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_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_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_quad_sphere(basis,radius) :
''' Generate an quads sphere and return an tuple from 2 arrays:
(lined displaying vertices sequence list, surface displaying vertices sequence list).
In relationship with the base for the sphere generating: faces count = basis * basis
and the given sphere radius.
'''
if not isinstance(basis,int) :
raise TypeError(int)
if basis < 6 or basis % 2 :
print "the basis for the sphere must be greater as 5 and basis % 2 == 0 "
quit()
if not isinstance(radius,int) and not isinstance(radius,float) :
raise TypeError(int,float)
# We generate the base polygon for the sphere generating with the given radius:
polygon_1=generate_polygon_on_xy_radius(basis,radius,Vertex(0.0,0.0,0.0),0)
polygons=[] # Container for the polygons.
i=2 # The iterator variable is initialise with the value 2
# because this one is used for string formating and the polygon_1 variable exist.
while i <= basis :
# Generate from empty lists by execution, with the directive exec(),
# from formattted strings.
# Instead of defining variables because the number of polygons is relativ to the basis argument value.
exec("polygon_{0}=[]".format(i))
exec("polygons.append(polygon_{0})".format(i))
i += 1
for v in polygon_1 :
# Iteration over every vertice from our base polygon.
i=0
angle=360.0/basis # Computing of the degress between 2 polygons on the XZ surface.
while i < len(polygons) :
# generating of all polygons containing the vertices from the sphere.
polygons[i].append(rotate_y(v,angle))
i += 1
angle += 360./basis
polygons_array=[] # temporary container variable definition.
i=1 # The iterator variable is initialise with the value 1
# because this one is used for string formating.
while i <= basis :
# Filling from the temporary container variable
# with the computed polygons containing the vertice from our sphere.
# Which we gonna need to compute the quads from composing the sphere .
exec("polygons_array.append(polygon_{0})".format(i))
i += 1
i=0
tmp_1=[]
while i < len(polygons_array) :
# Iteration over the temporary polygon container variable to compute the quads.
ii=0
tmp_2=[]
while ii < basis-1 :
# We compute the quads: from the polygons list to an quads list.
if not i == basis-1 :
tmp_2.append(polygons_array[i][ii])
tmp_2.append(polygons_array[i+1][ii])
tmp_2.append(polygons_array[i+1][ii+1])
tmp_2.append(polygons_array[i][ii+1])
else :
tmp_2.append(polygons_array[i][ii])
tmp_2.append(polygons_array[0][ii])
tmp_2.append(polygons_array[0][ii+1])
tmp_2.append(polygons_array[i][ii+1])
ii += 1
tmp_1.append(tmp_2)
i += 1
polygons_line_array=polygons_array # Affectation of the variable to return for the case of lined sphere displaying.
polygons_quad_array=tmp_1 # Affectation of the variable to return for the case of surfaces sphere displaying.
return (polygons_line_array,polygons_quad_array)
def generate_trigon_sphere(basis,radius) :
''' Sphere generating function which has for faces triangles and return an tuple from 2 arrays:
(lined displaying vertices sequence list, surface displaying vertices sequence list).
In relationship with the base for the sphere generating: faces count = basis * basis
and the given sphere radius.
'''
if not isinstance(basis,int) :
raise TypeError(int)
if basis < 8 or basis % 4 :
print "the basis for the sphere miust be greater as 7 and basis % 4 == 0 "
quit()
if not isinstance(radius,int) and not isinstance(radius,float) :
raise TypeError(int,float)
# We generate the base polygon for the sphere generating with the given radius:
base_polygon=generate_polygon_on_xy_radius(basis,radius,Vertex(0.0,0.0,0.0),0)
polygons=[] # Polygon for trigonized sphere generating container.
i=0
angle=360./basis # Computing of the degress between 2 polygons on the XZ surface.
while i < basis :
# Loop generating an quads sphere polygons list.
tmp=[]
for v in base_polygon :
# Iteration over every vertice from the base polygon
# and compting from the next polygon vertices rotate from
# the distance between the base polygon and the next polygon.
tmp.append(rotate_y(v,angle))
polygons.append(tmp)
i += 1
angle += 360./basis # Distance between the base polygon and the next polygon inctrementing.
boolean=False
tmp_1=[]
i=0
while i < len(polygons) :
# Iteration over the quads sphere polygons
# to compute the polygons on the XZ surface with an alternativ offset.
ii=0
tmp_2=[]
while ii < len(polygons[0]) :
if boolean :
tmp_2.append(rotate_y(polygons[ii][i],360./basis/2.))
else :
tmp_2.append(polygons[ii][i])
ii += 1
if boolean :
boolean=False
else :
boolean=True
i += 1
tmp_1.append(tmp_2)
tmp_2=tmp_1
i=-1
polygons_trigons_array=[]
boolean=False
while i < len(tmp_2)-1 :
# Loop to compute the triangles from our sphere.
# Throught iterating over the polygons on the XZ surface.
ii=-1
while ii < len(tmp_2[i])-1 :
tmp=[]
if boolean :
tmp.append(tmp_2[i][ii])
tmp.append(tmp_2[i][ii+1])
tmp.append(tmp_2[i+1][ii])
else :
tmp.append(tmp_2[i][ii])
tmp.append(tmp_2[i][ii+1])
tmp.append(tmp_2[i+1][ii+1])
polygons_trigons_array.append(tmp)
ii += 1
if boolean :
boolean=False
else :
boolean=True
i += 1
polygon_vertice_array=tmp_1
# Return an polygon array building an sphere and an array of triangles composing our trigon sphere.
return (polygon_vertice_array,polygons_trigons_array)
