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

Boris Aronov

doi:10.1007/BF01553882

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

Boris Aronov

Research output: Contribution to journal › Article › peer-review

Abstract

Given a simple polygon with n sides in the plane and a set of k 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 an O((n + k) log(n + k) log n)-time algorithm for solving this problem and sketch a faster O((n + k) log(n + k)) algorithm for the case when the set of sites includes all reflex vertices of the polygon in question.

Original language	English (US)
Pages (from-to)	109-140
Number of pages	32
Journal	Algorithmica
Volume	4
Issue number	1
DOIs	https://doi.org/10.1007/BF01553882
State	Published - Dec 1989

Keywords

Computational geometry
Geodesic metric
Shortest paths
Simple polygons
Voronoi diagrams

ASJC Scopus subject areas

General Computer Science
Computer Science Applications
Applied Mathematics

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10.1007/BF01553882

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AB - Given a simple polygon with n sides in the plane and a set of k 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 an O((n + k) log(n + k) log n)-time algorithm for solving this problem and sketch a faster O((n + k) log(n + k)) algorithm for the case when the set of sites includes all reflex vertices of the polygon in question.

KW - Computational geometry

KW - Geodesic metric

KW - Shortest paths

KW - Simple polygons

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

Abstract

Keywords

ASJC Scopus subject areas

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