Approximation of minimum energy curves

The problem of interpolating or approximating a given set of data points ob tained empirically by measurement frequently arises in a vast number of sci entific and engineering applications, for example, in the design of airplan e bodies, cross sections of ship hull and turbine blades, in signal process ing or even in less classical things like flow lines and moving boundaries from chemical processes. All these areas require fast, efficient, stable an d flexible algorithms for smooth interpolation and approximation to such da ta. Given a set of empirical data points in a plane, there are quite a few methods to estimate the curve by using only these data points. In this pape r, we consider using polynomial least squares approximation, polynomial int erpolation, cubic spline interpolation, exponential spline interpolation an d interpolatory subdivision algorithms. Through the investigation of a lot of examples, we find a 'reasonable good' fitting curve to the data. (C) 200 0 Elsevier Science Inc. All rights reserved.