\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)
CGAL 4.5 - dD Convex Hulls and Delaunay Triangulations
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dD Convex Hulls and Delaunay Triangulations Reference

convex_hull_d-teaser.png
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-chdt3-14b
License: GPL

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

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Classes

Modules

 Concepts
 

Classes

class  CGAL::Convex_hull_d< R >
 An instance C of type Convex_hull_d<R> is the convex hull of a multi-set S of points in \( d\)-dimensional space. More...
 
class  CGAL::Convex_hull_d_traits_3< R >
  More...
 
class  CGAL::Delaunay_d< R, Lifted_R >
 An instance DT of type Delaunay_d< R, Lifted_R > is the nearest and furthest site Delaunay triangulation of a set S of points in some d-dimensional space. More...