def generate_polygon_on_xz_side_length(edges,side_length,offset=0) :
''' Return an polygon on plan XZ: with edges edges from length side_length, with offset offset.
z
/
_____/____x
/
/ plan XZ.
'''
angle=360.0/side_length
polygon=[] # Polygon vertice container.
scale=360.0/edges # Computing of the angle separating 2 points from the polygon.
start_vertex1=Vertex(-side_length/2.,0.0,0)
start_vertex2=Vertex(side_length/2.,0.0,0)
point_to_rotate=start_vertex1
rotate_point=start_vertex2
polygon.append(point_to_rotate)
polygon.append(rotate_point)
i=2
while i < edges :
vertex=rotate_on_xz(rotate_point,abs(180-scale),point_to_rotate)
point_to_rotate=rotate_point
rotate_point=vertex
polygon.append(vertex)
i += 1
center=get_center_from_polygon(polygon) # Compute polygon center.
tmp=[]
for v in polygon :
# Translate polygon vertices so as his center is the display center.
tmp.append(translate(v,-center.wx,-center.wy,-center.wz))
if offset :
offset_set=[]
for v in tmp :
offset_set.append(rotate_y(v,offset))
tmp=offset_set
polygon=tmp
return polygon
def generate_toros(base,base_radius,toros_radius) :
''' Generate an toros in relationship to the given settings:
base: the toros basis polygon.
base_radius: the toros basis polygon radius.
toros_radius: the toros radius (without the base polygon radius).
and return an sequence of polygons base from the toros.
'''
base_polygon=generate_polygon_on_yz_radius(base,base_radius,Vertex(0.,0.,0.))
i=0
toros=[]
while i < 360.0 :
polygon=[]
for v in base_polygon :
vertex=rotate_y(translate(v,0.0,0.0,toros_radius),i)
polygon.append(vertex)
i += 360.0/base
toros.append(polygon)
return toros
def generate_toros(base, base_radius, toros_radius):
''' Generate an toros in relationship to the given settings:
base: the toros basis polygon.
base_radius: the toros basis polygon radius.
toros_radius: the toros radius (without the base polygon radius).
and return an sequence of polygons base from the toros.
'''
base_polygon = generate_polygon_on_yz_radius(base, base_radius,
Vertex(0., 0., 0.))
i = 0
toros = []
while i < 360.0:
polygon = []
for v in base_polygon:
vertex = rotate_y(translate(v, 0.0, 0.0, toros_radius), i)
polygon.append(vertex)
i += 360.0 / base
toros.append(polygon)
return toros
def generate_polyhedron_26_faces(side_length):
''' Generate an 26 faces polyhedron from the given side length
and return an array of triangles and an array of quads
composing the 26 faces of the polyhedron.
'''
# Generation of octogons, bases of the 32 polyhedron mesh.
octogon1 = generate_polygon_on_xy_side_length(8, side_length)
octogon2 = generate_polygon_on_xy_side_length(8, side_length)
octogon3 = generate_polygon_on_xz_side_length(8, side_length)
octogon4 = generate_polygon_on_xz_side_length(8, side_length)
octogon5 = generate_polygon_on_yz_side_length(8, side_length)
octogon6 = generate_polygon_on_yz_side_length(8, side_length)
# Translation to construct the polyhedron mesh.
res = []
for v in octogon1:
res.append(translate(v, 0.0, 0.0, -side_length / 2.0))
octogon1 = res
# Translation to construct the polyhedron mesh.
res = []
for v in octogon2:
res.append(translate(v, 0.0, 0.0, side_length / 2.0))
octogon2 = res
# Translation to construct the polyhedron mesh.
res = []
for v in octogon3:
res.append(translate(v, 0.0, -side_length / 2.0, 0.0))
octogon3 = res
# Translation to construct the polyhedron mesh.
res = []
for v in octogon4:
res.append(translate(v, 0.0, side_length / 2.0, 0.0))
octogon4 = res
# Translation to construct the polyhedron mesh.
res = []
for v in octogon5:
res.append(translate(v, -side_length / 2.0, 0.0, 0.0))
octogon5 = res
# Translation to construct the polyhedron mesh.
res = []
for v in octogon6:
res.append(translate(v, side_length / 2.0, 0.0, 0.0))
octogon6 = res
# We construct the polyhedron quads:
quads_xy = []
i = -1
while i < len(octogon1) - 1:
# by iterating overs octogon1 and octogon2
# which are in the plan XY.
# With clever indexing.
quads = []
quads.append(octogon1[i])
quads.append(octogon1[i + 1])
quads.append(octogon2[i + 1])
quads.append(octogon2[i])
quads_xy.append(quads)
i += 1
# We construct the polyhedron quads:
quads_xz = []
i = -1
while i < len(octogon3) - 1:
# by iterating overs octogon3 and octogon4
# which are in the plan XZ.
# With clever indexing.
quads = []
quads.append(octogon3[i])
quads.append(octogon3[i + 1])
quads.append(octogon4[i + 1])
quads.append(octogon4[i])
quads_xz.append(quads)
i += 1
# We construct the polyhedron quads:
quads_yz = []
i = -1
while i < len(octogon1) - 1:
