Walking around fat obstacles

Authors:
L. Paul Chew;Haggai David;Matthew J. Katz;Klara Kedem
Affiliations:
Computer Science Department, Cornell University, Ithaca, NY;Department of Computer Science, Ben-Gurion University, Beer-Sheva 84105, Israel;Department of Computer Science, Ben-Gurion University, Beer-Sheva 84105, Israel;Computer Science Department, Cornell University, Ithaca, NY and Department of Computer Science, Ben-Gurion University, Beer-Sheva 84105, Israel
Venue:
Information Processing Letters
Year:
2002

Citing 4
Cited 4

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Abstract

We prove that if an object O is convex and fat then, for any two points a and b on its boundary, there exists a path on O's boundary, from a to b, whose length is bounded by the length of the line segment ab times some constant β. This constant is a function of the dimension d and the fatness parameter. We prove bounds for β, and show how to efficiently find paths on the boundary of O whose lengths are within these bounds. As an application of this result, we briefly consider the problem of efficiently computing short paths in Rd in the presence of disjoint convex fat obstacles.