On translational motion planning in 3-space

Boris Aronov*, Micha Sharir

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

13 Scopus citations

Abstract

Let B be a convex polyhedron translating in 3-space amidst k convex polyhedral obstacles A1,....,Ak with pairwise disjoint interiors. The free configuration space (space of all collision-free placements) of B can be represented as the complement of the union of the Minkowski sums Pi Ai ⊕ (-B), for i = l,...,k. We show that the combinatorial complexity of the free configuration space of B is O(nk log2 k), where n is the total complexity of the individual Minkowski sums P1,..., Pk. The bound is almost tight in the worst case. We also derive an efficient randomized algorithm that constructs this configuration space in expected time O(nk log3 k).

Original languageEnglish
Title of host publicationProceedings of the Annual Symposium on Computational Geometry
PublisherAssociation for Computing Machinery (ACM)
Pages21-30
Number of pages10
ISBN (Print)0897916484, 9780897916486
DOIs
StatePublished - 1994
Externally publishedYes
EventProceedings of the 10th Annual Symposium on Computational Geometry - Stony Brook, NY, USA
Duration: 6 Jun 19948 Jun 1994

Publication series

NameProceedings of the Annual Symposium on Computational Geometry

Conference

ConferenceProceedings of the 10th Annual Symposium on Computational Geometry
CityStony Brook, NY, USA
Period6/06/948/06/94

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