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Voronoi Diagrams for a Moderate-Sized Point-Set in a Simple Polygon

Authors Eunjin Oh, Hee-Kap Ahn

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Eunjin Oh
Hee-Kap Ahn

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Eunjin Oh and Hee-Kap Ahn. Voronoi Diagrams for a Moderate-Sized Point-Set in a Simple Polygon. In 33rd International Symposium on Computational Geometry (SoCG 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 77, pp. 52:1-52:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017) https://doi.org/10.4230/LIPIcs.SoCG.2017.52

Abstract

Given a set of sites in a simple polygon, a geodesic Voronoi diagram partitions the polygon into regions based on distances to sites under the geodesic metric. We present algorithms for computing the geodesic nearest-point, higher-order and farthest-point Voronoi diagrams of m point sites in a simple n-gon, which improve the best known ones for m < n/polylog n. Moreover, the algorithms for the nearest-point and farthest-point Voronoi diagrams are optimal for m < n/polylog n. This partially answers a question posed by Mitchell in the Handbook of Computational Geometry.

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Keywords
  • Simple polygons
  • Voronoi diagrams
  • geodesic distance

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References

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