Abstract
Given a set of geometric objects a closest pair is a pair of objects whose mutual distance is smallest. We present a plane-sweep algorithm which finds a closest pair with respect to any LP -metric, 1≤p≤∞, for planar configurations consisting of n (possibly intersecting) compact convex objects such as line segments, circular discs and convex polygons. For configurations of line segments or discs the algorithm runs in asymptotically optimal time O(n log n). For a configuration of n convex m-gons given in a suitable representation it finds a closest pair with respect to the Euclidean metric L2 in time O(n log(n·m)).
Preview
Unable to display preview. Download preview PDF.
References
B. Chazelle, D. P. Dobkin: Intersection of Convex Objects in Two and Three Dimensions, Journal of the ACM, Vol. 34, No. 1 (1987), 1–27.
F. Chin, C. A. Wang: Optimal Algorithms for the Intersection and the Minimum Distance Problems between Planar Polygons, IEEE Trans. Comput. 32 (12), 1203–1207 (1983).
H. Edelsbrunner: Computing the Extreme Distances between two Convex Polygons, Journal of Algorithms 6, 213–224 (1985).
S. Fortune: A Sweepline Algorithm for Voronoi Diagrams, Algorithmica 2, 153–174 (1987).
K. Hinrichs, J. Nievergelt, P. Schorn: Plane-Sweep Solves the Closest Pair Problem Elegantly, Information Processing Letters 26, 255–261 (1988).
D. T. Lee: Two-Dimensional Voronoi Diagrams in the Lp-metric, Journal of the ACM 27 (4), 604–618 (1980).
F. P. Preparata, M. I. Shamos: Computational Geometry: An Introduction, Springer-Verlag, Berlin, Heidelberg, New York, 1985.
M. I. Shamos, D. Hoey: Geometric Intersection Problems, Proc. 17th Ann. IEEE Symp. on Foundations of Computer Science, 208–215 (1976).
M. Sharir: Intersection and Closest-Pair Problems for a Set of Planar Discs, SIAM J. Comput. 14, 448–468 (1985).
C. K. Yap: An O(n log n) Algorithm for the Voronoi Diagram of a Set of Simple Curve Segments, Discrete Comput. Geometry 2, 365–393 (1987).
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1992 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Bartling, F., Hinrichs, K. (1992). A plane-sweep algorithm for finding a closest pair among convex planar objects. In: Finkel, A., Jantzen, M. (eds) STACS 92. STACS 1992. Lecture Notes in Computer Science, vol 577. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-55210-3_186
Download citation
DOI: https://doi.org/10.1007/3-540-55210-3_186
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-55210-9
Online ISBN: 978-3-540-46775-5
eBook Packages: Springer Book Archive