## Graphe de l'hébesphéno-rotonde triangulaire

### Graphe de l'hébesphéno-rotonde triangulaire

Voici une application du fichier graphes.mac de Joffrey et Patrick pour la création du graphe d'un polyèdre.

Ici, je présente le graphe du solide de Johnson J92 : l'hébesphéno-rotonde triangulaire. En fait, je donne deux versions du graphe (il s'agit du même graphe : seul l'arrangement des sommets est différent)

Voici le code permettant d'obtenir ces deux graphes :

Code: Tout sélectionner
\begin{texgraph}[file,call]Cmd   [Fenetre(-3+4*i,15-5*i,1+i), Marges(0.5,0.5,0.5,0.5), Border(0)];   [theta:=0.6261, phi:=1.6036, OriginalCoord(1),IdMatrix()];   [IdMatrix3D(), ModelView(ortho)];Include   "graphes.mac";   "PolyedresII.mac";Mac    Init = [ Matrice:=[0,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,1,0,0,0,0,0,0,0,0,   0,0,1,1,0,1,0,0,0,1,1,0,0,0,0,0,0,0,1,1,0,0,0,0,0,1,0,0,0,0,1,1,0,0,0,0,0,0,0,0,1,   1,0,0,0,0,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,   0,0,0,0,1,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,   1,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,1,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,1,0,   1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,1,   0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,0,1,0,0,0,0,1,0,0,1,0,0,0,0,0,0,0,0,0,0,   0,1,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,0,0,0,0,0,0,0,0,0,0,   0,1,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,1,0,0,0,0,0,0,0,0,1,0,   0,0,0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0],    NbSommets:=20,    PosSommets:=[0,i,-0.86602540378443-0.5*i,0.86602540378443-0.5*i,-0.86602540378443+0.5*i,   -i,0.86602540378443+0.5*i,-1.73205080756888+i,-2*i,1.73205080756888+i,-1.73205080756888-i,   1.73205080756888-i,2*i,-2,-1-1.73205080756888*i,1-1.73205080756888*i,2,1+1.73205080756888*i,   -1+1.73205080756888*i,3-3*i],    typeGraphe:=-1,    Rayon:=3,    rayon:=0.25,    bouclescale:=1,    dotstyle:=-1,    linesep:=0.5,    arrowwidth:=8,    angledep:=Nil,    angledep:=Nil,    arrowposboucle:=[0.265,0.765],    arrowposarete:=[0.25,0.75],    ReCalc() ];    Sommet1 = "T";    optionsSommet1 = "[Color:=white, FillColor:=limegreen]";    Sommet2 = "P";    optionsSommet2 = "[Color:=black, FillColor:=gold]";    Sommet3 = "P";    optionsSommet3 = "[Color:=black, FillColor:=gold]";    Sommet4 = "P";    optionsSommet4 = "[Color:=black, FillColor:=gold]";    Sommet5 = "T";    optionsSommet5 = "[Color:=white, FillColor:=limegreen]";    Sommet6 = "T";    optionsSommet6 = "[Color:=white, FillColor:=limegreen]";    Sommet7 = "T";    optionsSommet7 = "[Color:=white, FillColor:=limegreen]";    Sommet8 = "C";    optionsSommet8 = "[Color:=white, FillColor:=navy]";    Sommet9 = "C";    optionsSommet9 = "[Color:=white, FillColor:=navy]";    Sommet10 = "C";    optionsSommet10 = "[Color:=white, FillColor:=navy]";    Sommet11 = "T";    optionsSommet11 = "[Color:=white, FillColor:=limegreen]";    Sommet12 = "T";    optionsSommet12 = "[Color:=white, FillColor:=limegreen]";    Sommet13 = "T";    