Initialisation du projet pst-solides3d.git (SVN revision 142)

[pst-solides3d.git] / doc / par-solidespredefinis.tex

\section[Paramètres]{Les principaux solides prédéfinis et leurs paramètres}

La commande de base est~:~
\Cadre{\textbackslash psSolid[object=\textsl{nom}]$(x, y ,z)$} qui permet
de tracer l'objet désigné par \textsl{nom} au point de coordonnées $(x, y,
z)$. 

Les objets disponibles sont~:
{\ttfamily%\flushleft \hyphenchar\font`\-%
cube, cylindre, cylindrecreux, cone, conecreux, tronccone,\\
troncconecreux, sphere, calottesphere, tore, anneau, 
tetrahedron, octahedron, dodecahedron,\\
isocahedron, prisme, grille, parallelepiped, face, ruban, surface,
plan, geode,vecteur.}

Le tableau ci-dessous donne un exemple de chacun des solides avec ses
paramètres propres~:

\begin{center}
\psset{lightsrc=10 5 20,viewpoint=50 20 30 rtp2xyz}
\begin{tabular}{>{\bfseries\sffamily\color{blue}}lcm{4cm}m{5cm}}
  \hline
\toptableau
\\\hline
 cube& \texttt{[a=4]} arête&
 \begin{pspicture}(-2,-2)(2,2)
% \psframe(-2,-2)(2,2)
 \psset{Decran=60}
 \psSolid[
 object=cube,a=2,action=draw*,fillcolor=magenta!20]%
 \axesIIID(1,1,1)(1.5,1.5,1.5)
 \end{pspicture}
 &
 \begin{minipage}{5cm}
 \begin{verbatim}
\psSolid[
   object=cube,
   a=2,
   action=draw*,
   fillcolor=magenta!20]
 \end{verbatim}
 \end{minipage}
\\\hline
 cylindre&
    \begin{tabular}{c}
     \texttt{[h=6,r=2]}\\
     hauteur et rayon\\
     le maillage :\\
     \texttt{[ngrid=n1 n2]}
     \end{tabular}
     &
 \begin{pspicture}(-2,-2.5)(2,3)
% \psframe(-2,-2)(2,2)
 \psset{Decran=30}
\psSolid[object=cylindre,h=5,r=2,fillcolor=white,ngrid=4 32](0,0,-3)
 \axesIIID(2,2,2.5)(3,3,3.5)
 \end{pspicture}
 &
 \begin{minipage}{5cm}
 \begin{verbatim}
\psSolid[
   object=cylindre,
  h=5,r=2,
  fillcolor=white,
  ngrid=4 32](0,0,-3)
 \end{verbatim}
 \end{minipage}
\\\hline
 cylindre creux&
    \begin{tabular}{c}
     \texttt{[h=6,r=2]}\\
     hauteur et rayon\\
     le maillage :\\
     \texttt{[ngrid=n1 n2]}
     \end{tabular}
     &
 \begin{pspicture}(-2,-2.5)(2,3)
% \psframe(-2,-2)(2,2)
 \psset{Decran=30}
\psSolid[object=cylindrecreux,h=5,r=2,fillcolor=white,mode=4,incolor=green!50](0,0,-2.5)
 \axesIIID(2,2,2.5)(3,3,4.5)
 \end{pspicture}
 &
 \begin{minipage}{5cm}
 \begin{verbatim}
\psSolid[
   object=cylindrecreux,
   h=5,r=2,
   fillcolor=white,
   mode=4,
   incolor=green!50]
   (0,0,-3)
 \end{verbatim}
 \end{minipage}
 \\\hline
\end{tabular}
\end{center}

