CGAL 4.7 - 3D Convex Hulls: Convex_hull_3/quickhull_3.cpp

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

CGAL 4.7 - 3D Convex Hulls

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Convex_hull_3/quickhull_3.cpp
#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
#include <CGAL/point_generators_3.h>
#include <CGAL/algorithm.h>
#include <CGAL/Polyhedron_3.h>
#include <CGAL/convex_hull_3.h>
#include <vector>
typedef CGAL::Exact_predicates_inexact_constructions_kernel K;
typedef CGAL::Polyhedron_3<K> Polyhedron_3;
typedef K::Segment_3 Segment_3;
// define point creator
typedef K::Point_3 Point_3;
typedef CGAL::Creator_uniform_3<double, Point_3> PointCreator;
//a functor computing the plane containing a triangular facet
struct Plane_from_facet {
Polyhedron_3::Plane_3 operator()(Polyhedron_3::Facet& f) {
Polyhedron_3::Halfedge_handle h = f.halfedge();
return Polyhedron_3::Plane_3( h->vertex()->point(),
h->next()->vertex()->point(),
h->opposite()->vertex()->point());
}
};
int main()
{
CGAL::Random_points_in_sphere_3<Point_3, PointCreator> gen(100.0);
// generate 250 points randomly on a sphere of radius 100.0
// and copy them to a vector
std::vector<Point_3> points;
CGAL::cpp11::copy_n( gen, 250, std::back_inserter(points) );
// define polyhedron to hold convex hull
Polyhedron_3 poly;
// compute convex hull of non-collinear points
CGAL::convex_hull_3(points.begin(), points.end(), poly);
std::cout << "The convex hull contains " << poly.size_of_vertices() << " vertices" << std::endl;
// assign a plane equation to each polyhedron facet using functor Plane_from_facet
std::transform( poly.facets_begin(), poly.facets_end(), poly.planes_begin(),Plane_from_facet());
return 0;
}