void write_faces(std::ofstream& fout,
const VectorI& faces,
const size_t vertex_per_face,
const VectorI& uv_indices=VectorI::Zero(0)) {
if (vertex_per_face != 3 && vertex_per_face != 4) {
std::stringstream err_msg;
err_msg << "OBJ format does not support non-triangle non-quad face with "
<< vertex_per_face << " vertices." << std::endl;
throw RuntimeError(err_msg.str());
}
const size_t num_faces = faces.size() / vertex_per_face;
const size_t num_uvs = uv_indices.size() / 2;
if (num_uvs == 0) {
for (size_t i=0; i<num_faces; i++) {
const auto& f = faces.segment(i*vertex_per_face, vertex_per_face);
fout << "f";
for (size_t j=0; j<vertex_per_face; j++) {
fout << " " << f[j] + 1;
}
fout << std::endl;
}
} else {
for (size_t i=0; i<num_faces; i++) {
const auto& f = faces.segment(i*vertex_per_face, vertex_per_face);
const auto& uv = uv_indices.segment(i*vertex_per_face, vertex_per_face);
fout << "f ";
for (size_t j=0; j<vertex_per_face; j++) {
fout << f[j] + 1 << "/" << uv[j] + 1 << " ";
}
fout << std::endl;
}
}
}
bool match(HashGrid::Ptr grid, const Vector3F& v) {
VectorI candidates = grid->get_items_near_point(v);
if (candidates.size() != 1) {
std::cout << "<" << v.transpose() << "> : " << candidates.transpose()
<< std::endl;
}
return candidates.size() > 0;
}
inline void assign_vector(
VectorI &v_src,
VectorI &v_ind,
VectorI &v_val,
VectorJ &v_out,
Accum accum)
{
using namespace detail;
if (v_val.size() != v_ind.size())
{
return;
}
assign_vector_helper(v_src, v_ind, v_val.begin(), v_out, accum);
}
ZSparseMatrix Assembler2D::getDisplacementStrainMatrix() {
typedef Eigen::Triplet<double> T;
std::vector<T> triplets;
for (size_t i=0; i<m_mesh->getNbrElements(); i++) {
Eigen::MatrixXd dN = m_DN[i];
VectorI idx = m_mesh->getElement(i);
assert(idx.size() == 3);
double V = m_mesh->getElementVolume(i);
// e_xx
size_t row = i * 3;
for (size_t k=0; k<3; k++) {
triplets.push_back(T(row, idx[k]*2, dN(k,0)));
}
// e_yy
row++;
for (size_t k=0; k<3; k++) {
triplets.push_back(T(row, idx[k]*2+1, dN(k,1)));
}
// e_xy
row++;
for (size_t k=0; k<3; k++) {
triplets.push_back(T(row, idx[k]*2 , dN(k,1) / 2.0));
triplets.push_back(T(row, idx[k]*2+1, dN(k,0) / 2.0));
}
}
Eigen::SparseMatrix<double> B = Eigen::SparseMatrix<double>(3*m_mesh->getNbrElements(), 2*m_mesh->getNbrNodes());
B.setFromTriplets(triplets.begin(), triplets.end());
return ZSparseMatrix(B);
}
void Assembler2D::precomputeShapeFunctionDerivatives() {
Eigen::MatrixXd selector = Eigen::MatrixXd::Zero(3,2);
selector << 0.0, 0.0,
1.0, 0.0,
0.0, 1.0;
m_DN.resize(m_mesh->getNbrElements());
for (size_t i=0; i<m_mesh->getNbrElements(); ++i)
{
VectorI idx = m_mesh->getElement(i);
assert(idx.size() == 3);
VectorF u[3];
u[0] = m_mesh->getNode(idx[0]);
u[1] = m_mesh->getNode(idx[1]);
u[2] = m_mesh->getNode(idx[2]);
Eigen::MatrixXd P = Eigen::MatrixXd::Zero(3,3);
P << 1.0, 1.0, 1.0,
u[0][0], u[1][0], u[2][0],
u[0][1], u[1][1], u[2][1];
