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_tetrahedron(side_length):
''' Generate an tetrahedron in relationship to the given side length.
And return an sequence from triangles composing the tetrahedron.
'''
# Compute cube side length to get the diagonale length egal to the given argument,
# so that the inscribe tetrahedron have the correct side length.
side_length = sqrt(pow(side_length, 2) + pow(side_length, 2)) / 2.
# Generate the cube where the tetrahedron is inscribe.
vertex_list = [ # We begin with the back side.
Vertex(-side_length / 2., -side_length / 2., -side_length / 2.),
Vertex(side_length / 2., -side_length / 2., -side_length / 2.),
Vertex(side_length / 2., side_length / 2., -side_length / 2.),
Vertex(-side_length / 2., side_length / 2., -side_length / 2.),
# Then with the front side.
Vertex(-side_length / 2., -side_length / 2., side_length / 2.),
Vertex(side_length / 2., -side_length / 2., side_length / 2.),
Vertex(side_length / 2., side_length / 2., side_length / 2.),
Vertex(-side_length / 2., side_length / 2., side_length / 2.)
]
# Define the 4 triangles composing the tetrahedron:
tetrahedron_triangle_1 = (vertex_list[6], vertex_list[3], vertex_list[4])
tetrahedron_triangle_2 = (vertex_list[6], vertex_list[3], vertex_list[1])
tetrahedron_triangle_3 = (vertex_list[4], vertex_list[1], vertex_list[3])
tetrahedron_triangle_4 = (vertex_list[4], vertex_list[1], vertex_list[6])
# Assemble triangles to an tetrahedron:
tetrahedron = (tetrahedron_triangle_1, tetrahedron_triangle_2,
tetrahedron_triangle_3, tetrahedron_triangle_4)
return tetrahedron
def __mul__(self,mult) :
''' Multiply sign wrapper. '''
if isinstance(mult,Vertex) :
# The right operator is an vertex.
res_x= mult.wx * self.main_matrix[0] + mult.wy * self.main_matrix[4] + mult.wz * self.main_matrix[8] + self.main_matrix[12]
res_y= mult.wx * self.main_matrix[1] + mult.wy * self.main_matrix[5] + mult.wz * self.main_matrix[9] + self.main_matrix[13]
res_z= mult.wx * self.main_matrix[2] + mult.wy * self.main_matrix[6] + mult.wz * self.main_matrix[10] + self.main_matrix[14]
return Vertex(res_x,res_y,res_z)
elif isinstance(mult,Vector) :
# The right operator is an vector.
x= mult.x*self.main_matrix[0] + mult.y*self.main_matrix[4] + mult.z*self.main_matrix[8]
y= mult.x*self.main_matrix[1] + mult.y*self.main_matrix[5] + mult.z*self.main_matrix[9]
z= mult.x*self.main_matrix[2] + mult.y*self.main_matrix[6] + mult.z*self.main_matrix[10]
return Vector(x,y,z)
else :
# The right operator is suppose to be an Localview otherwise.
try :
mult.pos=self.mult_vertex(mult.pos) # Localview position multiplying.
mult.right=self.mult_vector(mult.right) # Localview X axe vector multiplying.
mult.up=self.mult_vector(mult.up) # Localview Y axe vector multiplying.
mult.sight=self.mult_vector(mult.sight) # Localview Z axe vector multiplying.
return mult
except :
return None
def get_middle_from_segment(vertex1,vertex2) :
''' Return the middle point of an segment as an object from type Vertex '''
if not isinstance(vertex1,Vertex) or not isinstance(vertex2,Vertex) :
raise TypeError(Vertex)
return Vertex((vertex1.wx+vertex2.wx)/2.,(vertex1.wy+vertex2.wy)/2.,(vertex1.wz+vertex2.wz)/2.)
