mobius_02.tex

\documentclass{minimal}
\usepackage[dvipsnames,svgnames]{pstricks}
\usepackage{pst-solides3d}
 
\begin{document}
\pagestyle {empty}
 
\psset{unit=1.25}
\begin{pspicture}(-6,-3)(6,4)
\psframe*[linecolor=blue!20](-6,-3)(6,3)
\psset[pst-solides3d]{viewpoint=10 20 5,Decran=40,lightsrc=10 20 5}
\psSolid[object=parallelepiped,a=5,b=5,c=0.5](0,0,-0.5)
\psSolid[object=grille,base=-2.5 2.5 -2.5 2.5,ngrid=0.25,
   linewidth=0.5\pslinewidth](0,0,-0.25)
\defFunction[algebraic]{mobius1}(t)
   {(2+0.25*cos(t))*cos(2*t)}
   {(2+0.25*cos(t))*sin(2*t)}
   {0.25*sin(t)}
\psSolid[object=courbe,r=0,
        linewidth=0.1,
        resolution=360,range=0 pi,
%        normal=0 0 1,
        function=mobius1]%
\defFunction[algebraic]{mobius2}(t)
   {(2-0.25*cos(t))*cos(2*t)}
   {(2-0.25*cos(t))*sin(2*t)}
   {-0.25*sin(t)}
\psSolid[object=courbe,r=0,
        linewidth=0.1,
        resolution=360,range=0 pi,
%        normal=0 0 1,
        function=mobius2]%
% Parametric Surfaces
\defFunction{mobius}(u,v)
   {2 u v Cos mul add 2 v mul Cos mul}
   {2 u v Cos mul add 2 v mul Sin mul}
   {u v Sin mul}
\psSolid[object=surfaceparametree,linewidth=0.5\pslinewidth,
   base=-0.25 0.25 0 pi,fillcolor=cyan!50,incolor=red!50,
   function=mobius,
   ngrid=.05]%
\psSolid[object=parallelepiped,a=4.5,b=4.5,c=0.5,action=draw](0,0,0)
%% \psProjection[object=texte,
%%    fontsize=15,
%%    text={ruban de Möbius },
%%    normal=1 0 0 90](2.5,0,-0.5)
%% \psProjection[object=texte,
%%    fontsize=15,
%%    text={pst-solides3d},
%%    normal=0 1 0 180](0,2.5,-0.5)
\psset{solidmemory}
\psSolid[object=plan,
   definition=normalpoint,
   args={2.5 0 0 [1 0 0 90]},
   action=none,name=monplan]
\psProjection[object=texte,
   fontsize=15,pos=cc,
   text={ruban de Möbius},
   plan=monplan](0,-.5)
\psSolid[object=plan,
   definition=normalpoint,
   args={0 2.5 0 [0 1 0 180]},
   action=none,name=monplan]
\psProjection[object=texte,
   fontsize=15,
   text={pst-solides3d},
   plan=monplan](0,-0.5)
\psPoint(2.25,0,0){X1}\psPoint(3.5,0,0){X2}
\psPoint(0,2.25,0){Y1}\psPoint(0,3.5,0){Y2}
\psPoint(0,0,0){Z1}\psPoint(0,0,1.5){Z2}
\psline{->}(X1)(X2)\uput[dl](X2){$x$}
\psline{->}(Y1)(Y2)\uput[dr](Y2){$y$}
\psline{->}(Z1)(Z2)\uput[r](Z2){$z$}
\end{pspicture}
 
\end{document}