def plot_mesh_nrosy(viewer, V, F, N, PD1, S, b):
# Clear the mesh
viewer.data.clear()
viewer.data.set_mesh(V, F)
# Expand the representative vectors in the full vector set and plot them as lines
avg = igl.avg_edge_length(V, F)
Y = igl.eigen.MatrixXd()
representative_to_nrosy(V, F, PD1, N, Y)
B = igl.eigen.MatrixXd()
igl.barycenter(V, F, B)
Be = igl.eigen.MatrixXd(B.rows() * N, 3)
for i in range(0, B.rows()):
for j in range(0, N):
Be.setRow(i * N + j, B.row(i))
viewer.data.add_edges(Be, Be + Y * (avg / 2), igl.eigen.MatrixXd([[0, 0, 1]]))
# Plot the singularities as colored dots (red for negative, blue for positive)
for i in range(0, S.size()):
if S[i] < -0.001:
viewer.data.add_points(V.row(i), igl.eigen.MatrixXd([[1, 0, 0]]))
elif S[i] > 0.001:
viewer.data.add_points(V.row(i), igl.eigen.MatrixXd([[0, 1, 0]]));
# Highlight in red the constrained faces
C = igl.eigen.MatrixXd.Constant(F.rows(), 3, 1)
for i in range(0, b.size()):
C.setRow(b[i], igl.eigen.MatrixXd([[1, 0, 0]]))
viewer.data.set_colors(C)
def key_pressed(viewer, key, modifier):
global V
global U
global F
global L
if key == ord('r') or key == ord('R'):
U = V
elif key == ord(' '):
# Recompute just mass matrix on each step
M = igl.eigen.SparseMatrixd()
igl.massmatrix(U, F, igl.MASSMATRIX_TYPE_BARYCENTRIC, M)
# Solve (M-delta*L) U = M*U
S = (M - 0.001 * L)
solver = igl.eigen.SimplicialLLTsparse(S)
U = solver.solve(M * U)
# Compute centroid and subtract (also important for numerics)
dblA = igl.eigen.MatrixXd()
igl.doublearea(U, F, dblA)
print(dblA.sum())
area = 0.5 * dblA.sum()
BC = igl.eigen.MatrixXd()
igl.barycenter(U, F, BC)
centroid = igl.eigen.MatrixXd([[0.0, 0.0, 0.0]])
for i in range(0, BC.rows()):
centroid += 0.5 * dblA[i, 0] / area * BC.row(i)
U -= centroid.replicate(U.rows(), 1)
# Normalize to unit surface area (important for numerics)
U = U / math.sqrt(area)
else:
return False
# Send new positions, update normals, recenter
viewer.data.set_vertices(U)
viewer.data.compute_normals()
viewer.core.align_camera_center(U, F)
return True
def key_pressed(viewer, key, modifier):
global V
global U
global F
global L
if key == ord('r') or key == ord('R'):
U = V;
elif key == ord(' '):
# Recompute just mass matrix on each step
M = igl.eigen.SparseMatrixd()
igl.massmatrix(U,F,igl.MASSMATRIX_TYPE_BARYCENTRIC,M);
# Solve (M-delta*L) U = M*U
S = (M - 0.001*L)
solver = igl.eigen.SimplicialLLTsparse(S)
U = solver.solve(M*U)
# Compute centroid and subtract (also important for numerics)
dblA = igl.eigen.MatrixXd()
igl.doublearea(U,F,dblA)
print(dblA.sum())
area = 0.5*dblA.sum()
BC = igl.eigen.MatrixXd()
igl.barycenter(U,F,BC)
centroid = igl.eigen.MatrixXd([[0.0,0.0,0.0]])
for i in range(0,BC.rows()):
centroid += 0.5*dblA[i,0]/area*BC.row(i)
U -= centroid.replicate(U.rows(),1)
# Normalize to unit surface area (important for numerics)
U = U / math.sqrt(area)
else:
return False
# Send new positions, update normals, recenter
viewer.data.set_vertices(U)
