doc/par-positionnersolide.tex

   1 \newpage
   2 \section {Positionner un solide}
   3 \subsection{Translation}
   4 La commande suivante
   5 \verb+\psSolid[object=cube,+\textsl{options}\verb+](x,y,z)+ déplace le
   6 centre du cube au point de coordonnées $\mathtt{(x,y,z)}$.
   7
   8 L'exemple suivant va recopier le cube d'arête 1 \begin{pspicture}(-0.5,-0.5)(.5,.5)
   9 \psset{Decran=40,viewpoint=50 35 35,a=1,lightsrc=50 30 20}
  10 \psset{fillcolor=yellow,mode=3,
  11   fcol= 0 (Apricot)
  12         1 (Lavender)
  13         2 (SkyBlue)
  14         3 (LimeGreen)
  15         4 (OliveGreen)
  16         5 (Yellow)
  17         6 (GreenYellow)
  18         7 (Cerulean)
  19         8 (CarnationPink)}
  20 \psSolid[object=cube](0.5,0.5,0.5)% c1
  21 \end{pspicture}
  22  aux points de coordonnées $\mathtt{(0.5,0.5,0.5)}$, $\mathtt{(4.5,0.5,0.5)}$ etc. afin que ces copies occupent les coins d'un cube d'arête 5.
  23 \begin{center}
  24 \begin{pspicture}(-4,-5)(5,5)
  25 \psframe(-4,-5)(5,5)
  26 %\psset{SphericalCoor,Decran=3,viewpoint=10 35 35,a=1,lightsrc=50 20 10}
  27 \psset{Decran=40,viewpoint=50 35 35,a=1,lightsrc=50 30 20,
  28   fcol= 0 (Apricot)
  29         1 (Lavender)
  30         2 (SkyBlue)
  31         3 (LimeGreen)
  32         4 (OliveGreen)
  33         5 (Yellow)
  34         6 (GreenYellow)
  35         7 (Cerulean)
  36         8 (CarnationPink)}
  37 \psSolid[object=grille,base=0 6 0 6,fillcolor=blue!50]%%
  38 \psSolid[object=grille,base=0 6 0 6,RotY=90,fillcolor=blue!40](0,0,6)%
  39 \psSolid[object=grille,base=0 6 0 6,RotX=-90,fillcolor=blue!30](0,0,6)%
  40 \psPoint(1,0.5,0.5){c11}
  41 \psPoint(0.5,0.5,1){c12}
  42 \psPoint(0.5,1,0.5){c13}
  43 \psPoint(4.5,4.5,1){c21}
  44 \psPoint(4,4.5,0.5){c22}
  45 \psPoint(4.5,4,0.5){c23}
  46 \psPoint(4,0.5,0.5){c41}
  47 \psPoint(4.5,0.5,1){c42}
  48 \psPoint(4.5,1,0.5){c43}
  49 \psPoint(0.5,4,0.5){c51}
  50 \psPoint(0.5,4.5,1){c52}
  51 \psPoint(1,4.5,0.5){c53}
  52 \psPoint(0.5,0.5,4){c61}
  53 \psPoint(0.5,1,4.5){c62}
  54 \psPoint(1,0.5,4.5){c63}
  55 \psPoint(4,0.5,4.5){c71}
  56 \psPoint(4.5,1,4.5){c72}
  57 \psPoint(4.5,0.5,4){c73}
  58 \axesIIID(1,1,1)(6,6,6)
  59 {\psset{fillcolor=yellow,mode=3}
  60 \psSolid[object=cube](0.5,0.5,0.5)% c1
  61 \psline[linestyle=dashed,linecolor=red](c11)(c41)
  62 \psline[linestyle=dashed,linecolor=red](c12)(c61)
  63 \psline[linestyle=dashed,linecolor=red](c13)(c51)
  64 \psSolid[object=cube](4.5,0.5,0.5)
  65 \psSolid[object=cube](0.5,4.5,0.5)
  66 \psSolid[object=cube](0.5,0.5,4.5)
  67 \psSolid[object=cube](4.5,4.5,4.5)
  68 \psSolid[object=cube](4.5,0.5,4.5)
  69 \psSolid[object=cube](4.5,4.5,0.5)
  70 \psSolid[object=cube](0.5,4.5,4.5)}
