Abstract
The Voronoi diagram of n sites on the surface of a cone has a combinatorial structure rather different from the planar one. We present a sweepcircle algorithm that enables its computation within optimal time O(n log n), using linear storage.
Research supported by NSERC Grant No. A9173
Preview
Unable to display preview. Download preview PDF.
References
L.P.Chew and R.L.Drysdale III, "Voronoi diagrams based on convex distance functions", Proc. 1st ACM Symposium on Computational Geometry, Baltimore, MD, 1985, pp. 235–244
F. Dehne, R. Klein, "A sweepcircle algorithm for Voronoi diagrams on cones", Tech.Rep., School of Computer Science, Carleton University, Ottawa, Canada K1S5B6, 1987
S. Fortune, "A sweeline algorithm for Voronoi diagrams", Algorithmica, vol. 2, No.2, 1987, pp.153–174
R.Klein and D.Wood, "Voronoi diagram for general metrices in the plane", in preparation
Thurston, "The geometry of circles: Voronoi diagrams, Moebius transformations, convex hulls, Fortune's algorithm, the cut locus and parametrization of shapes", unpublished notes, Princeton, 1986
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1988 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Dehne, F., Klein, R. (1988). A sweepcircle algorithm for Voronoi diagrams. In: Göttler, H., Schneider, HJ. (eds) Graph-Theoretic Concepts in Computer Science. WG 1987. Lecture Notes in Computer Science, vol 314. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-19422-3_5
Download citation
DOI: https://doi.org/10.1007/3-540-19422-3_5
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-19422-4
Online ISBN: 978-3-540-39264-4
eBook Packages: Springer Book Archive