### Abstract

Let B be a set of n unit balls in ℝ^{3}. We show that the combinatorial complexity of the space of lines in ℝ^{3} 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 (US) |
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Title of host publication | Proceedings of the Twentieth Annual Symposium on Computational Geometry (SCG'04) |

Pages | 36-45 |

Number of pages | 10 |

State | Published - 2004 |

Event | Proceedings of the Twentieth Annual Symposium on Computational Geometry (SCG'04) - Brooklyn, NY, United States Duration: Jun 9 2004 → Jun 11 2004 |

### Other

Other | Proceedings of the Twentieth Annual Symposium on Computational Geometry (SCG'04) |
---|---|

Country | United States |

City | Brooklyn, NY |

Period | 6/9/04 → 6/11/04 |

### Fingerprint

### Keywords

- Combinatorial complexity
- Lines in space
- Visibility

### ASJC Scopus subject areas

- Software
- Geometry and Topology
- Safety, Risk, Reliability and Quality
- Chemical Health and Safety

### Cite this

*Proceedings of the Twentieth Annual Symposium on Computational Geometry (SCG'04)*(pp. 36-45)

**On lines avoiding unit balls in three dimensions.** / Agarwal, Pankaj K.; Aronov, Boris; Koltun, Vladlen; Sharir, Micha.

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

*Proceedings of the Twentieth Annual Symposium on Computational Geometry (SCG'04).*pp. 36-45, Proceedings of the Twentieth Annual Symposium on Computational Geometry (SCG'04), Brooklyn, NY, United States, 6/9/04.

}

TY - GEN

T1 - On lines avoiding unit balls in three dimensions

AU - Agarwal, Pankaj K.

AU - Aronov, Boris

AU - Koltun, Vladlen

AU - Sharir, Micha

PY - 2004

Y1 - 2004

N2 - 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.

AB - 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.

KW - Combinatorial complexity

KW - Lines in space

KW - Visibility

UR - http://www.scopus.com/inward/record.url?scp=4544360682&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=4544360682&partnerID=8YFLogxK

M3 - Conference contribution

SP - 36

EP - 45

BT - Proceedings of the Twentieth Annual Symposium on Computational Geometry (SCG'04)

ER -