""" Great Dodecahemidodecahedron 10.06.2021 www.3d-meier.de http://dmccooey.com/polyhedra/GreatDodecahemidodecahedron.html """ import c4d import math # Variablen und Konstanten Titel = 'Great Dodecahemidodecahedron' # Name NP = 30 # Anzahl Punkte N5P = 12 # Anzahl Pentagramme N10D = 6 # Anzahl Dekagramme Radius = 0.50 # Radius der Eckpunktkugeln C0 = (3 - math.sqrt(5)) / 4 C1 = (math.sqrt(5) - 1) / 4 C2 = (math.sqrt(5) - 1) / 2 Punkte = [( 0.0, 0.0, C2), ( 0.0, 0.0, -C2), ( 0.0, C2, 0.0), ( 0.0, -C2, 0.0), ( C2, 0.0, 0.0), ( -C2, 0.0, 0.0), ( C1, -0.5, -C0), ( C1, -0.5, C0), ( -C1, -0.5, -C0), ( -C1, -0.5, C0), ( C1, 0.5, -C0), ( C1, 0.5, C0), ( -C1, 0.5, -C0), ( -C1, 0.5, C0), (-0.5, -C0, C1), (-0.5, -C0, -C1), ( 0.5, -C0, C1), ( 0.5, -C0, -C1), (-0.5, C0, C1), (-0.5, C0, -C1), ( 0.5, C0, C1), ( 0.5, C0, -C1), ( -C0, C1, -0.5), ( -C0, C1, 0.5), ( C0, C1, -0.5), ( C0, C1, 0.5), ( -C0, -C1, -0.5), ( -C0, -C1, 0.5), ( C0, -C1, -0.5), ( C0, -C1, 0.5)] Dekagramme = [( 0, 29, 7, 6, 28, 1, 22, 12, 13, 23), ( 0, 27, 9, 8, 26, 1, 24, 10, 11, 25), ( 2, 13, 18, 14, 9, 3, 6, 17, 21, 10), ( 2, 12, 19, 15, 8, 3, 7, 16, 20, 11), ( 4, 21, 24, 22, 19, 5, 14, 27, 29, 16), ( 4, 20, 25, 23, 18, 5, 15, 26, 28, 17)] Pentagramme = [( 0, 14, 8, 6, 16 ), ( 0, 20, 10, 12, 18 ), ( 1, 17, 7, 9, 15 ), ( 1, 19, 13, 11, 21 ), ( 2, 22, 15, 14, 23 ), ( 2, 25, 16, 17, 24 ), ( 3, 27, 18, 19, 26 ), ( 3, 28, 21, 20, 29 ), ( 4, 11, 23, 27, 7 ), ( 4, 6, 26, 22, 10 ), ( 5, 12, 24, 28, 8 ), ( 5, 9, 29, 25, 13 )] Faktor = 100 # Skalierungsfaktor k = 1 # Korrekturfaktor fuer Kantenlaenge ku = 256 # Unterteilung der Kugeln ru = (math.sqrt(5)-1)/2 # Umkugelradius rk = math.sqrt(5-2*math.sqrt(5))/2 # Kantenkugelradius ri5 = math.sqrt(5*(5-2*math.sqrt(5)))/5 # Inkugelradius Pentagramm #************************************************************************ # Geradengleichung def Gerade(a, b, r): c = b-a d = a + r*c return d #************************************************************************ def CreateNullobjekt1(): obj = c4d.BaseObject(c4d.Onull) obj.SetName(Titel) obj.Message(c4d.MSG_UPDATE) return obj #************************************************************************ def CreateNullobjekt2(): obj = c4d.BaseObject(c4d.Onull) obj.SetName('Ecken') obj.Message(c4d.MSG_UPDATE) return obj #************************************************************************ def CreateNullobjekt3(): obj = c4d.BaseObject(c4d.Onull) obj.SetName('Kanten') obj.Message(c4d.MSG_UPDATE) return obj #************************************************************************ def CreateNullobjekt4(): obj = c4d.BaseObject(c4d.Onull) obj.SetName('Polygone') obj.Message(c4d.MSG_UPDATE) return obj #************************************************************************ def CreateNullobjekt5(): obj = c4d.BaseObject(c4d.Onull) obj.SetName('Kugeln') obj.Message(c4d.MSG_UPDATE) return obj #************************************************************************ def CreatePentagramme(): obj = c4d.BaseObject(c4d.Opolygon) obj.ResizeObject(NP + N5P*5, N5P*7) obj.SetName('Pentagramme') phi = (1 + math.sqrt(5))/2.0 # Goldener Schnitt r1 = phi/(2*phi + 1) r2 = (phi + 1)/(2*phi + 1) # Punkte uebergeben for i in xrange(NP): obj.SetPoint(i, c4d.Vector(Punkte[i][0]*Faktor*k, Punkte[i][1]*Faktor*k, Punkte[i][2]*Faktor*k)) for i in xrange(N5P): # Eckpunkte des Pentagramms in Vektoren umwandeln P0 = c4d.Vector(Punkte[Pentagramme[i][0]][0], Punkte[Pentagramme[i][0]][1], Punkte[Pentagramme[i][0]][2]) P1 = c4d.Vector(Punkte[Pentagramme[i][1]][0], Punkte[Pentagramme[i][1]][1], Punkte[Pentagramme[i][1]][2]) P2 = c4d.Vector(Punkte[Pentagramme[i][2]][0], Punkte[Pentagramme[i][2]][1], Punkte[Pentagramme[i][2]][2]) P3 = c4d.Vector(Punkte[Pentagramme[i][3]][0], Punkte[Pentagramme[i][3]][1], Punkte[Pentagramme[i][3]][2]) P4 = c4d.Vector(Punkte[Pentagramme[i][4]][0], Punkte[Pentagramme[i][4]][1], Punkte[Pentagramme[i][4]][2]) # Neue Punkte P5 = Gerade(P0, P2, r1) P6 = Gerade(P0, P2, r2) P7 = Gerade(P1, P3, r2) P8 = Gerade(P3, P0, r1) P9 = Gerade(P3, P0, r2) # Neue Punkte an Polygonobjekt uebergeben obj.SetPoint(5*i+NP, P5*Faktor*k) obj.SetPoint(5*i+NP+1, P6*Faktor*k) obj.SetPoint(5*i+NP+2, P7*Faktor*k) obj.SetPoint(5*i+NP+3, P8*Faktor*k) obj.SetPoint(5*i+NP+4, P9*Faktor*k) # Polygone setzen obj.SetPolygon(7*i+0, c4d.CPolygon(Pentagramme[i][0], 5*i+NP , 5*i+NP+4, 5*i+NP+4)) obj.SetPolygon(7*i+1, c4d.CPolygon(Pentagramme[i][1], 5*i+NP+1, 5*i+NP , 5*i+NP )) obj.SetPolygon(7*i+2, c4d.CPolygon(Pentagramme[i][2], 5*i+NP+2, 5*i+NP+1, 5*i+NP+1)) obj.SetPolygon(7*i+3, c4d.CPolygon(Pentagramme[i][3], 5*i+NP+3, 5*i+NP+2, 5*i+NP+2)) obj.SetPolygon(7*i+4, c4d.CPolygon(Pentagramme[i][4], 5*i+NP+4, 5*i+NP+3, 5*i+NP+3)) obj.SetPolygon(7*i+5, c4d.CPolygon(5*i+NP , 5*i+NP+1, 5*i+NP+2, 5*i+NP+3)) obj.SetPolygon(7*i+6, c4d.CPolygon(5*i+NP+3 , 5*i+NP+4, 5*i+NP , 5*i+NP )) obj.Message(c4d.MSG_UPDATE) return obj #************************************************************************ def CreateDekagramme(): obj = c4d.BaseObject(c4d.Opolygon) obj.ResizeObject(NP + N10D*20, N10D*24) obj.SetName('Dekagramme') phi = (1+math.sqrt(5))/2.0 r1 = math.sqrt(5) - 2 r2 = (3 - math.sqrt(5))/2 r3 = (math.sqrt(5) - 1)/2 r4 = 3 - math.sqrt(5) # Punkte uebergeben for i in xrange(NP): obj.SetPoint(i, c4d.Vector(Punkte[i][0]*Faktor*k, Punkte[i][1]*Faktor*k, Punkte[i][2]*Faktor*k)) for i in xrange(N10D): # Eckpunkte des Dekagramms in Vektoren umwandeln P0 = c4d.Vector(Punkte[Dekagramme[i][0]][0], Punkte[Dekagramme[i][0]][1], Punkte[Dekagramme[i][0]][2]) P1 = c4d.Vector(Punkte[Dekagramme[i][1]][0], Punkte[Dekagramme[i][1]][1], Punkte[Dekagramme[i][1]][2]) P2 = c4d.Vector(Punkte[Dekagramme[i][2]][0], Punkte[Dekagramme[i][2]][1], Punkte[Dekagramme[i][2]][2]) P3 = c4d.Vector(Punkte[Dekagramme[i][3]][0], Punkte[Dekagramme[i][3]][1], Punkte[Dekagramme[i][3]][2]) P4 = c4d.Vector(Punkte[Dekagramme[i][4]][0], Punkte[Dekagramme[i][4]][1], Punkte[Dekagramme[i][4]][2]) P5 = c4d.Vector(Punkte[Dekagramme[i][5]][0], Punkte[Dekagramme[i][5]][1], Punkte[Dekagramme[i][5]][2]) P6 = c4d.Vector(Punkte[Dekagramme[i][6]][0], Punkte[Dekagramme[i][6]][1], Punkte[Dekagramme[i][6]][2]) P7 = c4d.Vector(Punkte[Dekagramme[i][7]][0], Punkte[Dekagramme[i][7]][1], Punkte[Dekagramme[i][7]][2]) P8 = c4d.Vector(Punkte[Dekagramme[i][8]][0], Punkte[Dekagramme[i][8]][1], Punkte[Dekagramme[i][8]][2]) P9 = c4d.Vector(Punkte[Dekagramme[i][9]][0], Punkte[Dekagramme[i][9]][1], Punkte[Dekagramme[i][9]][2]) # Neue Punkte P10 = Gerade(P0, P3, r1) P11 = Gerade(P1, P4, r1) P12 = Gerade(P2, P5, r1) P13 = Gerade(P3, P6, r1) P14 = Gerade(P4, P7, r1) P15 = Gerade(P5, P8, r1) P16 = Gerade(P6, P9, r1) P17 = Gerade(P7, P0, r1) P18 = Gerade(P8, P1, r1) P19 = Gerade(P9, P2, r1) P20 = Gerade(P9, P2, r2) P21 = Gerade(P0, P3, r2) P22 = Gerade(P1, P4, r2) P23 = Gerade(P2, P5, r2) P24 = Gerade(P3, P6, r2) P25 = Gerade(P4, P7, r2) P26 = Gerade(P5, P8, r2) P27 = Gerade(P6, P9, r2) P28 = Gerade(P7, P0, r2) P29 = Gerade(P8, P1, r2) # Neue Punkte an Polygonobjekt uebergeben obj.SetPoint(20*i+NP , P10*Faktor*k) obj.SetPoint(20*i+NP+1 , P11*Faktor*k) obj.SetPoint(20*i+NP+2 , P12*Faktor*k) obj.SetPoint(20*i+NP+3 , P13*Faktor*k) obj.SetPoint(20*i+NP+4 , P14*Faktor*k) obj.SetPoint(20*i+NP+5 , P15*Faktor*k) obj.SetPoint(20*i+NP+6 , P16*Faktor*k) obj.SetPoint(20*i+NP+7 , P17*Faktor*k) obj.SetPoint(20*i+NP+8 , P18*Faktor*k) obj.SetPoint(20*i+NP+9 , P19*Faktor*k) obj.SetPoint(20*i+NP+10, P20*Faktor*k) obj.SetPoint(20*i+NP+11, P21*Faktor*k) obj.SetPoint(20*i+NP+12, P22*Faktor*k) obj.SetPoint(20*i+NP+13, P23*Faktor*k) obj.SetPoint(20*i+NP+14, P24*Faktor*k) obj.SetPoint(20*i+NP+15, P25*Faktor*k) obj.SetPoint(20*i+NP+16, P26*Faktor*k) obj.SetPoint(20*i+NP+17, P27*Faktor*k) obj.SetPoint(20*i+NP+18, P28*Faktor*k) obj.SetPoint(20*i+NP+19, P29*Faktor*k) # Polygone