, Volume 10, Issue 1, pp 47-65

Edge insertion for optimal triangulations

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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.

The research of the second author was supported by the National Science Foundation under Grant No. CCR-8921421 and under the Alan T. Waterman award, Grant No. CCR-9118874. Any opinions, findings, and conclusions or recommendations expressed in this publication are those of the authors and do not necessarily reflect the view of the National Science Foundation. Part of the work was done while the second, third, and fourth authors visited the Xerox Palo Alto Research Center, and while the fifth author was on study leave at the University of Illinois.