Discrete & Computational Geometry

, Volume 26, Issue 3, pp 353–374 | Cite as

Maintaining the Extent of a Moving Point Set

  • P. K. Agarwal
  • L. J. Guibas
  • J. Hershberger
  • E. Veach


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 S . If the points in S move with algebraic motions, these structures process O(n 2+\eps ) events. We also give constructions showing that Ω(n 2 ) combinatorial changes are possible for these extent functions even if each point is moving with constant velocity. We give a similar construction and upper bound for the convex hull, improving known results.

Copyright information

© Springer-Verlag New York Inc. 2001

Authors and Affiliations

  • P. K. Agarwal
    • 1
  • L. J. Guibas
    • 2
  • J. Hershberger
    • 3
  • E. Veach
    • 4
  1. 1.Center for Geometric Computing, Department of Computer Science, Duke University, Box 90129, Durham, NC 27708, USA pankaj@cs.duke.eduUSA
  2. 2.Computer Science Department, Stanford University, Stanford, CA 94305, USA guibas@cs.stanford.eduUSA
  3. 3.Mentor Graphics Corporation, 8005 SW Boeckman Road, Wilsonville, OR 97070, USA john_hershberger@mentorg.comUSA
  4. 4.Pixar Animation Studios, 1001 West Cutting Boulevard, Richmond, CA 94804, USAUSA

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