def get_result(self) : ''' Return an vertex issue from the main matrix multiplying. ''' res_x= self.x * self.main_matrix[0] + self.y * self.main_matrix[4] + self.z * self.main_matrix[8] + self.main_matrix[12] res_y= self.x * self.main_matrix[1] + self.y * self.main_matrix[5] + self.z * self.main_matrix[9] + self.main_matrix[13] res_z= self.x * self.main_matrix[2] + self.y * self.main_matrix[6] + self.z * self.main_matrix[10] + self.main_matrix[14] return Vertex(res_x,res_y,res_z)
def scale(vertex, factor):
''' Scale from the given factor. '''
if not isinstance(vertex, Vertex):
# Type control.
raise TypeError(Vertex)
# We simply multiply every vertex component (wx,wy,wz) with the given scaling factor.
return Vertex(vertex.wx * factor, vertex.wy * factor, vertex.wz * factor)
def __init__(self,x=0.0,y=0.0,z=0.0) :
''' Create an localview object with:
-) an position represented by an Vertex.
-) 3 free axes initialise as the X, Y, Z axes.
'''
self.pos=Vertex(x,y,z) # Position from the localview.
self.right=Vector(1.,0.,0.) # Axe X representing vector.
self.up=Vector(0.,1.,0.) # Axe Y representing vector.
self.sight=Vector(0.,0.,1.) # Axe Z representing vector.
def add_vertex(self,vertex,vector=False) :
''' Add the given vertex and vector and return the result as an Vertex object. '''
if not isinstance(vertex,Vertex) :
raise TypeError(Vertex)
if vector :
if not isinstance(vector,Vector) :
raise TypeError(Vector)
return Vertex(vector.x + vertex.wx, vector.y + vertex.wy, vector.z + vertex.wz)
else :
self.x=self.x + vertex.wx
self.y=self.y + vertex.wy
self.z=self.z + vertex.wz
return Vertex(self.x,self.y,self.z)
def div_segment_into_vertices(vertex1, vertex2, divider):
''' Return an sequence from vertices between vertex1 and vertex2.
which has divide the segment (vertex1,vertex2) in the given number of vertices.
'''
if not isinstance(vertex1, Vertex) or not isinstance(vertex2, Vertex):
raise TypeError(Vertex)
if not isinstance(divider, int):
raise TypeError(int)
if divider <= 1:
raise ValueError(divider)
# Define a vertice representing the length between vertex1 and vertex2
length_vertex = Vertex(vertex2.wx - vertex1.wx, vertex2.wy - vertex1.wy,
vertex2.wz - vertex1.wz)
divider += 1 # Increment divider to get the right result.
mult = 1.0 / divider # Compute the value for step unit setting.
# Define a step vertice representing a step in the segment division into vertices.
step_vertex = Vertex(length_vertex.wx * mult, length_vertex.wy * mult,
length_vertex.wz * mult)
position = vertex1 # Setting the start position.
steps_vertices = []
# Add the initial position to the result:
steps_vertices.append(position)
for x in range(divider):
# Computing next vertice.
position = Vertex(position.wx + step_vertex.wx,
position.wy + step_vertex.wy,
position.wz + step_vertex.wz)
steps_vertices.append(position)
return steps_vertices # We could return only the vertices between the start and end position: steps_vertices[1:-1]
def mult_vertex(self,vertex) :
''' Multiply the current main matrix with the given vertex.
And return the result as an Vertex.
'''
if not isinstance(vertex,Vertex) :
raise TypeError(Vertex)
res_x= vertex.wx * self.main_matrix[0] + vertex.wy * self.main_matrix[4] + vertex.wz * self.main_matrix[8] + self.main_matrix[12]
res_y= vertex.wx * self.main_matrix[1] + vertex.wy * self.main_matrix[5] + vertex.wz * self.main_matrix[9] + self.main_matrix[13]
res_z= vertex.wx * self.main_matrix[2] + vertex.wy * self.main_matrix[6] + vertex.wz * self.main_matrix[10] + self.main_matrix[14]
return Vertex(res_x,res_y,res_z)
def get_center_from_polyhedron(points) :
''' Return the center of an polyhedron as an object from type Vertex '''
if not isinstance(points,tuple) and not isinstance(points,list) :
raise TypeError(tuple,list)
for v in points :
if not isinstance(v,Vertex) :
raise TypeError(Vertex)
center=[(max(map(lambda e : e.wx ,points))+min(map(lambda e : e.wx,points)))/2.,(max(map(lambda e : e.wy,points))+min(map(lambda e : e.wy,points)))/2.,(max(map(lambda e : e.wz,points))+min(map(lambda e : e.wz,points)))/2.]
