\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)
CGAL 4.3 - Optimal Distances
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Optimal Distances Reference

dist.png
Kaspar Fischer, Bernd Gärtner, Thomas Herrmann, Michael Hoffmann, and Sven Schönherr
This package provides algorithms for computing the distance between the convex hulls of two point sets in d-dimensional space, without explicitely constructing the convex hulls. It further provides an algorithm to compute the width of a point set, and the furthest point for each vertex of a convex polygon.


Introduced in: CGAL 1.1
BibTeX: cgal:fghhs-od-13b
License: GPL

Assertions

The optimization code uses infix OPTIMISATION in the assertions, e.g. defining the compiler flag CGAL_OPTIMISATION_NO_PRECONDITIONS switches precondition checking off, cf. Section Checks.

Classified Reference Pages

All furthest neighbors

Width

Polytope Distance

Modules

 Concepts
 

Classes

class  CGAL::Polytope_distance_d< Traits >
 An object of the class Polytope_distance_d represents the (squared) distance between two convex polytopes, given as the convex hulls of two finite point sets in \( d\)-dimensional Euclidean space \( \E^d\). More...
 
class  CGAL::Polytope_distance_d_traits_2< K, ET, NT >
 The class Polytope_distance_d_traits_2 is a traits class for the \( d\)-dimensional optimisation algorithms using the two-dimensional CGAL kernel. More...
 
class  CGAL::Polytope_distance_d_traits_3< K, ET, NT >
 The class Polytope_distance_d_traits_3 is a traits class for the \( d\)-dimensional optimisation algorithms using the three-dimensional CGAL kernel. More...
 
class  CGAL::Polytope_distance_d_traits_d< K, ET, NT >
 The class Polytope_distance_d_traits_d is a traits class for the \( d\)-dimensional optimisation algorithms using the \( d\)-dimensional CGAL kernel. More...
 
class  CGAL::Width_3< Traits >
 Given a set of points \( \mathcal{S}=\left\{p_1,\ldots , p_n\right\}\) in \( \mathbb{R}^3\). More...
 
class  CGAL::Width_default_traits_3< K >
 The class Width_default_traits_3 is a traits class for Width_3<Traits> using the three-dimensional CGAL kernel. More...
 

Functions

OutputIterator CGAL::all_furthest_neighbors_2 (RandomAccessIterator points_begin, RandomAccessIterator points_end, OutputIterator o, Traits t=Default_traits)
 computes all furthest neighbors for the vertices of the convex polygon described by the range [points_begin, points_end), writes their indices (relative to points_begin) to othe furthest neighbor of points_begin[i] is points_begin[i-th number written to o] and returns the past-the-end iterator of this sequence. More...