%% $Id: pst-hyperboloid-doc-exa4.tex 1273 2026-06-02 10:47:27Z herbert $

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\DocumentMetadata{}
\documentclass{article}
\pagestyle{empty}
\usepackage{libertinus}
%StartVisiblePreamble
\usepackage[dvipsnames,svgnames]{pstricks}
\usepackage{pst-hyperboloid}
%StopVisiblePreamble
\begin{document}
\begin{pspicture}(-5,-7)(10,6)
\psframe(-5,-7)(10,6)
\psset{solidmemory,viewpoint=50 20 20 rtp2xyz,lightsrc=viewpoint,Decran=40}
\pstVerb{/X0 0.5 def}%
\psSolid[object=grille,base=-4 4 -4 8,ngrid=8 12,linewidth=0.5\pslinewidth,linecolor=red](0,0,-4)%
\psHyperboloid[hollow,R=4,incolor=yellow!50,fillcolor=ForestGreen!20,plansepare={[0 1 ConeAsymptote -1]},
   name=coupeHyperboloidTest,action=none]
\psSolid[object=load,incolor=yellow!50,fillcolor=ForestGreen!20,linewidth=0.5\pslinewidth,
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   rm=236,load=coupeHyperboloidTest0](0,5,0)
\psSolid[object=plan,definition=equation,args={[0 1 ConeAsymptote -1] 180},linecolor=red,
   planmarks,base=-4 4 -5 5,showBase,action=draw]%
\defFunction[algebraic]{parabole1}(t)%
  {DemiAxeFocal*sqrt(1+(t/DemiAxeNonFocal)^2-((1-ConeAsymptote*t)/DemiAxeFocal)^2)}{1-ConeAsymptote*t}{t}
\defFunction[algebraic]{parabole2}(t)%
  {-DemiAxeFocal*sqrt(1+(t/DemiAxeNonFocal)^2-((1-ConeAsymptote*t)/DemiAxeFocal)^2)}{1-ConeAsymptote*t}{t}
\psSolid[object=courbe,r=0,range=0 4,linecolor=blue,linewidth=0.05,resolution=360,function=parabole1]%
\psSolid[object=courbe,r=0,range=0 4,linecolor=blue,linewidth=0.05,resolution=360,function=parabole2]%
\composeSolid
\gridIIID[Zmin=-4,Zmax=4](-4,4)(-4,8)
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