Interpolation/surface_neighbor_coordinates_3.cpp

// example with random points on a sphere

#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>

#include <CGAL/point_generators_3.h>
#include <CGAL/algorithm.h>
#include <CGAL/Origin.h>

#include <CGAL/surface_neighbor_coordinates_3.h>

#include <iostream>
#include <iterator>
#include <vector>

typedef CGAL::Exact_predicates_inexact_constructions_kernel  K;
typedef K::FT                                                Coord_type;
typedef K::Point_3                                           Point_3;
typedef K::Vector_3                                          Vector_3;
typedef std::vector< std::pair< Point_3, K::FT > >           Point_coordinate_vector;

int main()
{
  int n = 100;
  std::vector< Point_3> points;
  points.reserve(n);

  std::cout << "Generate " << n << " random points on a sphere." << std::endl;
  CGAL::Random_points_on_sphere_3<Point_3> g(1);
  std::copy_n(g, n, std::back_inserter(points));

  Point_3 p(1, 0, 0);
  Vector_3 normal(p - CGAL::ORIGIN);
  std::cout << "Compute surface neighbor coordinates for " << p << std::endl;
  Point_coordinate_vector coords;
  CGAL::Triple<std::back_insert_iterator<Point_coordinate_vector>, K::FT, bool> result =
    CGAL::surface_neighbor_coordinates_3(points.begin(), points.end(),
                                         p, normal,
                                         std::back_inserter(coords),
                                         K());
  if(!result.third)
  {
    //Undersampling:
    std::cout << "The coordinate computation was not successful." << std::endl;
    return 0;
  }

  K::FT norm = result.second;

  std::cout << "Testing the barycentric property " << std::endl;
  Point_3 b(0, 0, 0);
  for(const std::pair< Point_3, Coord_type >& pc : coords)
    b = b + (pc.second/norm) * (pc.first - CGAL::ORIGIN);

  std::cout << "    weighted barycenter: " << b <<std::endl;
  std::cout << "    squared distance: " << CGAL::squared_distance(p,b) << std::endl;

  return EXIT_SUCCESS;
}