### 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) |
---|---|

Pages (from-to) | 373-388 |

Number of pages | 16 |

Journal | Discrete and Computational Geometry |

Volume | 21 |

Issue number | 3 |

State | Published - 1999 |

### Fingerprint

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computational Theory and Mathematics
- Discrete Mathematics and Combinatorics
- Geometry and Topology

### Cite this

*Discrete and Computational Geometry*,

*21*(3), 373-388.

**Line transversals of balls and smallest enclosing cylinders in three dimensions.** / Agarwal, P. K.; Aronov, Boris; Sharir, M.

Research output: Contribution to journal › Article

*Discrete and Computational Geometry*, vol. 21, no. 3, pp. 373-388.

}

TY - JOUR

T1 - Line transversals of balls and smallest enclosing cylinders in three dimensions

AU - Agarwal, P. K.

AU - Aronov, Boris

AU - Sharir, M.

PY - 1999

Y1 - 1999

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.

UR - http://www.scopus.com/inward/record.url?scp=0033441871&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0033441871&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0033441871

VL - 21

SP - 373

EP - 388

JO - Discrete and Computational Geometry

JF - Discrete and Computational Geometry

SN - 0179-5376

IS - 3

ER -