CGAL 5.1 - Polygon Mesh Processing
#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
#include <CGAL/Polyhedron_3.h>
#include <CGAL/Surface_mesh_default_triangulation_3.h>
#include <CGAL/make_surface_mesh.h>
#include <CGAL/Implicit_surface_3.h>
#include <CGAL/IO/facets_in_complex_2_to_triangle_mesh.h>
#include <CGAL/Poisson_reconstruction_function.h>
#include <CGAL/property_map.h>
#include <CGAL/IO/read_xyz_points.h>
#include <CGAL/compute_average_spacing.h>
#include <CGAL/Polygon_mesh_processing/distance.h>
#include <boost/iterator/transform_iterator.hpp>
#include <vector>
#include <fstream>
// Types
typedef Kernel::FT FT;
typedef Kernel::Point_3 Point;
typedef Kernel::Vector_3 Vector;
typedef std::pair<Point, Vector> Point_with_normal;
typedef Kernel::Sphere_3 Sphere;
typedef std::vector<Point_with_normal> PointList;
typedef CGAL::Polyhedron_3<Kernel> Polyhedron;
typedef CGAL::Poisson_reconstruction_function<Kernel> Poisson_reconstruction_function;
typedef CGAL::Surface_mesh_default_triangulation_3 STr;
typedef CGAL::Surface_mesh_complex_2_in_triangulation_3<STr> C2t3;
typedef CGAL::Implicit_surface_3<Kernel, Poisson_reconstruction_function> Surface_3;
int main(void)
// Poisson options
FT sm_angle = 20.0; // Min triangle angle in degrees.
FT sm_radius = 30; // Max triangle size w.r.t. point set average spacing.
FT sm_distance = 0.375; // Surface Approximation error w.r.t. point set average spacing.
// Reads the point set file in points[].
// Note: read_xyz_points_and_normals() requires an iterator over points
// + property maps to access each point's position and normal.
PointList points;
std::ifstream stream("data/");
if (!stream ||
CGAL::parameters::point_map (Point_map()).
normal_map (Normal_map())))
std::cerr << "Error: cannot read file data/" << std::endl;
// Creates implicit function from the read points using the default solver.
// Note: this method requires an iterator over points
// + property maps to access each point's position and normal.
Poisson_reconstruction_function function(points.begin(), points.end(), Point_map(), Normal_map());
// Computes the Poisson indicator function f()
// at each vertex of the triangulation.
if ( ! function.compute_implicit_function() )
// Computes average spacing
FT average_spacing = CGAL::compute_average_spacing<CGAL::Sequential_tag>
(points, 6 /* knn = 1 ring */,
CGAL::parameters::point_map (Point_map()));
// Gets one point inside the implicit surface
// and computes implicit function bounding sphere radius.
Point inner_point = function.get_inner_point();
Sphere bsphere = function.bounding_sphere();
FT radius = std::sqrt(bsphere.squared_radius());
// Defines the implicit surface: requires defining a
// conservative bounding sphere centered at inner point.
FT sm_sphere_radius = 5.0 * radius;
FT sm_dichotomy_error = sm_distance*average_spacing/1000.0; // Dichotomy error must be << sm_distance
Surface_3 surface(function,
// 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
// 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
if(tr.number_of_vertices() == 0)
// saves reconstructed surface mesh
std::ofstream out("");
Polyhedron output_mesh;
CGAL::facets_in_complex_2_to_triangle_mesh(c2t3, output_mesh);
out << output_mesh;
// computes the approximation error of the reconstruction
double max_dist =
CGAL::make_range (boost::make_transform_iterator
std::cout << "Max distance to point_set: " << max_dist << std::endl;