lorenz/animXYZ_Lorenz-PSTricks.tex

   1 \documentclass{article}
   2 \usepackage[a4paper,margin=2cm]{geometry}
   3 \usepackage{animate}
   4 \usepackage{pst-node,pst-eqdf}
   5
   6 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
   7 % Essai de Manuel Luque 19 février 2003
   8 % transformé par Denis Girou le 25 février 2003
   9 % révision le 14 septembre 2011
  10 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  11 \makeatletter
  12 \pst@addfams{pst-plothsb}
  13
  14 \define@key[psset]{pst-plothsb}{HueBegin}{% Between 0 and 1
  15 \edef\PstParametricplotHSB@HueBegin{#1}}
  16
  17 \define@key[psset]{pst-plothsb}{HueEnd}{% Between 0 and 1
  18 \edef\PstParametricplotHSB@HueEnd{#1}}
  19
  20 \newif\ifPst@HSB
  21 \define@key[psset]{pst-plothsb}{HSB}[true]{\@nameuse{Pst@HSB#1}}
  22
  23 % Default values
  24 \psset{HueBegin=0,HueEnd=1,HSB=true}
  25
  26 \def\parametricplotHSB{\pst@object{parametricplotHSB}}
  27 \def\parametricplotHSB@i{\@ifnextchar[{\parametricplotHSB@do}{\parametricplotHSB@do[]}}
  28 \def\parametricplotHSB@do[#1]#2#3#4{{%
  29 \psset{#1}%
  30 \begin@ClosedObj
  31 \addto@pscode{%
  32 /t  #2 def
  33 /dt #3 t sub \psk@plotpoints\space div def
  34 /t t dt sub def
  35 /Counter 0 def
  36 \psk@plotpoints {
  37   /t t dt add def
  38   /Counter Counter 1 add def
  39 /F@pstplot \ifPst@algebraic (#4)
  40                     tx@AlgToPs begin AlgToPs end cvx
  41                  \else { #4 }
  42           \fi
  43    def
  44 \ifPst@algebraic
  45    F@pstplot
  46     \else  #4
  47 \fi
  48   \pst@number\psyunit mul exch
  49   \pst@number\psxunit mul exch
  50   1 Counter eq
  51     {moveto}                    % First point
  52     {\ifPst@HSB                 % Other points than the first one
  53        /PointY exch def
  54        /PointX exch def
  55        Counter \psk@plotpoints\space div
  56            \PstParametricplotHSB@HueEnd\space
  57              \PstParametricplotHSB@HueBegin\space sub mul
  58            \PstParametricplotHSB@HueBegin\space add
  59          1 1 sethsbcolor
  60        PointX PointY lineto
  61        stroke
  62        PointX PointY moveto
  63      \else
  64        lineto
  65      \fi} ifelse
  66     } repeat}% fin du code ps
  67 \end@ClosedObj}} % fin de la commande PSTricks
  68
  69 \makeatother
  70
  71 \makeatletter
  72 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  73 % adaptation de \parametricplotHSB
  74 % à \lisplotHSB
  75 % le 10 juin 2012
  76 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  77 \def\listplotHSB{\pst@object{listplotHSB}}
  78 \def\listplotHSB@i#1{%
  79 \begin@ClosedObj
  80   \addto@pscode{%
  81   /Counter 0 def
  82      /XY@ [ #1 ] def
  83      XY@ 0 get
  84      XY@ 1 get
  85   \pst@number\psyunit mul exch
  86   \pst@number\psxunit mul exch
  87        moveto
  88      /L XY@ length def
  89      2 2 L 2 sub {/i exch def
  90    /x1  XY@ i get \pst@number\psxunit mul def
  91    /y1  XY@ i 1 add get \pst@number\psyunit mul def
  92     x1 y1
  93     \ifPst@HSB
  94     Counter L 2 div div
  95     \PstParametricplotHSB@HueEnd\space
  96     \PstParametricplotHSB@HueBegin\space sub mul
  97     \PstParametricplotHSB@HueBegin\space add
  98     1 1 sethsbcolor
  99     /Counter Counter 1 add def
 100     \fi
 101      lineto
 102      stroke
 103   x1 y1 moveto
 104   } for
 105   }%
 106 \end@ClosedObj}
 107 \makeatother
 108 \def\formules{%
 109     /xObservateur abscisse Sin1 mul neg ordonnee Cos1 mul add def
 110     /yObservateur abscisse Cos1Sin2 mul neg ordonnee Sin1Sin2 mul sub cote Cos2 mul add def
 111     /zObservateur abscisse neg Cos1Cos2 mul ordonnee Sin1Cos2 mul sub cote Sin2 mul sub Dobs add def
 112     /xScreen DScreen xObservateur mul zObservateur div def
 113     /yScreen DScreen yObservateur mul zObservateur div def
 114   xScreen yScreen}
 115
 116 \makeatletter
 117 \pst@addfams{pst-pnodeTroisD}
 118
 119 \define@key[psset]{pst-pnodeTroisD}{THETA}{\edef\psk@TroisD@Theta{#1 }}
 120 \define@key[psset]{pst-pnodeTroisD}{PHI}{\edef\psk@TroisD@Phi{#1 }}
 121 \define@key[psset]{pst-pnodeTroisD}{Dobs}{\edef\psk@TroisD@Dobs{#1 }}
 122 \define@key[psset]{pst-pnodeTroisD}{Decran}{\edef\psk@TroisD@Ecran{#1 }}
 123 \psset{THETA=300,PHI=20,Dobs=200,Decran=25}
 124 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 125 \def\pnodeTroisD{\@ifnextchar[{\pst@pnodeTroisD}{\pst@pnodeTroisD[]}}
 126
 127 \def\pst@pnodeTroisD[#1](#2,#3,#4)#5{{%
 128 \pst@killglue
 129 \use@par
 130 \psset{#1}%
 131 \pnode(!
