Pipes, cigars, and kreplach: The union of Minkowski sums in three dimensions

Pankaj K. Agarwal*, Micha Sharir

*Corresponding author for this work

Research output: Contribution to conferencePaperpeer-review

Abstract

Let Ω be a set of pairwise-disjoint 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.

Original languageEnglish
Pages143-153
Number of pages11
StatePublished - 1999
Externally publishedYes
EventProceedings of the 1999 15th Annual Symposium on Computational Geometry - Miami Beach, FL, USA
Duration: 13 Jun 199916 Jun 1999

Conference

ConferenceProceedings of the 1999 15th Annual Symposium on Computational Geometry
CityMiami Beach, FL, USA
Period13/06/9916/06/99

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