**F. Aurenhammer**

A set
in Euclidean space is called a sphere
with center and positive radius . For an arbitrary point ,
is the power of with respect to . Extending these concepts to
imaginary radii, they are exploited to show the equivalence of two types of
cell complexes: those that can be obtained by projection of convex polyhedra,
and those that come from projecting levels in arrangement of hyperplanes. As
a consequence, higher-order Voronoi diagrams can be constructed by
determining a convex hull.