On the generality of power diagrams
in Euclidean space is called a sphere
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.
Reference: F. Aurenhammer.
On the generality of power diagrams.
IIG Report F126, TU Graz, Austria, 1983.