mirror of https://github.com/CGAL/cgal
Make it work with Heat_method_traits_3
This commit is contained in:
Andreas Fabri
parent
347fab4d34
commit
470ce56df5
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@ -32,7 +32,11 @@ public:
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typedef unspecified_type Compute_y_3;
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typedef unspecified_type Compute_z_3;
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typedef unspecified_type Construct_vector_3;
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typedef unspecified_type Construct_sum_of_vectors_3;
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typedef unspecified_type Construct_scaled_vector_3;
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typedef unspecified_type Construct_cross_product_vector_3;
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typedef unspecified_type Compute_scalar_product_3;
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typedef unspecified_type Compute_squared_distance_3;
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/// @}
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@ -33,7 +33,8 @@ step will roughly double the overall preprocessing cost.
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In the next section we give some examples. Section \ref sec_HM_definitions presents
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the mathematical theory of the Heat method. The last section is about the \ref sec_HM_history.
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Note that this package requires the third party \ref thirdpartyEigen library.
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Note that this package depends on the third party \ref thirdpartyEigen library, or another
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model of the concept `SparseLinearAlgebraWithFactorTraits_d`.
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This implementation is based on \cgalCite{cgal:cww-ghnac-13} and \cgalCite{cgal:fsbs-acidt-06}
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@ -37,6 +37,8 @@ source vertices. }
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## Classes ##
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- `CGAL::Heat_method_3::Surface_mesh_geodesic_distances_3`
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- `CGAL::Heat_method_3::Direct`
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- `CGAL::Heat_method_3::Intrinsic_Delaunay`
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## Functions ##
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@ -54,6 +54,7 @@ include_directories( BEFORE include )
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include( CGAL_CreateSingleSourceCGALProgram )
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create_single_source_cgal_program( "heat_method.cpp" )
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create_single_source_cgal_program( "heat_method_concept.cpp" )
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create_single_source_cgal_program( "heat_method_polyhedron.cpp" )
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create_single_source_cgal_program( "heat_method_surface_mesh.cpp" )
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create_single_source_cgal_program( "heat_method_surface_mesh_intrinsic.cpp" )
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@ -231,6 +231,7 @@ private:
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double
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summation_of_edges() const
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{
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typename Traits::Compute_squared_distance_3 squared_distance = Traits().compute_squared_distance_3_object();
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double edge_sum = 0;
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CGAL::Vertex_around_face_iterator<TriangleMesh> vbegin, vend, vmiddle;
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BOOST_FOREACH(face_descriptor f, faces(tm)) {
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@ -245,9 +246,9 @@ private:
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VertexPointMap_reference pi = get(vpm,current);
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VertexPointMap_reference pj = get(vpm, neighbor_one);
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VertexPointMap_reference pk = get(vpm, neighbor_two);
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edge_sum += (CGAL::is_border(opposite(hd,tm),tm)?1.0:0.5) * std::sqrt(CGAL::squared_distance(pi,pj));
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edge_sum += (CGAL::is_border(opposite(hd2,tm),tm)?1.0:0.5) * std::sqrt(CGAL::squared_distance(pj,pk)) ;
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edge_sum += (CGAL::is_border(opposite(hd3,tm),tm)?1.0:0.5) * std::sqrt(CGAL::squared_distance(pk,pi)) ;
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edge_sum += (CGAL::is_border(opposite(hd,tm),tm)?1.0:0.5) * std::sqrt(squared_distance(pi,pj));
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edge_sum += (CGAL::is_border(opposite(hd2,tm),tm)?1.0:0.5) * std::sqrt(squared_distance(pj,pk)) ;
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edge_sum += (CGAL::is_border(opposite(hd3,tm),tm)?1.0:0.5) * std::sqrt(squared_distance(pk,pi)) ;
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}
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return edge_sum;
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}
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@ -312,6 +313,11 @@ private:
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void
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compute_unit_gradient()
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{
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Traits::Construct_vector_3 construct_vector = Traits().construct_vector_3_object();
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Traits::Construct_sum_of_vectors_3 sum = Traits().construct_sum_of_vectors_3_object();
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Traits::Compute_scalar_product_3 scalar_product = Traits().compute_scalar_product_3_object();
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Traits::Construct_cross_product_vector_3 cross_product = Traits().construct_cross_product_vector_3_object();
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Traits::Construct_scaled_vector_3 scale = Traits().construct_scaled_vector_3_object();
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if(X.empty()){
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X.resize(num_faces(tm));