viewer.data.compute_normals()
viewer.core.align_camera_center(U,F)
return True
viewer.data().show_texture = True
viewer.data().set_colors(igl.eigen.MatrixXd([[1, 1, 1]]))
viewer.data().set_texture(texture_R, texture_B, texture_G)
viewer.core.align_camera_center(viewer.data().V, viewer.data().F)
return False
# Load a mesh in OFF format
igl.readOFF(TUTORIAL_SHARED_PATH + "3holes.off", V, F)
# Compute face barycenters
igl.barycenter(V, F, B)
# Compute scale for visualizing fields
global_scale = .5 * igl.avg_edge_length(V, F)
# Contrain one face
b = igl.eigen.MatrixXd([[0]]).castint()
bc = igl.eigen.MatrixXd([[1, 0, 0]])
# Create a smooth 4-RoSy field
S = igl.eigen.MatrixXd()
igl.comiso.nrosy(V, F, b, bc, igl.eigen.MatrixXi(), igl.eigen.MatrixXd(), igl.eigen.MatrixXd(), 4, 0.5, X1, S)
# Find the orthogonal vector
B1 = igl.eigen.MatrixXd()
viewer.core.show_texture = True
viewer.data.set_colors(igl.eigen.MatrixXd([[1, 1, 1]]))
viewer.data.set_texture(texture_R, texture_B, texture_G)
viewer.core.align_camera_center(viewer.data.V, viewer.data.F)
return False
# Load a mesh in OFF format
igl.readOFF(TUTORIAL_SHARED_PATH + "3holes.off", V, F)
# Compute face barycenters
igl.barycenter(V, F, B)
# Compute scale for visualizing fields
global_scale = .5 * igl.avg_edge_length(V, F)
# Contrain one face
b = igl.eigen.MatrixXi([[0]])
bc = igl.eigen.MatrixXd([[1, 0, 0]])
# Create a smooth 4-RoSy field
S = igl.eigen.MatrixXd()
igl.comiso.nrosy(V, F, b, bc, igl.eigen.MatrixXi(), igl.eigen.MatrixXd(), igl.eigen.MatrixXd(), 4, 0.5, X1, S)
# Find the the orthogonal vector
B1 = igl.eigen.MatrixXd()
# 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) # Or for gradient magnitude # igl.jet(GU_mag,True,C) viewer.data().set_colors(C) # Average edge length divided by average gradient (for scaling) max_size = igl.avg_edge_length(V, F) / GU_mag.mean() # Draw a black segment in direction of gradient at face barycenters BC = igl.eigen.MatrixXd() igl.barycenter(V, F, BC) black = igl.eigen.MatrixXd([[0.0, 0.0, 0.0]]) viewer.data().add_edges(BC, BC + max_size * GU, black) # Hide wireframe viewer.data().show_lines = False viewer.launch()
from shared import TUTORIAL_SHARED_PATH, check_dependencies dependencies = ["viewer"] check_dependencies(dependencies) V = igl.eigen.MatrixXd() F = igl.eigen.MatrixXi() igl.readOFF(TUTORIAL_SHARED_PATH + "decimated-knight.off", V, F) # Sort barycenters lexicographically BC = igl.eigen.MatrixXd() sorted_BC = igl.eigen.MatrixXd() igl.barycenter(V, F, BC) I = igl.eigen.MatrixXi() J = igl.eigen.MatrixXi() # sorted_BC = BC(I,:) igl.sortrows(BC, True, sorted_BC, I) # Get sorted "place" from sorted indices J.resize(I.rows(), 1) # J(I) = 1:numel(I) igl.slice_into(igl.coloni(0, I.size() - 1), I, J) # Pseudo-color based on sorted place C = igl.eigen.MatrixXd()
V = igl.eigen.MatrixXd()
BC = igl.eigen.MatrixXd()
W = igl.eigen.MatrixXd()
