We study the amortized number of combinatorial changes (edge insertions and removals) needed to update the graph structure of the Voronoi diagram VD(S) (and several variants thereof) of a set S of n sites in the plane as sites are added to the set. To that effect, we define a general update operation for planar graphs that can be used to model the incremental construction of several variants of...

Given an anisotropic Voronoi diagram, we address the fundamental question of when its dual is embedded. We show that, by requiring only that the primal be orphan-free (have connected Voronoi regions), its dual is always guaranteed to be an embedded triangulation. Further, the primal diagram and its dual have properties that parallel those of ordinary Voronoi diagrams: the primal’s vertices, edg...

AVNEESH SUD: Efficient Computation of Discrete Voronoi Diagram and Homotopy-Preserving Simplified Medial Axis of a 3D Polyhedron. (Under the direction of Dinesh Manocha.) The Voronoi diagram is a fundamental geometric data structure and has been well studied in computational geometry and related areas. A Voronoi diagram defined using the Euclidean distance metric is also closely related to the ...

We present a simplified system of axioms for Abstract Voronoi Diagrams that should pave the way for new applications in theory and practice.

In this paper we describe a generic C++ adaptor, that adapts a 2-dimensional triangulated Delaunay graph and to the corresponding a Voronoi diagram, represented as a doubly connected edge list (DCEL) data structure. Our adaptor has the ability to automatically eliminate, in a consistent manner, degenerate features of the Voronoi diagram, that are artifacts of the requirement that Delaunay graph...

This paper presents the Voronoi diagram-based evolutionary algorithm (VorEAl). VorEAl partitions input space in abnormal/normal subsets using Voronoi diagrams. Diagrams are evolved using a multiobjective bio-inspired approach in order to conjointly optimize classification metrics while also being able to represent areas of the data space that are not present in the training dataset. As part of ...