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# Boost.Geometry.Index (Spatial Indexes Library)
#
# Copyright (c) 2008 Federico J. Fernandez.
# Copyright (c) 2011 Adam Wulkiewicz.
# Use, modification and distribution is subject to the Boost Software License,
# Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
# http://www.boost.org/LICENSE_1_0.txt)
project boost/doc ;
import boostbook : boostbook ;
boostbook geometry-index-doc
:
index.xml
:
<xsl:param>boost.root=http://www.boost.org/doc/libs/release
<format>pdf:<xsl:param>boost.url.prefix=http://www.boost.org/doc/libs/release/doc/html
;

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<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Chapter&#160;1.&#160;Boost.Geometry.Index</title>
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<div class="chapter">
<div class="titlepage"><div>
<div><h2 class="title">
<a name="index"></a>Chapter&#160;1.&#160;Boost.Geometry.Index</h2></div>
<div><div class="author"><h3 class="author">
<span class="firstname">Federico J.</span> <span class="surname">Fernandez</span>
</h3></div></div>
<div><div class="author"><h3 class="author">
<span class="firstname">Adam</span> <span class="surname">Wulkiewicz</span>
</h3></div></div>
<div><p class="copyright">Copyright &#169; 2008 Federico J. Fernandez</p></div>
<div><p class="copyright">Copyright &#169; 2011 Adam Wulkiewicz</p></div>
<div><div class="legalnotice">
<a name="id824565"></a><p>Use, modification and distribution is subject to the Boost
Software License, Version 1.0. (See accompanying file
<code class="filename">LICENSE_1_0.txt</code> or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)</p>
</div></div>
</div></div>
<div class="toc">
<p><b>Table of Contents</b></p>
<dl>
<dt><span class="section"><a href="index.html#index.intro">Introduction</a></span></dt>
<dt><span class="section"><a href="index/rtree.html">R-tree</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="index/rtree.html#id824613">R-tree creation</a></span></dt>
<dt><span class="section"><a href="index/rtree.html#id824657">Values, Indexables and default Translator</a></span></dt>
<dt><span class="section"><a href="index/rtree.html#id824700">Inserting and splitting algorithms</a></span></dt>
<dt><span class="section"><a href="index/rtree.html#id824739">Inserting and removing Values</a></span></dt>
<dt><span class="section"><a href="index/rtree.html#id824765">Spatial queries</a></span></dt>
<dt><span class="section"><a href="index/rtree.html#id824804">Spatial predicates</a></span></dt>
<dt><span class="section"><a href="index/rtree.html#id824839">Nearest neighbor queries</a></span></dt>
</dl></dd>
</dl>
</div>
<div class="section">
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="index.intro"></a>Introduction</h2></div></div></div>
<p>The Boost.Geometry.Index library is intetended to gather containers
(spatial indexes) used for speeding spatial queries up. In general, indexes
stores geometric objects' representations and allows searching for objects
occupying some space or close to some point in space.
</p>
<p>Currently, only one spatial index is implemented - the R-tree.</p>
</div>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
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<head>
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>R-tree</title>
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<meta name="generator" content="DocBook XSL Stylesheets V1.76.1">
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<link rel="prev" href="../index.html" title="Chapter&#160;1.&#160;Boost.Geometry.Index">
</head>
<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
<table cellpadding="2" width="100%"><tr>
<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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</div>
<div class="section">
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="index.rtree"></a>R-tree</h2></div></div></div>
<div class="toc"><dl>
<dt><span class="section"><a href="rtree.html#id824613">R-tree creation</a></span></dt>
<dt><span class="section"><a href="rtree.html#id824657">Values, Indexables and default Translator</a></span></dt>
<dt><span class="section"><a href="rtree.html#id824700">Inserting and splitting algorithms</a></span></dt>
<dt><span class="section"><a href="rtree.html#id824739">Inserting and removing Values</a></span></dt>
<dt><span class="section"><a href="rtree.html#id824765">Spatial queries</a></span></dt>
<dt><span class="section"><a href="rtree.html#id824804">Spatial predicates</a></span></dt>
<dt><span class="section"><a href="rtree.html#id824839">Nearest neighbor queries</a></span></dt>
</dl></div>
<p>
R-tree is a self-balancing search tree with nodes stored with their axis aligned
bounding boxes. Each node's box describes the space occupied by children nodes.
