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Predicates and DistancePredicates are stored by value in visitors. Each predicate is stored by value in expression tuple. Examples and docs updated. [SVN r83232]
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<title>Introduction</title>
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<link rel="home" href="../../index.html" title="Chapter 1. Geometry Index">
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<link rel="up" href="../r_tree.html" title="R-tree">
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<link rel="prev" href="../r_tree.html" title="R-tree">
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<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="http://www.boost.org/doc/libs/release/boost.png"></td>
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<td align="center"><a href="http://www.boost.org/doc/libs/release/index.html">Home</a></td>
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<a accesskey="p" href="../r_tree.html"><img src="http://www.boost.org/doc/libs/release/doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../r_tree.html"><img src="http://www.boost.org/doc/libs/release/doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="http://www.boost.org/doc/libs/release/doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="rtree_quickstart.html"><img src="http://www.boost.org/doc/libs/release/doc/src/images/next.png" alt="Next"></a>
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</div>
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<div class="section">
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<div class="titlepage"><div><div><h3 class="title">
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<a name="geometry_index.r_tree.introduction"></a><a class="link" href="introduction.html" title="Introduction">Introduction</a>
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</h3></div></div></div>
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<p>
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R-tree is a tree data structure used for spatial searching. It was proposed
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by Antonin Guttman in 1984 <a href="#ftn.geometry_index.r_tree.introduction.f0" class="footnote"><sup class="footnote"><a name="geometry_index.r_tree.introduction.f0"></a>[1]</sup></a> as an expansion of B-tree for multi-dimensional data. It may
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be used to store points or volumetric data in order to perform a spatial
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query later. This query may return objects that are inside some area or are
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close to some point in space <a href="#ftn.geometry_index.r_tree.introduction.f1" class="footnote"><sup class="footnote"><a name="geometry_index.r_tree.introduction.f1"></a>[2]</sup></a>.
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</p>
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<p>
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The R-tree structure is presented on the image below. Each R-tree's node
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store a box descring the space occupied by its children nodes. At the bottom
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of the structure, there are leaf-nodes which contains values (geometric objects
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representations).
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</p>
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<p>
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<span class="inlinemediaobject"><img src="../../../images/rstar.png" alt="rstar"></span>
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</p>
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<p>
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The number of maximum and mininimum node's elements must be specified by
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the user. If the number of elements reaches it's maximum the new node is
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created and elements are split between nodes. If the number of elements in
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node is too small, the node is deleted and elements are reinserted into the
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tree.
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</p>
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<p>
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The R-tree is a self-balanced data structure. The key part of balancing algorithm
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is node splitting algorithm <a href="#ftn.geometry_index.r_tree.introduction.f2" class="footnote"><sup class="footnote"><a name="geometry_index.r_tree.introduction.f2"></a>[3]</sup></a> <a href="#ftn.geometry_index.r_tree.introduction.f3" class="footnote"><sup class="footnote"><a name="geometry_index.r_tree.introduction.f3"></a>[4]</sup></a>. Each algorithm produces different splits so the internal structure
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of a tree may be different for each one of them. In general more complex
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algorithms analyses elements better and produces less overlapping nodes.
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In the searching process less nodes must be traversed in order to find desired
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obejcts. On the other hand more complex analysis takes more time. In general
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faster inserting will result in slower searching and vice versa. The performance
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of the R-tree depends on balancing algorithm, parameters and data inserted
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into the container. Example structures of trees created by use of three different
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algorithms and operations time are presented below. Data used in benchmark
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was random, non-overlapping boxes.
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</p>
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<div class="informaltable"><table class="table">
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<colgroup>
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<col>
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<col>
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<col>
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<col>
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</colgroup>
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<thead><tr>
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<th>
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</th>
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<th>
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<p>
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linear algorithm
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</p>
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</th>
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<th>
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<p>
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quadratic algorithm
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</p>
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</th>
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<th>
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<p>
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R*-tree
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</p>
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</th>
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</tr></thead>
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<tbody>
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<tr>
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<td>
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<p>
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<span class="bold"><strong>Example structure</strong></span>
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</p>
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</td>
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<td>
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<p>
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<span class="inlinemediaobject"><img src="../../../images/linear.png" alt="linear"></span>
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</p>
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</td>
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<td>
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<p>
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<span class="inlinemediaobject"><img src="../../../images/quadratic.png" alt="quadratic"></span>
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</p>
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</td>
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<td>
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<p>
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<span class="inlinemediaobject"><img src="../../../images/rstar.png" alt="rstar"></span>
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</p>
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</td>
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</tr>
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<tr>
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<td>
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<p>
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<span class="bold"><strong>1M Values inserts</strong></span>
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</p>
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</td>
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<td>
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<p>
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2.11s
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</p>
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</td>
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<td>
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<p>
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2.98s
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</p>
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</td>
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<td>
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<p>
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5.49s
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</p>
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</td>
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</tr>
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<tr>
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<td>
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<p>
