# Chapter 6

dD Convex Hulls and Delaunay Triangulations

*Susan Hert and Michael Seel*

A subset $$*S *^{3} is convex if for any two points $$*p* and $$*q*
in the set the line segment with endpoints $$*p* and $$*q* is contained
in $$*S*. The convex hull
of a set $$*S* is
the smallest convex set containing
$$*S*. The convex hull of a set of points $$*P* is a convex
polytope with vertices in $$*P*. A point in $$*P* is an extreme point
(with respect to $$*P*)
if it is a vertex
of the convex hull of $$*P*.

CGAL provides functions for computing convex hulls in two, three
and arbitrary dimensions as well as functions for testing if a given set of
points in is strongly convex or not. This chapter describes the class
available for arbitrary dimensions and its companion class for
computing the nearest and furthest side Delaunay triangulation.

### Concepts

*ConvexHullTraits_d*

*DelaunayLiftedTraits_d*

*DelaunayTraits_d*

### Classes

*CGAL::Convex_hull_d_traits_3<R>*

*CGAL::Convex_hull_d<R>*

*CGAL::Delaunay_d< R, Lifted_R >*

### Alphabetical Listing of Reference Pages