\begin{center}
\psset{lightsrc=10 20 30,viewpoint=50 20 30 rtp2xyz}
\begin{tabular}{>{\bfseries\sffamily\color{blue}}lcm{4cm}m{5cm}}
  \hline
\toptableau
\\\hline
 cone&
     \begin{tabular}{c}
     \texttt{[h=6,r=2]}\\
     hauteur et rayon\\
     le maillage :\\
     \texttt{[ngrid=n1 n2]}
     \end{tabular}
     &
 \begin{pspicture}(-2,-1)(2,4)
% \psframe(-2,-2)(2,2)
 \psset{Decran=30}
 \psSolid[object=cone,h=5,r=2,fillcolor=cyan,mode=4]%
 \axesIIID(2,2,5)(2.5,2.5,6)
 \end{pspicture}
 &
 \begin{minipage}{5cm}
 \begin{verbatim}
 \psSolid[
    object=cone,
    h=5,r=2,
    fillcolor=cyan,
    mode=4]%
 \end{verbatim}
 \end{minipage}
\\\hline
 cone creux&
     \begin{tabular}{c}
     \texttt{[h=6,r=2]}\\
     hauteur et rayon\\
     le maillage :\\
     \texttt{[ngrid=n1 n2]}
     \end{tabular}
     &
 \begin{pspicture}(-2,-1)(2,4)
% \psframe(-2,-2)(2,2)
 \psset{Decran=30}
 \psSolid[object=conecreux,h=5,r=2,fillcolor=white,mode=4,RotY=-60,incolor=green!50]%
 \axesIIID(2,2,5)(2.5,2.5,6)
 \end{pspicture}
 &
 \begin{minipage}{5cm}
 \begin{verbatim}
 \psSolid[
    object=conecreux,
    h=5,r=2,
    RotY=-60,
    fillcolor=white,
    incolor=green!50,
    mode=4]%
 \end{verbatim}
 \end{minipage}
 \\\hline
 tronc de cone&
     \begin{tabular}{c}
     \texttt{[h=6,r0=4,r1=1.5]}\\
     hauteur et rayons\\
     le maillage :\\
     \texttt{[ngrid=n1 n2]}
     \end{tabular}
     &
 \begin{pspicture}(-2,-1)(2,4)
% \psframe(-2,-2)(2,2)
 \psset{Decran=30}
 \psSolid[object=tronccone,r0=2,r1=1.5,h=5,fillcolor=cyan,mode=4]%
 \axesIIID(2,2,5)(2.5,2.5,6)
 \end{pspicture}
 &
 \begin{minipage}{5cm}
 \begin{verbatim}
 \psSolid[
    object=tronccone,
    r0=2,r1=1.5,h=5,
    fillcolor=cyan,
    mode=4]%
 \end{verbatim}
 \end{minipage}
\\\hline
     \begin{tabular}{c}
     tronc de \\
     cone creux
     \end{tabular}
     &
     \begin{tabular}{c}
     \texttt{[h=6,r0=4,r1=1.5]}\\
     hauteur et rayons\\
     le maillage :\\
     \texttt{[ngrid=n1 n2]}
     \end{tabular}
     &
 \begin{pspicture}(-2,-1)(2,4)
% \psframe(-2,-2)(2,2)
 \psset{Decran=30}
 \psSolid[object=troncconecreux,r0=2,r1=1,h=5,fillcolor=white,mode=4]%
 \axesIIID(2,2,5)(2.5,2.5,6)
 \end{pspicture}
 &
 \begin{minipage}{5cm}
 \begin{verbatim}
\psSolid[
   object=troncconecreux,
   r0=2,r1=1,h=5,
   fillcolor=white,
   mode=4]%
 \end{verbatim}
 \end{minipage}
\\\hline
\end{tabular}
\end{center}

