doc/possible_extensions.tex

   1 \documentclass[12pt]{article}
   2 \usepackage{pst-anamorphosis-add,pst-plot}
   3 \usepackage[T1]{fontenc}
   4 \usepackage[ansinew]{inputenc}
   5 \usepackage{amsmath,amssymb}
   6 \usepackage[a4paper]{geometry}
   7
   8 \makeatletter
   9 \def\psparametricplotA{\pst@object{parametricplotA}}%   hv 2008-11-22
  10 \def\parametricplotA{\pst@object{parametricplotA}}
  11 \def\parametricplotA@i#1#2{\@ifnextchar[{\parametricplotA@x{#1}{#2}}{\parametricplotA@x{#1}{#2}[]}}
  12 \def\parametricplotA@x#1#2[#3]{\@ifnextchar[{\parametricplotA@xi{#1}{#2}[#3]}{\parametricplotA@xi{#1}{#2}[#3][]}}
  13 \def\parametricplotA@xi#1#2[#3][#4]#5{%
  14   \pst@killglue%
  15   \begingroup%
  16     \use@par%
  17     \@nameuse{beginplot@\psplotstyle}%
  18     \addto@pscode{%
  19     \tx@optionsanamorphosis
  20     \tx@optionsanamorphosisAdd
  21       #3 %prefix PS code
  22       \psplot@init
  23       /t #1 def
  24       /t1 #2 def
  25       /dt t1 t sub \psk@plotpoints div def
  26       /F@pstplot \ifPst@algebraic (#5)
  27                     \ifx\psk@PlotDerivative\@none\else
  28                       \psk@PlotDerivative\space { (t) tx@Derive begin Derive end } repeat
  29                     \fi\space
  30                     tx@AlgToPs begin AlgToPs end cvx
  31                  \else { #5 } \fi  def
  32       \ifPst@VarStep
  33          /StillZero 0 def /LastNonZeroStep dt def
  34          /F2@pstplot tx@Derive begin (#5) (t) Derive (t) Derive end
  35                      \ifx\psk@PlotDerivative\@none\else
  36                        \psk@PlotDerivative\space { (t) tx@Derive begin Derive end } repeat
  37                      \fi\space
  38                     tx@AlgToPs begin AlgToPs end cvx def
  39          %% computation of the tolerance defined by plotpoints
  40          /epsilon12 \ifx\psk@VarStepEpsilon\@default
  41                        tx@Derive begin F2@pstplot end Pyth
  42                        dt 3 exp abs mul
  43                     \else\psk@VarStepEpsilon\space 12 mul \fi def
  44          /ComputeStep {
  45            dup 1e-4 lt
  46            { pop StillZero 2 ge { LastNonZeroStep 2 mul } { LastNonZeroStep } ifelse /StillZero StillZero 1 add def }
  47            { epsilon12 exch div 1 3 div exp /StillZero 0 def }
  48            ifelse } bind def
  49       \fi
  50       /xy {
  51         \ifPst@algebraic F@pstplot \else #5 \fi
  52         \pst@number\psyunit mul exch
  53         \pst@number\psxunit mul exch
  54         tx@anamorphosisPathDict begin Anamorphose end
  55       } def
  56       }%
  57     \gdef\psplot@init{}%
  58     \@pstfalse
  59     \@nameuse{testqp@\psplotstyle}%
  60     \if@pst\parametricplotA@ii{#4}\else\parametricplotA@iii{#4}\fi
  61   \endgroup%
  62   \ignorespaces}
  63 %
  64 \def\parametricplotA@ii#1{% para is the post code
  65   \ifPst@VarStep%
  66     \addto@pscode{%
  67       mark xy \@nameuse{beginqp@\psplotstyle}
  68       { F2@pstplot Pyth ComputeStep
  69         t 2 copy add dup t1 gt {pop t1} if /t exch def F2@pstplot Pyth ComputeStep
  70         /t 3 -1 roll def 2 copy gt { exch } if pop
  71         /t t 3 -1 roll add dup t1 gt {pop t1} if def
  72         xy \@nameuse{doqp@\psplotstyle}
  73         t t1 eq { exit } if } loop}%
  74   \else\pst@killglue%
  75     \addto@pscode{%
  76       /ps@Exit false def
  77       xy \@nameuse{beginqp@\psplotstyle}
  78       \psk@plotpoints 1 sub {
  79         /t t dt add def
