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#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
#include <CGAL/Convex_hull_3/dual/halfspace_intersection_3.h>
#include <CGAL/point_generators_3.h>
#include <CGAL/Surface_mesh.h>
#include <list>
typedef CGAL::Exact_predicates_inexact_constructions_kernel K;
typedef K::Plane_3 Plane;
typedef K::Point_3 Point;
typedef CGAL::Surface_mesh<Point> Surface_mesh;
// compute the tangent plane of a point
template <typename K>
typename K::Plane_3 tangent_plane (typename K::Point_3 const& p) {
typename K::Vector_3 v(p.x(), p.y(), p.z());
v = v / sqrt(v.squared_length());
typename K::Plane_3 plane(v.x(), v.y(), v.z(), -(p - CGAL::ORIGIN) * v);
return plane;
}
int main (void) {
// number of generated planes
int N = 200;
// generates random planes on a sphere
std::list<Plane> planes;
CGAL::Random_points_on_sphere_3<Point> g;
for (int i = 0; i < N; i++) {
planes.push_back(tangent_plane<K>(*g++));
}
// define polyhedron to hold the intersection
Surface_mesh chull;
// compute the intersection
// if no point inside the intersection is provided, one
// will be automatically found using linear programming
CGAL::halfspace_intersection_3(planes.begin(),
planes.end(),
chull );
std::cout << "The convex hull contains " << num_vertices(chull) << " vertices" << std::endl;
return 0;
}
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