void igl::copyleft::cgal::order_facets_around_edge(
const Eigen::PlainObjectBase<DerivedV>& V,
const Eigen::PlainObjectBase<DerivedF>& F,
size_t s,
size_t d,
const std::vector<int>& adj_faces,
Eigen::PlainObjectBase<DerivedI>& order, bool debug)
{
// Although we only need exact predicates in the algorithm,
// exact constructions are needed to avoid degeneracies due to
// casting to double.
typedef CGAL::Exact_predicates_exact_constructions_kernel K;
typedef K::Point_3 Point_3;
typedef K::Plane_3 Plane_3;
auto get_face_index = [&](int adj_f)->size_t
{
return abs(adj_f) - 1;
};
auto get_opposite_vertex = [&](size_t fid)->size_t
{
typedef typename DerivedF::Scalar Index;
if (F(fid, 0) != (Index)s && F(fid, 0) != (Index)d) return F(fid, 0);
if (F(fid, 1) != (Index)s && F(fid, 1) != (Index)d) return F(fid, 1);
if (F(fid, 2) != (Index)s && F(fid, 2) != (Index)d) return F(fid, 2);
assert(false);
return -1;
};
// Handle base cases
if (adj_faces.size() == 0)
{
order.resize(0, 1);
return;
} else if (adj_faces.size() == 1)
{
order.resize(1, 1);
order(0, 0) = 0;
return;
} else if (adj_faces.size() == 2)
{
const size_t o1 = get_opposite_vertex(get_face_index(adj_faces[0]));
const size_t o2 = get_opposite_vertex(get_face_index(adj_faces[1]));
const Point_3 ps(V(s, 0), V(s, 1), V(s, 2));
const Point_3 pd(V(d, 0), V(d, 1), V(d, 2));
const Point_3 p1(V(o1, 0), V(o1, 1), V(o1, 2));
const Point_3 p2(V(o2, 0), V(o2, 1), V(o2, 2));
order.resize(2, 1);
switch (CGAL::orientation(ps, pd, p1, p2))
{
case CGAL::POSITIVE:
order(0, 0) = 1;
order(1, 0) = 0;
break;
case CGAL::NEGATIVE:
order(0, 0) = 0;
order(1, 0) = 1;
break;
case CGAL::COPLANAR:
{
switch (CGAL::coplanar_orientation(ps, pd, p1, p2)) {
case CGAL::POSITIVE:
// Duplicated face, use index to break tie.
order(0, 0) = adj_faces[0] < adj_faces[1] ? 0:1;
order(1, 0) = adj_faces[0] < adj_faces[1] ? 1:0;
break;
case CGAL::NEGATIVE:
// Coplanar faces, one on each side of the edge.
// It is equally valid to order them (0, 1) or (1, 0).
// I cannot think of any reason to prefer one to the
// other. So just use (0, 1) ordering by default.
order(0, 0) = 0;
order(1, 0) = 1;
break;
case CGAL::COLLINEAR:
std::cerr << "Degenerated triangle detected." <<
std::endl;
assert(false);
break;
default:
assert(false);
}
}
break;
default:
assert(false);
}
return;
}
const size_t num_adj_faces = adj_faces.size();
const size_t o = get_opposite_vertex( get_face_index(adj_faces[0]));
const Point_3 p_s(V(s, 0), V(s, 1), V(s, 2));
const Point_3 p_d(V(d, 0), V(d, 1), V(d, 2));
const Point_3 p_o(V(o, 0), V(o, 1), V(o, 2));
const Plane_3 separator(p_s, p_d, p_o);
if (separator.is_degenerate()) {
throw std::runtime_error(
"Cannot order facets around edge due to degenerated facets");
}
std::vector<Point_3> opposite_vertices;
for (size_t i=0; i<num_adj_faces; i++)
{
const size_t o = get_opposite_vertex( get_face_index(adj_faces[i]));
opposite_vertices.emplace_back(
V(o, 0), V(o, 1), V(o, 2));
}
std::vector<int> positive_side;
std::vector<int> negative_side;
std::vector<int> tie_positive_oriented;
std::vector<int> tie_negative_oriented;
std::vector<size_t> positive_side_index;
std::vector<size_t> negative_side_index;
std::vector<size_t> tie_positive_oriented_index;
std::vector<size_t> tie_negative_oriented_index;
for (size_t i=0; i<num_adj_faces; i++)
{
const int f = adj_faces[i];
const Point_3& p_a = opposite_vertices[i];
auto orientation = separator.oriented_side(p_a);
switch (orientation) {
case CGAL::ON_POSITIVE_SIDE:
positive_side.push_back(f);
positive_side_index.push_back(i);
break;
case CGAL::ON_NEGATIVE_SIDE:
negative_side.push_back(f);
negative_side_index.push_back(i);
break;
case CGAL::ON_ORIENTED_BOUNDARY:
{
auto inplane_orientation = CGAL::coplanar_orientation(
p_s, p_d, p_o, p_a);
switch (inplane_orientation) {
case CGAL::POSITIVE:
tie_positive_oriented.push_back(f);
tie_positive_oriented_index.push_back(i);
break;
case CGAL::NEGATIVE:
tie_negative_oriented.push_back(f);
tie_negative_oriented_index.push_back(i);
break;
case CGAL::COLLINEAR:
default:
throw std::runtime_error(
"Degenerated facet detected.");
break;
}
}
break;
default:
// Should not be here.
