Abstract
We consider an arrangement A of n hyperplanes in Rd and the zone Z in A of the boundary of an arbitrary convex set in Rd in such an arrangement. We show that, whereas the combinatorial complexity of Z is known only to be O(nd−1logn)[3], the outer part of the zone has complexity O(nd−1) (without the logarithmic factor). Whether this bound also holds for the complexity of the inner part of the zone is still an open question (even for d=2).
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