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


Given a set of sites in a simple polygon, a geodesic Voronoi diagram of the sites 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 \(m \le n/{\text {polylog}}n\). Moreover, the algorithms for the geodesic nearest-point and farthest-point Voronoi diagrams are optimal for \(m \le n/{\text {polylog}}n\). This partially answers a question posed by Mitchell in the Handbook of Computational Geometry.

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Correspondence to Hee-Kap Ahn.

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This research was supported by the MSIT (Ministry of Science and ICT), Korea, under the SW Starlab support program (IITP-2017-0-00905) supervised by the IITP (Institute for Information & communications Technology Promotion).

Editor in Charge: Kenneth Clarkson

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Oh, E., Ahn, HK. Voronoi Diagrams for a Moderate-Sized Point-Set in a Simple Polygon. Discrete Comput Geom 63, 418–454 (2020). https://doi.org/10.1007/s00454-019-00063-4

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  • Voronoi diagrams
  • Geodesic distance
  • Simple Polygons

Mathematics Subject Classification

  • 65D18