At the bottom of the structure, there are leaf-nodes which contains values
(geometric objects representations). Minimal and maximal numbers of values/children
which may be stored inside the node are user defined.
</p>
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="id824613"></a>R-tree creation</h3></div></div></div>
<p>
R-tree has 4 parameters:
</p>
<pre class="programlisting">
rtree&lt;Value, Parameters, Translator, Allocator&gt;
</pre>
<p>
</p>
<div class="itemizedlist"><ul class="itemizedlist" type="disc">
<li class="listitem">
Value - type of object which will be stored in the container.
</li>
<li class="listitem">
Parameters - compile-time parameters, e.g. inserting/splitting algorithm with min and max nodes' elements numbers.
</li>
<li class="listitem">
Translator - type of object translating Value objects to Indexable objects (Point or Box) which R-tree can handle.
</li>
<li class="listitem">
Allocator - the allocator.
</li>
</ul></div>
<p>
</p>
<p>
In order to create a R-tree object storing values of type std::pair&lt;Box, int&gt; one may use the following code
</p>
<pre class="programlisting">
using namespace boost::geometry;
typedef std::pair&lt;Box, int&gt; Value;
index::rtree&lt; Value, index::quadratic&lt;32, 8&gt; &gt; rt;
</pre>
<p>
</p>
</div>
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="id824657"></a>Values, Indexables and default Translator</h3></div></div></div>
<p>
R-tree may store Values of any type as long as there is passed the Translator which knows how to interpret
those Values and extract an object understandable by the R-tree. Those objects are called Indexables
and they are simply of type adapted to Point or Box concept. Default translator
index::translator::def&lt;Value&gt; is able to handle Points, Boxes, std::pairs, pointers and iterators.
</p>
<div class="itemizedlist"><ul class="itemizedlist" type="disc">
<li class="listitem">Indexable = Point | Box</li>
<li class="listitem">BasicValue = Indexable | std::pair&lt;Indexable, T&gt; | std::pair&lt;T, Indexable&gt;</li>
<li class="listitem">Value = BasicValue | BasicValue* | Iterator&lt;BasicValue&gt;</li>
</ul></div>
<p>
Examples of Value types:
</p>
<div class="itemizedlist"><ul class="itemizedlist" type="disc">
<li class="listitem">geometry::model::point&lt;...&gt;</li>
<li class="listitem">geometry::model::point_xy&lt;...&gt;</li>
<li class="listitem">geometry::model::box&lt;...&gt;</li>
<li class="listitem">std::pair&#8804;geometry::model::box&lt;...&gt;, size_t&gt;</li>
</ul></div>
<p>
</p>
</div>
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="id824700"></a>Inserting and splitting algorithms</h3></div></div></div>
<p>
Values may be inserted to the R-tree in many various ways. Final structure of nodes depends
on algorithms used in the process, especially nodes' splitting algorithm. Currently, three
well-known types of R-trees may be created.
</p>
<div class="itemizedlist"><ul class="itemizedlist" type="disc">
<li class="listitem">
Linear - classic R-tree using splitting algorithm of linear complexity
<pre class="programlisting">
index::rtree&lt; Value, index::linear&lt;32, 8&gt; &gt; rt;
</pre>
</li>
<li class="listitem">
Quadratic - classic R-tree using splitting algorithm of quadratic complexity
<pre class="programlisting">
index::rtree&lt; Value, index::quadratic&lt;32, 8&gt; &gt; rt;
</pre>
</li>
<li class="listitem">
R*-tree - splitting algorithm minimizing nodes' overlap with forced reinsertions
<pre class="programlisting">
index::rtree&lt; Value, index::rstar&lt;32, 8&gt; &gt; rt;
</pre>
</li>
</ul></div>
<p>
</p>
</div>
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="id824739"></a>Inserting and removing Values</h3></div></div></div>
<p>
Create
</p>
<pre class="programlisting">
using namespace boost::geometry;
typedef std::pair&lt;Box, int&gt; Value;
index::rtree&lt; Value, index::quadratic&lt;32, 8&gt; &gt; rt;
</pre>
<p>
Insert and remove by method call
</p>
<pre class="programlisting">
rt.insert(std::make_pair(Box(...), 0));
rt.remove(std::make_pair(Box(...), 0));
</pre>
<p>
or by function call
</p>
<pre class="programlisting">
index::insert(rt, std::make_pair(Box(...), 0));
index::remove(rt, std::make_pair(Box(...), 0));
</pre>
<p>
</p>
</div>
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="id824765"></a>Spatial queries</h3></div></div></div>
<p>
There are three ways to perform a spatial query. Following queries returns
Values intersecting some box_region.
