CGAL 6.1.2 - Triangulated Surface Mesh Approximation

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Surface_mesh_approximation/vsa_isotropic_metric_example.cpp
#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
#include <CGAL/Surface_mesh.h>
#include <CGAL/property_map.h>
#include <CGAL/Variational_shape_approximation.h>
#include <CGAL/Polygon_mesh_processing/IO/polygon_mesh_io.h>
#include <iostream>
#include <fstream>
typedef CGAL::Exact_predicates_inexact_constructions_kernel Kernel;
typedef Kernel::FT FT;
typedef Kernel::Vector_3 Vector_3;
typedef Kernel::Point_3 Point_3;
typedef CGAL::Surface_mesh<Point_3> Mesh;
typedef boost::graph_traits<Mesh>::face_descriptor face_descriptor;
typedef boost::graph_traits<Mesh>::halfedge_descriptor halfedge_descriptor;
typedef boost::property_map<Mesh, boost::vertex_point_t>::type Vertex_point_map;
typedef Mesh::Property_map<face_descriptor, FT> Face_area_map;
typedef Mesh::Property_map<face_descriptor, Point_3> Face_center_map;
namespace VSA = CGAL::Surface_mesh_approximation;
// user-defined "compact" error metric using type Point_3 as proxy
struct Compact_metric_point_proxy
{
// use point as proxy
typedef Point_3 Proxy;
// we keep a precomputed property map to speed up computations
Compact_metric_point_proxy(const Face_center_map &center_pmap_, const Face_area_map &area_pmap_)
: center_pmap(center_pmap_), area_pmap(area_pmap_)
{ }
// compute and return error from a face to a proxy,
// defined as the Euclidean distance between
// the face center of mass and proxy point.
FT compute_error(const face_descriptor &f, const Mesh &, const Proxy &px) const
{
return CGAL::sqrt(CGAL::squared_distance(center_pmap[f], px));
}
// template functor to compute a best-fit
// proxy from a range of faces
template <typename FaceRange>
Proxy fit_proxy(const FaceRange &faces, const Mesh &) const
{
// fitting center
Vector_3 center = CGAL::NULL_VECTOR;
FT sum_areas = FT(0.0);
for(const face_descriptor& f : faces) {
center = center + (center_pmap[f] - CGAL::ORIGIN) * area_pmap[f];
sum_areas += area_pmap[f];
}
// deal with case where sum = 0
if (center == CGAL::NULL_VECTOR || sum_areas <= FT(0.0))
{
std::cerr << "Error: degenerate geometry." << std::endl;
std::exit(EXIT_FAILURE);
}
center = center / sum_areas;
return CGAL::ORIGIN + center;
}
const Face_center_map center_pmap;
const Face_area_map area_pmap;
};
typedef CGAL::Variational_shape_approximation<
Mesh, Vertex_point_map, Compact_metric_point_proxy> Approximation;
int main(int argc, char** argv)
{
const std::string filename = (argc > 1) ? argv[1] : CGAL::data_file_path("meshes/bear.off");
// reads input surface triangle mesh
Mesh mesh;
if(!CGAL::Polygon_mesh_processing::IO::read_polygon_mesh(filename, mesh) ||
!CGAL::is_triangle_mesh(mesh))
{
std::cerr << "Invalid input file." << std::endl;
return EXIT_FAILURE;
}
// constructs precomputed face normal and area map
Vertex_point_map vpmap = get(boost::vertex_point, const_cast<Mesh &>(mesh));
Face_area_map area_pmap = mesh.add_property_map<face_descriptor, FT>("f:area", FT(0.0)).first;
Face_center_map center_pmap = mesh.add_property_map<face_descriptor, Point_3>("f:center", CGAL::ORIGIN).first;
for(face_descriptor f : faces(mesh))
{
const halfedge_descriptor he = halfedge(f, mesh);
const Point_3 &p0 = vpmap[source(he, mesh)];
const Point_3 &p1 = vpmap[target(he, mesh)];
const Point_3 &p2 = vpmap[target(next(he, mesh), mesh)];
put(area_pmap, f, CGAL::sqrt(CGAL::squared_area(p0, p1, p2)));
put(center_pmap, f, CGAL::centroid(p0, p1, p2));
}
// error metric and fitting function
Compact_metric_point_proxy error_metric(center_pmap, area_pmap);
// creates compact metric approximation algorithm instance
Approximation approx(mesh, vpmap, error_metric);
// approximates via 200 proxies and 30 iterations
approx.initialize_seeds(CGAL::parameters::seeding_method(VSA::HIERARCHICAL)
.max_number_of_proxies(200));
approx.run(30);
return EXIT_SUCCESS;
}
CGAL::Exact_predicates_inexact_constructions_kernel
CGAL::Surface_mesh
CGAL::Variational_shape_approximation
Main class for Variational Shape Approximation algorithm.
Definition: Variational_shape_approximation.h:88
Kernel::Point_3
Kernel::Vector_3
CGAL::Polygon_mesh_processing::IO::read_polygon_mesh
bool read_polygon_mesh(const std::string &fname, PolygonMesh &g, const NamedParameters &np=parameters::default_values())
CGAL::sqrt
NT sqrt(const NT &x)
CGAL::is_triangle_mesh
bool is_triangle_mesh(const FaceGraph &g)
CGAL::centroid
CGAL::Point_2< Kernel > centroid(const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q, const CGAL::Point_2< Kernel > &r)
CGAL::NULL_VECTOR
const CGAL::Null_vector NULL_VECTOR
CGAL::ORIGIN
const CGAL::Origin ORIGIN
CGAL::squared_area
Kernel::FT squared_area(const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r)
CGAL::squared_distance
Kernel::FT squared_distance(Type1< Kernel > obj1, Type2< Kernel > obj2)
Kernel