Edge insertion for optimal triangulations

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. © 1993 Springer-Verlag New York Inc.