Voronoi diagrams for parallel halflines and line segments in space

Franz Aurenhammer, Bert Jüttler, Günter Paulini

Research output: Chapter in Book/Report/Conference proceedingConference paper


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.
Original languageEnglish
Title of host publicationLIPIcs-Leibniz International Proceedings in Informatics
PublisherSchloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH
ISBN (Electronic)978-395977054-5
Publication statusPublished - 2017
Event28th International Symposium on Algorithms and Computation: ISAAC 2017 - Phuket, Thailand
Duration: 9 Dec 201712 Dec 2017


Conference28th International Symposium on Algorithms and Computation


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