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}
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@ -335,9 +341,13 @@ private:
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//cross that with eij, ejk, eki
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//so (Ncross eij) *uk and so on
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//sum all of those then multiply by 1./(2a)
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Vector_3 cross = CGAL::cross_product((p_j-p_i), (p_k-p_i));
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double N_cross = (CGAL::sqrt(cross*cross));
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Vector_3 unit_cross = cross/N_cross;
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Vector_3 v_ij = construct_vector(p_i,p_j);
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Vector_3 v_ik = construct_vector(p_i,p_k);
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Vector_3 cross = cross_product(v_ij, v_ik);
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double N_cross = (CGAL::sqrt(scalar_product(cross,cross)));
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Vector_3 unit_cross = scale(cross, 1./N_cross);
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double area_face = N_cross * (1./2);
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double u_i = CGAL::abs(solved_u(i));
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double u_j = CGAL::abs(solved_u(j));
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@ -349,25 +359,24 @@ private:
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u_j = u_j * r_Mag;
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u_k = u_k * r_Mag;
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}
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Vector_3 edge_sums = u_k * CGAL::cross_product(unit_cross,(p_j-p_i));
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edge_sums = edge_sums + u_i * (CGAL::cross_product(unit_cross, (p_k-p_j)));
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edge_sums = edge_sums + u_j * CGAL::cross_product(unit_cross, (p_i-p_k));
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edge_sums = edge_sums * (1./area_face);
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double e_magnitude = CGAL::sqrt(edge_sums*edge_sums);
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X[face_i] = edge_sums*(1./e_magnitude);
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Vector_3 edge_sums = scale(cross_product(unit_cross,v_ij), u_k);
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edge_sums = sum(edge_sums, scale(cross_product(unit_cross, construct_vector(p_j,p_k)), u_i));
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edge_sums = sum(edge_sums, scale(cross_product(unit_cross, construct_vector(p_k,p_i)), u_j));
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edge_sums = scale(edge_sums, (1./area_face));
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double e_magnitude = CGAL::sqrt(scalar_product(edge_sums,edge_sums));
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X[face_i] = scale(edge_sums,(1./e_magnitude));
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}
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}
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double
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dot_eigen_vector(const Vector_3& a, const Vector_3& b) const
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{
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return (a.x()*b.x() + a.y()*b.y() + a.z()*b.z());
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}
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void
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compute_divergence()
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{
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Traits::Construct_cross_product_vector_3 cross_product = Traits().construct_cross_product_vector_3_object();
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Traits::Compute_scalar_product_3 scalar_product = Traits().compute_scalar_product_3_object();
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Traits::Construct_vector_3 construct_vector = Traits().construct_vector_3_object();
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Matrix indexD(dimension,1);
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CGAL::Vertex_around_face_iterator<TriangleMesh> vbegin, vend, vmiddle;
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BOOST_FOREACH(face_descriptor f, faces(tm)) {
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@ -382,24 +391,32 @@ private:
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VertexPointMap_reference p_j = get(vpm, neighbor_one);
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VertexPointMap_reference p_k = get(vpm, neighbor_two);
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Index face_i = get(face_id_map, f);
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Vector_3 cross = CGAL::cross_product((p_j-p_i), (p_k-p_i));
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double norm_cross = (CGAL::sqrt(cross*cross));
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double dot = (p_j-p_i)*(p_k-p_i);
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Vector_3 v_ij = construct_vector(p_i,p_j);
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Vector_3 v_ik = construct_vector(p_i,p_k);
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Vector_3 cross = cross_product(v_ij, v_ik);
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double norm_cross = CGAL::sqrt(scalar_product(cross,cross));
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double dot = scalar_product(v_ij, v_ik);
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double cotan_i = dot/norm_cross;
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cross = CGAL::cross_product((p_i-p_j), (p_k-p_j));
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dot = to_double((p_i-p_j)*(p_k-p_j));
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Vector_3 v_ji = construct_vector(p_j, p_i);
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Vector_3 v_jk = construct_vector(p_j, p_k);
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cross = cross_product(v_ji, v_jk);
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dot = to_double(scalar_product(v_ji, v_jk));
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double cotan_j = dot/norm_cross;
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cross = CGAL::cross_product((p_i-p_k), (p_j-p_k));
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dot = to_double((p_i-p_k)*(p_j-p_k));
