mirror of
https://github.com/boostorg/geometry.git
synced 2025-05-11 13:34:10 +00:00
94 lines
5.2 KiB
Plaintext
94 lines
5.2 KiB
Plaintext
[/============================================================================
|
|
Boost.Geometry Index
|
|
|
|
Copyright (c) 2011-2013 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]
|
|
|
|
The __boost_geometry_index__ is intended to gather data structures called spatial
|
|
indexes which may be used to accelerate searching for objects in space. In general,
|
|
spatial indexes stores geometric objects' representations and allows searching for
|
|
objects occupying some space or close to some point in space.
|
|
|
|
Currently, only one spatial index is implemented - __rtree__.
|
|
|
|
[heading __rtree__]
|
|
|
|
__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. This query may for example 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/].
|
|
It's possible to insert new objects or to remove the ones already stored.
|
|
|
|
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).
|
|
|
|
[$img/index/rtree/rstar.png]
|
|
|
|
The __rtree__ is a self-balanced data structure. The key part of balancing algorithm is node splitting algorithm
|
|
[footnote Greene, D. (1989). /An implementation and performance analysis of spatial data access methods/]
|
|
[footnote Beckmann, N.; Kriegel, H. P.; Schneider, R.; Seeger, B. (1990). /The R*-tree: an efficient and robust access method for points and rectangles/].
|
|
Each algorithm produces different splits so the internal structure of a tree may be different for each one of them.
|
|
In general, more complex algorithms analyses elements better and produces less overlapping nodes. In the searching process less nodes must be traversed
|
|
in order to find desired objects. On the other hand more complex analysis takes more time. In general faster inserting will result in slower searching
|
|
and vice versa. The performance of the R-tree depends on balancing algorithm, parameters and data inserted into the container.
|
|
|
|
Additionally there are also algorithms creating R-tree containing some, possibly big, number of objects. This technique is called bulk loading and is
|
|
done by use of packing algorithm
|
|
[footnote Leutenegger, Scott T.; Edgington, Jeffrey M.; Lopez, Mario A. (1997). /STR: A Simple and Efficient Algorithm for R-Tree Packing/]
|
|
[footnote Garcia, Yvan J.; Lopez, Mario A.; Leutenegger, Scott T. (1997). /A Greedy Algorithm for Bulk Loading R-trees/].
|
|
This method is faster and results in R-trees with better internal structure. This means that the query performance is increased.
|
|
|
|
The examples of structures of trees created by use of different algorithms and exemplary operations times are presented below.
|
|
Data used in benchmark was random 2-dimensional boxes. Trees was created for Max=16, Min=8.
|
|
|
|
[table
|
|
[[] [Linear algorithm] [Quadratic algorithm] [R*-tree] [Packing algorithm]]
|
|
[[*Example structure*] [[$img/index/rtree/linear.png]] [[$img/index/rtree/quadratic.png]] [[$img/index/rtree/rstar.png]] [[$img/index/rtree/bulk.png]]]
|
|
[[*1M Values inserts*] [1.76s] [2.47s] [8.39s] [1.67s]]
|
|
[[*100k spatial queries*] [2.21] [0.51s] [0.12s] [0.07s]]
|
|
[[*100k knn queries*] [3.25s] [1.41s] [0.51s] [?]]
|
|
]
|
|
|
|
The performance of the R-tree for different values of Max and Min parameters is presented in the table below.
|
|
The configuration of the machine used for testing is: /Intel(R) Core(TM) i7 870 @ 2.93GHz, 8GB RAM, MS Windows 7 x64/.
|
|
|
|
[table
|
|
[[] [building] [querying]]
|
|
[[*t(Max)*] [[$img/index/rtree/build_max.png]] [[$img/index/rtree/query_max.png]]]
|
|
[[*t(Min)*] [[$img/index/rtree/build_min.png]] [[$img/index/rtree/query_min.png]]]
|
|
]
|
|
|
|
[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]
|
|
|
|
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.
|
|
|
|
[endsect]
|
|
|