// DN is a 4x3 matrix containing the gradients of the
// 4 shape functions (one for each node)
//
m_DN[i] = P.inverse() * selector /* * -1.0 */;
}
}
std::vector<VectorI> enumerate(const VectorI& repetitions) {
std::vector<VectorI> result;
const size_t dim = repetitions.size();
if (dim == 2) {
for (size_t i=0; i<repetitions[0]; i++) {
for (size_t j=0; j<repetitions[1]; j++) {
result.push_back(Vector2I(i,j));
}
}
} else if (dim == 3) {
for (size_t i=0; i<repetitions[0]; i++) {
for (size_t j=0; j<repetitions[1]; j++) {
for (size_t k=0; k<repetitions[2]; k++) {
result.push_back(Vector3I(i,j,k));
}
}
}
} else {
std::stringstream err_msg;
err_msg << "Unsupported dim: " << dim;
throw NotImplementedError(err_msg.str());
}
return result;
}
void VertexNormalAttribute::compute_vertex_normals_from_face(Mesh& mesh) {
const size_t dim = mesh.get_dim();
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 VectorF& normals = get_attribute(mesh, "face_normal");
const VectorF& areas = get_attribute(mesh, "face_area");
assert(normals.size() == 3 * num_faces);
assert(areas.size() == num_faces);
VectorF& v_normals = m_values;
v_normals = VectorF::Zero(dim * num_vertices);
for (size_t i=0; i<num_faces; i++) {
VectorI face = mesh.get_face(i);
assert(face.size() == vertex_per_face);
VectorF face_normal = normals.segment(i*dim, dim);
Float face_area = areas[i];
for (size_t j=0; j<vertex_per_face; j++) {
size_t vi = face[j];
v_normals.segment(vi*dim, dim) += face_normal * face_area;
}
}
for (size_t i=0; i<num_vertices; i++) {
VectorF n = v_normals.segment(dim*i, dim);
Float n_len = n.norm();
if (n_len > 0.0) n /= n_len;
v_normals.segment(dim*i, dim) = n;
}
}
VectorF Assembler::getCurlNorm(double* vector_field, int num_vector_field) {
size_t num_node = m_mesh->getNbrNodes();
size_t num_elem = m_mesh->getNbrElements();
size_t dim = m_mesh->getDim();
assert(num_vector_field == dim*num_node);
VectorF curl_norm(num_elem);
for (size_t i=0; i<num_elem; i++) {
VectorI elem = m_mesh->getElement(i);
const Eigen::MatrixXd& DN = m_DN[i];
Eigen::Vector3d curl(0, 0, 0);
for (size_t j=0; j<elem.size(); j++) {
Eigen::Vector3d v(0, 0, 0);
Eigen::Vector3d grad(0, 0, 0);
for (size_t k=0; k<dim; k++) {
v[k] = vector_field[elem[j]*dim+k];
grad[k] = DN(j, k);
}
curl = curl + grad.cross(v);
}
curl_norm[i] = curl.norm();
}
return curl_norm;
}
ZSparseMatrix Assembler2D::getLaplacianMatrix() {
typedef Eigen::Triplet<double> T;
std::vector<T> triplets;
for (size_t i=0; i<m_mesh->getNbrElements(); ++i)
{
VectorI idx = m_mesh->getElement(i);
assert(idx.size() == 3);
Eigen::MatrixXd& dN = m_DN[i];
// Small strain-displacement matrix
//
Eigen::MatrixXd B(2,3);
B << dN(0,0), dN(1,0), dN(2,0),
dN(0,1), dN(1,1), dN(2,1);
Eigen::MatrixXd k_el = B.transpose() * B * m_mesh->getElementVolume(i);
for (size_t j=0; j<3; ++j)
for (size_t k=0; k<3; ++k)
triplets.push_back(T(idx[j], idx[k], k_el(j,k)));
}
Eigen::SparseMatrix<double> L = Eigen::SparseMatrix<double>(m_mesh->getNbrNodes(), m_mesh->getNbrNodes());
