Les dessins de la page d'accueil de la FAQ

Le dessin des trois dés jetés sur un tapis de jeu vient d'un travail de Manuel Luque, réalisé avec PStricks, et réutilisé avec son aimable autorisation.

• Version originale,
• Une version plus récente est disponible sur son site web, utilisant pst-solides3d.

pnode3D.tex

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -*- Mode: Latex -*- %%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%
%% pnode3D.tex--- Manuel Luque <Mluque5130@aol.com> (June 2000 - April 2002)
%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\documentclass{article}
\usepackage[a4paper,margin=2cm]{geometry}
\usepackage[T1]{fontenc}
\usepackage[latin1]{inputenc}%
\usepackage{pstricks}
\usepackage{pst-node}
\usepackage{pst-plot}
% fp est de Michael Mehlich
\usepackage[nomessages]{fp}
% Dés en 3D
% 31 mars 2002 - 27 mai 2002(documentation version 0.2)
% Avec les remarques et les modifications de Denis Girou de 27 mars 2002
% Le générateur de nombres aléatoires est de
% Donald Arseneau
% http://ctan.mines-albi.fr/macros/generic/misc/random.tex
\input random
\makeatletter
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\pst@addfams{pst-die}
\define@key[psset]{pst-die}{THETA}{\edef\psk@IIID@Theta{#1}}
\define@key[psset]{pst-die}{PHI}{\edef\psk@IIID@Phi{#1}}
\define@key[psset]{pst-die}{Dobs}{\edef\psk@IIID@Dobs{#1}}
\define@key[psset]{pst-die}{Decran}{\edef\psk@IIID@Ecran{#1}}
\define@key[psset]{pst-die}{Side}{\edef\psk@Die@Side{#1}}
\psset{THETA=60,PHI=60,Dobs=30,Decran=10,Side=2}
%
\define@key[psset]{pst-die}{thetax}{\edef\psk@Die@Thetax{#1}}
\define@key[psset]{pst-die}{thetay}{\edef\psk@Die@Thetay{#1}}
\define@key[psset]{pst-die}{thetaz}{\edef\psk@Die@Thetaz{#1}}
\define@key[psset]{pst-die}{CX}{\edef\psk@Die@CX{#1}}
\define@key[psset]{pst-die}{CY}{\edef\psk@Die@CY{#1}}
\define@key[psset]{pst-die}{CZ}{\edef\psk@Die@CZ{#1}}
\define@key[psset]{pst-die}{K}{\edef\psk@Die@K{#1}}
%
\psset{thetax=0,thetay=0,thetaz=0,CX=0,CY=0,CZ=0,K=0.75,linejoin=1}
%
\newif\ifPst@Axes%
\define@key[psset]{pst-die}{axes}[true]{\@nameuse{Pst@Axes#1}}%
\psset{axes=false}
%
\newif\ifPst@carpet%
\define@key[psset]{pst-die}{carpet}[true]{\@nameuse{Pst@carpet#1}}%
\psset{carpet=false}
%
\newpsstyle{sol}{fillstyle=vlines,hatchcolor=lightgray,hatchwidth=0.2\pslinewidth,hatchsep=1\pslinewidth}
\newpsstyle{Side}{fillstyle=solid,fillcolor=yellow}%grandes faces
\newpsstyle{side}{fillstyle=solid,fillcolor=magenta}%coins facettes
\newpsstyle{points}{fillstyle=solid,fillcolor=black,linestyle=none}% la couleur des points
\definecolor{MonGris}{rgb}{0.8,0.8,0.8}
\definecolor{MonRouge}{rgb}{0.8,0,0}
\SpecialCoor
 
