IGL_INLINE void igl::copyleft::cgal::propagate_winding_numbers(
const Eigen::PlainObjectBase<DerivedV>& V,
const Eigen::PlainObjectBase<DerivedF>& F,
const Eigen::PlainObjectBase<DerivedL>& labels,
Eigen::PlainObjectBase<DerivedW>& W) {
const size_t num_faces = F.rows();
//typedef typename DerivedF::Scalar Index;
Eigen::MatrixXi E, uE;
Eigen::VectorXi EMAP;
std::vector<std::vector<size_t> > uE2E;
igl::unique_edge_map(F, E, uE, EMAP, uE2E);
if (!propagate_winding_numbers_helper::is_orientable(F, uE, uE2E)) {
std::cerr << "Input mesh is not orientable!" << std::endl;
}
Eigen::VectorXi P;
const size_t num_patches = igl::extract_manifold_patches(F, EMAP, uE2E, P);
DerivedW per_patch_cells;
const size_t num_cells =
igl::copyleft::cgal::extract_cells(
V, F, P, E, uE, uE2E, EMAP, per_patch_cells);
typedef std::tuple<size_t, bool, size_t> CellConnection;
std::vector<std::set<CellConnection> > cell_adjacency(num_cells);
for (size_t i=0; i<num_patches; i++) {
const int positive_cell = per_patch_cells(i,0);
const int negative_cell = per_patch_cells(i,1);
cell_adjacency[positive_cell].emplace(negative_cell, false, i);
cell_adjacency[negative_cell].emplace(positive_cell, true, i);
}
auto save_cell = [&](const std::string& filename, size_t cell_id) {
std::vector<size_t> faces;
for (size_t i=0; i<num_patches; i++) {
if ((per_patch_cells.row(i).array() == cell_id).any()) {
for (size_t j=0; j<num_faces; j++) {
if ((size_t)P[j] == i) {
faces.push_back(j);
}
}
}
}
Eigen::MatrixXi cell_faces(faces.size(), 3);
for (size_t i=0; i<faces.size(); i++) {
cell_faces.row(i) = F.row(faces[i]);
}
Eigen::MatrixXd vertices(V.rows(), 3);
for (size_t i=0; i<(size_t)V.rows(); i++) {
assign_scalar(V(i,0), vertices(i,0));
assign_scalar(V(i,1), vertices(i,1));
assign_scalar(V(i,2), vertices(i,2));
}
writePLY(filename, vertices, cell_faces);
};
#ifndef NDEBUG
{
// Check for odd cycle.
Eigen::VectorXi cell_labels(num_cells);
cell_labels.setZero();
Eigen::VectorXi parents(num_cells);
parents.setConstant(-1);
auto trace_parents = [&](size_t idx) {
std::list<size_t> path;
path.push_back(idx);
while ((size_t)parents[path.back()] != path.back()) {
path.push_back(parents[path.back()]);
}
return path;
};
for (size_t i=0; i<num_cells; i++) {
if (cell_labels[i] == 0) {
cell_labels[i] = 1;
std::queue<size_t> Q;
Q.push(i);
parents[i] = i;
while (!Q.empty()) {
size_t curr_idx = Q.front();
Q.pop();
int curr_label = cell_labels[curr_idx];
for (const auto& neighbor : cell_adjacency[curr_idx]) {
if (cell_labels[std::get<0>(neighbor)] == 0) {
cell_labels[std::get<0>(neighbor)] = curr_label * -1;
Q.push(std::get<0>(neighbor));
parents[std::get<0>(neighbor)] = curr_idx;
} else {
if (cell_labels[std::get<0>(neighbor)] !=
curr_label * -1) {
std::cerr << "Odd cell cycle detected!" << std::endl;
auto path = trace_parents(curr_idx);
path.reverse();
auto path2 = trace_parents(std::get<0>(neighbor));
path.insert(path.end(),
path2.begin(), path2.end());
for (auto cell_id : path) {
std::cout << cell_id << " ";
std::stringstream filename;
