Voronoi diagrams of semi-algebraic sets

Voronoi diagrams of semi-algebraic sets

On computing Voronoi diagrams for sorted point sets

We show that the Voronoi diagram of a nite sequence of points in the plane which gives sorted order of the points with respect to two perpendicular directions can be computed in linear time. In contrast, we observe that the problem of computing the Voronoi diagram of a nite sequence of points in the plane which gives the sorted order of the points with respect to a single direction requires (n ...

Towards Exact Numerical Voronoi Diagrams (Invited Talk)

Voronoi diagrams are extremely versatile as a data structure for many geometric applications. Computing this diagram “exactly” for a polyhedral set in 3D has been a quest of computational geometers for over two decades; this quest is still unrealized. We will locate the difficulty in this quest, thanks to a recent result of Everett et al (2009). More generally, it points to the need for alterna...

Optimal Voronoi diagram construction with convex sites in three dimensions

Lee and Drysdale [13] and Sharir [16] have given suboptimal algorithms for computing the Voronoi diagrams of line-segments or discs in the plane. This paper adapts their methods to constructing the Voronoi diagram for disjoint convex sites in three dimensions. Let be an upper bound on the number of features in any diagram involving sites in three dimensions. Even for point sites, is , so it is ...

Abstract Voronoi diagrams revisited

Voronoi Diagrams Revisited Rolf Klein∗ Elmar Langetepe∗ Zahra Nilforoushan† Abstract Abstract Voronoi diagrams [21] were designed as a unifying concept that should include as many concrete types of diagrams as possible. To ensure that abstract Voronoi diagrams, built from given sets of bisecting curves, are finite graphs, it was required that any two bisecting curves intersect only finitely oft...