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Reports (Research Report) Year : 2009

Self-Adapting Point Location

Pedro M. M. de Castro
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Olivier Devillers


Point location in spatial subdivision is one of the most studied problems in computational geometry. In the case of triangulations of Rd, we revisit the problem to exploit a possible coherence between the query-points. For a single query, walking in the triangulation is a classical strategy with good practical behavior and expected complexity O(n^(1/d)) if the points are evenly distributed. For a batch of query-points, the main idea is to use previous queries to improve the current one; we compare various strategies that have an influence on the constant hidden in the big-O notation. Still regarding the complexity of a query, we show how the Delaunay hierarchy can be used to answer, under some hypotheses, a query q with a O(log #(pq) ) randomized expected complexity, where #(.) indicates the number of simplices crossed by the line pq, and p is a previously located query. The data structure has O(n log n) construction complexity and O(n) memory complexity.
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Dates and versions

inria-00438486 , version 1 (04-12-2009)
inria-00438486 , version 2 (15-03-2010)
inria-00438486 , version 3 (12-07-2010)


  • HAL Id : inria-00438486 , version 3


Pedro M. M. de Castro, Olivier Devillers. Self-Adapting Point Location. [Research Report] RR-7132, INRIA. 2009, pp.24. ⟨inria-00438486v3⟩
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