def generate_icosahedron(side_length) :
''' Generate an icosahedron from the given side length and
return an array of 20 triangles component from the icosahedron
and his construction base quad set. '''
side_lt=side_length # Define the littler side of the rectangle.
side_gt=side_length*((1+sqrt(5))/2.) # Compute the length of the greater side with the gold number ( (1+sqrt(5))/2. )
# Define the base quad so that his center is Vertex(0.0, 0.0, 0.0) :
quad1=[Vertex(-side_lt/2.,-side_gt/2.,0.0),Vertex(side_lt/2.,-side_gt/2.,0.0),Vertex(side_lt/2.,side_gt/2.,0.0),Vertex(-side_lt/2.,side_gt/2.,0.0)]
# Rotate the base quad on the y and z axes from 90°, to obtain the second crossing quad.
quad2=[rotate_z(rotate_y(quad1[0],90),90), rotate_z(rotate_y(quad1[1],90),90), rotate_z(rotate_y(quad1[2],90),90), rotate_z(rotate_y(quad1[3],90),90)]
# Rotate the base quad on the y and x axes from 90°, to obtain the third crossing quad.
quad3=[rotate_x(rotate_y(quad1[0],90),90), rotate_x(rotate_y(quad1[1],90),90), rotate_x(rotate_y(quad1[2],90),90), rotate_x(rotate_y(quad1[3],90),90)]
icosahedron_base_quads=[quad1,quad2,quad3] # We set the bases quads for our polyhedron: an icosahedron.
# Define an array composed of triangles because an icosahedron is composed from 20 equilateral triangles:
icosahedron_triangle_array=[(icosahedron_base_quads[0][0],icosahedron_base_quads[0][1],icosahedron_base_quads[2][1]),
(icosahedron_base_quads[0][1],icosahedron_base_quads[1][0],icosahedron_base_quads[1][1]),
(icosahedron_base_quads[0][0],icosahedron_base_quads[0][1],icosahedron_base_quads[2][2]),
(icosahedron_base_quads[0][0],icosahedron_base_quads[1][2],icosahedron_base_quads[1][3]),
(icosahedron_base_quads[0][0],icosahedron_base_quads[1][3],icosahedron_base_quads[2][1]),
(icosahedron_base_quads[0][1],icosahedron_base_quads[2][1],icosahedron_base_quads[1][0]),
(icosahedron_base_quads[0][1],icosahedron_base_quads[1][1],icosahedron_base_quads[2][2]),
(icosahedron_base_quads[0][0],icosahedron_base_quads[2][2],icosahedron_base_quads[1][2]),
(icosahedron_base_quads[0][2],icosahedron_base_quads[0][3],icosahedron_base_quads[2][3]),
(icosahedron_base_quads[0][3],icosahedron_base_quads[1][2],icosahedron_base_quads[1][3]),
(icosahedron_base_quads[0][2],icosahedron_base_quads[0][3],icosahedron_base_quads[2][0]),
(icosahedron_base_quads[0][2],icosahedron_base_quads[1][0],icosahedron_base_quads[1][1]),
(icosahedron_base_quads[0][2],icosahedron_base_quads[1][1],icosahedron_base_quads[2][3]),
(icosahedron_base_quads[0][3],icosahedron_base_quads[2][3],icosahedron_base_quads[1][2]),
(icosahedron_base_quads[0][3],icosahedron_base_quads[1][3],icosahedron_base_quads[2][0]),
(icosahedron_base_quads[0][2],icosahedron_base_quads[2][0],icosahedron_base_quads[1][0]),
(icosahedron_base_quads[2][0],icosahedron_base_quads[2][1],icosahedron_base_quads[1][3]),
(icosahedron_base_quads[2][0],icosahedron_base_quads[2][1],icosahedron_base_quads[1][0]),
(icosahedron_base_quads[2][2],icosahedron_base_quads[2][3],icosahedron_base_quads[1][1]),
(icosahedron_base_quads[2][2],icosahedron_base_quads[2][3],icosahedron_base_quads[1][2])]
# We return the base quad set and the triangle array.
return [quad1,quad2,quad3],icosahedron_triangle_array
def generate_polygon_on_yz_side_length(edges,side_length,offset=0) :
''' Return an polygon on plan YZ: with edges edges from length side_length, with offset offset.
y z
| /
|/
/|
/ | plan YZ.
