Voronoi Diagrams for Parallel Halflines and Line Segments in Space

Aurenhammer, Franz; Jüttler, Bert; Paulini, Günter

doi:10.4230/LIPIcs.ISAAC.2017.7

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Voronoi Diagrams for Parallel Halflines and Line Segments in Space

Authors Franz Aurenhammer, Bert Jüttler, Günter Paulini

Part of: Volume: 28th International Symposium on Algorithms and Computation (ISAAC 2017)
Part of: Series: Leibniz International Proceedings in Informatics (LIPIcs)
Part of: Conference: International Symposium on Algorithms and Computation (ISAAC)
License: Creative Commons Attribution 3.0 Unported license
Publication Date: 2017-12-07

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Document Identifiers

DOI: 10.4230/LIPIcs.ISAAC.2017.7
URN: urn:nbn:de:0030-drops-82157

Subject Classification

Keywords

Voronoi diagram
line segments
space-sweep algorithm

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Abstract

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, 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.

Cite As Get BibTex

Franz Aurenhammer, Bert Jüttler, and Günter Paulini. Voronoi Diagrams for Parallel Halflines and Line Segments in Space. In 28th International Symposium on Algorithms and Computation (ISAAC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 92, pp. 7:1-7:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017) https://doi.org/10.4230/LIPIcs.ISAAC.2017.7

Author Details

Franz Aurenhammer

Bert Jüttler

Günter Paulini

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