A SWEEPLINE ALGORITHM FOR VORONOI DIAGRAMS PDF

We'd like to understand how you use our websites in order to improve them. Register your interest. We introduce a geometric transformation that allows Voronoi diagrams to be computed using a sweepline technique. The transformation is used to obtain simple algorithms for computing the Voronoi diagram of point sites, of line segment sites, and of weighted point sites. All algorithms have O n log n worst-case running time and use O n space. This is a preview of subscription content, log in to check access.

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We'd like to understand how you use our websites in order to improve them. Register your interest. We introduce a geometric transformation that allows Voronoi diagrams to be computed using a sweepline technique. The transformation is used to obtain simple algorithms for computing the Voronoi diagram of point sites, of line segment sites, and of weighted point sites.

All algorithms have O n log n worst-case running time and use O n space. This is a preview of subscription content, log in to check access. Rent this article via DeepDyve.

Aurenhammer and H. Edelsbrunner, An optimal algorithm for constructing the weighted Voronoi diagram in the plane, Pattern Recognition , 17 , — Bentley, B. Weide, and A. Software , 6 , — Chew and R. Drysdale, Voronoi diagrams based on convex distance functions, Proceedings of the Symposium on Computational Geometry , , pp. Driscoll, N. Sarnak, D. Sleator, and R. Edelsbrunner, L. Guibas, and J. Google Scholar.

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Japan , 27 , — Preparata and M. Shamos and D. Download references. Reprints and Permissions. Fortune, S. A sweepline algorithm for Voronoi diagrams. Algorithmica 2, Download citation. Received : 06 April Revised : 12 October Search SpringerLink Search. Abstract We introduce a geometric transformation that allows Voronoi diagrams to be computed using a sweepline technique.

Immediate online access to all issues from Subscription will auto renew annually. References [1] F. Edelsbrunner, private communication, You can also search for this author in PubMed Google Scholar. Additional information Communicated by Bernard Chazelle. Rights and permissions Reprints and Permissions. About this article Cite this article Fortune, S.

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A sweepline algorithm for Voronoi diagrams

The algorithm maintains both a sweep line and a beach line , which both move through the plane as the algorithm progresses. The sweep line is a straight line, which we may by convention assume to be vertical and moving left to right across the plane. At any time during the algorithm, the input points left of the sweep line will have been incorporated into the Voronoi diagram, while the points right of the sweep line will not have been considered yet. The beach line is not a straight line, but a complicated, piecewise curve to the left of the sweep line, composed of pieces of parabolas ; it divides the portion of the plane within which the Voronoi diagram can be known, regardless of what other points might be right of the sweep line, from the rest of the plane.

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