From: Juergen Gilg Date: Fri, 22 Jun 2012 10:08:35 +0000 (+0200) Subject: Ajouté \datRoot dans pst-eqdf.tex pour usage distiller et mettre pstricks-add.tex... X-Git-Url: https://melusine.eu.org/syracuse/G/git/?p=pst-eqdf.git;a=commitdiff_plain;h=be8718baa5658e074feaefd6af07caef1a501f4a Ajouté \datRoot dans pst-eqdf.tex pour usage distiller et mettre pstricks-add.tex dans le repertoire... Structuration du repertoire gravitation ... --- diff --git a/gravitation/LISTE.txt b/gravitation/LISTE.txt index d6cc6c6..dc03eea 100644 --- a/gravitation/LISTE.txt +++ b/gravitation/LISTE.txt @@ -5,6 +5,11 @@ gravitation_01.tex gravitation_01.pdf gravitation_02.tex gravitation_02.pdf +== Exemples avec Adobe Distiller +gravitation_01_distiller.tex +gravitation_01_distiller.pdf +== Les fichiers du package pst-eqdf.tex pst-eqdf.sty +pstricks-add.tex diff --git a/gravitation/gravitation_01_distiller.pdf b/gravitation/gravitation_01_distiller.pdf new file mode 100644 index 0000000..2d06370 Binary files /dev/null and b/gravitation/gravitation_01_distiller.pdf differ diff --git a/gravitation/gravitation_01_distiller.tex b/gravitation/gravitation_01_distiller.tex new file mode 100644 index 0000000..5049dc3 --- /dev/null +++ b/gravitation/gravitation_01_distiller.tex @@ -0,0 +1,473 @@ +\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} diff --git a/gravitation/pst-eqdf.tex b/gravitation/pst-eqdf.tex index b4dd3cf..0585839 100644 --- a/gravitation/pst-eqdf.tex +++ b/gravitation/pst-eqdf.tex @@ -28,6 +28,12 @@ \catcode`\@=11\relax % Definition of the parameters % ---------------------------- +% Added by JG, 2012 06 20 +\def\datRoot{} +% Definition of a "Root" within the hard drive for Distiller users +% Note: The root must be set with "slashes" not "backslashes" like +% \def\datRoot{C:/Users/Desktop/datfolder/} +% By default the \datRoot is left empty (for non-Distiller usage) \pst@addfams{pst-eqd} \define@key[psset]{pst-eqd}{method}{\edef\psk@method{#1}}% \define@key[psset]{pst-eqd}{whichabs}{\edef\psk@whichabs{#1}}% @@ -35,7 +41,7 @@ \define@key[psset]{pst-eqd}{plotfuncx}{\edef\psk@plotfuncx{#1}}% \define@key[psset]{pst-eqd}{plotfuncy}{\edef\psk@plotfuncy{#1}}% \define@key[psset]{pst-eqd}{tabname}{\edef\psk@tabname{#1}}% -\define@key[psset]{pst-eqd}{filename}{\edef\psk@filename{#1}}% +\define@key[psset]{pst-eqd}{filename}{\edef\psk@filename{\datRoot #1}}% \newif\ifPst@buildvector% \define@key[psset]{pst-eqd}{buildvector}[true]{\@nameuse{Pst@buildvector#1}}% \newif\ifPst@saveData% @@ -50,7 +56,7 @@ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% #1-#2 x range %% #3 initial value of y (which is a vector) -%% #4 value of the dérivative (y and t can be used) +%% #4 value of the d\'{e}rivative (y and t can be used) \def\psequadiff{\def\pst@par{}\pst@object{psequadiff}} \def\psequadiff@i#1#2#3#4{% \pst@killglue diff --git a/gravitation/pstricks-add.tex b/gravitation/pstricks-add.tex new file mode 100644 index 0000000..e26a324 --- /dev/null +++ b/gravitation/pstricks-add.tex @@ -0,0 +1,2411 @@ +%% $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 +%% Michael Sharpe +%% +%% This program can be redistributed and/or modified under the terms +%% of the LaTeX Project Public License Distributed from CTAN archives +%% in directory macros/latex/base/lppl.txt. +%% +%% DESCRIPTION: +%% `pstricks-add' is a PSTricks package for additionals to the standard +%% pstricks package +%% +\csname PSTricksAddLoaded\endcsname +\let\PSTricksAddLoaded\endinput +% +% Requires some packages +\ifx\PSTricksLoaded\endinput\else \input pstricks \fi +\ifx\PSTplotLoaded\endinput\else \input pst-plot \fi +\ifx\PSTnodesLoaded\endinput\else \input pst-node \fi +\ifx\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 +