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Example

In the following example you can see the given disturbed curve from figure 5 and the results of the two methods. Removing the inner knots in order to get a $C^1$ continuity leads to a smooth curve in a very short time. Using the new functional, the result in not of the same quality as in the case before and also the time is much higher, although the resulting curve is much better than the given one.

Figure: Fairing the curve from figure 5(top) by removing knots (max_error=$0.16\%$, 0.58 sec.) and with the new functional (max_error=$0.66\%$, 2.3 sec.).
\begin{figure}\centerline{\epsfxsize 120mm \epsfbox{sinus_ori_red_cont.ps}}\end{figure}