CGAL 6.2 - 3D Convex Hulls: Convexity Checking

CGAL 6.2 - 3D Convex Hulls

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Functions
Convexity Checking
Reference Manual

##

## 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 concept`FaceListGraph`.
  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.