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Vector_3 v_ki = construct_vector(p_k,p_i);
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Vector_3 v_kj = construct_vector(p_k,p_j);
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cross = cross_product(v_ki, v_kj);
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dot = to_double(scalar_product(v_ki,v_kj));
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double cotan_k = dot/norm_cross;
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const Vector_3& a = X[face_i];
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double i_entry = cotan_k*(dot_eigen_vector(a,(p_j-p_i))) + cotan_j*(dot_eigen_vector(a,(p_k-p_i)));
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double j_entry = cotan_i*(dot_eigen_vector(a,(p_k-p_j))) + cotan_k*(dot_eigen_vector(a,(p_i-p_j)));
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double k_entry = cotan_j*(dot_eigen_vector(a,(p_i-p_k))) + cotan_i*(dot_eigen_vector(a,(p_j-p_k)));
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double i_entry = (scalar_product(a,v_ij) * cotan_k) + (scalar_product(a,v_ik) * cotan_j);
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double j_entry = (scalar_product(a,v_jk) * cotan_i) + (scalar_product(a,v_ji) * cotan_k);
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double k_entry = (scalar_product(a,v_ki) * cotan_j) + (scalar_product(a,v_kj) * cotan_i);
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indexD.add_coef(i, 0, (1./2)*i_entry);
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indexD.add_coef(j, 0, (1./2)*j_entry);
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@ -499,6 +516,10 @@ private:
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void
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build()
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{
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Traits::Construct_cross_product_vector_3 cross_product = Traits().construct_cross_product_vector_3_object();
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Traits::Compute_scalar_product_3 scalar_product = Traits().compute_scalar_product_3_object();
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Traits::Construct_vector_3 construct_vector = Traits().construct_vector_3_object();
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source_change_flag = false;
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CGAL_precondition(is_triangle_mesh(tm));
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@ -540,27 +561,35 @@ private:
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pj = p_j;
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pk = p_k;
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Vector_3 cross = CGAL::cross_product((pj-pi), (pk-pi));
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double dot = (pj-pi)*(pk-pi);
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double norm_cross = (CGAL::sqrt(cross*cross));
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Vector_3 v_ij = construct_vector(p_i,p_j);
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Vector_3 v_ik = construct_vector(p_i,p_k);
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Vector_3 cross = cross_product(v_ij, v_ik);
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double dot = scalar_product(v_ij,v_ik);
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double norm_cross = (CGAL::sqrt(scalar_product(cross,cross)));
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double cotan_i = dot/norm_cross;
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m_cotan_matrix.add_coef(j,k ,-(1./2)*cotan_i);
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m_cotan_matrix.add_coef(k,j,-(1./2)* cotan_i);
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m_cotan_matrix.add_coef(j,j,(1./2)*cotan_i);
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m_cotan_matrix.add_coef(k,k,(1./2)* cotan_i);
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cross = CGAL::cross_product((pi-pj), (pk-pj));
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dot = to_double((pi-pj)*(pk-pj));
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Vector_3 v_ji = construct_vector(p_j,p_i);
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Vector_3 v_jk = construct_vector(p_j,p_k);
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cross = cross_product(v_ji, v_jk);
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dot = to_double(scalar_product(v_ji, v_jk));
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double cotan_j = dot/norm_cross;
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m_cotan_matrix.add_coef(i,k ,-(1./2)*cotan_j);
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m_cotan_matrix.add_coef(k,i,-(1./2)* cotan_j);
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m_cotan_matrix.add_coef(i,i,(1./2)* cotan_j);
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m_cotan_matrix.add_coef(k,k,(1./2)* cotan_j);
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cross = CGAL::cross_product((pi-pk), (pj-pk));
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dot = to_double((pi-pk)*(pj-pk));
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Vector_3 v_ki = construct_vector(p_k,p_i);
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Vector_3 v_kj = construct_vector(p_k,p_j);
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cross = cross_product(v_ki, v_kj);
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dot = to_double(scalar_product(v_ki,v_kj));
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double cotan_k = dot/norm_cross;
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m_cotan_matrix.add_coef(i,j,-(1./2)*cotan_k);
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m_cotan_matrix.add_coef(j,i,-(1./2)* cotan_k);
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@ -604,9 +633,7 @@ private:
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Vector solved_phi;
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std::set<Index> source_index;
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bool source_change_flag;
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std::vector<Eigen::Triplet<double> > m_triplets;
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};
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template <typename TriangleMesh,
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@ -859,7 +886,8 @@ public:
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/// \ingroup PkgHeatMethod
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/// computes for each vertex of the triangle mesh `tm` the estimated geodesic distance to a given source vertex.
