def mesh_geodesic_distances(mesh, sources, m=1.0):
Lc = trimesh_cotangent_laplacian_matrix(mesh)
key_index = mesh.key_index()
vertices = mesh.get_vertices_attributes('xyz')
faces = [[key_index[key] for key in mesh.face_vertices(fkey)] for fkey in mesh.faces()]
V = array(vertices)
F = array(faces, dtype=int)
# Laplacian matrix with symmetric cotangent weights
# W = empty(0)
# I = empty(0, dtype=int)
# J = empty(0, dtype=int)
# for i1, i2, i3 in [(0, 1, 2), (1, 2, 0), (2, 0, 1)]:
# v1 = F[:, i1]
# v2 = F[:, i2]
# v3 = F[:, i3]
# e1 = V[v2] - V[v1]
# e2 = V[v3] - V[v1]
# cotan = 0.5 * sum(e1 * e2, axis=1) / normrow(cross(e1, e2)).ravel()
# W = append(W, cotan)
# I = append(I, v2)
# J = append(J, v3)
# W = append(W, cotan)
# I = append(I, v3)
# J = append(J, v2)
# Lc = csr_matrix((W, (I, J)), shape=(V.shape[0], V.shape[0]))
# Lc = Lc - spdiags(Lc * ones(V.shape[0]), 0, V.shape[0], V.shape[0])
# Step I
# Heat *u* is allowed to diffuse for a brief period of time (t)
e01 = V[F[:, 1]] - V[F[:, 0]]
e12 = V[F[:, 2]] - V[F[:, 1]]
e20 = V[F[:, 0]] - V[F[:, 2]]
normal = cross(e01, e12)
A2 = normrow(normal)
A3 = A2.ravel() / 6
VA = zeros(V.shape[0])
for i in (0, 1, 2):
b = bincount(F[:, i], A3)
VA[:len(b)] += b
VA = spdiags(VA, 0, V.shape[0], V.shape[0])
h = mean([normrow(e01), normrow(e12), normrow(e20)])
t = m * h ** 2
u0 = zeros(V.shape[0])
u0[sources] = 1.0
A = VA - t * Lc
print(A.sum(axis=1))
u = splu((VA - t * Lc).tocsc()).solve(u0)
# u = spsolve(VA - t * Lc, u0)
# A = VA - t * Lc
# b = u0
# u = spsolve(A.transpose().dot(A), A.transpose().dot(b))
unit = normal / A2
unit_e01 = cross(unit, e01)
unit_e12 = cross(unit, e12)
unit_e20 = cross(unit, e20)
grad_u = (
unit_e01 * u[F[:, 2], None] +
unit_e12 * u[F[:, 0], None] +
unit_e20 * u[F[:, 1], None]
) / A2
X = - grad_u / normrow(grad_u)
div_X = zeros(V.shape[0])
for i1, i2, i3 in [(0, 1, 2), (1, 2, 0), (2, 0, 1)]:
v1 = F[:, i1]
v2 = F[:, i2]
v3 = F[:, i3]
e1 = V[v2] - V[v1]
e2 = V[v3] - V[v1]
e0 = V[v3] - V[v2]
a = 1 / tan(arccos(sum(normalizerow(-e2) * normalizerow(-e0), axis=1)))
b = 1 / tan(arccos(sum(normalizerow(-e1) * normalizerow(+e0), axis=1)))
div_X += bincount(
v1,
0.5 * (a * sum(e1 * X, axis=1) + b * sum(e2 * X, axis=1)),
minlength=V.shape[0]
)
print(Lc.sum(axis=1))
phi = splu(Lc.tocsc()).solve(div_X)
# phi = spsolve(Lc, div_X)
# A = Lc
# b = div_X
# phi = spsolve(A.transpose().dot(A), A.transpose().dot(b))
phi -= phi.min()
return phi
def mesh_geodesic_distances(mesh, sources, m=1.0):
"""Compute geodesic from the vertices of a mesh to given source vertices.
Parameters
----------
mesh : compas.datastructures.Mesh
A mesh instance.
sources : list
A list of vertex identifiers from which the distances should be calculated.
m : float (1.0)
?
Returns
-------
array
Distance values.
"""
Lc = trimesh_cotangent_laplacian_matrix(mesh)
key_index = mesh.key_index()
vertices = mesh.get_vertices_attributes('xyz')
faces = [[key_index[key] for key in mesh.face_vertices(fkey)]
for fkey in mesh.faces()]
V = array(vertices)
F = array(faces, dtype=int)
e01 = V[F[:, 1]] - V[F[:, 0]]
e12 = V[F[:, 2]] - V[F[:, 1]]
e20 = V[F[:, 0]] - V[F[:, 2]]
normal = cross(e01, e12)
A2 = normrow(normal)
A3 = A2.ravel() / 6
VA = zeros(V.shape[0])
for i in (0, 1, 2):
b = bincount(F[:, i], A3)
VA[:len(b)] += b
VA = spdiags(VA, 0, V.shape[0], V.shape[0])
h = mean([normrow(e01), normrow(e12), normrow(e20)])
t = m * h**2
u0 = zeros(V.shape[0])
u0[sources] = 1.0
# A = VA - t * Lc
# print(A.sum(axis=1))
u = splu((VA - t * Lc).tocsc()).solve(u0)
unit = normal / A2
unit_e01 = cross(unit, e01)
unit_e12 = cross(unit, e12)
unit_e20 = cross(unit, e20)
grad_u = (unit_e01 * u[F[:, 2], None] + unit_e12 * u[F[:, 0], None] +
unit_e20 * u[F[:, 1], None]) / A2
X = -grad_u / normrow(grad_u)
div_X = zeros(V.shape[0])
for i1, i2, i3 in [(0, 1, 2), (1, 2, 0), (2, 0, 1)]:
v1 = F[:, i1]
v2 = F[:, i2]
v3 = F[:, i3]
e1 = V[v2] - V[v1]
e2 = V[v3] - V[v1]
e0 = V[v3] - V[v2]
a = 1 / tan(arccos(sum(normalizerow(-e2) * normalizerow(-e0), axis=1)))
b = 1 / tan(arccos(sum(normalizerow(-e1) * normalizerow(+e0), axis=1)))
div_X += bincount(v1,
0.5 *
(a * sum(e1 * X, axis=1) + b * sum(e2 * X, axis=1)),
minlength=V.shape[0])
# print(Lc.sum(axis=1))
phi = splu(Lc.tocsc()).solve(div_X)
phi -= phi.min()
return phi