CGAL 5.1.3 - Triangulated Surface Mesh Approximation
#include <iostream>
#include <fstream>
#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
#include <CGAL/Surface_mesh.h>
#include <CGAL/property_map.h>
#include <CGAL/Variational_shape_approximation.h>
typedef Kernel::FT FT;
typedef Kernel::Vector_3 Vector_3;
typedef Kernel::Point_3 Point_3;
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;
// 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;
center = center / sum_areas;
return CGAL::ORIGIN + center;
const Face_center_map center_pmap;
const Face_area_map area_pmap;
Mesh, Vertex_point_map, Compact_metric_point_proxy> Approximation;
int main()
// reads input mesh
Mesh mesh;
std::ifstream file("data/");
file >> mesh;
// 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