The function is_strongly_convex_3 determines if the vertices of a given polyhedron represents a strongly convex set of points or not. A set of points is said to be strongly convex if it consists of only extreme points (i.e., vertices of the convex hull).

#include <CGAL/convexity_check_3.h>

template<class Polyhedron_3, class Traits>
bool is_strongly_convex_3 ( Polyhedron_3& P, Traits traits = Default_traits)
determines if the set of vertices of the polyhedron P represent a strongly convex set of points or not.
Precondition: The equations of the facet planes of the polyhedron must have already been computed.

The default traits class is the kernel in which the type Polyhedron_3::Point_3 is defined.


  1. Polyhedron_3::Point_3 is equivalent to Traits::Point_3.
  2. Traits is a model of the concept IsStronlyConvexTraits_3
  3. Polyhedron_3 must define the following types: and the following member functions: The vertex type of Polyhedron_3 must be a model of ConvexHullPolyhedronVertex_3; the facet type must be ConvexHullPolyhedronFacet_3.

See Also



This function implements the tests described in [MNS+96] to determine convexity and requires O(e + f) time for a polyhedron with e edges and f faces.