return Vertex(vertexv=center)
def rotate_z(vertex, angle):
''' Rotate an vertice around the z axe and return the result position vertice. '''
if not isinstance(vertex, Vertex):
# Type control.
raise TypeError(Vertex)
x = cos(radians(angle)) * vertex.wx - sin(
radians(angle)) * vertex.wy # Sea explications.
y = sin(radians(angle)) * vertex.wx + cos(
radians(angle)) * vertex.wy # Sea explications.
z = vertex.wz # Because we rotate on the z axe the z value don't change.
return Vertex(x, y, z)
def rotate_x(vertex, angle):
''' Rotate an vertice around the x axe and return the result position vertice. '''
if not isinstance(vertex, Vertex):
# Type control.
raise TypeError(Vertex)
x = vertex.wx # Because we rotate on the x axe the x value don't change.
y = (cos(radians(angle)) * vertex.wy) - (sin(radians(angle)) * vertex.wz
) # Sea explications.
z = (sin(radians(angle)) * vertex.wy) + (cos(radians(angle)) * vertex.wz
) # Sea explications.
return Vertex(x, y, z)
def generate_cube(side_length):
''' Generate an cube in relationship to the given side length.
And return an sequence from quads composing the cube.
'''
cube_vertex_list = [ # We begin with the back side.
Vertex(-side_length / 2., side_length / 2., side_length / 2.),
Vertex(side_length / 2., side_length / 2., side_length / 2.),
Vertex(side_length / 2., -side_length / 2., side_length / 2.),
Vertex(-side_length / 2., -side_length / 2., side_length / 2.),
# Then with the front side.
Vertex(-side_length / 2., side_length / 2., -side_length / 2.),
Vertex(side_length / 2., side_length / 2., -side_length / 2.),
Vertex(side_length / 2., -side_length / 2., -side_length / 2.),
Vertex(-side_length / 2., -side_length / 2., -side_length / 2.)
]
front = [
cube_vertex_list[4], cube_vertex_list[5], cube_vertex_list[6],
cube_vertex_list[7]
] # Front QUADS.
back = [
cube_vertex_list[0], cube_vertex_list[1], cube_vertex_list[2],
cube_vertex_list[3]
] # Back QUADS.
left = [
cube_vertex_list[0], cube_vertex_list[4], cube_vertex_list[7],
cube_vertex_list[3]
] # Left QUADS.
right = [
cube_vertex_list[5], cube_vertex_list[1], cube_vertex_list[2],
cube_vertex_list[6]
] # right QUADS.
up = [
cube_vertex_list[0], cube_vertex_list[1], cube_vertex_list[5],
cube_vertex_list[4]
] # up QUADS.
down = [
cube_vertex_list[7], cube_vertex_list[6], cube_vertex_list[2],
cube_vertex_list[3]
] # down QUADS.
return (front, back, left, right, up, down)
def translate(vertex, value_x, value_y, value_z):
''' Translate an vertice from the given offset in every axe. '''
if not isinstance(vertex, Vertex):
# Type control.
raise TypeError(Vertex)
x = (
value_x + vertex.wx
) # We simply add the given value to translate vertex in direction x, even if it is an negativ value it work.
y = (
value_y + vertex.wy
) # We simply add the given value to translate vertex in direction y, even if it is an negativ value it work.
z = (
value_z + vertex.wz
) # We simply add the given value to translate vertex in direction z, even if it is an negativ value it work.
return Vertex(x, y, z)
def rotate_on_xz(center, angle, vertex):
''' Function to rotate an vertex given as the argument vertex
around a center vertex in the xz plan from the value angle in clock sens.
