Building Convex Space Partitions Induced by Pairwise Interior-disjoint Simplices
نویسنده
چکیده
Given a set S of n pairwise interior-disjoint (d?1)-simplices in d-space, for d 3, a Convex Space Partition induced by S (denoted CSP(S)) is a partition of d-space into convex cells such that the interior of each cell does not intersect the interior of any simplex in S. In this paper it is shown that a CSP(S) of size O(n d?1) can be computed deterministically in time O(n d?1). These bounds are worst case optimal for d = 3. The results are proved using a variation of the eecient hierarchical cuttings of Chazelle.
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