Article

Discrete & Computational Geometry

, Volume 10, Issue 1, pp 47-65

First online:

Edge insertion for optimal triangulations

  • M. BernAffiliated withXerox Palo Alto Research Center
  • , H. EdelsbrunnerAffiliated withDepartment of Computer Science, University of Illinois
  • , D. EppsteinAffiliated withDepartment of Information and Computer Science, University of California
  • , S. MitchellAffiliated withCenter for Applied Mathematics, Cornell University
  • , T. S. TanAffiliated withDepartment of Information Systems and Computer Science, National University of Singapore

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Abstract

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.