Return the rotated vertex as an object from <type 'Vertex'>.
'''
if not isinstance(center, Vertex):
raise TypeError(Vertex)
if not isinstance(vertex, Vertex):
raise TypeError(Vertex)
return_x = vertex.wx * cos(radians(angle)) - vertex.wz * sin(
radians(angle)) + center.wx * (
1 - cos(radians(angle))) + center.wz * sin(radians(angle))
return_z = vertex.wx * sin(radians(angle)) + vertex.wz * cos(
radians(angle)) + center.wz * (
1 - cos(radians(angle))) - center.wx * sin(radians(angle))
return Vertex(return_x, 0., return_z)
def get_center_from_polygon(points) :
''' Return the center of an polygon as an object from type Vertex '''
if not isinstance(points,tuple) and not isinstance(points,list) :
raise TypeError(tuple,list)
for v in points :
if not isinstance(v,Vertex) :
raise TypeError(Vertex)
tmp=[]
i=-1
while i < len(points)-1 :
# We compute the inner (inscribe) circle points. To get the right polygone center.
tmp.append(get_middle_from_segment(points[i],points[i+1]))
i += 1
points=tmp
center=[(max(map(lambda e : e.wx ,points))+min(map(lambda e : e.wx,points)))/2.,(max(map(lambda e : e.wy,points))+min(map(lambda e : e.wy,points)))/2.,(max(map(lambda e : e.wz,points))+min(map(lambda e : e.wz,points)))/2.]
return Vertex(vertexv=center)
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_polygon_on_xz_radius(edges,radius,center,offset=0) :
''' Return an polygon on plan XZ: from edges sides, from radius radius, with offset offset.
z
/
_____/____x
/
/ plan XZ.
'''
if not isinstance(center,Vertex) :
raise TypeError(Vertex)
polygon=[] # Polygon vertice container.
scale=360./edges # Computing of the angle separating 2 points from the polygon.
i=0
while i < edges :
polygon.append(Vertex(radius*cos(radians((scale*i)+offset))+center.wx,center.wy,radius*sin(radians((scale*i)+offset))+center.wz))
i += 1
return polygon
def __init__(self,base_polygon,base_radius,toros_radius,display_mode="lined",lines_color=False,faces_color=False,lines_width=1,display_ls=False) :
''' Generate an toros object with the given radius and basis polygone settings.
base_polygon = the toros basis polygon.
base_radius = the toros basis polygon radius.
toros_radius = the toros radius (without the base polygon radius).
display_mode = "lined" -> only the lines will be displayed.
display_mode = "faced" -> only the faces will be displayed.
display_mode = "twice" -> The lines and the faces will be displayed.
lines_color = an objet <type 'Color'> representing the lines color.
faces_color = an objet <type 'Color'> representing the faces color.
line_width = an integer representing the lines width.
'''
if not isinstance(base_polygon,int) :
raise TypeError("base_polygon argument",int)
if base_polygon <= 2 :
print "the base polygon must be greater than 2 "
quit()
if not isinstance(base_radius,int) and not isinstance(base_radius,float) :
raise TypeError("base_radius argument",int,float)
elif base_radius <= 0.0 :
raise ValueError("Value of base_radius must be greater than 0.0")
if not isinstance(toros_radius,int) and not isinstance(toros_radius,float) :
raise TypeError("toros_radius argument",int,float)
elif toros_radius <= 0.0 :
raise ValueError("Value of toros_radius must be greater than 0.0")
if display_mode == "lined" or display_mode == "faced" or display_mode == "twice" :
self.display_mode=display_mode
else :
raise ValueError("Argument display_mode","lined","faced","twice")
if lines_color :
if not isinstance(lines_color,Color) :
raise TypeError("Argument lines_color",Color)
if faces_color :
if not isinstance(faces_color,Color) :
raise TypeError("Argument faces_color",Color)
if not isinstance(lines_width,int) :
raise TypeError(lines_width,int)
elif lines_width < 1 :
raise ValueError("Lines width value too little.")