 
\def\pnodeIIID{\def\pst@par{}\pst@object{pnodeIIID}}
\def\pnodeIIID@i(#1,#2,#3)#4{{%
  \begin@SpecialObj
\pstVerb{%
 /THETA \psk@IIID@Theta\space def
 /PHI \psk@IIID@Phi\space def
 /Dobs \psk@IIID@Dobs\space def
 /DScreen \psk@IIID@Ecran\space def
 /Sin1 THETA sin def
 /Sin2 PHI sin def
 /Cos1 THETA cos def
 /Cos2 PHI cos def
 /Cos1Sin2 Cos1 Sin2 mul def
 /Sin1Sin2 Sin1 Sin2 mul def
 /Cos1Cos2 Cos1 Cos2 mul def
 /Sin1Cos2 Sin1 Cos2 mul def
 /XpointVue Dobs Cos1Cos2 mul def
 /YpointVue Dobs Sin1Cos2 mul def
 /ZpointVue Dobs Sin2 mul def
}
 %
\pnode(!
 /xObservateur #1 Sin1 mul neg #2 Cos1 mul add def
 /yObservateur #1 Cos1Sin2 mul neg #2 Sin1Sin2 mul sub #3 Cos2 mul add def
 /zObservateur #1 neg Cos1Cos2 mul #2 Sin1Cos2 mul sub #3 Sin2 mul sub Dobs add def
 /xScreen DScreen xObservateur mul zObservateur div def
 /yScreen DScreen yObservateur mul zObservateur div def
  xScreen yScreen){#4}
\end@SpecialObj}}
%
\def\Die{\def\pst@par{}\pst@object{Die}}
\def\Die@i{{%
\pst@killglue
  \begin@SpecialObj
\pstVerb{%
 /CX \psk@Die@CX\space def
 /CY \psk@Die@CY\space def
 /CZ \psk@Die@CZ\space def
 /K \psk@Die@K\space def
 /thetax \psk@Die@Thetax\space def
 /thetay \psk@Die@Thetay\space def
 /thetaz \psk@Die@Thetaz\space def
 /sinthetax thetax sin def
 /costhetax thetax cos def
 /sinthetay thetay sin def
 /costhetay thetay cos def
 /sinthetaz thetaz sin def
 /costhetaz thetaz cos def
 /M11 costhetaz costhetay mul def
 /M12 costhetaz sinthetay mul sinthetax mul sinthetaz costhetax
 mul sub def
 /M13 costhetaz sinthetay mul costhetax mul sinthetaz sinthetax
 mul add def
 /M21 sinthetaz costhetay mul def
 /M22 sinthetaz sinthetay mul sinthetax mul costhetaz costhetax
 mul add def
 /M23 sinthetaz sinthetay mul costhetax mul costhetaz sinthetax
 mul sub def
 /M31 sinthetay neg def
 /M32 sinthetax costhetay mul def
 /M33 costhetax costhetay mul def
 /Side \psk@Die@Side\space def
 /Point Side 4 div def} % rayon des points
 \CalculsTeX
 \MatriceRotTeX
 \CoordinatesFaces
 \CoordinatesSummit
 \TestVisibilitySide
 \TestVisibilitySummit
 \pnodeIIID(0,0,0){fictif}
 \ifPst@carpet
    \Sol
 \fi
 \Cube
 \ifPst@Axes
    \Axes
 \fi
\end@SpecialObj
}}
%
\def\MatriceRot{% postscript
    /abscisse M11 abscisse1 mul M12 ordonnee1 mul add M13 cote1 mul add CX add def
    /ordonnee M21 abscisse1 mul M22 ordonnee1 mul add M23 cote1 mul add CY add def
    /cote M31 abscisse1 mul M32 ordonnee1 mul add M33 cote1 mul add CZ add def}
%%%%%%%%
\def\MatriceRotTeX{%
        \FPeval\Thetax{(\psk@Die@Thetax) * \FPpi/180}
        \FPeval\Thetay{(\psk@Die@Thetay) * \FPpi/180}
        \FPeval\Thetaz{(\psk@Die@Thetaz) * \FPpi/180}
        \FPcos\CosThetax{\Thetax}
        \FPsin{\SinThetax}{\Thetax}
        \FPcos\CosThetay{\Thetay}
        \FPsin{\SinThetay}{\Thetay}
        \FPcos\CosThetaz{\Thetaz}
        \FPsin{\SinThetaz}{\Thetaz}
        \FPeval\Moneone{(\CosThetaz)*(\CosThetay)}
        \FPeval\Monetwo{(\CosThetaz)*(\SinThetay)*(\SinThetax) -
        (\SinThetaz)*(\CosThetax)}
        \FPeval\Monethree{(\CosThetaz)*(\SinThetay)*(\CosThetax) +
        (\SinThetaz)*(\SinThetax)}
        \FPeval\Mtwoone{(\SinThetaz)*(\CosThetay)}
        \FPeval\Mtwotwo{(\SinThetaz)*(\SinThetay)*(\SinThetax) +
        (\CosThetaz)*(\CosThetax)}
        \FPeval\Mtwothree{(\SinThetaz)*(\SinThetay)*(\CosThetax) -
        (\CosThetaz)*(\SinThetax)}
        \FPeval\Mthreeone{(\SinThetay)*(-1)}
        \FPeval\Mthreetwo{(\SinThetax)*(\CosThetay)}
        \FPeval\Mthreethree{(\CosThetax)*(\CosThetay)}
        }
%
\def\CoordinatesFaces{%
    \FPeval\abscisseOne{(\psk@Die@Side)*(\Moneone)+(\psk@Die@CX)}
    \FPeval\ordonneeOne{(\psk@Die@Side)*(\Mtwoone)+(\psk@Die@CY)}
    \FPeval\coteOne{(\psk@Die@Side)*(\Mthreeone)+(\psk@Die@CZ)}
    \FPeval\abscisseTwo{(\psk@Die@Side)*(\Monetwo)+(\psk@Die@CX)}
    \FPeval\ordonneeTwo{(\psk@Die@Side)*(\Mtwotwo)+(\psk@Die@CY)}
    \FPeval\coteTwo{(\psk@Die@Side)* (\Mthreetwo)+(\psk@Die@CZ)}% ?
    \FPeval\abscisseThree{(-\psk@Die@Side)*(\Moneone)+(\psk@Die@CX)}
    \FPeval\ordonneeThree{(-\psk@Die@Side)*(\Mtwoone)+(\psk@Die@CY)}
    \FPeval\coteThree{(-\psk@Die@Side)*(\Mthreeone)+(\psk@Die@CZ)}
    \FPeval\abscisseFour{(-\psk@Die@Side)*(\Monetwo)+(\psk@Die@CX)}
    \FPeval\ordonneeFour{(-\psk@Die@Side)*(\Mtwotwo)+(\psk@Die@CY)}
    \FPeval\coteFour{(-\psk@Die@Side)* (\Mthreetwo)+(\psk@Die@CZ)}% ?
    \FPeval\abscisseFive{(-\psk@Die@Side)*(\Monethree)+(\psk@Die@CX)}
    \FPeval\ordonneeFive{(-\psk@Die@Side)*(\Mtwothree)+(\psk@Die@CY)}
    \FPeval\coteFive{(-\psk@Die@Side)*(\Mthreethree)+(\psk@Die@CZ)}
    \FPeval\abscisseSix{(\psk@Die@Side)*(\Monethree)+(\psk@Die@CX)}
    \FPeval\ordonneeSix{(\psk@Die@Side)*(\Mtwothree)+(\psk@Die@CY)}