throw std::runtime_error("Unknown CGAL state detected.");
}
}
if (debug) {
std::cout << "tie positive: " << std::endl;
for (auto& f : tie_positive_oriented) {
std::cout << get_face_index(f) << " ";
}
std::cout << std::endl;
std::cout << "positive side: " << std::endl;
for (auto& f : positive_side) {
std::cout << get_face_index(f) << " ";
}
std::cout << std::endl;
std::cout << "tie negative: " << std::endl;
for (auto& f : tie_negative_oriented) {
std::cout << get_face_index(f) << " ";
}
std::cout << std::endl;
std::cout << "negative side: " << std::endl;
for (auto& f : negative_side) {
std::cout << get_face_index(f) << " ";
}
std::cout << std::endl;
}
auto index_sort = [](std::vector<int>& data) -> std::vector<size_t>{
const size_t len = data.size();
std::vector<size_t> order(len);
for (size_t i=0; i<len; i++) { order[i] = i; }
auto comp = [&](size_t i, size_t j) { return data[i] < data[j]; };
std::sort(order.begin(), order.end(), comp);
return order;
};
Eigen::PlainObjectBase<DerivedI> positive_order, negative_order;
order_facets_around_edge(V, F, s, d, positive_side, positive_order, debug);
order_facets_around_edge(V, F, s, d, negative_side, negative_order, debug);
std::vector<size_t> tie_positive_order = index_sort(tie_positive_oriented);
std::vector<size_t> tie_negative_order = index_sort(tie_negative_oriented);
// Copy results into order vector.
const size_t tie_positive_size = tie_positive_oriented.size();
const size_t tie_negative_size = tie_negative_oriented.size();
const size_t positive_size = positive_order.size();
const size_t negative_size = negative_order.size();
order.resize(
tie_positive_size + positive_size + tie_negative_size + negative_size,1);
size_t count=0;
for (size_t i=0; i<tie_positive_size; i++)
{
order(count+i, 0) = tie_positive_oriented_index[tie_positive_order[i]];
}
count += tie_positive_size;
for (size_t i=0; i<negative_size; i++)
{
order(count+i, 0) = negative_side_index[negative_order(i, 0)];
}
count += negative_size;
for (size_t i=0; i<tie_negative_size; i++)
{
order(count+i, 0) = tie_negative_oriented_index[tie_negative_order[i]];
}
count += tie_negative_size;
for (size_t i=0; i<positive_size; i++)
{
order(count+i, 0) = positive_side_index[positive_order(i, 0)];
}
count += positive_size;
assert(count == num_adj_faces);
// Find the correct start point.
size_t start_idx = 0;
for (size_t i=0; i<num_adj_faces; i++)
{
const Point_3& p_a = opposite_vertices[order(i, 0)];
const Point_3& p_b =
opposite_vertices[order((i+1)%num_adj_faces, 0)];
auto orientation = CGAL::orientation(p_s, p_d, p_a, p_b);
if (orientation == CGAL::POSITIVE)
{
// Angle between triangle (p_s, p_d, p_a) and (p_s, p_d, p_b) is
// more than 180 degrees.
start_idx = (i+1)%num_adj_faces;
break;
} else if (orientation == CGAL::COPLANAR &&
Plane_3(p_s, p_d, p_a).orthogonal_direction() !=
Plane_3(p_s, p_d, p_b).orthogonal_direction())
{
// All 4 points are coplanar, but p_a and p_b are on each side of
// the edge (p_s, p_d). This means the angle between triangle
// (p_s, p_d, p_a) and (p_s, p_d, p_b) is exactly 180 degrees.
start_idx = (i+1)%num_adj_faces;
break;
}
}
DerivedI circular_order = order;
for (size_t i=0; i<num_adj_faces; i++)
{
order(i, 0) = circular_order((start_idx + i)%num_adj_faces, 0);
}
}
