Discrete & Computational Geometry

, Volume 21, Issue 3, pp 373–388 | Cite as

Line Transversals of Balls and Smallest Enclosing Cylinders in Three Dimensions

  • P. K. Agarwal
  • B. Aronov
  • M. Sharir


We establish a near-cubic upper bound on the complexity of the space of line transversals of a collection of n balls in three dimensions, and show that the bound is almost tight, in the worst case. We apply this bound to obtain a near-cubic algorithm for computing a smallest infinite cylinder enclosing a given set of points or balls in 3-space. We also present an approximation algorithm for computing a smallest enclosing cylinder.


Approximation Algorithm Line Transversal Infinite Cylinder Small Enclose Enclose Cylinder 
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Copyright information

© Springer-Verlag New York Inc. 1999

Authors and Affiliations

  • P. K. Agarwal
    • 1
  • B. Aronov
    • 2
  • M. Sharir
    • 3
  1. 1.Department of Computer Science, Box 90129, Duke University, Durham, NC 27708-0129, USA US
  2. 2.Department of Computer and Information Science, Polytechnic University, Brooklyn, NY 11201, USA US
  3. 3.School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978, Israel and Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, USAUS

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