On Some Polyhedra Covering Problems

Cao An Wang (), Bo-Ting Yang and Binhai Zhu ()
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Cao An Wang: Memorial University of Newfoundland
Bo-Ting Yang: Memorial University of Newfoundland
Binhai Zhu: Montana State University

Journal of Combinatorial Optimization, 2000, vol. 4, issue 4, No 3, 437-447

Abstract: Abstract Let P 0, P 1 be two simple polyhedra and let P 2 be a convex polyhedron in E 3. Polyhedron P 0 is said to be covered by polyhedra P 1 and P 2 if every point of P 0 is a point of P 1 ∪ P 2. The following polyhedron covering problem is studied: given the positions of P 0, P 1, and P 2 in the xy-coordinate system, determine whether or not P 0 can be covered by P 1 ∪ P 2 via translation and rotation of P 1 and P 2; furthermore, find the exact covering positions of these polyhedra if such a cover exists. It is shown in this paper that if only translation is allowed, then the covering problem of P 0, P 1 and P 2 can be solved in O(m 2 n 2(m + n)l)) polynomial time, where m, n, and l are the sizes of P 0, P 1, and P 2, respectively. The method can be easily extended to the problem in E d for any fixed d > 3.

Keywords: computational geometry; polyhedra covering; NP-hard (search for similar items in EconPapers)
Date: 2000
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Citations: View citations in EconPapers (1)

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DOI: 10.1023/A:1009833410742

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