Years and Authors of Summarized Original Work
2000; De Berg
2010; De Berg, Haverkort, Thite, Toma
Problem Definition
Many algorithmic problems on spatial data can be solved efficiently if a suitable decomposition of the ambient space is available. Two desirable properties of the decomposition are that its cells have a nice shape – convex and/or of constant complexity – and that each cell intersects only a few objects from the given data set. Another desirable property is that the decomposition is hierarchical, meaning that the space is partitioned in a recursive manner. Popular hierarchical space decompositions include quadtrees and binary space partitions.
When the objects in the given data set are nonpoint objects, they can be fragmented by the partitioning process. This fragmentation has a negative impact on the storage requirements of the decomposition and on the efficiency of algorithms operating on it. Hence, it is desirable to minimize fragmentation. In this chapter, we describe...
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Recommended Reading
De Berg M (2000) Linear size binary space partitions for uncluttered scenes. Algorithmica 28(3):353–366
De Berg M, Cheong O, Van Kreveld M, Overmars M (2008) Computational geometry: algorithms and applications, 3rd edn. Springer, Berlin/Heidelberg
De Berg M, Katz M, Van der Stappen AF, Vleugels J (2002) Realistic input models for geometric algorithms. Algorithmica 34(1):81–97
De Berg M, Haverkort H, Thite S, Toma L (2010) Star-quadtrees and guard-quadtrees: I/O-efficient indexes for fat triangulations and low-density planar subdivisions. Comput Geom Theory Appl 43:493–513
Chazelle B (1984) Convex partitions of polyhedra: a lower bound and worst-case optimal algorithm. SIAM J Comput 13(3):488–507
Paterson MS and Yao FF (1990) Efficient binary space partitions for hidden-surface removal and solid modeling. Discret Comput Geom 5(5):485–503
Tóth CD (2003) A note on binary plane partitions. Discret Comput Geom 30(1):3–16
Tóth CD (2011) Binary plane partitions for disjoint line segments. Discret Comput Geom 45(4):617–646
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de Berg, M. (2016). Hierarchical Space Decompositions for Low-Density Scenes. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2864-4_590
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DOI: https://doi.org/10.1007/978-1-4939-2864-4_590
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