127 lines
7.0 KiB
Plaintext
127 lines
7.0 KiB
Plaintext
[/============================================================================
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Boost.Geometry Index
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Copyright (c) 2011-2013 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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The __boost_geometry_index__ is intended to gather data structures called spatial
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indexes which may be used to accelerate searching for objects in space. In general,
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spatial indexes stores geometric objects' representations and allows searching for
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objects occupying some space or close to some point in space.
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Currently, only one spatial index is implemented - __rtree__.
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[heading __rtree__]
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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. This query may for example 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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It's possible to insert new objects or to remove the ones already stored.
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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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Additionally there are also algorithms creating R-tree containing some, number of objects. This technique is called bulk loading and is
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done by use of packing algorithm
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[footnote Leutenegger, Scott T.; Edgington, Jeffrey M.; Lopez, Mario A. (1997). /STR: A Simple and Efficient Algorithm for R-Tree Packing/]
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[footnote Garcia, Yvan J.; Lopez, Mario A.; Leutenegger, Scott T. (1997). /A Greedy Algorithm for Bulk Loading R-trees/].
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This method is faster and results in R-trees with better internal structure. This means that the query performance is increased.
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The examples of structures of trees created by use of different algorithms and exemplary operations times are presented below.
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[table
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[[] [Linear algorithm] [Quadratic algorithm] [R*-tree] [Packing algorithm]]
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[[*Example structure*] [[$img/index/rtree/linear.png]] [[$img/index/rtree/quadratic.png]] [[$img/index/rtree/rstar.png]] [[$img/index/rtree/bulk.png]]]
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[[*1M Values inserts*] [1.76s] [2.47s] [6.19s] [0.64s]]
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[[*100k spatial queries*] [2.21s] [0.51s] [0.12s] [0.07s]]
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[[*100k knn queries*] [6.37s] [2.09s] [0.64s] [0.52s]]
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]
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The configuration of the machine used for testing was: /Intel(R) Core(TM) i7 870 @ 2.93GHz, 8GB RAM, MS Windows 7 x64/.
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The code was compiled with optimization for speed (`O2`).
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The performance of the R-tree for different values of Max parameter and Min=0.5*Max is presented in the table below.
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In the two upper figures you can see the performance of the __rtree__ storing random, relatively small, non-overlapping, 2d boxes.
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In the lower ones, the performance of the __rtree__ also storing random, 2d boxes, but this time quite big and possibly overlapping.
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As you can see, the __rtree__ performance is different in both cases.
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[table
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[[] [building] [querying]]
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[[*non overlapping*] [[$img/index/rtree/build_non_ovl.png]] [[$img/index/rtree/query_non_ovl.png]]]
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[[*overlapping*] [[$img/index/rtree/build_ovl.png]] [[$img/index/rtree/query_ovl.png]]]
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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 balancing algorithms - linear, quadratic or rstar,
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* creation using packing algorithm,
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* parameters (including maximal and minimal number of elements) may be passed as compile- or run-time parameters, in compile-time
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version nodes elements are stored in static-size containers,
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* advanced queries, e.g. search for 5 nearest Values to some point and intersecting some Geometry but not within the other one,
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* iterative queries by use of iterators,
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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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* in-memory storage by use of the default std::allocator<>,
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* other storage options - shared memory and mapped file by use of Boost.Interprocess allocators.
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[/
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[heading Planned features]
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Below you can find features that will (or probably will) be added in the future releases:
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/]
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[/ Done
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* rstar optimization (planned for release in Boost 1.55),
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* bulk loading (planned for release in Boost 1.55),
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* 'reversed' spatial predicates or additional spatial predicates like contains(),
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* iterative queries - query iterators / type-erased query iterators,
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/]
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[/
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* path/ray query predicate - search for Values along Segment or LineString, closest to the starting point,
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* user-defined distance calculation in nearest() predicate,
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* serialization,
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* persistent storage.
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/]
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[/ Maybe
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* other geometries as Indexables, e.g. NSpheres. Rings would probably require using move semantics instead of copying
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* bounding tree - rtree variation capable to use other Geometries as bounds, e.g. NSpheres, Rings/convex polygons/ (moving required), Capsules, Elipses, Variants etc.
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* moving instead of copying + optimizations for movable/nonthrowing/trivialy copied elements
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* passing more than one nearest/path predicate - "returned value is one of k1 nearest values to p1 and ... and one of kN nearest values to pN"
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/]
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[heading Dependencies]
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R-tree depends on Boost.Container, Boost.Core, Boost.Move, Boost.MPL, Boost.Range, Boost.Tuple.
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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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