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• W2041492362 abstract "We show how any BSP tree T P for the endpoints of a set of n disjoint segments in the plane can be used to obtain a BSP tree of size O ( n ⋅ depth ( T P ) ) for the segments themselves, such that the range-searching efficiency remains almost the same. We apply this technique to obtain a BSP tree of size O ( n log n ) such that ɛ -approximate range searching queries with any constant-complexity convex query range can be answered in O ( min ɛ > 0 { ( 1 / ɛ ) + k ɛ } log n ) time, where k ɛ is the number of segments intersecting the ɛ -extended range. The same result can be obtained for disjoint constant-complexity curves, if we allow the BSP to use splitting curves along the given curves. We also describe how to construct a linear-size BSP tree for low-density scenes consisting of n objects in R d such that ɛ -approximate range searching with any constant-complexity convex query range can be done in O ( log n + min ɛ > 0 { ( 1 / ɛ d − 1 ) + k ɛ } ) time." @default.
• W2041492362 created "2016-06-24" @default.
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• W2041492362 date "2006-02-01" @default.
• W2041492362 modified "2023-10-01" @default.
• W2041492362 title "Approximate range searching using binary space partitions" @default.
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• W2041492362 doi "https://doi.org/10.1016/j.comgeo.2005.08.003" @default.
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