Representing ordered order-k Voronoi diagrams

Abstract

The ordered order-k Voronoi diagram is a popular generalization of the ordinary Voronoi diagram modeling ordered k nearest sites. Despite of the usefulness of the ordered order-k Voronoi diagram, its structural complexity and wealth of information captured result in poor readability. Most research has focused on computational complexity, and visualization/representation of the ordered order-k Voronoi diagram has received little attention. This paper attempts to represent the ordered order-k Voronoi diagram through its relationship with other higher order Voronoi diagrams. The proposed method highlights topological relationships between/among higher order Voronoi diagram families, and enhances the readability of the ordered order-k diagram.