Voronoi Diagrams for Oriented Spheres

We consider finite sets of oriented spheres in R^k-1 and, by interpreting such spheres as points in R^k, study the Voronoi diagrams they induce for several variants of distance between spheres. We give bounds on the combinatorial complexity of these diagrams in R² and R³ and derive properties useful for constructing them. Our results are motivated by applications to special relativity theory.