  80         xy \@nameuse{doqp@\psplotstyle}
  81         ps@Exit { exit } if
  82       } repeat
  83       ps@Exit not {
  84         /t t1 def
  85         xy \@nameuse{doqp@\psplotstyle}
  86       } if
  87     }%
  88   \fi%
  89   \addto@pscode{ #1 }%
  90   \@nameuse{endqp@\psplotstyle}}
  91 %
  92 \def\parametricplotA@iii#1{%
  93   \ifPst@VarStep%
  94     \addto@pscode{%
  95       /n 2 def
  96       mark
  97       { xy n 2 roll F2@pstplot Pyth
  98         ComputeStep t 2 copy add dup t1 gt {pop t1} if
  99         /t exch def F2@pstplot Pyth ComputeStep
 100         /t 3 -1 roll def 2 copy gt { exch } if pop
 101         /t t 3 -1 roll dup /LastNonZeroStep exch def add dup t1 gt {pop t1} if def /n n 2 add def
 102         t t1 eq { exit } if } loop
 103       xy n 2 roll}%
 104   \else\pst@killglue%
 105     \addto@pscode{
 106       mark
 107       /n 2 def
 108       \psk@plotpoints {
 109         xy
 110         n 2 roll
 111         /n n 2 add def
 112         /t t dt add def
 113       } repeat
 114       /t t1 def
 115       xy
 116       n 2 roll}%
 117   \fi%
 118   \addto@pscode{ #1 }%
 119   \@nameuse{endplot@\psplotstyle}}
 120 %
 121 %%%%%%%\psframeA ---------------------
 122 \def\psframeA{\pst@object{psframeA}}
 123 \def\psframeA@i(#1){%
 124 \@ifnextchar({\psframeA@ii(#1)}{\psframeA@ii(0,0)(#1)}}
 125 \def\psframeA@ii(#1)(#2){%
 126 \begin@ClosedObj
 127 \pst@getcoor{#1}\pst@tempa%
 128 \pst@@getcoor{#2}%
 129 \def\pst@linetype{2}%
 130 \addto@pscode{%
 131     \tx@optionsanamorphosis
 132     \tx@optionsanamorphosisAdd
 133     \pst@tempa
 134     \pst@coor
 135     /Y2 ED
 136     /X2 ED
 137     /Y1 ED
 138     /X1 ED
 139     X1 Y1  tx@anamorphosisPathDict begin Anamorphose end
 140     moveto
 141     0 0.005 1.0 { %(X1,Y1)->(X2,Y1)
 142     /K exch def
 143     K X2 mul 1 K sub X1 mul add
 144     Y1
 145     tx@anamorphosisPathDict begin Anamorphose end
 146     lineto
 147     } for
 148     0 0.005 1.0 { % (X2,Y1)->(X2,Y2)
 149     /K exch def
 150     X2
 151     K Y2 mul 1 K sub Y1 mul add
 152     tx@anamorphosisPathDict begin Anamorphose end
 153     lineto
 154     } for
 155     0 0.005 1.0 { % (X2,Y2)->(X1,Y2)
 156     /K exch def
 157     K X1 mul 1 K sub X2 mul add
 158     Y2
 159     tx@anamorphosisPathDict begin Anamorphose end
 160     lineto
 161     } for
 162     0 0.005 1.0 { % (X1,Y2)->(X1,Y1)
 163     /K exch def
 164     X1
 165     K Y1 mul 1 K sub Y2 mul add
 166     tx@anamorphosisPathDict begin Anamorphose end
 167     lineto
 168     } for
 169 }%
 170 \showpointsfalse
 171 \end@ClosedObj}
 172 %
 173 %%%%%%%\translateA ---------------------------
 174 \def\translateA{\def\pst@par{}\pst@object{translateA}}
 175 \def\translateA@i(#1){{%
 176 \pst@@getcoor{#1}%
 177 \addto@pscode{
 178     \tx@optionsanamorphosis
 179     \tx@optionsanamorphosisAdd
 180  \pst@coor
 181 tx@anamorphosisPathDict begin Anamorphose end
 182     translate}}}%
 183 %
 184
 185 \title{pst-anamorphosis : extensions possibles}
 186 \author{Jürgen Gilg, Manuel Luque, Jean-Michel Sarlat}
 187 \date{21 octobre 2011}
 188 \begin{document}
 189 \maketitle
 190 \begin{abstract}
 191 Il est relativement facile d'adapter les commandes de \textsf{PStricks} à \textsf{pst-anamorphosis}. C'est ainsi que la plupart des macros de \textsf{pst-anamorphosis-add} sont des adaptations de celles de \textsf{PStricks}. Toutes ne l'on pas été pour ne pas alourdir inutilement le package. Nous allons détailler sur un exemple la façon de procéder.