%\newpage

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{center}
\psset{lightsrc=10 20 30,viewpoint=50 20 30 rtp2xyz}
%\begin{tabular}{>{\bfseries\sffamily\color{blue}}lcm{4cm}m{5cm}}
\begin{tabular}{
   >{\bfseries\sffamily\color{blue}} l 
   >{\centering} m{4cm} m{4cm} m{5cm}}
  \hline
\toptableau
\\\hline
 sphère &
     \begin{tabular}{c}
     \texttt{[r=2]} rayon\\
     le maillage :\\
     \texttt{[ngrid=n1 n2]}
    \end{tabular}
     &
 \begin{pspicture}(-2,-2)(2,3)
% \psframe(-2,-2)(2,2)
 \psset{Decran=30}
 \psSolid[object=sphere,r=3,fillcolor=red!25,ngrid=18 18,linewidth=0.2\pslinewidth]%
 \axesIIID(3,3,3)(4,4,4)
 \end{pspicture}
 &
 \begin{minipage}{5cm}
 \begin{verbatim}
 \psSolid[
    object=sphere,
    r=2,fillcolor=red!25,
    ngrid=18 18]%
 \end{verbatim}
 \end{minipage}
\\\hline
     \begin{tabular}{c}
     calotte \\
     sphérique
     \end{tabular} &
     \begin{tabular}{c}
     \texttt{[r=2]} rayon\\
     \texttt{[phi=0,theta=90]} \\
     latitudes pour découper\\
     la calotte respectivement \\
     vers le bas et le haut \\
    \end{tabular}
     &
\psset{unit=0.44}
\begin{pspicture}(-4,-5)(5,5.5)
\psset{lightsrc=42 24 13,viewpoint=50 30 15 rtp2xyz,Decran=50}
\psSolid[object=calottesphere,r=3,ngrid=16 18,
   fillcolor=cyan!50,incolor=yellow,theta=45,phi=-30,hollow,RotY=-80]%
\axesIIID(0,3,3)(6,5,4)
\end{pspicture}
 &
 \begin{minipage}{5cm}
 \begin{verbatim}
\psSolid[
   object=calottesphere,
   r=3,ngrid=16 18,
   theta=45,phi=-30,
   hollow,RotY=-80]%
 \end{verbatim}
 \end{minipage}
\\\hline
 tore &
     \begin{tabular}{c}
     \texttt{[r0=4,r1=1.5]} \\
     rayon intérieur\\
     rayon moyen\\
     le maillage :\\
     \texttt{[ngrid=n1 n2]}
     \end{tabular}
     &
 \begin{pspicture}(-2,-2)(2,3)
% \psframe(-2,-2)(2,2)
 \psset{Decran=30,unit=0.9}
 \psSolid[r1=2.5,r0=1.5,object=tore,ngrid=18 36,fillcolor=green!30,action=draw**]%
  \axesIIID(4,4,0)(5,5,4)
 \end{pspicture}
 &
 \begin{minipage}{5cm}
 \begin{verbatim}
 \psSolid[
    r1=2.5,r0=1.5,
    object=tore,
    ngrid=18 36,
    fillcolor=green!30,
    action=draw*]%
 \end{verbatim}
 \end{minipage}
\\\hline
     \begin{tabular}{c}
     anneau \\
     cylindrique
     \end{tabular}
      &
     \begin{tabular}{c}
     \texttt{[r1=2.5,r0=1.5,}
          \\
     \texttt{h=6,section=...]}
          \\
          rayon extérieur
          \\
          rayon intérieur
          \\
          hauteur
          \\
          section \\
          rectangulaire
     \end{tabular}
     &
 \begin{pspicture}(-2,-2)(2,3)
%  \psframe(-2,-2)(2,2)
 \psset{Decran=30}
\psSolid[object=anneau,fillcolor=yellow,h=1.5,r1=4,r0=3]%
 \axesIIID(4,4,0)(5,5,4)
 \end{pspicture}
 &
 \begin{minipage}{5cm}
 \begin{verbatim}
 \psSolid[
    object=anneau,
    fillcolor=yellow,
    h=1.5,r1=4,r0=3]%
 \end{verbatim}
 \end{minipage}
\\\hline
\end{tabular}
\end{center}
Une documentation spécifique aux anneaux circulaires et aux
parallélépipèdes est fournie dans la partie exemples :
\begin{itemize}
  \item \texttt{doc-grille-parallelepiped.tex(.pdf)} ;
  \item \texttt{doc-anneau.tex(.pdf).}
\end{itemize}

