Line transversals of balls and smallest enclosing cylinders in three dimensions

Pankaj K. Agarwal; Boris Aronov; Micha Sharir

Line transversals of balls and smallest enclosing cylinders in three dimensions

Pankaj K. Agarwal, Boris Aronov, Micha Sharir

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

We establish a near-cubic upper bound on the complexity of the space of line transversals of a collection of n balls in three dimensions; and show that the bound is almost tight, in the worst case. We apply this bound to obtain a near-cubic algorithm for computing a smallest infinite cylinder enclosing a given set of points or balls in 3-space. We also present an approximation algorithm for computing a smallest enclosing cylinder.

Original language	English (US)
Title of host publication	Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms
Editors	Anon
Publisher	ACM
Pages	483-492
Number of pages	10
State	Published - 1997
Event	Proceedings of the 1996 8th Annual ACM-SIAM Symposium on Discrete Algorithms - New Orleans, LA, USA Duration: Jan 5 1997 → Jan 7 1997

Other

Other	Proceedings of the 1996 8th Annual ACM-SIAM Symposium on Discrete Algorithms
City	New Orleans, LA, USA
Period	1/5/97 → 1/7/97

ASJC Scopus subject areas

Chemical Health and Safety
Software
Safety, Risk, Reliability and Quality
Discrete Mathematics and Combinatorics

Cite this

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title = "Line transversals of balls and smallest enclosing cylinders in three dimensions",

abstract = "We establish a near-cubic upper bound on the complexity of the space of line transversals of a collection of n balls in three dimensions; and show that the bound is almost tight, in the worst case. We apply this bound to obtain a near-cubic algorithm for computing a smallest infinite cylinder enclosing a given set of points or balls in 3-space. We also present an approximation algorithm for computing a smallest enclosing cylinder.",

author = "Agarwal, {Pankaj K.} and Boris Aronov and Micha Sharir",

year = "1997",

language = "English (US)",

pages = "483--492",

editor = "Anon",

booktitle = "Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms",

publisher = "ACM",

note = "Proceedings of the 1996 8th Annual ACM-SIAM Symposium on Discrete Algorithms ; Conference date: 05-01-1997 Through 07-01-1997",

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AU - Agarwal, Pankaj K.

AU - Aronov, Boris

AU - Sharir, Micha

PY - 1997

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N2 - We establish a near-cubic upper bound on the complexity of the space of line transversals of a collection of n balls in three dimensions; and show that the bound is almost tight, in the worst case. We apply this bound to obtain a near-cubic algorithm for computing a smallest infinite cylinder enclosing a given set of points or balls in 3-space. We also present an approximation algorithm for computing a smallest enclosing cylinder.

AB - We establish a near-cubic upper bound on the complexity of the space of line transversals of a collection of n balls in three dimensions; and show that the bound is almost tight, in the worst case. We apply this bound to obtain a near-cubic algorithm for computing a smallest infinite cylinder enclosing a given set of points or balls in 3-space. We also present an approximation algorithm for computing a smallest enclosing cylinder.

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M3 - Conference contribution

AN - SCOPUS:0030834867

SP - 483

EP - 492

BT - Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

A2 - Anon, null

PB - ACM

T2 - Proceedings of the 1996 8th Annual ACM-SIAM Symposium on Discrete Algorithms

Y2 - 5 January 1997 through 7 January 1997

ER -

Line transversals of balls and smallest enclosing cylinders in three dimensions

Abstract

Other

ASJC Scopus subject areas

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