'''
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(0.0,-side_length/2.,0)
start_vertex2=Vertex(0.0,side_length/2.,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_yz(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_x(v,offset))
tmp=offset_set
polygon=tmp
return polygon
def generate_icosahedron(side_length):
''' Generate an icosahedron from the given side length and
return an array of 20 triangles component from the icosahedron
and his construction base quad set. '''
side_lt = side_length # Define the littler side of the rectangle.
side_gt = side_length * (
(1 + sqrt(5)) / 2.
) # Compute the length of the greater side with the gold number ( (1+sqrt(5))/2. )
# Define the base quad so that his center is Vertex(0.0, 0.0, 0.0) :
quad1 = [
Vertex(-side_lt / 2., -side_gt / 2., 0.0),
Vertex(side_lt / 2., -side_gt / 2., 0.0),
Vertex(side_lt / 2., side_gt / 2., 0.0),
Vertex(-side_lt / 2., side_gt / 2., 0.0)
]
# Rotate the base quad on the y and z axes from 90°, to obtain the second crossing quad.
quad2 = [
rotate_z(rotate_y(quad1[0], 90), 90),
rotate_z(rotate_y(quad1[1], 90), 90),
rotate_z(rotate_y(quad1[2], 90), 90),
rotate_z(rotate_y(quad1[3], 90), 90)
]
# Rotate the base quad on the y and x axes from 90°, to obtain the third crossing quad.
quad3 = [
rotate_x(rotate_y(quad1[0], 90), 90),
rotate_x(rotate_y(quad1[1], 90), 90),
rotate_x(rotate_y(quad1[2], 90), 90),
rotate_x(rotate_y(quad1[3], 90), 90)
]
icosahedron_base_quads = [
quad1, quad2, quad3
] # We set the bases quads for our polyhedron: an icosahedron.
# Define an array composed of triangles because an icosahedron is composed from 20 equilateral triangles:
icosahedron_triangle_array = [
(icosahedron_base_quads[0][0], icosahedron_base_quads[0][1],
icosahedron_base_quads[2][1]),
(icosahedron_base_quads[0][1], icosahedron_base_quads[1][0],
icosahedron_base_quads[1][1]),
(icosahedron_base_quads[0][0], icosahedron_base_quads[0][1],
icosahedron_base_quads[2][2]),
(icosahedron_base_quads[0][0], icosahedron_base_quads[1][2],
icosahedron_base_quads[1][3]),
(icosahedron_base_quads[0][0], icosahedron_base_quads[1][3],
icosahedron_base_quads[2][1]),
(icosahedron_base_quads[0][1], icosahedron_base_quads[2][1],
icosahedron_base_quads[1][0]),
(icosahedron_base_quads[0][1], icosahedron_base_quads[1][1],
icosahedron_base_quads[2][2]),
(icosahedron_base_quads[0][0], icosahedron_base_quads[2][2],
icosahedron_base_quads[1][2]),
(icosahedron_base_quads[0][2], icosahedron_base_quads[0][3],
icosahedron_base_quads[2][3]),
(icosahedron_base_quads[0][3], icosahedron_base_quads[1][2],
icosahedron_base_quads[1][3]),
(icosahedron_base_quads[0][2], icosahedron_base_quads[0][3],
icosahedron_base_quads[2][0]),
(icosahedron_base_quads[0][2], icosahedron_base_quads[1][0],
icosahedron_base_quads[1][1]),
(icosahedron_base_quads[0][2], icosahedron_base_quads[1][1],
icosahedron_base_quads[2][3]),
(icosahedron_base_quads[0][3], icosahedron_base_quads[2][3],
icosahedron_base_quads[1][2]),
(icosahedron_base_quads[0][3], icosahedron_base_quads[1][3],
icosahedron_base_quads[2][0]),
(icosahedron_base_quads[0][2], icosahedron_base_quads[2][0],
icosahedron_base_quads[1][0]),
(icosahedron_base_quads[2][0], icosahedron_base_quads[2][1],
icosahedron_base_quads[1][3]),
(icosahedron_base_quads[2][0], icosahedron_base_quads[2][1],
icosahedron_base_quads[1][0]),
(icosahedron_base_quads[2][2], icosahedron_base_quads[2][3],
icosahedron_base_quads[1][1]),
(icosahedron_base_quads[2][2], icosahedron_base_quads[2][3],
icosahedron_base_quads[1][2])
]
# We return the base quad set and the triangle array.
return [quad1, quad2, quad3], icosahedron_triangle_array