filename << "cell_" << cell_id << ".ply";
save_cell(filename.str(), cell_id);
}
std::cout << std::endl;
}
assert(cell_labels[std::get<0>(neighbor)] == curr_label * -1);
}
}
}
}
}
}
#endif
size_t outer_facet;
bool flipped;
Eigen::VectorXi I;
I.setLinSpaced(num_faces, 0, num_faces-1);
igl::copyleft::cgal::outer_facet(V, F, I, outer_facet, flipped);
const size_t outer_patch = P[outer_facet];
const size_t infinity_cell = per_patch_cells(outer_patch, flipped?1:0);
Eigen::VectorXi patch_labels(num_patches);
const int INVALID = std::numeric_limits<int>::max();
patch_labels.setConstant(INVALID);
for (size_t i=0; i<num_faces; i++) {
if (patch_labels[P[i]] == INVALID) {
patch_labels[P[i]] = labels[i];
} else {
assert(patch_labels[P[i]] == labels[i]);
}
}
assert((patch_labels.array() != INVALID).all());
const size_t num_labels = patch_labels.maxCoeff()+1;
Eigen::MatrixXi per_cell_W(num_cells, num_labels);
per_cell_W.setConstant(INVALID);
per_cell_W.row(infinity_cell).setZero();
std::queue<size_t> Q;
Q.push(infinity_cell);
while (!Q.empty()) {
size_t curr_cell = Q.front();
Q.pop();
for (const auto& neighbor : cell_adjacency[curr_cell]) {
size_t neighbor_cell, patch_idx;
bool direction;
std::tie(neighbor_cell, direction, patch_idx) = neighbor;
if ((per_cell_W.row(neighbor_cell).array() == INVALID).any()) {
per_cell_W.row(neighbor_cell) = per_cell_W.row(curr_cell);
for (size_t i=0; i<num_labels; i++) {
int inc = (patch_labels[patch_idx] == (int)i) ?
(direction ? -1:1) :0;
per_cell_W(neighbor_cell, i) =
per_cell_W(curr_cell, i) + inc;
}
Q.push(neighbor_cell);
} else {
#ifndef NDEBUG
for (size_t i=0; i<num_labels; i++) {
if ((int)i == patch_labels[patch_idx]) {
int inc = direction ? -1:1;
assert(per_cell_W(neighbor_cell, i) ==
per_cell_W(curr_cell, i) + inc);
} else {
assert(per_cell_W(neighbor_cell, i) ==
per_cell_W(curr_cell, i));
}
}
#endif
}
}
}
W.resize(num_faces, num_labels*2);
for (size_t i=0; i<num_faces; i++) {
const size_t patch = P[i];
const size_t positive_cell = per_patch_cells(patch, 0);
const size_t negative_cell = per_patch_cells(patch, 1);
for (size_t j=0; j<num_labels; j++) {
W(i,j*2 ) = per_cell_W(positive_cell, j);
W(i,j*2+1) = per_cell_W(negative_cell, j);
}
}
}
IGL_INLINE void igl::copyleft::cgal::propagate_winding_numbers(
const Eigen::PlainObjectBase<DerivedV>& V,
const Eigen::PlainObjectBase<DerivedF>& F,
const Eigen::PlainObjectBase<DerivedL>& labels,
Eigen::PlainObjectBase<DerivedW>& W) {
#ifdef PROPAGATE_WINDING_NUMBER_TIMING
const auto & tictoc = []()
{
static double t_start = igl::get_seconds();
double diff = igl::get_seconds()-t_start;
t_start += diff;
return diff;
};
tictoc();
#endif
const size_t num_faces = F.rows();
//typedef typename DerivedF::Scalar Index;
Eigen::MatrixXi E, uE;
Eigen::VectorXi EMAP;
std::vector<std::vector<size_t> > uE2E;
igl::unique_edge_map(F, E, uE, EMAP, uE2E);
if (!propagate_winding_numbers_helper::is_orientable(F, uE, uE2E)) {
std::cerr << "Input mesh is not orientable!" << std::endl;
}
Eigen::VectorXi P;
const size_t num_patches = igl::extract_manifold_patches(F, EMAP, uE2E, P);