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/// \tparam TriangleMesh a triangulated surface mesh, model of `FaceListGraph` and `HalfedgeListGraph`
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/// \tparam TriangleMesh a triangulated surface mesh, model of `FaceListGraph` and `HalfedgeListGraph`.
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/// It must have an internal vertex point property map with the value type being a 3D point from a cgal Kernel model
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/// \tparam VertexDistanceMap a property map model of `WritablePropertyMap`
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/// with `boost::graph_traits<TriangleMesh>::vertex_descriptor` as key type and `double` as value type.
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/// \tparam Mode either the tag `Direct` or `Intrinsic_Delaunay`, which determines if the geodesic distance
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@ -867,7 +895,7 @@ public:
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/// The default is `Direct`.
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///
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/// \sa CGAL::Heat_method_3::Surface_mesh_geodesic_distances_3
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template <typename TriangleMesh, typename VertexDistanceMap,Mode>
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template <typename TriangleMesh, typename VertexDistanceMap, typename Mode>
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void
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estimate_geodesic_distances(const TriangleMesh& tm,
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VertexDistanceMap vdm,
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@ -879,7 +907,8 @@ estimate_geodesic_distances(const TriangleMesh& tm,
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hm.estimate_geodesic_distances(vdm);
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}
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#ifndef DOXYGEN_RUNNING
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template <typename TriangleMesh, typename VertexDistanceMap>
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void
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estimate_geodesic_distances(const TriangleMesh& tm,
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@ -890,11 +919,13 @@ estimate_geodesic_distances(const TriangleMesh& tm,
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hm.add_source(source);
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hm.estimate_geodesic_distances(vdm);
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}
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#endif
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/// \ingroup PkgHeatMethod
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/// \ingroup PkgHeatMethod
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/// computes for each vertex of the triangle mesh `tm` the estimated geodesic distance to a given set of source vertices.
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/// \tparam TriangleMesh a triangulated surface mesh, model of `FaceListGraph` and `HalfedgeListGraph`
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/// It must have an internal vertex point property map with the value type being a 3D point from a cgal Kernel model
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/// \tparam VertexDistanceMap a property map model of `WritablePropertyMap`
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/// with `boost::graph_traits<TriangleMesh>::vertex_descriptor` as key type and `double` as value type.