</p>
<div class="itemizedlist"><ul class="itemizedlist" type="disc">
<li class="listitem">
Method call
<pre class="programlisting">
std::vector&lt;Value&gt; returned_values;
Box box_region(...);
rt.query(box_region, std::back_inserter(returned_values));
</pre>
</li>
<li class="listitem">
Function call
<pre class="programlisting">
std::vector&lt;Value&gt; returned_values;
Box box_region(...);
index::query(rt, box_region, std::back_inserter(returned_values));
</pre>
</li>
<li class="listitem">
Use of operator | (as with ranges)
<pre class="programlisting">
Box box_region(...);
BOOST_FOREACH(Value &amp;v, rt | index::query_filtered(box_region))
;// do something with v
</pre>
</li>
</ul></div>
<p>
</p>
</div>
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="id824804"></a>Spatial predicates</h3></div></div></div>
<p>
It is possible to define other relations between queried Values and region/regions
of interest. Names of predicates corresponds to names of Boost.Geometry algorithms.
</p>
<pre class="programlisting">
rt.query(box, std::back_inserter(result)); // default case - intersects
rt.query(index::intersects(box), std::back_inserter(result)); // same as default
rt.query(index::covered_by(box), std::back_inserter(result));
rt.query(index::disjont(box), std::back_inserter(result));
rt.query(index::overlaps(box), std::back_inserter(result));
rt.query(index::within(box), std::back_inserter(result));
</pre>
<p>
All predicates may be negated, e.g.:
</p>
<pre class="programlisting">
rt.query(index::not_intersects(box), std::back_inserter(result));
// or
rt.query(!index::intersects(box), std::back_inserter(result));
// the same as
rt.query(index::disjoint(box), std::back_inserter(result));
</pre>
<p>
It's possible to use some number of predicates by passing std::pair&lt;P1, P2&gt;
</p>
<pre class="programlisting">
rt.query(
std::make_pair(index::intersects(box1), !index::within(box2))
, std::back_inserter(result));
</pre>
<p>
or boost::tuple&lt;P1, P2, P3, ...&gt;
</p>
<pre class="programlisting">
rt.query(
boost::make_tuple(index::intersects(box1), !index::within(box2), index::overlaps(box3))
, std::back_inserter(result));
</pre>
<p>
There is special predicate index::value taking user-defined function/functor
which checks if Value should be returned by the query.
</p>
<pre class="programlisting">
bool fun(Value const&amp; v)
{
return v.is_red();
}
// ...
