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

CGAL 4.8 - dD Range and Segment Trees

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CGAL::Range_tree_k< Traits > Class Template Reference
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`#include <CGAL/Range_tree_k.h>`

## Definition

An object of the class `Range_tree_k` is a \( k\)-dimensional range tree that can store k-dimensional keys of type `Key`.

The class allows to perform window queries on the keys. The class `Range_tree_k` is parameterized with a range tree traits class `Traits` that defines, among other things, the type of the `Key`.

CGAL provides traits class implementations that allow to use the range tree with point classes from the CGAL kernel as keys. These classes are `CGAL::Range_segment_tree_traits_set_2<R>`, `CGAL::Range_segment_tree_traits_set_3<R>`, `CGAL::Range_tree_traits_map_2<R>` and `CGAL::Range_tree_traits_map_3<R>`. The concept RangeSegmentTreeTraits_d defines the requirements that range tree traits classes must fulfill. This allows the advanced user to develop further range tree traits classes.

Example

The following example program uses the predefined `Range_tree_2` data structure together with the predefined traits class `Range_tree_map_traits_2` which has two template arguments specifying the type of the point data in each dimension (`CGAL::Cartesian<double>`) and the value type of the 2-dimensional point data (`char`). Therefore the `Range_tree_2` is defined on 2-dimensional point data (`CGAL::Point_2<Cartesian<double> >`) each of which is associated with a character. Then, a few data items are created and put into a list. After that the tree is constructed according to that list, a window query is performed, and the query elements are given out.

#include <CGAL/Cartesian.h>
#include <CGAL/Range_segment_tree_traits.h>
#include <CGAL/Range_tree_k.h>
typedef CGAL::Cartesian<double> K;
typedef CGAL::Range_tree_map_traits_2<K, char> Traits;
typedef CGAL::Range_tree_2<Traits> Range_tree_2_type;
int main()
{
typedef Traits::Key Key;
typedef Traits::Interval Interval;
std::vector<Key> InputList, OutputList;
InputList.push_back(Key(K::Point_2(8,5.1), 'a'));
InputList.push_back(Key(K::Point_2(1,1.1), 'b'));
InputList.push_back(Key(K::Point_2(3,2.1), 'c'));
Range_tree_2_type Range_tree_2(InputList.begin(),InputList.end());
Interval win(Interval(K::Point_2(4,8.1), K::Point_2(5,8.2)));
std::cout << "\n Window Query:\n ";
Range_tree_2.window_query(win, std::back_inserter(OutputList));
std::vector<Key>::iterator current=OutputList.begin();
while(current!=OutputList.end()){
std::cout << (*current).first.x() << "," << (*current).first.y()
<< ":" << (*current++).second << std::endl;
}
}

## Types
typedef Traits::Key | Key
typedef Traits::Interval | Interval

## Creation
| Range_tree_k ()
| Introduces an empty range tree `R`.
template<class ForwardIterator >
| Range_tree_k (ForwardIterator first, ForwardIterator last)
| Introduces a range tree `R` and initializes it with the data in the range `[first, last)`. More...

## Operations
template<class ForwardIterator >
void | make_tree (ForwardIterator first, ForwardIterator last)
| Introduces a range tree `R` and initializes it with the data in the range `[first, last)`. More...
template<class OutputIterator >
OutputIterator | window_query (Interval window, OutputIterator out)
| writes all data that are in the interval `window` to the container where `out` points to, and returns an output iterator that points to the last location the function wrote to. More...

## Constructor & Destructor Documentation

template<typename Traits >
template<class ForwardIterator >

CGAL::Range_tree_k< Traits >::Range_tree_k | ( | ForwardIterator | first,
|  | ForwardIterator | last
| ) |  |

Introduces a range tree `R` and initializes it with the data in the range `[first, last)`.

Precondition
  `value_type(first) == Traits::Key`.

## Member Function Documentation

template<typename Traits >
template<class ForwardIterator >

void CGAL::Range_tree_k< Traits >::make_tree | ( | ForwardIterator | first,
|  | ForwardIterator | last
| ) |  |

Introduces a range tree `R` and initializes it with the data in the range `[first, last)`.

This function can only be applied once on an empty range tree.

Precondition
  `value_type(first) == Traits::Key`.

template<typename Traits >
template<class OutputIterator >

OutputIterator CGAL::Range_tree_k< Traits >::window_query | ( | Interval | window,
|  | OutputIterator | out
| ) |  |

writes all data that are in the interval `window` to the container where `out` points to, and returns an output iterator that points to the last location the function wrote to.

Precondition
  `value_type(out) == Traits::Key`.