%% $Id: pst-hyperboloid-doc-exa9.tex 1275 2026-06-03 13:31:25Z herbert $

\begin{externalDocument}[
  compiler=lualatex, runs=1, crop,
  %xindex, xindexOptions={-l DE --config AU},
  %mpwidth=0.6\linewidth, 
  usefancyvrb=false,
  docType=latex,
]{voss}
\DocumentMetadata{}
\documentclass{article}
\pagestyle{empty}
\usepackage{libertinus}
%StartVisiblePreamble
\usepackage[dvipsnames,svgnames]{pstricks}
\usepackage{pst-hyperboloid}
%StopVisiblePreamble
\begin{document}
\begin{pspicture}(-8,-7)(8,7)
\psset{solidmemory, viewpoint=50 30 20 rtp2xyz,lightsrc=viewpoint,Decran=50}
\pstVerb{/Hauteur 8 def          /nEtages 20 def
         /Pas 1 nEtages div def  /nMeridiens 36 def
         /DemiAxeFocal 1 def % rayon de l'étranglement au milieu
         /RayonBases 4 def
         /DemiAxeNonFocal Hauteur 2 div RayonBases dup mul DemiAxeFocal dup mul sub sqrt div DemiAxeFocal mul def
         /X0 1.5 def    /Z0 DemiAxeNonFocal X0 DemiAxeFocal div dup mul 1 sub sqrt mul def
         /Ymax DemiAxeFocal Hauteur 2 DemiAxeNonFocal mul div dup mul 1 add X0 DemiAxeFocal div dup mul sub sqrt mul def}%
\psSolid[object=grille,base=-4 4 -4 4,linewidth=0.5\pslinewidth](0,0,Hauteur 2 div neg)
\psSolid[object=new,incolor=yellow!50, fillcolor=ForestGreen!20, hollow,
         sommets=
           0.5 Pas neg -0.5 Pas neg add{
             /k exch def
             0 1 nMeridiens 1 sub {
               /i exch def
               /r 4 k dup mul mul RayonBases dup mul DemiAxeFocal dup mul sub mul DemiAxeFocal dup mul add sqrt def
               360 nMeridiens div i mul cos r mul
               360 nMeridiens div i mul sin r mul
               k Hauteur mul
             } for
           } for,
    faces={ 0 1 nEtages 1 sub {
	        /k1 exch def
            k1 nMeridiens mul 1 add 1 k1 1 add nMeridiens mul 1 sub {
              /i exch def
              [i i 1 sub nMeridiens i add 1 sub nMeridiens i add]
            } for
            [k1 nMeridiens mul k1 1 add nMeridiens mul 1 sub k1 2 add nMeridiens mul 1 sub k1 1 add nMeridiens mul]
          } for},
  plansepare={[1 0 0 -1.5]},name=coupeHyperboloidTest,action=none]
\psSolid[object=load,deactivatecolor=true, %fillcolor=red!50,incolor=yellow,rm=0,
         linewidth=0.5\pslinewidth,rm=0,load=coupeHyperboloidTest1]
\psSolid[object=plan,definition=equation,args={[1 0 0 -1.5] 90},linecolor=blue,%   fillcolor=Aquamarine,
   planmarks,base=-4 4 -4 4,name=PlanCoupe,showBase,action=draw]
\defFunction[algebraic]{hyperbol1}(t){X0}{t}{sqrt(((X0^2+t^2)/(DemiAxeFocal^2)-1))*DemiAxeNonFocal}
\defFunction[algebraic]{hyperbol2}(t){X0}{t}{-sqrt(((X0^2+t^2)/(DemiAxeFocal^2)-1))*DemiAxeNonFocal}
\psSolid[object=courbe,linewidth=2\pslinewidth,function=hyperbol1,range=Ymax neg Ymax,r=0,linecolor=red]%
\psSolid[object=courbe,linewidth=2\pslinewidth,function=hyperbol2,range=Ymax neg Ymax,r=0,linecolor=red]%
\gridIIID[Zmin=-4,Zmax=4](-4,4)(-4,4)
\end{pspicture}
\end{document}
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