CGAL 5.6.3 - 2D and Surface Function Interpolation

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Interpolation/nn_coordinates_with_info_2.cpp
#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
#include <CGAL/Delaunay_triangulation_2.h>
#include <CGAL/natural_neighbor_coordinates_2.h>
#include <CGAL/Triangulation_vertex_base_with_info_2.h>
#include <iostream>
#include <iterator>
#include <utility>
#include <vector>
typedef CGAL::Exact_predicates_inexact_constructions_kernel K;
typedef K::FT Coord_type;
typedef CGAL::Triangulation_vertex_base_with_info_2<Coord_type, K> Vb;
typedef CGAL::Triangulation_data_structure_2<Vb> Tds;
typedef CGAL::Delaunay_triangulation_2<K, Tds> Delaunay_triangulation;
// The functor 'Identity' matches anything to itself
typedef Delaunay_triangulation::Vertex_handle Vertex_handle;
typedef CGAL::Identity<std::pair<Vertex_handle, Coord_type> > Identity;
// Resulting points-coordinates pairs are here stored in an object of this type:
typedef std::vector<std::pair<Vertex_handle, Coord_type> > Point_coordinate_vector;
int main()
{
Delaunay_triangulation dt;
for(int y=0; y<3; ++y)
for(int x=0; x<3; ++x)
dt.insert(K::Point_2(x, y));
// coordinates computation
K::Point_2 p(1.2, 0.7); // query point
Point_coordinate_vector coords;
// The functor Identity is passed to the method
CGAL::Triple<std::back_insert_iterator<Point_coordinate_vector>, K::FT, bool> result =
CGAL::natural_neighbor_coordinates_2(dt, p, std::back_inserter(coords), Identity());
if(!result.third)
{
std::cout << "The coordinate computation was not successful." << std::endl;
std::cout << "The point (" << p << ") lies outside the convex hull." << std::endl;
}
// Assign the coordinates to the vertices
std::cout << "Coordinates for point: (" << p << ") are the following: " << std::endl;
for(std::size_t i=0; i<coords.size(); ++i)
{
Vertex_handle vh = coords[i].first;
vh->info() = coords[i].second;
std::cout << " Vertex: (" << vh->point() << ") coeff: " << vh->info() << std::endl;
}
return EXIT_SUCCESS;
}
CGAL::Delaunay_triangulation_2
CGAL::Exact_predicates_inexact_constructions_kernel
CGAL::Triangulation_vertex_base_with_info_2
CGAL::Triple
CGAL::Triple::third
T3 third
CGAL::natural_neighbor_coordinates_2
CGAL::Triple< CoordinateOutputIterator, typename Dt::Geom_traits::FT, bool > natural_neighbor_coordinates_2(const Dt &dt, const typename Dt::Geom_traits::Point_2 &p, CoordinateOutputIterator out, OutputFunctor fct, typename Dt::Face_handle start=typename Dt::Face_handle())
Computes the natural neighbor coordinates for p with respect to the points in the two-dimensional Del...
CGAL::Identity