if isinstance(lines_color,Color) :
if type(lines_color.a) == bool :
lines_color.a=0
if isinstance(faces_color,Color) :
if type(faces_color.a) == bool :
faces_color.a=0
if isinstance(display_ls,bool) :
self.display_ls=display_ls
self.base_polygon=base_polygon
self.base_radius=base_radius
self.toros_radius=toros_radius
self.lines_color=lines_color
self.faces_color=faces_color
self.lines_width=lines_width
self.toros=generate_toros(base_polygon,base_radius,toros_radius)
self.ls=Localview()
self.center=Vertex(0.0,0.0,0.0)
def __init__(self,
side_length,
display_mode="lined",
lines_color=False,
quads_color=False,
triangles_color=False,
lines_width=1,
display_ls=False):
''' generate an 26 faces polyhedron object with the given side length settings.
display_mode = "lined" -> only the lines will be displayed.
display_mode = "faced" -> only the faces will be displayed.
display_mode = "twice" -> The lines and the faces will be displayed.
lines_color = an objet <type 'Color'> representing the lines color.
quads_color = an objet <type 'Color'> representing the quads color.
an 18-items-list contains <type 'Color'> objects.
triangles_color = an objet <type 'Color'> representing the triangles color.
an 8-items-list contains <type 'Color'> objects.
line_width = an integer representing the lines width.
'''
if not isinstance(side_length, int) and not isinstance(
side_length, float):
raise TypeError(int, float)
elif side_length < 0.0:
raise ValueError("Value of side_length must be greater than 0.0")
if display_mode == "lined" or display_mode == "faced" or display_mode == "twice":
self.display_mode = display_mode
else:
raise ValueError("lined", "faced", "twice")
if lines_color:
if not isinstance(lines_color, Color):
raise TypeError(lines_color, Color)
if quads_color:
if not isinstance(quads_color, Color) and not isinstance(
quads_color, list):
raise TypeError(quads_color, Color, list)
elif isinstance(quads_color, list) and len(quads_color) != 18:
print "Error quads_color argument:\nYou must give an list from 18 Color objects.\nOne Color object per face."
quit()
elif isinstance(quads_color, list) and len(quads_color) == 18:
tmp = []
quads_color_index = 0
while quads_color_index < 18:
if type(quads_color[quads_color_index].a) == bool:
quads_color[quads_color_index].a = 0
quads_color_index += 1
if triangles_color:
if not isinstance(triangles_color, Color) and not isinstance(
triangles_color, list):
raise TypeError(triangles_color, Color, list)
elif isinstance(triangles_color,
list) and len(triangles_color) != 8:
print "Error triangles_color argument:\nYou must give an list from 8 Color objects.\nOne Color object per face."
quit()
elif isinstance(triangles_color,
list) and len(triangles_color) == 8:
tmp = []
triangles_color_index = 0
while triangles_color_index < 8:
if type(triangles_color[triangles_color_index].a) == bool:
triangles_color[triangles_color_index].a = 0
triangles_color_index += 1
if not isinstance(lines_width, int):
raise TypeError(lines_width, int)
elif lines_width < 1:
raise ValueError(lines_width, "Lines width value too little.")
if isinstance(lines_color, Color):
if type(lines_color.a) == bool:
lines_color.a = 0
if isinstance(quads_color, Color):
if type(quads_color.a) == bool:
quads_color.a = 0
if isinstance(triangles_color, Color):
if type(triangles_color.a) == bool:
triangles_color.a = 0
if isinstance(display_ls, bool):
self.display_ls = display_ls
self.side_length = side_length
self.lines_color = lines_color
self.quads_color = quads_color
self.triangles_color = triangles_color
self.lines_width = lines_width
self.triangles, self.quads = generate_polyhedron_26_faces(side_length)
self.ls = Localview()
self.center = Vertex(0.0, 0.0, 0.0)
def __init__(self,
side_length,
display_mode="lined",
lines_color=False,
pentagons_color=False,
hexagons_color=False,
lines_width=1,
display_ls=False):
''' generate an cube object with the given side length settings.
