VectorF convert_voxel_attribute_to_vertex_attribute(
Mesh& mesh, const VectorF& attribute) {
const size_t num_vertices = mesh.get_num_vertices();
const size_t vertex_per_voxel = mesh.get_vertex_per_voxel();
const size_t num_voxels = mesh.get_num_voxels();
const size_t attr_size = attribute.size();
const size_t stride = attr_size / num_voxels;
const VectorI& voxels = mesh.get_voxels();
if (!mesh.has_attribute("voxel_volume")) {
mesh.add_attribute("voxel_volume");
}
const VectorF& weights = mesh.get_attribute("voxel_volume");
VectorF result = VectorF::Zero(num_vertices * stride);
VectorF result_weights = VectorF::Zero(num_vertices);
for (size_t i=0; i<num_voxels; i++) {
const VectorI& voxel =
voxels.segment(i*vertex_per_voxel, vertex_per_voxel);
Float per_vertex_weight = weights[i] / vertex_per_voxel;
for (size_t j=0; j<vertex_per_voxel; j++) {
result_weights[voxel[j]] += per_vertex_weight;
result.segment(voxel[j]*stride, stride) +=
per_vertex_weight * attribute.segment(i*stride, stride);
}
}
for (size_t i=0; i<num_vertices; i++) {
result.segment(i*stride, stride) /= result_weights[i];
}
return result;
}
VectorF convert_face_attribute_to_vertex_attribute(
Mesh& mesh, const VectorF& attribute) {
const size_t num_vertices = mesh.get_num_vertices();
const size_t vertex_per_face = mesh.get_vertex_per_face();
const size_t num_faces = mesh.get_num_faces();
const size_t attr_size = attribute.size();
const size_t stride = attr_size / num_faces;
const VectorI& faces = mesh.get_faces();
const VectorF& weights = mesh.get_attribute("face_area");
VectorF result = VectorF::Zero(num_vertices * stride);
VectorF result_weights = VectorF::Zero(num_vertices);
for (size_t i=0; i<num_faces; i++) {
const VectorI& face =
faces.segment(i*vertex_per_face, vertex_per_face);
Float per_vertex_weight = weights[i] / vertex_per_face;
for (size_t j=0; j<vertex_per_face; j++) {
result_weights[face[j]] += per_vertex_weight;
result.segment(face[j]*stride, stride) +=
per_vertex_weight * attribute.segment(i*stride, stride);
}
}
for (size_t i=0; i<num_vertices; i++) {
result.segment(i*stride, stride) /= result_weights[i];
}
return result;
}
void correct_tet_orientation(const VectorF& vertices, VectorI& voxels) {
const size_t num_voxels = voxels.size() / 4;
for (size_t i=0; i<num_voxels; i++) {
const VectorI tet = voxels.segment(i*4, 4);
const Vector3F& v1 = vertices.segment(tet[0]*3, 3);
const Vector3F& v2 = vertices.segment(tet[1]*3, 3);
const Vector3F& v3 = vertices.segment(tet[2]*3, 3);
const Vector3F& v4 = vertices.segment(tet[3]*3, 3);
if (!positive_orientated(v1, v2, v3, v4)) {
voxels[i*4] = tet[1];
voxels[i*4+1] = tet[0];
}
}
}
void VertexIsotropicOffsetParameter::apply(VectorF& results,
const PatternParameter::Variables& vars) {
const size_t dim = m_wire_network->get_dim();
const size_t num_vertices = m_wire_network->get_num_vertices();
const size_t roi_size = m_roi.size();
const VectorF center = m_wire_network->center();
const VectorF bbox_max = m_wire_network->get_bbox_max();
assert(results.size() == dim * num_vertices);
assert(roi_size == m_transforms.size());
if (m_formula != "") evaluate_formula(vars);
const MatrixFr& vertices = m_wire_network->get_vertices();
size_t seed_vertex_index = m_roi.minCoeff();
VectorF seed_vertex = vertices.row(seed_vertex_index);
VectorF seed_offset = VectorF::Zero(dim);
seed_offset = (bbox_max - center).cwiseProduct(m_dof_dir) * m_value;
for (size_t i=0; i<roi_size; i++) {
size_t v_idx = m_roi[i];
assert(v_idx < num_vertices);
const MatrixF& trans = m_transforms[i];
results.segment(v_idx*dim, dim) += trans * seed_offset;
}
}
VectorF convert_vertex_attribute_to_voxel_attribute(Mesh& mesh,
const VectorF& attribute) {
const size_t num_vertices = mesh.get_num_vertices();
const size_t num_voxels = mesh.get_num_voxels();
const size_t vertex_per_voxel = mesh.get_vertex_per_voxel();
const size_t attr_size = attribute.size();
const size_t stride = attr_size / num_vertices;
const VectorI& voxels = mesh.get_voxels();
VectorF result = VectorF::Zero(num_voxels * stride);
for (size_t i=0; i<num_voxels; i++) {
const VectorI& voxel = voxels.segment(i*vertex_per_voxel,
vertex_per_voxel);
for (size_t j=0; j<vertex_per_voxel; j++) {
result.segment(i*stride, stride) +=
