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. This research was supported by Grant 037-1193086-2771, by the Ministry of science, higher education and sports of the Republic of Croatia.