#ifdef PROPAGATE_WINDING_NUMBER_TIMING
std::cout << "extract manifold patches: " << tictoc() << std::endl;
#endif
DerivedW per_patch_cells;
const size_t num_cells =
igl::copyleft::cgal::extract_cells(
V, F, P, E, uE, uE2E, EMAP, per_patch_cells);
#ifdef PROPAGATE_WINDING_NUMBER_TIMING
std::cout << "extract cells: " << tictoc() << std::endl;;
#endif
typedef std::tuple<size_t, bool, size_t> CellConnection;
std::vector<std::set<CellConnection> > cell_adjacency(num_cells);
for (size_t i=0; i<num_patches; i++) {
const int positive_cell = per_patch_cells(i,0);
const int negative_cell = per_patch_cells(i,1);
cell_adjacency[positive_cell].emplace(negative_cell, false, i);
cell_adjacency[negative_cell].emplace(positive_cell, true, i);
}
#ifdef PROPAGATE_WINDING_NUMBER_TIMING
std::cout << "cell connection: " << tictoc() << std::endl;
#endif
auto save_cell = [&](const std::string& filename, size_t cell_id) {
std::vector<size_t> faces;
for (size_t i=0; i<num_patches; i++) {
if ((per_patch_cells.row(i).array() == cell_id).any()) {
for (size_t j=0; j<num_faces; j++) {
if ((size_t)P[j] == i) {
faces.push_back(j);
}
}
}
}
Eigen::MatrixXi cell_faces(faces.size(), 3);
for (size_t i=0; i<faces.size(); i++) {
cell_faces.row(i) = F.row(faces[i]);
}
Eigen::MatrixXd vertices(V.rows(), 3);
for (size_t i=0; i<(size_t)V.rows(); i++) {
assign_scalar(V(i,0), vertices(i,0));
assign_scalar(V(i,1), vertices(i,1));
assign_scalar(V(i,2), vertices(i,2));
}
writePLY(filename, vertices, cell_faces);
};
#ifndef NDEBUG
{
// Check for odd cycle.
Eigen::VectorXi cell_labels(num_cells);
cell_labels.setZero();
Eigen::VectorXi parents(num_cells);
parents.setConstant(-1);
auto trace_parents = [&](size_t idx) {
std::list<size_t> path;
path.push_back(idx);
while ((size_t)parents[path.back()] != path.back()) {
path.push_back(parents[path.back()]);
}
return path;
};
for (size_t i=0; i<num_cells; i++) {
if (cell_labels[i] == 0) {
cell_labels[i] = 1;
std::queue<size_t> Q;
Q.push(i);
parents[i] = i;
while (!Q.empty()) {
size_t curr_idx = Q.front();
Q.pop();
int curr_label = cell_labels[curr_idx];
for (const auto& neighbor : cell_adjacency[curr_idx]) {
if (cell_labels[std::get<0>(neighbor)] == 0) {
cell_labels[std::get<0>(neighbor)] = curr_label * -1;
Q.push(std::get<0>(neighbor));
parents[std::get<0>(neighbor)] = curr_idx;
} else {
if (cell_labels[std::get<0>(neighbor)] !=
curr_label * -1) {
std::cerr << "Odd cell cycle detected!" << std::endl;
auto path = trace_parents(curr_idx);
path.reverse();
auto path2 = trace_parents(std::get<0>(neighbor));
path.insert(path.end(),
path2.begin(), path2.end());
for (auto cell_id : path) {
std::cout << cell_id << " ";
std::stringstream filename;
filename << "cell_" << cell_id << ".ply";
save_cell(filename.str(), cell_id);
}
std::cout << std::endl;
}
// Do not fail when odd cycle is detected because the resulting
// integer winding number field, although inconsistent, may still
// be used if the problem region is local and embedded within a
// valid volume.
