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

CGAL 4.8 - dD Spatial Searching

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dD Spatial Searching Reference

##

Hans Tangelder and Andreas Fabri
This package implements exact and approximate distance browsing by providing exact and approximate algorithms for range searching, k-nearest and k-furthest neighbor searching, as well as incremental nearest and incremental furthest neighbor searching, where the query items are points in dD Euclidean space.

Introduced in: CGAL 3.0
BibTeX: cgal:tf-ssd-16a
License: GPL
Windows Demo: 2D Spatial Searching
Common Demo Dlls: dlls

This package provides data structures and algorithms for exact and approximate distance browsing, supporting

- both nearest and furthest neighbor searching,
- both exact and approximate searching,
- (approximate) range searching,
- (approximate) `k`-nearest and `k`-furthest neighbor searching,
- (approximate) incremental nearest and incremental furthest neighbor searching,
- query items representing points and spatial objects.

The spatial searching package consists of the following concepts and classes that are described in the reference pages.

## Classified Reference Pages

## Search Classes

- `CGAL::K_neighbor_search<Traits, GeneralDistance, Splitter, SpatialTree>`
- `CGAL::Incremental_neighbor_search<Traits, GeneralDistance, Splitter, SpatialTree>`
- `CGAL::Orthogonal_incremental_neighbor_search<Traits, OrthogonalDistance, Splitter, SpatialTree>`
- `CGAL::Orthogonal_k_neighbor_search<Traits, OrthogonalDistance, Splitter, SpatialTree>`
- `CGAL::Kd_tree<Traits, Splitter, UseExtendedNode>`

## Range Query Item Classes

- `CGAL::Fuzzy_iso_box<Traits>`
- `CGAL::Fuzzy_sphere<Traits>`

## Search Traits Classes

- `CGAL::Search_traits_2<Kernel>`
- `CGAL::Search_traits_3<Kernel>`
- `CGAL::Search_traits_d<Kernel>`
- `CGAL::Search_traits<NT,Point,CartesianIterator,ConstructCartesianIterator,ConstructMinVertex,ConstructMaxVertex>`
- `CGAL::Search_traits_adapter<Key,PointPropertyMap,BaseTraits>`

## Distance Classes

- `CGAL::Euclidean_distance<Traits>`
- `CGAL::Euclidean_distance_sphere_point<Traits>`
- `CGAL::Manhattan_distance_iso_box_point<Traits>`
- `CGAL::Weighted_Minkowski_distance<Traits>`
- `CGAL::Distance_adapter<Key,PointPropertyMap,Base_distance>`

## Splitter Classes

- `CGAL::Sliding_midpoint<Traits, SpatialSeparator>`
- `CGAL::Sliding_fair<Traits, SpatialSeparator>`
- `CGAL::Fair<Traits, SpatialSeparator>`
- `CGAL::Median_of_max_spread<Traits, SpatialSeparator>`
- `CGAL::Median_of_rectangle<Traits, SpatialSeparator>`
- `CGAL::Midpoint_of_max_spread<Traits, SpatialSeparator>`
- `CGAL::Midpoint_of_rectangle<Traits, SpatialSeparator>`

## Advanced Classes

- `CGAL::Kd_tree_node<Traits, Splitter, UseExtendedNode>`
- `CGAL::Kd_tree_leaf_node<Traits, Splitter, UseExtendedNode>`
- `CGAL::Kd_tree_internal_node<Traits, Splitter, UseExtendedNode>`
- `CGAL::Kd_tree_rectangle<FT,Dimension>`
- `CGAL::Plane_separator<FT>`
- `CGAL::Point_container<Traits>`

## Concepts

- `FuzzyQueryItem`
- `GeneralDistance`
- `OrthogonalDistance`
- `SearchTraits`
- `RangeSearchTraits`
- `SpatialSeparator`
- `SpatialTree`
- `Splitter`

## Modules
| Concepts
| Search Classes
| Range Query Item Classes
| Search Traits Classes
| Distance Classes
| Splitter Classes
| Advanced Classes