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On the geodesic voronoi diagram of point sites in a simple polygon

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Abstract

Given a simple polygon withn sides in the plane and a set ofk point “sites” in its interior or on the boundary, compute the Voronoi diagram of the set of sites using the internal “geodesic” distance inside the polygon as the metric. We describe anO((n + k) log(n + k) logn)-time algorithm for solving this problem and sketch a fasterO((n + k) log(n + k)) algorithm for the case when the set of sites includes all reflex vertices of the polygon in question.

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Authors and Affiliations

  1. Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, 10012, New York, NY, USA

    Boris Aronov

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  1. Boris Aronov
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Additional information

Communicated by Chee-Keng Yap.

Work on this paper was performed while the author held an AT&T Bell Laboratories Ph.D. Scholarship at New York University.

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Aronov, B. On the geodesic voronoi diagram of point sites in a simple polygon. Algorithmica 4, 109–140 (1989). https://doi.org/10.1007/BF01553882

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  • DOI: https://doi.org/10.1007/BF01553882

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