def compute_distortion_energies_3D(mesh):
if mesh.num_voxels > 0 and mesh.vertex_per_voxel != 4:
raise RuntimeError(
"Only tet mesh is supported for distortion computation")
regular_tet = pymesh.generate_regular_tetrahedron()
assembler = pymesh.Assembler(regular_tet)
G = assembler.assemble("gradient")
vertices = mesh.vertices
tets = mesh.voxels
Js = [G * vertices[tet] for tet in tets]
J_F = np.array([np.trace(np.dot(J.T, J)) for J in Js])
J_det = np.array([numpy.linalg.det(J) for J in Js])
invert_J = lambda args: np.full(
(3, 3), np.inf) if args[1] == 0 else numpy.linalg.inv(args[0])
J_inv = map(invert_J, zip(Js, J_det))
J_inv_F = np.array([np.trace(np.dot(Ji.T, Ji)) for Ji in J_inv])
conformal_amips = np.divide(J_F, np.cbrt(np.square(J_det)))
finite_conformal_amips = np.isfinite(conformal_amips)
symmetric_dirichlet = J_F + J_inv_F
finite_symmetric_dirichlet = np.isfinite(symmetric_dirichlet)
orientations = pymesh.get_tet_orientations(mesh)
orientations[orientations > 0] = 1
orientations[orientations < 0] = -1
num_degenerate_tets = np.count_nonzero(orientations == 0)
num_inverted_tets = np.count_nonzero(orientations < 0)
num_nonfinite_amips = np.count_nonzero(
np.logical_not(finite_conformal_amips))
num_nonfinite_dirichlet =\
np.count_nonzero(np.logical_not(finite_symmetric_dirichlet))
logger = logging.getLogger("Distorsion")
if num_degenerate_tets > 0:
logger.warn("degenerate tets: {}".format(num_degenerate_tets))
if num_inverted_tets > 0:
logger.warn("inverted tets: {}".format(num_inverted_tets))
if num_nonfinite_amips > 0:
logger.warn(
"Non-finite conformal AMIPS: {}".format(num_nonfinite_amips))
if num_nonfinite_dirichlet > 0:
logger.warn("Non-finite symmetric Dirichlet: {}".format(
num_nonfinite_dirichlet))
mesh.add_attribute("conformal_AMIPS")
mesh.set_attribute("conformal_AMIPS", conformal_amips)
mesh.add_attribute("finite_conformal_AMIPS")
mesh.set_attribute("finite_conformal_AMIPS", finite_conformal_amips)
mesh.add_attribute("symmetric_Dirichlet")
mesh.set_attribute("symmetric_Dirichlet", symmetric_dirichlet)
mesh.add_attribute("finite_symmetric_Dirichlet")
mesh.set_attribute("finite_symmetric_Dirichlet",
finite_symmetric_dirichlet)
mesh.add_attribute("orientations")
mesh.set_attribute("orientations", orientations)
def main():
args = parse_args()
basename, ext = os.path.splitext(args.output_mesh)
mesh = pymesh.load_mesh(args.input_mesh)
mesh = generate_tet_mesh(mesh)
pymesh.save_mesh("{}_source.msh".format(basename), mesh)
bd_vertex_indices, bd_vertex_positions = map_boundary_to_sphere(
mesh, basename)
out_mesh = tutte_3D(mesh, bd_vertex_indices, bd_vertex_positions)
tet_orientations = pymesh.get_tet_orientations(out_mesh)
out_mesh.add_attribute("orientation")
out_mesh.set_attribute("orientation", tet_orientations)
pymesh.save_mesh(args.output_mesh, out_mesh, "orientation")
def main():
args = parse_args();
basename, ext = os.path.splitext(args.output_mesh);
mesh = pymesh.load_mesh(args.input_mesh);
mesh = generate_tet_mesh(mesh);
pymesh.save_mesh("{}_source.msh".format(basename), mesh);
bd_vertex_indices, bd_vertex_positions = map_boundary_to_sphere(
mesh, basename);
out_mesh = tutte_3D(mesh, bd_vertex_indices, bd_vertex_positions);
tet_orientations = pymesh.get_tet_orientations(out_mesh);
out_mesh.add_attribute("orientation");
out_mesh.set_attribute("orientation", tet_orientations);
pymesh.save_mesh(args.output_mesh, out_mesh, "orientation");
