engleski

Knot insertion algorithms for Chebyshev splines

In this thesis our point of interest are canonical complete Chebyshev CCC-systems and splines associated with them. We are interested in finding numerically stable algorithms for calculating with such splines, and we do that by generalizing the knot insertion based algorithms for polynomial splines to CCC-systems. To be able to construct these algorithms, we introduce knot insertion matrices, and then develop Oslo type algorithms and the generalized de Boor algorithm. To show the practical value of these algorithms, we apply them on four kinds of splines: weighted, q-splines, tension and cycloidal splines. Weighted and tension splines are particularly interesting, since weighted splines are the only splines of order higher than 4 which can be stably evaluated, and tension splines because of their wide application. For each of these splines, algorithms are developed with all the details specific for the spline in question. Finally to illustrate the practical computer use of given algorithms, we list program codes involved in calculating with C^1 and C^2 tension splines.

Chebyshev splines; knot insertion; weighted splines; q-splines; tension splines; cycloidal splines

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