Computation of Certain Measures of Proximity Between Convex Polytopes: A Complexity Viewpoint

Sancheti, NK and Keerthi, SS (1992) Computation of Certain Measures of Proximity Between Convex Polytopes: A Complexity Viewpoint. In: IEEE International Conference on Robotics and Automation, 1992, 12-14 May, Nice,France, Vol.3, 2508-2513.

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Abstract

Four problems of proximity between two convex polytopes in R^8 are considered. The convex polytopes are represented as convex hulls of finite sets of points. Let the total number of points in the two finite sets be n. We show that three of the proximity problems, viz., checking intersection, checking whether the polytopes are just touching and finding the distance between them, can be solved in O(n) time for fixed s and in polynomial time for vayings. We also show that the fourth proximity problem of finding the intensity of collision for varying s is NP-complete.

Item Type:	Conference Paper
Publisher:	IEEE
Additional Information:	Copyright 1992 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE
Department/Centre:	Division of Electrical Sciences > Computer Science & Automation
Date Deposited:	25 Aug 2008
Last Modified:	19 Sep 2010 04:28
URI:	http://eprints.iisc.ac.in/id/eprint/7197

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