doc/fig3d-anacon.tex

   1 \begin{center}
   2 \psscalebox{0.7}{
   3 \begin{pspicture}(-7,-8)(7,9)
   4 \newcommand\R{3}
   5 \newcommand\hauteur{5}
   6 \newcommand\pas{10}
   7 \FPeval{\pasrad}{\pas*\FPpi/180}
   8  \FPmul{\Largeur}{\R}{\pasrad}
   9  \FPdiv{\largeur}{\Largeur}{2}
  10 %Les coordonn\'{e}es de viewpoint
  11 \def\vx{1}\def\vy{-0.8}\def\vz{1}
  12 \FPeval{\RH}{(\R)/(\hauteur)}
  13  \FParctan{\phy}{\RH}
  14  \FPeval{\OH}{sin(\phy)*\hauteur}
  15  \FPeval{\zH}{sin(\phy)*\OH}
  16  \FPeval{\OK}{cos(\phy)*\OH}
  17  \FPeval{\generatrice}{root(2,(\hauteur*\hauteur)+(\R*\R))}
  18 \psset{viewpoint={\vx} {\vy} {\vz}}
  19 \ThreeDput[normal=0 0 1](0,0,0){%%
  20 \psframe*[linecolor=lightgray!25](-10,-10)(10,10)
  21 \psgrid[subgriddiv=0,gridcolor=lightgray,gridlabels=0pt](-10,-10)(10,10)
  22 \psaxes(0,0)(-10,-10)(10,10)
  23 \pscircle[doubleline=true]{3}
  24 \psset{type=conical}
  25 \multido{\n=-1.50+0.50}{7}{%
  26     \pnode(! \n\space -2.50){A}
  27     \pnode(! \n\space -0.50){B}
  28     \psline[linecolor=green](A)(B)
  29     \pslineA[linecolor=green](A)(B)
  30     }
  31 \multido{\N=-2.50+0.50}{5}{%
  32     \pnode(!-1.50 \N){A}
  33     \pnode(!1.50 \N){B}
  34     \pslineA[linecolor=green](A)(B)
  35     \psline[linecolor=green](A)(B)
  36     }
  37 %
  38 \multido{\n=-1.50+0.50}{7}{%
  39     \pnode(! \n\space 2.50){A}
  40     \pnode(! \n\space 0.50){B}
  41     \psline[linecolor=green](A)(B)
  42     \pslineA[linecolor=green](A)(B)
  43     }
  44 \multido{\N=2.50+-0.50}{5}{%
  45     \pnode(!-1.50 \N){A}
  46     \pnode(!1.50 \N){B}
  47     \pslineA[linecolor=green](A)(B)
  48     \psline[linecolor=green](A)(B)
  49     }
  50 \multido{\n=-1.50+0.50}{7}{%
  51     \pnode(! \n\space -2.50){A}
  52     \pnode(! \n\space -0.50){B}
  53     \psline(A)(B)
  54     \pslineA(A)(B)
  55     }
  56 \multido{\N=-2.50+0.50}{5}{%
  57     \pnode(!-1.50 \N){A}
  58     \pnode(!1.50 \N){B}
  59     \pslineA(A)(B)
  60     \psline(A)(B)
  61     }
  62 \multido{\n=-1.50+0.50}{7}{%
  63     \pnode(! \n\space 2.50){A}
  64     \pnode(! \n\space 0.50){B}
  65     \psline(A)(B)
  66     \pslineA(A)(B)
  67     }
  68 \multido{\N=2.50+-0.50}{5}{%
  69     \pnode(!-1.50 \N){A}
  70     \pnode(!1.50 \N){B}
  71     \pslineA(A)(B)
  72     \psline(A)(B)
  73     }
  74 \psanamorphosis[type=conical,scale=-0.7 -0.7](0,1.5){tiger.eps}
  75 \pstextA[fontsize=15,fillcolor=green,scale=1 -1](0,-0.5){Anamorphose}
  76 \pscircle[doubleline=true]{3}}
  77 \newcount\n \n=0
  78      \loop
  79      \FPmul{\tempa}{\FPpi}{\the\n}
  80      \FPdiv{\angle}{\tempa}{180}
  81      \FPsin{\SIN}{\angle}\FPcos{\COS}{\angle}
  82      \FPmul{\xH}{\COS}{\OK}
  83      \FPmul{\yH}{\SIN}{\OK}
  84      \FPdiv{\grise}{\the\n}{360}
  85      \FPsub{\gris}{1}{\grise}
  86      \FPdiv{\teinte}{\grise}{2}
  87 \definecolor{gris}{cmyk}{\teinte,\teinte,\teinte,0}
  88 %tester les faces visibles
  89 %le produit scalaire du vecteur viewpoint et du vecteur normal \`{a} la face >0 ?
  90 \FPeval{\costest}{(\vx)*\xH+(\vy)*\yH+(\vz)*\zH}
  91    \FPifpos{\costest}
  92    \ThreeDput[normal={\xH} {\yH} \zH](0,0,\hauteur){%
  93         \pspolygon[linecolor=BleuCiel]%[fillstyle=solid,fillcolor=gris,dimen=outer]%
  94         (0,0)(-\largeur,-\generatrice)(\largeur,-\generatrice)}\else{}\fi
  95    \FPifneg{\costest}
  96    \ThreeDput[normal={\xH} {\yH} \zH](0,0,\hauteur){%
  97    \psline[linestyle=dashed,linecolor=gray](0,0)(\largeur,-\generatrice)}\else{}\fi
  98      \ifnum\n<360 \advance\n by \pas
  99 \repeat
 100 %Dessin des faces de dessus et de dessous
 101 %\FPifneg\vz
 102 %face de dessous
 103 %\ThreeDput[normal=0 0 -1](0,0,0){%
 104 %\pscircle[fillstyle=solid,fillcolor=lightgray](0,0){\R}\rput(0,0){\Large\textbf{\textsf{Dessous}}}}\fi
 105 \ThreeDput[normal=1 0 0](0,0,0){%
 106 \psaxes(1,10)
 107 \rput{90}(0,12){\oeil}%
 108 {\boldmath
 109 \red
 110 \pnode(0,10){V}
 111 \uput[0](V){$V$}
 112 \pnode(0,5){S}
 113 \uput[0](S){$S$}
 114 \pnode(-1.5,2.5){I}
 115 \uput[180](I){$I$}
 116 \qdisk(I){2pt}
 117 \pnode(-2,0){P}
 118 \uput[135](P){$P$}
 119 \pnode(-4.545,0){P'}
 120 \uput[135](P'){$P'$}
 121 \psset{linecolor=red}
 122 \psline(V)(I)(P')
 123 \pcline[nodesepB=2,nodesepA=1,linecolor=red,arrowsize=0.175,arrowinset=0.075]{->}(P')(I)
 124 \pcline[nodesepB=4,nodesepA=1,linecolor=red,arrowsize=0.175,arrowinset=0.075]{->}(I)(V)
 125 \psline[linestyle=dashed](I)(P)}}%
 126 \end{pspicture}
 127 }
 128 \end{center}