Conclusion

We presented in this paper an algorithm which automatically fairs B-spline curves of general order. The key idea was to minimize the integral of the squared

-th derivative of a given curve iteratively by changing only one control point in every step. The control points at which the B-spline curve has to be faired, are selected automatically by a fairness criterion. Furthermore, the algorithm is very fast because we need to calculate the appearing integrals only once.

We tested this algorithm in many examples with given disturbances and we drew our conclusion that if the knots are shared well the fairing results are very good. This means, the influence of the parametrization to the fairing process is an area for more investigation.

Finally, we want to mention that the method obviously can be extended to surfaces. In (Hadenfeld, 1994) it is especially outlined that in case of tensor product B-spline surfaces very good results can be obtained which are again comparable to those in (Kallay, 1993) and (Greiner, 1994).