T = igl.eigen.MatrixXi()
F = igl.eigen.MatrixXi()
G = igl.eigen.MatrixXi()
slice_z = 0.5
overlay = 0
# Load mesh: (V,T) tet-mesh of convex hull, F contains facets of input
# surface mesh _after_ self-intersection resolution
igl.readMESH(TUTORIAL_SHARED_PATH + "big-sigcat.mesh", V, T, F)
# Compute barycenters of all tets
igl.barycenter(V, T, BC)
# Compute generalized winding number at all barycenters
print("Computing winding number over all %i tets..." % T.rows())
igl.winding_number(V, F, BC, W)
# Extract interior tets
Wt = sum(W > 0.5)
CT = igl.eigen.MatrixXi(Wt, 4)
k = 0
for t in range(T.rows()):
if W[t] > 0.5:
CT.setRow(k, T.row(t))
k += 1
# find bounary facets of interior tets
V_temp.setRow(i * 4 + 3, TV.row(TT[s[i], 3]))
F_temp.setRow(i * 4 + 0, igl.eigen.MatrixXd([[(i*4)+0, (i*4)+1, (i*4)+3]]).castint())
F_temp.setRow(i * 4 + 1, igl.eigen.MatrixXd([[(i*4)+0, (i*4)+2, (i*4)+1]]).castint())
F_temp.setRow(i * 4 + 2, igl.eigen.MatrixXd([[(i*4)+3, (i*4)+2, (i*4)+0]]).castint())
F_temp.setRow(i * 4 + 3, igl.eigen.MatrixXd([[(i*4)+1, (i*4)+2, (i*4)+3]]).castint())
viewer.data().clear()
viewer.data().set_mesh(V_temp, F_temp)
viewer.data().set_face_based(True)
else:
return False
return True
# Load a surface mesh
igl.readOFF(TUTORIAL_SHARED_PATH + "fertility.off", V, F)
# Tetrahedralize the interior
igl.tetgen.tetrahedralize(V, F, "pq1.414Y", TV, TT, TF)
# Compute barycenters
igl.barycenter(TV, TT, B)
# Plot the generated mesh
key_down(viewer, ord('5'), 0)
viewer.callback_key_down = key_down
viewer.launch()
V = igl.eigen.MatrixXd()
BC = igl.eigen.MatrixXd()
W = igl.eigen.MatrixXd()
T = igl.eigen.MatrixXi()
F = igl.eigen.MatrixXi()
G = igl.eigen.MatrixXi()
slice_z = 0.5
overlay = 0
# Load mesh: (V,T) tet-mesh of convex hull, F contains facets of input
# surface mesh _after_ self-intersection resolution
igl.readMESH(TUTORIAL_SHARED_PATH + "big-sigcat.mesh", V, T, F)
# Compute barycenters of all tets
igl.barycenter(V, T, BC)
# Compute generalized winding number at all barycenters
print("Computing winding number over all %i tets..." % T.rows())
igl.winding_number(V, F, BC, W)
# Extract interior tets
Wt = sum(W > 0.5)
CT = igl.eigen.MatrixXi(Wt, 4)
k = 0
for t in range(T.rows()):
if W[t] > 0.5:
CT.setRow(k, T.row(t))
k += 1
# find bounary facets of interior tets
igl.eigen.MatrixXd([[(i * 4) + 3, (i * 4) + 2,
(i * 4) + 0]]).castint())
F_temp.setRow(
i * 4 + 3,
igl.eigen.MatrixXd([[(i * 4) + 1, (i * 4) + 2,
(i * 4) + 3]]).castint())
viewer.data().clear()
viewer.data().set_mesh(V_temp, F_temp)
viewer.data().set_face_based(True)
else:
return False
return True
# Load a surface mesh
igl.readOFF(TUTORIAL_SHARED_PATH + "fertility.off", V, F)
# Tetrahedralize the interior
igl.tetgen.tetrahedralize(V, F, "pq1.414Y", TV, TT, TF)
# Compute barycenters
igl.barycenter(TV, TT, B)
# Plot the generated mesh
key_down(viewer, ord('5'), 0)
viewer.callback_key_down = key_down
viewer.launch()
