\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)
CGAL - dD Spatial Searching
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CGAL::Kd_tree< Traits, Splitter, UseExtendedNode > Class Template Reference

#include <CGAL/Kd_tree.h>

Definition

The class Kd_tree defines a k-d tree.

Template Parameters
Traitsmust be a model of the concept SearchTraits, for example Search_traits_2<Simple_cartesian<double> >.
Splittermust be a model for the concept Splitter. It defaults to Sliding_midpoint<Traits>.
UseExtendedNodemust be Tag_true, if the tree shall be built with extended nodes, and Tag_false otherwise.
See Also
CGAL::Kd_tree_node<Traits>
CGAL::Search_traits_2<Kernel>
CGAL::Search_traits_3<Kernel>
CGAL::Search_traits<FT_,Point,CartesianIterator,ConstructCartesianIterator>
Examples:
Spatial_searching/circular_query.cpp, Spatial_searching/fuzzy_range_query.cpp, Spatial_searching/iso_rectangle_2_query.cpp, and Spatial_searching/searching_with_circular_query.cpp.

Types

typedef unspecified_type D
 Dimension tag.
 
typedef Traits::Point_d Point_d
 Point class.
 
typedef Traits::FT FT
 Number type.
 
typedef unspecified_type Splitter
 Splitter type.
 
typedef unspecified_type iterator
 Bidirectional const iterator with value type Point_d that allows to enumerate all points in the tree.
 
typedef unspecified_type Node_handle
 A handle with value type Kd_tree_node<Traits,Splitter>.
 
typedef unspecified_type Node_const_handle
 A const handle with value type Kd_tree_node<Traits,Splitter>.
 
typedef unspecified_type Point_d_iterator
 Random access const iterator with value type const Point_d*.
 
typedef unspecified_type size_type
 A type that counts the number of elements in a k-d tree.
 

Creation

 Kd_tree (Splitter s=Splitter(), Traits t=Traits())
 Constructs an empty k-d tree.
 
template<class InputIterator >
 Kd_tree (InputIterator first, InputIterator beyond, Splitter s=Splitter(), Traits t=Traits())
 Constructs a k-d tree on the elements from the sequence [first, beyond) using the splitting rule implemented by s. More...
 
void build ()
 The constructor does not build the internal data structure, and it is also not updated after calls to insert(). More...
 
void invalidate_build ()
 This clears the internal data structure, which then gets rebuilt either by an explicit call to build() or implicitly by the next query or removal. More...
 

Operations

void insert (Point_d p)
 Inserts the point p in the k-d tree. More...
 
template<class InputIterator >
void insert (InputIterator first, InputIterator beyond)
 Inserts the elements from the sequence [first, beyond) in the k-d tree. More...
 
template<class Identify_point >
void remove (Point_d p, Identify_point equal_to_p)
 Removes the point p from the k-d tree. More...
 
void remove (Point_d p)
 Removes point p, calling the 2-argument function remove() with a functor that simply compares coordinates.
 
void reserve (size_t size)
 
size_t capacity ()
 
template<class FuzzyQueryItem >
boost::optional< Point_dsearch_any_point (FuzzyQueryItem q) const
 Reports any point that is approximately contained by q. More...
 
template<class OutputIterator , class FuzzyQueryItem >
OutputIterator search (OutputIterator it, FuzzyQueryItem q) const
 Reports the points that are approximately contained by q. More...
 
iterator begin () const
 Returns a const iterator to the first point in the tree. More...
 
iterator end () const
 Returns the appropriate past-the-end const iterator.
 
void clear ()
 Removes all points from the k-d tree.
 
size_type size () const
 Returns the number of points that are stored in the tree.
 
Traits traits () const
 return the instance of the traits used to construct the tree.
 
Node_handle root ()
 Returns a handle to the root node of the tree.
 
Node_const_handle root () const
 Returns a const handle to the root node of the tree.
 
const Kd_tree_rectangle< FT, D > & bounding_box () const
 Returns a const reference to the bounding box of the root node of the tree.
 
std::ostream & statistics (std::ostream &s) const
 Inserts statistics of the tree into the output stream s.
 