    \FPeval\coteSix{(\psk@Die@Side)*(\Mthreethree)+(\psk@Die@CZ)}
    }
%
\def\CoordinatesSummit{%
    \FPeval\abscisseA{((\psk@Die@Side)*(\Moneone)) +
    ((\psk@Die@Side)*(\Monetwo)) +
    ((\psk@Die@Side)*(\Monethree))+(\psk@Die@CX)}
    \FPeval\ordonneeA{((\psk@Die@Side)*(\Mtwoone)) +
    ((\psk@Die@Side)*(\Mtwotwo)) +
    ((\psk@Die@Side)*(\Mtwothree))+(\psk@Die@CY)}
    \FPeval\coteA{((\psk@Die@Side)*(\Mthreeone)) +
    ((\psk@Die@Side)*(\Mthreetwo)) +
    ((\psk@Die@Side)*(\Mthreethree))+(\psk@Die@CZ)}
    %
    \FPeval\abscisseB{(\psk@Die@Side)*(\Moneone)+
    (-\psk@Die@Side)*(\Monetwo) +
    (\psk@Die@Side)*(\Monethree)+(\psk@Die@CX)}
    \FPeval\ordonneeB{(\psk@Die@Side)*(\Mtwoone) +
    (-\psk@Die@Side)*(\Mtwotwo) +
    (\psk@Die@Side)*(\Mtwothree)+(\psk@Die@CY)}
    \FPeval\coteB{(\psk@Die@Side)*(\Mthreeone) +
    (-\psk@Die@Side)*(\Mthreetwo) +
    (\psk@Die@Side)*(\Mthreethree)+(\psk@Die@CZ)}
    %
    \FPeval\abscisseC{(\psk@Die@Side)*(\Moneone) +
    (-\psk@Die@Side)*(\Monetwo) +
    (-\psk@Die@Side)*(\Monethree)+(\psk@Die@CX)}
    \FPeval\ordonneeC{(\psk@Die@Side)*(\Mtwoone) +
    (-\psk@Die@Side)*(\Mtwotwo)+
    (-\psk@Die@Side)*(\Mtwothree)+(\psk@Die@CY)}
    \FPeval\coteC{(\psk@Die@Side)*(\Mthreeone) +
    (-\psk@Die@Side)*(\Mthreetwo) +
    (-\psk@Die@Side)*(\Mthreethree)+(\psk@Die@CZ)}
    %
    \FPeval\abscisseD{(\psk@Die@Side)*(\Moneone) +
    (\psk@Die@Side)*(\Monetwo) +
    (-\psk@Die@Side)*(\Monethree)+(\psk@Die@CX)}
    \FPeval\ordonneeD{(\psk@Die@Side)*(\Mtwoone) +
    (\psk@Die@Side)*(\Mtwotwo) +
    (-\psk@Die@Side)*(\Mtwothree)+(\psk@Die@CY)}
    \FPeval\coteD{(\psk@Die@Side)*(\Mthreeone) +
    (\psk@Die@Side)*(\Mthreetwo) +
    (-\psk@Die@Side)*(\Mthreethree)+(\psk@Die@CZ)}
    %
    \FPeval\abscisseE{(-\psk@Die@Side)*(\Moneone) +
    (\psk@Die@Side)*(\Monetwo)+
    (\psk@Die@Side)*(\Monethree)+(\psk@Die@CX)}
    \FPeval\ordonneeE{(-\psk@Die@Side)*(\Mtwoone) +
    (\psk@Die@Side)*(\Mtwotwo)+
    (\psk@Die@Side)*(\Mtwothree)+(\psk@Die@CY)}
    \FPeval\coteE{(-\psk@Die@Side)*(\Mthreeone) +
    (\psk@Die@Side)*(\Mthreetwo) +
    (\psk@Die@Side)*(\Mthreethree)+(\psk@Die@CZ)}
    %
    \FPeval\abscisseF{(-\psk@Die@Side)*(\Moneone) +
    (-\psk@Die@Side)*(\Monetwo) +
    (\psk@Die@Side)*(\Monethree)+(\psk@Die@CX)}
    \FPeval\ordonneeF{(-\psk@Die@Side)*(\Mtwoone) +
    (-\psk@Die@Side)*(\Mtwotwo) +
    (\psk@Die@Side)*(\Mtwothree)+(\psk@Die@CY)}
    \FPeval\coteF{(-\psk@Die@Side)*(\Mthreeone) +
    (-\psk@Die@Side)*(\Mthreetwo) +
    (\psk@Die@Side)*(\Mthreethree)+(\psk@Die@CZ)}
    %
    \FPeval\abscisseG{(-\psk@Die@Side)*(\Moneone) +
    (-\psk@Die@Side)*(\Monetwo) +
    (-\psk@Die@Side)*(\Monethree)+(\psk@Die@CX)}
    \FPeval\ordonneeG{(-\psk@Die@Side)*(\Mtwoone) +
    (-\psk@Die@Side)*(\Mtwotwo) +
    (-\psk@Die@Side)*(\Mtwothree)+(\psk@Die@CY)}
    \FPeval\coteG{(-\psk@Die@Side)*(\Mthreeone) +
    (-\psk@Die@Side)*(\Mthreetwo) +
    (-\psk@Die@Side)*(\Mthreethree)+(\psk@Die@CZ)}
    %
    \FPeval\abscisseH{(-\psk@Die@Side)*(\Moneone) +
    (\psk@Die@Side)*(\Monetwo) +
    (-\psk@Die@Side)*(\Monethree)+(\psk@Die@CX)}
    \FPeval\ordonneeH{(-\psk@Die@Side)*(\Mtwoone) +
    (\psk@Die@Side)*(\Mtwotwo) +
    (-\psk@Die@Side)*(\Mtwothree)+(\psk@Die@CY)}
    \FPeval\coteH{(-\psk@Die@Side)*(\Mthreeone) +
    (\psk@Die@Side)*(\Mthreetwo) +
    (-\psk@Die@Side)*(\Mthreethree)+(\psk@Die@CZ)}
}
\def\TestVisibilitySide{%
    \FPeval\VisibilityFaceOne{((\abscisseOne)-(\psk@Die@CX))*((\xObs)-(\abscisseOne))
    + ((\ordonneeOne)-(\psk@Die@CY))*((\yObs)-(\ordonneeOne)) +
    ((\coteOne)-(\psk@Die@CZ))*((\zObs)-(\coteOne))}
    \FPeval\VisibilityFaceTwo{((\abscisseTwo)-(\psk@Die@CX))*((\xObs)-(\abscisseTwo))
    + ((\ordonneeTwo)-(\psk@Die@CY))*((\yObs)-(\ordonneeTwo)) +
    ((\coteTwo)-(\psk@Die@CZ))*((\zObs)-(\coteTwo))}
    \FPeval\VisibilityFaceThree{((\abscisseThree)-(\psk@Die@CX))*((\xObs)-(\abscisseThree))
    + ((\ordonneeThree)-(\psk@Die@CY))*((\yObs)-(\ordonneeThree)) +
    ((\coteThree)-(\psk@Die@CZ))*((\zObs)-(\coteThree))}
    \FPeval\VisibilityFaceFour{((\abscisseFour)-(\psk@Die@CX))*((\xObs)-(\abscisseFour))
    + ((\ordonneeFour)-(\psk@Die@CY))*((\yObs)-(\ordonneeFour)) +
    ((\coteFour)-(\psk@Die@CZ))*((\zObs)-(\coteFour))}
    \FPeval\VisibilityFaceFive{((\abscisseFive)-(\psk@Die@CX))*((\xObs)-(\abscisseFive))
    + ((\ordonneeFive)-(\psk@Die@CY))*((\yObs)-(\ordonneeFive)) +
    ((\coteFive)-(\psk@Die@CZ))*((\zObs)-(\coteFive))}
    \FPeval\VisibilityFaceSix{((\abscisseSix)-(\psk@Die@CX))*((\xObs)-(\abscisseSix))
    + ((\ordonneeSix)-(\psk@Die@CY))*((\yObs)-(\ordonneeSix)) +
    ((\coteSix)-(\psk@Die@CZ))*((\zObs)-(\coteSix))}}
 
