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

CGAL 4.8 - 3D Convex Hulls

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Convex_hull_3/halfspace_intersection_3.cpp
#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 <list>
typedef CGAL::Exact_predicates_inexact_constructions_kernel K;
typedef K::Plane_3 Plane;
typedef K::Point_3 Point;
typedef CGAL::Polyhedron_3<K> Polyhedron_3;
// 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
Polyhedron_3 P;
// 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(),
P,
boost::make_optional(Point(0, 0, 0)) );
return 0;
}