%\clearpage

\begin{center}
\psset{lightsrc=10 20 30,viewpoint=50 20 30 rtp2xyz}
%\begin{tabular}{>{\bfseries\sffamily\color{blue}}lcm{4cm}m{6cm}}
\begin{tabular}{
   >{\bfseries\sffamily\color{blue}} l 
   >{\centering} m{4cm} m{4cm} m{5cm}}
  \hline
\toptableau
\\\hline
 tétraèdre&
     \begin{tabular}{c}
     \texttt{[a=2]} rayon\\
     de la sphère\\
     circonscrite
     \end{tabular}
     &
 \begin{pspicture}(-2,-2)(2,2)
% \psframe(-2,-2)(2,2)
 \psset{Decran=30}
 \psSolid[object=tetrahedron,r=3,linecolor=blue,action=draw]%
 \end{pspicture}
 &
 \begin{minipage}{5cm}
 \begin{verbatim}
\psSolid[
   object=tetrahedron,
   r=3,
   linecolor=blue,
   action=draw]%
 \end{verbatim}
 \end{minipage}
\\\hline
octaèdre &
     \begin{tabular}{c}
     \texttt{[a=2]} rayon\\
     de la sphère\\
     circonscrite
     \end{tabular}
     &
 \begin{pspicture}(-2,-1.85)(2,2.85)
%  \psframe(-2,-2)(2,2)
 \psset{Decran=30}
 \psSolid[object=octahedron,a=3,linecolor=blue,fillcolor=Turquoise]%
 \axesIIID(3,3,3)(4,4,4)
 \end{pspicture}
 &
 \begin{minipage}{5cm}
 \begin{verbatim}
 \psSolid[
    object=octahedron,
    a=3,
    linecolor=blue,
    fillcolor=Turquoise]%
 \end{verbatim}
 \end{minipage}
\\\hline
 dodécaèdre &
     \begin{tabular}{c}
     \texttt{[a=2]} rayon\\
     de la sphère\\
     circonscrite
     \end{tabular}
     &
 \begin{pspicture}(-2,-1.85)(2,1.85)
% \psframe(-2,-2)(2,2)
 \psset{Decran=30}
 \psSolid[object=dodecahedron,a=2.5,RotZ=90,action=draw*,fillcolor=OliveGreen]%
 \end{pspicture}
 &
 \begin{minipage}{5cm}
 \begin{verbatim}
 \psSolid[
    object=dodecahedron,
    a=2.5,RotZ=90,
    action=draw*,
    fillcolor=OliveGreen]%
 \end{verbatim}
 \end{minipage}
\\ \hline
icosaèdre &
     \begin{tabular}{c}
     \texttt{[a=2]} rayon\\
     de la sphère\\
     circonscrite
     \end{tabular}
     &
 \begin{pspicture}(-2,-1.85)(2,2.85)
% \psframe(-2,-2)(2,2)
 \psset{Decran=30}
 \psSolid[object=icosahedron,a=3,action=draw*,fillcolor=green!50]%
 \axesIIID(3,3,3)(4,4,4)
 \end{pspicture}
 &
 \begin{minipage}{5cm}
 \begin{verbatim}
\psSolid[
   object=icosahedron,
   a=3,
   action=draw*,
   fillcolor=green!50]%
 \end{verbatim}
 \end{minipage}
\\\hline
     prisme
      &
     \begin{tabular}{c}
     \texttt{[axe=0 0 1]}
          \\
     direction de l'axe
          \\
     \texttt{[base=}\\
     \texttt{-1 -1 1 -1 0 1]}
          \\
     coordonnées\\
     des sommets\\
     de la base\\
     \texttt{[h=6]} hauteur
     \end{tabular}
     &
 \begin{pspicture}(-2,-2)(2,3)
%  \psframe(-2,-2)(2,2)
 \psset{Decran=30,unit=0.9}
\psSolid[object=prisme,action=draw*,linecolor=red,h=4,fillcolor=gray!50]%
\psSolid[object=grille,base=-3 3 -3 3,action=draw]%
 \axesIIID(3,3,4)(5,5,5)
 \end{pspicture}
 &
 \begin{minipage}{5cm}
 \begin{verbatim}
\psSolid[
   object=prisme,
   action=draw*,
   linecolor=red,
   h=4]%
 \end{verbatim}
 \end{minipage}
 \\\hline
\end{tabular}
\end{center}