 192
 193 Remarque : toutes les macros ne sont pas adaptables, cela serait le cas si les anamorphoses transformaient une ligne droite en une ligne droite. Or, à part la perspective, ce n'est pas le cas. En conséquence, \verb+\psline+, \verb+\psframe+, \verb+\pspolygon+ doivent être réécrits en divisant le segment initial en un grand nombre de petits segments : pour  \verb+\pslineA+ par exemple chaque segment initial est divisé en 200 parties et ceci quelle que soit sa longueur, dans l'idéal il faudrait tenir compte de la longueur du segment avant de choisir le nombre de segmentations.
 194 \end{abstract}
 195 \section{\textbackslash{}psparametricplotA}
 196 \subsection{Adaptation}
 197 À partir d'une copie de \textbackslash{}\textsf{psparametricplot} :
 198 \begin{enumerate}
 199   \item On remplace parout \textsf{psparametricplot} par \textsf{psparametricplotA} ;
 200   \item dans le premier \verb+\addto@pscode{%+
 201   \begin{verbatim}
 202   \addto@pscode{%
 203     \tx@optionsanamorphosis
 204     \tx@optionsanamorphosisAdd
 205       #3 %prefix PS code
 206       \psplot@init
 207   \end{verbatim}
 208   on introduit juste au début les variables de \textsf{pst-anamorphosis} ;
 209   \item et pour terminer dans \verb+/xy {+:
 210 \begin{verbatim}
 211           /xy {
 212         \ifPst@algebraic F@pstplot \else #5 \fi
 213         \pst@number\psyunit mul exch
 214         \pst@number\psxunit mul exch
 215         tx@anamorphosisPathDict begin Anamorphose end
 216       } def
 217 \end{verbatim}
 218  on insère à la fin les calculs propres à l'anamorphose. C'est terminé, la macro est opérationnelle !
 219 \end{enumerate}
 220 \subsection{Exemple}
 221 \begin{center}
 222 \begin{pspicture}(-6,-6)(6,6)
 223 \pscircle[doubleline=true]{3}
 224 \psset{type=conical}
 225 \pscircle[linecolor=blue](0,0){1}
 226 \pscircleA[linecolor=blue](0,0){1}
 227 \pscircle[linecolor=blue](0,0){2}
 228 \pscircleA[linecolor=blue](0,0){2}
 229 \psframeA[linecolor=blue,fillstyle=solid,fillcolor=cyan](1,1)(2,2)
 230 \psframeA[linecolor=blue,fillstyle=solid,fillcolor=cyan](-1,-1)(-2,-2)
 231 \psframeA[linecolor=blue,fillstyle=solid,fillcolor=cyan](-1,1)(-2,2)
 232 \psframeA[linecolor=blue,fillstyle=solid,fillcolor=cyan](1,-1)(2,-2)
 233 \psframe[linecolor=blue,fillstyle=solid,fillcolor=cyan](1,1)(2,2)
 234 \psframe[linecolor=blue,fillstyle=solid,fillcolor=cyan](-1,-1)(-2,-2)
 235 \psframe[linecolor=blue,fillstyle=solid,fillcolor=cyan](-1,1)(-2,2)
 236 \psframe[linecolor=blue,fillstyle=solid,fillcolor=cyan](1,-1)(2,-2)
 237 \parametricplotA[plotpoints=3600,linecolor=red,linewidth=1mm]{0}{360}{%
 238   /Radius 1.5 0.5 t 10 mul sin mul add def
 239   Radius t cos mul
 240   Radius t sin mul
 241     }
 242 \parametricplot[plotpoints=3600,linecolor=red,linewidth=1mm]{0}{360}{%
