"""
Johnson Körper J25
29.01.2021
www.3d-meier.de
"""

import c4d
import math

# Variablen und Konstanten
Titel = 'Johnson Körper J25' # Name

NP = 30    # Anzahl Punkte
N3 = 30    # Anzahl Dreiecke
N5 =  6    # Anzahl Fuenfecke
N10 = 1    # Anzahl Zehnecke

Radius = 2 # Radius der Eckpunktkugeln

sec = 1/math.cos(math.pi/(2*10))
h = math.sqrt(1-(sec**2)/4)      # Höhe Antiprisma

C0  = math.sqrt(10 * (5 - math.sqrt(5))) / 20
C1  = math.sqrt(10 * (5 + math.sqrt(5))) / 20
C2  = math.sqrt(2 * (math.sqrt(2 * (25 + 11 * math.sqrt(5))) - 2 * math.sqrt(5) - 4)) / 4
C3  = math.sqrt(5 * (5 + 2 * math.sqrt(5))) / 10
C4  = (1 + math.sqrt(5)) / 4
C5  = math.sqrt(10 * (5 + math.sqrt(5))) / 10
C6  = math.sqrt(2 * (5 + math.sqrt(5))) / 4
C7  = math.sqrt(10 * (25 + 11 * math.sqrt(5))) / 20
C8  = (2 * math.sqrt(10 * (5 + math.sqrt(5))) + 5 * math.sqrt(2 * (math.sqrt(2 * (25 + 11 * math.sqrt(5))) - 2 * math.sqrt(5) - 4))) / 20
C9  = (3 + math.sqrt(5)) / 4
C10 = math.sqrt(5 * (5 + 2 * math.sqrt(5))) / 5
C11 = math.sqrt(5 + 2 * math.sqrt(5)) / 2
C12 = (1 + math.sqrt(5)) / 2
C13 = (4 * math.sqrt(5 * (5 + 2 * math.sqrt(5))) + 5 * math.sqrt(2 * (math.sqrt(2 * (25 + 11 * math.sqrt(5))) - 2 * math.sqrt(5) - 4))) / 20

Punkte = [( C12,  C2+h/2,  0.0),
          (-C12,  C2+h/2,  0.0),
          (  C9,  C2+h/2,   C6),
          (  C9,  C2+h/2,  -C6),
          ( -C9,  C2+h/2,   C6),
          ( -C9,  C2+h/2,  -C6),
          ( 0.5,  C2+h/2,  C11),
          ( 0.5,  C2+h/2, -C11),
          (-0.5,  C2+h/2,  C11),
          (-0.5,  C2+h/2, -C11),
          ( C11, -C2+h/2,  0.5),
          ( C11, -C2+h/2, -0.5),
          (-C11, -C2+h/2,  0.5),
          (-C11, -C2+h/2, -0.5),
          (  C6, -C2+h/2,   C9),
          (  C6, -C2+h/2,  -C9),
          ( -C6, -C2+h/2,   C9),
          ( -C6, -C2+h/2,  -C9),
          ( 0.0, -C2+h/2,  C12),
          ( 0.0, -C2+h/2, -C12),
          (  C9,  C8+h/2,  -C1),
          ( -C9,  C8+h/2,  -C1),
          (  C4,  C8+h/2,   C7),
          ( -C4,  C8+h/2,   C7),
          ( 0.0,  C8+h/2, -C10),
          (  C4, C13+h/2,   C0),
          ( -C4, C13+h/2,   C0),
          ( 0.5, C13+h/2,  -C3),
          (-0.5, C13+h/2,  -C3),
          ( 0.0, C13+h/2,   C5)]

Zehnecke = [( 10, 11, 15, 19, 17, 13, 12, 16, 18, 14 )]

Fuenfecke = [( 25, 29, 26, 28, 27 ),
             (  2, 22, 25, 20,  0 ),
             (  8, 23, 29, 22,  6 ),
             (  1, 21, 26, 23,  4 ),
             (  9, 24, 28, 21,  5 ),
             (  3, 20, 27, 24,  7 )]