%\newpage
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{center}
\psset{lightsrc=10 20 30,viewpoint=50 20 30 rtp2xyz}
%\begin{tabular}{>{\bfseries\sffamily\color{blue}}lcm{4cm}m{6cm}}
\begin{tabular}{
   >{\bfseries\sffamily\color{blue}} l 
   >{\centering} m{4cm} m{4cm} m{5cm}}
  \hline
\toptableau
\\\hline
     grille
      &
     \begin{tabular}{c}
     \texttt{[base=-X +X -Y +Y]}
     \end{tabular}
     &
 \begin{pspicture}(-1.5,-2)(2,3)
%  \psframe(-2,-2)(2,2)
 \psset{Decran=30,unit=0.9}
\psSolid[object=grille,base=-5 5 -3 3]%
 \axesIIID(5,3,0)(6,4,4)
 \end{pspicture}
 &
 \begin{minipage}{5cm}
 \begin{verbatim}
\psSolid[
   object=grille,
   base=-5 5 -3 3]%
 \end{verbatim}
 \end{minipage}
\\\hline
%
   parallélépipède
      &
     \begin{tabular}{c}
     \texttt{[a=4,b=a,c=a]}\\
     centre en O
     \end{tabular}
     &
 \begin{pspicture}(-1.5,-2)(2,3)
 \psset{Decran=30}
\psSolid[object=parallelepiped,a=5,b=6,c=2,fillcolor=bleuciel](0,0,c 2 div)
\psSolid[object=grille,base=-2.5 2.5 -3 3,action=draw](0,0,2)
\psSolid[object=grille,base=-1 1 -3 3,RotY=90,action=draw](2.5,0,1)
\psSolid[object=grille,base=-2.5 2.5 -1 1,RotX=-90,action=draw](0,3,1)
 \axesIIID(2.5,3,2)(3.5,4,4)
 \end{pspicture}
 &
 \begin{minipage}{5cm}
 \begin{verbatim}
\psSolid[
   object=parallelepiped,%
   a=5,b=6,c=2,
   fillcolor=yellow]%
   (0,0,c 2 div)
 \end{verbatim}
 \end{minipage}
\\\hline
%
   face
      &
     \begin{tabular}{l}
     \texttt{[base=x0 y0 x1 y1}\\ 
     \texttt{~     x2 y2 etc.]}\\
     les coordonnées \\
     des sommets\\
     dans le sens trigo
     \end{tabular}
     &
\psset{unit=0.4}
\psset{viewpoint=50 -20 30 rtp2xyz,Decran=50}
\begin{pspicture}(-4,-4)(5,4)
\psSolid[object=grille,base=-4 6 -4 4,action=draw,linecolor=gray](0,0,0)
\psSolid[object=face,fillcolor=yellow,
      incolor=blue,
      base=0 0 3 0 1.5 3
      ](0,1,0)
\psSolid[object=face,fillcolor=yellow,
      incolor=blue,
      base=0 0 3 0 1.5 3,
      RotX=180](0,-1,0)
\axesIIID(0,0,0)(6,6,3)
\end{pspicture}
 &
 \begin{minipage}{5cm}
 \begin{verbatim}
\psSolid[
   object=face,
   fillcolor=yellow,
   incolor=blue,
   base=0 0 3 0 1.5 3
   ](0,1,0)
\psSolid[
   object=face,
   fillcolor=yellow,
   incolor=blue,
   base=0 0 3 0 1.5 3,
   RotX=180](0,-1,0)
 \end{verbatim}
 \end{minipage}
\\\hline
%
   ruban
      &
     \begin{tabular}{l}
     \texttt{[base=x0 y0 x1 y1}\\
     \texttt{~     x2 y2 etc.]}\\
     \texttt{[h=hauteur]}\\
     \texttt{[ngrid=valeur]}\\
     nombre de mailles\\ 
     verticalement\\
     \texttt{[axe=0 0 1]}\\
     direction de l'inclinaison\\
     du ruban
     \end{tabular}
     &
\psset{lightsrc=10 0 10,viewpoint=50 -20 30 rtp2xyz,Decran=50,unit=0.5}
\begin{pspicture}(-2,-4)(5,7)
\psSolid[object=grille,base=-4 6 -2 4,action=draw,linecolor=gray](0,0,0)
\psSolid[object=ruban,h=3,fillcolor=red!50,
      base=0 0 2 2 4 0 6 2,
      num=0 1 2 3,
      show=0 1 2 3,
      ngrid=3]%
\axesIIID(0,2,0)(6,6,6)
\end{pspicture}
 &
 \begin{minipage}{5cm}
 \begin{verbatim}
\psSolid[
   object=ruban,h=3,
   fillcolor=red!50,
   base=0 0 2 2 4 0 6 2,
   num=0 1 2 3,
   show=0 1 2 3,
   ngrid=3])
 \end{verbatim}
 \end{minipage}
\\\hline
\end{tabular}
\end{center}

