\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)

CGAL 4.8 - 3D Convex Hulls

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Convex_hull_3/dynamic_hull_3.cpp
#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
#include <CGAL/point_generators_3.h>
#include <CGAL/Delaunay_triangulation_3.h>
#include <CGAL/Polyhedron_3.h>
#include <CGAL/convex_hull_3_to_polyhedron_3.h>
#include <CGAL/algorithm.h>
#include <list>
typedef CGAL::Exact_predicates_inexact_constructions_kernel K;
typedef K::Point_3 Point_3;
typedef CGAL::Delaunay_triangulation_3<K> Delaunay;
typedef Delaunay::Vertex_handle Vertex_handle;
typedef CGAL::Polyhedron_3<K> Polyhedron_3;
int main()
{
CGAL::Random_points_in_sphere_3<Point_3> gen(100.0);
std::list<Point_3> points;
// generate 250 points randomly on a sphere of radius 100.0
// and insert them into the triangulation
CGAL::cpp11::copy_n(gen, 250, std::back_inserter(points) );
Delaunay T;
T.insert(points.begin(), points.end());
std::list<Vertex_handle> vertices;
T.incident_vertices(T.infinite_vertex(), std::back_inserter(vertices));
std::cout << "This convex hull of the 250 points has "
<< vertices.size() << " points on it." << std::endl;
// remove 25 of the input points
std::list<Vertex_handle>::iterator v_set_it = vertices.begin();
for (int i = 0; i < 25; i++)
{
T.remove(*v_set_it);
v_set_it++;
}
//copy the convex hull of points into a polyhedron and use it
//to get the number of points on the convex hull
Polyhedron_3 chull;
CGAL::convex_hull_3_to_polyhedron_3(T,chull);
std::cout << "After removal of 25 points, there are "
<< chull.size_of_vertices() << " points on the convex hull." << std::endl;
return 0;
}