Algorithms for smoothing data with periodic and parametric splines

This paper deals with the problem of fitting splines to measured data which either describe a periodic function or some parametric curve, closed, or otherwise. Algorithms are presented which are extensions of an existing semiautomatic curve fitting algorithm. The knots of the splines are chosen automatically but a single parameter is expected to control the tradeoff between closeness of fit and smoothness of fit. The user will interactively change this smoothing factor and examine the corresponding curve graphically, until he can accept the result as satisfactory. Numerical and practical examples illustrate the accuracy of the algorithms and their applicability in image processing and related fields.