Sections du tore par un plan passant par l'un des points de bitangence

Le message précédent avait pour objet des cercles de Villarceau : section du tore par un plan bitangent.

Maintenant on étudie la section du tore par un plan passant par l'un des points de bitangence en prenant un angle un peu plus grand ou un peu plus petit par rapport au plan bitangent.

Dans une première étape il faut décommenter (rendre actives) les lignes débutant par %(en supprimant ce signe) et une fois les fichiers enregistrés les rendre inactives comme au départ.

toresections

\documentclass{article}
\usepackage[a4paper,margin=2cm]{geometry}
\usepackage[latin1]{inputenc}
\usepackage{bera}
\usepackage[T1]{fontenc}
\usepackage{pst-solides3d}
\title{Sections du tore par un plan \textit{bitangent} : cercles de Villarceau}
\date{Février 2013}
\begin{document}

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%   dup 1 eq {
%      90
%   } {
%      dup
%      dup mul neg 1 add sqrt
%      atan
%      dup 90 lt
%         {}
%         {360 sub}
%      ifelse
%   } ifelse
%} def
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%         /r_0 1.5 def
%         /Phi 0.5 arcsin def
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%         /cz alpha sin def
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%         /xB {OB Phi cos mul neg} bind def
%         /zB {OB Phi sin mul} bind def
%         /dH {ax xB mul cz zB mul add neg} bind def
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%         name=incline,
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%         file=tore2460Phi65C1,action=writesolid](0,0,0)
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         /cz alpha sin def
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         /xB {OB Phi cos mul neg} bind def
         /zB {OB Phi sin mul} bind def
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         /xO2 7 25 cos mul def
         /zO2 7 25 sin mul neg def
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%\psset{viewpoint=50 -45 10 rtp2xyz,Decran=50}
%\pstVerb{/arcsin {
%   dup 1 eq {
%      90
%   } {
%      dup
%      dup mul neg 1 add sqrt
%      atan
%      dup 90 lt
%         {}
%         {360 sub}
%      ifelse
%   } ifelse
%} def
%         /r_1 3 def
%         /r_0 1.5 def
%         /Phi 0.5 arcsin def
%         /Phi' 90 Phi sub def
%        /alpha 55 def
%         /ax alpha cos def
%         /cz alpha sin def
%         /OB {r_1 dup mul r_0 dup mul sub sqrt} bind def
%         /xB {OB Phi cos mul neg} bind def
%         /zB {OB Phi sin mul} bind def
%         /dH {ax xB mul cz zB mul add neg} bind def
%         }%
%\psset{solidmemory}
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%         plansepare={[ax 0 cz dH]},
%         name=incline,
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\psset{unit=0.7}
\begin{pspicture}(-6,-7)(12,4)
\pstVerb{/arcsin {
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      90
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      atan
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   } ifelse
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         /r_0 1.5 def
         /Phi 0.5 arcsin def
         /Phi' 90 Phi sub def
         /alpha 55 def
         /ax alpha cos def
         /cz alpha sin def
         /OB {r_1 dup mul r_0 dup mul sub sqrt} bind def
         /xB {OB Phi cos mul neg} bind def
         /zB {OB Phi sin mul} bind def
         /dH {ax xB mul cz zB mul add neg} bind def
         /xO2 6 35 cos mul def
         /zO2 6 35 sin mul neg def
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