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 offsetLine(v1, v2, offset):
v = subtract(v2, v1)
v = unitize(v)
v = scale(v, offset)
t = v.x
v.x = -v.y
v.y = t
v.z = 0
return _Vertex(add(v1, v), add(v2, v))
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 lineLineIntersection(a, b, c, d):
deltaABX = b.x - a.x
deltaABY = b.y - a.y
deltaDCX = d.x - c.x
deltaDCY = d.y - c.y
denominator = deltaABX * deltaDCY - deltaABY * deltaDCX
if denominator == 0:
return None
numerator = (a.y - c.y) * deltaDCX - (a.x - c.x) * deltaDCY
r = numerator / denominator
x = a.x + r * deltaABX
y = a.y + r * deltaABY
return _Vertex(x, y, 0)
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
def cross(v1, v2):
return _Vertex(v1.y * v2.z - v2.y * v1.z, v1.z * v2.x - v2.z * v1.x,
v1.x * v2.y - v2.x * v1.y)
def _getTorusVertex(ringRadius, tubeRadius, ph, th):
x = ringRadius * _math.cos(ph) + tubeRadius * _math.cos(th) * _math.cos(ph)
y = ringRadius * _math.sin(ph) + tubeRadius * _math.cos(th) * _math.sin(ph)
z = tubeRadius * _math.sin(th)
return _Vertex(x, y, z)
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 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 center(v1, v2):
return _Vertex((v1.x + v2.x) / 2, (v1.y + v2.y) / 2, (v1.z + v2.z) / 2)
def betweenRel(v1, v2, f):
return _Vertex((v2.x - v1.x) * f + v1.x, (v2.y - v1.y) * f + v1.y,
(v2.z - v1.z) * f + v1.z)
def rot2D90(vertex):
return _Vertex(-vertex.y, vertex.x, vertex.z)
def divide(v, factor):
return _Vertex(v.x / factor, v.y / factor, v.z / factor)
def scale(v, factor):
return _Vertex(v.x * factor, v.y * factor, v.z * factor)
def subtract(v1, v2):
return _Vertex(v1.x - v2.x, v1.y - v2.y, v1.z - v2.z)
def add(v1, v2):
return _Vertex(v1.x + v2.x, v1.y + v2.y, v1.z + v2.z)
