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 sliceWithZ(v1, v2, z):
if v1.z == z: return Vertex(v1.x, v1.y, z)
if v1.z <= z and v2.z <= z:
return None
if v1.z >= z and v2.z >= z:
return None
dX = v2.x - v1.x
dY = v2.y - v1.y
dZ = v2.z - v1.z
if dZ == 0: return None
f = (z - v1.z) / dZ
return Vertex(f * dX + v1.x, f * dY + v1.y, z)
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 _catmullVertices(mesh):
for face in mesh.faces:
face.vertex = faceUtils.center(face)
for edge in mesh.edges:
if edge.face1 == None or edge.face2 == None:
edge.v1.fix = True
edge.v2.fix = True
edge.vertex = edge.getCenter()
else:
vsum = Vertex()
nElements = 2
vsum = vec.add(vsum, edge.v1)
vsum = vec.add(vsum, edge.v2)
if edge.face1 != None:
vsum = vec.add(vsum, edge.face1.vertex)
nElements += 1
if edge.face2 != None:
vsum = vec.add(vsum, edge.face2.vertex)
nElements += 1
vsum = vec.divide(vsum, nElements)
edge.vertex = vsum
if edge.v1.fix and edge.v2.fix:
edge.vertex.fix = True
for vertex in mesh.vertices:
if vertex.fix:
vertex.vertex = copy.copy(vertex)
else:
averageFaces = Vertex()
averageEdges = Vertex()
nEdges = len(vertex.edges)
for edge in vertex.edges:
face = edge.face1
if edge.v2 is vertex:
face = edge.face2
if face != None:
averageFaces = vec.add(averageFaces, face.vertex)
averageEdges=vec.add(averageEdges,edge.getCenter())
averageEdges = vec.scale(averageEdges, 2.0/nEdges)
averageFaces = vec.scale(averageFaces, 1.0/nEdges)
v = Vertex(vertex.x, vertex.y, vertex.z)
v = vec.scale(v,nEdges-3)
v = vec.add(v,averageFaces)
v = vec.add(v,averageEdges)
v = vec.scale(v,1.0/nEdges)
vertex.vertex = v
def offset(mesh,offset=1,doclose=True):
newMesh=Mesh()
# calculate vertex normals
for vertex in mesh.vertices:
vertex.vertex = Vertex(0,0,0)
vertex.nfaces = 0
for face in mesh.faces:
normal = faceUtils.normal(face)
for vertex in face.vertices:
vertex.vertex.add(normal)
vertex.nfaces += 1
for vertex in mesh.vertices:
vertex.vertex.scale(offset / vertex.nfaces)
vertex.vertex.add(vertex)
# create faces
for face in mesh.faces:
offsetVertices = []
for vertex in face.vertices:
offsetVertices.append(vertex.vertex)
offsetVertices.reverse()
newFace = Face(offsetVertices)
newMesh.faces.append(newFace)
newMesh.faces.append(face)
# create sides
if doclose:
for edge in mesh.edges:
if edge.face1 == None or edge.face2 == None:
offsetVertices = [edge.v1, edge.v2, edge.v2.vertex, edge.v1.vertex]
if edge.face2 == None:
offsetVertices.reverse()
newFace = Face(offsetVertices)
newMesh.faces.append(newFace)
newMesh.updateAdjacencies()
return newMesh
def subdivide(mesh):
for face in mesh.faces:
face.vertex=faceUtils.center(face)
for edge in mesh.edges:
edge.vertex = edge.getCenter()
for vertex in mesh.vertices:
vertex.vertex = Vertex(vertex.x,vertex.y,vertex.z)
return _collectNewFaces(mesh)
def subdivide_translate_facevertices(mesh,values):
for face in mesh.faces:
face.vertex=faceUtils.center(face)
for edge in mesh.edges:
edge.vertex = edge.getCenter()
for vertex in mesh.vertices:
vertex.vertex = Vertex(vertex.x,vertex.y,vertex.z)
_translateFaceVertices(mesh,values)
return _collectNewFaces(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 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 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[i2],verticesBottom[i],centerBottom]))
mesh.faces.append(Face(list(reversed(verticesBottom))))
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]))
mesh.faces.append(Face(verticesTop))
return mesh
def centerFromVertices(vertices):
"""
Returns the center point (type Vertex) of a list of vertices.
