Combinatorial complexity of translating a box in polyhedral 3-space

7Citations
Citations of this article
6Readers
Mendeley users who have this article in their library.

Abstract

We study the space of free translations of a box amidst polyhedral obstacles with n vertices. We show that the combinatorial complexity of this space is O(n2α(n)), where α(n) is the inverse Ackermann function. Our bound is within an α(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). For the case of a convex polygon of fixed (constant) size translating in the same setting (namely, a two-dimensional polygon translating in three-dimensional space), we show a tight bound Θ(n2α(n)) on the complexity of the free space. © 1998 Elsevier Science B.V.

Cite

CITATION STYLE

APA

Halperin, D., & Yap, C. K. (1998). Combinatorial complexity of translating a box in polyhedral 3-space. Computational Geometry: Theory and Applications, 9(3), 181–196. https://doi.org/10.1016/S0925-7721(97)00030-8

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free