CGAL 5.6.3 - 2D Triangulations on the Sphere

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Triangulation_on_sphere_2/triang_on_sphere_exact.cpp
#include <CGAL/Exact_predicates_exact_constructions_kernel_with_sqrt.h>
#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
#include <CGAL/Delaunay_triangulation_on_sphere_2.h>
#include <CGAL/Projection_on_sphere_traits_3.h>
#include <iostream>
#include <fstream>
template <typename Kernel>
void create_triangulation(const std::string& filename)
{
typedef typename Kernel::FT FT;
typedef CGAL::Projection_on_sphere_traits_3<Kernel> Traits;
typedef CGAL::Delaunay_triangulation_on_sphere_2<Traits> DToS2;
typedef typename Traits::Point_3 Point_3;
std::cout << "\n-- Constructing triangulation with Kernel: " << typeid(Kernel).name() << " --" << std::endl;
std::vector<Point_3> points;
double x, y, z;
std::ifstream in(filename);
if(!in)
{
std::cerr << "Invalid input file: " << filename << std::endl;
return;
}
while(in >> x >> y >> z)
points.emplace_back(x, y, z);
// Add an extra point that would be too close to 'p' with a basic kernel such as CGAL::EPICK,
const Point_3& p = points.back();
const FT tiny = 100 * std::numeric_limits<double>::epsilon();
points.emplace_back(p.x() + tiny, p.y() - tiny, p.z() + tiny);
std::cout << "Adding point " << points.back() << "\nvery close to " << p << std::endl;
std::cout << "Squared distance between points " << CGAL::squared_distance(points.back(), p) << std::endl;
std::cout << points.size() << " points in input" << std::endl;
Traits traits(Point_3(0, 0, 0), 100); // centered on (0,0,0), with radius 100
DToS2 dtos(points.begin(), points.end(), traits);
std::cout << dtos.number_of_vertices() << " vertices" << std::endl;
std::cout << dtos.number_of_faces() << " faces" << std::endl;
}
int main(int argc, char** argv)
{
std::cout.precision(17);
// This kernel CAN represent exactly all points of the sphere
typedef CGAL::Exact_predicates_exact_constructions_kernel_with_sqrt EPECK_w_SQRT;
// This kernel CANNOT represent exactly all points of the sphere
// and thus a separation mechanism is needed to ensure that no points are hidden
typedef CGAL::Exact_predicates_inexact_constructions_kernel EPICK;
const std::string filename = (argc > 1) ? argv[1] : CGAL::data_file_path("points_3/poste_france.xyz");
create_triangulation<EPICK>(filename);
create_triangulation<EPECK_w_SQRT>(filename);
return EXIT_SUCCESS;
}
CGAL::Delaunay_triangulation_on_sphere_2
The class Delaunay_triangulation_on_sphere_2 is designed to represent the Delaunay triangulation of a...
Definition: Delaunay_triangulation_on_sphere_2.h:32
CGAL::Exact_predicates_exact_constructions_kernel_with_sqrt
CGAL::Exact_predicates_inexact_constructions_kernel
CGAL::Projection_on_sphere_traits_3
The class Projection_on_sphere_traits_3 is a model of the concept DelaunayTriangulationOnSphereTraits...
Definition: Projection_on_sphere_traits_3.h:23
CGAL::squared_distance
Kernel::FT squared_distance(Type1< Kernel > obj1, Type2< Kernel > obj2)
Kernel