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Voronoi Diagrams of Lines in 3-Space Under Polyhedral Convex Distance Functions

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Emo Welzl
Institut für Informatik
Freie Universität Berlin
email: emo@inf.fu-berlin.de
(joint work with L. Paul Chew, Klara Kedem, Micha Sharir and Boaz Tagansky)
Report B 95-06
April 1995

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Voronoi Diagrams of Lines in 3-Space Under Polyhedral Convex Distance Functions
The combinatorial complexity of the Voronoi diagram
of $n$ lines in three dimensions under a convex
distance function induced by a polytope with a constant number of edges
is shown to be $\vorPPcompl$, where $\alpha$ is a
slowly growing inverse of the Ackermann function.
There are arrangements of $n$ lines where this complexity can be as
large as $\Omega(n^2 \alpha(n))$.