rt.query(
boost::make_pair(index::intersects(box), index::value(fun))
, std::back_inserter(result));
</pre>
<p>
</p>
</div>
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="id824839"></a>Nearest neighbor queries</h3></div></div></div>
TODO
</div>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"></td>
<td align="right"><div class="copyright-footer">Copyright &#169; 2008 Federico J. Fernandez<br>Copyright &#169; 2011 Adam Wulkiewicz<p>Use, modification and distribution is subject to the Boost
Software License, Version 1.0. (See accompanying file
<code class="filename">LICENSE_1_0.txt</code> or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)</p>
</div></td>
</tr></table>
<hr>
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<?xml version="1.0" encoding="utf-8"?>
<!DOCTYPE library PUBLIC "-//Boost//DTD BoostBook XML V1.0//EN"
"http://www.boost.org/tools/boostbook/dtd/boostbook.dtd">
<library name="Geometry.Index" dirname="index" id="index"
xmlns:xi="http://www.w3.org/2001/XInclude">
<libraryinfo>
<author>
<firstname>Federico J.</firstname>
<surname>Fernandez</surname>
</author>
<author>
<firstname>Adam</firstname>
<surname>Wulkiewicz</surname>
</author>
<copyright>
<year>2008</year>
<holder>Federico J. Fernandez</holder>
</copyright>
<copyright>
<year>2011</year>
<holder>Adam Wulkiewicz</holder>
</copyright>
<legalnotice>
<para>Use, modification and distribution is subject to the Boost
Software License, Version 1.0. (See accompanying file
<filename>LICENSE_1_0.txt</filename> or copy at <ulink
url="http://www.boost.org/LICENSE_1_0.txt">http://www.boost.org/LICENSE_1_0.txt</ulink>)</para>
</legalnotice>
<librarypurpose>Spatial indexes for faster spatial and knn queries.</librarypurpose>
<librarycategory name="category:data-structures"/>
</libraryinfo>
<title>Boost.Geometry.Index</title>
<section id="index.intro">
<title>Introduction</title>
<para>The Boost.Geometry.Index library is intetended to gather containers
(spatial indexes) used for speeding spatial queries up. In general, indexes
stores geometric objects' representations and allows searching for objects
occupying some space or close to some point in space.
</para>
<para>Currently, only one spatial index is implemented - the R-tree.</para>
</section>
<section id="index.rtree">
<title>R-tree</title>
<para>
R-tree is a self-balancing search tree with nodes stored with their axis aligned
bounding boxes. Each node's box describes the space occupied by children nodes.
At the bottom of the structure, there are leaf-nodes which contains values
(geometric objects representations). Minimal and maximal numbers of values/children
which may be stored inside the node are user defined.
</para>
<section>
<title>R-tree creation</title>
<para>
R-tree has 4 parameters:
<programlisting>
rtree&lt;Value, Parameters, Translator, Allocator&gt;
</programlisting>
<itemizedlist>
<listitem>
Value - type of object which will be stored in the container.
</listitem>
<listitem>
Parameters - compile-time parameters, e.g. inserting/splitting algorithm with min and max nodes' elements numbers.
</listitem>
<listitem>
Translator - type of object translating Value objects to Indexable objects (Point or Box) which R-tree can handle.
</listitem>
<listitem>
Allocator - the allocator.
</listitem>
</itemizedlist>
</para>
<para>
In order to create a R-tree object storing values of type std::pair&lt;Box, int&gt; one may use the following code
<programlisting>
using namespace boost::geometry;
typedef std::pair&lt;Box, int&gt; Value;
index::rtree&lt; Value, index::quadratic&lt;32, 8&gt; &gt; rt;
</programlisting>
</para>
</section>
<section>
<title>Values, Indexables and default Translator</title>
<para>
R-tree may store Values of any type as long as there is passed the Translator which knows how to interpret
those Values and extract an object understandable by the R-tree. Those objects are called Indexables
and they are simply of type adapted to Point or Box concept. Default translator
index::translator::def&lt;Value&gt; is able to handle Points, Boxes, std::pairs, pointers and iterators.
<itemizedlist>
<listitem>Indexable = Point | Box</listitem>
<listitem>BasicValue = Indexable | std::pair&lt;Indexable, T&gt; | std::pair&lt;T, Indexable&gt;</listitem>
<listitem>Value = BasicValue | BasicValue* | Iterator&lt;BasicValue&gt;</listitem>
</itemizedlist>
Examples of Value types:
<itemizedlist>
<listitem>geometry::model::point&lt;...&gt;</listitem>
<listitem>geometry::model::point_xy&lt;...&gt;</listitem>
<listitem>geometry::model::box&lt;...&gt;</listitem>
<listitem>std::pair&le;geometry::model::box&lt;...&gt;, size_t&gt;</listitem>
</itemizedlist>
</para>
</section>
<section>
<title>Inserting and splitting algorithms</title>
<para>
Values may be inserted to the R-tree in many various ways. Final structure of nodes depends
on algorithms used in the process, especially nodes' splitting algorithm. Currently, three
well-known types of R-trees may be created.
