Math @ Duke

Publications [#235413] of Pankaj K. Agarwal
Papers Published
 Agarwal, PK; Sharir, M, Pipes, cigars, and kreplach: The union of Minkowski sums in three dimensions,
in Fifteenth Annual Symposium on Computational Geometry,
Proceedings of the Annual Symposium on Computational Geometry
(1999),
pp. 143153
(last updated on 2018/03/19)
Abstract: Let Ω be a set of pairwisedisjoint polyhedral obstacles in R3 with a total of n vertices, and let B be a ball. We show that the combinatorial complexity of the free configuration space F of B amid Ω, i.e., the set of all placements of B at which B does not intersect any obstacle, is O(n2+ε), for any ε>0; the constant of proportionality depends on ε. This upper bound almost matches the known quadratic lower bound on the maximum possible complexity of F. We also present a randomized algorithm to compute the boundary of F whose expected running time is O(n2+ε), for any ε>0.


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