The function convex_hull_3 computes the convex hull of a given set of threedimensional points Two versions of this function are available. The first can be used when it is known that the result will be a polyhedron and the second when a degenerate hull may also be possible.
#include <CGAL/convex_hull_3.h>
 

 
computes the convex hull of the set of points in the range
[first, last). The polyhedron P is cleared, then
the convex hull is stored in P
and the plane equations of each face are computed.
 
 

 
computes the convex hull of the set of points in the range [first, last). The result, which may be a point, a segment, a triangle, or a polyhedron, is stored in ch_object. When the result is a polyhedron, the plane equations of each face are computed. 
Both functions have an additional requirement for the polyhedron that is to be constructed. For the first version this is that:
The default traits class for both versions of convex_hull_3 is Convex_hull_traits_3<R>,with the representation R determined by InputIterator::value_type.
CGAL::convex_hull_incremental_3
CGAL::ch_eddy
CGAL::convex_hull_2
The following program computes the convex hull of a set of 250 random points chosen from a sphere of radius 100. It then determines if the resulting hull is a segment or a polyhedron. Notice that the traits class is not necessary in the call to convex_hull_3 but is used in the definition of Polyhedron_3.
File: examples/Convex_hull_3/quickhull_3.cpp
#include <CGAL/Homogeneous.h> #include <CGAL/point_generators_3.h> #include <CGAL/copy_n.h> #include <CGAL/Convex_hull_traits_3.h> #include <CGAL/convex_hull_3.h> #include <vector> #ifdef CGAL_USE_GMP #include <CGAL/Gmpz.h> typedef CGAL::Gmpz RT; #else #include <CGAL/MP_Float.h> typedef CGAL::MP_Float RT; #endif typedef CGAL::Homogeneous<RT> K; typedef CGAL::Convex_hull_traits_3<K> Traits; typedef Traits::Polyhedron_3 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; 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::copy_n( gen, 250, std::back_inserter(points) ); // define object to hold convex hull CGAL::Object ch_object; // compute convex hull CGAL::convex_hull_3(points.begin(), points.end(), ch_object); // determine what kind of object it is Segment_3 segment; Polyhedron_3 polyhedron; if ( CGAL::assign(segment, ch_object) ) std::cout << "convex hull is a segment " << std::endl; else if ( CGAL::assign (polyhedron, ch_object) ) std::cout << "convex hull is a polyhedron " << std::endl; else std::cout << "convex hull error!" << std::endl; return 0; }