// Poisson reconstruction method: // Reconstructs a surface mesh from a point set and returns it as a polyhedron. Polyhedron* poisson_reconstruct(const Point_set& points, Kernel::FT sm_angle, // Min triangle angle (degrees). Kernel::FT sm_radius, // Max triangle size w.r.t. point set average spacing. Kernel::FT sm_distance, // Approximation error w.r.t. point set average spacing. const QString& solver_name, bool use_two_passes) // solver name { CGAL::Timer task_timer; task_timer.start(); //*************************************** // Checks requirements //*************************************** if (points.size() == 0) { std::cerr << "Error: empty point set" << std::endl; return NULL; } bool points_have_normals = (points.begin()->normal() != CGAL::NULL_VECTOR); if ( ! points_have_normals ) { std::cerr << "Input point set not supported: this reconstruction method requires oriented normals" << std::endl; return NULL; } CGAL::Timer reconstruction_timer; reconstruction_timer.start(); //*************************************** // Computes implicit function //*************************************** std::cerr << "Computes Poisson implicit function " << "using " << solver_name.toLatin1().data() << " solver...\n"; // Creates implicit function from the point set. // Note: this method requires an iterator over points // + property maps to access each point's position and normal. // The position property map can be omitted here as we use iterators over Point_3 elements. Poisson_reconstruction_function function( points.begin(), points.end(), CGAL::make_normal_of_point_with_normal_pmap(Point_set::value_type())); bool ok = false; #ifdef CGAL_EIGEN3_ENABLED if(solver_name=="Eigen - built-in simplicial LDLt") { CGAL::Eigen_solver_traits<Eigen::SimplicialCholesky<CGAL::Eigen_sparse_matrix<double>::EigenType> > solver; ok = function.compute_implicit_function(solver, use_two_passes); } if(solver_name=="Eigen - built-in CG") { CGAL::Eigen_solver_traits<Eigen::ConjugateGradient<CGAL::Eigen_sparse_matrix<double>::EigenType> > solver; solver.solver().setTolerance(1e-6); solver.solver().setMaxIterations(1000); ok = function.compute_implicit_function(solver, use_two_passes); } #endif // Computes the Poisson indicator function f() // at each vertex of the triangulation. if ( ! ok ) { std::cerr << "Error: cannot compute implicit function" << std::endl; return NULL; } // Prints status std::cerr << "Total implicit function (triangulation+refinement+solver): " << task_timer.time() << " seconds\n"; task_timer.reset(); //*************************************** // Surface mesh generation //*************************************** std::cerr << "Surface meshing...\n"; // Computes average spacing Kernel::FT average_spacing = CGAL::compute_average_spacing(points.begin(), points.end(), 6 /* knn = 1 ring */); // Gets one point inside the implicit surface Kernel::Point_3 inner_point = function.get_inner_point(); Kernel::FT inner_point_value = function(inner_point); if(inner_point_value >= 0.0) { std::cerr << "Error: unable to seed (" << inner_point_value << " at inner_point)" << std::endl; return NULL; } // Gets implicit function's radius Kernel::Sphere_3 bsphere = function.bounding_sphere(); Kernel::FT radius = std::sqrt(bsphere.squared_radius()); // Defines the implicit surface: requires defining a // conservative bounding sphere centered at inner point. Kernel::FT sm_sphere_radius = 5.0 * radius; Kernel::FT sm_dichotomy_error = sm_distance*average_spacing/1000.0; // Dichotomy error must be << sm_distance Surface_3 surface(function, Kernel::Sphere_3(inner_point,sm_sphere_radius*sm_sphere_radius), sm_dichotomy_error/sm_sphere_radius); // Defines surface mesh generation criteria CGAL::Surface_mesh_default_criteria_3<STr> criteria(sm_angle, // Min triangle angle (degrees) sm_radius*average_spacing, // Max triangle size sm_distance*average_spacing); // Approximation error CGAL_TRACE_STREAM << " make_surface_mesh(sphere center=("<<inner_point << "),\n" << " sphere radius="<<sm_sphere_radius<<",\n" << " angle="<<sm_angle << " degrees,\n" << " triangle size="<<sm_radius<<" * average spacing="<<sm_radius*average_spacing<<",\n" << " distance="<<sm_distance<<" * average spacing="<<sm_distance*average_spacing<<",\n" << " dichotomy error=distance/"<<sm_distance*average_spacing/sm_dichotomy_error<<",\n" << " Manifold_with_boundary_tag)\n"; // Generates surface mesh with manifold option STr tr; // 3D Delaunay triangulation for