On rational parametric curve approximation
A new method is proposed for the rational approximation of functions. The autors describe extensions to the basic method which permit the generation of approximations satisfying point constraints and derivative constraints of arbitrary order at the endpoints of the interval of interest. In a CAGD context, this allows the segment by segment approximation of piecewise defined curves in such a way that continuity characteristics of the original curve are retained by the overall approximant. In the present method, an error function is chosen to avoid nonlinearity in the computation; the result is not a ``best'' approximation, but is usually good enough for many practical purposes. The same basic approach can be used for approximating either scalar or vector-valued functions.
scientific article; zbMATH DE number 431244