optionsSommet13 = "[Color:=white, FillColor:=limegreen]";    Sommet14 = "T";    optionsSommet14 = "[Color:=white, FillColor:=limegreen]";    Sommet15 = "T";    optionsSommet15 = "[Color:=white, FillColor:=limegreen]";    Sommet16 = "T";    optionsSommet16 = "[Color:=white, FillColor:=limegreen]";    Sommet17 = "T";    optionsSommet17 = "[Color:=white, FillColor:=limegreen]";    Sommet18 = "T";    optionsSommet18 = "[Color:=white, FillColor:=limegreen]";    Sommet19 = "T";    optionsSommet19 = "[Color:=white, FillColor:=limegreen]";    Sommet20 = "H";    optionsSommet20 = "[Color:=white, FillColor:=crimson]";    aux = "[LineStyle:=noline]";    poids1_1 = "";    auxOptionsAretes = "[LineStyle:=noline]";    userOptions = "Liste(Set(rayon,0.25),Set(Width,thicklines),Set(FillColor,limegreen))";    optionsArete8_20 = "[LineStyle:=noline]";    optionsArete9_20 = "[LineStyle:=noline]";    optionsArete10_20 = "[LineStyle:=noline]";    optionsArete11_20 = "[LineStyle:=noline]";    optionsArete12_20 = "[LineStyle:=noline]";    optionsArete13_20 = "[LineStyle:=noline]";Graph objet1 = [   tMin:=-2.7,tMax:=4.2,DotScale:=1+i,   Fenetre(-3-5*i, 15+4*i, 1+i),   $Mat:=ReadData("GrapheJ92.txt", 1), PosSommets:=[0, i, exp(-5*i*pi/6), exp(-i*pi/6), exp(5*i*pi/6), -i, exp(i*pi/6), 2*exp(5*i*pi/6), -2*i, 2*exp(i*pi/6), 2*exp(-5*i*pi/6), 2*exp(-i*pi/6), 2*i, -2, 2*exp(-2*i*pi/3), 2*exp(-i*pi/3), 2, 2*exp(i*pi/3), 2*exp(2*i*pi/3), 3-3*i], DefMatrice(Mat), DefLabels("T", "", "P", "", "P", "", "P", "", "T", "", "T", "", "T", "", "C", "", "C", "", "C", "", "T", "", "T", "", "T", "", "T", "", "T", "", "T", "", "T", "", "T", "", "T", "", "H", ""), DefOptionsAretes([8, 20, 9, 20, 10, 20, 11, 20, 12, 20, 13, 20], "[LineStyle:=noline]"), DefOptionsSommets(20, "[Color:=white, FillColor:=crimson]", [2, 3, 4], "[Color:=black, FillColor:=gold]", [8, 9, 10], "[Color:=white, FillColor:=navy]", [1, 5, 6, 7, 11, 12, 13, 14, 15, 16, 17, 18, 19], "[Color:=white, FillColor:=limegreen]"), { Tracé des six arêtes non droite } Width:=thicklines,$P:=PosSommets[20],   $P1:=PosSommets[8],$P2:=PosSommets[9], $P3:=PosSommets[10],$P4:=PosSommets[11], $P5:=PosSommets[12],$P6:=PosSommets[13],   Path([P1, (2*P1+P)/3-0.8*exp(i*pi/3)*(P-P1), (P1+2*P)/3-0.8*exp(2*i*pi/3)*(P-P1), P, bezier,      P2, move, ((P2+P)/2)-0.25*i*(P-P2), P, bezier,      P3, move, ((P3+P)/2)+0.25*i*(P-P3), P, bezier,      P4, move, ((P4+P)/2)-0.65*i*(P-P4), P, bezier,      P5, move, P, line,      P6, move, (2*P6+P)/3+0.65*exp(2*i*pi/3)*(P-P6), (P6+2*P)/3+0.65*exp(i*pi/3)*(P-P6), P, bezier]),      { Tracé du reste du graphe }   Dgraphe([rayon:=0.25, Width:=thicklines, FillColor:=limegreen]),      { Affichage du polyèdre J92 }   SetMatrix([10-i, 3, 3*i]),   opacity:=0.75, StyleL:=Thicklines, LineCap:=round,   HebesphenoRotondeT(Origin, vecI, A, B, C, D, E),   Build3D(A, B, C, D, E),   Display3D(),      { Titre du graphique }   SetMatrix([0, 1, i]),   LabelStyle:=center, LabelSize:=Large,   Label((Xmin+Xmax)/2+i*Ymax, "Graphe de l'hébesphéno-rotonde triangulaire ($\mathcal{J}_{92}$)"),];\end{texgraph}

