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

CGAL 4.8 - dD Spatial Searching

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CGAL::Orthogonal_k_neighbor_search< Traits, OrthogonalDistance, Splitter, SpatialTree > Class Template Reference
Search Classes

`#include <CGAL/Orthogonal_k_neighbor_search.h>`

## Definition

The class `Orthogonal_k_neighbor_search` implements approximate`k`-nearest and `k`-furthest neighbor searching on a tree using an orthogonal distance class.

Template Parameters

  Traits | must be a model of the concept `SearchTraits`, for example `Search_traits_2<Simple_cartesian<double> >`.
  OrthogonalDistance | must be a model of the concept `OrthogonalDistance`. If `Traits` is `Search_traits_adapter<Key,PointPropertyMap,BaseTraits>` the default type is `Distance_adapter<Key,PointPropertyMap,Euclidean_distance<BaseTraits> >`, and `Euclidean_distance<Traits>` otherwise.

The default type is `Euclidean_distance<Traits>`.

Template Parameters

  Splitter | must be a model of the concept `Splitter`. The default type is `Sliding_midpoint<Traits>`.
  SpatialTree | must be a model of the concept `SpatialTree`. The default type is `Kd_tree<Traits, Splitter, Tag_true>`. The template argument must be `Tag_true` because orthogonal search needs extended kd tree nodes.

See Also
  `CGAL::K_neighbor_search<Traits, GeneralDistance, Splitter, SpatialTree>`

Examples:
  Spatial_searching/nearest_neighbor_searching.cpp, Spatial_searching/searching_polyhedron_vertices.cpp, Spatial_searching/searching_sphere_orthogonally.cpp, Spatial_searching/searching_surface_mesh_vertices.cpp, Spatial_searching/searching_with_point_with_info.cpp, Spatial_searching/searching_with_point_with_info_inplace.cpp, Spatial_searching/searching_with_point_with_info_pmap.cpp, Spatial_searching/splitter_worst_cases.cpp, Spatial_searching/user_defined_point_and_distance.cpp, Spatial_searching/using_fair_splitting_rule.cpp, and Spatial_searching/weighted_Minkowski_distance.cpp.

## Types
typedef Traits::Point_d | Point_d
| Point type.
typedef Traits::FT | FT
| Number type.
typedef OrthogonalDistance | Distance
| Distance type.
typedef GeneralDistance::Query_item | Query_item
| Query item.
typedef std::pair< Point_d, FT > | Point_with_transformed_distance
| Pair of point and transformed distance.
typedef unspecified_type | iterator
| Bidirectional const iterator with value type `Point_with_transformed_distance` for enumerating approximate neighbors.
typedef SpatialTree | Tree
| The tree type.

## Operations
| Orthogonal_k_neighbor_search (SpatialTree tree, Query_item query, unsigned int k=1, FT eps=FT(0.0), bool search_nearest=true, OrthogonalDistance d=OrthogonalDistance(), bool sorted=true)
| Constructor for searching approximately `k` neighbors of the query item `query` in the points stored in `tree` using distance `d` and approximation factor `eps`. More...
iterator | begin () const
| Returns a const iterator to the approximate nearest or furthest neighbor.
iterator | end () const
| Returns the appropriate past-the-end const iterator.
std::ostream & | statistics (std::ostream &s)
| Inserts statistics of the search process into the output stream `s`.

## Constructor & Destructor Documentation

template<typename Traits , typename OrthogonalDistance , typename Splitter , typename SpatialTree >

CGAL::Orthogonal_k_neighbor_search< Traits, OrthogonalDistance, Splitter, SpatialTree >::Orthogonal_k_neighbor_search | ( | SpatialTree | tree,
|  | Query_item | query,
|  | unsigned int | k = `1`,
|  | FT | eps = `FT(0.0)`,
|  | bool | search_nearest = `true`,
|  | OrthogonalDistance | d = `OrthogonalDistance()`,
|  | bool | sorted = `true`
| ) |  |

Constructor for searching approximately `k` neighbors of the query item `query` in the points stored in `tree` using distance `d` and approximation factor `eps`.

`sorted` indicates if the computed sequence of `k`-nearest neighbors needs to be sorted.