L.setFromTriplets(triplets.begin(), triplets.end());
return ZSparseMatrix(L);
}
void Deform::set_soft_ctrs(const VectorF &T, const VectorI &idx_T)
{
assert(T.size()/3 == idx_T.size());
for (int i = 0, i_end = idx_T.size(); i < i_end; ++ i)
{
int cid = idx_T[i];
Eigen::Vector3f ctr;
ctr << T[3*i], T[3*i+1], T[3*i+2];
soft_ctrs.push_back(Constraint(ctr, cid));
}
std::sort(soft_ctrs.begin(), soft_ctrs.end(), ConstraintCompare());
}
ZSparseMatrix Assembler2D::getMassMatrix(bool lumped, int repeats) {
double p = m_density;
typedef Eigen::Triplet<double> T;
std::vector<T> triplets;
if (lumped) {
for (size_t i=0; i<m_mesh->getNbrElements(); i++) {
VectorI idx = m_mesh->getElement(i);
assert(idx.size() == 3);
double V = m_mesh->getElementVolume(i);
for (size_t j=0; j<idx.size(); j++)
for (size_t l=0; l<repeats; l++)
triplets.push_back(T(repeats*idx[j]+l,
repeats*idx[j]+l, p*V/3.0));
}
} else {
double coeff_jj = 1.0 / 6.0,
coeff_jk = 1.0 / 12.0;
for (size_t i=0; i<m_mesh->getNbrElements(); ++i) {
VectorI idx = m_mesh->getElement(i);
assert(idx.size() == 3);
double V = m_mesh->getElementVolume(i);
for (size_t j=0; j<3; ++j) {
for (size_t k=0; k<3; ++k) {
if (idx[j] == idx[k]) {
for (size_t l=0; l<repeats; ++l)
triplets.push_back(
T(repeats*idx[j]+l, repeats*idx[k]+l, p*V*coeff_jj));
} else {
for (size_t l=0; l<repeats; ++l)
triplets.push_back(
T(repeats*idx[j]+l, repeats*idx[k]+l, p*V*coeff_jk));
}
}
}
}
}
Eigen::SparseMatrix<double> M = Eigen::SparseMatrix<double>(
repeats*m_mesh->getNbrNodes(), repeats*m_mesh->getNbrNodes());
M.setFromTriplets(triplets.begin(), triplets.end());
return ZSparseMatrix(M);
}
VectorI map_indices(const VectorI& face, const VectorI& index_map) {
const size_t vertex_per_face = face.size();
VectorI index(vertex_per_face);
for (size_t i=0; i<vertex_per_face; i++) {
index[i] = index_map[face[i]];
}
return index;
}
Float ElementWiseMaterial::get_material_tensor(
size_t i, size_t j, size_t k, size_t l, VectorF coord) const {
const VectorI voxel_ids = look_up_voxels(coord);
assert(voxel_ids.size() > 0);
const size_t voxel_id = voxel_ids[0];
assert(voxel_id < m_materials.size());
return m_materials[voxel_id]->get_material_tensor(i,j,k,l,coord);
}
MatrixF ElementWiseMaterial::strain_to_stress(
const MatrixF& strain, VectorF coord) const {
const VectorI voxel_ids = look_up_voxels(coord);
assert(voxel_ids.size() > 0);
const size_t voxel_id = voxel_ids[0];
assert(voxel_id < m_materials.size());
return m_materials[voxel_id]->strain_to_stress(strain, coord);
}
void MeshGeometry::extract_faces_from_hexes() {
const VectorI& voxels = m_voxels;
typedef std::map<Multiplet, int> FaceCounter;
FaceCounter face_counter;
for (size_t i=0; i<voxels.size(); i+= m_vertex_per_voxel) {
VectorI voxel = voxels.segment(i, m_vertex_per_voxel);
// Note that the order of vertices below are predefined by MSH format,
// each face should have normal pointing outward.