def print_extended_info(mesh, info):
print_section_header("Extended info")
num_cc = mesh.num_components
num_f_cc = mesh.num_surface_components
if mesh.num_voxels > 0:
num_v_cc = mesh.num_volume_components
else:
num_v_cc = 0
isolated_vertices = mesh.num_isolated_vertices
duplicated_faces = mesh.num_duplicated_faces
unique_vertices = pymesh.unique_rows(mesh.vertices)[0]
duplicated_vertices = mesh.num_vertices - len(unique_vertices)
degenerated_indices = pymesh.get_degenerated_faces(mesh)
num_degenerated = len(degenerated_indices)
if num_degenerated > 0:
degenerated_faces = mesh.faces[degenerated_indices]
combinatorially_degenerated_faces = \
[f for f in degenerated_faces if len(set(f)) != len(f) ]
num_combinatorial_degenerated_faces =\
len(combinatorially_degenerated_faces)
else:
num_combinatorial_degenerated_faces = 0
print_property("num connected components", num_cc)
print_property("num connected surface components", num_f_cc)
print_property("num connected volume components", num_v_cc)
print_property("num isolated vertices", isolated_vertices, 0)
print_property("num duplicated vertices", duplicated_vertices, 0)
print_property("num duplicated faces", duplicated_faces, 0)
print_property("num boundary edges", mesh.num_boundary_edges)
print_property("num boundary loops", mesh.num_boundary_loops)
print_property("num degenerated faces", num_degenerated, 0)
if num_degenerated > 0:
print_property(" combinatorially degenerated",
num_combinatorial_degenerated_faces, 0)
print_property(" geometrically degenerated",
num_degenerated - num_combinatorial_degenerated_faces,
0)
info["num_connected_components"] = num_cc
info["num_connected_surface_components"] = num_f_cc
info["num_connected_volume_components"] = num_v_cc
info["num_isolated_vertices"] = isolated_vertices
info["num_duplicated_vertices"] = duplicated_vertices
info["num_duplicated_faces"] = duplicated_faces
info["num_boundary_edges"] = mesh.num_boundary_edges
info["num_boundary_loops"] = mesh.num_boundary_loops
info["num_degenerated_faces"] = num_degenerated
info["num_combinatorial_degenerated_faces"] =\
num_combinatorial_degenerated_faces
info["num_geometrical_degenerated_faces"] =\
num_degenerated - num_combinatorial_degenerated_faces
if mesh.dim == 2 and mesh.vertex_per_face == 3:
tri_orientations = pymesh.get_triangle_orientations(mesh)
num_inverted_tris = np.sum(tri_orientations < 0)
print_property("num inverted triangles:", num_inverted_tris, 0)
info["num_inverted_triangles"] = int(num_inverted_tris)
if mesh.num_voxels > 0 and mesh.vertex_per_voxel == 4:
tet_orientations = pymesh.get_tet_orientations(mesh)
num_degenerate_tets = np.sum(tet_orientations == 0)
num_inverted_tets = np.sum(tet_orientations < 0)
print_property("num degenerated tets:", num_degenerate_tets, 0)
print_property("num inverted tets:", num_inverted_tets, 0)
info["num_degenerated_tets"] = int(num_degenerate_tets)
info["num_inverted_tets"] = int(num_inverted_tets)
is_closed = mesh.is_closed()
is_edge_manifold = mesh.is_edge_manifold()
is_vertex_manifold = mesh.is_vertex_manifold()
is_oriented = mesh.is_oriented()
euler = mesh.euler_characteristic
print_property("oriented", is_oriented, True)
print_property("closed", is_closed, True)
print_property("edge manifold", is_edge_manifold, True)
print_property("vertex manifold", is_vertex_manifold, True)
print_property("euler characteristic", euler)
info["oriented"] = is_oriented
info["closed"] = is_closed
