void print_point_set (const Point_set& point_set) { std::cerr << "Content of point set:" << std::endl; for (Point_set::const_iterator it = point_set.begin(); it != point_set.end(); ++ it) std::cerr << "* Point " << *it << ": " << point_set.point(*it) // or point_set[it] << " with normal " << point_set.normal(*it) << std::endl; }
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; }
unsigned int scale_of_noise (const Point_set& points, double& size) { Tree tree(points.begin_or_selection_begin(), points.end(), Tree::Splitter(), Search_traits (points.point_map())); Distance tr_dist (points.point_map()); double ratio_kept = (points.size() < 1000) ? 1. : 1000. / (points.size()); std::vector<Point> subset; for (Point_set::const_iterator it = points.begin(); it != points.end(); ++ it) if (rand() / (double)RAND_MAX < ratio_kept) subset.push_back (points.point(*it)); std::vector<unsigned int> scales; generate_scales (std::back_inserter (scales)); std::vector<unsigned int> chosen; for (std::size_t i = 0; i < subset.size (); ++ i) { Neighbor_search search(tree, subset[i],scales.back(), 0, true, tr_dist); double current = 0.; unsigned int nb = 0; std::size_t index = 0; double minimum = (std::numeric_limits<double>::max)(); unsigned int c = 0; for (Search_iterator search_iterator = search.begin(); search_iterator != search.end (); ++ search_iterator, ++ nb) { current += search_iterator->second; if (nb + 1 == scales[index]) { double score = std::sqrt (current / scales[index]) / std::pow (scales[index], 0.375); // NB ^ (5/12) if (score < minimum) { minimum = score; c = scales[index]; } ++ index; if (index == scales.size ()) break; } } chosen.push_back (c); } std::sort (chosen.begin (), chosen.end()); unsigned int noise_scale = chosen[chosen.size() / 2]; size = 0.; for (std::size_t i = 0; i < subset.size (); ++ i) { Neighbor_search search(tree, subset[i], noise_scale, 0, true, tr_dist); size += std::sqrt ((-- search.end())->second); } size /= subset.size(); return noise_scale; }
void scale_space (const Point_set& points, ItemsInserter items, unsigned int scale, bool generate_smooth = false, bool separate_shells = false, bool force_manifold = true, unsigned int samples = 300, unsigned int iterations = 4) { ScaleSpace reconstruct (scale, samples); reconstruct.reconstruct_surface(points.points().begin(), points.points().end(), iterations, separate_shells, force_manifold); for( unsigned int sh = 0; sh < reconstruct.number_of_shells(); ++sh ) { Scene_polygon_soup_item* new_item = new Scene_polygon_soup_item (); new_item->setColor(Qt::lightGray); new_item->setRenderingMode(FlatPlusEdges); new_item->init_polygon_soup(points.size(), reconstruct.number_of_triangles ()); Scene_polygon_soup_item* smooth_item = NULL; if (generate_smooth) { smooth_item = new Scene_polygon_soup_item (); smooth_item->setColor(Qt::lightGray); smooth_item->setRenderingMode(FlatPlusEdges); smooth_item->init_polygon_soup(points.size(), reconstruct.number_of_triangles ()); } std::map<unsigned int, unsigned int> map_i2i; unsigned int current_index = 0; for (ScaleSpace::Triple_iterator it = reconstruct.shell_begin (sh); it != reconstruct.shell_end (sh); ++ it) { for (unsigned int ind = 0; ind < 3; ++ ind) { if (map_i2i.find ((*it)[ind]) == map_i2i.end ()) { map_i2i.insert (std::make_pair ((*it)[ind], current_index ++)); Point p = points.point(*(points.begin_or_selection_begin() + (*it)[ind])); new_item->new_vertex (p.x (), p.y (), p.z ()); if (generate_smooth) { p = *(reconstruct.points_begin() + (*it)[ind]); smooth_item->new_vertex (p.x (), p.y (), p.z ()); } } } new_item->new_triangle( map_i2i[(*it)[0]], map_i2i[(*it)[1]], map_i2i[(*it)[2]] ); if (generate_smooth) smooth_item->new_triangle( map_i2i[(*it)[0]], map_i2i[(*it)[1]], map_i2i[(*it)[2]] ); } *(items ++) = new_item; if (generate_smooth) *(items ++) = smooth_item; } if (force_manifold) { std::ptrdiff_t num = std::distance( reconstruct.garbage_begin( ), reconstruct.garbage_end( ) ); Scene_polygon_soup_item* new_item = new Scene_polygon_soup_item (); new_item->setColor(Qt::blue); new_item->setRenderingMode(FlatPlusEdges); new_item->init_polygon_soup(points.size(), num); Scene_polygon_soup_item* smooth_item = NULL; if (generate_smooth) { smooth_item = new Scene_polygon_soup_item (); smooth_item->setColor(Qt::blue); smooth_item->setRenderingMode(FlatPlusEdges); smooth_item->init_polygon_soup(points.size(), num); } std::map<unsigned int, unsigned int> map_i2i; unsigned int current_index = 0; for (ScaleSpace::Triple_iterator it=reconstruct.garbage_begin(), end=reconstruct.garbage_end();it!=end;++it) { for (unsigned int ind = 0; ind < 3; ++ ind) { if (map_i2i.find ((*it)[ind]) == map_i2i.end ()) { map_i2i.insert (std::make_pair ((*it)[ind], current_index ++)); Point p = points.point(*(points.begin_or_selection_begin() + (*it)[ind])); new_item->new_vertex (p.x (), p.y (), p.z ()); if (generate_smooth) { p = *(reconstruct.points_begin() + (*it)[ind]); smooth_item->new_vertex (p.x (), p.y (), p.z ()); } } } new_item->new_triangle( map_i2i[(*it)[0]], map_i2i[(*it)[1]], map_i2i[(*it)[2]] ); if (generate_smooth) smooth_item->new_triangle( map_i2i[(*it)[0]], map_i2i[(*it)[1]], map_i2i[(*it)[2]] ); } *(items ++) = new_item; if (generate_smooth) *(items ++) = smooth_item; } }
unsigned int scale_of_anisotropy (const Point_set& points, double& size) { Tree tree(points.begin_or_selection_begin(), points.end(), Tree::Splitter(), Search_traits (points.point_map())); double ratio_kept = (points.size() < 1000) ? 1. : 1000. / (points.size()); std::vector<Point> subset; for (Point_set::const_iterator it = points.begin(); it != points.end(); ++ it) if (rand() / (double)RAND_MAX < ratio_kept) subset.push_back (points.point(*it)); std::vector<unsigned int> scales; generate_scales (std::back_inserter (scales)); std::vector<unsigned int> chosen; Distance tr_dist (points.point_map()); for (std::size_t i = 0; i < subset.size (); ++ i) { Neighbor_search search(tree, subset[i],scales.back(), 0, true, tr_dist); double current = 0.; unsigned int nb = 0; std::size_t index = 0; double maximum = 0.; unsigned int c = 0; for (Search_iterator search_iterator = search.begin(); search_iterator != search.end (); ++ search_iterator, ++ nb) { current += search_iterator->second; if (nb + 1 == scales[index]) { double score = std::sqrt (current / scales[index]) / std::pow (scales[index], 0.75); // NB ^ (3/4) if (score > maximum) { maximum = score; c = scales[index]; } ++ index; if (index == scales.size ()) break; } } chosen.push_back (c); } double mean = 0.; for (std::size_t i = 0; i < chosen.size(); ++ i) mean += chosen[i]; mean /= chosen.size(); unsigned int aniso_scale = static_cast<unsigned int>(mean); size = 0.; for (std::size_t i = 0; i < subset.size (); ++ i) { Neighbor_search search(tree, subset[i], aniso_scale, 0, true, tr_dist); size += std::sqrt ((-- search.end())->second); } size /= subset.size(); return aniso_scale; }