assert(voxel.size() == 8);
Multiplet voxel_faces[6] = {
Multiplet(Vector4I(voxel[0], voxel[1], voxel[5], voxel[4])), // Bottom
Multiplet(Vector4I(voxel[2], voxel[3], voxel[7], voxel[6])), // Top
Multiplet(Vector4I(voxel[0], voxel[4], voxel[7], voxel[3])), // Left
Multiplet(Vector4I(voxel[1], voxel[2], voxel[6], voxel[5])), // Right
Multiplet(Vector4I(voxel[4], voxel[5], voxel[6], voxel[7])), // Front
Multiplet(Vector4I(voxel[0], voxel[3], voxel[2], voxel[1])) // Back
};
for (size_t j=0; j<6; j++) {
if (face_counter.find(voxel_faces[j]) == face_counter.end()) {
face_counter[voxel_faces[j]] = 1;
} else {
face_counter[voxel_faces[j]] += 1;
}
}
}
std::vector<int> vertex_buffer;
for (FaceCounter::const_iterator itr = face_counter.begin();
itr!=face_counter.end(); itr++) {
if (itr->second != 1 && itr->second != 2) {
const Vector4I& face = itr->first.get_ori_data();
std::stringstream err_msg;
err_msg << "Non-manifold mesh detected!" << std::endl;
err_msg << "Face <"
<< face[0] << ", "
<< face[1] << ", "
<< face[2] << ", "
<< face[3] << "> has "
<< itr->second << " adjacent volume elements";
throw RuntimeError(err_msg.str());
}
if (itr->second == 1) {
const VectorI& f = itr->first.get_ori_data();
assert(f.size() == 4);
vertex_buffer.push_back(f[0]);
vertex_buffer.push_back(f[1]);
vertex_buffer.push_back(f[2]);
vertex_buffer.push_back(f[3]);
}
}
m_faces.resize(vertex_buffer.size());
std::copy(vertex_buffer.begin(), vertex_buffer.end(), m_faces.data());
m_vertex_per_face = 4;
}
ALGEB minpoly(MKernelVector kv, ALGEB* args)
{
int i;
ALGEB retlist, blank;
char err[] = "ERROR! Associated blackbox object does not exist!";
int key = MapleToInteger32(kv,args[1]), flag;
std::map<int,int>::iterator f_i;
std::map<int,void*>::iterator h_i;
// Get the data from the hash table
f_i = typeTable.find(key);
if( f_i == typeTable.end() )
MapleRaiseError(kv,err);
else
flag = f_i->second;
h_i = hashTable.find(key);
if(h_i != hashTable.end() ) { // We've got data
switch( flag ) {
// Getting the minimal polynomial is rather complicated, so both instances of this code were
// wrapped up inside a block, to cut down at the clutter at the top of this function.
// First declares a vector of the proper type and casts the pointer. Then computes the minimal
// polynomial. It then builds the proper Maple list structure for this application.
case BlackBoxi: {
Vectorl mpreturn;
Vectorl::iterator mp_i;
TriplesBBi* BB = (TriplesBBi*) h_i->second;
LinBox::minpoly( mpreturn, *BB, BB->field() );
retlist = MapleListAlloc(kv, mpreturn.size() );
for(i = 1, mp_i = mpreturn.begin(); mp_i != mpreturn.end(); ++mp_i, ++i)
MapleListAssign(kv, retlist, i, ToMapleInteger(kv, *mp_i));
}
break;
case BlackBoxI: {
VectorI mpreturn;
VectorI::iterator mp_i;
TriplesBBI* BB = (TriplesBBI*) h_i->second;
LinBox::minpoly( mpreturn, *BB, BB->field() );
retlist = MapleListAlloc(kv, mpreturn.size());
for(i = 1, mp_i = mpreturn.begin(); mp_i != mpreturn.end(); ++mp_i, ++i)
MapleListAssign(kv, retlist, i, LiToM(kv, *mp_i, blank));
}
break;
}
}
else
MapleRaiseError(kv,err);
return retlist;
}
bool SimpleInflator::belong_to_the_same_loop(
const VectorI& indices, const VectorI& source_ids) const {
const size_t size = indices.size();
assert(size > 0);
const int id = source_ids[indices[0]];
for (size_t i=1; i<size; i++) {
if (id != source_ids[indices[i]]) return false;
}
return true;
}
ZSparseMatrix Assembler::getBoundaryBlurMatrix(double radius) {
typedef std::priority_queue<Item, std::vector<Item>, ItemComp> Queue;
typedef Eigen::Triplet<double> T;
std::vector<T> triplets;
size_t num_bd_vertices = m_mesh->getNbrBoundaryNodes();
double sd = radius / 3.0;
const double A = 2.50662827463; // A = sqrt(2*pi);
std::vector<int> visited(num_bd_vertices, -1);
for (size_t i=0; i<num_bd_vertices; i++) {
size_t seed = i;
Queue Q;
Q.push(Item(i, 0.0));
VectorF seed_n = m_mesh->getBoundaryNodeNormal(seed);