attribute.segment(voxel[j]*stride, stride);
}
}
result /= vertex_per_voxel;
return result;
}
VectorF convert_vertex_attribute_to_face_attribute(Mesh& mesh,
const VectorF& attribute) {
const size_t num_vertices = mesh.get_num_vertices();
const size_t num_faces = mesh.get_num_faces();
const size_t vertex_per_face = mesh.get_vertex_per_face();
const size_t attr_size = attribute.size();
const size_t stride = attr_size / num_vertices;
const VectorI& faces = mesh.get_faces();
VectorF result = VectorF::Zero(num_faces * stride);
for (size_t i=0; i<num_faces; i++) {
const VectorI& face = faces.segment(i*vertex_per_face,
vertex_per_face);
for (size_t j=0; j<vertex_per_face; j++) {
result.segment(i*stride, stride) +=
attribute.segment(face[j]*stride, stride);
}
}
result /= vertex_per_face;
return result;
}
VectorF convert_voxel_attribute_to_face_attribute(
Mesh& mesh, const VectorF& attribute) {
const size_t num_faces = mesh.get_num_faces();
const size_t num_voxels = mesh.get_num_voxels();
const size_t attr_size = attribute.size();
const size_t stride = attr_size / num_voxels;
const size_t vertex_per_voxel = mesh.get_vertex_per_voxel();
const size_t vertex_per_face = mesh.get_vertex_per_face();
if (vertex_per_voxel != 4)
throw NotImplementedError("Voxel type is not yet supported");
if (vertex_per_face != 3)
throw NotImplementedError("Face type is not yet supported");
const VectorI& faces = mesh.get_faces();
const VectorI& voxels = mesh.get_voxels();
std::map<Triplet, VectorF> per_face_values;
for (size_t i=0; i<num_voxels; i++) {
const VectorI& voxel = voxels.segment(
i*vertex_per_voxel, vertex_per_voxel);
const VectorF& value = attribute.segment(
i*stride, stride);
per_face_values[Triplet(voxel[0], voxel[1], voxel[2])] = value;
per_face_values[Triplet(voxel[0], voxel[1], voxel[3])] = value;
per_face_values[Triplet(voxel[0], voxel[2], voxel[3])] = value;
per_face_values[Triplet(voxel[1], voxel[2], voxel[3])] = value;
}
VectorF result = VectorF::Zero(num_faces*stride);
for (size_t i=0; i<num_faces; i++) {
const VectorI& face = faces.segment(i*vertex_per_face, vertex_per_face);
result.segment(i*stride, stride) = per_face_values[
Triplet(face[0], face[1], face[2])];
}
return result;
}
void VertexMeanCurvatureAttribute::compute_from_mesh(Mesh& mesh) {
const size_t dim = mesh.get_dim();
const size_t num_vertices = mesh.get_num_vertices();
VectorF laplacian = compute_laplacian_vectors(mesh);
VectorF normals = compute_vertex_normals(mesh);
assert(laplacian.size() == dim*num_vertices);
assert(normals.size() == dim*num_vertices);
if (!mesh.has_attribute("vertex_voronoi_area")) {
mesh.add_attribute("vertex_voronoi_area");
}
const auto& area = mesh.get_attribute("vertex_voronoi_area");
VectorF& mean_curvature = m_values;
mean_curvature = VectorF::Zero(num_vertices);
for (size_t i=0; i<num_vertices; i++) {
mean_curvature[i] = laplacian.segment(dim*i,dim).norm() * 0.5;
Float sign = laplacian.segment(dim*i, dim).dot(normals.segment(dim*i,dim));
if (sign < 0) {
mean_curvature[i] *= -1;
}
}
mean_curvature = mean_curvature.array() / area.array();
}
void write_vertices(std::ofstream& fout,
const VectorF& vertices, const size_t dim) {
if (dim != 2 && dim != 3) {
throw IOError("Unsupported mesh dimension: " + std::to_string(dim));
}
fout.precision(16);
size_t num_vertices = vertices.size() / dim;
for (size_t i=0; i<num_vertices; i++) {
const auto& v = vertices.segment(i*dim, dim);
fout << "v";
for (size_t j=0; j<dim; j++) {
fout << " " << v[j];
}
fout << std::endl;
}
}
void EigenSolver::compute_batch_symmetric_2x2(const VectorF& matrices) {
const size_t dim = 2;
const size_t flatten_size = 3;
const size_t num_matrices = matrices.size() / flatten_size;
m_eigen_values = VectorF(num_matrices * dim);
m_eigen_vectors = MatrixF(num_matrices * dim, dim);
for (size_t i=0; i<num_matrices; i++) {
const VectorF& entries = matrices.segment(i*flatten_size, flatten_size);
MatrixF M(dim, dim);
size_t base_idx = i*flatten_size;
M << matrices[base_idx ], matrices[base_idx+2],
matrices[base_idx+2], matrices[base_idx+1],
m_solver.compute(M);
m_eigen_values.segment(i*dim, dim) = m_solver.eigenvalues().real();
m_eigen_vectors.block(i*dim, 0, dim, dim) =
m_solver.eigenvectors().real();
}
}