Order-fc voronoi diagrams, fc-sections, and k-sets

Abstract

In this paper we characterize all-dimensional faces of order- k Voronoi diagrams. First we introduce the notion of fc-section to give a precise definition of these faces. Then, we characterize the unbounded faces by extending the classical notion of k-set. Finally, by studying some relations between fc-sections, we give a new proof of the size of order-A: Voronoi diagrams in the plane.