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Discrete & Computational Geometry

, Volume 20, Issue 4, pp 499–514 | Cite as

Pushing Disks Together—The Continuous-Motion Case

  • M. Bern
  • A. Sahai

Abstract.

If disks are moved so that each center—center distance does not increase, must the area of their union also be nonincreasing? We show that the answer is yes, assuming that there is a continuous motion such that each center—center distance is a nonincreasing function of time. This generalizes a previous result on unit disks. Our proof relies on a recent construction of Edelsbrunner and on new isoperimetric inequalities of independent interest. We go on to show analogous results for the intersection and for holes between disks.

Keywords

Unit Disk Analogous Result Isoperimetric Inequality Independent Interest Continuous Motion 
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Copyright information

© Springer-Verlag New York Inc. 1998

Authors and Affiliations

  • M. Bern
    • 1
  • A. Sahai
    • 2
  1. 1.Xerox Palo Alto Research Center, 3333 Coyote Hill Rd., Palo Alto, CA 94304, USA bern@parc.xerox.com US
  2. 2.MIT Laboratory for Computer Science, 545 Technology Square, Cambridge, MA 02139, USA amits@theory.lcs.mit.eduUS

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