# by iterating overs octogon3 and octogon4
# which are in the plan XZ.
# With clever indexing.
quads = []
quads.append(octogon5[i])
quads.append(octogon5[i + 1])
quads.append(octogon6[i + 1])
quads.append(octogon6[i])
quads_yz.append(quads)
i += 1
# Finally we keep only the needed quads. To not have doubles.
polyhedron = []
for v in quads_xz:
polyhedron.append(v)
polyhedron.append(quads_xy[0])
polyhedron.append(quads_xy[1])
polyhedron.append(quads_xy[2])
polyhedron.append(quads_xy[4])
polyhedron.append(quads_xy[5])
polyhedron.append(quads_xy[6])
polyhedron.append(quads_yz[0])
polyhedron.append(quads_yz[2])
polyhedron.append(quads_yz[4])
polyhedron.append(quads_yz[6])
# Finally we construct the triangles of the polyhedron.
triangle1 = [polyhedron[1][1], polyhedron[3][0], polyhedron[12][3]]
triangle2 = [polyhedron[3][1], polyhedron[5][0], polyhedron[12][0]]
triangle3 = [polyhedron[5][1], polyhedron[6][1], polyhedron[12][1]]
triangle4 = [polyhedron[7][1], polyhedron[1][0], polyhedron[12][2]]
triangle5 = [polyhedron[7][2], polyhedron[1][3], polyhedron[9][3]]
triangle6 = [polyhedron[5][3], polyhedron[4][3], polyhedron[9][1]]
triangle7 = [polyhedron[6][3], polyhedron[7][3], polyhedron[9][0]]
triangle8 = [polyhedron[1][2], polyhedron[2][2], polyhedron[9][2]]
return [
triangle1, triangle2, triangle3, triangle4, triangle5, triangle6,
triangle7, triangle8
], polyhedron
def generate_polyhedron_26_faces(side_length) :
''' Generate an 26 faces polyhedron from the given side length
and return an array of triangles and an array of quads
composing the 26 faces of the polyhedron.
'''
# Generation of octogons, bases of the 32 polyhedron mesh.
octogon1=generate_polygon_on_xy_side_length(8,side_length)
octogon2=generate_polygon_on_xy_side_length(8,side_length)
octogon3=generate_polygon_on_xz_side_length(8,side_length)
octogon4=generate_polygon_on_xz_side_length(8,side_length)
octogon5=generate_polygon_on_yz_side_length(8,side_length)
octogon6=generate_polygon_on_yz_side_length(8,side_length)
# Translation to construct the polyhedron mesh.
res=[]
for v in octogon1 :
res.append(translate(v,0.0,0.0,-side_length/2.0))
octogon1=res
# Translation to construct the polyhedron mesh.
res=[]
for v in octogon2 :
res.append(translate(v,0.0,0.0,side_length/2.0))
octogon2=res
# Translation to construct the polyhedron mesh.
res=[]
for v in octogon3 :
res.append(translate(v,0.0,-side_length/2.0,0.0))
octogon3=res
# Translation to construct the polyhedron mesh.
res=[]
for v in octogon4 :
res.append(translate(v,0.0,side_length/2.0,0.0))
octogon4=res
# Translation to construct the polyhedron mesh.
res=[]
for v in octogon5 :
res.append(translate(v,-side_length/2.0,0.0,0.0))
octogon5=res
# Translation to construct the polyhedron mesh.
res=[]
for v in octogon6 :
res.append(translate(v,side_length/2.0,0.0,0.0))
octogon6=res
# We construct the polyhedron quads:
quads_xy=[]
i=-1
while i < len(octogon1)-1 :
# by iterating overs octogon1 and octogon2
# which are in the plan XY.
# With clever indexing.
quads=[]
quads.append(octogon1[i])
quads.append(octogon1[i+1])
quads.append(octogon2[i+1])
quads.append(octogon2[i])
quads_xy.append(quads)
i += 1
# We construct the polyhedron quads:
quads_xz=[]
i=-1
while i < len(octogon3)-1 :
# by iterating overs octogon3 and octogon4
# which are in the plan XZ.
# With clever indexing.
quads=[]
quads.append(octogon3[i])
quads.append(octogon3[i+1])
quads.append(octogon4[i+1])
quads.append(octogon4[i])
quads_xz.append(quads)
i += 1
# We construct the polyhedron quads:
quads_yz=[]
i=-1
while i < len(octogon1)-1 :
# by iterating overs octogon3 and octogon4
# which are in the plan XZ.
# With clever indexing.
quads=[]
quads.append(octogon5[i])
quads.append(octogon5[i+1])
quads.append(octogon6[i+1])
quads.append(octogon6[i])
quads_yz.append(quads)
i += 1
# Finally we keep only the needed quads. To not have doubles.
polyhedron=[]
for v in quads_xz :
polyhedron.append(v)
polyhedron.append(quads_xy[0])
polyhedron.append(quads_xy[1])
polyhedron.append(quads_xy[2])
polyhedron.append(quads_xy[4])
polyhedron.append(quads_xy[5])
polyhedron.append(quads_xy[6])
polyhedron.append(quads_yz[0])
polyhedron.append(quads_yz[2])
polyhedron.append(quads_yz[4])
polyhedron.append(quads_yz[6])
# Finally we construct the triangles of the polyhedron.
triangle1=[polyhedron[1][1],polyhedron[3][0],polyhedron[12][3]]
triangle2=[polyhedron[3][1],polyhedron[5][0],polyhedron[12][0]]
triangle3=[polyhedron[5][1],polyhedron[6][1],polyhedron[12][1]]
triangle4=[polyhedron[7][1],polyhedron[1][0],polyhedron[12][2]]
triangle5=[polyhedron[7][2],polyhedron[1][3],polyhedron[9][3]]
triangle6=[polyhedron[5][3],polyhedron[4][3],polyhedron[9][1]]
triangle7=[polyhedron[6][3],polyhedron[7][3],polyhedron[9][0]]
triangle8=[polyhedron[1][2],polyhedron[2][2],polyhedron[9][2]]
return [triangle1,triangle2,triangle3,triangle4,triangle5,triangle6,triangle7,triangle8], polyhedron