""" 22.05.2021 www.3d-meier.de http://dmccooey.com/polyhedra/Rhombidodecadodecahedron.html """ import c4d import math # Variablen und Konstanten Titel = 'Rhombidodecadodecahedron' # Name NP = 60 # Anzahl Punkte N4 = 30 # Anzahl Vierecke N5 = 12 # Anzahl Fuenfecke N6 = 20 # Anzahl Sechsecke N5P = 12 # Anzahl Pentagramme Radius = 2 # Radius der Eckpunktkugeln phi = (1 + math.sqrt(5))/2.0 # Goldener Schnitt C0 = (3 - math.sqrt(5)) / 4 C1 = (math.sqrt(5) - 1) / 4 C2 = (1 + math.sqrt(5)) / 4 C3 = math.sqrt(5) / 2 C4 = (3 + math.sqrt(5)) / 4 Punkte = [( C0, 0.0, C4), ( C0, 0.0, -C4), ( -C0, 0.0, C4), ( -C0, 0.0, -C4), ( C4, C0, 0.0), ( C4, -C0, 0.0), ( -C4, C0, 0.0), ( -C4, -C0, 0.0), ( 0.0, C4, C0), ( 0.0, C4, -C0), ( 0.0, -C4, C0), ( 0.0, -C4, -C0), ( 0.5, 0.5, C3), ( 0.5, 0.5, -C3), ( 0.5, -0.5, C3), ( 0.5, -0.5, -C3), (-0.5, 0.5, C3), (-0.5, 0.5, -C3), (-0.5, -0.5, C3), (-0.5, -0.5, -C3), ( C3, 0.5, 0.5), ( C3, 0.5, -0.5), ( C3, -0.5, 0.5), ( C3, -0.5, -0.5), ( -C3, 0.5, 0.5), ( -C3, 0.5, -0.5), ( -C3, -0.5, 0.5), ( -C3, -0.5, -0.5), ( 0.5, C3, 0.5), ( 0.5, C3, -0.5), ( 0.5, -C3, 0.5), ( 0.5, -C3, -0.5), (-0.5, C3, 0.5), (-0.5, C3, -0.5), (-0.5, -C3, 0.5), (-0.5, -C3, -0.5), ( C1, C2, 1.0), ( C1, C2, -1.0), ( C1, -C2, 1.0), ( C1, -C2, -1.0), ( -C1, C2, 1.0), ( -C1, C2, -1.0), ( -C1, -C2, 1.0), ( -C1, -C2, -1.0), ( 1.0, C1, C2), ( 1.0, C1, -C2), ( 1.0, -C1, C2), ( 1.0, -C1, -C2), (-1.0, C1, C2), (-1.0, C1, -C2), (-1.0, -C1, C2), (-1.0, -C1, -C2), ( C2, 1.0, C1), ( C2, 1.0, -C1), ( C2, -1.0, C1), ( C2, -1.0, -C1), ( -C2, 1.0, C1), ( -C2, 1.0, -C1), ( -C2, -1.0, C1), ( -C2, -1.0, -C1)] Fuenfecke = [( 0, 40, 24, 26, 42 ), ( 1, 43, 27, 25, 41 ), ( 2, 38, 22, 20, 36 ), ( 3, 37, 21, 23, 39 ), ( 4, 46, 30, 31, 47 ), ( 5, 45, 29, 28, 44 ), ( 6, 51, 35, 34, 50 ), ( 7, 48, 32, 33, 49 ), ( 8, 53, 13, 17, 57 ), ( 9, 56, 16, 12, 52 ), ( 10, 59, 19, 15, 55 ), ( 11, 54, 14, 18, 58 )] Pentagramme = [( 0, 14, 46, 44, 12), ( 1, 13, 45, 47, 15), ( 2, 16, 48, 50, 18), ( 3, 19, 51, 49, 17), ( 4, 21, 53, 52, 20), ( 5, 22, 54, 55, 23), ( 6, 24, 56, 57, 25), ( 7, 27, 59, 58, 26), ( 8, 32, 40, 36, 28), ( 9, 29, 37, 41, 33), (10, 30, 38, 42, 34), (11, 35, 43, 39, 31)] Vierecke = [( 0, 42, 30, 46 ), ( 0, 44, 28, 40 ), ( 1, 41, 29, 45 ), ( 1, 47, 31, 43 ), ( 3, 39, 35, 51 ), ( 3, 49, 33, 37 ), ( 5, 44, 14, 54 ), ( 5, 55, 15, 45 ), ( 6, 50, 16, 56 ), ( 6, 57, 17, 51 ), ( 7, 49, 19, 59 ), ( 7, 58, 18, 48 ), ( 8, 36, 20, 53 ), ( 8, 57, 24, 40 ), ( 9, 41, 25, 56 ), ( 9, 52, 21, 37 ), ( 11, 39, 23, 54 ), ( 11, 58, 27, 43 ), ( 12, 16, 18, 14 ), ( 12, 46, 4, 52 ), ( 13, 15, 19, 17 ), ( 13, 53, 4, 47 ), ( 22, 23, 21, 20 ), ( 22, 38, 10, 55 ), ( 26, 24, 25, 27 ), ( 26, 59, 10, 42 ), ( 32, 28, 29, 33 ), ( 32, 48, 2, 36 ), ( 34, 35, 31, 30 ), ( 34, 38, 2, 50 )] Sechsecke = [( 3, 17, 41, 37, 13, 1), (13, 37, 29, 53, 21, 45), (45, 21, 4, 5, 23, 47), ( 5, 4, 20, 44, 46, 22), (53, 29, 9, 8, 28, 52), ( 8, 9, 33, 57, 56, 32), (33, 41, 17, 49, 25, 57), (25, 49, 51, 27, 7, 6), (19, 43, 35, 