An improved algorithm for automatic fairing of non-uniform parametric cubic splines

Kjellander has reported an algorithm for fairing (i.e. smoothing) parametric cubic splines, which is restricted to splines that are uniformly parametrized (Comput.-Aided Des. Vol 15 No 3 (1983) pp 175-179). In many commercial systems, non-uniform splines are required and therefore Kjellander's method of fairing cannot be used. This paper presents a new algorithm which extends that of Kjellander to the fairing of non-uniformly parametrized cubic splines, thus allowing the method to be used in automatic fairing for a wider range of curves. As with Kjellander's method, the new algorithm can be applied to splines in three dimensions as well as in two.