display_mode = "lined" -> only the lines will be displayed.
display_mode = "faced" -> only the faces will be displayed.
display_mode = "twice" -> The lines and the faces will be displayed.
lines_color = an objet <type 'Color'> representing the lines color.
pentagons_color = an objet <type 'Color'> representing the pentagons color.
an 12-items-list contains <type 'Color'> objects.
hexagons_color = an objet <type 'Color'> representing the hexagons color.
an 20-items-list contains <type 'Color'> objects.
line_width = an integer representing the lines width.
'''
if not isinstance(side_length, int) and not isinstance(
side_length, float):
raise TypeError(int, float)
elif side_length <= 0.0:
raise ValueError("Value of side_length must be greater than 0.0")
if display_mode == "lined" or display_mode == "faced" or display_mode == "twice":
self.display_mode = display_mode
else:
raise ValueError("lined", "faced", "twice")
if lines_color:
if not isinstance(lines_color, Color):
raise TypeError(lines_color, Color)
if pentagons_color:
if not isinstance(pentagons_color, Color) and not isinstance(
pentagons_color, list):
raise TypeError(pentagons_color, Color, list)
elif isinstance(pentagons_color,
list) and len(pentagons_color) != 12:
print "Error pentagons_color argument:\nYou must give an list from 12 Color objects.\nOne Color object per face."
quit()
elif isinstance(pentagons_color,
list) and len(pentagons_color) == 12:
tmp = []
pentagons_color_index = 0
while pentagons_color_index < 12:
if type(pentagons_color[pentagons_color_index].a) == bool:
pentagons_color[pentagons_color_index].a = 0
pentagons_color_index += 1
if hexagons_color:
if not isinstance(hexagons_color, Color) and not isinstance(
hexagons_color, list):
raise TypeError(hexagons_color, Color, list)
elif isinstance(hexagons_color,
list) and len(hexagons_color) != 20:
print "Error hexagons_color argument:\nYou must give an list from 20 Color objects.\nOne Color object per face."
quit()
elif isinstance(hexagons_color,
list) and len(hexagons_color) == 20:
tmp = []
hexagons_color_index = 0
while hexagons_color_index < 20:
if type(hexagons_color[hexagons_color_index].a) == bool:
hexagons_color[hexagons_color_index].a = 0
hexagons_color_index += 1
if not isinstance(lines_width, int):
raise TypeError(lines_width, int)
elif lines_width < 1:
raise ValueError(lines_width, "Lines width value too little.")
if isinstance(lines_color, Color):
if type(lines_color.a) == bool:
lines_color.a = 0
if isinstance(pentagons_color, Color):
if type(pentagons_color.a) == bool:
pentagons_color.a = 0
if isinstance(hexagons_color, Color):
if type(hexagons_color.a) == bool:
hexagons_color.a = 0
if isinstance(display_ls, bool):
self.display_ls = display_ls
self.side_length = side_length
self.lines_color = lines_color
self.pentagons_color = pentagons_color
self.hexagons_color = hexagons_color
self.lines_width = lines_width
self.hexagons, self.pentagons = generate_fulleren(side_length)
self.ls = Localview()
self.center = Vertex(0.0, 0.0, 0.0)
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)
def __init__(self,
side_length,
display_mode="lined",
lines_color=False,
faces_color=False,
lines_width=1,
display_ls=False):
''' Generate an Icosahedron object with the given side length settings.
display_mode = "lined" -> Only the lines will be displayed.
display_mode = "faced" -> Only the faces will be displayed.
display_mode = "twice" -> The lines and the faces will be displayed.
lines_color = An objet <type 'Color'> representing the lines color.
faces_color = An objet <type 'Color'> representing the faces color.
An 8-items-list from object <type 'Color'>.
