Field<T,VertexHandle> gaussian_curvatures(const TriMesh& mesh) {
// Compute mixed areas
Field<T,VertexHandle> area(mesh.n_vertices()); // Actually 8*area
for (const auto f : mesh.face_handles()) {
const auto v = mesh.vertex_handles(f);
const TV x0 = mesh.point(v.x),
x1 = mesh.point(v.y),
x2 = mesh.point(v.z),
x01 = x1-x0,
x12 = x2-x1,
x20 = x0-x2;
const T cot0 = cot(x01,x20),
cot1 = cot(x01,x12),
cot2 = cot(x12,x20);
// Compute A_mixed as in Meyer et al.
if (cot0<=0 && cot1<=0 && cot2<=0) { // Voronoi case
const T area0 = cot0*sqr_magnitude(x12),
area1 = cot1*sqr_magnitude(x20),
area2 = cot2*sqr_magnitude(x01);
area[v.x] -= (area1+area2);
area[v.y] -= (area2+area0);
area[v.z] -= (area0+area1);
} else { // One of the triangles is obtuse
const T a = 2*mesh.area(f);
area[v.x] += (1+(cot0>0))*a;
area[v.y] += (1+(cot1>0))*a;
area[v.z] += (1+(cot2>0))*a;
}
}
// Compute curvatures
Field<T,VertexHandle> K(mesh.n_vertices(),uninit);
for (const auto v : mesh.vertex_handles()) {
const TV x = mesh.point(v);
T sum = 0;
for (auto e=mesh.cvoh_iter(v);e;++e)
if (!mesh.is_boundary(e)) {
const auto v0 = mesh.to_vertex_handle(e),
v1 = mesh.from_vertex_handle(mesh.prev_halfedge_handle(e));
sum += angle_between(mesh.point(v0)-x,mesh.point(v1)-x);
}
K[v] = 8*((1+!mesh.is_boundary(v))*pi-sum)/area(v);
}
return K;
}
void MeshDenoisingViaL0Minimization::calculateAreaBasedEdgeOperator(TriMesh &mesh,
std::vector<TriMesh::Point> &area_based_edge_operator,
std::vector< std::vector<TriMesh::VertexHandle> > &edge_vertex_handle,
std::vector< std::vector<double> > &coef)
{
std::vector<double> face_area;
getFaceArea(mesh, face_area);
area_based_edge_operator.resize((int)mesh.n_edges(), TriMesh::Point(0.0, 0.0, 0.0));
std::vector<double> temp_coef(4, 0.0);
coef.resize(mesh.n_edges(), temp_coef);
std::vector<TriMesh::VertexHandle> vertex_handle(4);
edge_vertex_handle.resize(mesh.n_edges(), vertex_handle);
for(TriMesh::EdgeIter e_it = mesh.edges_begin(); e_it != mesh.edges_end(); e_it++)
{
if(!mesh.is_boundary(*e_it))
{
int index = e_it->idx();
double edge_length = mesh.calc_edge_length(*e_it);
// get four vertices correspond to edge *e_it
TriMesh::HalfedgeHandle he = mesh.halfedge_handle(*e_it, 0);
TriMesh::VertexHandle v1 = mesh.from_vertex_handle(he);
TriMesh::VertexHandle v3 = mesh.to_vertex_handle(he);
TriMesh::HalfedgeHandle he_next = mesh.next_halfedge_handle(he);
TriMesh::VertexHandle v4 = mesh.to_vertex_handle(he_next);
TriMesh::HalfedgeHandle he_oppo = mesh.opposite_halfedge_handle(he);
TriMesh::HalfedgeHandle he_oppo_next = mesh.next_halfedge_handle(he_oppo);
TriMesh::VertexHandle v2 = mesh.to_vertex_handle(he_oppo_next);
// two faces
TriMesh::FaceHandle f1 = mesh.face_handle(he);
TriMesh::FaceHandle f2 = mesh.face_handle(he_oppo);
// the area of two faces correspond to edge *e_it
double area134 = face_area[f1.idx()];
double area123 = face_area[f2.idx()];
double totalArea = area123 + area134;
TriMesh::Point p1 = mesh.point(v1);
TriMesh::Point p2 = mesh.point(v2);
TriMesh::Point p3 = mesh.point(v3);
TriMesh::Point p4 = mesh.point(v4);
TriMesh::Point p12 = p1 - p2;
TriMesh::Point p13 = p1 - p3;
TriMesh::Point p14 = p1 - p4;
TriMesh::Point p23 = p2 - p3;
TriMesh::Point p34 = p3 - p4;
// calc coefficient
temp_coef[0] = (area123 * (p34 | p13) - area134 * (p13 | p23)) / (edge_length * edge_length * totalArea);
temp_coef[1] = area134 / totalArea;
temp_coef[2] = (-area123 * (p13 | p14) - area134 * (p12 | p13)) / (edge_length * edge_length * totalArea);
temp_coef[3] = area123 / totalArea;
coef[index] = temp_coef;
vertex_handle[0] = v1;
vertex_handle[1] = v2;
vertex_handle[2] = v3;
vertex_handle[3] = v4;
edge_vertex_handle[index] = vertex_handle;
// calc area-based edge operator
TriMesh::Point pt = p1 * temp_coef[0] + p2 * temp_coef[1] + p3 * temp_coef[2] + p4 * temp_coef[3];
area_based_edge_operator[index] = pt;
}
}
}
