\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)
CGAL 4.5.2 - dD Range and Segment Trees
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CGAL::Range_tree_d< Data, Window, Traits > Class Template Reference
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#include <CGAL/Range_tree_d.h>

Definition

A \( d\)-dimensional range tree stores points and can be used to determine all points that lie inside a given \( d\)-dimensional interval.

Implementation

The construction of a \( d\)-dimensional range tree takes \( {O}(n\log n^{d-1})\) time. The points in the query window are reported in time \( {O}(k+{\log}^d n )\), where \( k\) is the number of reported points. The tree uses \( {O}(n\log n^{d-1})\) storage.

Types

typedef unspecified_type Data
 container Data.
 
typedef unspecified_type Window
 container Window.
 

Creation

Range_tree_d< Data, Window,
Traits > 		r (Tree_base< Data, Window > sublayer_tree)
 A range tree is constructed, such that the subtree of each vertex is of the same type prototype sublayer_tree is. More...
 

Operations

template<class ForwardIterator >
bool make_tree (ForwardIterator first, ForwardIterator last)
 The tree is constructed according to the data items in the sequence between the element pointed by iterator first and iterator last. More...
 
template<class OutputIterator >
OutputIterator window_query (Window win, OutputIterator result)
 All elements that lay inside the \( d\)-dimensional interval defined through win are placed in the sequence container of OutputIterator; the output iterator that points to the last location the function wrote to is returned.
 
bool is_valid ()
 The tree structure is checked. More...
 
bool is_inside (Window win, Data object)
 returns true, if the data of object lies between the start and endpoint of interval win. More...
 
bool is_anchor ()
 returns false.
 

Member Function Documentation

template<typename Data , typename Window , typename Traits >
bool CGAL::Range_tree_d< Data, Window, Traits >::is_inside ( Window  win,
Data  object 
)
protected

returns true, if the data of object lies between the start and endpoint of interval win.

Returns false otherwise.

template<typename Data , typename Window , typename Traits >
bool CGAL::Range_tree_d< Data, Window, Traits >::is_valid ( )

The tree structure is checked.

For each vertex the subtree is checked on being valid and it is checked whether the value of the Key_type of a vertex corresponds to the highest Key_type value of the left subtree.

template<typename Data , typename Window , typename Traits >
template<class ForwardIterator >
bool CGAL::Range_tree_d< Data, Window, Traits >::make_tree ( ForwardIterator  first,
ForwardIterator  last 
)

The tree is constructed according to the data items in the sequence between the element pointed by iterator first and iterator last.

The data items of the iterator must have type Data.

Precondition
This function can only be called once. If it is the first call the tree is build and true is returned. Otherwise, nothing is done but a CGAL warning is given and false returned.
template<typename Data , typename Window , typename Traits >
Range_tree_d<Data, Window, Traits> CGAL::Range_tree_d< Data, Window, Traits >::r ( Tree_base< Data, Window >  sublayer_tree)

A range tree is constructed, such that the subtree of each vertex is of the same type prototype sublayer_tree is.

We assume that the dimension of the tree is \( d\). This means, that sublayer_tree is a prototype of a \( d-1\)-dimensional tree. All data items of the \( d\)-dimensional range tree have container type Data. The query window of the tree has container type Window. Traits provides access to the corresponding data slots of container Data and Window for the \( d\)-th dimension. The traits class Traits must at least provide all functions and type definitions as described in, for example, the reference page for tree_point_traits. The template class described there is fully generic and should fulfill the most requirements one can have. In order to generate a one-dimensional range tree instantiate Tree_anchor<Data, Window> sublayer_tree with the same template parameters (Data and Window) Range_tree_d is defined. In order to construct a two-dimensional range tree, create Range_tree_d with a one-dimensional Range_tree_d with the corresponding Traits class of the first dimension.

Precondition
Traits::Data==Data and Traits::Window==Window.