volume 31, issue 1, P83-124 2004
DOI: 10.1007/s00454-003-2950-5
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Abstract: We show that the complexity of the Voronoi diagram of a collection of disjoint polyhedra in general position in 3-space that have n vertices overall, under a convex distance function induced by a polyhedron with O(1) facets, is O(n 2+ε ), for any ε > 0. We also show that when the sites are n segments in 3-space, this complexity is O(n 2 α(n) log n). This generalizes previous results by Chew et al. [10] and by Aronov and Sharir [4], and solves an open problem put forward by Agarwal and Sharir [2]. Specific dis…

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