info["vertex_manifold"] = is_vertex_manifold
info["edge_manifold"] = is_edge_manifold
info["euler_characteristic"] = euler
def print_extended_info(mesh, info):
print_section_header("Extended info");
num_cc = mesh.num_components;
num_f_cc = mesh.num_surface_components;
if mesh.num_voxels > 0:
num_v_cc = mesh.num_volume_components;
else:
num_v_cc = 0;
isolated_vertices = mesh.num_isolated_vertices;
duplicated_faces = mesh.num_duplicated_faces;
degenerated_indices = pymesh.get_degenerated_faces(mesh);
num_degenerated = len(degenerated_indices);
if num_degenerated > 0:
degenerated_faces = mesh.faces[degenerated_indices];
combinatorially_degenerated_faces = \
[f for f in degenerated_faces if len(set(f)) != len(f) ];
num_combinatorial_degenerated_faces =\
len(combinatorially_degenerated_faces);
else:
num_combinatorial_degenerated_faces = 0;
print_property("num connected components", num_cc);
print_property("num connected surface components", num_f_cc);
print_property("num connected volume components", num_v_cc);
print_property("num isolated vertices", isolated_vertices, 0);
print_property("num duplicated faces", duplicated_faces, 0);
print_property("num boundary edges", mesh.num_boundary_edges);
print_property("num boundary loops", mesh.num_boundary_loops);
print_property("num degenerated faces", num_degenerated, 0)
if num_degenerated > 0:
print_property(" combinatorially degenerated",
num_combinatorial_degenerated_faces, 0);
print_property(" geometrically degenerated",
num_degenerated - num_combinatorial_degenerated_faces, 0);
info["num_connected_components"] = num_cc;
info["num_connected_surface_components"] = num_f_cc;
info["num_connected_volume_components"] = num_v_cc;
info["num_isolated_vertices"] = isolated_vertices;
info["num_duplicated_faces"] = duplicated_faces;
info["num_boundary_edges"] = mesh.num_boundary_edges;
info["num_boundary_loops"] = mesh.num_boundary_loops;
info["num_degenerated_faces"] = num_degenerated;
info["num_combinatorial_degenerated_faces"] =\
num_combinatorial_degenerated_faces;
info["num_geometrical_degenerated_faces"] =\
num_degenerated - num_combinatorial_degenerated_faces;
if mesh.num_voxels > 0 and mesh.vertex_per_voxel == 4:
tet_orientations = pymesh.get_tet_orientations(mesh);
num_degenerate_tets = np.sum(tet_orientations == 0);
num_inverted_tets = np.sum(tet_orientations < 0);
print_property("num degenerated tets:", num_degenerate_tets, 0);
print_property("num inverted tets:", num_inverted_tets, 0);
info["num_degenerated_tets"] = int(num_degenerate_tets);
info["num_inverted_tets"] = int(num_inverted_tets);
is_closed = mesh.is_closed();
is_edge_manifold = mesh.is_edge_manifold();
is_vertex_manifold = mesh.is_vertex_manifold();
is_oriented = mesh.is_oriented();
euler = mesh.euler_characteristic;
print_property("oriented", is_oriented, True);
print_property("closed", is_closed, True)
print_property("edge manifold", is_edge_manifold, True);
print_property("vertex manifold", is_vertex_manifold, True);
print_property("euler characteristic", euler);
info["oriented"] = is_oriented;
info["closed"] = is_closed;
info["vertex_manifold"] = is_vertex_manifold;
info["edge_manifold"] = is_edge_manifold;
info["euler_characteristic"] = euler;
def print_extended_info(mesh, info):
print_section_header("Extended info");
num_cc = mesh.num_components;
num_f_cc = mesh.num_surface_components;
if mesh.num_voxels > 0:
num_v_cc = mesh.num_volume_components;