while (!Q.empty()) {
Item cur_item = Q.top();
Q.pop();
// Check if visited before
if (visited[cur_item.first] == seed) continue;
visited[cur_item.first] = seed;
size_t curr_glob_idx = m_mesh->getBoundaryNode(cur_item.first);
VectorF curr_n = m_mesh->getBoundaryNodeNormal(cur_item.first);
double normal_factor = fmax(0.0, curr_n.dot(seed_n));
// Use gaussian distribution as weights
triplets.push_back(T(seed, cur_item.first,
exp(-0.5 * pow(cur_item.second / sd, 2)) /
(sd*A) * normal_factor));
VectorI neighbors = m_mesh->getBoundaryNodeAdjacentBoundaryNodes(
cur_item.first);
for (size_t j=0; j<neighbors.size(); j++) {
size_t next = neighbors[j];
if (visited[next] == seed) continue;
size_t next_glob_idx = m_mesh->getBoundaryNode(next);
double next_dist = cur_item.second +
(m_mesh->getNode(curr_glob_idx) -
m_mesh->getNode(next_glob_idx)).norm();
if (next_dist > 2*sd) continue;
Q.push(Item(next, next_dist));
}
}
}
Eigen::SparseMatrix<double> Bd_Blur = Eigen::SparseMatrix<double>(num_bd_vertices, num_bd_vertices);
Bd_Blur.setFromTriplets(triplets.begin(), triplets.end());
return ZSparseMatrix(Bd_Blur);
}
void Deform::find_share_vertex(int pi, int pj, VectorI &share_vertex)
{
vector<int> vertices;
set_intersection(adj_list[pi].begin(), adj_list[pi].end(), adj_list[pj].begin(), adj_list[pj].end(), back_inserter(vertices));
for (auto &i : vertices) {
vector<int> f;
f.push_back(pi);
f.push_back(pj);
f.push_back(i);
sort(f.begin(), f.end());
vector<Vector3i>::iterator it = find(face_list.begin(), face_list.end(), Map<Vector3i>(&f[0]));
if (it != face_list.end()) {
if ((*it)(0) != pi && (*it)(0) != pj) share_vertex.push_back((*it)(0));
else if ((*it)(1) != pi && (*it)(1) != pj) share_vertex.push_back((*it)(1));
else share_vertex.push_back((*it)(2));
}
}
if (share_vertex.size() > 2) {
cout << "share vertices number warning: " << share_vertex.size() << endl;
}
}
void MeshGeometry::extract_faces_from_tets() {
const VectorI& voxels = m_voxels;
typedef std::map<Triplet, unsigned short> FaceCounter;
FaceCounter face_counter;
for (size_t i=0; i<voxels.size(); i+= m_vertex_per_voxel) {
VectorI voxel = voxels.segment(i, m_vertex_per_voxel);
// Note that the order of vertices below are predefined by MSH format,
// each face should have normal pointing outward.
assert(voxel.size() == 4);
Triplet voxel_faces[4] = {
{voxel[0], voxel[2], voxel[1]},
{voxel[0], voxel[1], voxel[3]},
{voxel[0], voxel[3], voxel[2]},
{voxel[1], voxel[2], voxel[3]}
};
for (size_t j=0; j<4; j++) {
if (face_counter.find(voxel_faces[j]) == face_counter.end()) {
face_counter[voxel_faces[j]] = 1;
} else {
face_counter[voxel_faces[j]] += 1;
}
}
}
std::vector<int> vertex_buffer;
for (FaceCounter::const_iterator itr = face_counter.begin();
itr!=face_counter.end(); itr++) {
if (itr->second != 1 && itr->second != 2) {
const Vector3I& triplet = itr->first.get_ori_data();
std::stringstream err_msg;
err_msg << "Non-manifold mesh detected!" << std::endl;
err_msg << "Face <"
<< triplet[0] << ", "
<< triplet[1] << ", "
<< triplet[2] << "> has "
<< itr->second << " adjacent volume elements";
throw RuntimeError(err_msg.str());
}
if (itr->second == 1) {
const VectorI& f = itr->first.get_ori_data();
assert(f.size() == 3);
vertex_buffer.push_back(f[0]);
vertex_buffer.push_back(f[1]);
vertex_buffer.push_back(f[2]);
}
}
m_faces.resize(vertex_buffer.size());
std::copy(vertex_buffer.begin(), vertex_buffer.end(), m_faces.data());
m_vertex_per_face = 3;
}
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 MSHWriter::write(const VectorF& vertices, const VectorI& faces, const VectorI& voxels,
size_t dim, size_t vertex_per_face, size_t vertex_per_voxel) {
MshSaver saver(m_filename, !m_in_ascii);
MshSaver::ElementType type;
if (voxels.size() == 0) {
type = get_face_type(vertex_per_face);
saver.save_mesh(vertices, faces, dim, type);
} else {
type = get_voxel_type(vertex_per_voxel);
