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Point location in Voronoi diagrams of polygons

Weizhen Wang, Chenglei Yang, Xiaoting Wang, Xiangxu Meng, Min Wei, Zheng Sun

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Abstract

Given a query point and the Voronoi diagram of a polygon (VD(P)), how to efficiently find the Voronoi region (VR) containing the query point, i.e., the point location in VD(P), is a fundamental operation for many other algorithms based on VD(P), such as path planning, visibility, and so on. A triangulation refinement method for VD(P) is presented in this paper, and then a point-location data structure is provided so that the VR containing the query point can be reported in O(logn) time. The algorithm takes O(n) space and O(nlogn) preprocessing time.

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What this paper is about

Given a query point and the Voronoi diagram of a polygon (VD(P)), how to efficiently find the Voronoi region (VR) containing the query point, i.e., the point location in VD(P), is a fundamental operation for many other algorithms based on VD(P), such as path planning, visibility, and so on. A triangulation refinement method for VD(P) is presented in this paper, and then a point-location data structure is provided so that the VR containing the query point can be reported in O(logn) time. The algorithm takes O(n) space and O(nlogn) preprocessing time.

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Available abstract

Given a query point and the Voronoi diagram of a polygon (VD(P)), how to efficiently find the Voronoi region (VR) containing the query point, i.e., the point location in VD(P), is a fundamental operation for many other algorithms based on VD(P), such as path planning, visibility, and so on. A triangulation refinement method for VD(P) is presented in this paper, and then a point-location data structure is provided so that the VR containing the query point can be reported in O(logn) time. The algorithm takes O(n) space and O(nlogn) preprocessing time.

Key concepts: Voronoi diagram, Centroidal Voronoi tessellation, Point location, Point in polygon, Power diagram, Polygon (computer graphics), Weighted Voronoi diagram, Point (geometry)

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