Dynamically maintaining a hierarchical planar voronoi diagram approximation

Abstract

An approach for computing a hierarchical approximation of planar Voronoi diagrams for different site shapes (points, line-segments, curve-arc segments, ...) and different distance functions (Euclidean metrics, convex distance functions, ...) was presented in [3]. The approach is based on the Voronoi-Quadtree, a quadtree data structure from which a polygonal approximation, represented by a DCEL structure, of the associated Voronoi region boundaries can be computed at different levels of detail. In this paper we describe efficient algorithms for dynamically maintaining, under the insertion or deletion of sites, the Voronoi-Quadtree and the corresponding DCEL structure representing an approximation of a Generalized Voronoi diagram. © Springer-Verlag 2003.