Constructor & Destructor Documentation

template<typename Traits , typename Splitter , typename UseExtendedNode >
template<class InputIterator >
CGAL::Kd_tree< Traits, Splitter, UseExtendedNode >::Kd_tree ( InputIterator  first,
InputIterator  beyond,
Splitter  s = Splitter(),
Traits  t = Traits() 
)

Constructs a k-d tree on the elements from the sequence [first, beyond) using the splitting rule implemented by s.

The value type of the InputIterator must be Point_d.

Member Function Documentation

template<typename Traits , typename Splitter , typename UseExtendedNode >
iterator CGAL::Kd_tree< Traits, Splitter, UseExtendedNode >::begin ( ) const

Returns a const iterator to the first point in the tree.

Note
Starting with CGAL 4.6, the order of the points in the iterator range [begin() , end()) is not the order of insertion of the points into the tree. This was not guaranteed before but might have beeen observed and exploited.
template<typename Traits , typename Splitter , typename UseExtendedNode >
void CGAL::Kd_tree< Traits, Splitter, UseExtendedNode >::build ( )

The constructor does not build the internal data structure, and it is also not updated after calls to insert().

The method build() is called implicitly at the first call to a query or removal member function. You can call build() explicitly to ensure that the next call to query functions will not trigger the reconstruction of the data structure.

template<typename Traits , typename Splitter , typename UseExtendedNode >
void CGAL::Kd_tree< Traits, Splitter, UseExtendedNode >::insert ( Point_d  p)

Inserts the point p in the k-d tree.

Note
Insertions do not dynamically update the internal data structure. The next query, or a call to build(), automatically triggers a rebuild of the whole structure.
Examples:
Spatial_searching/circular_query.cpp.
template<typename Traits , typename Splitter , typename UseExtendedNode >
template<class InputIterator >
void CGAL::Kd_tree< Traits, Splitter, UseExtendedNode >::insert ( InputIterator  first,
InputIterator  beyond 
)

Inserts the elements from the sequence [first, beyond) in the k-d tree.

The value type of the InputIterator must be Point_d.

template<typename Traits , typename Splitter , typename UseExtendedNode >
void CGAL::Kd_tree< Traits, Splitter, UseExtendedNode >::invalidate_build ( )

This clears the internal data structure, which then gets rebuilt either by an explicit call to build() or implicitly by the next query or removal.

The only reason to call this function explicitly is to rebalance the tree after some number of removals.

template<typename Traits , typename Splitter , typename UseExtendedNode >
template<class Identify_point >
void CGAL::Kd_tree< Traits, Splitter, UseExtendedNode >::remove ( Point_d  p,
Identify_point  equal_to_p 
)

Removes the point p from the k-d tree.

It uses equal_to_p to identify the point after locating it, which can matter in particular when 2 points are in the same place. Identify_point is a unary functor that takes a Point_d and returns a bool. This is a limited and naive implementation that does not rebalance the tree. On the other hand, the tree remains valid and ready for queries. If the internal data structure is not already built, for instance because the last operation was an insertion, it first calls build().

template<typename Traits , typename Splitter , typename UseExtendedNode >
template<class OutputIterator , class FuzzyQueryItem >
OutputIterator CGAL::Kd_tree< Traits, Splitter, UseExtendedNode >::search ( OutputIterator  it,
FuzzyQueryItem  q 
) const

Reports the points that are approximately contained by q.

The types FuzzyQueryItem::Point_d and Point_d must be equivalent. To use this function Traits must be a model of the concept RangeSearchTraits.

template<typename Traits , typename Splitter , typename UseExtendedNode >
template<class FuzzyQueryItem >
boost::optional<Point_d> CGAL::Kd_tree< Traits, Splitter, UseExtendedNode >::search_any_point ( FuzzyQueryItem  q) const

Reports any point that is approximately contained by q.

The types FuzzyQueryItem::Point_d and Point_d must be equivalent. To use this function Traits must be a model of the concept RangeSearchTraits.