Voronoi Diagrams for Oriented Spheres

We consider finite sets of oriented spheres in Rk−1 and, by interpreting such spheres as points in Rk , 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.

• Type: Conference
• Year: 2007
• Where: ISVD
• Authors: Franz Aurenhammer, Johannes Wallner, Martin Peternell, Helmut Pottmann
• Keywords: ISVD 2007, Oriented Spheres, Special Relativity Theory, Theoretical Computer Science, Voronoi Diagrams