def construct_matrices(self):
"""
Construct FEM matrices
"""
V = p2e(self.vertices)
F = p2e(self.faces)
# Compute gradient operator: #F*3 by #V
G = igl.eigen.SparseMatrixd()
L = igl.eigen.SparseMatrixd()
M = igl.eigen.SparseMatrixd()
N = igl.eigen.MatrixXd()
A = igl.eigen.MatrixXd()
igl.grad(V, F, G)
igl.cotmatrix(V, F, L)
igl.per_face_normals(V, F, N)
igl.doublearea(V, F, A)
igl.massmatrix(V, F, igl.MASSMATRIX_TYPE_VORONOI, M)
G = e2p(G)
L = e2p(L)
N = e2p(N)
A = e2p(A)
M = e2p(M)
M = M.data
# Compute latitude and longitude directional vector fields
NS = np.reshape(G.dot(self.lat), [self.nf, 3], order='F')
EW = np.cross(NS, N)
# Compute F2V matrix (weigh by area)
# adjacency
i = self.faces.ravel()
j = np.arange(self.nf).repeat(3)
one = np.ones(self.nf * 3)
adj = sparse.csc_matrix((one, (i, j)), shape=(self.nv, self.nf))
tot_area = adj.dot(A)
norm_area = A.ravel().repeat(3) / np.squeeze(tot_area[i])
F2V = sparse.csc_matrix((norm_area, (i, j)), shape=(self.nv, self.nf))
# Compute interpolation matrix
if self.level > 0:
intp = self.intp[self.nv_prev:]
i = np.concatenate(
(np.arange(self.nv), np.arange(self.nv_prev, self.nv)))
j = np.concatenate((np.arange(self.nv_prev), intp[:, 0], intp[:,
1]))
ratio = np.concatenate(
(np.ones(self.nv_prev), 0.5 * np.ones(2 * intp.shape[0])))
intp = sparse.csc_matrix((ratio, (i, j)),
shape=(self.nv, self.nv_prev))
else:
intp = sparse.csc_matrix(np.eye(self.nv))
# Compute vertex mean matrix
self.G = G # gradient matrix
self.L = L # laplacian matrix
self.N = N # normal vectors (per-triangle)
self.NS = NS # north-south vectors (per-triangle)
self.EW = EW # east-west vectors (per-triangle)
self.F2V = F2V # map face quantities to vertices
self.M = M # mass matrix (area of voronoi cell around node. for integration)
self.Seq = self._rotseq(self.vertices)
self.Intp = intp
V = igl.eigen.MatrixXd() F = igl.eigen.MatrixXi() # Load a mesh in OFF format igl.readOFF(TUTORIAL_SHARED_PATH + "cheburashka.off", V, F) # Read scalar function values from a file, U: #V by 1 U = igl.eigen.MatrixXd() igl.readDMAT(TUTORIAL_SHARED_PATH + "cheburashka-scalar.dmat", U) U = U.col(0) # Compute gradient operator: #F*3 by #V G = igl.eigen.SparseMatrixd() igl.grad(V, F, G) # Compute gradient of U GU = (G * U).MapMatrix(F.rows(), 3) # Compute gradient magnitude GU_mag = GU.rowwiseNorm() viewer = igl.glfw.Viewer() viewer.data().set_mesh(V, F) # Compute pseudocolor for original function C = igl.eigen.MatrixXd() igl.jet(U, True, C)
L = igl.eigen.SparseMatrixd()
viewer = igl.viewer.Viewer()
# Load a mesh in OFF format
igl.readOFF("../../tutorial/shared/cow.off", V, F)
# Compute Laplace-Beltrami operator: #V by #V
igl.cotmatrix(V,F,L)
# Alternative construction of same Laplacian
G = igl.eigen.SparseMatrixd()
K = igl.eigen.SparseMatrixd()
# Gradient/Divergence
igl.grad(V,F,G);
# Diagonal per-triangle "mass matrix"
dblA = igl.eigen.MatrixXd()
igl.doublearea(V,F,dblA)
# Place areas along diagonal #dim times
T = (dblA.replicate(3,1)*0.5).asDiagonal() * 1
# Laplacian K built as discrete divergence of gradient or equivalently
# discrete Dirichelet energy Hessian
temp = -G.transpose()
K = -G.transpose() * T * G
print("|K-L|: ",(K-L).norm())
L = igl.eigen.SparseMatrixd()
viewer = igl.viewer.Viewer()
# Load a mesh in OFF format
igl.readOFF("../../tutorial/shared/cow.off", V, F)
# Compute Laplace-Beltrami operator: #V by #V
igl.cotmatrix(V, F, L)
# Alternative construction of same Laplacian
G = igl.eigen.SparseMatrixd()
K = igl.eigen.SparseMatrixd()
# Gradient/Divergence
igl.grad(V, F, G)
# Diagonal per-triangle "mass matrix"
dblA = igl.eigen.MatrixXd()
igl.doublearea(V, F, dblA)
# Place areas along diagonal #dim times
T = (dblA.replicate(3, 1) * 0.5).asDiagonal() * 1
# Laplacian K built as discrete divergence of gradient or equivalently
# discrete Dirichelet energy Hessian
temp = -G.transpose()
K = -G.transpose() * T * G
print("|K-L|: ", (K - L).norm())