# Voronoi Diagrams for Oriented Spheres

**F. Aurenhammer, M. Peternell, H. Pottmann, and J. Wallner**

### Abstract:

We consider finite sets of oriented spheres in (k-1)-space and, by interpreting
such spheres as points in k-space, study the Voronoi diagrams they induce for
several variants of distance between spheres. We give bounds on the
combinatorial complexity of these diagrams in the plane and in 3-space, and
derive properties useful for constructing them. Our results are motivated by
applications to special relativity theory.

**Reference:** F. Aurenhammer, M. Peternell, H. Pottmann, and J. Wallner.
Voronoi diagrams for oriented spheres.
In *Proc. 4th Int. Symp. on Voronoi Diagrams in Science and Engineering,
ISVD'07*, pages 33-37, Pontypridd, UK, 2007.