\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)

CGAL 4.8 - 2D Range and Neighbor Search

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2D Range and Neighbor Search Reference

##

Matthias Bäsken
This package supports circular, triangular, and isorectangular range search queries as well as (k) nearest neighbor search queries on 2D point sets. In contrast to the spatial searching package, this package uses a Delaunay triangulation as underlying data structure.

Introduced in: CGAL 2.1
Depends on: 2D Triangulation
BibTeX: cgal:b-ss2-16a
License: GPL

The two dimensional point set is a class for geometric queries. It supports circular, triangular and iso rectangular range searches and nearest neighbor searches. The point set is inherited from the CGAL Delaunay triangulation data type. That means that it is a dynamic data structure supporting the insertion and deletion of points.

This package also provides function template versions of the range search and nearest neighbor query operations. They all have to be templated by the type of a CGAL Delaunay triangulation and provide functionality similar to the corresponding member functions of the point set class.

## Classified Reference Pages

## Concepts

- `PointSetTraits`

## Classes

- `CGAL::Point_set_2`

## Functions

- `CGAL::nearest_neighbor()`
- `CGAL::nearest_neighbors()`
- `CGAL::range_search()`

## Modules
| Concepts
| Range Search
| There are six versions of the function template `range_search()` that perform range searches on Delaunay triangulations.
| Nearest Neighbor Search

## Classes
class | CGAL::Point_set_2< Gt, Tds >
| An instance `PS` of the data type `Point_set_2` is a Delaunay Triangulation of its vertex set. More...