%\newpage

%\begin{center}
%\psset{lightsrc=10 20 30,viewpoint=50 20 30 rtp2xyz}
%%\begin{tabular}{>{\bfseries\sffamily\color{blue}}lcm{4cm}m{6cm}}
%\begin{tabular}{
%   >{\bfseries\sffamily\color{blue}} l 
%   >{\centering} m{4cm} m{4cm} m{5cm}}
%  \hline
%\toptableau
%%    chemin
%%       &
%%      \begin{tabular}{l}
%%      dessine un chemin\\
%%      défini en postscript\\
%%      sur un plan
%%      \end{tabular}
%%      &
%% \psset{unit=0.4}
%% \begin{pspicture}(-2,-5)(6,8)%
%% \psframe*[linecolor=blue!50](-6,-5)(6,7)
%% \psset{lightsrc=50 20 20,viewpoint=50 30 15,Decran=60}
%% \psProjection[object=chemin,fillstyle=solid,fillcolor=white,
%%             linewidth=.05,linecolor=red,
%%             normal=1 1 2 180,
%%             path=newpath
%%                 -4 -4 smoveto
%%                 -4 4 slineto
%%                 4 4 slineto
%%                 4 -4 slineto
%%                 closepath
%%             ](1,1,2)
%% \psProjection[object=chemin,
%%       linewidth=.02,
%%       normal=1 1 2 180,
%%       path=newpath
%%           -4 1 4
%%           {-4 exch smoveto
%%            8 0 srlineto} for
%%            -4 1 4
%%           {-4 smoveto
%%            0 8 srlineto} for
%%             ](1,1,2)
%% \psProjection[object=chemin,fillstyle=hlines,hatchcolor=yellow,
%%             linecolor=red,
%%             normal=1 1 2 180,
%%             path=newpath
%%             2 0 moveto
%%             0 2 360 {
%%                 /x exch def
%%                 x cos 2 mul
%%              x sin 2 mul
%%                 slineto
%%          } for
%%             ](1,1,2)
%% \psPoint(0,0,0){O}
%% \psPoint(1,1,2){O1}\psPoint(1.4,1.4,2.8){K}
%% \psline[linewidth=.1,linecolor=red](O1)(K)
%% \psline[linestyle=dashed](O)(O1)
%% \psProjection[object=chemin,
%%       linewidth=.1,
%%       linecolor=green,
%%       normal=1 1 2 180,
%%       path=
%%          newpath
%%             0 0 smoveto
%%             1 0 slineto](1,1,2)
%% \psProjection[object=chemin,
%%       linewidth=.1,
%%       linecolor=blue,
%%       normal=1 1 2 180,
%%       path=
%%          newpath
%%             0 0 smoveto
%%             0 1 slineto](1,1,2)
%% \axesIIID(4,4,2)(5,5,6)
%% \end{pspicture}
%%  &
%%  \begin{minipage}{6cm}
%%  \begin{verbatim}
%%     \psProjection[object=chemin,
%%     fillstyle=hlines,
%%     hatchcolor=yellow,
%%     linecolor=red,
%%     normal=1 1 2 180,
%%     path=newpath
%%     2 0 smoveto
%%     0 2 360 {
%%      /x exch def
%%      x cos 2 mul
%%      x sin 2 mul
%%      slineto
%%     } for
%%     ](1,1,2)
%%  \end{verbatim}
%%  \end{minipage}
%\end{tabular}
%\end{center}