  71 \psSolid[object=grille,base=0 5 0 5,action=draw,linecolor=gray!50](0,0,5)%
  72 \psSolid[object=grille,base=0 5 0 5,action=draw,linecolor=gray!50,RotY=90](5,0,5)%
  73 \psSolid[object=grille,base=0 5 0 5,action=draw,RotX=-90,linecolor=gray!50](0,5,5)%
  74 \end{pspicture}
  75 \end{center}
  76 \begin{verbatim}
  77 \psset{fillcolor=yellow,mode=3}
  78 \psSolid[object=cube](0.5,0.5,0.5)
  79 \psSolid[object=cube](4.5,0.5,0.5)
  80 \psSolid[object=cube](0.5,4.5,0.5)
  81 \psSolid[object=cube](0.5,0.5,4.5)
  82 \psSolid[object=cube](4.5,4.5,4.5)
  83 \psSolid[object=cube](4.5,0.5,4.5)
  84 \psSolid[object=cube](4.5,4.5,0.5)
  85 \psSolid[object=cube](0.5,4.5,4.5)
  86 \end{verbatim}
  87 \subsection{Rotation}
  88 La rotation s'effectue dans l'ordre autour des axes $Ox$, $Oy$ et $Oz$. Prenons l'exemple d'un parallélépipède rectangle,
  89 \begin{pspicture}(-1,-0.2)(1,.5)
  90 \psset{Decran=40,viewpoint=50 35 35,a=2,b=3,c=1,lightsrc=50 30 30}
  91 \psset{fillcolor=yellow,unit=0.5,
  92   fcol= 0 (Apricot)
  93         1 (Lavender)
  94         2 (SkyBlue)
  95         3 (LimeGreen)
  96         4 (OliveGreen)
  97         5 (Yellow)
  98         6 (Bittersweet)}
  99 \psSolid[object=parallelepiped](0.5,0.5,0.5)%
 100 \end{pspicture}
 101 que l'on va faire tourner
 102 successivement autour des axes $Ox$, $Oy$ et $Oz$.
 103
 104 \begin{multicols}{4}
 105 \psset{Decran=40,viewpoint=50 35 35,a=2,b=3,c=1}
 106 \psset{unit=0.5,
 107   fcol= 0 (Apricot)
 108         1 (Lavender)
 109         2 (SkyBlue)
 110         3 (LimeGreen)
 111         4 (OliveGreen)
 112         5 (Yellow)
 113         6 (Bittersweet),
 114   object=parallelepiped}
 115 \setlength{\columnseprule}{1pt}
 116 \centerline{
 117 \begin{pspicture}(-2.5,-2.5)(2.5,2.5)
 118 \psframe(-2.5,-2.5)(2.5,2.5)
 119 \psSolid%%
 120 \axesIIID(1,1.5,1)(3,3,2)
 121 \end{pspicture}}
 122 \columnbreak
 123 \centerline{
 124 \begin{pspicture}(-2.5,-2.5)(2.5,2.5)
 125 \psframe(-2.5,-2.5)(2.5,2.5)
 126 \psSolid[RotZ=60]%%
 127 \psSolid[action=draw,linewidth=0.5\pslinewidth]%%
 128 \axesIIID(1,1.5,1)(2,3,2)
 129 \end{pspicture}}
 130
 131 \centerline{\texttt{[RotZ=60]}}
 132
 133 \columnbreak
 134 \centerline{
 135 \begin{pspicture}(-2.5,-2.5)(2.5,2.5))
 136 \psframe(-2.5,-2.5)(2.5,2.5)
 137 \psSolid[RotX=30]%%
 138 \psSolid[action=draw,linewidth=0.5\pslinewidth]%%
 139 \axesIIID(1,1.5,1)(2,3,2)
 140 \end{pspicture}}
 141
 142 \centerline{\texttt{[RotX=30]}}
 143
 144 \columnbreak
 145 \centerline{
 146 \begin{pspicture}(-2.5,-2.5)(2.5,2.5)
 147 \psframe(-2.5,-2.5)(2.5,2.5)
 148 \psSolid[RotY=45]%%
 149 \psSolid[action=draw,linewidth=0.5\pslinewidth]%%
 150 \axesIIID(1,1.5,1)(2,3,2)
 151 \end{pspicture}}
 152
 153 \centerline{\texttt{[RotY=-45]}}
 154 \end{multicols}