Walking around fat obstacles

L. Paul Chew; Haggai David; Matthew J. Katz; Klara Kedem

doi:10.1016/S0020-0190(01)00321-0

Walking around fat obstacles

L. Paul Chew, Haggai David, Matthew J. Katz, Klara Kedem

Department of Computer Science

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

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 ℝ^d in the presence of disjoint convex fat obstacles.

Original language	English
Pages (from-to)	135-140
Number of pages	6
Journal	Information Processing Letters
Volume	83
Issue number	3
DOIs	https://doi.org/10.1016/S0020-0190(01)00321-0
State	Published - 16 Aug 2002

Keywords

Computational geometry
Fat objects
Short paths

ASJC Scopus subject areas

Theoretical Computer Science
Signal Processing
Information Systems
Computer Science Applications

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10.1016/S0020-0190(01)00321-0

Cite this

@article{485e906eb52c47c3ab5260dc9e76158c,

title = "Walking around fat obstacles",

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.",

keywords = "Computational geometry, Fat objects, Short paths",

author = "Chew, {L. Paul} and Haggai David and Katz, {Matthew J.} and Klara Kedem",

note = "Funding Information: 2M. Katz and K. Kedem were supported in part by a grant from the Israel Science Foundation. K. Kedem was also supported by the Mary Upson Award from the College of Engineering at Cornell University, and by a grant from the US–Israeli Binational Science Foundation. Funding Information: 1L.P. Chew was supported in part by the National Science Foundation (EIA-9726388), by DARPA through ONR (N00014-96-1-0699), and by a grant from the US–Israeli Binational Science Foundation.",

year = "2002",

month = aug,

day = "16",

doi = "10.1016/S0020-0190(01)00321-0",

language = "English",

volume = "83",

pages = "135--140",

journal = "Information Processing Letters",

issn = "0020-0190",

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TY - JOUR

T1 - Walking around fat obstacles

AU - Chew, L. Paul

AU - David, Haggai

AU - Katz, Matthew J.

AU - Kedem, Klara

N1 - Funding Information: 2M. Katz and K. Kedem were supported in part by a grant from the Israel Science Foundation. K. Kedem was also supported by the Mary Upson Award from the College of Engineering at Cornell University, and by a grant from the US–Israeli Binational Science Foundation. Funding Information: 1L.P. Chew was supported in part by the National Science Foundation (EIA-9726388), by DARPA through ONR (N00014-96-1-0699), and by a grant from the US–Israeli Binational Science Foundation.

PY - 2002/8/16

Y1 - 2002/8/16

N2 - 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.

AB - 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.

KW - Computational geometry

KW - Fat objects

KW - Short paths

UR - http://www.scopus.com/inward/record.url?scp=0037119070&partnerID=8YFLogxK

U2 - 10.1016/S0020-0190(01)00321-0

DO - 10.1016/S0020-0190(01)00321-0

M3 - Article

AN - SCOPUS:0037119070

SN - 0020-0190

VL - 83

SP - 135

EP - 140

JO - Information Processing Letters

JF - Information Processing Letters

IS - 3

ER -

Walking around fat obstacles

Abstract

Keywords

ASJC Scopus subject areas

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