""" Great Icosidodecahedron 10.06.2021 www.3d-meier.de http://dmccooey.com/polyhedra/GreatIcosidodecahedron.html """ import c4d import math # Variablen und Konstanten Titel = 'Great Icosidodecahedron' # Name NP = 30 # Anzahl Punkte N3 = 20 # Anzahl Dreiecke N5P = 12 # Anzahl Pentagramme Radius = 1.0 # 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)] Dreiecke = [( 0, 6, 10, 10 ), ( 0, 12, 8, 8 ), ( 1, 9, 13, 13 ), ( 1, 11, 7, 7 ), ( 2, 14, 16, 16 ), ( 2, 17, 15, 15 ), ( 3, 19, 21, 21 ), ( 3, 20, 18, 18 ), ( 4, 22, 23, 23 ), ( 4, 27, 26, 26 ), ( 5, 25, 24, 24 ), ( 5, 28, 29, 29 ), ( 6, 14, 22, 22 ), ( 7, 23, 15, 15 ), ( 8, 24, 16, 16 ), ( 9, 17, 25, 25 ), ( 10, 26, 18, 18 ), ( 11, 19, 27, 27 ), ( 12, 20, 28, 28 ), ( 13, 29, 21, 21 )] 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 ri3 = (3*math.sqrt(3)-math.sqrt(15))/6 # Inkugelradius Dreieck 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 CreateDreiecke(): obj = c4d.BaseObject(c4d.Opolygon) obj.ResizeObject(NP,N3) obj.SetName('Dreiecke') # 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)) # Dreiecke setzen for i in xrange(N3): obj.SetPolygon( i, c4d.CPolygon(Dreiecke[i][0], Dreiecke[i][1], Dreiecke[i][2], Dreiecke[i][3])) 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 CreateSplineDreiecke(): obj = c4d.BaseObject(c4d.Ospline) obj.SetName("Spline-Dreiecke") obj.ResizeObject(N3*3) zz = 0 for i in xrange(N3): for j in xrange(3): x = Punkte[Dreiecke[i][j]][0] y = Punkte[Dreiecke[i][j]][1] z = Punkte[Dreiecke[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, N3) for i in range(0, N3): obj.SetSegment(i, 3, 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() # Umkugel, etc. plyobj1 = CreateDreiecke() plyobj2 = CreatePentagramme() splobj1 = CreateSplineDreiecke() splobj2 = CreateSplinePentagramme() 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 (Dreieck) erzeugen obj = c4d.BaseObject(c4d.Osphere) obj[c4d.PRIM_SPHERE_SUB] = ku obj[c4d.PRIM_SPHERE_RAD] = ri3*Faktor*k obj.SetName('Inkugel Dreieck') 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()