Point Enclosure Problem for Homothetic Polygons

12/03/2021

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by   Waseem Akram, et al.

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In this paper, we investigate the homothetic point enclosure problem: given a set S of n triangles with sides parallel to three fixed directions, find a data structure for S that can report all the triangles of S that contain a query point efficiently. The problem is "inverse" of the homothetic range search problem. We present an O(nlog n) space solution that supports the queries in O(log n + k) time, where k is the output size. The preprocessing time is O(nlog n). The same results also hold for homothetic polygons.