CGAL 6.2 - 2D and Surface Function Interpolation

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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;
}
CGAL::Exact_predicates_inexact_constructions_kernel
CGAL::Triple
CGAL::Triple::third
T3 third
CGAL::Triple::second
T2 second
CGAL::surface_neighbor_coordinates_3
CGAL::Triple< OutputIterator, typename Kernel::FT, bool > surface_neighbor_coordinates_3(InputIterator first, InputIterator beyond, const typename Kernel::Point_3 &p, const typename Kernel::Vector_3 &normal, OutputIterator out, const Kernel &K)
The sample points are provided in the range [first, beyond).
CGAL::ORIGIN
const CGAL::Origin ORIGIN
CGAL::squared_distance
Kernel::FT squared_distance(Type1< Kernel > obj1, Type2< Kernel > obj2)