The Voronoi-Quadtree: construction and visualization

Abstract

We define a quadtree-based planar Voronoi diagram codification, the Voronoi-Quadtree, valid for generalized sites (points, line-segments, curve-arc segments, ...) and for different distance functions (Euclidean metrics, convex distance functions, ...).We present an algorithm for constructing, at a prefixed level of detail, the Voronoi-Quadtree associated to a Voronoi diagram determined by a set of sites and a given distance function. A second algorithm that, taking as input a Voronoi-Quadtree, visualizes a polygonal approximation of the boundary of the Voronoi diagram is also described

This work was supported by DURSI 2001SGR-00296. The first author was supported in part by grants TIC2000-1009 and TIC2001-2226-C02-02. The second and third authors were supported in part by grants MEC-DGES-SEUID PB98-0933, and TIC2001-2392-C03-01