Discrete & Computational Geometry

, Volume 10, Issue 1, pp 47–65

Edge insertion for optimal triangulations

  • M. Bern
  • H. Edelsbrunner
  • D. Eppstein
  • S. Mitchell
  • T. S. Tan


Edge insertion iteratively improves a triangulation of a finite point set in ℜ2 by adding a new edge, deleting old edges crossing the new edge, and retriangulating the polygonal regions on either side of the new edge. This paper presents an abstract view of the edge insertion paradigm, and then shows that it gives polynomial-time algorithms for several types of optimal triangulations, including minimizing the maximum slope of a piecewise-linear interpolating surface.


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Copyright information

© Springer-Verlag New York Inc. 1993

Authors and Affiliations

  • M. Bern
    • 1
  • H. Edelsbrunner
    • 2
  • D. Eppstein
    • 3
  • S. Mitchell
    • 4
  • T. S. Tan
    • 5
  1. 1.Xerox Palo Alto Research CenterPalo AltoUSA
  2. 2.Department of Computer ScienceUniversity of IllinoisUrbanaUSA
  3. 3.Department of Information and Computer ScienceUniversity of CaliforniaIrvineUSA
  4. 4.Center for Applied MathematicsCornell UniversityIthacaUSA
  5. 5.Department of Information Systems and Computer ScienceNational University of SingaporeRepublic of Singapore

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