X-Git-Url: https://melusine.eu.org/syracuse/G/git/?a=blobdiff_plain;f=lorenz%2FanimXZ_Lorenz-PSTricks.tex;fp=lorenz%2FanimXZ_Lorenz-PSTricks.tex;h=dd5aba2e684324d62fe69cdf7009336b9ef7b7c6;hb=fda32923f8b15421e227324231c7f46c220da950;hp=0000000000000000000000000000000000000000;hpb=eaa4e47d6338f5e5e679c1b5ef9bdc3501c3110e;p=pst-eqdf.git

diff --git a/lorenz/animXZ_Lorenz-PSTricks.tex b/lorenz/animXZ_Lorenz-PSTricks.tex
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+\documentclass{article}
+\usepackage[a4paper,margin=2cm]{geometry}
+\usepackage{animate}
+\usepackage{pst-node,pst-eqdf}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% Essai de Manuel Luque 19 février 2003
+% transformé par Denis Girou le 25 février 2003
+% révision le 14 septembre 2011
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\makeatletter
+\pst@addfams{pst-plothsb}
+
+\define@key[psset]{pst-plothsb}{HueBegin}{% Between 0 and 1
+\edef\PstParametricplotHSB@HueBegin{#1}}
+
+\define@key[psset]{pst-plothsb}{HueEnd}{% Between 0 and 1
+\edef\PstParametricplotHSB@HueEnd{#1}}
+
+\newif\ifPst@HSB
+\define@key[psset]{pst-plothsb}{HSB}[true]{\@nameuse{Pst@HSB#1}}
+
+% Default values
+\psset{HueBegin=0,HueEnd=1,HSB=true}
+
+\def\parametricplotHSB{\pst@object{parametricplotHSB}}
+\def\parametricplotHSB@i{\@ifnextchar[{\parametricplotHSB@do}{\parametricplotHSB@do[]}}
+\def\parametricplotHSB@do[#1]#2#3#4{{%
+\psset{#1}%
+\begin@ClosedObj
+\addto@pscode{%
+/t  #2 def
+/dt #3 t sub \psk@plotpoints\space div def
+/t t dt sub def
+/Counter 0 def
+\psk@plotpoints {
+  /t t dt add def
+  /Counter Counter 1 add def
+/F@pstplot \ifPst@algebraic (#4)
+                    tx@AlgToPs begin AlgToPs end cvx
+                 \else { #4 }
+          \fi
+   def
+\ifPst@algebraic
+   F@pstplot
+    \else  #4
+\fi
+  \pst@number\psyunit mul exch
+  \pst@number\psxunit mul exch
+  1 Counter eq
+    {moveto}                    % First point
+    {\ifPst@HSB                 % Other points than the first one
+       /PointY exch def
+       /PointX exch def
+       Counter \psk@plotpoints\space div
+           \PstParametricplotHSB@HueEnd\space
+             \PstParametricplotHSB@HueBegin\space sub mul
+           \PstParametricplotHSB@HueBegin\space add
+         1 1 sethsbcolor
+       PointX PointY lineto
+       stroke
+       PointX PointY moveto
+     \else
+       lineto
+     \fi} ifelse
+    } repeat}% fin du code ps
+\end@ClosedObj}} % fin de la commande PSTricks
+
+\makeatother
+
+\makeatletter
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% adaptation de \parametricplotHSB
+% à \lisplotHSB
+% le 10 juin 2012
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\def\listplotHSB{\pst@object{listplotHSB}}
+\def\listplotHSB@i#1{%
+\begin@ClosedObj
+  \addto@pscode{%
+  /Counter 0 def
+     /XY@ [ #1 ] def
+     XY@ 0 get
+     XY@ 1 get
+  \pst@number\psyunit mul exch
+  \pst@number\psxunit mul exch
+       moveto
+     /L XY@ length def
+     2 2 L 2 sub {/i exch def
+   /x1  XY@ i get \pst@number\psxunit mul def
+   /y1  XY@ i 1 add get \pst@number\psyunit mul def
+    x1 y1
+    \ifPst@HSB
+    Counter L 2 div div
+    \PstParametricplotHSB@HueEnd\space
+    \PstParametricplotHSB@HueBegin\space sub mul
+    \PstParametricplotHSB@HueBegin\space add
+    1 1 sethsbcolor
+    /Counter Counter 1 add def
+    \fi
+     lineto
+     stroke
+  x1 y1 moveto
+  } for
+  }%
+\end@ClosedObj}
+\makeatother
+\def\formules{%
+    /xObservateur abscisse Sin1 mul neg ordonnee Cos1 mul add def
+    /yObservateur abscisse Cos1Sin2 mul neg ordonnee Sin1Sin2 mul sub cote Cos2 mul add def
+    /zObservateur abscisse neg Cos1Cos2 mul ordonnee Sin1Cos2 mul sub cote Sin2 mul sub Dobs add def
+    /xScreen DScreen xObservateur mul zObservateur div def
+    /yScreen DScreen yObservateur mul zObservateur div def
+  xScreen yScreen}
+
+\makeatletter
+\pst@addfams{pst-pnodeTroisD}
+
+\define@key[psset]{pst-pnodeTroisD}{THETA}{\edef\psk@TroisD@Theta{#1 }}
+\define@key[psset]{pst-pnodeTroisD}{PHI}{\edef\psk@TroisD@Phi{#1 }}
+\define@key[psset]{pst-pnodeTroisD}{Dobs}{\edef\psk@TroisD@Dobs{#1 }}
+\define@key[psset]{pst-pnodeTroisD}{Decran}{\edef\psk@TroisD@Ecran{#1 }}
+\psset{THETA=300,PHI=20,Dobs=200,Decran=25}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\def\pnodeTroisD{\@ifnextchar[{\pst@pnodeTroisD}{\pst@pnodeTroisD[]}}
+
+\def\pst@pnodeTroisD[#1](#2,#3,#4)#5{{%
+\pst@killglue
+\psset{#1}%
+\pnode(!
