def laplacian_matrix(mesh):
n = mesh.num_vertices
#e = np.c_[mesh.faces[:,:2], mesh.faces[:,1:], mesh.faces[:,2], mesh.faces[:,0]]
e = mesh.edges
A = sp_matrix((n, n))
A[e[:, 0], e[:, 1]] = -1
D = sp_matrix(A.shape)
D.setdiag(np.sum(A, axis=1))
L = D - A
return L
def mass_matrix(mesh):
nv = mesh.num_vertices
mass = np.ones((nv))
for i in range(nv):
volumes = []
if mesh.mesh_is_volumetric:
if mesh.polys.shape[1] == 4:
_, volumes = tet_volume(mesh.vertices,
mesh.polys[mesh.adj_vtx2poly[i]])
else:
_, volumes = hex_volume(mesh.vertices,
mesh.polys[mesh.adj_vtx2poly[i]])
elif mesh.mesh_is_surface:
if (mesh.polys.shape[1] == 3):
_, volumes = triangle_area(mesh.vertices,
mesh.polys[mesh.adj_vtx2poly[i]])
else:
_, volumes = quad_area(mesh.vertices,
mesh.polys[mesh.adj_vtx2poly[i]])
mass[i] *= (np.sum(volumes) / volumes.shape[0])
MM = sp_matrix((nv, nv))
MM.setdiag(mass)
return MM
def mass_matrix(mesh):
nv = mesh.num_vertices
mass = np.ones((nv))
for i in range(nv):
volumes = []
if (hasattr(mesh, 'hexes')):
v2p = mesh.vtx2hex[i]
_, volumes = hex_volume(mesh.vertices, mesh.hexes[v2p])
elif (hasattr(mesh, 'tets')):
v2p = mesh.vtx2tet[i]
_, volumes = tet_volume(mesh.vertices, mesh.tets[v2p])
elif (hasattr(mesh, 'faces')):
v2p = mesh.vtx2face[i]
if (mesh.faces.shape[1] == 3):
_, volumes = triangle_area(mesh.vertices, mesh.faces[v2p])
else:
_, volumes = quad_area(mesh.vertices, mesh.faces[v2p])
mass[i] *= (np.sum(volumes) / volumes.shape[0])
MM = sp_matrix((nv, nv))
MM.setdiag(mass)
return MM
def adjacency_matrix(mesh, type='std'):
assert (type == 'std' or type == 'cot')
n = mesh.num_vertices
e = mesh.edges
A = sp_matrix((n, n), dtype=np.float64)
if type == 'std':
A[e[:, 0], e[:, 1]] = 1
A[e[:, 1], e[:, 0]] = 1
else:
raise NotImplementedError("not implemented yet")
return A
def degree_matrix(A):
D = sp_matrix(A.shape, dtype=np.float64)
D.setdiag(np.sum(A, axis=1))
return D