%
\def\TestVisibilitySummit{%
    \FPeval\VisibilitySummitA{((\abscisseA)-(\psk@Die@CX))*((\xObs)-(\abscisseA))
    + ((\ordonneeA)-(\psk@Die@CY))*((\yObs)-(\ordonneeA)) +
    ((\coteA)-(\psk@Die@CZ))*((\zObs)-(\coteA))}
    \FPeval\VisibilitySummitB{((\abscisseB)-(\psk@Die@CX))*((\xObs)-(\abscisseB))
    + ((\ordonneeB)-(\psk@Die@CY))*((\yObs)-(\ordonneeB)) +
    ((\coteB)-(\psk@Die@CZ))*((\zObs)-(\coteB))}
    \FPeval\VisibilitySummitC{((\abscisseC)-(\psk@Die@CX))*((\xObs)-(\abscisseC))
    + ((\ordonneeC)-(\psk@Die@CY))*((\yObs)-(\ordonneeC)) +
    ((\coteC)-(\psk@Die@CZ))*((\zObs)-(\coteC))}
    \FPeval\VisibilitySummitD{((\abscisseD)-(\psk@Die@CX))*((\xObs)-(\abscisseD))
    + ((\ordonneeD)-(\psk@Die@CY))*((\yObs)-(\ordonneeD)) +
    ((\coteD)-(\psk@Die@CZ))*((\zObs)-(\coteD))}
    \FPeval\VisibilitySummitE{((\abscisseE)-(\psk@Die@CX))*((\xObs)-(\abscisseE))
    + ((\ordonneeE)-(\psk@Die@CY))*((\yObs)-(\ordonneeE)) +
    ((\coteE)-(\psk@Die@CZ))*((\zObs)-(\coteE))}
    \FPeval\VisibilitySummitF{((\abscisseF)-(\psk@Die@CX))*((\xObs)-(\abscisseF))
    + ((\ordonneeF)-(\psk@Die@CY))*((\yObs)-(\ordonneeF)) +
    ((\coteF)-(\psk@Die@CZ))*((\zObs)-(\coteF))}
    \FPeval\VisibilitySummitG{((\abscisseG)-(\psk@Die@CX))*((\xObs)-(\abscisseG))
    + ((\ordonneeG)-(\psk@Die@CY))*((\yObs)-(\ordonneeG)) +
    ((\coteG)-(\psk@Die@CZ))*((\zObs)-(\coteG))}
    \FPeval\VisibilitySummitH{((\abscisseH)-(\psk@Die@CX))*((\xObs)-(\abscisseH))
    + ((\ordonneeH)-(\psk@Die@CY))*((\yObs)-(\ordonneeH)) +
    ((\coteH)-(\psk@Die@CZ))*((\zObs)-(\coteH))}}
%
\def\formulesIIID{%
    /xObservateur abscisse Sin1 mul neg ordonnee Cos1 mul add def
    /yObservateur abscisse Cos1Sin2 mul neg ordonnee Sin1Sin2 mul sub cote Cos2 mul add def
    /zObservateur abscisse neg Cos1Cos2 mul ordonnee Sin1Cos2 mul sub cote Sin2 mul sub Dobs add def
    /xScreen DScreen xObservateur mul zObservateur div def
    /yScreen DScreen yObservateur mul zObservateur div def
  xScreen yScreen}
 