59, 27, 51), ( 1, 15, 39, 43, 19, 3), (23, 55, 31, 39, 15, 47), (54, 30, 10, 11, 31, 55), (34, 58, 59, 35, 11, 10), (42, 18, 50, 26, 58, 34), (14, 0, 2, 18, 42, 38), (12, 36, 40, 16, 2, 0), (44, 20, 52, 28, 36, 12), (30, 54, 22, 46, 14, 38), ( 7, 26, 50, 48, 24, 6), (24, 48, 16, 40, 32, 56)] Faktor = 100 # Skalierungsfaktor k = 1 # Korrekturfaktor fuer Kantenlaenge #************************************************************************ # 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('Huellkurve') obj.Message(c4d.MSG_UPDATE) obj[c4d.ID_BASEOBJECT_VISIBILITY_EDITOR] = 1 obj[c4d.ID_BASEOBJECT_VISIBILITY_RENDER] = 1 return obj #************************************************************************ def CreateVierecke(): obj = c4d.BaseObject(c4d.Opolygon) obj.ResizeObject(NP, N4) obj.SetName('Vierecke') # 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)) # Vierecke setzen for i in xrange(N4): obj.SetPolygon(i, c4d.CPolygon(Vierecke[i][0], Vierecke[i][1], Vierecke[i][2], Vierecke[i][3])) obj.Message(c4d.MSG_UPDATE) return obj #************************************************************************ def CreateFuenfecke(): obj = c4d.BaseObject(c4d.Opolygon) obj.ResizeObject(NP, N5*2) obj.SetName('Fuenfecke') # 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)) zz = 0 # Zähler für Polygone zurücksetzen for i in xrange(N5): obj.SetPolygon(zz, c4d.CPolygon(Fuenfecke[i][0], Fuenfecke[i][1], Fuenfecke[i][2], Fuenfecke[i][4])) zz = zz + 1 obj.SetPolygon(zz, c4d.CPolygon(Fuenfecke[i][2], Fuenfecke[i][3], Fuenfecke[i][4], Fuenfecke[i][4])) zz = zz + 1 obj.Message(c4d.MSG_UPDATE) return obj #************************************************************************ def CreateFuenfecke1(): obj = c4d.BaseObject(c4d.Opolygon) obj.ResizeObject(NP, N5P*2) obj.SetName('Fuenfecke') # 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)) zz = 0 # Zaehler fuer Polygone zuruecksetzen for i in xrange(N5P): obj.SetPolygon(zz, c4d.CPolygon(Pentagramme[i][0], Pentagramme[i][1], Pentagramme[i][2], Pentagramme[i][4])) zz = zz + 1 obj.SetPolygon(zz, c4d.CPolygon(Pentagramme[i][2], Pentagramme[i][3], Pentagramme[i][4], Pentagramme[i][4])) zz = zz + 1 obj.Message(c4d.MSG_UPDATE) return obj #************************************************************************ def CreateSechsecke(): obj = c4d.BaseObject(c4d.Opolygon) obj.ResizeObject(NP, N6*2) obj.SetName('Sechsecke') # 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)) # Vierecke setzen zz = 0 # Zähler für Polygone zurücksetzen for i in xrange(N6): obj.SetPolygon(zz, c4d.CPolygon(Sechsecke[i][0], Sechsecke[i][1], Sechsecke[i][2], Sechsecke[i][5])) zz = zz + 1 obj.SetPolygon(zz, c4d.CPolygon(Sechsecke[i][2], Sechsecke[i][3], Sechsecke[i][4], Sechsecke[i][5])) zz = zz + 1 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 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 CreateSplineVierecke(): obj = c4d.BaseObject(c4d.Ospline) obj.SetName("Spline-Vierecke") obj.ResizeObject(N4*4) zz = 0 