%\newpage
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{center}
\psset{lightsrc=10 20 30,viewpoint=50 20 30 rtp2xyz}
%\begin{tabular}{>{\bfseries\sffamily\color{blue}}lcm{4cm}m{6cm}}
\begin{tabular}{
   >{\bfseries\sffamily\color{blue}} l 
   >{\centering} m{4cm} m{4cm} m{5cm}}
  \hline
\toptableau
\\\hline
   surface
      &
     \begin{tabular}{l}
     voir la \\
     documentation\\
     spécifique
     \end{tabular}
     &
\psset{unit=0.4}
\psset{lightsrc=30 30 25}
\psset{viewpoint=50 40 30 rtp2xyz,Decran=50}
\begin{pspicture}(-4,-8)(6,8)
\psSurface[ngrid=.25 .25,incolor=white,axesboxed](-4,-4)(4,4){%
   x dup mul y dup mul 3 mul sub x mul 32 div}
\end{pspicture}
 &
 \begin{minipage}{5cm}
 \begin{verbatim}
\psSurface[ngrid=.25 .25,
  incolor=Wwhite,axesboxed]
  (-4,-4)(4,4){%
  x dup mul y dup mul 3 mul
  sub x mul 32 div}
 \end{verbatim}
 \end{minipage}
\\\hline
%
   new
      &
     \begin{tabular}{l}
     solide défini\\
     par les coordonnées \\
     des sommets\\
     et les faces
     \end{tabular}
     &
\psset{unit=0.4}
\psset{viewpoint=50 -20 30 rtp2xyz,Decran=50}
\begin{pspicture}(-5,-4)(5,9)
%\psframe(-7,-4)(7,9)
\psSolid[object=new,
         action=draw,
         sommets=
         2  4  3
        -2  4  3
        -2 -4  3
         2 -4  3
         2  4  0
        -2  4  0
        -2 -4  0
         2 -4  0
         0  4  5
         0 -4  5,
    faces={
        [0 1 2 3]
        [7 6 5 4]
        [0 3 7 4]
        [3 9 2]
        [1 8 0]
        [8 9 3 0]
        [9 8 1 2]
        [6 7 3 2]
        [2 1 5 6]},
        num=all,
      show=all]%
\axesIIID(0,0,0)(5,5,7)
\end{pspicture}
 &
 \begin{minipage}{5cm}
 \begin{verbatim}
 \psSolid[object=new,
         action=draw,
         sommets=
         2  4  3
        -2  4  3
        -2 -4  3
         2 -4  3
         2  4  0
        -2  4  0
        -2 -4  0
         2 -4  0
         0  4  5
         0 -4  5,
    faces={
        [0 1 2 3]
        [7 6 5 4]
        [0 3 7 4]
        [3 9 2]
        [1 8 0]
        [8 9 3 0]
        [9 8 1 2]
        [6 7 3 2]
        [2 1 5 6]}]%
 \end{verbatim}
 \end{minipage}
\\\hline
%
   courbe
      &
     \begin{tabular}{l}
     tracé d'une fonction\\
     R --> R\textsuperscript{3}\\
     définie par ses\\
     équations paramétriques\\
     \end{tabular}
     &
\psset{unit=0.35}
\psset{lightsrc=10 -20 50,viewpoint=50 -20 20 rtp2xyz,Decran=50}
\begin{pspicture}(-6,-3)(5,8)
\psframe*[linecolor=blue!50](-6,-3)(6,8)
\psSolid[object=grille,base=-4 4 -4 4,linecolor=red,linewidth=0.5\pslinewidth]%