% les sommets
\def\sommets{
    \pnode(! /abscisse1 Side def
        /ordonnee1 Side K mul def
        /cote1 Side def
        \MatriceRot
        \formulesIIID){A1}
    \pnode(! /abscisse1 Side def
        /ordonnee1 Side K neg mul def
        /cote1 Side def
        \MatriceRot
        \formulesIIID){B1}
    \pnode(! /abscisse1 Side def
        /ordonnee1 Side neg def
        /cote1 Side K mul def
        \MatriceRot
        \formulesIIID){C1}
    \pnode(! /abscisse1 Side def
        /ordonnee1 Side neg def
        /cote1 Side K neg mul def
        \MatriceRot
        \formulesIIID){D1}
    \pnode(! /abscisse1 Side def
        /ordonnee1 Side K mul neg def
        /cote1 Side neg def
        \MatriceRot
        \formulesIIID){E1}
    \pnode(! /abscisse1 Side def
        /ordonnee1 Side K mul def
        /cote1 Side neg def
        \MatriceRot
        \formulesIIID){F1}
    \pnode(! /abscisse1 Side def
        /ordonnee1 Side def
        /cote1 Side K mul neg def
        \MatriceRot
        \formulesIIID){G1}
    \pnode(! /abscisse1 Side def
        /ordonnee1 Side def
        /cote1 Side K mul def
        \MatriceRot
        \formulesIIID){H1}
    \pnode(! /abscisse1 Side neg def
        /ordonnee1 Side K mul def
        /cote1 Side def
        \MatriceRot
        \formulesIIID){A2}
    \pnode(! /abscisse1 Side neg def
        /ordonnee1 Side K neg mul def
        /cote1 Side def
        \MatriceRot
        \formulesIIID){B2}
    \pnode(! /abscisse1 Side neg def
        /ordonnee1 Side neg def
        /cote1 Side K mul def
        \MatriceRot
        \formulesIIID){C2}
    \pnode(! /abscisse1 Side neg def
        /ordonnee1 Side neg def
        /cote1 Side K neg mul def
        \MatriceRot
        \formulesIIID){D2}
    \pnode(! /abscisse1 Side neg def
        /ordonnee1 Side K mul neg def
        /cote1 Side neg def
        \MatriceRot
        \formulesIIID){E2}
    \pnode(! /abscisse1 Side neg def
        /ordonnee1 Side K mul def
        /cote1 Side neg def
        \MatriceRot
        \formulesIIID){F2}
    \pnode(! /abscisse1 Side neg def
        /ordonnee1 Side def
        /cote1 Side K mul neg def
        \MatriceRot
        \formulesIIID){G2}
    \pnode(! /abscisse1 Side neg def
        /ordonnee1 Side def
        /cote1 Side K mul def
        \MatriceRot
        \formulesIIID){H2}
    \pnode(! /abscisse1 Side K mul def
        /ordonnee1 Side def
        /cote1 Side def
        \MatriceRot
        \formulesIIID){I1}
    \pnode(! /abscisse1 Side K neg mul def
        /ordonnee1 Side def
        /cote1 Side def
        \MatriceRot
        \formulesIIID){J1}
    \pnode(! /abscisse1 Side K mul neg def
        /ordonnee1 Side neg def
        /cote1 Side def
        \MatriceRot
        \formulesIIID){K1}
    \pnode(! /abscisse1 Side K mul def
        /ordonnee1 Side neg def
        /cote1 Side def
        \MatriceRot
        \formulesIIID){L1}
    \pnode(! /abscisse1 Side K mul def
        /ordonnee1 Side def
        /cote1 Side neg def
        \MatriceRot
        \formulesIIID){I2}
    \pnode(! /abscisse1 Side K neg mul def
        /ordonnee1 Side def
        /cote1 Side neg def
        \MatriceRot
        \formulesIIID){J2}
    \pnode(! /abscisse1 Side K mul neg def
        /ordonnee1 Side neg def
        /cote1 Side neg def
        \MatriceRot
        \formulesIIID){K2}
    \pnode(! /abscisse1 Side K mul def
        /ordonnee1 Side neg def
        /cote1 Side neg def
        \MatriceRot
        \formulesIIID){L2}
% les sommets du cube initial
    \pnode(! /abscisse1 Side def
        /ordonnee1 Side def
        /cote1 Side def
        \MatriceRot
        \formulesIIID){A}
    \pnode(! /abscisse1 Side def
        /ordonnee1 Side neg def
        /cote1 Side def
        \MatriceRot
        \formulesIIID){B}
    \pnode(! /abscisse1 Side def
        /ordonnee1 Side neg def
        /cote1 Side neg def
        \MatriceRot
        \formulesIIID){C}
    \pnode(! /abscisse1 Side def
        /ordonnee1 Side def
        /cote1 Side neg def
        \MatriceRot
        \formulesIIID){D}
    \pnode(! /abscisse1 Side neg def
        /ordonnee1 Side def
        /cote1 Side def
        \MatriceRot
        \formulesIIID){E}
    \pnode(! /abscisse1 Side neg def
        /ordonnee1 Side neg def
        /cote1 Side def
        \MatriceRot
        \formulesIIID){F}
    \pnode(! /abscisse1 Side neg def
        /ordonnee1 Side neg def
        /cote1 Side neg def
        \MatriceRot
        \formulesIIID){G}
    \pnode(! /abscisse1 Side neg def
        /ordonnee1 Side def
        /cote1 Side neg def
        \MatriceRot
        \formulesIIID){H}
        }
% les coins
\def\coinA{%
\pscustom[style=side]{% Denis Girou
    \pspolygon[fillstyle=solid,fillcolor=yellow](A1)(H1)(I1)}}
\def\coinE{%
\pscustom[style=side]{% D.G.
    \pspolygon[fillstyle=solid,fillcolor=yellow](J1)(A2)(H2)}}
\def\coinH{%
\pscustom[style=side]{% D.G.
    \pspolygon[fillstyle=solid,fillcolor=yellow](J2)(F2)(G2)}}
\def\coinD{%
\pscustom[style=side]{% D.G.
    \pspolygon[fillstyle=solid,fillcolor=yellow](F1)(I2)(G1)}}
\def\coinB{%
\pscustom[style=side]{% D.G.
    \pspolygon[fillstyle=solid,fillcolor=yellow](L1)(B1)(C1)}}
\def\coinF{%
\pscustom[style=side]{% D.G.
    \pspolygon[fillstyle=solid,fillcolor=yellow](B2)(K1)(C2)}}
\def\coinG{%
\pscustom[style=side]{% D.G.
    \pspolygon[fillstyle=solid,fillcolor=yellow](D2)(E2)(K2)}}
\def\coinC{%
\pscustom[style=side]{% D.G.
    \pspolygon[fillstyle=solid,fillcolor=yellow](D1)(L2)(E1)}}
%
%
\def\Cube{%
\sommets
% face 1
\FPifpos\VisibilityFaceOne
\pscustom[style=Side]{% Denis Girou
        \pspolygon[style=Side](A1)(B1)(C1)(D1)(E1)(F1)(G1)(H1)}
        \parametricplot[style=points]{0}{360}{%
        /ordonnee1 t cos Point mul def
        /cote1 t sin Point mul def
        /abscisse1 Side def
        \MatriceRot
        \formulesIIID}
   \fi
% face number 3
\FPifpos\VisibilityFaceTwo
\pscustom[style=Side]{% D.G.
        \pspolygon[style=Side](H1)(I1)(J1)(H2)(G2)(J2)(I2)(G1)}
    \parametricplot[style=points]{0}{360}{%
        /abscisse1 t cos Point mul def
        /cote1 t sin Point mul def
        /ordonnee1 Side def
        \MatriceRot
        \formulesIIID}
    \parametricplot[style=points]{0}{360}{%
        /abscisse1 t cos Point mul Side 2 div sub def
        /cote1 t sin Point mul Side 2 div add def
        /ordonnee1 Side def
        \MatriceRot
        \formulesIIID}
    \parametricplot[style=points]{0}{360}{%
        /abscisse1 t cos Point mul Side 2 div add def
        /cote1 t sin Point mul Side 2 div sub def
        /ordonnee1 Side def
        \MatriceRot
        \formulesIIID}
\fi
% face number 4
\FPifpos\VisibilityFaceFour
\pscustom[style=Side]{% D.G.
        \pspolygon[style=Side](L1)(C1)(D1)(L2)(K2)(D2)(C2)(K1)}
    \parametricplot[style=points]{0}{360}{%
        /abscisse1 t cos Point mul Side 2 div sub def
        /cote1 t sin Point mul Side 2 div add def
        /ordonnee1 Side neg def
        \MatriceRot
        \formulesIIID}
    \parametricplot[style=points]{0}{360}{%
        /abscisse1 t cos Point mul Side 2 div add def