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/// \tparam VertexRange a range with value type `boost::graph_traits<TriangleMesh>::vertex_descriptor`
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@ -24,6 +24,8 @@
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#include <CGAL/license/Heat_method_3.h>
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#ifndef DOXYGEN_RUNNING
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namespace CGAL {
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namespace Heat_method_3 {
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@ -39,7 +41,7 @@ namespace Heat_method_3 {
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return t;
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}
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};
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#endif
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} // namespace Heat_method_3
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} // namespace CGAL
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#endif //CGAL_HEAT_METHOD_3_INTERNAL_V2V_H
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@ -53,6 +53,7 @@ include( CGAL_CreateSingleSourceCGALProgram )
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create_single_source_cgal_program( "validate.cpp" )
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create_single_source_cgal_program( "idt.cpp" )
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create_single_source_cgal_program( "heat_method_concept.cpp" )
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create_single_source_cgal_program( "heat_method_surface_mesh_test.cpp" )
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create_single_source_cgal_program( "heat_method_intrinsic_surface_mesh_test.cpp" )
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create_single_source_cgal_program( "intrinsic_delaunay_triangulation_test.cpp" )
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@ -0,0 +1,123 @@
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struct Heat_method_traits_3
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{
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typedef double FT;
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struct Point_3 {
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Point_3()
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{}
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Point_3(double, double,double)
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{}
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Point_3(const Point_3&)
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{}
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};
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struct Vector_3 {
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Vector_3()
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{}
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Vector_3(double, double, double)
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{}
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Vector_3(const Vector_3&)
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{}
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};
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struct Point_2 {
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Point_2()
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{}
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Point_2(double, double)
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{}
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Point_2(const Point_2&)
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{}
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};
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struct Compute_x_2 {
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double operator()(const Point_2&)const
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{return 0;}
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};
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struct Compute_y_2 {
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double operator()(const Point_2&)const
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{return 0;}
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};
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struct Construct_vector_3{
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Vector_3 operator()(const Point_3&, const Point_3&) const
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{ return Vector_3();}
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};
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struct Construct_scaled_vector_3{
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Vector_3 operator()(const Vector_3&, double) const
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{ return Vector_3();}
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};
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struct Construct_cross_product_vector_3 {
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Vector_3 operator()(const Vector_3&, const Vector_3&) const
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{ return Vector_3();}
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};
