\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)
CGAL 4.12 - 3D Convex Hulls
Functions
Convexity Checking
3D Convex Hulls Reference

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. More...
 

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
PolygonMeshmust be a model of the conceptFaceListGraph.
Traitsmust 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.