surface mesh generation C2t3 c2t3(tr); // 2D complex in 3D Delaunay triangulation CGAL::make_surface_mesh(c2t3, // reconstructed mesh surface, // implicit surface criteria, // meshing criteria CGAL::Manifold_with_boundary_tag()); // require manifold mesh // Prints status std::cerr << "Surface meshing: " << task_timer.time() << " seconds, " << tr.number_of_vertices() << " output vertices" << std::endl; task_timer.reset(); if(tr.number_of_vertices() == 0) return NULL; // Converts to polyhedron Polyhedron* output_mesh = new Polyhedron; CGAL::output_surface_facets_to_polyhedron(c2t3, *output_mesh); // Prints total reconstruction duration std::cerr << "Total reconstruction (implicit function + meshing): " << reconstruction_timer.time() << " seconds\n"; //*************************************** // Computes reconstruction error //*************************************** // Constructs AABB tree and computes internal KD-tree // data structure to accelerate distance queries AABB_tree tree(faces(*output_mesh).first, faces(*output_mesh).second, *output_mesh); tree.accelerate_distance_queries(); // Computes distance from each input point to reconstructed mesh double max_distance = DBL_MIN; double avg_distance = 0; for (Point_set::const_iterator p=points.begin(); p!=points.end(); p++) { double distance = std::sqrt(tree.squared_distance(*p)); max_distance = (std::max)(max_distance, distance); avg_distance += distance; } avg_distance /= double(points.size()); std::cerr << "Reconstruction error:\n" << " max = " << max_distance << " = " << max_distance/average_spacing << " * average spacing\n" << " avg = " << avg_distance << " = " << avg_distance/average_spacing << " * average spacing\n"; return output_mesh; }
bool poisson_reconstruct(FaceGraph* graph, Point_set& points, typename Traits::FT sm_angle, // Min triangle angle (degrees). typename Traits::FT sm_radius, // Max triangle size w.r.t. point set average spacing. typename Traits::FT sm_distance, // Approximation error w.r.t. point set average spacing. const QString& solver_name, // solver name bool use_two_passes, bool do_not_fill_holes) { // Poisson implicit function typedef CGAL::Poisson_reconstruction_function<Traits> Poisson_reconstruction_function; // Surface mesher typedef CGAL::Surface_mesh_default_triangulation_3 STr; typedef CGAL::Surface_mesh_complex_2_in_triangulation_3<STr> C2t3; typedef CGAL::Implicit_surface_3<Traits, Poisson_reconstruction_function> Surface_3; // AABB tree typedef CGAL::AABB_face_graph_triangle_primitive<FaceGraph> Primitive; typedef CGAL::AABB_traits<Traits, Primitive> AABB_traits; typedef CGAL::AABB_tree<AABB_traits> AABB_tree; CGAL::Timer task_timer; task_timer.start(); //*************************************** // Checks requirements //*************************************** if (points.size() == 0) { std::cerr << "Error: empty point set" << std::endl; return false; } bool points_have_normals = points.has_normal_map(); if ( ! points_have_normals ) { std::cerr << "Input point set not supported: this reconstruction method requires oriented normals" << std::endl; return false; } CGAL::Timer reconstruction_timer; reconstruction_timer.start(); //*************************************** // Computes implicit function //*************************************** std::cerr << "Computes Poisson implicit function " << "using " << solver_name.toLatin1().data() << " solver...\n"; // Creates implicit function from the point set. // Note: this method requires an iterator over points // + property maps to access each point's position and normal. Poisson_reconstruction_function function(points.begin_or_selection_begin(), points.end(), points.point_map(), points.normal_map()); bool ok = false; #ifdef CGAL_EIGEN3_ENABLED if(solver_name=="Eigen - built-in simplicial LDLt") { CGAL::Eigen_solver_traits<Eigen::SimplicialCholesky<CGAL::Eigen_sparse_matrix<double>::EigenType> > solver; ok = function.compute_implicit_function(solver, use_two_passes); } if(solver_name=="Eigen - built-in CG") { CGAL::Eigen_solver_traits<Eigen::ConjugateGradient<CGAL::Eigen_sparse_matrix<double>::EigenType> > solver; solver.solver().setTolerance(1e-6); solver.solver().setMaxIterations(1000); ok = function.compute_implicit_function(solver, use_two_passes); } #endif // Computes the Poisson indicator function f() // at each vertex of the triangulation. if ( ! ok ) { std::cerr << "Error: cannot compute implicit function" << std::endl; return false; } // Prints status std::cerr << "Total implicit function (triangulation+refinement+solver): " << task_timer.time() << " seconds\n"; task_timer.reset(); //*************************************** // Surface mesh generation //*************************************** std::cerr << "Surface meshing...