### Abstract

Original language | English |
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Title of host publication | Proceedings of the 32nd European Workshop on Computational Geometry EuroCG'2016 |

Publication status | Published - 30 Mar 2016 |

Event | EuroCG 2016: 32nd European Workshop on Computational Geometry - Lugano, Switzerland Duration: 29 Mar 2016 → 1 Apr 2016 |

### Conference

Conference | EuroCG 2016 |
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Abbreviated title | EuroCG 2016 |

Country | Switzerland |

City | Lugano |

Period | 29/03/16 → 1/04/16 |

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### Cite this

*Proceedings of the 32nd European Workshop on Computational Geometry EuroCG'2016*

**Voronoi diagrams for parallel halflines in 3D.** / Aurenhammer, Franz; Paulini, Günter; Jüttler, Bert.

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

*Proceedings of the 32nd European Workshop on Computational Geometry EuroCG'2016.*EuroCG 2016, Lugano, Switzerland, 29/03/16.

}

TY - GEN

T1 - Voronoi diagrams for parallel halflines in 3D

AU - Aurenhammer, Franz

AU - Paulini, Günter

AU - Jüttler, Bert

PY - 2016/3/30

Y1 - 2016/3/30

N2 - We consider the Euclidean Voronoi diagram for a set of n parallel halflines in 3-space. A relation of this diagram to planar power diagrams is shown, and is used to analyze its geometric and topological properties. Moreover, a simple plane-sweep algorithm is given that computes the Voronoi diagram for parallel halflines at logarithmic cost per face.

AB - We consider the Euclidean Voronoi diagram for a set of n parallel halflines in 3-space. A relation of this diagram to planar power diagrams is shown, and is used to analyze its geometric and topological properties. Moreover, a simple plane-sweep algorithm is given that computes the Voronoi diagram for parallel halflines at logarithmic cost per face.

M3 - Conference contribution

BT - Proceedings of the 32nd European Workshop on Computational Geometry EuroCG'2016

ER -