saver.save_mesh(vertices, voxels, dim, type);
}
if (m_attr_names.size() != 0) {
std::cerr << "Warning: all attributes are ignored." << std::endl;
}
}
VectorF Assembler::getDivergence(double* vector_field, int num_vector_field) {
size_t num_node = m_mesh->getNbrNodes();
size_t num_elem = m_mesh->getNbrElements();
size_t dim = m_mesh->getDim();
assert(num_vector_field == dim*num_node);
VectorF div(num_elem);
for (size_t i=0; i<num_elem; i++) {
div[i] = 0;
VectorI elem = m_mesh->getElement(i);
const Eigen::MatrixXd& DN = m_DN[i];
for (size_t j=0; j<elem.size(); j++) {
for (size_t k=0; k<dim; k++) {
div[i] += DN(j,k) * vector_field[elem[j]*dim+k];
}
}
}
return div;
}
ZSparseMatrix Assembler2D::getStiffnessMatrix() {
// Elastic modulii
//
Eigen::MatrixXd& D = m_D;
Eigen::MatrixXd& C = m_C;
typedef Eigen::Triplet<double> T;
std::vector<T> triplets;
for (size_t i=0; i<m_mesh->getNbrElements(); ++i)
{
VectorI idx = m_mesh->getElement(i);
assert(idx.size() == 3);
Eigen::MatrixXd& dN = m_DN[i];
// Small strain-displacement matrix
//
Eigen::MatrixXd B(3,6);
B << dN(0,0), 0.0,dN(1,0), 0.0,dN(2,0), 0.0,
0.0 ,dN(0,1), 0.0,dN(1,1), 0.0,dN(2,1),
0.5*dN(0,1),0.5*dN(0,0),
0.5*dN(1,1),0.5*dN(1,0),
0.5*dN(2,1),0.5*dN(2,0);
Eigen::MatrixXd k_el = B.transpose() * D * C * B * m_mesh->getElementVolume(i);
for (size_t j=0; j<3; ++j)
for (size_t k=0; k<3; ++k)
for (size_t l=0; l<2; ++l)
for (size_t m=0; m<2; ++m)
triplets.push_back(T(2*idx[j]+l, 2*idx[k]+m, k_el(2*j+l, 2*k+m)));
}
Eigen::SparseMatrix<double> K = Eigen::SparseMatrix<double>(2*m_mesh->getNbrNodes(), 2*m_mesh->getNbrNodes());
K.setFromTriplets(triplets.begin(), triplets.end());
ZSparseMatrix tmp = ZSparseMatrix(K);
return tmp;
}
ZSparseMatrix Assembler2D::getBdLaplacianMatrix() {
typedef Eigen::Triplet<double> T;
std::vector<T> triplets;
size_t num_bdv = m_mesh->getNbrBoundaryNodes();
size_t num_bdf = m_mesh->getNbrBoundaryFaces();
// Compute lumped mass
VectorF lumped_mass(num_bdv);
for (size_t i=0; i<num_bdv; i++) {
VectorI neighbor_faces = m_mesh->getBoundaryNodeAdjacentBoundaryFaces(i);
assert(neighbor_faces.size() == 2);
double total_weight =
m_mesh->getBoundaryFaceArea(neighbor_faces[0]) +
m_mesh->getBoundaryFaceArea(neighbor_faces[1]);
lumped_mass[i] = 0.5 * total_weight;
}
// Compute laplacian matrix.
for (size_t i=0; i<num_bdf; i++) {
VectorI face = m_mesh->getBoundaryFace(i);
assert(face.size() == 2);
double l = m_mesh->getBoundaryFaceArea(i);
size_t v1 = m_mesh->getBoundaryIndex(face[0]);
size_t v2 = m_mesh->getBoundaryIndex(face[1]);
double weight = 1.0 / l;
triplets.push_back(T(v1, v1, -weight / lumped_mass[v1]));
triplets.push_back(T(v1, v2, weight / lumped_mass[v1]));
triplets.push_back(T(v2, v1, weight / lumped_mass[v2]));
triplets.push_back(T(v2, v2, -weight / lumped_mass[v2]));
}
Eigen::SparseMatrix<double> Lb = Eigen::SparseMatrix<double>(num_bdv, num_bdv);
Lb.setFromTriplets(triplets.begin(), triplets.end());
return ZSparseMatrix(Lb);
}
void OffsetParameters::add(const VectorI& roi,
const std::string& formula, Float value, size_t axis) {
const Float tol = 1e-12;
const size_t dim = m_wire_network->get_dim();
const size_t num_vertices = m_wire_network->get_num_vertices();
const VectorF bbox_min = m_wire_network->get_bbox_min();
const VectorF bbox_max = m_wire_network->get_bbox_max();
const VectorF bbox_center = 0.5 * (bbox_min + bbox_max);
const MatrixFr& vertices = m_wire_network->get_vertices();
assert(axis < dim);
VectorF roi_min = bbox_max;
VectorF roi_max = bbox_min;
const size_t num_roi = roi.size();
for (size_t i=0; i<num_roi; i++) {
size_t v_idx = roi[i];
assert(v_idx < num_vertices);
const VectorF& v = vertices.row(v_idx);
roi_min = roi_min.cwiseMin(v);
roi_max = roi_max.cwiseMax(v);
}
if (fabs(roi_max[axis] - bbox_center[axis]) < tol &&
fabs(roi_min[axis] - bbox_center[axis]) < tol) {
// No dof in this axis without destroy symmetry.
