# Chapter 54
2D Search Structures

Matthias Bäsken

## Summary

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. Previous versions of the two dimensional point set class were inherited from the LEDA graph data type storing its own Delaunay triangulation, but to make the class independent from LEDA we switched to the CGAL Delaunay triangulation data type.
We now also provide 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.

### Concepts

PointSetTraits

### Classes

CGAL::Point_set_2

### Functions

CGAL::nearest_neighbor
CGAL::nearest_neighbors
CGAL::range_search

### Alphabetical List of Reference Pages

- Point_set_2<Gt,Tds>

- PointSetTraits

- nearest_neighbor

- nearest_neighbors

- range_search