 243   /Radius 1.5 0.5 t 10 mul sin mul add def
 244   Radius t cos mul
 245   Radius t sin mul
 246     }
 247 \multido{\n=0.5+0.5,\N=0.5+0.5}{4}{%
 248     \pnode(! \n\space -2){A}
 249     \pnode(! \n\space 2){B}
 250     \psline(A)(B)
 251     \pslineA(A)(B)
 252     \pnode(!-2 \N){A}
 253     \pnode(!2 \N){B}
 254     \pslineA(A)(B)
 255     \psline(A)(B)
 256     }
 257 \multido{\n=-2.0+0.5,\N=-2.0+0.5}{4}{%
 258     \pnode(! \n\space -2){A}
 259     \pnode(! \n\space 2){B}
 260     \psline(A)(B)
 261     \pslineA(A)(B)
 262     \pnode(!-2 \N){A}
 263     \pnode(!2 \N){B}
 264     \pslineA(A)(B)
 265     \psline(A)(B)
 266     }
 267 \psline(-2,0)(2,0)
 268 \psline(0,-2)(0,2)
 269 \pslineA(0,-2)(0,-0.5)
 270 \pslineA(0,2)(0,0.5)
 271 \pslineA(-2,0)(-0.5,0)
 272 \pslineA(2,0)(0.5,0)
 273 \psdot[dotstyle=x,dotsize=.2](0,0)
 274 \end{pspicture}
 275 \end{center}
 276 \begin{verbatim}
 277 \parametricplotA[plotpoints=3600,linecolor=red,linewidth=1mm]{0}{360}{%
 278   /Radius 1.5 0.5 t 10 mul sin mul add def
 279   Radius t cos mul
 280   Radius t sin mul
 281     }
 282 \parametricplot[plotpoints=3600,linecolor=red,linewidth=1mm]{0}{360}{%
 283   /Radius 1.5 0.5 t 10 mul sin mul add def
 284   Radius t cos mul
 285   Radius t sin mul
 286 \end{verbatim}
 287 \section{\textbackslash{}psframeA}
 288 \verb+\psframeA(x1,y1)(x2,y2)+ a les mêmes propriétés que \verb+\psframe+
 289 \begin{center}
 290 \begin{pspicture}(-6,-6)(6,6.5)
 291 \psset{type=conical,Rmirror=3}
 292 \psframeA[fillstyle=solid,fillcolor=blue,linecolor=blue](-0.25,-0.25)(-0.01,-0.01)
 293 \psframeA[fillstyle=solid,fillcolor=blue,linecolor=blue](-0.25,0.25)(-0.01,0.01)
 294 \psframeA[fillstyle=solid,fillcolor=blue,linecolor=blue](0.01,0.01)(0.25,0.25)
 295 \psframeA[fillstyle=solid,fillcolor=blue,linecolor=blue](0.01,-0.01)(0.25,-0.25)
 296 \multido{\ry=-2.75+1,\rY=-2.25+1}{6}{
 297 \multido{\n=-2.75+1.00,\N=-2.25+1.00}{7}{%
 298     \psframeA[fillstyle=solid,fillcolor=red,linecolor=red](\n,\ry)(\N,\rY)}
 299     }
 300 \multido{\ry=-3.25+1,\rY=-2.75+1}{3}{
 301 \multido{\n=-3.25+1.00,\N=-2.75+1.00}{7}{%
 302     \psframeA[fillstyle=solid,fillcolor=blue,linecolor=blue](\n,\ry)(\N,\rY)}
 303     }
 304 \multido{\ry=0.75+1,\rY=1.25+1}{3}{
 305 \multido{\n=-3.25+1.00,\N=-2.75+1.00}{7}{%
 306     \psframeA[fillstyle=solid,fillcolor=blue,linecolor=blue](\n,\ry)(\N,\rY)}
 307     }
 308 \multido{\n=-3.25+1.00,\N=-2.75+1.00}{3}{%
 309     \psframeA[fillstyle=solid,fillcolor=blue,linecolor=blue](\n,-0.25)(\N,0.25)}
 310 \multido{\n=0.75+1.00,\N=1.25+1.00}{3}{%
 311     \psframeA[fillstyle=solid,fillcolor=blue,linecolor=blue](\n,-0.25)(\N,0.25)}
 312 \begin{psclip}{\pscircle[fillstyle=solid,fillcolor=white,linestyle=none]{3}}
