Maintaining the extent of a moving point set
Let S be a set of n moving points in the plane. We give new efficient and compact kinetic data structures for maintaining the diameter, width, and smallest area or perimeter bounding rectangle of the points. When the points in S move with pseudo-algebraic motions, these structures process O(n2+ε) events. We also give constructions showing that μ(n2) combinatorial changes are possible in these extent functions even when the points move on straight lines with constant velocities. We give a similar construction and upper bound for the convex hull, improving known results.
KeywordsConvex Hull Linear Motion Priority Queue Antipodal Point Flight Plan
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- 1.P. Agarwal, O. Schwarzkopf, and M. Sharir. The overlay of lower envelopes and its applications. Discr. Comput. Geom., 15:1–13, 1996.Google Scholar
- 2.M. J. Atallah. Some dynamic computational geometry problems. Comput. Math. Appl., 11:1171–1181, 1985.Google Scholar
- 3.J. Basch, L. Guibas, and J. Hershberger. Data structures for mobile data. In Proceedings of the Eighth Annual ACM-SIAM Symposium on Discrete Algorithms, pages 747–756, 1997.Google Scholar
- 4.Y.-J. Chiang and R. Tamassia. Dynamic algorithms in computational geometry. Proc. IEEE, 80(9):1412–1434, September 1992.Google Scholar
- 5.D. Eppstein. Average case analysis of dynamic geometric optimization. Comp. Geom.: Theory and Appl., 6:45–68, 1996.Google Scholar
- 6.F. P. Preparata and M. I. Shamos. Computational Geometry. Springer-Verlag, New York, 1985.Google Scholar
- 7.M. Sharir and P. K. Agarwal. Davenport-Schinzel Sequences and Their Geometric Applications. Cambridge University Press, New York, 1995.Google Scholar
- 8.G. Toussaint. Solving geometric problems with the “rotating calipers”. In Proceedings of IEEE MELECON '83, 1983.Google Scholar