A Simple Dynamization of Trapezoidal Point Location in Planar Subdivisions
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We study how to dynamize the Trapezoidal Search Tree - a well known randomized point location structure for planar subdivisions of kinetic line segments. Our approach naturally extends incremental leaf-level insertions to recursive methods and allows adaptation for the online setting. Moreover, the dynamization carries over to the Trapezoidal Search DAG, offering a linear sized data structure with logarithmic point location costs as a by-product. On a set S of non-crossing segments, each update performs expected O(log^2|S|) operations. We demonstrate the practicality of our method with an open-source implementation, based on the Computational Geometry Algorithms Library, and experiments on the update performance.
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