et le fichier dans lequel j'ai enregistré ma matrice :
Code: Tout sélectionner
0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 01 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 1 1 01 0 0 0 1 1 0 0 0 0 0 0 0 1 1 0 0 0 0 01 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 1 0 0 00 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 00 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 00 1 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 00 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 1 10 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 0 0 10 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 10 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 10 0 1 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 00 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 00 0 0 1 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 00 0 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 00 1 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 00 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 00 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0
Ya Ba Da Ba Dooo!!!

Alphonse Capriani

Messages: 576
Inscription: 18 Juil 2009 19:10
Localisation: East Harlem - NY

### Re: Graphe de l'hébesphéno-rotonde triangulaire

Salut Alphonse,

Il est inutile d'ajouter le fichier contenant la matrice, elle est déjà dans ton source, mais elle n'est pas prise en compte lors du chargement du fichier, il aurait fallu modifier l'élément graphique. Ce n'est pas grave.

Voilà ce que donne le code de l'élément graphique avec la version 0.2 de graphes.mod (il faut aussi charger PolyedresII.mod):

Code: Tout sélectionner
[Fenetre(-3-5*i, 15+4*i, 1+i),DefMatrice([0,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,1,1,0,1,0,0,0,1,1,0,0,0,0,0,0,0,1,1,0,0,0,0,0,1,0,0,0,0,1,1,0,0,0,0,0,0,0,0,1,1,0,0,0,0,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,1,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,1,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,0,1,0,0,0,0,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]),PosSommets:=[0,           i, exp(-5*i*pi/6), exp(-i*pi/6),           exp(5*i*pi/6), -i, exp(i*pi/6),           2*exp(5*i*pi/6), -2*i, 2*exp(i*pi/6),           2*exp(-5*i*pi/6), 2*exp(-i*pi/6), 2*i,           -2, 2*exp(-2*i*pi/3), 2*exp(-i*pi/3), 2, 2*exp(i*pi/3), 2*exp(2*i*pi/3),           3-3*i],DefLabels("T", "", "P", "", "P", "", "P", "", "T", "", "T", "", "T", "", "C", "", "C", "", "C", "",           "T", "", "T", "", "T", "", "T", "", "T", "", "T", "", "T", "", "T", "", "T", "", "H", ""),DefOptionsSommets(20, "[labelColor:=white, backColor:=crimson]",           [2, 3, 4], "[labelColor:=black, backColor:=gold]",           [8, 9, 10], "[labelColor:=white, backColor:=navy]",           [1, 5, 6, 7, 11, 12, 13, 14, 15, 16, 17, 18, 19], "[labelColor:=white, backColor:=limegreen]"),DefOptionsAretes(        [8,20], "[auto:=0,angleA:=-135,angleB:=-135,dist:=1.5]",        [9,20], "[auto:=0,angleA:=-50,angleB:=-180,dist:=0.75]",        [10,20], "[auto:=0,angleA:=-50,angleB:=90,dist:=1]",        [11,20], "[auto:=0,angleA:=-80,angleB:=-160,dist:=1]",        [13,20], "[auto:=0,angleA:=30,angleB:=45,dist:=1.25]",        ),       { Tracé du reste du graphe }Dgraphe([rayon:=0.25, Width:=thicklines, circleColor:=white]),       { Affichage du polyèdre J92 }SetMatrix([10-i, 3, 3*i]),opacity:=0.75, StyleL:=Thicklines, LineCap:=round,HebesphenoRotondeT(Origin, vecI, A, B, C, D, E),Build3D(A, B, C, D, E),Display3D(),       { Titre du graphique }SetMatrix([0, 1, i]),LabelStyle:=center, LabelSize:=Large,Label((Xmin+Xmax)/2+i*(Ymax-0.5), "Graphe de l'hébesphéno-rotonde triangulaire ($\mathcal{J}_{92}$)"),]

grapheAlphonse.png (48.32 Kio) Consulté 5757 fois
P.Fradin

P.Fradin
Administrateur du site

Messages: 1837
Inscription: 29 Oct 2008 15:04

### Re: Graphe de l'hébesphéno-rotonde triangulaire

Ca m'a l'air parfait tout ca!!!

Le code est nettement plus propre qu'avec mon bidouillage. Encore une fois, je suis impatient de tester cette nouvelle version de graphes.mac...
Ya Ba Da Ba Dooo!!!

Alphonse Capriani

Messages: 576
Inscription: 18 Juil 2009 19:10
Localisation: East Harlem - NY

### Re: Graphe de l'hébesphéno-rotonde triangulaire

Je te met une version test en fichier joint. Pour ta question sur la courbe de Bezier je finis un schéma et je le poste.
graphes0.2.zip
(6.78 Kio) Téléchargé 609 fois
P.Fradin

P.Fradin
Administrateur du site

Messages: 1837
Inscription: 29 Oct 2008 15:04

### Re: Graphe de l'hébesphéno-rotonde triangulaire

Ok d'ac : c'est parfait!!!

Je vais tester dès ce soir cette mise à jour. Je pense qu'avec ton exemple précédent, je devrait déja y voir plus clair.

Affaire à suivre...
Ya Ba Da Ba Dooo!!!

Alphonse Capriani

Messages: 576
Inscription: 18 Juil 2009 19:10
Localisation: East Harlem - NY

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