\axesIIID(0,0,0)(4,4,7)
\defFunction[algebraic]{helice}(t){3*cos(4*t)}{3*sin(4*t)}{t}
\psSolid[object=courbe,r=0,
        range=0 6,
        linecolor=blue,linewidth=0.1,
        resolution=360,
        function=helice]%
\end{pspicture}
 &
 \begin{minipage}{5cm}
 \footnotesize
 \begin{verbatim}
\defFunction[algebraic]%
   {helice}(t)
   {3*cos(4*t)}{3*sin(4*t)}{t}
\psSolid[object=courbe,r=0,
   range=0 6,
   linecolor=blue,linewidth=0.1,
   resolution=360,
   function=helice]%
 \end{verbatim}
 \end{minipage}
\\\hline
%%    courbeR2
%%       &
%%      \begin{tabular}{l}
%%      tracé d'une fonction\\
%%      R --> R\textsuperscript{2}\\
%%      définie par ses\\
%%      équations paramétriques\\
%%      \end{tabular}
%%      &
%% \psset{unit=0.4}
%% \begin{pspicture}(-6,-7)(6,6)
%% \psframe*[linecolor=yellow!50](-6,-6)(6,6)
%% \psset{viewpoint=50 -20 30 rtp2xyz,Decran=50}
%% {\psset{linewidth=0.5\pslinewidth,linecolor=gray}
%% \psSolid[object=grille,base=-4 4 -4 0,RotX=90,RotZ=90]%
%% \psSolid[object=grille,base=-4 4 -4 4]%
%% \psSolid[object=grille,base=-4 4 0 4,RotX=90,RotZ=90]}
%% \defFunction{parabole}(t){t}{t dup mul}{}
%% \defFunction{droite}(t){t}{t 2 add }{}
%% \axesIIID(0,0,0)(4,4,4)
%% \psProjection[object=chemin,
%%       linewidth=.1,
%%       linecolor=blue,
%%       normal=0 1 0 1 0 0,
%%       path=
%%          newpath
%%             0 0 moveto
%%             1 0 lineto]
%% \psProjection[object=chemin,
%%       linewidth=.1,
%%       linecolor=red,
%%       normal=0 1 0 1 0 0,
%%       path=
%%          newpath
%%             0 0 moveto
%%             0 1 lineto]
%% \psProjection[object=courbeR2,
%%    range=-1 2,fillstyle=vlines,hatchwidth=0.5\pslinewidth,
%%    normal=0 1 0 1 0 0,
%%    function=parabole]
%% \psProjection[object=courbeR2,
%%    range=-2 2,
%%    linecolor=green,
%%    normal=0 1 0 1 0 0,
%%    function=parabole]
%% \psProjection[object=courbeR2,
%%    range=-2 2 ,
%%    linecolor=red,
%%    normal=0 1 0 1 0 0,
%%    function=droite]
%% \psPoint(0,0,4.15){Z1}
%% \uput*[60](Z1){$z=y^2$}
%% \rput(0,-6.5){\psframebox[linecolor=yellow!50]{\texttt{$\backslash${}defFunction\{parabole\}(t)\{t\}\{t dup mul\}\{\}}}}
%% \end{pspicture}
%%  &
%%  \begin{minipage}{6cm}
%%  \footnotesize
%%  \begin{verbatim}
%% \psProjection[object=courbeR2,
%%    range=-2 2,
%%    linecolor=green,
%%    normal=0 1 0 1 0 0,
%%    function=parabole]
%%  \end{verbatim}
%%  \end{minipage}
%% \\\hline
\end{tabular}
\end{center}