Voronoi Diagrams for Parallel Halflines and Line Segments in Space

Authors Franz Aurenhammer, Bert Jüttler, Günter Paulini

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Franz Aurenhammer
Bert Jüttler
Günter Paulini

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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)


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.
  • Voronoi diagram
  • line segments
  • space-sweep algorithm


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