def makeLaplacianMatrixSolverIGLHard(VPos, ITris, anchorsIdx):
VPosE = igl.eigen.MatrixXd(VPos)
ITrisE = igl.eigen.MatrixXi(ITris)
L = igl.eigen.SparseMatrixd()
M = igl.eigen.SparseMatrixd()
M_inv = igl.eigen.SparseMatrixd()
igl.cotmatrix(VPosE,ITrisE,L)
igl.massmatrix(VPosE,ITrisE,igl.MASSMATRIX_TYPE_VORONOI,M)
igl.invert_diag(M,M_inv)
L = M_inv*L
deltaCoords = L*VPosE
deltaCoords = np.array(deltaCoords)
#Bi-laplacian
Q = L.transpose()*L
viewer.data.set_mesh(V, F) viewer.core.show_lines = False viewer.callback_key_down = key_down # One fixed point on belly b = igl.eigen.MatrixXi([[2556]]) bc = igl.eigen.MatrixXd([[1]]) # Construct Laplacian and mass matrix L = igl.eigen.SparseMatrixd() M = igl.eigen.SparseMatrixd() Minv = igl.eigen.SparseMatrixd() igl.cotmatrix(V, F, L) igl.massmatrix(V, F, igl.MASSMATRIX_TYPE_VORONOI, M) igl.invert_diag(M, Minv) # Bi-Laplacian Q = L.transpose() * (Minv * L) # Zero linear term B = igl.eigen.MatrixXd.Zero(V.rows(), 1) # Lower and upper bound lx = igl.eigen.MatrixXd.Zero(V.rows(), 1) ux = igl.eigen.MatrixXd.Ones(V.rows(), 1) # Equality constraint constrain solution to sum to 1 Beq = igl.eigen.MatrixXd([[0.08]]) Aeq = M.diagonal().transpose().sparseView()
viewer.data.set_mesh(V, F) viewer.core.show_lines = False viewer.callback_key_down = key_down # One fixed point on belly b = igl.eigen.MatrixXi([[2556]]) bc = igl.eigen.MatrixXd([[1]]) # Construct Laplacian and mass matrix L = igl.eigen.SparseMatrixd() M = igl.eigen.SparseMatrixd() Minv = igl.eigen.SparseMatrixd() igl.cotmatrix(V,F,L) igl.massmatrix(V,F,igl.MASSMATRIX_TYPE_VORONOI,M); igl.invert_diag(M,Minv) # Bi-Laplacian Q = L.transpose() * (Minv * L) # Zero linear term B = igl.eigen.MatrixXd.Zero(V.rows(),1) # Lower and upper bound lx = igl.eigen.MatrixXd.Zero(V.rows(),1) ux = igl.eigen.MatrixXd.Ones(V.rows(),1) # Equality constraint constrain solution to sum to 1 Beq = igl.eigen.MatrixXd([[0.08]]) Aeq = M.diagonal().sparseView().transpose()
def makeLaplacianMatrixSolverIGLSoft(VPos, ITris, anchorsIdx, anchorWeights, makeSolver = True):
VPosE = igl.eigen.MatrixXd(VPos)
ITrisE = igl.eigen.MatrixXi(ITris)
'''
#Doing this check slows things down by more than a factor of 2 (convert to numpy to make faster?)
for f in range(ITrisE.rows()):
v_list = ITrisE.row(f)
v1 = VPosE.row(v_list[0])
v2 = VPosE.row(v_list[1])
v3 = VPosE.row(v_list[2])
if (v1-v2).norm() < 1e-10 and (v1-v3).norm() < 1e-10 and (v2-v3).norm() < 1e-10:
print 'zero area triangle!',f
'''
L = igl.eigen.SparseMatrixd()
M = igl.eigen.SparseMatrixd()
M_inv = igl.eigen.SparseMatrixd()
igl.cotmatrix(VPosE,ITrisE,L)
igl.massmatrix(VPosE,ITrisE,igl.MASSMATRIX_TYPE_VORONOI,M)
#np.set_printoptions(threshold='nan')
#print 'what is M?',M.diagonal()
igl.invert_diag(M,M_inv)
#L = M_inv*L
deltaCoords = (M_inv*L)*VPosE
#TODO: What to do with decaying_anchor_weights?
'''
anchor_dists = []
for i in range(VPosE.rows()):
anchor_dists.append(min([ (VPosE.row(i)-VPosE.row(j)).norm() for j in anchorsIdx ]))
max_anchor_dist = max(anchor_dists)
# assume linear weighting for anchor weights -> we are 0 at the anchors, anchorWeights at max_anchor_dist
decaying_anchor_weights = []
for anchor_dist in anchor_dists:
decaying_anchor_weights.append(anchorWeights*(anchor_dist/max_anchor_dist))
'''
solver = None
if makeSolver:
Q = L*(M_inv*M_inv)*L
#Now add in sparse constraints
diagTerms = igl.eigen.SparseMatrixd(VPos.shape[0], VPos.shape[0])
# anchor points
for a in anchorsIdx:
diagTerms.insert(a, a, anchorWeights)
# off points
'''
for adx,decay_weight in enumerate(decaying_anchor_weights):
if decay_weight == 0:
diagTerms.insert(adx, adx, anchorWeights)
else:
diagTerms.insert(adx, adx, decay_weight)
'''
Q = Q + diagTerms
Q.makeCompressed()
start_time = time.time()
solver = igl.eigen.SimplicialLLTsparse(Q)
#solver = igl.eigen.CholmodSupernodalLLT(Q)
end_time = time.time()
print 'factorization elapsed time:',end_time-start_time,'seconds'
return (L, M_inv, solver, np.array(deltaCoords))
