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

CGAL 4.3 - 3D Convex Hulls

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Convex_hull_3/incremental_hull_class_3.cpp
#include <CGAL/Cartesian.h>
#include <CGAL/point_generators_3.h>
#include <CGAL/Convex_hull_d.h>
#include <CGAL/Convex_hull_d_traits_3.h>
#include <CGAL/Convex_hull_d_to_polyhedron_3.h>
#include <CGAL/Polyhedron_3.h>
#include <CGAL/algorithm.h>
#include <vector>
#include <cassert>
#ifdef CGAL_USE_GMP
#include <CGAL/Gmpq.h>
typedef CGAL::Gmpq RT;
#else
#include <CGAL/MP_Float.h>
typedef CGAL::Quotient<CGAL::MP_Float> RT;
#endif
typedef CGAL::Cartesian<RT> K;
typedef K::Point_3 Point_3;
typedef CGAL::Polyhedron_3< K> Polyhedron_3;
typedef CGAL::Convex_hull_d_traits_3<K> Hull_traits_3;
typedef CGAL::Convex_hull_d< Hull_traits_3 > Convex_hull_3;
typedef CGAL::Creator_uniform_3<double, Point_3> Creator;
int main ()
{
Convex_hull_3 CH(3); // create instance of the class with dimension == 3
// generate 250 points randomly on a sphere of radius 100
// and insert them into the convex hull
CGAL::Random_points_in_sphere_3<Point_3, Creator> gen(100);
for (int i = 0; i < 250 ; i++, ++gen)
CH.insert(*gen);
assert(CH.is_valid());
// define polyhedron to hold convex hull and create it
Polyhedron_3 P;
CGAL::convex_hull_d_to_polyhedron_3(CH,P);
std::cout << "The convex hull has " << P.size_of_vertices()
<< " vertices" << std::endl;
return 0;
}