Voronoi diagrams for parallel halflines and line segments in space

F. Aurenhammer; B. Jüttler; G. Paulini

doi:10.4230/LIPIcs.ISAAC.2017.7

Voronoi diagrams for parallel halflines and line segments in space

F. Aurenhammer, B. Jüttler, G. Paulini

Institut für Grundlagen der Informationsverarbeitung (7080)

Publikation: Beitrag in Buch/Bericht/Konferenzband › Beitrag in einem Konferenzband › Begutachtung

Abstract

We consider the Euclidean Voronoi diagram for a set of n parallel halflines in R3. A relation of this diagram to planar power diagrams is shown, and is used to analyze its geometric and topological properties. Moreover, an easy-To-implement space sweep algorithm is proposed that computes the Voronoi diagram for parallel halflines at logarithmic cost per face. Previously only an approximation algorithm for this problem was known. Our method of construction generalizes to Voronoi diagrams for parallel line segments, and to higher dimensions.

Originalsprache	englisch
Titel	Proc. 28th International Symposium on Algorithms and Computation (ISAAC'17)
Erscheinungsort	Phuket, Thailand
Herausgeber (Verlag)	Schloss Dagstuhl - Leibniz-Zentrum für Informatik
Seiten	#7
Band	92
ISBN (elektronisch)	978-395977054-5
DOIs	https://doi.org/10.4230/LIPIcs.ISAAC.2017.7
Publikationsstatus	Veröffentlicht - 2017
Veranstaltung	28th International Symposium on Algorithms and Computation: ISAAC 2017 - Phuket, Thailand Dauer: 9 Dez. 2017 → 12 Dez. 2017

Konferenz

Konferenz	28th International Symposium on Algorithms and Computation
Land/Gebiet	Thailand
Ort	Phuket
Zeitraum	9/12/17 → 12/12/17

Zugriff auf Dokument

10.4230/LIPIcs.ISAAC.2017.7Lizenz: CC BY 4.0

Andere Dateien und Links

http://drops.dagstuhl.de/opus/volltexte/2017/8215/

Dieses zitieren

Voronoi diagrams for parallel halflines and line segments in space. / Aurenhammer, F.; Jüttler, B.; Paulini, G.
Proc. 28th International Symposium on Algorithms and Computation (ISAAC'17). Band 92 Phuket, Thailand: Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2017. S. #7.

Publikation: Beitrag in Buch/Bericht/Konferenzband › Beitrag in einem Konferenzband › Begutachtung

Aurenhammer, F, Jüttler, B & Paulini, G 2017, Voronoi diagrams for parallel halflines and line segments in space. in Proc. 28th International Symposium on Algorithms and Computation (ISAAC'17). Bd. 92, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, Phuket, Thailand, S. #7, 28th International Symposium on Algorithms and Computation, Phuket, Thailand, 9/12/17. https://doi.org/10.4230/LIPIcs.ISAAC.2017.7

@inproceedings{40b6e897b308478b88c7174340c7ddb4,

title = "Voronoi diagrams for parallel halflines and line segments in space",

abstract = "We consider the Euclidean Voronoi diagram for a set of n parallel halflines in R3. A relation of this diagram to planar power diagrams is shown, and is used to analyze its geometric and topological properties. Moreover, an easy-To-implement space sweep algorithm is proposed that computes the Voronoi diagram for parallel halflines at logarithmic cost per face. Previously only an approximation algorithm for this problem was known. Our method of construction generalizes to Voronoi diagrams for parallel line segments, and to higher dimensions.",

author = "F. Aurenhammer and B. J{\"u}ttler and G. Paulini",

year = "2017",

doi = "10.4230/LIPIcs.ISAAC.2017.7",

language = "English",

volume = "92",

pages = "#7",

booktitle = "Proc. 28th International Symposium on Algorithms and Computation (ISAAC'17)",

publisher = "Schloss Dagstuhl - Leibniz-Zentrum f{\"u}r Informatik",

address = "Germany",

note = "28th International Symposium on Algorithms and Computation : ISAAC 2017 ; Conference date: 09-12-2017 Through 12-12-2017",

}

TY - GEN

T1 - Voronoi diagrams for parallel halflines and line segments in space

AU - Aurenhammer, F.

AU - Jüttler, B.

AU - Paulini, G.

PY - 2017

Y1 - 2017

N2 - We consider the Euclidean Voronoi diagram for a set of n parallel halflines in R3. A relation of this diagram to planar power diagrams is shown, and is used to analyze its geometric and topological properties. Moreover, an easy-To-implement space sweep algorithm is proposed that computes the Voronoi diagram for parallel halflines at logarithmic cost per face. Previously only an approximation algorithm for this problem was known. Our method of construction generalizes to Voronoi diagrams for parallel line segments, and to higher dimensions.

AB - We consider the Euclidean Voronoi diagram for a set of n parallel halflines in R3. A relation of this diagram to planar power diagrams is shown, and is used to analyze its geometric and topological properties. Moreover, an easy-To-implement space sweep algorithm is proposed that computes the Voronoi diagram for parallel halflines at logarithmic cost per face. Previously only an approximation algorithm for this problem was known. Our method of construction generalizes to Voronoi diagrams for parallel line segments, and to higher dimensions.

UR - http://drops.dagstuhl.de/opus/volltexte/2017/8215/

U2 - 10.4230/LIPIcs.ISAAC.2017.7

DO - 10.4230/LIPIcs.ISAAC.2017.7

M3 - Conference paper

VL - 92

SP - #7

BT - Proc. 28th International Symposium on Algorithms and Computation (ISAAC'17)

PB - Schloss Dagstuhl - Leibniz-Zentrum für Informatik

CY - Phuket, Thailand

T2 - 28th International Symposium on Algorithms and Computation

Y2 - 9 December 2017 through 12 December 2017

ER -

Voronoi diagrams for parallel halflines and line segments in space

Abstract

Konferenz

Zugriff auf Dokument

Andere Dateien und Links

Fingerprint

Dieses zitieren