Interpolation/sibson_interpolation_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/Interpolation_gradient_fitting_traits_2.h>
#include <CGAL/sibson_gradient_fitting.h>
#include <CGAL/interpolation_functions.h>

#include <iostream>
#include <iterator>
#include <map>
#include <utility>
#include <vector>

typedef CGAL::Exact_predicates_inexact_constructions_kernel K;
typedef CGAL::Delaunay_triangulation_2<K>                   Delaunay_triangulation;
typedef CGAL::Interpolation_gradient_fitting_traits_2<K>    Traits;

typedef K::FT                                               Coord_type;
typedef K::Point_2                                          Point;
typedef std::map<Point, Coord_type, K::Less_xy_2>           Point_value_map ;
typedef std::map<Point, K::Vector_2 , K::Less_xy_2>         Point_vector_map;

int main()
{
  Delaunay_triangulation T;

  Point_value_map value_function;
  Point_vector_map gradient_function;

  //parameters for spherical function:
  Coord_type a(0.25), bx(1.3), by(-0.7), c(0.2);
  for (int y=0; y<4; y++) {
    for (int x=0; x<4; x++) {
      K::Point_2 p(x,y);
      T.insert(p);
      value_function.insert(std::make_pair(p,a + bx* x+ by*y + c*(x*x+y*y)));
    }
  }

  sibson_gradient_fitting_nn_2(T, std::inserter(gradient_function,
                                                gradient_function.begin()),
                               CGAL:: Data_access<Point_value_map>(value_function),
                               Traits());

  for(const Point_vector_map::value_type& pv : gradient_function)
  {
    std::cout << pv.first << "  "  << pv.second << std::endl;
  }
  // coordinate computation
  K::Point_2 p(1.6, 1.4);
  std::vector< std::pair< Point, Coord_type > > coords;
  Coord_type norm = CGAL::natural_neighbor_coordinates_2(T, p, std::back_inserter(coords)).second;


  //Sibson interpolant: version without sqrt:
  std::pair<Coord_type, bool> res =
    CGAL::sibson_c1_interpolation_square(coords.begin(),
                                         coords.end(), norm, p,
                                         CGAL::Data_access<Point_value_map>(value_function),
                                         CGAL::Data_access<Point_vector_map>(gradient_function),
                                         Traits());

  if(res.second)
    std::cout << "Tested interpolation on " << p
              << " interpolation: " << res.first << " exact: "
              << a + bx*p.x() + by*p.y() + c*(p.x()*p.x()+p.y()*p.y())
              << std::endl;
  else
    std::cout << "C^1 Interpolation not successful." << std::endl
              << " not all gradients are provided." << std::endl
              << " You may resort to linear interpolation." << std::endl;

  return EXIT_SUCCESS;
}