Note: not the center of gravity, just the average of the vertices.
Arguments:
----------
vertices : list of mola.core.Vertex
The list of vertices to be measured
"""
n = len(vertices)
cx = sum([v.x for v in vertices]) / n
cy = sum([v.y for v in vertices]) / n
cz = sum([v.z for v in vertices]) / n
return Vertex(cx, cy, cz)
def centerFromLine(v1,v2):
"""
Returns the center of a line defined by two vertices.
Arguments:
----------
v1, v2 : mola.core.Vertex
start and end points of the line
Returns:
--------
mola.core.Vertex
the center point of the line
"""
return Vertex((v1.x + v2.x) / 2, (v1.y + v2.y) / 2, (v1.z + v2.z) / 2)
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 = [float(c) for c in values[1:4]]
#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 _getTorusVertex(ringRadius, tubeRadius, ph,th):
x = math.cos(th) * (ringRadius + tubeRadius * math.cos(ph))
y = math.sin(th) * (ringRadius + tubeRadius * math.cos(ph))
z = tubeRadius * math.sin(ph)
return Vertex(x, y, z)
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 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 divide(v, factor):
return Vertex(v.x / factor, v.y / factor, v.z / factor)
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 subtract(v1, v2):
return Vertex(v1.x - v2.x, v1.y - v2.y, v1.z - v2.z)
def scale(v, factor):
return Vertex(v.x * factor, v.y * factor, v.z * factor)
def add(v1, v2):
return Vertex(v1.x + v2.x, v1.y + v2.y, v1.z + v2.z)
def rot2D90(vertex):
return Vertex(-vertex.y, vertex.x, vertex.z)
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 marchingCubes(nX, nY, nZ, values, iso):
mesh = Mesh()
nYZ = nY * nZ
index = 0
n = [0] * 8
switcher = {
0: lambda: Vertex(x + _v(n[0], n[1], iso), y + 1, z),
1: lambda: Vertex(x + 1, y + _v(n[2], n[1], iso), z),
2: lambda: Vertex(x + _v(n[3], n[2], iso), y, z),
3: lambda: Vertex(x, y + _v(n[3], n[0], iso), z),
4: lambda: Vertex(x + _v(n[4], n[5], iso), y + 1, z + 1),
5: lambda: Vertex(x + 1, y + _v(n[6], n[5], iso), z + 1),
6: lambda: Vertex(x + _v(n[7], n[6], iso), y, z + 1),
7: lambda: Vertex(x, y + _v(n[7], n[4], iso), z + 1),
8: lambda: Vertex(x, y + 1, z + _v(n[0], n[4], iso)),
9: lambda: Vertex(x + 1, y + 1, z + _v(n[1], n[5], iso)),
10: lambda: Vertex(x, y, z + _v(n[3], n[7], iso)),
11: lambda: Vertex(x + 1, y, z + _v(n[2], n[6], iso))
}
for x in range(nX - 1):
for y in range(nY - 1):
for z in range(nZ - 1):
caseNumber = 0
index = z + y * nZ + x * nYZ
# collecting the values
n[0] = values[index + nZ] # 0,1,0
n[1] = values[index + nYZ + nZ] #1,1,0
n[2] = values[index + nYZ] # 1,0,0
n[3] = values[index] # 0,0,0
n[4] = values[index + nZ + 1] # 0,1,1
n[5] = values[index + nYZ + nZ + 1] # 1,1,1
n[6] = values[index + nYZ + 1] # 1,0,1
n[7] = values[index + 1] # 0,0,1
for i in range(7, -1, -1):
if n[i] > iso:
caseNumber += 1
if i > 0:
caseNumber = caseNumber << 1
# collecting the faces
offset = caseNumber * 15
for i in range(offset, offset + 15, 3):
if _faces[i] > -1:
vs = []
for j in range(i, i + 3):
v = switcher[_faces[j]]()
mesh.vertices.append(v)
vs.append(v)
if len(vs) == 3:
mesh.faces.append(Face(vs))
return mesh
def constructDodecahedron(cx,cy,cz,radius):
"""
Constructs a dodecaheron mesh.
Arguments:
----------
cx, cy, cz : float
The center point of the dodecaheron
radius : float
The radius of the containing sphere
"""
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]
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]]])
mesh.faces.append(f)
return mesh
