Convexity Checking

Functions
template<class PolygonMesh , class Traits >
bool	CGAL::is_strongly_convex_3 (PolygonMesh &pm, const Traits &traits=Default_traits)
	determines if the vertices of a given polyhedron represents a strongly convex set of points or not.

Function Documentation

is_strongly_convex_3()

template<class PolygonMesh , class Traits >

bool CGAL::is_strongly_convex_3	(	PolygonMesh &	pm,
		const Traits &	traits = Default_traits
	)

#include <CGAL/convexity_check_3.h>

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).

Template Parameters

PolygonMesh	must be a model of the conceptFaceListGraph.
Traits	must be a model of the concept IsStronglyConvexTraits_3.

Implementation

This function implements the tests described in [2] to determine convexity and requires \(O(e + f)\) time for a polyhedron with \( e\) edges and \( f\) faces.