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