""" Small stellated truncated dodecahedron 28.05.2021 www.3d-meier.de """ import c4d import math # Variablen und Konstanten Titel = 'Small stellated truncated dodecahedron' # Name NP = 60 # Anzahl Punkte N5 = 12 # Anzahl Fuenfecke N10D = 12 # Anzahl Dekagramme Radius = 2 # Radius der Eckpunktkugeln phi = (1 + math.sqrt(5))/2.0 # Goldener Schnitt a = phi*phi*phi b = phi*phi c = phi d = 2.0*phi e = 2.0+phi Punkte = [( 1, 1, a), ( 1, 1, -a), ( 1, -1, a), ( 1, -1, -a), ( -1, 1, a), ( -1, 1, -a), ( -1, -1, a), ( -1, -1, -a), ( b, c, d), ( b, c, -d), ( b, -c, d), ( b, -c, -d), ( -b, c, d), ( -b, c, -d), ( -b, -c, d), ( -b, -c, -d), ( e, 0, b), ( e, 0, -b), ( -e, 0, b), ( -e, 0, -b), ( 1, a, 1), ( 1, -a, 1), ( -1, a, 1), ( -1, -a, 1), ( 1, a, -1), ( 1, -a, -1), ( -1, a, -1), ( -1, -a, -1), ( c, d, b), ( c, -d, b), ( -c, d, b), ( -c, -d, b), ( c, d, -b), ( c, -d, -b), ( -c, d, -b), ( -c, -d, -b), ( 0, b, e), ( 0, -b, e), ( 0, b, -e), ( 0, -b, -e), ( a, 1, 1), ( -a, 1, 1), ( a, 1, -1), ( -a, 1, -1), ( a, -1, 1), ( -a, -1, 1), ( a, -1, -1), ( -a, -1, -1), ( d, b, c), ( -d, b, c), ( d, b, -c), ( -d, b, -c), ( d, -b, c), ( -d, -b, c), ( d, -b, -c), ( -d, -b, -c), ( b, e, 0), ( -b, e, 0), ( b, -e, 0), ( -b, -e, 0)] Fuenfecke = [( 19, 26, 48, 52, 27 ), ( 0, 56, 1, 35, 31 ), ( 58, 2, 30, 34, 3 ), ( 15, 11, 40, 36, 41 ), ( 24, 49, 53, 25, 17 ), ( 28, 32, 7, 59, 6 ), ( 14, 10, 42, 38, 43 ), ( 12, 8, 46, 39, 47 ), ( 29, 33, 5, 57, 4 ), ( 16, 20, 51, 55, 21 ), ( 37, 45, 13, 9, 44 ), ( 54, 23, 18, 22, 50 )] Dekagramme = [( 9, 50, 56, 20, 22, 57, 51, 13, 5, 1), (38, 34, 51, 43, 47, 55, 35, 39, 3, 1), (54, 33, 39, 7, 5, 38, 32, 50, 42, 46), (16, 40, 42, 17, 11, 33, 25, 21, 29, 10), (53, 31, 37, 2, 0, 36, 30, 49, 41, 45), (36, 28, 48, 40, 44, 52, 29, 37, 6, 4), ( 6, 2, 10, 52, 58, 25, 27, 59, 53, 14), (59, 23, 21, 58, 54, 11, 3, 7, 15, 55), (23, 27, 35, 15, 19, 43, 41, 18, 14, 31), (49, 57, 26, 24, 56, 48, 8, 0, 4, 12), (26, 22, 30, 12, 18, 45, 47, 19, 13, 34), (20, 24, 32, 9, 17, 46, 44, 16, 8, 28)] Faktor = 100 # Skalierungsfaktor k = 0.5 # Korrekturfaktor k = 1/(2*phi+2) # Korrekturfaktor fuer Kantenlaenge 1 #************************************************************************ # 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 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 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 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 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 plyobj1 = CreateFuenfecke() plyobj2 = CreateDekagramme() splobj1 = CreateSplineFuenfecke() splobj2 = CreateSplineDekagramme() doc.InsertObject(nullobj1, None, 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) c4d.EventAdd() if __name__=='__main__': main()