Algorithm 514: A New Method of Cubic Curve Fitting Using Local Data [E2]

Abstract

This algorithm is a local interpolation method to find an approximating function y = f(x) through a set of given data points (x,, y,) with xl < "-. < x, < x,+l < ..-. Probably the best known methods for this are cubic splines Both of these methods are nonlocal, i.e. the interpolated values depend on all the data points. Under many circumstances, however, it is desirable to use a local interpolation method for which the values of the interpolating function depend only on a few of the nearest data points. For example, a local method may be preferred in an interactive system where one does not want to recalculate a complete picture when one point is changed, or where one wants to save storage in multidimensional interpolation.