for i in xrange(N4): for j in xrange(4): x = Punkte[Vierecke[i][j]][0] y = Punkte[Vierecke[i][j]][1] z = Punkte[Vierecke[i][j]][2] obj.SetPoint(zz, c4d.Vector(x*Faktor*k, y*Faktor*k, z*Faktor*k)) zz = zz + 1 # Segmente erzeugen obj.MakeVariableTag(c4d.Tsegment, N4) for i in range(0, N4): obj.SetSegment(i, 4, True) # Spline schliessen obj[c4d.SPLINEOBJECT_CLOSED] = True obj.Message(c4d.MSG_UPDATE) return obj #************************************************************************ def CreateSplineFuenfecke(): obj = c4d.BaseObject(c4d.Ospline) obj.SetName("Spline-Fuenfecke") obj.ResizeObject(N5*5) zz = 0 for i in xrange(N5): for j in xrange(5): x = Punkte[Fuenfecke[i][j]][0] y = Punkte[Fuenfecke[i][j]][1] z = Punkte[Fuenfecke[i][j]][2] obj.SetPoint(zz, c4d.Vector(x*Faktor*k, y*Faktor*k, z*Faktor*k)) zz = zz + 1 # Segmente erzeugen obj.MakeVariableTag(c4d.Tsegment, N5) for i in range(0, N5): obj.SetSegment(i, 5, True) # Spline schliessen obj[c4d.SPLINEOBJECT_CLOSED] = True obj.Message(c4d.MSG_UPDATE) return obj #************************************************************************ def CreateSplineFuenfecke1(): obj = c4d.BaseObject(c4d.Ospline) obj.SetName("Spline-Fuenfecke") obj.ResizeObject(N5P*5) zz = 0 for i in xrange(N5): for j in xrange(5): x = Punkte[Pentagramme[i][j]][0] y = Punkte[Pentagramme[i][j]][1] z = Punkte[Pentagramme[i][j]][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 CreateSplineSechsecke(): obj = c4d.BaseObject(c4d.Ospline) obj.SetName("Spline-Sechsecke") obj.ResizeObject(N6*6) zz = 0 for i in xrange(N6): for j in xrange(6): x = Punkte[Sechsecke[i][j]][0] y = Punkte[Sechsecke[i][j]][1] z = Punkte[Sechsecke[i][j]][2] obj.SetPoint(zz, c4d.Vector(x*Faktor*k, y*Faktor*k, z*Faktor*k)) zz = zz + 1 # Segmente erzeugen obj.MakeVariableTag(c4d.Tsegment, N6) for i in range(0, N6): obj.SetSegment(i, 6, True) # Spline schliessen obj[c4d.SPLINEOBJECT_CLOSED] = True 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 main(): nullobj1 = CreateNullobjekt1() nullobj2 = CreateNullobjekt2() # Ecken nullobj3 = CreateNullobjekt3() # Kanten nullobj4 = CreateNullobjekt4() # Polygone nullobj5 = CreateNullobjekt5() # Huellkurve plyobj1 = CreateVierecke() plyobj2 = CreateFuenfecke() plyobj3 = CreatePentagramme() plyobj4 = CreateSechsecke() plyobj5 = CreateFuenfecke1() splobj1 = CreateSplineVierecke() splobj2 = CreateSplineFuenfecke() splobj3 = CreateSplinePentagramme() splobj4 = CreateSplineSechsecke() splobj5 = CreateSplineFuenfecke1() 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(splobj5, nullobj5, None, True) doc.InsertObject(splobj4, nullobj5, None, True) doc.InsertObject(splobj3, nullobj3, None, True) doc.InsertObject(splobj2, nullobj3, None, True) doc.InsertObject(splobj1, nullobj3, None, True) doc.InsertObject(plyobj5, nullobj5, None, True) doc.InsertObject(plyobj4, nullobj5, None, True) doc.InsertObject(plyobj3, nullobj4, 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) c4d.EventAdd() if __name__=='__main__': main()