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#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
#include <CGAL/Delaunay_triangulation_3.h>
#include <CGAL/natural_neighbor_coordinates_3.h>
#include <fstream>
typedef double NT; //Number Type
typedef CGAL::Exact_predicates_inexact_constructions_kernel K;
typedef K::Point_3 Point3;
typedef K::Vector_3 Vector3;
typedef K::Sphere_3 Sphere_3;
typedef CGAL::Delaunay_triangulation_3<K, CGAL::Fast_location> Dh;
typedef Dh::Facet Facet;
typedef Dh::Vertex_handle Vertex_handle;
typedef Dh::Cell_handle Cell_handle;
typedef Dh::Finite_vertices_iterator Finite_vertices_iterator;
typedef Dh::Vertex_iterator Vertex_iterator;
typedef Dh::Facet_circulator Facet_circulator;
typedef Dh::Cell_iterator Cell_iterator;
typedef K::Construct_circumcenter_3 Construct_circumcenter_3;
int main()
{
Dh triangulation;
std::fstream iFile("data/points3", std::ios::in);
Point3 p;
while ( iFile >> p )
triangulation.insert(p);
Point3 pp[3];
std::cout << "Consider the natural coordinates of P1, P2 and P3 with regard to the triangulation of data/points3 " << std::endl;
pp[0]=Point3(106.55,112.57,110.4); //inside data/points3 convex hull
std::cout << "P1 is inside the convex hull" << std::endl;
pp[1]=Point3(250,100,140); //on data/points3 convex hull
std::cout << "P2 is on a vertex of the triangulation" << std::endl;
pp[2]=Point3(0,0,0); //outside data/points3 convex hull
std::cout << "P2 is outside the convex hull" << std::endl;
for(int ii=0;ii<3;ii++)
{
std::vector< std::pair< Vertex_handle,NT> > coor_laplace;
std::vector< std::pair< Vertex_handle,NT> > coor_sibson;
NT norm_coeff_laplace, norm_coeff_sibson;
std::cout << "Point P"<< ii+1 << " : "<<pp[ii].x() << " "
<< pp[ii].y() << " "
<< pp[ii].z() << std::endl;
laplace_natural_neighbor_coordinates_3(triangulation,pp[ii],
std::back_inserter(coor_laplace),
norm_coeff_laplace);
std::cout << "Linear combination of natural neighbors with Laplace natural coordinates";
std::cout << " + correctness (ensured only with an exact number type supporting sqrt)" << std::endl;
std::cout << is_correct_natural_neighborhood(triangulation,pp[ii],
coor_laplace.begin(),
coor_laplace.end(),
norm_coeff_laplace)
<< std::endl;
sibson_natural_neighbor_coordinates_3(triangulation,pp[ii],
std::back_inserter(coor_sibson),
norm_coeff_sibson);
std::cout << "Linear combination of natural neighbors with Sibson natural coordinates" << std::endl;
std::cout << " + correctness (ensured only with an exact number type)" << std::endl;
std::cout << is_correct_natural_neighborhood(triangulation,pp[ii],
coor_sibson.begin(),
coor_sibson.end(),
norm_coeff_sibson)
<< std::endl;
}
std::cout << "done" << std::endl;
return 0;
}
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