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Susan Hert and Michael Seel

This package provides functions for computing convex hulls and Delaunay triangulations in \( d\)-dimensional Euclidean space.

Introduced in: CGAL 2.3
BibTeX: cgal:hs-chdt3-15a
License: GPL

Deprecated:: This package is deprecated since the version 4.6 of CGAL. The package dD Triangulations should be used instead.

A subset \( S \subseteq \mathbb{R}^d\) 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 site Delaunay triangulation.

Classified Reference Pages

Concepts

Classes

Modules
	Concepts

Classes
class	CGAL::Convex_hull_d< R >

class	CGAL::Convex_hull_d_traits_3< R >

class	CGAL::Delaunay_d< R, Lifted_R >

Types
enum	CGAL::Delaunay_d< R, Lifted_R >::Delaunay_voronoi_kind { CGAL::Delaunay_d< R, Lifted_R >::NEAREST, CGAL::Delaunay_d< R, Lifted_R >::FURTHEST }
	interface flags More...

typedef unspecified_type	CGAL::Delaunay_d< R, Lifted_R >::Simplex_handle
	handles to the simplices of the complex. More...

typedef unspecified_type	CGAL::Delaunay_d< R, Lifted_R >::Vertex_handle
	handles to vertices of the complex. More...

typedef unspecified_type	CGAL::Delaunay_d< R, Lifted_R >::Point_d
	the point type More...

typedef unspecified_type	CGAL::Delaunay_d< R, Lifted_R >::Sphere_d
	the sphere type More...

typedef unspecified_type	CGAL::Delaunay_d< R, Lifted_R >::Point_const_iterator
	the iterator for points. More...

typedef unspecified_type	CGAL::Delaunay_d< R, Lifted_R >::Vertex_iterator
	the iterator for vertices. More...

typedef unspecified_type	CGAL::Delaunay_d< R, Lifted_R >::Simplex_iterator
	the iterator for simplices. More...