lorenz/animXY_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 \psset{#1}%
 130 \pnode(!
 131  /THETA \psk@TroisD@Theta\space def
 132  /PHI \psk@TroisD@Phi\space def
 133  /Dobs \psk@TroisD@Dobs\space def
 134  /DScreen \psk@TroisD@Ecran\space def
 135  /Sin1 THETA sin def
 136  /Sin2 PHI sin def
 137  /Cos1 THETA cos def
 138  /Cos2 PHI cos def
 139  /Cos1Sin2 Cos1 Sin2 mul def
 140  /Sin1Sin2 Sin1 Sin2 mul def
 141  /Cos1Cos2 Cos1 Cos2 mul def
 142  /Sin1Cos2 Sin1 Cos2 mul def
 143  /xObservateur #2 Sin1 mul neg #3 Cos1 mul add def
 144  /yObservateur #2 Cos1Sin2 mul neg #3 Sin1Sin2 mul sub #4 Cos2 mul add def
 145  /zObservateur #2 neg Cos1Cos2 mul #3 Sin1Cos2 mul sub #4 Sin2 mul sub Dobs add def
 146  /xScreen DScreen xObservateur mul zObservateur div def
 147  /yScreen DScreen yObservateur mul zObservateur div def
 148   xScreen yScreen){#5}}}
 149 \makeatother
 150 %timeline
 151 \begin{filecontents}{lorenzxy.txt}
 152 ::0x0
 153 ::1
 154 ::2
 155 ::3
 156 ::4
 157 ::5
 158 ::6
 159 ::7
 160 ::8
 161 ::9
 162 ::10
 163 ::11
 164 ::12
 165 ::13
 166 ::14
 167 ::15
 168 ::16
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 170 ::18
 171 ::19
 172 ::20
 173 ::21
 174 ::22
 175 ::23
 176 ::24
 177 ::25
 178 ::26
 179 ::27
 180 ::28
 181 ::29
 182 ::30
 183 ::31
 184 ::32
 185 ::33
 186 ::34
 187 ::35
 188 ::36
 189 ::37
 190 ::38
 191 ::39
 192 ::40
 193 ::41
 194 ::42
 195 ::43
 196 ::44
 197 ::45
 198 ::46
 199 ::47
 200 ::48
 201 ::49
 202 ::50
 203 ::51
 204 \end{filecontents}
 205 \title{L'attracteur de Lorenz avec PSTricks}
 206 \date{12 juin 2012}
 207 \begin{document}
 208 \def\parametres{
 209     /Pr 10 def
 210     /Rh 28 def
 211     /beta 8 3 div def
 212 }%
 213 % y[0] y[1] y[2]
 214  % x    y     z
 215 \def\Lorenz{
 216 Pr*(y[1]-y[0])|%
 217 Rh*y[0]-y[1]-y[0]*y[2]|%
 218 y[0]*y[1]-beta*y[2]%
 219 }
 220 \def\conditionsInitiales{10 10 30}
 221 \begin{center}
 222 \begin{pspicture}(-8,-.01)(8,0.01)
 223 %\psgrid[subgriddiv=0,gridcolor=lightgray,griddots=10,gridlabels=0pt]%
 224 \pstVerb{\parametres}%
 225   \psequadiff[% x,y
 226   tabname=tabXY,
 227   method=rk4,
 228   whichabs=0,whichord=1,
 229   saveData,filename=LorenzXY.dat,
 230   plotpoints=2501,algebraic]{0}{25}{\conditionsInitiales}{\Lorenz}
 231 %% une commande PSTricks est indispensable si on ne vaut pas tracer le courbe
 232  \psdot[linecolor=white,dotsize=0.001](0,0)
 233 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 234 %\listplotHSB[unit=0.25]{tabXY aload pop}%
 235 %\uput[r](8,0){$x$}
 236 %\uput[u](0,8){$y$}
 237 \end{pspicture}
 238 \end{center}
 239 \begin{center}
 240 \def\nFrames{51}% 200 images
 241 \pstVerb{/XYlorentz [ (LorenzXY.dat) run ] def}%
 242 \begin{animateinline}[controls,timeline=lorenzxy.txt,%
 243                      begin={\begin{pspicture}(-8,-6)(8,7)},
 244                      end={\end{pspicture}}]{10}% 10 images/s
 245 \psgrid[subgriddiv=0,gridcolor=lightgray,griddots=10,gridlabels=0pt]%
 246 \rput(0,6.5){\large\textbf{XY}$(x_0=10,y_0=10,z_0=30)$}
 247 \listplotHSB[unit=0.25,HSB=false,linecolor=gray]{XYlorentz aload pop}%
 248 \newframe
 249 \multiframe{\nFrames}{i=0+100}{% 1 point sur 10
 250  \pstVerb{      /XYpartiel {0 2 \i\space {/i exch def
 251                  XYlorentz i get
 252                  XYlorentz i 1 add get
 253                  } for
 254                  }def
 255                  }%
 256 \listplotHSB[unit=0.25,linewidth=0.2]{XYpartiel}%
 257 }
 258 \end{animateinline}
 259 \end{center}
 260 \end{document}
 261