Data dependent triangulations

Abstract

Although Delaunay triangulations have well-shaped triangles in the plane and satisfy an optimum principle by the MaxMin angle criterion, they are not necessarily optimal as domains for surfaces. In this chapter we are concerned with surfaces in 3D space defined over triangulations, and in particular surfaces represented by piecewise linear functions over triangulations in the plane. The main concern in this respect is to construct triangulations from 3D point sets where the triangulations are optimal according to local and global cost functions which are designed to reflect properties of the underlying physical model from which the points have been sampled.