\n"; // Computes average spacing Kernel::FT average_spacing = CGAL::compute_average_spacing<Concurrency_tag>(points.all_or_selection_if_not_empty(), 6 /* knn = 1 ring */, points.parameters()); // Gets one point inside the implicit surface Kernel::Point_3 inner_point = function.get_inner_point(); Kernel::FT inner_point_value = function(inner_point); if(inner_point_value >= 0.0) { std::cerr << "Error: unable to seed (" << inner_point_value << " at inner_point)" << std::endl; return false; } // Gets implicit function's radius Kernel::Sphere_3 bsphere = function.bounding_sphere(); Kernel::FT radius = std::sqrt(bsphere.squared_radius()); // Defines the implicit surface: requires defining a // conservative bounding sphere centered at inner point. Kernel::FT sm_sphere_radius = 5.0 * radius; Kernel::FT sm_dichotomy_error = sm_distance*average_spacing/1000.0; // Dichotomy error must be << sm_distance Surface_3 surface(function, Kernel::Sphere_3(inner_point,sm_sphere_radius*sm_sphere_radius), sm_dichotomy_error/sm_sphere_radius); // Defines surface mesh generation criteria CGAL::Surface_mesh_default_criteria_3<STr> criteria(sm_angle, // Min triangle angle (degrees) sm_radius*average_spacing, // Max triangle size sm_distance*average_spacing); // Approximation error CGAL_TRACE_STREAM << " make_surface_mesh(sphere center=("<<inner_point << "),\n" << " sphere radius="<<sm_sphere_radius<<",\n" << " angle="<<sm_angle << " degrees,\n" << " triangle size="<<sm_radius<<" * average spacing="<<sm_radius*average_spacing<<",\n" << " distance="<<sm_distance<<" * average spacing="<<sm_distance*average_spacing<<",\n" << " dichotomy error=distance/"<<sm_distance*average_spacing/sm_dichotomy_error<<",\n" << " Manifold_with_boundary_tag)\n"; // Generates surface mesh with manifold option STr tr; // 3D Delaunay triangulation for surface mesh generation C2t3 c2t3(tr); // 2D complex in 3D Delaunay triangulation CGAL::make_surface_mesh(c2t3, // reconstructed mesh surface, // implicit surface criteria, // meshing criteria CGAL::Manifold_with_boundary_tag()); // require manifold mesh // Prints status std::cerr << "Surface meshing: " << task_timer.time() << " seconds, " << tr.number_of_vertices() << " output vertices" << std::endl; task_timer.reset(); if(tr.number_of_vertices() == 0) return false; // Converts to polyhedron CGAL::facets_in_complex_2_to_triangle_mesh(c2t3, *graph); // Prints total reconstruction duration std::cerr << "Total reconstruction (implicit function + meshing): " << reconstruction_timer.time() << " seconds\n"; //*************************************** // Computes reconstruction error //*************************************** // Constructs AABB tree and computes internal KD-tree // data structure to accelerate distance queries AABB_tree tree(faces(*graph).first, faces(*graph).second, *graph); tree.accelerate_distance_queries(); // Computes distance from each input point to reconstructed mesh double max_distance = DBL_MIN; double avg_distance = 0; std::set<typename boost::graph_traits<FaceGraph>::face_descriptor> faces_to_keep; for (Point_set::const_iterator p=points.begin_or_selection_begin(); p!=points.end(); p++) { typename AABB_traits::Point_and_primitive_id pap = tree.closest_point_and_primitive (points.point (*p)); double distance = std::sqrt(CGAL::squared_distance (pap.first, points.point(*p))); max_distance = (std::max)(max_distance, distance); avg_distance += distance; typename boost::graph_traits<FaceGraph>::face_descriptor f = pap.second; faces_to_keep.insert (f); } avg_distance /= double(points.size()); std::cerr << "Reconstruction error:\n" << " max = " << max_distance << " = " << max_distance/average_spacing << " * average spacing\n" << " avg = " << avg_distance << " = " << avg_distance/average_spacing << " * average spacing\n"; if (do_not_fill_holes) { typename boost::graph_traits<FaceGraph>::face_iterator it = faces(*graph).begin (); while (it != faces(*graph).end ()) { typename boost::graph_traits<FaceGraph>::face_iterator current = it ++; if (faces_to_keep.find (*current) == faces_to_keep.end ()) { CGAL::Euler::remove_face(halfedge (*current, *graph), *graph); } } } return true; }