On lines avoiding unit balls in three dimensions

Pankaj K. Agarwal; Boris Aronov; Vladlen Koltun; Micha Sharir

doi:10.1145/997817.997826

On lines avoiding unit balls in three dimensions

Pankaj K. Agarwal^*, Boris Aronov, Vladlen Koltun, Micha Sharir

^*Corresponding author for this work

School of Computer Science

Research output: Contribution to conference › Paper › peer-review

Abstract

Let B be a set of n unit balls in ℝ³. We show that the combinatorial complexity of the space of lines in ℝ³ that avoid all the balls of B is O(n^3+ε), for any ε > 0. This result has connections to problems in visibility, ray shooting, motion planning and geometric optimization.

Original language	English
Pages	36-45
Number of pages	10
DOIs	https://doi.org/10.1145/997817.997826
State	Published - 2004
Event	Proceedings of the Twentieth Annual Symposium on Computational Geometry (SCG'04) - Brooklyn, NY, United States Duration: 9 Jun 2004 → 11 Jun 2004

Conference

Conference	Proceedings of the Twentieth Annual Symposium on Computational Geometry (SCG'04)
Country/Territory	United States
City	Brooklyn, NY
Period	9/06/04 → 11/06/04

Keywords

Combinatorial complexity
Lines in space
Visibility

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10.1145/997817.997826

Cite this

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title = "On lines avoiding unit balls in three dimensions",

abstract = "Let B be a set of n unit balls in ℝ3. We show that the combinatorial complexity of the space of lines in ℝ3 that avoid all the balls of B is O(n3+ε), for any ε > 0. This result has connections to problems in visibility, ray shooting, motion planning and geometric optimization.",

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AU - Aronov, Boris

AU - Koltun, Vladlen

AU - Sharir, Micha

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KW - Combinatorial complexity

KW - Lines in space

KW - Visibility

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On lines avoiding unit balls in three dimensions

Abstract

Conference

Keywords

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