return;
}
if (roi_min[axis] > bbox_min[axis] + tol &&
roi_max[axis] < bbox_max[axis] - tol) {
m_params.emplace_back(PatternParameter::Ptr(
new VertexOffsetParameter(m_wire_network, axis)));
PatternParameter::Ptr param = m_params.back();
param->set_roi(roi);
param->set_value(value);
param->set_formula(formula);
}
}
size_t DuplicatedVertexRemoval::run(Float tol) {
const size_t dim = m_vertices.cols();
HashGrid::Ptr grid = HashGrid::create(tol, dim);
const size_t num_vertices = m_vertices.rows();
const size_t num_faces = m_faces.rows();
const size_t vertex_per_face = m_faces.cols();
m_index_map.resize(num_vertices);
std::vector<size_t> source_index;
size_t count = 0;
size_t num_duplications = 0;
for (size_t i=0; i<num_vertices; i++) {
int curr_importance_level = m_importance_level[i];
if (curr_importance_level < 0) {
m_index_map[i] = count;
source_index.push_back(i);
count++;
continue;
}
const VectorF& v = m_vertices.row(i);
VectorI candidates = grid->get_items_near_point(v);
const size_t num_candidates = candidates.size();
if (num_candidates > 0) {
VectorF dists(num_candidates);
for (size_t j=0; j<num_candidates; j++) {
dists[j] = (m_vertices.row(candidates[j]) - v.transpose()).norm();
}
size_t min_idx;
Float min_dist = dists.minCoeff(&min_idx);
if (min_dist < tol) {
size_t best_match_idx = candidates[min_idx];
size_t output_idx = m_index_map[best_match_idx];
m_index_map[i] = output_idx;
int matched_importance_level =
m_importance_level[source_index[output_idx]];
if (curr_importance_level > matched_importance_level) {
source_index[output_idx] = i;
}
num_duplications++;
continue;
}
}
// No match, add this vertex in the book.
grid->insert(i, v);
m_index_map[i] = count;
source_index.push_back(i);
count++;
}
assert(source_index.size() == count);
MatrixFr vertices(count, dim);
for (size_t i=0; i<count; i++) {
assert(m_index_map[source_index[i]] == i);
vertices.row(i) = m_vertices.row(source_index[i]);
}
m_vertices = vertices;
for (size_t i=0; i<num_faces; i++) {
for (size_t j=0; j<vertex_per_face; j++) {
size_t v_index = m_faces(i,j);
m_faces(i,j) = m_index_map[v_index];
}
}
return num_duplications;
}
ALGEB getVector(MKernelVector kv, ALGEB* args)
{
// Get the key, declare variables
int key = MapleToInteger32(kv,args[1]), flag;
char err[] = "ERROR! The associated Vector object does not exist!";
M_INT index, bound[2];
RTableData d;
RTableSettings s;
ALGEB rtable, blank;
char MapleStatement[100] = "rtable(1..";
// Check to see if the object pointed to by key is in the type table. If not, panic
std::map<int,int>::iterator f_i = typeTable.find(key);
if(f_i == typeTable.end() ) {
MapleRaiseError(kv, err);
}
// Otherwise, we have our object
flag = f_i->second;
// Get a pointer to the actual data
std::map<int,void*>::iterator h_i = hashTable.find(key);
if(h_i != hashTable.end() ) {
// Diverge over whether we are using maple 7 or 8 ( and 5 & 6)
// in Maple, arg 3 is a flag indicating which method to use
switch( MapleToInteger32(kv, args[3])) {
// In this case, Maple 7 is being used, we have to construct a call using "EvalMapleStatement()"
// to call the RTable constructor
case 1:
switch(flag) {
case SmallV:{
// Get the vector
Vectorl* V = (Vectorl*) h_i->second;
Vectorl::const_iterator V_i;
// Create the Maple object
sprintf(MapleStatement + strlen(MapleStatement), "%d", V->size() );
strcat(MapleStatement, ", subtype=Vector[column], storage=sparse)");
rtable = kv->evalMapleStatement(MapleStatement);