        /cote1 t sin Point mul Side 2 div sub def
        /ordonnee1 Side neg def
        \MatriceRot
        \formulesIIID}
    \parametricplot[style=points]{0}{360}{%
        /abscisse1 t cos Point mul Side 2 div sub def
        /cote1 t sin Point mul Side 2 div sub def
        /ordonnee1 Side neg def
        \MatriceRot
        \formulesIIID}
    \parametricplot[style=points]{0}{360}{%
        /abscisse1 t cos Point mul Side 2 div add def
        /cote1 t sin Point mul Side 2 div add def
        /ordonnee1 Side neg def
        \MatriceRot
        \formulesIIID}
\fi
% face 6
\FPifpos\VisibilityFaceThree
\pscustom[style=Side]{% D.G.
\pspolygon[style=Side](A2)(B2)(C2)(D2)(E2)(F2)(G2)(H2)}
    \parametricplot[style=points]{0}{360}{%
        /ordonnee1 t cos Point mul Side 2 div add def
        /cote1 t sin Point mul Side 2 div add def
        /abscisse1 Side neg def
        \MatriceRot
        \formulesIIID}
    \parametricplot[style=points]{0}{360}{%
        /ordonnee1 t cos Point mul Side 2 div add def
        /cote1 t sin Point mul Side 2 div sub def
        /abscisse1 Side neg def
        \MatriceRot
        \formulesIIID}
    \parametricplot[style=points]{0}{360}{%
        /ordonnee1 t cos Point mul Side 2 div sub def
        /cote1 t sin Point mul Side 2 div add def
        /abscisse1 Side neg def
        \MatriceRot
        \formulesIIID}
    \parametricplot[style=points]{0}{360}{%
        /ordonnee1 t cos Point mul Side 2 div sub def
        /cote1 t sin Point mul Side 2 div sub def
        /abscisse1 Side neg def
        \MatriceRot
        \formulesIIID}
    \parametricplot[style=points]{0}{360}{%
        /ordonnee1 t cos Point mul def
        /cote1 t sin Point mul Side 2 div sub def
        /abscisse1 Side neg def
        \MatriceRot
        \formulesIIID}
    \parametricplot[style=points]{0}{360}{%
        /ordonnee1 t cos Point mul def
        /cote1 t sin Point mul Side 2 div add def
        /abscisse1 Side neg def
        \MatriceRot
        \formulesIIID}
\fi
% face 2
\FPifpos\VisibilityFaceSix
\pscustom[style=Side]{% D.G.
        \pspolygon[style=Side](A1)(I1)(J1)(A2)(B2)(K1)(L1)(B1)}
    \parametricplot[style=points]{0}{360}{%
        /cote1  Side def
        /ordonnee1 t sin Point mul Side 2 div sub def
        /abscisse1 t cos Point mul Side 2 div sub def
        \MatriceRot
        \formulesIIID}
    \parametricplot[style=points]{0}{360}{%
        /cote1 Side def
        /ordonnee1 t sin Point mul Side 2 div add def
        /abscisse1 t cos Point mul Side 2 div add def
        \MatriceRot
        \formulesIIID}
   \fi
% face number 3
\FPifpos\VisibilityFaceTwo
\pscustom[style=Side]{% D.G.
        \pspolygon[style=Side](H1)(I1)(J1)(H2)(G2)(J2)(I2)(G1)
        }
   \parametricplot[style=points]{0}{360}{%
        /abscisse1 t cos Point mul def
        /cote1 t sin Point mul def
        /ordonnee1 Side def
        \MatriceRot
        \formulesIIID}
    \parametricplot[style=points]{0}{360}{%
        /abscisse1 t cos Point mul Side 2 div sub def
        /cote1 t sin Point mul Side 2 div add def
        /ordonnee1 Side def
        \MatriceRot
        \formulesIIID}
    \parametricplot[style=points]{0}{360}{%
        /abscisse1 t cos Point mul Side 2 div add def
        /cote1 t sin Point mul Side 2 div sub def
        /ordonnee1 Side def
        \MatriceRot
        \formulesIIID}
\fi
% face 5
\FPifpos\VisibilityFaceFive
\pscustom[style=Side]{% D.G.
        \pspolygon[style=Side](F1)(I2)(J2)(F2)(E2)(K2)(L2)(E1)}
    \parametricplot[style=points]{0}{360}{%
        /abscisse1 t cos Point mul Side 2 div sub def
        /ordonnee1 t sin Point mul Side 2 div add def
        /cote1 Side neg def
        \MatriceRot
        \formulesIIID}
    \parametricplot[style=points]{0}{360}{%
        /abscisse1 t cos Point mul Side 2 div add def
        /ordonnee1 t sin Point mul Side 2 div sub def
        /cote1 Side neg def
        \MatriceRot
        \formulesIIID}
    \parametricplot[style=points]{0}{360}{%
        /abscisse1 t cos Point mul Side 2 div sub def
        /ordonnee1 t sin Point mul Side 2 div sub def
        /cote1 Side neg def
        \MatriceRot
        \formulesIIID}
    \parametricplot[style=points]{0}{360}{%
        /abscisse1 t cos Point mul Side 2 div add def
        /ordonnee1 t sin Point mul Side 2 div add def
        /cote1 Side neg def
        \MatriceRot
        \formulesIIID}
    \parametricplot[style=points]{0}{360}{%
        /abscisse1 t cos Point mul def
        /ordonnee1 t sin Point mul def
        /cote1 Side neg def
        \MatriceRot
        \formulesIIID}
\fi
\FPifpos\VisibilitySummitA
    \coinA
\fi
\FPifpos\VisibilitySummitB
    \coinB
\fi
\FPifpos\VisibilitySummitC
    \coinC
\fi
\FPifpos\VisibilitySummitD
    \coinD
\fi
\FPifpos\VisibilitySummitE
    \coinE
\fi
\FPifpos\VisibilitySummitF
    \coinF
\fi
\FPifpos\VisibilitySummitG
    \coinG
\fi
\FPifpos\VisibilitySummitH
    \coinH
\fi
}
%%%%%%%%%%%%
%
%%%%%%%%%%%
%
\def\Sol{\def\pst@par{}\pst@object{Sol}}
\def\Sol@i{{%
\begin@SpecialObj
    \pnodeIIID(-10,-10,-\psk@Die@Side){A}
    \pnodeIIID(-10,10,-\psk@Die@Side){B}
    \pnodeIIID(10,10,-\psk@Die@Side){C}
    \pnodeIIID(10,-10,-\psk@Die@Side){D}
    \pspolygon[style=sol](A)(B)(C)(D)
\multido{\iY=-10+2,\iX=-10+2}{10}{
    \pnodeIIID(-10,\iY,-\psk@Die@Side){A}
    \pnodeIIID(10,\iY,-\psk@Die@Side){B}
    \psline[linecolor=red](A)(B)
    \pnodeIIID(\iX,-10,-\psk@Die@Side){C}
    \pnodeIIID(\iX,10,-\psk@Die@Side){D}
    \psline[linecolor=red](C)(D)
    \pnodeIIID(-10,\iY,-\psk@Die@Side){C}
    \pnodeIIID(10,\iY,-\psk@Die@Side){D}
    \psline[linecolor=blue](C)(D)
    }
\end@SpecialObj
}}
%
%
\def\CalculsTeX{%
        \FPeval{\ThetaObsRadian}{(\psk@IIID@Theta) * (\FPpi/180)}
        \FPeval{\PhiObsRadian}{(\psk@IIID@Phi) * \FPpi/180}
        \FPcos{\CosThetaObs}{\ThetaObsRadian}
        \FPsin{\SinThetaObs}{\ThetaObsRadian}
        \FPcos{\CosPhiObs}{\PhiObsRadian}
        \FPsin{\SinPhiObs}{\PhiObsRadian}
        \FPeval{\xObs}{\psk@IIID@Dobs*\CosThetaObs*\CosPhiObs}
        \FPeval{\yObs}{\psk@IIID@Dobs*\SinThetaObs*\CosPhiObs}
        \FPeval{\zObs}{\psk@IIID@Dobs*\SinPhiObs}
        }
%
\def\Axes{%
    \pnodeIIID(0,0,-\psk@Die@Side){O}
    \pnodeIIID(0,10,-\psk@Die@Side){Y}
    \pnodeIIID(10,0,-\psk@Die@Side){X}
    \pnodeIIID(0,0,10){Z}
    \bgroup
        \psset{linestyle=dashed,arrowsize=0.2}
        \psline{->}(O)(X)
        \psline{->}(O)(Y)
        \psline{->}(O)(Z)
    \egroup
    \uput[90](X){$x$}
    \uput[90](Y){$y$}
    \uput[90](Z){$z$}
    \uput[270](O){O}
    }
\makeatother
\newpsstyle{sol}{fillstyle=vlines,hatchcolor=green,hatchwidth=0.2\pslinewidth,hatchsep=1\pslinewidth}
\pagestyle{empty}
\psset{dimen=middle}
\newcount\diex
\newcount\diey
\newdimen{\diez}
\newcount\CY
\newcount\CX
\newdimen{\vuePhi}
\newdimen{\vueTheta}
%
\makeatletter
%
\define@key[psset]{pst-die}{randomi1}{\edef\psk@ThreeDies@randomiDieA{#1}}
\define@key[psset]{pst-die}{randomi2}{\edef\psk@ThreeDies@randomiDieB{#1}}
\define@key[psset]{pst-die}{randomi3}{\edef\psk@ThreeDies@randomiDieC{#1}}
%
\psset{randomi1=182048360,randomi2=17483647,randomi3=568003}
 