Dreiecke = [(  2,  0, 10, 10 ),
            (  8,  6, 18, 18 ),
            (  1,  4, 12, 12 ),
            (  9,  5, 17, 17 ),
            (  3,  7, 15, 15 ),
            (  2, 10, 14, 14 ),
            (  8, 18, 16, 16 ),
            (  1, 12, 13, 13 ),
            (  9, 17, 19, 19 ),
            (  3, 15, 11, 11 ),
            (  2, 14,  6,  6 ),
            (  8, 16,  4,  4 ),
            (  1, 13,  5,  5 ),
            (  9, 19,  7,  7 ),
            (  3, 11,  0,  0 ),
            (  2,  6, 22, 22 ),
            (  8,  4, 23, 23 ),
            (  1,  5, 21, 21 ),
            (  9,  7, 24, 24 ),
            (  3,  0, 20, 20 ),
            (  6, 14, 18, 18 ),
            (  4, 16, 12, 12 ),
            (  5, 13, 17, 17 ),
            (  7, 19, 15, 15 ),
            (  0, 11, 10, 10 ),
            ( 25, 27, 20, 20 ),
            ( 29, 25, 22, 22 ),
            ( 26, 29, 23, 23 ),
            ( 28, 26, 21, 21 ),
            ( 27, 28, 24, 24 )]


Faktor = 100      # Skalierungsfaktor
k = 1             # Korrekturfaktor fuer Kantenlaenge 1


#************************************************************************
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 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 CreateFuenfecke():
    obj = c4d.BaseObject(c4d.Opolygon)
    obj.ResizeObject(NP, N5*2)
    obj.SetName('Fünfecke')
  # 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(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 CreateZehnecke():
    obj = c4d.BaseObject(c4d.Opolygon)
    obj.ResizeObject(NP, N10*5)
    obj.SetName('Zehnecke')
  # 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(N10):
        obj.SetPolygon(zz, c4d.CPolygon(Zehnecke[i][0], Zehnecke[i][1], Zehnecke[i][9], Zehnecke[i][9]))
        zz = zz + 1
        obj.SetPolygon(zz, c4d.CPolygon(Zehnecke[i][1], Zehnecke[i][2], Zehnecke[i][8], Zehnecke[i][9]))
        zz = zz + 1
        obj.SetPolygon(zz, c4d.CPolygon(Zehnecke[i][2], Zehnecke[i][3], Zehnecke[i][7], Zehnecke[i][8]))
        zz = zz + 1
        obj.SetPolygon(zz, c4d.CPolygon(Zehnecke[i][3], Zehnecke[i][4], Zehnecke[i][6], Zehnecke[i][7]))
        zz = zz + 1
        obj.SetPolygon(zz, c4d.CPolygon(Zehnecke[i][4], Zehnecke[i][5], Zehnecke[i][6], Zehnecke[i][6]))
        zz = zz + 1

    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 CreateSplineFuenfecke():
    obj = c4d.BaseObject(c4d.Ospline)
    obj.SetName("Spline-Fünfecke")
    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 CreateSplineZehnecke():
    obj = c4d.BaseObject(c4d.Ospline)
    obj.SetName("Spline-Zehnecke")
    obj.ResizeObject(N10*10)
    zz = 0
    for i in xrange(N10):
        for j in xrange(10):
            x = Punkte[Zehnecke[i][j]][0]
            y = Punkte[Zehnecke[i][j]][1]
            z = Punkte[Zehnecke[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, N10)
    for i in range(0, N10):
        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 = CreateDreiecke()
    plyobj2 = CreateFuenfecke()
    plyobj3 = CreateZehnecke()

    splobj1 = CreateSplineDreiecke()
    splobj2 = CreateSplineFuenfecke()
    splobj3 = CreateSplineZehnecke()

    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(splobj3, nullobj3, None, True)
    doc.InsertObject(splobj2, nullobj3, None, True)
    doc.InsertObject(splobj1, nullobj3, 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()