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||||
|
||||
struct Construct_sum_of_vectors_3 {
|
||||
|
||||
Vector_3 operator()(const Vector_3&, const Vector_3&) const
|
||||
{ return Vector_3();}
|
||||
};
|
||||
struct Compute_scalar_product_3 {
|
||||
|
||||
double operator()(const Vector_3&, const Vector_3&) const
|
||||
{ return 0;}
|
||||
};
|
||||
|
||||
struct Compute_squared_distance_3 {
|
||||
|
||||
double operator()(const Point_3&, const Point_3&) const
|
||||
{ return 0;}
|
||||
};
|
||||
|
||||
Compute_x_2 compute_x_2_object() const
|
||||
{
|
||||
return Compute_x_2();
|
||||
}
|
||||
|
||||
Compute_y_2 compute_y_2_object() const
|
||||
{
|
||||
return Compute_y_2();
|
||||
}
|
||||
|
||||
|
||||
Construct_vector_3 construct_vector_3_object() const
|
||||
{
|
||||
return Construct_vector_3();
|
||||
}
|
||||
Construct_scaled_vector_3 construct_scaled_vector_3_object() const
|
||||
{
|
||||
return Construct_scaled_vector_3();
|
||||
}
|
||||
|
||||
Construct_cross_product_vector_3 construct_cross_product_vector_3_object() const
|
||||
{
|
||||
return Construct_cross_product_vector_3();
|
||||
}
|
||||
|
||||
Compute_squared_distance_3 compute_squared_distance_3_object() const
|
||||
{
|
||||
return Compute_squared_distance_3();
|
||||
}
|
||||
|
||||
Compute_scalar_product_3 compute_scalar_product_3_object() const
|
||||
{
|
||||
return Compute_scalar_product_3();
|
||||
}
|
||||
|
||||
Construct_sum_of_vectors_3 construct_sum_of_vectors_3_object() const
|
||||
{
|
||||
return Construct_sum_of_vectors_3();
|
||||
}
|
||||
};
|
||||
|
|
@ -0,0 +1,63 @@
|
|||
#include <CGAL/Simple_cartesian.h>
|
||||
#include <CGAL/Surface_mesh.h>
|
||||
#include <CGAL/Heat_method_3/Surface_mesh_geodesic_distances_3.h>
|
||||
|
||||
#include "Heat_method_3/Heat_method_traits_3.h"
|
||||
|
||||
#include <fstream>
|
||||
#include <iostream>
|
||||
|
||||
#include <boost/foreach.hpp>
|
||||
|
||||
typedef Heat_method_traits_3 Kernel;
|
||||
typedef Kernel::Point_3 Point_3;
|
||||
typedef CGAL::Surface_mesh<Point_3> Surface_mesh;
|
||||
|
||||
typedef boost::graph_traits<Surface_mesh>::vertex_descriptor vertex_descriptor;
|
||||
typedef Surface_mesh::Property_map<vertex_descriptor,double> Vertex_distance_map;
|
||||
typedef CGAL::Heat_method_3::Surface_mesh_geodesic_distances_3<Surface_mesh,
|
||||
CGAL::Heat_method_3::Direct,
|
||||
CGAL::Eigen_solver_traits<Eigen::SimplicialLDLT<CGAL::Eigen_sparse_matrix<double>::EigenType > >,
|
||||
boost::property_map< Surface_mesh, CGAL::vertex_point_t>::const_type,
|
||||
Kernel> Heat_method;
|
||||
|
||||
|
||||
|
||||
int main(int argc, char* argv[])
|
||||
{
|
||||
//read in mesh
|
||||
Surface_mesh sm;
|
||||
|
||||
//the heat intensity will hold the distance values from the source set
|
||||
Vertex_distance_map heat_intensity = sm.add_property_map<vertex_descriptor, double>("v:heat_intensity", 0).first;
|
||||
|
||||
Heat_method hm(sm);
|
||||
|
||||
//add the first vertex as the source set
|
||||
vertex_descriptor source = *(vertices(sm).first);
|
||||
hm.add_source(source);
|
||||
hm.estimate_geodesic_distances(heat_intensity);
|
||||
|
||||
Point_3 sp = sm.point(source);
|
||||
|
||||
vertex_descriptor far;
|
||||
double sdistance = 0;
|
||||
|
||||
BOOST_FOREACH(vertex_descriptor vd , vertices(sm)){
|
||||
std::cout << vd << " is at distance " << get(heat_intensity, vd) << " from " << source << std::endl;
|
||||
/*
|
||||
if(squared_distance(sp,sm.point(vd)) > sdistance){
|
||||
far = vd;
|
||||
sdistance = squared_distance(sp,sm.point(vd));
|
||||
}
|
||||
*/
|
||||
}
|
||||
hm.add_source(far);
|
||||
hm.estimate_geodesic_distances(heat_intensity);
|
||||
|
||||
BOOST_FOREACH(vertex_descriptor vd , vertices(sm)){
|
||||
std::cout << vd << " is at distance " << get(heat_intensity, vd) << " " << std::endl;
|
||||
}
|
||||
|
||||
return 0;
|
||||
}
|
||||
|
|
@ -10,7 +10,7 @@
|
|||
#include <QMessageBox>
|
||||
#include <CGAL/boost/graph/helpers.h>
|
||||
#include <CGAL/Polygon_mesh_processing/compute_normal.h>
|
||||
#include <CGAL/Heat_method_3/Heat_method_3.h>
|
||||
#include <CGAL/Heat_method_3/Surface_mesh_geodesic_distances_3.h>
|
||||
|
||||
#include "Scene_points_with_normal_item.h"
|
||||
#include "Messages_interface.h"
|
||||
|
|
@ -309,8 +309,8 @@ class DisplayPropertyPlugin :
|
|||
Q_INTERFACES(CGAL::Three::Polyhedron_demo_plugin_interface)
|
||||
Q_PLUGIN_METADATA(IID "com.geometryfactory.PolyhedronDemo.PluginInterface/1.0")
|
||||
typedef SMesh::Property_map<boost::graph_traits<SMesh>::vertex_descriptor, double> Vertex_distance_map;
|
||||
typedef CGAL::Heat_method_3::Heat_method_3<SMesh> Heat_method;
|
||||
typedef CGAL::Heat_method_3::Heat_method_3<SMesh, CGAL::Tag_true> Heat_method_idt;
|
||||
typedef CGAL::Heat_method_3::Surface_mesh_geodesic_distances_3<SMesh> Heat_method;
|
||||
typedef CGAL::Heat_method_3::Surface_mesh_geodesic_distances_3<SMesh, CGAL::Heat_method_3::Intrinsic_Delaunay> Heat_method_idt;
|
||||
|
||||
public:
|
||||
|
||||
|
|
@ -769,9 +769,9 @@ private Q_SLOTS:
|
|||
}
|
||||
|
||||
if(iDT){
|
||||
hm_idt->fill_distance_map(heat_intensity);
|
||||
hm_idt->estimate_geodesic_distances(heat_intensity);
|
||||
}else{
|
||||
hm->fill_distance_map(heat_intensity);
|
||||
hm->estimate_geodesic_distances(heat_intensity);
|
||||
}
|
||||
|
||||
double max = 0;
|
||||
|
|
|
|||
Loading…
Reference in New Issue