//assert(cell_labels[std::get<0>(neighbor)] == curr_label * -1);
}
}
}
}
}
#ifdef PROPAGATE_WINDING_NUMBER_TIMING
std::cout << "check for odd cycle: " << tictoc() << std::endl;
#endif
}
#endif
size_t outer_facet;
bool flipped;
Eigen::VectorXi I;
I.setLinSpaced(num_faces, 0, num_faces-1);
igl::copyleft::cgal::outer_facet(V, F, I, outer_facet, flipped);
#ifdef PROPAGATE_WINDING_NUMBER_TIMING
std::cout << "outer facet: " << tictoc() << std::endl;
#endif
const size_t outer_patch = P[outer_facet];
const size_t infinity_cell = per_patch_cells(outer_patch, flipped?1:0);
Eigen::VectorXi patch_labels(num_patches);
const int INVALID = std::numeric_limits<int>::max();
patch_labels.setConstant(INVALID);
for (size_t i=0; i<num_faces; i++) {
if (patch_labels[P[i]] == INVALID) {
patch_labels[P[i]] = labels[i];
} else {
assert(patch_labels[P[i]] == labels[i]);
}
}
assert((patch_labels.array() != INVALID).all());
const size_t num_labels = patch_labels.maxCoeff()+1;
Eigen::MatrixXi per_cell_W(num_cells, num_labels);
per_cell_W.setConstant(INVALID);
per_cell_W.row(infinity_cell).setZero();
std::queue<size_t> Q;
Q.push(infinity_cell);
while (!Q.empty()) {
size_t curr_cell = Q.front();
Q.pop();
for (const auto& neighbor : cell_adjacency[curr_cell]) {
size_t neighbor_cell, patch_idx;
bool direction;
std::tie(neighbor_cell, direction, patch_idx) = neighbor;
if ((per_cell_W.row(neighbor_cell).array() == INVALID).any()) {
per_cell_W.row(neighbor_cell) = per_cell_W.row(curr_cell);
for (size_t i=0; i<num_labels; i++) {
int inc = (patch_labels[patch_idx] == (int)i) ?
(direction ? -1:1) :0;
per_cell_W(neighbor_cell, i) =
per_cell_W(curr_cell, i) + inc;
}
Q.push(neighbor_cell);
} else {
#ifndef NDEBUG
// Checking for winding number consistency.
// This check would inevitably fail for meshes that contain open
// boundary or non-orientable. However, the inconsistent winding number
// field would still be useful in some cases such as when problem region
// is local and embedded within the volume. This, unfortunately, is the
// best we can do because the problem of computing integer winding
// number is ill-defined for open and non-orientable surfaces.
for (size_t i=0; i<num_labels; i++) {
if ((int)i == patch_labels[patch_idx]) {
int inc = direction ? -1:1;
//assert(per_cell_W(neighbor_cell, i) ==
// per_cell_W(curr_cell, i) + inc);
} else {
//assert(per_cell_W(neighbor_cell, i) ==
// per_cell_W(curr_cell, i));
}
}
#endif
}
}
}
#ifdef PROPAGATE_WINDING_NUMBER_TIMING
std::cout << "propagate winding number: " << tictoc() << std::endl;
#endif
W.resize(num_faces, num_labels*2);
for (size_t i=0; i<num_faces; i++) {
const size_t patch = P[i];
const size_t positive_cell = per_patch_cells(patch, 0);
const size_t negative_cell = per_patch_cells(patch, 1);
for (size_t j=0; j<num_labels; j++) {
W(i,j*2 ) = per_cell_W(positive_cell, j);
W(i,j*2+1) = per_cell_W(negative_cell, j);
}
}
#ifdef PROPAGATE_WINDING_NUMBER_TIMING
std::cout << "save result: " << tictoc() << std::endl;
#endif
}