One item per icosahedron face.
lines_width = An integer representing the lines width.
display_ls = Define if the localview should be display.
'''
if not isinstance(side_length, int) and not isinstance(
side_length, float):
raise TypeError("Argument side_length", int, float)
elif side_length <= 0.0:
raise ValueError(
"Value of argument side_length must be greater than 0.0")
if display_mode == "lined" or display_mode == "faced" or display_mode == "twice":
self.display_mode = display_mode
else:
raise ValueError("Argument display_mode", "lined", "faced",
"twice")
if lines_color:
if not isinstance(lines_color, Color):
raise TypeError("Argument lines_color", Color)
if faces_color:
if not isinstance(faces_color, Color) and not isinstance(
faces_color, list):
raise TypeError(faces_color, Color, list)
elif isinstance(faces_color, list) and len(faces_color) != 20:
print "Error faces_color argument:\nYou must give an list from 20 Color objects.\nOne Color object per face."
quit()
elif isinstance(faces_color, list) and len(faces_color) == 20:
tmp = []
faces_color_index = 0
while faces_color_index < 20:
if type(faces_color[faces_color_index].a) == bool:
faces_color[faces_color_index].a = 0
faces_color_index += 1
if not isinstance(lines_width, int):
raise TypeError("Argument lines_width", int)
elif lines_width < 1:
raise ValueError(lines_width, "Lines width value too little.")
if isinstance(lines_color, Color):
if type(lines_color.a) == bool:
lines_color.a = 0
if isinstance(faces_color, Color):
if type(faces_color.a) == bool:
faces_color.a = 0
if isinstance(display_ls, bool):
self.display_ls = display_ls
self.side_length = side_length
self.lines_color = lines_color
self.faces_color = faces_color
self.lines_width = lines_width
self.polyhedron = generate_icosahedron(side_length)[1]
self.ls = Localview()
self.center = Vertex(0.0, 0.0, 0.0)
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 __init__(self,radius,basis,display_mode="lined",lines_color=False,faces_color=False,lines_width=1,display_ls=False) :
''' generate an trigon sphere object with the given radius and polygone basis.
basis = Integer taken as basis for the sphere generating.
radius = Radius of the sphere.
display_mode = "lined" -> only the lines will be displayed.
display_mode = "faced" -> only the faces will be displayed.
display_mode = "twice" -> The lines and the faces will be displayed.
lines_color = an objet <type 'Color'> representing the lines color.
faces_color = an objet <type 'Color'> representing the faces color.
line_width = an integer representing the lines width.
'''
if not isinstance(radius,int) and not isinstance(radius,float) :
raise TypeError(int,float)
elif radius <= 0.0 :
raise ValueError("Value of radius must be greater than 0.0")
if not isinstance(basis,int) :
raise TypeError(int)
if basis < 6 or basis % 4 :
print "the basis for the sphere must be greater as 5 and basis % 4 == 0 "
quit()
if display_mode == "lined" or display_mode == "faced" or display_mode == "twice" :
self.display_mode=display_mode
else :
raise ValueError("Argument display_mode","lined","faced","twice")
if lines_color :
if not isinstance(lines_color,Color) :
raise TypeError("Argument lines_color",Color)
if faces_color :
if not isinstance(faces_color,Color) :
raise TypeError("Argument faces_color",Color)
if not isinstance(lines_width,int) :
raise TypeError(lines_width,int)
elif lines_width < 1 :
raise ValueError("Lines width value too little.")
if isinstance(lines_color,Color) :
if type(lines_color.a) == bool :
lines_color.a=0
if not type(faces_color) == bool :
if type(faces_color.a) == bool :
faces_color.a=0
if isinstance(display_ls,bool) :
self.display_ls=display_ls
self.lines_color=lines_color
self.faces_color=faces_color
self.lines_width=lines_width
self.basis=basis
self.radius=radius
self.trigons=generate_trigon_sphere(basis,radius)[0]
self.ls=Localview()
self.center=Vertex(0.0,0.0,0.0)