 132  /THETA \psk@TroisD@Theta\space def
 133  /PHI \psk@TroisD@Phi\space def
 134  /Dobs \psk@TroisD@Dobs\space def
 135  /DScreen \psk@TroisD@Ecran\space def
 136  /Sin1 THETA sin def
 137  /Sin2 PHI sin def
 138  /Cos1 THETA cos def
 139  /Cos2 PHI cos def
 140  /Cos1Sin2 Cos1 Sin2 mul def
 141  /Sin1Sin2 Sin1 Sin2 mul def
 142  /Cos1Cos2 Cos1 Cos2 mul def
 143  /Sin1Cos2 Sin1 Cos2 mul def
 144  /xObservateur #2 Sin1 mul neg #3 Cos1 mul add def
 145  /yObservateur #2 Cos1Sin2 mul neg #3 Sin1Sin2 mul sub #4 Cos2 mul add def
 146  /zObservateur #2 neg Cos1Cos2 mul #3 Sin1Cos2 mul sub #4 Sin2 mul sub Dobs add def
 147  /xScreen DScreen xObservateur mul zObservateur div def
 148  /yScreen DScreen yObservateur mul zObservateur div def
 149   xScreen yScreen){#5}}}
 150  %
 151  \let\pskTroisDTheta \psk@TroisD@Theta
 152  \let\pskTroisDPhi \psk@TroisD@Phi
 153  \let\pskTroisDDobs \psk@TroisD@Dobs
 154  \let\pskTroisDEcran \psk@TroisD@Ecran
 155 \makeatother
 156
 157 \title{L'attracteur de Lorenz avec PSTricks}
 158 \date{12 juin 2012}
 159 \begin{document}
 160 \def\parametres{
 161     /Pr 10 def
 162     /Rh 28 def
 163     /beta 8 3 div def
 164 }%
 165 % y[0] y[1] y[2]
 166  % x    y     z
 167 \def\Lorenz{
 168 Pr*(y[1]-y[0])|%
 169 Rh*y[0]-y[1]-y[0]*y[2]|%
 170 y[0]*y[1]-beta*y[2]%
 171 }
 172 \def\conditionsInitiales{10 10 30}
 173 \begin{center}
 174 \def\nFrames{51}% 200 images
 175 \pstVerb{/XY [(LorenzXY.dat) run ] def
 176          /XZ [(LorenzXZ.dat) run ] def
 177          /YZ [(LorenzYZ.dat) run ] def
 178 /tabXYZ [
 179     0 2 XY length 2 sub {/i exch def
 180     [ XY i get
 181       XY i 1 add get
 182       YZ i 1 add get
 183     ]
 184     } for
 185    ]def}%
 186 \def\nFrames{72}% 72 images
 187 \begin{animateinline}[controls,loop,%
 188                      begin={\begin{pspicture}(-8,-3)(8,12)},
 189                      end={\end{pspicture}}]{5}% 5 images/s
 190 \multiframe{\nFrames}{i=0+5}{% tous les 10 degres
 191 \psframe*(-8,-4)(8,14)
 192 \psset{THETA=\i,PHI=20,Dobs=2000,Decran=400}
 193 \pstVerb{
 194  /THETA \pskTroisDTheta def
 195  /PHI \pskTroisDPhi def
 196  /Dobs \pskTroisDDobs def
 197  /DScreen \pskTroisDEcran def
 198  }%
 199 \pstVerb{
 200  /Sin1 THETA sin def
 201  /Sin2 PHI sin def
 202  /Cos1 THETA cos def
 203  /Cos2 PHI cos def
 204  /Cos1Sin2 Cos1 Sin2 mul def
 205  /Sin1Sin2 Sin1 Sin2 mul def
 206  /Cos1Cos2 Cos1 Cos2 mul def
 207  /Sin1Cos2 Sin1 Cos2 mul def
 208  /IIID {
 209  0 1 tabXYZ length 1 sub {/i exch def
 210  /TAB tabXYZ i get def
 211  /abscisse TAB 0 get def
 212  /ordonnee TAB 1 get def
 213  /cote TAB 2 get def
 214  \formules} for
 215  } def
 216  }%
 217 {\psset{unit=2.5,linestyle=dashed,linecolor=white}
 218 \pnodeTroisD(0,0,0){O}
 219 \pnodeTroisD(0,0,5){Z}
 220 \pnodeTroisD(5,0,0){X}
 221 \pnodeTroisD(0,5,0){Y}
 222 \pnodeTroisD(-10,-10,0){A}
 223 \pnodeTroisD(-10,-10,20){B}
 224 \pnodeTroisD(-10,10,20){C}
 225 \pnodeTroisD(-10,10,0){D}
 226 \pnodeTroisD(10,-10,0){E}
 227 \pnodeTroisD(10,-10,20){F}
 228 \pnodeTroisD(10,10,20){G}
 229 \pnodeTroisD(10,10,0){H}
 230 \pspolygon(A)(B)(C)(D)
 231 \pspolygon(E)(F)(G)(H)
 232 \psline(A)(E)
 233 \psline(B)(F)
 234 \psline(D)(H)
 235 \psline(C)(G)
 236 \psset{linestyle=solid,linecolor=red}
 237 \psline{->}(O)(X)
 238 \psline{->}(O)(Y)
 239 \psline{->}(O)(Z)}
 240 \listplotHSB[unit=1,linewidth=0.05]{IIID}
 241 }
 242 \end{animateinline}
 243 \end{center}
 244 \end{document}
 245