else:
num_v_cc = 0;
isolated_vertices = mesh.num_isolated_vertices;
duplicated_faces = mesh.num_duplicated_faces;
unique_vertices = pymesh.unique_rows(mesh.vertices)[0];
duplicated_vertices = mesh.num_vertices - len(unique_vertices);
degenerated_indices = pymesh.get_degenerated_faces(mesh);
num_degenerated = len(degenerated_indices);
if num_degenerated > 0:
degenerated_faces = mesh.faces[degenerated_indices];
combinatorially_degenerated_faces = \
[f for f in degenerated_faces if len(set(f)) != len(f) ];
num_combinatorial_degenerated_faces =\
len(combinatorially_degenerated_faces);
else:
num_combinatorial_degenerated_faces = 0;
print_property("num connected components", num_cc);
print_property("num connected surface components", num_f_cc);
print_property("num connected volume components", num_v_cc);
print_property("num isolated vertices", isolated_vertices, 0);
print_property("num duplicated vertices", duplicated_vertices, 0);
print_property("num duplicated faces", duplicated_faces, 0);
print_property("num boundary edges", mesh.num_boundary_edges);
print_property("num boundary loops", mesh.num_boundary_loops);
print_property("num degenerated faces", num_degenerated, 0)
if num_degenerated > 0:
print_property(" combinatorially degenerated",
num_combinatorial_degenerated_faces, 0);
print_property(" geometrically degenerated",
num_degenerated - num_combinatorial_degenerated_faces, 0);
info["num_connected_components"] = num_cc;
info["num_connected_surface_components"] = num_f_cc;
info["num_connected_volume_components"] = num_v_cc;
info["num_isolated_vertices"] = isolated_vertices;
info["num_duplicated_vertices"] = duplicated_vertices;
info["num_duplicated_faces"] = duplicated_faces;
info["num_boundary_edges"] = mesh.num_boundary_edges;
info["num_boundary_loops"] = mesh.num_boundary_loops;
info["num_degenerated_faces"] = num_degenerated;
info["num_combinatorial_degenerated_faces"] =\
num_combinatorial_degenerated_faces;
info["num_geometrical_degenerated_faces"] =\
num_degenerated - num_combinatorial_degenerated_faces;
if mesh.dim == 2 and mesh.vertex_per_face == 3:
tri_orientations = pymesh.get_triangle_orientations(mesh);
num_inverted_tris = np.sum(tri_orientations < 0);
print_property("num inverted triangles:", num_inverted_tris, 0);
info["num_inverted_triangles"] = int(num_inverted_tris);
if mesh.num_voxels > 0 and mesh.vertex_per_voxel == 4:
tet_orientations = pymesh.get_tet_orientations(mesh);
num_degenerate_tets = np.sum(tet_orientations == 0);
num_inverted_tets = np.sum(tet_orientations < 0);
print_property("num degenerated tets:", num_degenerate_tets, 0);
print_property("num inverted tets:", num_inverted_tets, 0);
info["num_degenerated_tets"] = int(num_degenerate_tets);
info["num_inverted_tets"] = int(num_inverted_tets);
is_closed = mesh.is_closed();
is_edge_manifold = mesh.is_edge_manifold();
is_vertex_manifold = mesh.is_vertex_manifold();
is_oriented = mesh.is_oriented();
euler = mesh.euler_characteristic;
print_property("oriented", is_oriented, True);
print_property("closed", is_closed, True)
print_property("edge manifold", is_edge_manifold, True);
print_property("vertex manifold", is_vertex_manifold, True);
print_property("euler characteristic", euler);
info["oriented"] = is_oriented;
info["closed"] = is_closed;
info["vertex_manifold"] = is_vertex_manifold;
info["edge_manifold"] = is_edge_manifold;
info["euler_characteristic"] = euler;
