def constructTetrahedron(cx,cy,cz,side):
"""
Constructs a tetrahedron mesh.
Arguments:
----------
cx, cy, cz : float
The center point of the tetrahedron
side : float
The edge length of the tetrahedron
"""
mesh = Mesh()
coord = 1 / math.sqrt(2)
mesh.vertices = [Vertex(+1, 0, -coord),
Vertex(-1, 0, -coord),
Vertex(0, +1, +coord),
Vertex(0, -1, +coord)]
for i in range(len(mesh.vertices)):
mesh.vertices[i] = vec.scale(mesh.vertices[i], side / 2)
mesh.vertices[i] = vec.add(mesh.vertices[i], Vertex(cx, cy, cz))
f1 = Face([mesh.vertices[0], mesh.vertices[1], mesh.vertices[2]])
f2 = Face([mesh.vertices[1], mesh.vertices[0], mesh.vertices[3]])
f3 = Face([mesh.vertices[2], mesh.vertices[3], mesh.vertices[0]])
f4 = Face([mesh.vertices[3], mesh.vertices[2], mesh.vertices[1]])
mesh.faces = [f1, f2, f3, f4]
return mesh
def constructBox(x1,y1,z1,x2,y2,z2):
"""
Creates and returns a mesh box with six quad faces.
Arguments:
----------
x1,y1,z1 : float
The coordinates of the bottom left front corner
x2,y2,z2 : float
The coordinates of the top right back corner
"""
mesh = Mesh()
v1 = Vertex(x1, y1, z1)
v2 = Vertex(x1, y2, z1)
v3 = Vertex(x2, y2, z1)
v4 = Vertex(x2, y1, z1)
v5 = Vertex(x1, y1, z2)
v6 = Vertex(x1, y2, z2)
v7 = Vertex(x2, y2, z2)
v8 = Vertex(x2, y1, z2)
mesh.vertices = [v1, v2, v3, v4, v5, v6, v7, v8]
f1 = Face([v1, v2, v3, v4])
f2 = Face([v8, v7, v6, v5])
f3 = Face([v4, v3, v7, v8])
f4 = Face([v3, v2, v6, v7])
f5 = Face([v2, v1, v5, v6])
f6 = Face([v1, v4, v8, v5])
mesh.faces = [f1, f2, f3, f4, f5, f6]
return mesh
def constructSingleFace(vertices):
"""
Creates and returns a single face mesh from the vertices.
Arguments:
----------
vertices : list of mola.core.Vertex
The vertices describing the face
"""
mesh = Mesh()
mesh.vertices = vertices
mesh.faces = [Face(vertices)]
return mesh
def getQuadMesh(self, functionIn, functionOut):
faces = []
for x in range(self.nX):
for y in range(self.nY):
for z in range(self.nZ):
index = self.getIndex(x, y, z)
if functionIn(self.values[index]):
# (x,y) (x1,y) (x1,y1) (x,y1)
if x == self.nX - 1 or functionOut(
self.get_xyz(x + 1, y, z)):
v1 = Vertex(x + 1, y, z)
v2 = Vertex(x + 1, y + 1, z)
v3 = Vertex(x + 1, y + 1, z + 1)
v4 = Vertex(x + 1, y, z + 1)
faces.append(Face([v1, v2, v3, v4]))
if x == 0 or functionOut(self.get_xyz(x - 1, y, z)):
v1 = Vertex(x, y + 1, z)
v2 = Vertex(x, y, z)
v3 = Vertex(x, y, z + 1)
v4 = Vertex(x, y + 1, z + 1)
faces.append(Face([v1, v2, v3, v4]))
if y == self.nY - 1 or functionOut(
self.get_xyz(x, y + 1, z)):
v1 = Vertex(x + 1, y + 1, z)
v2 = Vertex(x, y + 1, z)
v3 = Vertex(x, y + 1, z + 1)
v4 = Vertex(x + 1, y + 1, z + 1)
faces.append(Face([v1, v2, v3, v4]))
if y == 0 or functionOut(self.get_xyz(x, y - 1, z)):
v1 = Vertex(x, y, z)
v2 = Vertex(x + 1, y, z)
v3 = Vertex(x + 1, y, z + 1)
v4 = Vertex(x, y, z + 1)
faces.append(Face([v1, v2, v3, v4]))
if z == self.nZ - 1 or functionOut(
self.get_xyz(x, y, z + 1)):
v1 = Vertex(x, y, z + 1)
v2 = Vertex(x + 1, y, z + 1)
v3 = Vertex(x + 1, y + 1, z + 1)
v4 = Vertex(x, y + 1, z + 1)
faces.append(Face([v1, v2, v3, v4]))
if z == 0 or functionOut(self.get_xyz(x, y, z - 1)):
v1 = Vertex(x, y + 1, z)
v2 = Vertex(x + 1, y + 1, z)
v3 = Vertex(x + 1, y, z)
v4 = Vertex(x, y, z)
faces.append(Face([v1, v2, v3, v4]))
mesh = Mesh()
mesh.faces = faces
return mesh
def constructIcosahedron(cx,cy,cz,radius):
"""
Creates and returns a mesh in the form of an icosahedron.
Arguments:
----------
cx,cy,cz : float
The coordinates of the center point
radius : float
The radius of the containing sphere
"""
mesh = Mesh()
phi = (1 + 5 ** 0.5) / 2
coordA = 1 / (2 * math.sin(2 * math.pi / 5))
coordB = phi / (2 * math.sin(2 * math.pi / 5))
mesh.vertices = [Vertex(0, -coordA, coordB),
Vertex(coordB, 0, coordA),
Vertex(coordB, 0, -coordA),
Vertex(-coordB, 0, -coordA),
Vertex(-coordB, 0, coordA),
Vertex(-coordA, coordB, 0),
Vertex(coordA, coordB, 0),
Vertex(coordA, -coordB, 0),
Vertex(-coordA, -coordB, 0),
Vertex(0, -coordA, -coordB),
Vertex(0, coordA, -coordB),
Vertex(0, coordA, coordB)]
for i in range(len(mesh.vertices)):
mesh.vertices[i] = vec.scale(mesh.vertices[i], radius)
mesh.vertices[i] = vec.add(mesh.vertices[i], Vertex(cx,cy,cz))
indices = [1, 2, 6, 1, 7, 2, 3, 4, 5, 4, 3, 8, 6, 5, 11, 5, 6, 10, 9, 10, 2, 10, 9, 3, 7, 8, 9, 8, 7, 0, 11, 0, 1, 0, 11, 4, 6, 2, 10, 1, 6, 11, 3, 5, 10, 5, 4, 11, 2, 7, 9, 7, 1, 0, 3, 9, 8, 4, 8, 0]
faces = []
for i in range(0,len(indices),3):
f = Face([mesh.vertices[indices[i]], mesh.vertices[indices[i + 1]], mesh.vertices[indices[i + 2]]])
faces.append(f)
mesh.faces = faces
return mesh
