A Simple Dynamization of Trapezoidal Point Location in Planar Subdivisions

Abstract

We study how to dynamize the Trapezoidal Search Tree (TST) -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 (TSD), 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.