def constructCone(z1,z2,radius1,radius2,nSegments,capBottom=True,capTop=True):
"""
Creates and returns a conic cylinder.
"""
delaAngle=_math.radians(360.0/nSegments)
angle=0
verticesBottom=[]
verticesTop=[]
for i in range(nSegments):
x1=radius1*_math.cos(angle)
y1=radius1*_math.sin(angle)
verticesBottom.append(_Vertex(x1,y1,z1))
x2=radius2*_math.cos(angle)
y2=radius2*_math.sin(angle)
verticesTop.append(_Vertex(x2,y2,z2))
angle+=delaAngle
mesh=_Mesh()
mesh.vertices.extend(verticesBottom)
mesh.vertices.extend(verticesTop)
for i in range(nSegments):
i2=(i+1)%nSegments
mesh.faces.append(_Face([verticesBottom[i],verticesBottom[i2],verticesTop[i2],verticesTop[i]]))
if capBottom:
centerBottom=_Vertex(0,0,z1)
mesh.vertices.append(centerBottom)
for i in range(nSegments):
i2=(i+1)%nSegments
mesh.faces.append(_Face([verticesBottom[i],verticesBottom[i2],centerBottom]))
if capTop:
centerTop=_Vertex(0,0,z2)
mesh.vertices.append(centerTop)
for i in range(nSegments):
i2=(i+1)%nSegments
mesh.faces.append(_Face([verticesTop[i],verticesTop[i2],centerTop]))
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 constructDodecahedron(cx,cy,cz,radius):
mesh=_Mesh()
phi = (1 + 5**0.5)/2
mesh.vertices = [_Vertex( 1, 1, 1),
_Vertex( 1, 1,-1),
_Vertex( 1,-1, 1),
_Vertex( 1,-1,-1),
_Vertex(-1, 1, 1),
_Vertex(-1, 1,-1),
_Vertex(-1,-1, 1),
_Vertex(-1,-1,-1),
_Vertex(0,-phi,-1/phi),
_Vertex(0,-phi, 1/phi),
_Vertex(0, phi,-1/phi),
_Vertex(0, phi, 1/phi),
_Vertex(-phi,-1/phi,0),
_Vertex(-phi, 1/phi,0),
_Vertex( phi,-1/phi,0),
_Vertex( phi, 1/phi,0),
_Vertex(-1/phi,0,-phi),
_Vertex( 1/phi,0,-phi),
_Vertex(-1/phi,0, phi),
_Vertex( 1/phi,0, phi)]
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 = [2,9,6,18,19,
4,11,0,19,18,
18,6,12,13,4,
19,0,15,14,2,
4,13,5,10,11,
14,15,1,17,3,
1,15,0,11,10,
3,17,16,7,8,
2,14,3,8,9,
6,9,8,7,12,
1,10,5,16,17,
12,7,16,5,13]
faces = []
for i in range(0,len(indices),5):
f = _Face([mesh.vertices[indices[i]],
mesh.vertices[indices[i + 1]],
mesh.vertices[indices[i + 2]],
mesh.vertices[indices[i + 3]],
mesh.vertices[indices[i + 4]]])
faces.append(f)
# make triangles
newfaces = []
for f in faces:
v = _faceUtils.center(f)
mesh.vertices.append(v)
for i,cv in enumerate(f.vertices):
nv = f.vertices[(i+1)%len(f.vertices)]
newfaces.append(_Face([cv,v,nv]))
mesh.faces = newfaces
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 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
def _collectNewFaces(_mesh):
newMesh=_Mesh()
for face in _mesh.faces:
v1=face.vertices[-2]
v2=face.vertices[-1]
for v3 in face.vertices:
edge1=_mesh.getEdgeAdjacentToVertices(v1,v2)
edge2=_mesh.getEdgeAdjacentToVertices(v2,v3)
if (edge1 != None) and (edge2!= None):
newFace=_Face([edge1.vertex,v2.vertex,edge2.vertex,face.vertex])
newFace.color=face.color
newFace.group=face.group
newMesh.faces.append(newFace)
v1=v2
v2=v3
newMesh.updateAdjacencies()
return newMesh
def constructTorus(ringRadius, tubeRadius, ringN=16, tubeN=16):
mesh = _Mesh()
phi = 2 * _math.pi / ringN
theta = 2 * _math.pi / tubeN
for i in range(ringN):
for j in range(tubeN):
v0 = _getTorusVertex(ringRadius, tubeRadius,
phi * ((i + 1) % ringN), theta * j)
v1 = _getTorusVertex(ringRadius, tubeRadius,
phi * ((i + 1) % ringN),
theta * ((j + 1) % tubeN))
v2 = _getTorusVertex(ringRadius, tubeRadius, phi * i,
theta * ((j + 1) % tubeN))
v3 = _getTorusVertex(ringRadius, tubeRadius, phi * i, theta * j)
f = _Face([v0, v1, v2, v3])
mesh.faces.append(f)
return mesh
def constructTetrahedron(cx,cy,cz,side):
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 importOBJ(filename):
"""Loads a Wavefront OBJ file. """
mesh = _Mesh()
group = ""
for line in open(filename, "r"):
if line.startswith('#'): continue
values = line.split()
if not values: continue
if values[0] == 'g':
group = values[1]
elif values[0] == 'v':
v = map(float, values[1:4])
mesh.vertices.append(_Vertex(v[0], v[1], v[2]))
elif values[0] == 'f':
face = _Face([])
face.group = group
for v in values[1:]:
w = v.split('/')
vertex = mesh.vertices[int(w[0]) - 1]
face.vertices.append(vertex)
mesh.faces.append(face)
return mesh
