An optimal algorithm to construct all Voronoi diagrams for k nearest neighbor search in T/sup 2/

We generalize to the oriented projective plane T/sup 2/ an algorithm for constructing all order k Voronoi diagrams in the Euclidean plane. We also show that, for fixed k and for a finite set of sites, an order k Voronoi diagram in T/sup 2/ has an exact number of regions. Furthermore, we show that the order k Voronoi diagram of a set of n sites in T/sup 2/ is antipodal to its order n-k Voronoi diagram, /spl forall/k: 1/spl les/k