\def\ThreeDies{\def\pst@par{}\pst@object{ThreeDies}}
\def\ThreeDies@i{{%
  \begin@SpecialObj
\begin{pspicture}(-5,-5)(5,5)
\randomi=\psk@ThreeDies@randomiDieA
\setrannum{\diex}{-2}{2}
\setrannum{\diey}{-2}{2}
\setrannum{\CX}{-8}{8}
\setrannum{\CY}{-8}{-6}
\setrandim{\diez}{0pt}{360pt}
\setrandim{\vuePhi}{10pt}{80pt}
\setrandim{\vueTheta}{0pt}{90pt}
\FPeval\ithetax{(\the\diex)*(90)}
\FPeval\ithetay{(\the\diey)*(90)}
\psset{thetax=\ithetax,thetay=\ithetay,thetaz={\pointless\diez},%
    PHI={\pointless\vuePhi},THETA={\pointless\vueTheta}}
\Die[carpet=true,CX={\the\CX},CY={\the\CY}]
\randomi=\psk@ThreeDies@randomiDieB
\setrannum{\diex}{-2}{2}
\setrannum{\diey}{-2}{2}
\setrannum{\CX}{-8}{-2}
\setrannum{\CY}{-3}{8}
\setrandim{\diez}{0pt}{360pt}
\FPeval\ithetax{(\the\diex)*(90)}
\FPeval\ithetay{(\the\diey)*(90)}
\psset{thetax=\ithetax,thetay=\ithetay,thetaz={\pointless\diez}}
\Die[CX={\the\CX},CY={\the\CY}]
\randomi=\psk@ThreeDies@randomiDieC
\setrannum{\diex}{-2}{2}
\setrannum{\diey}{-2}{2}
\setrannum{\CX}{2}{8}
\setrannum{\CY}{2}{8}
\setrandim{\diez}{0pt}{360pt}
\FPeval\ithetax{(\the\diex)*(90)}
\FPeval\ithetay{(\the\diey)*(90)}
\psset{thetax=\ithetax,thetay=\ithetay,thetaz={\pointless\diez}}
\Die[CX={\the\CX},CY={\the\CY}]
\end{pspicture}
\end@SpecialObj
}}
\makeatother
 