<itemizedlist>
<listitem>
Linear - classic R-tree using splitting algorithm of linear complexity
<programlisting>
index::rtree&lt; Value, index::linear&lt;32, 8&gt; &gt; rt;
</programlisting>
</listitem>
<listitem>
Quadratic - classic R-tree using splitting algorithm of quadratic complexity
<programlisting>
index::rtree&lt; Value, index::quadratic&lt;32, 8&gt; &gt; rt;
</programlisting>
</listitem>
<listitem>
R*-tree - splitting algorithm minimizing nodes' overlap with forced reinsertions
<programlisting>
index::rtree&lt; Value, index::rstar&lt;32, 8&gt; &gt; rt;
</programlisting>
</listitem>
</itemizedlist>
</para>
</section>
<section>
<title>Inserting and removing Values</title>
<para>
Create
<programlisting>
using namespace boost::geometry;
typedef std::pair&lt;Box, int&gt; Value;
index::rtree&lt; Value, index::quadratic&lt;32, 8&gt; &gt; rt;
</programlisting>
Insert and remove by method call
<programlisting>
rt.insert(std::make_pair(Box(...), 0));
rt.remove(std::make_pair(Box(...), 0));
</programlisting>
or by function call
<programlisting>
index::insert(rt, std::make_pair(Box(...), 0));
index::remove(rt, std::make_pair(Box(...), 0));
</programlisting>
</para>
</section>
<section>
<title>Spatial queries</title>
<para>
There are three ways to perform a spatial query. Following queries returns
Values intersecting some box_region.
<itemizedlist>
<listitem>
Method call
<programlisting>
std::vector&lt;Value&gt; returned_values;
Box box_region(...);
rt.query(box_region, std::back_inserter(returned_values));
</programlisting>
</listitem>
<listitem>
Function call
<programlisting>
std::vector&lt;Value&gt; returned_values;
Box box_region(...);
index::query(rt, box_region, std::back_inserter(returned_values));
</programlisting>
</listitem>
<listitem>
Use of operator | (as with ranges)
<programlisting>
Box box_region(...);
BOOST_FOREACH(Value &amp;v, rt | index::query_filtered(box_region))
;// do something with v
</programlisting>
</listitem>
</itemizedlist>
</para>
</section>
<section>
<title>Spatial predicates</title>
<para>
It is possible to define other relations between queried Values and region/regions
of interest. Names of predicates corresponds to names of Boost.Geometry algorithms.
<programlisting>
rt.query(box, std::back_inserter(result)); // default case - intersects
rt.query(index::intersects(box), std::back_inserter(result)); // same as default
rt.query(index::covered_by(box), std::back_inserter(result));
rt.query(index::disjont(box), std::back_inserter(result));
rt.query(index::overlaps(box), std::back_inserter(result));
rt.query(index::within(box), std::back_inserter(result));
</programlisting>
All predicates may be negated, e.g.:
<programlisting>
rt.query(index::not_intersects(box), std::back_inserter(result));
// or
rt.query(!index::intersects(box), std::back_inserter(result));
// the same as
rt.query(index::disjoint(box), std::back_inserter(result));
</programlisting>
It's possible to use some number of predicates by passing std::pair&lt;P1, P2&gt;
<programlisting>
rt.query(
std::make_pair(index::intersects(box1), !index::within(box2))
, std::back_inserter(result));
</programlisting>
or boost::tuple&lt;P1, P2, P3, ...&gt;
<programlisting>
rt.query(
boost::make_tuple(index::intersects(box1), !index::within(box2), index::overlaps(box3))
, std::back_inserter(result));
</programlisting>
There is special predicate index::value taking user-defined function/functor
which checks if Value should be returned by the query.
<programlisting>
bool fun(Value const&amp; v)
{
return v.is_red();
}
// ...
rt.query(
boost::make_pair(index::intersects(box), index::value(fun))
, std::back_inserter(result));
</programlisting>
</para>
</section>
<section>
<title>Nearest neighbor queries</title>
TODO
</section>
</section>
</library>