CGAL 4.7 - 2D and Surface Function Interpolation
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_functions.h>
typedef CGAL::Delaunay_triangulation_2<K> Delaunay_triangulation;
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 function_values;
//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);
function_values.insert(std::make_pair(p,a + bx* x+ by*y + c*(x*x+y*y)));
}
(function_values),
Traits());
//coordiante 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 =
(coords.begin(),
coords.end(),norm,p,
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 function_gradients are provided." << std::endl
<< " You may resort to linear interpolation." << std::endl;
std::cout << "done" << std::endl;
return 0;
}