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#include <CGAL/Exact_predicates_inexact_constructions_kernel.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 <CGAL/Regular_triangulation_2.h>
#include <iostream>
#include <iterator>
#include <map>
#include <utility>
#include <vector>
typedef CGAL::Exact_predicates_inexact_constructions_kernel K;
typedef CGAL::Regular_triangulation_2<K> Regular_triangulation;
typedef CGAL::Interpolation_gradient_fitting_traits_2<K> Traits;
typedef K::FT Coord_type;
typedef K::Weighted_point_2 Point;
struct Less
{
bool operator()(const Point& p, const Point& q) const {
return K::Less_xy_2()(p.point(), q.point());
}
};
typedef std::map<Point, Coord_type, Less> Point_value_map ;
typedef std::map<Point, K::Vector_2 , Less> Point_vector_map;
int main()
{
Regular_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++) {
Point 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_rn_2(T,
std::inserter(gradient_function, gradient_function.begin()),
CGAL::Data_access<Point_value_map>(value_function),
Traits());
for(Point_vector_map::iterator it = gradient_function.begin();
it != gradient_function.end(); ++it) {
std::cout << it->first << " " << it->second << std::endl;
}
//coordinate computation
Point p(1.6, 1.4);
std::vector<std::pair<Point, Coord_type> > coords;
Coord_type norm = CGAL::regular_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 0;
}
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