Voronoi diagrams for oriented spheres

F. Aurenhammer; J. Wallner; M. Peternell; H. Pottmann

doi:10.1109/ISVD.2007.45

Voronoi diagrams for oriented spheres

F. Aurenhammer^*, J. Wallner, M. Peternell, H. Pottmann

^*Corresponding author for this work

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

2 Scopus citations

Abstract

We consider finite sets of oriented spheres in R^k-1 and, by interpreting such spheres as points in R^k, study the Voronoi diagrams they induce for several variants of distance between spheres. We give bounds on the combinatorial complexity of these diagrams in R² and R ³ and derive properties useful for constructing them. Our results are motivated by applications to special relativity theory.

Original language	English (US)
Title of host publication	Proceedings - ISVD 2007 The 4th International Symposium on Voronoi Diagrams in Science and Engineering 2007
Pages	33-37
Number of pages	5
DOIs	https://doi.org/10.1109/ISVD.2007.45
State	Published - 2007
Externally published	Yes
Event	4th International Symposium on Voronoi Diagrams in Science and Engineering 2007, ISVD 2007 - Pontypridd, United Kingdom Duration: Jul 9 2007 → Jul 11 2007

Publication series

Name	Proceedings - ISVD 2007 The 4th International Symposium on Voronoi Diagrams in Science and Engineering 2007

Other

Other	4th International Symposium on Voronoi Diagrams in Science and Engineering 2007, ISVD 2007
Country/Territory	United Kingdom
City	Pontypridd
Period	07/9/07 → 07/11/07

ASJC Scopus subject areas

Computational Theory and Mathematics
Computational Mechanics

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10.1109/ISVD.2007.45

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Aurenhammer, F., Wallner, J., Peternell, M., & Pottmann, H. (2007). Voronoi diagrams for oriented spheres. In Proceedings - ISVD 2007 The 4th International Symposium on Voronoi Diagrams in Science and Engineering 2007 (pp. 33-37). Article 4276102 (Proceedings - ISVD 2007 The 4th International Symposium on Voronoi Diagrams in Science and Engineering 2007). https://doi.org/10.1109/ISVD.2007.45

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title = "Voronoi diagrams for oriented spheres",

abstract = "We consider finite sets of oriented spheres in Rk-1 and, by interpreting such spheres as points in Rk, study the Voronoi diagrams they induce for several variants of distance between spheres. We give bounds on the combinatorial complexity of these diagrams in R2 and R 3 and derive properties useful for constructing them. Our results are motivated by applications to special relativity theory.",

author = "F. Aurenhammer and J. Wallner and M. Peternell and H. Pottmann",

year = "2007",

doi = "10.1109/ISVD.2007.45",

language = "English (US)",

isbn = "0769528694",

series = "Proceedings - ISVD 2007 The 4th International Symposium on Voronoi Diagrams in Science and Engineering 2007",

pages = "33--37",

booktitle = "Proceedings - ISVD 2007 The 4th International Symposium on Voronoi Diagrams in Science and Engineering 2007",

note = "4th International Symposium on Voronoi Diagrams in Science and Engineering 2007, ISVD 2007 ; Conference date: 09-07-2007 Through 11-07-2007",

}

Aurenhammer, F, Wallner, J, Peternell, M & Pottmann, H 2007, Voronoi diagrams for oriented spheres. in Proceedings - ISVD 2007 The 4th International Symposium on Voronoi Diagrams in Science and Engineering 2007., 4276102, Proceedings - ISVD 2007 The 4th International Symposium on Voronoi Diagrams in Science and Engineering 2007, pp. 33-37, 4th International Symposium on Voronoi Diagrams in Science and Engineering 2007, ISVD 2007, Pontypridd, United Kingdom, 07/9/07. https://doi.org/10.1109/ISVD.2007.45

Voronoi diagrams for oriented spheres. / Aurenhammer, F.; Wallner, J.; Peternell, M. et al.
Proceedings - ISVD 2007 The 4th International Symposium on Voronoi Diagrams in Science and Engineering 2007. 2007. p. 33-37 4276102 (Proceedings - ISVD 2007 The 4th International Symposium on Voronoi Diagrams in Science and Engineering 2007).

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

TY - GEN

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AU - Aurenhammer, F.

AU - Wallner, J.

AU - Peternell, M.

AU - Pottmann, H.

PY - 2007

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AB - We consider finite sets of oriented spheres in Rk-1 and, by interpreting such spheres as points in Rk, study the Voronoi diagrams they induce for several variants of distance between spheres. We give bounds on the combinatorial complexity of these diagrams in R2 and R 3 and derive properties useful for constructing them. Our results are motivated by applications to special relativity theory.

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M3 - Conference contribution

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BT - Proceedings - ISVD 2007 The 4th International Symposium on Voronoi Diagrams in Science and Engineering 2007

T2 - 4th International Symposium on Voronoi Diagrams in Science and Engineering 2007, ISVD 2007

Y2 - 9 July 2007 through 11 July 2007

ER -

Voronoi diagrams for oriented spheres

Abstract

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Other

ASJC Scopus subject areas

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