"""
Small ditrigonary icosidodecahedron
20.05.2021
www.3d-meier.de
"""

import c4d
import math

# Variablen und Konstanten
Titel = 'Small ditrigonary icosidodecahedron' # Name

NP = 20    # Anzahl Punkte
N3 = 20    # Anzahl Dreiecke
N5P = 12   # Anzahl Pentagramme

Radius = 0.4 # Radius der Eckpunktkugeln    

phi = (1+math.sqrt(5))/2.0
a = 0.5
b = (1+math.sqrt(5))/4.0
c = (math.sqrt(5)-1)/4.0

Punkte = [( a,  a,  a),
          ( a,  a, -a),
          ( a, -a,  a),
          ( a, -a, -a),
          (-a,  a,  a),
          (-a,  a, -a),
          (-a, -a,  a),
          (-a, -a, -a),
          ( b,  c,  0), 
          ( b, -c,  0), 
          (-b,  c,  0), 
          (-b, -c,  0), 
          ( c,  0,  b),  
          (-c,  0,  b),  
          ( c,  0, -b),  
          (-c,  0, -b),  
          ( 0,  b,  c),
          ( 0,  b, -c),
          ( 0, -b,  c),
          ( 0, -b, -c)]

Dreiecke = [(10,  7,  6,  6),
            (11, 18, 13, 13),
            (11, 15, 19, 19),
            ( 3, 18,  7,  7),
            (12, 18,  9,  9),
            ( 0,  9,  1,  1),
            ( 8, 14, 17, 17),
            (17, 15, 10, 10),
            ( 1,  3, 15, 15),
            ( 9, 19, 14, 14),
            (13,  2,  0,  0),
            ( 4,  6, 12, 12),
            (17,  4,  0,  0),
            ( 5, 11,  4,  4),
            (13, 16, 10, 10),
            (12,  8, 16, 16),
            ( 3,  8,  2,  2),
            ( 2,  6, 19, 19),
            (14,  7,  5,  5),
            ( 1,  5, 16, 16)]

Pentagramme = [( 4, 16, 17,  5, 10),
               (12,  0, 16,  4, 13),  
               (13,  4, 10, 11,  6),
               ( 0,  8,  1, 17, 16),  
               ( 1,  8,  9,  3, 14),
               (14,  3, 19,  7, 15),
               (19,  3,  9,  2, 18),
               ( 7, 11, 10,  5, 15),
               ( 2,  9,  8,  0, 12),
               (14, 15,  5, 17,  1),
               (12, 13,  6, 18,  2),
               (19, 18,  6, 11,  7)]
            
Faktor = 100   # Skalierungsfaktor
k = 1          # Korrekturfaktor fuer Kantenlaenge

ku = 256                                   # Unterteilung der Kugeln
ru = Faktor*k*math.sqrt(3)/2.0             # Umkugelradius

#************************************************************************
# 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')
    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
    obj.SetName('Umkugel')
    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()