Numerically Stable Algorithm for Cycloidal Splines

We propose a knot insertion algorithm for splines that are piecewisely in L{1, x, sin x, cos x}. Since an ECC–system on [0, 2π] in this case does not exist, we construct a CCC–system by choosing the appropriate measures in the canonical representation. In this way, a B-basis can be constructed in much the same way as for weighted and tension splines. Thus we develop a corner cutting algorithm for lower order cycloidal curves, though a straightforward generalization to higher order curves, where ECC–systems exist, is more complex. The important feature of the algorithm is high numerical stability and simple implementation. AMS subject classification: 41A50, 65D07, 65D17