Discrete & Computational Geometry

, Volume 10, Issue 1, pp 47–65

Edge insertion for optimal triangulations


  • M. Bern
    • Xerox Palo Alto Research Center
  • H. Edelsbrunner
    • Department of Computer ScienceUniversity of Illinois
  • D. Eppstein
    • Department of Information and Computer ScienceUniversity of California
  • S. Mitchell
    • Center for Applied MathematicsCornell University
  • T. S. Tan
    • Department of Information Systems and Computer ScienceNational University of Singapore

DOI: 10.1007/BF02573962

Cite this article as:
Bern, M., Edelsbrunner, H., Eppstein, D. et al. Discrete Comput Geom (1993) 10: 47. doi:10.1007/BF02573962


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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© Springer-Verlag New York Inc. 1993