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<span class="bold"><strong>100k spatial queries</strong></span>
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</p>
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</td>
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<td>
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<p>
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1.52s
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</p>
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</td>
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<td>
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<p>
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0.45s
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</p>
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</td>
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<td>
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<p>
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0.17s
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</p>
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</td>
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</tr>
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<tr>
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<td>
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<p>
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<span class="bold"><strong>100k knn queries</strong></span>
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</p>
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</td>
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<td>
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<p>
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4.51s
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</p>
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</td>
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<td>
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<p>
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2.22s
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</p>
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</td>
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<td>
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<p>
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0.6s
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</p>
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</td>
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</tr>
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</tbody>
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</table></div>
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<h5>
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<a name="geometry_index.r_tree.introduction.h0"></a>
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<span class="phrase"><a name="geometry_index.r_tree.introduction.implementation_details"></a></span><a class="link" href="introduction.html#geometry_index.r_tree.introduction.implementation_details">Implementation
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details</a>
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</h5>
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<p>
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Key features of this implementation of the R-tree are:
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</p>
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<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
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<li class="listitem">
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capable to store arbitrary Value type,
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</li>
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<li class="listitem">
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three different creation algorithms - linear, quadratic or rstar,
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</li>
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<li class="listitem">
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parameters (including maximal and minimal number of elements) may be
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passed as compile- or run-time parameters,
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</li>
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<li class="listitem">
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advanced queries - e.g. search for 5 nearest values to some point and
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intersecting some region but not within the other one,
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</li>
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<li class="listitem">
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C++11 conformant: move semantics, stateful allocators,
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</li>
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<li class="listitem">
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capable to store Value type with no default constructor.
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</li>
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</ul></div>
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<h5>
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<a name="geometry_index.r_tree.introduction.h1"></a>
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<span class="phrase"><a name="geometry_index.r_tree.introduction.dependencies"></a></span><a class="link" href="introduction.html#geometry_index.r_tree.introduction.dependencies">Dependencies</a>
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</h5>
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<p>
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R-tree depends on <span class="bold"><strong>Boost.Move</strong></span>, <span class="bold"><strong>Boost.Container</strong></span>, <span class="bold"><strong>Boost.Tuple</strong></span>,
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<span class="bold"><strong>Boost.Utility</strong></span>, <span class="bold"><strong>Boost.MPL</strong></span>.
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</p>
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<h5>
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<a name="geometry_index.r_tree.introduction.h2"></a>
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<span class="phrase"><a name="geometry_index.r_tree.introduction.contributors"></a></span><a class="link" href="introduction.html#geometry_index.r_tree.introduction.contributors">Contributors</a>
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</h5>
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<p>
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The spatial index was originally started by Federico J. Fernandez during
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the Google Summer of Code 2008 program, mentored by Hartmut Kaiser.
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</p>
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<h5>
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<a name="geometry_index.r_tree.introduction.h3"></a>
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<span class="phrase"><a name="geometry_index.r_tree.introduction.spatial_thanks"></a></span><a class="link" href="introduction.html#geometry_index.r_tree.introduction.spatial_thanks">Spatial
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thanks</a>
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</h5>
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<p>
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I'd like to thank Barend Gehrels, Bruno Lalande, Mateusz Łoskot, Lucanus
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J. Simonson for their support and ideas.
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</p>
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<div class="footnotes">
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<br><hr style="width:100; align:left;">
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<div id="ftn.geometry_index.r_tree.introduction.f0" class="footnote"><p><a href="#geometry_index.r_tree.introduction.f0" class="para"><sup class="para">[1] </sup></a>
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Guttman, A. (1984). <span class="emphasis"><em>R-Trees: A Dynamic Index Structure for Spatial
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Searching</em></span>
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</p></div>
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<div id="ftn.geometry_index.r_tree.introduction.f1" class="footnote"><p><a href="#geometry_index.r_tree.introduction.f1" class="para"><sup class="para">[2] </sup></a>
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Cheung, K.; Fu, A. (1998). <span class="emphasis"><em>Enhanced Nearest Neighbour Search
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on the R-tree</em></span>
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</p></div>
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<div id="ftn.geometry_index.r_tree.introduction.f2" class="footnote"><p><a href="#geometry_index.r_tree.introduction.f2" class="para"><sup class="para">[3] </sup></a>
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Greene, D. (1989). <span class="emphasis"><em>An implementation and performance analysis
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of spatial data access methods</em></span>
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</p></div>
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<div id="ftn.geometry_index.r_tree.introduction.f3" class="footnote"><p><a href="#geometry_index.r_tree.introduction.f3" class="para"><sup class="para">[4] </sup></a>
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Beckmann, N.; Kriegel, H. P.; Schneider, R.; Seeger, B. (1990). <span class="emphasis"><em>The
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R*-tree: an efficient and robust access method for points and rectangles</em></span>
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</p></div>
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</div>
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</div>
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<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
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<td align="left"></td>
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<td align="right"><div class="copyright-footer">Copyright © 2011-2013 Adam Wulkiewicz<p>
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Distributed under the Boost Software License, Version 1.0. (See accompanying
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file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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</p>
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</div></td>
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</tr></table>
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<hr>
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