst@colorB ] aload length 1 eq { dup dup } if 3 array astore
+ [ \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@key[psset]{pstricks-add}{colorType}[0]{\def\psk@colorType{#1}}
+\define@key[psset]{pstricks-add}{colorTypeDef}[{}]{\def\psk@colorTypeDef{#1\space}}
+\psset[pstricks-add]{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{
+ (#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
+ \psk@Xoffset\space \psk@Yoffset\space translate
+ \@nameuse{psds@\psk@dotstyle} %
+ /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 Dot%
+ \ifcase\psk@colorType
+ } { pop } ifelse
+ \fi
+ /n n 1 add def
+ } for
+ } for
+ }%
+ \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@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%
+ \def\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{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%
+ \pswedge[linecolor={chartFillColor\the\pst@cnta},fillstyle=solid,fillcolor={chartFillColor\the\pst@cnta}]%
+ (\psk@chartSep\p@;\pst@number\pst@dimo){\pst@chartRadius}{\pst@number\pst@dimn}{\pst@number\pst@dimm}%
+ \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%
+ \pswedge[linecolor={chartFillColor\the\pst@cnta},fillstyle=solid,fillcolor={chartFillColor\the\pst@cnta}](0,0)%
+ {\pst@chartRadius}{\pst@number\pst@dimn}{\pst@number\pst@dimm}%
+ \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{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%
+}
+%
+\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@tempA%
+ \pstVerb{tx@Dict begin
+ \pst@tempA
+ \pst@number\psyunit div /cp.Y exch def
+ \pst@number\psxunit div /cp.X exch def end }}
+%
+\def\psVector{\pst@object{psVector}}
+\def\psVector@i(#1){%
+ \pst@killglue%
+ \addbefore@par{arrows=->,arrowsize=6pt}%
+ \pst@getcoor{#1}\pst@tempCoor%
+ \begingroup
+ \use@par%
+ \rput(! cp.X cp.Y ){%
+ \psline(0,0)(#1)%
+ \ifPst@markAngle
+ \psarc[style=psMarkAngleStyle](0,0){1}{0}{!\pst@tempCoor exch atan}%
+ \psline[style=psMarkAngleLineStyle](1.5,0)%
+ \fi}%
+ \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{%tx@Dict begin
+ \pst@tempCoor
+ \pst@number\psyunit div cp.Y add /cp.Y exch def
+ \pst@number\psxunit div cp.X add /cp.X exch def %end
+ }%
+ \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%
+ \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%
+ \pnode(#1){E@Cntr}% center of ellipse
+ \pnode(#2){@@TMP}% semimajor, semiminor
+ \pnode(#3){@@@TMP}% 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{@@TMP}\space
+ /B @@TMP.y def% semiminor
+ /A @@TMP.x def% semimajor
+ /A2 A dup mul def /B2 B dup mul def
+ /C2 B A div dup mul def
+ \psGetNodeCenter{@TMP}\space
+ /Xp @TMP.x def /Yp @TMP.y def % center to viewpoint
+ /Xp2 Xp dup mul def /Yp2 Yp dup mul def
+ \psGetNodeCenter{E@Cntr}\space
+ /Xc E@Cntr.x def /Yc E@Cntr.y 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 Yta Yc add ) {#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}%
+%
+\def\resetOptions{%
+ \def\pst@linetype{0}%
+ \pstScalePoints(1,1){}{}%
+ \psset[pstricks-add]{%
+ hooklength=3mm, hookwidth=1mm,
+ ArrowFill=true,
+ ArrowInside={}, ArrowInsidePos=0.5,
+ ArrowInsideNo=1, ArrowInsideOffset=0,
+ randomPoints=1000,color=false,
+ whichabs={},whichord={},
+ plotfuncx={},plotfuncy={},buildvector=false,
+ Derive={},adamsorder=4,
+ Tnormal=false,
+ braceWidth=2\pslinewidth,
+ bracePos=0.5,
+ braceWidthInner=10\pslinewidth,
+ braceWidthOuter=10\pslinewidth,
+ chartNodeI=0.75,
+ chartNodeO=1.5,
+ markAngle=false,
+ }}
+%
+\resetOptions
+%
+\catcode`\@=\PstAtCode\relax
+%
+%% END: pstricks-add.tex
+\endinput
+
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