Recent Advances in Macro-Element Methods for Fitting Scattered Data
by
Larry L. Schumaker
Vanderbilt University

Many of the most successful methods for fitting surfaces to bivariate scattered data are based on piecewise polynomials defined over either a rectangular or triangular partition of the domain of interest. These types of methods are particularly effective when the interpolation process can be described locally, i.e., the polynomial piece of the spline associated with a given subset T can be constructed from data associated with points in (or near) T. Such methods are often referred to as macro element methods. Among the best-known are the classical polynomial, Clough-Tocher, and Powell-Sabin elements. In this presentation we show how recent results in the theory of splines over triangulations can be used to construct new macro elements and improve existing ones in terms of smoothness, accuracy, degrees of freedom, and amount of derivative data required.

http://math.vanderbilt.edu/~schumake/

Date received: January 23, 1999