+ /THETA \psk@TroisD@Theta\space def
+ /PHI \psk@TroisD@Phi\space def
+ /Dobs \psk@TroisD@Dobs\space def
+ /DScreen \psk@TroisD@Ecran\space def
+ /Sin1 THETA sin def
+ /Sin2 PHI sin def
+ /Cos1 THETA cos def
+ /Cos2 PHI cos def
+ /Cos1Sin2 Cos1 Sin2 mul def
+ /Sin1Sin2 Sin1 Sin2 mul def
+ /Cos1Cos2 Cos1 Cos2 mul def
+ /Sin1Cos2 Sin1 Cos2 mul def
+ /xObservateur #2 Sin1 mul neg #3 Cos1 mul add def
+ /yObservateur #2 Cos1Sin2 mul neg #3 Sin1Sin2 mul sub #4 Cos2 mul add def
+ /zObservateur #2 neg Cos1Cos2 mul #3 Sin1Cos2 mul sub #4 Sin2 mul sub Dobs add def
+ /xScreen DScreen xObservateur mul zObservateur div def
+ /yScreen DScreen yObservateur mul zObservateur div def
+  xScreen yScreen){#5}}}
+\makeatother
+%timeline
+\begin{filecontents}{lorenzXZ.txt}
+::0x0
+::1
+::2
+::3
+::4
+::5
+::6
+::7
+::8
+::9
+::10
+::11
+::12
+::13
+::14
+::15
+::16
+::17
+::18
+::19
+::20
+::21
+::22
+::23
+::24
+::25
+::26
+::27
+::28
+::29
+::30
+::31
+::32
+::33
+::34
+::35
+::36
+::37
+::38
+::39
+::40
+::41
+::42
+::43
+::44
+::45
+::46
+::47
+::48
+::49
+::50
+::51
+\end{filecontents}
+\title{L'attracteur de Lorenz avec PSTricks}
+\date{12 juin 2012}
+\begin{document}
+\def\parametres{
+    /Pr 10 def
+    /Rh 28 def
+    /beta 8 3 div def
+}%
+% y[0] y[1] y[2]
+ % x    y     z
+\def\Lorenz{
+Pr*(y[1]-y[0])|%
+Rh*y[0]-y[1]-y[0]*y[2]|%
+y[0]*y[1]-beta*y[2]%
+}
+\def\conditionsInitiales{10 10 30}
+\begin{center}
+\begin{pspicture}(-8,-.01)(8,0.01)
+%\psgrid[subgriddiv=0,gridcolor=lightgray,griddots=10,gridlabels=0pt]%
+\pstVerb{\parametres}%
+  \psequadiff[% x,y
+  tabname=tabXZ,
+  method=rk4,
+  whichabs=0,whichord=2,
+  saveData,filename=LorenzXZ.dat,
+  plotpoints=2501,algebraic]{0}{25}{\conditionsInitiales}{\Lorenz}
+%% une commande PSTricks est indispensable si on ne vaut pas tracer le courbe
+ \psdot[linecolor=white,dotsize=0.001](0,0)
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%\listplotHSB[unit=0.25]{tabXY aload pop}%
+%\uput[r](8,0){$x$}
+%\uput[u](0,8){$y$}
+\end{pspicture}
+\end{center}
+\begin{center}
+\def\nFrames{51}% 200 images
+\pstVerb{/XZlorenz [ (LorenzXZ.dat) run ] def}%
+\begin{animateinline}[controls,timeline=lorenzxy.txt,%
+                     begin={\begin{pspicture}(-8,-1)(8,14)},
+                     end={\end{pspicture}}]{10}% 10 images/s
+\psgrid[subgriddiv=0,gridcolor=lightgray,griddots=10,gridlabels=0pt]%
+\rput(0,13.5){\large\textbf{XZ}$(x_0=10,y_0=10,z_0=30)$}
+\listplotHSB[unit=0.25,HSB=false,linecolor=gray]{XZlorenz aload pop}%
+\newframe
+\multiframe{\nFrames}{i=0+100}{% tous les 100 pts
+ \pstVerb{      /XZpartiel {0 2 \i\space {/i exch def
+                 XZlorenz i get
+                 XZlorenz i 1 add get
+                 } for
+                 }def
+                 }%
+\listplotHSB[unit=0.25,linewidth=0.2,HueBegin=.25,HueEnd=0.65]{XZpartiel}%
+}
+\end{animateinline}
+\end{center}
+\end{document}
+