CGAL 6.2 - 2D and Surface Function Interpolation

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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;
}
CGAL::Delaunay_triangulation_2
CGAL::Exact_predicates_inexact_constructions_kernel
CGAL::Interpolation_gradient_fitting_traits_2
Interpolation_gradient_fitting_traits_2 is a model for the concepts InterpolationTraits and GradientF...
Definition: Interpolation_gradient_fitting_traits_2.h:23
CGAL::sibson_c1_interpolation_square
ValueFunctor::result_type sibson_c1_interpolation_square(CoordinateInputIterator first, CoordinateInputIterator beyond, const typename std::iterator_traits< CoordinateInputIterator >::value_type::second_type &norm, const Point &p, ValueFunctor value_function, GradFunctor gradient_function, const Traits &traits)
Same as sibson_c1_interpolation(), except that no square root operation is required for the number ty...
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::Data_access
The struct Data_access implements a functor that allows to retrieve data from an associative containe...
Definition: interpolation_functions.h:26