setzen obj.SetPolygon(24*i+0, c4d.CPolygon(Dekagramme[i][1], 20*i+NP+1, 20*i+NP+11, 20*i+NP )) obj.SetPolygon(24*i+1, c4d.CPolygon(Dekagramme[i][2], 20*i+NP+2, 20*i+NP+12, 20*i+NP+1 )) obj.SetPolygon(24*i+2, c4d.CPolygon(Dekagramme[i][3], 20*i+NP+3, 20*i+NP+13, 20*i+NP+2 )) obj.SetPolygon(24*i+3, c4d.CPolygon(Dekagramme[i][4], 20*i+NP+4, 20*i+NP+14, 20*i+NP+3 )) obj.SetPolygon(24*i+4, c4d.CPolygon(Dekagramme[i][5], 20*i+NP+5, 20*i+NP+15, 20*i+NP+4 )) obj.SetPolygon(24*i+5, c4d.CPolygon(Dekagramme[i][6], 20*i+NP+6, 20*i+NP+16, 20*i+NP+5 )) obj.SetPolygon(24*i+6, c4d.CPolygon(Dekagramme[i][7], 20*i+NP+7, 20*i+NP+17, 20*i+NP+6 )) obj.SetPolygon(24*i+7, c4d.CPolygon(Dekagramme[i][8], 20*i+NP+8, 20*i+NP+18, 20*i+NP+7 )) obj.SetPolygon(24*i+8, c4d.CPolygon(Dekagramme[i][9], 20*i+NP+9, 20*i+NP+19, 20*i+NP+8 )) obj.SetPolygon(24*i+9, c4d.CPolygon(Dekagramme[i][0], 20*i+NP , 20*i+NP+10, 20*i+NP+9 )) obj.SetPolygon(24*i+10, c4d.CPolygon(20*i+NP , 20*i+NP+11, 20*i+NP+10, 20*i+NP+10 )) obj.SetPolygon(24*i+11, c4d.CPolygon(20*i+NP+1 , 20*i+NP+12, 20*i+NP+11, 20*i+NP+11 )) obj.SetPolygon(24*i+12, c4d.CPolygon(20*i+NP+2 , 20*i+NP+13, 20*i+NP+12, 20*i+NP+12 )) obj.SetPolygon(24*i+13, c4d.CPolygon(20*i+NP+3 , 20*i+NP+14, 20*i+NP+13, 20*i+NP+13 )) obj.SetPolygon(24*i+14, c4d.CPolygon(20*i+NP+4 , 20*i+NP+15, 20*i+NP+14, 20*i+NP+14 )) obj.SetPolygon(24*i+15, c4d.CPolygon(20*i+NP+5 , 20*i+NP+16, 20*i+NP+15, 20*i+NP+15 )) obj.SetPolygon(24*i+16, c4d.CPolygon(20*i+NP+6 , 20*i+NP+17, 20*i+NP+16, 20*i+NP+16 )) obj.SetPolygon(24*i+17, c4d.CPolygon(20*i+NP+7 , 20*i+NP+18, 20*i+NP+17, 20*i+NP+17 )) obj.SetPolygon(24*i+18, c4d.CPolygon(20*i+NP+8 , 20*i+NP+19, 20*i+NP+18, 20*i+NP+18 )) obj.SetPolygon(24*i+19, c4d.CPolygon(20*i+NP+9 , 20*i+NP+10, 20*i+NP+19, 20*i+NP+19 )) obj.SetPolygon(24*i+20, c4d.CPolygon(20*i+NP+10, 20*i+NP+11, 20*i+NP+12, 20*i+NP+19 )) obj.SetPolygon(24*i+21, c4d.CPolygon(20*i+NP+12, 20*i+NP+13, 20*i+NP+18, 20*i+NP+19 )) obj.SetPolygon(24*i+22, c4d.CPolygon(20*i+NP+13, 20*i+NP+14, 20*i+NP+17, 20*i+NP+18 )) obj.SetPolygon(24*i+23, c4d.CPolygon(20*i+NP+14, 20*i+NP+15, 20*i+NP+16, 20*i+NP+17 )) obj.Message(c4d.MSG_UPDATE) return obj #************************************************************************ def CreateSplinePentagramme(): obj = c4d.BaseObject(c4d.Ospline) obj.SetName("Spline-Pentagramme") obj.ResizeObject(N5P*5) zz = 0 for i in xrange(N5P): x = Punkte[Pentagramme[i][0]][0] y = Punkte[Pentagramme[i][0]][1] z = Punkte[Pentagramme[i][0]][2] obj.SetPoint(zz, c4d.Vector(x*Faktor*k, y*Faktor*k, z*Faktor*k)) zz = zz + 1 x = Punkte[Pentagramme[i][2]][0] y = Punkte[Pentagramme[i][2]][1] z = Punkte[Pentagramme[i][2]][2] obj.SetPoint(zz, c4d.Vector(x*Faktor*k, y*Faktor*k, z*Faktor*k)) zz = zz + 1 x = Punkte[Pentagramme[i][4]][0] y = Punkte[Pentagramme[i][4]][1] z = Punkte[Pentagramme[i][4]][2] obj.SetPoint(zz, c4d.Vector(x*Faktor*k, y*Faktor*k, z*Faktor*k)) zz = zz + 1 x = Punkte[Pentagramme[i][1]][0] y = Punkte[Pentagramme[i][1]][1] z = Punkte[Pentagramme[i][1]][2] obj.SetPoint(zz, c4d.Vector(x*Faktor*k, y*Faktor*k, z*Faktor*k)) zz = zz + 1 x = Punkte[Pentagramme[i][3]][0] y = Punkte[Pentagramme[i][3]][1] z = Punkte[Pentagramme[i][3]][2] obj.SetPoint(zz, c4d.Vector(x*Faktor*k, y*Faktor*k, z*Faktor*k)) zz = zz + 1 # Segmente erzeugen obj.MakeVariableTag(c4d.Tsegment, N5P) for i in range(0, N5P): obj.SetSegment(i, 5, True) # Spline schliessen obj[c4d.SPLINEOBJECT_CLOSED] = True obj.Message(c4d.MSG_UPDATE) return obj #************************************************************************ def CreateSplineDekagramme(): obj = c4d.BaseObject(c4d.Ospline) obj.SetName("Spline-Dekaagramme") obj.ResizeObject(N10D*10) zz = 0 for i in xrange(N10D): x = Punkte[Dekagramme[i][0]][0] y = Punkte[Dekagramme[i][0]][1] z = Punkte[Dekagramme[i][0]][2] obj.SetPoint(zz, c4d.Vector(x*Faktor*k, y*Faktor*k, z*Faktor*k)) zz = zz + 1 x = Punkte[Dekagramme[i][3]][0] y = Punkte[Dekagramme[i][3]][1] z = Punkte[Dekagramme[i][3]][2] obj.SetPoint(zz, c4d.Vector(x*Faktor*k, y*Faktor*k, z*Faktor*k)) zz = zz + 1 x = Punkte[Dekagramme[i][6]][0] y = Punkte[Dekagramme[i][6]][1] z = Punkte[Dekagramme[i][6]][2] obj.SetPoint(zz, c4d.Vector(x*Faktor*k, y*Faktor*k, z*Faktor*k)) zz = zz + 1 x = Punkte[Dekagramme[i][9]][0] y = Punkte[Dekagramme[i][9]][1] z = Punkte[Dekagramme[i][9]][2] obj.SetPoint(zz, c4d.Vector(x*Faktor*k, y*Faktor*k, z*Faktor*k)) zz = zz + 1 x = Punkte[Dekagramme[i][2]][0] y = Punkte[Dekagramme[i][2]][1] z = Punkte[Dekagramme[i][2]][2] obj.SetPoint(zz, c4d.Vector(x*Faktor*k, y*Faktor*k, z*Faktor*k)) zz = zz + 1 x = Punkte[Dekagramme[i][5]][0] y = Punkte[Dekagramme[i][5]][1] z = Punkte[Dekagramme[i][5]][2] obj.SetPoint(zz, c4d.Vector(x*Faktor*k, y*Faktor*k, z*Faktor*k)) zz = zz + 1 x = Punkte[Dekagramme[i][8]][0] y = Punkte[Dekagramme[i][8]][1] z = Punkte[Dekagramme[i][8]][2] obj.SetPoint(zz, c4d.Vector(x*Faktor*k, y*Faktor*k, z*Faktor*k)) zz = zz + 1 x = Punkte[Dekagramme[i][1]][0] y = Punkte[Dekagramme[i][1]][1] z = Punkte[Dekagramme[i][1]][2] obj.SetPoint(zz, c4d.Vector(x*Faktor*k, y*Faktor*k, z*Faktor*k)) zz = zz + 1 x = Punkte[Dekagramme[i][4]][0] y = Punkte[Dekagramme[i][4]][1] z = Punkte[Dekagramme[i][4]][2] obj.SetPoint(zz, c4d.Vector(x*Faktor*k, y*Faktor*k, z*Faktor*k)) zz = zz + 1 x = Punkte[Dekagramme[i][7]][0] y = Punkte[Dekagramme[i][7]][1] z = Punkte[Dekagramme[i][7]][2] obj.SetPoint(zz, c4d.Vector(x*Faktor*k, y*Faktor*k, z*Faktor*k)) zz = zz + 1 # Segmente erzeugen obj.MakeVariableTag(c4d.Tsegment, N10D) for i in range(0, N10D): obj.SetSegment(i, 10, True) # Spline schliessen obj[c4d.SPLINEOBJECT_CLOSED] = True obj.Message(c4d.MSG_UPDATE) return obj #************************************************************************ def main(): nullobj1 = CreateNullobjekt1() nullobj2 = CreateNullobjekt2() # Ecken nullobj3 = CreateNullobjekt3() # Kanten nullobj4 = CreateNullobjekt4() # Polygone nullobj5 = CreateNullobjekt5() # Umkugel, etc. plyobj1 = CreatePentagramme() plyobj2 = CreateDekagramme() splobj1 = CreateSplinePentagramme() splobj2 = CreateSplineDekagramme() doc.InsertObject(nullobj1, None, None, True) doc.InsertObject(nullobj5, nullobj1, None, True) doc.InsertObject(nullobj4, nullobj1, None, True) doc.InsertObject(nullobj3, nullobj1, None, True) doc.InsertObject(nullobj2, nullobj1, None, True) doc.InsertObject(splobj2, nullobj3, None, True) doc.InsertObject(splobj1, nullobj3, None, True) doc.InsertObject(plyobj2, nullobj4, None, True) doc.InsertObject(plyobj1, nullobj4, None, True) # Kugeln auf Eckpunkte setzen for i in range(0, NP): obj = c4d.BaseObject(c4d.Osphere) obj[c4d.PRIM_SPHERE_RAD] = Radius obj.SetName(str(i)) x = Punkte[i][0] y = Punkte[i][1] z = Punkte[i][2] obj.SetAbsPos(c4d.Vector(x*Faktor*k, y*Faktor*k, z*Faktor*k)) doc.InsertObject(obj, nullobj2, None, True) # Umkugel erzeugen obj = c4d.BaseObject(c4d.Osphere) obj[c4d.PRIM_SPHERE_SUB] = ku obj[c4d.PRIM_SPHERE_RAD] = ru*Faktor*k obj.SetName('Umkugel') obj[c4d.ID_BASEOBJECT_VISIBILITY_EDITOR] = 1 obj[c4d.ID_BASEOBJECT_VISIBILITY_RENDER] = 1 doc.InsertObject(obj, nullobj5, None, True) # Kantenkugel erzeugen obj = c4d.BaseObject(c4d.Osphere) obj[c4d.PRIM_SPHERE_SUB] = ku obj[c4d.PRIM_SPHERE_RAD] = rk*Faktor*k obj.SetName('Kantenkugel') obj[c4d.ID_BASEOBJECT_VISIBILITY_EDITOR] = 1 obj[c4d.ID_BASEOBJECT_VISIBILITY_RENDER] = 1 doc.InsertObject(obj, nullobj5, None, True) # Inkugel (Pentagramm) erzeugen obj = c4d.BaseObject(c4d.Osphere) obj[c4d.PRIM_SPHERE_SUB] = ku obj[c4d.PRIM_SPHERE_RAD] = ri5*Faktor*k obj.SetName('Inkugel Pentagramm') obj[c4d.ID_BASEOBJECT_VISIBILITY_EDITOR] = 1 obj[c4d.ID_BASEOBJECT_VISIBILITY_RENDER] = 1 doc.InsertObject(obj, nullobj5, None, True) c4d.EventAdd() if __name__=='__main__': main()