 313 \multido{\ry=-2.75+1,\rY=-2.25+1}{6}{
 314 \multido{\n=-2.75+1.00,\N=-2.25+1.00}{6}{%
 315     \psframe*[linecolor=red](\n,\ry)(\N,\rY)}
 316     }
 317 \multido{\ry=-3.25+1,\rY=-2.75+1}{7}{
 318 \multido{\n=-3.25+1.00,\N=-2.75+1.00}{7}{%
 319     \psframe*[linecolor=blue](\n,\ry)(\N,\rY)}
 320     }
 321 \pscircle[doubleline=true]{3}
 322 \end{psclip}
 323 \end{pspicture}
 324 \end{center}
 325 \begin{verbatim}
 326     \multido{\ry=-2.75+1,\rY=-2.25+1}{6}{
 327 \multido{\n=-2.75+1.00,\N=-2.25+1.00}{7}{%
 328     \psframeA[fillstyle=solid,fillcolor=red,linecolor=red](\n,\ry)(\N,\rY)}
 329     }
 330 \multido{\ry=-3.25+1,\rY=-2.75+1}{3}{
 331 \multido{\n=-3.25+1.00,\N=-2.75+1.00}{7}{%
 332     \psframeA[fillstyle=solid,fillcolor=blue,linecolor=blue](\n,\ry)(\N,\rY)}
 333     }
 334 \end{verbatim}
 335 \section{\textbackslash{}pspolygonA}
 336 En réalité la macro \verb+pspolygonA+ n'a pas été écrite. En effet il suffit de servir de \verb+\pslineA+ et de boucler le chemin en revenant au point origine.
 337 \begin{center}
 338 \begin{pspicture}(-5,-5)(5,5)
 339 \psset{type=conical,Rmirror=3}
 340 \pspolygon[linecolor=red,linewidth=1mm](2.5;30)(2.5;90)(2.5;150)(2.5;210)(2.5;270)(2.5;330)
 341 \pslineA[linecolor=red,linewidth=1mm](2.5;30)(2.5;90)(2.5;150)(2.5;210)(2.5;270)(2.5;330)(2.5;30)
 342 \rput(1.25,1){\pspolygon[linecolor=blue,fillstyle=solid,linewidth=1mm,fillcolor={[rgb]{1 0.875 0.5}}](0.75;30)(0.75;90)(0.75;150)(0.75;210)(0.75;270)(0.75;330)}
 343 \multido{\i=30+60,\I=1+1}{6}{%
 344     \pnode(!\i\space cos 0.75 mul 1.25 add \i\space sin 0.75 mul 1 add){A\I}
 345     }
 346 \pslineA[linecolor=blue,fillstyle=solid,linewidth=1mm,fillcolor={[rgb]{1 0.875 0.5}}](A1)(A2)(A3)(A4)(A5)(A1)
 347 \pscircle[doubleline=true]{3}
 348 \psdot[dotstyle=x](0,0)
 349 \end{pspicture}
 350 \end{center}
 351 \begin{verbatim}
 352 \begin{pspicture}(-5,-5)(5,5)
 353 \psset{type=conical,Rmirror=3}
 354 \pspolygon[linecolor=red,linewidth=1mm](2.5;30)(2.5;90)(2.5;150)(2.5;210)(2.5;270)(2.5;330)
 355 \pslineA[linecolor=red,linewidth=1mm](2.5;30)(2.5;90)(2.5;150)(2.5;210)(2.5;270)(2.5;330)(2.5;30)
 356 \rput(1.25,1){\pspolygon[linecolor=blue,fillstyle=solid,linewidth=1mm,fillcolor={[rgb]{1 0.875 0.5}}](0.75;30)(0.75;90)(0.75;150)(0.75;210)(0.75;270)(0.75;330)}
 357 \multido{\i=30+60,\I=1+1}{6}{%
 358     \pnode(!\i\space cos 0.75 mul 1.25 add \i\space sin 0.75 mul 1 add){A\I}
 359     }
 360 \pslineA[linecolor=blue,fillstyle=solid,linewidth=1mm,fillcolor={[rgb]{1 0.875 0.5}}](A1)(A2)(A3)(A4)(A5)(A1)
 361 \pscircle[doubleline=true]{3}
 362 \psdot[dotstyle=x](0,0)
 363 \end{pspicture}
 364 \end{verbatim}
 365 On remarquera que le \verb+\rput(1.25,1)+ doit être remplacé par un calcul adapté. La macro \verb+\rputA+ n'a pas été définie.
 366 \end{document}