On the union of Jordan regions and collision-free translational motion amidst polygonal obstacles
Discrete & Computational Geometry
On the general motion-planning problem with two degrees of freedom
Discrete & Computational Geometry - Selected papers from the fourth ACM symposium on computational geometry, Univ. of Illinois, Urbana-Champaign, June 6 8, 1988
Planning algorithm for a convex polygonal object in two-dimensional polygonal space
Discrete & Computational Geometry
SCG '92 Proceedings of the eighth annual symposium on Computational geometry
Robot Motion Planning
On translational motion planning in 3-space
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
Recent Developments in the Theory of Arrangements of Surfaces
Proceedings of the 19th Conference on Foundations of Software Technology and Theoretical Computer Science
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We study the space of free translations of a box amidst polyhedral obstacles with n features. We show that the combinatorial complexity of this space is O(n2&agr;(n)) where &agr;(n) is the inverse Ackermann function. Our bound is within an &agr;(n) factor off the lower bound, and it constitutes an improvement of almost an order of magnitude over the best previously known (and naive) bound for this problem, O(n3).