\begin{document}
\input{random_dices.tex}
\end{document}

Un script Perl produit une nouvelle image à intervalles aléatoires sur notre site web:

generate_random_dices.pl

#!/usr/bin/perl
 
use strict ;
use warnings ;
 
## Ne pas dépasser 2^31-1=2147483647, pour chaque valeur,
## voir la doc de ramdom.tex
my $seed1 = int rand(2**31) ;
my $seed2 = int rand(2**31) ;
my $seed3 = int rand(2**31) ;
 
open( RANDOM_DICES, '>random_dices.tex' ) or die "Cannot create file random_dices.tex" ;
print RANDOM_DICES qq#\\ThreeDies[randomi1=${seed1},randomi2=${seed2},randomi3=${seed3}]\n# ;
close( RANDOM_DICES ) or die "Cannot write file random_dices.tex" ;
 
system( 'latex dices.tex > dices.latex_out 2> dices.latex_err' ) ;
system( 'dvips dices.dvi > dices.dvips_out 2> dices.dvips_err' ) ;
system( '/usr/bin/convert -density 60 -trim -transparent "#FFFFFF"  dices.ps dices.png > dices.convert_out 2> dices.convert_err' ) ;
 
exit ;

Nous employons une équipe d'une trentaine de canards pour assurer la sécurité du site web. Ils utilisent le package TikZducks. Un script Perl assure leur rotation aléatoire.