// populate the Maple vector w/ the entries from V above
for(index = 1, V_i = V->begin(); V_i != V->end(); ++V_i, ++index) {
d.dag = ToMapleInteger(kv, *V_i); // d is a union, dag is the
// ALGEB union field
RTableAssign(kv, rtable, &index, d);
}
}
break;
case LargeV: {
// This part works the same way as above
VectorI* V = (VectorI*) h_i->second;
VectorI::const_iterator V_i;
sprintf(MapleStatement + strlen(MapleStatement), "%d", V->size() );
strcat(MapleStatement, ",subtype=Vector[column], storage=sparse)");
rtable = kv->evalMapleStatement(MapleStatement);
// Use maple callback to call the procedure from Maple that translates a gmp integer
// into a large maple integer. Then put this into the Maple vector
for(index = 1, V_i = V->begin(); V_i != V->end(); ++V_i, ++index) {
/* Okay, here's how this line works. Basically,
* in order to set the entries of this RTable to
* multi-precision integers, I have to first use my own conversion
* method, LiToM, to convert the integer entry to a ALGEB structure,
* then do a callback into Maple that calls the ExToM procedure,
* which converts the results of LiToM into a Maple multi-precision
* integer. At the moment, this is the best idea I've got as to
* how to convert a GMP integer into a Maple representation in one shot.
*/
d.dag = EvalMapleProc(kv,args[2],1,LiToM(kv, *V_i, blank));
RTableAssign(kv, rtable, &index, d);
}
}
break;
default:
MapleRaiseError(kv, err);
break;
}
break;
// In this case, use the simpler RTableCreate function, rather than building a string
// that must be parsed by maple
case 2:
kv->rtableGetDefaults(&s); // Get default settings - set datatype to Maple,
// DAGTAG to anything
s.subtype = 2; // Subtype set to column vector
s.storage = 4; // Storage set to rectangular
s.num_dimensions = 1; // What do you think this means :-)
bound[0] = 1; // Set the lower bounds of each dimension to 0
switch(flag) {// Switch on data type of vector
case SmallV:{ // single word integer entry vector
Vectorl* V = (Vectorl*) h_i->second;
Vectorl::const_iterator V_i;
bound[1] = V->size();
rtable = kv->rtableCreate(&s, NULL, bound); // Create the Maple vector
for(index = 1, V_i = V->begin(); V_i != V->end(); ++V_i, ++index) {
d.dag = ToMapleInteger(kv, *V_i); // d is a union, dag is the
// ALGEB union field
RTableAssign(kv, rtable, &index, d);
}
}
break;
case LargeV: { // Same as above for multi-word integer entry vector
VectorI* V = (VectorI*) h_i->second;
VectorI::const_iterator V_i;
bound[1] = V->size();
rtable = kv->rtableCreate(&s, NULL, bound);
for(index = 1, V_i = V->begin(); V_i != V->end(); ++V_i, ++index) {
/* Okay, here's how this line works. Basically,
* in order to set the entries of this RTable to
* multi-precision integers, I have to first use my own conversion
* method, LiToM, to convert the integer entry to a ALGEB structure,
* then do a callback into Maple that calls the ExToM procedure,
* which converts the results of LiToM into a Maple multi-precision
* integer. At the moment, this is the best idea I've got as to
* how to convert a GMP integer into a Maple representation in one shot.
*/
d.dag = EvalMapleProc(kv,args[2],1,LiToM(kv, *V_i, blank));
RTableAssign(kv, rtable, &index, d);
}
}
break;
default:
MapleRaiseError(kv, err);
break;
}
break; // breaks case 2.
// This was causing a wicked error :-)
default:
MapleRaiseError(kv, err);
break;
}
}
else {
MapleRaiseError(kv, err);
}
return rtable;
}