69 lines
3.6 KiB
Plaintext
69 lines
3.6 KiB
Plaintext
[/============================================================================
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Boost.Geometry Index
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Copyright (c) 2011-2012 Adam Wulkiewicz.
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Use, modification and distribution is subject to the Boost Software License,
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Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
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http://www.boost.org/LICENSE_1_0.txt)
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=============================================================================/]
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[section Introduction]
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__rtree__ is a tree data structure used for spatial searching. It was proposed by
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Antonin Guttman in 1984 [footnote Guttman, A. (1984). /R-Trees: A Dynamic Index Structure for Spatial Searching/]
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as an expansion of B-tree for multi-dimensional data. It may be used to store points or volumetric data in order to
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perform a spatial query later. This query may return objects that are inside some area or are close to some point in space
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[footnote Cheung, K.; Fu, A. (1998). /Enhanced Nearest Neighbour Search on the R-tree/].
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The __rtree__ structure is presented on the image below. Each __rtree__'s node store a box describing the space occupied by
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its children nodes. At the bottom of the structure, there are leaf-nodes which contains values
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(geometric objects representations).
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[$img/index/rtree/rstar.png]
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The __rtree__ is a self-balanced data structure. The key part of balancing algorithm is node splitting algorithm
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[footnote Greene, D. (1989). /An implementation and performance analysis of spatial data access methods/]
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[footnote Beckmann, N.; Kriegel, H. P.; Schneider, R.; Seeger, B. (1990). /The R*-tree: an efficient and robust access method for points and rectangles/].
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Each algorithm produces different splits so the internal structure of a tree may be different for each one of them.
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In general more complex algorithms analyses elements better and produces less overlapping nodes. In the searching process less nodes must be traversed
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in order to find desired objects. On the other hand more complex analysis takes more time. In general faster inserting will result in slower searching
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and vice versa. The performance of the R-tree depends on balancing algorithm, parameters and data inserted into the container.
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Example structures of trees created by use of three different algorithms and operations time are presented below. Data used in benchmark was random,
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non-overlapping boxes.
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[table
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[[] [linear algorithm] [quadratic algorithm] [R*-tree]]
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[[*Example structure*] [[$img/index/rtree/linear.png]] [[$img/index/rtree/quadratic.png]] [[$img/index/rtree/rstar.png]]]
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[[*1M Values inserts*] [1.65s] [2.51s] [4.96s]]
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[[*100k spatial queries*] [0.87s] [0.25s] [0.09s]]
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[[*100k knn queries*] [3.25s] [1.41s] [0.51s]]
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]
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[heading Implementation details]
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Key features of this implementation of the __rtree__ are:
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* capable to store arbitrary __value__ type,
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* three different creation algorithms - linear, quadratic or rstar,
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* parameters (including maximal and minimal number of elements) may be passed as compile- or run-time parameters,
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* advanced queries - e.g. search for 5 nearest values to some point and intersecting some region but not within the other one,
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* C++11 conformant: move semantics, stateful allocators,
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* capable to store __value__ type with no default constructor.
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[heading Dependencies]
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R-tree depends on *Boost.Move*, *Boost.Container*, *Boost.Tuple*, *Boost.Utility*, *Boost.MPL*.
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[heading Contributors]
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The spatial index was originally started by Federico J. Fernandez during the Google Summer of Code 2008 program, mentored by Hartmut Kaiser.
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[heading Spatial thanks]
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I'd like to thank Barend Gehrels, Bruno Lalande, Mateusz Łoskot, Lucanus J. Simonson for their support and ideas.
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[endsect]
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