engleski

A deBoor Type Algorithm for Tension Splines

We consider a special knot insertion algorithm for tension splines, which are piecewisely in the linear space spanned by $\{1, x, \exp{\pm (p x)}\}$, \ie tension splines with uniform tension $p>0$. Tension splines are treated as Chebyshev ones, associated with the differential operator $D^2(D^2-p^2)$. Various product representations of this operator exist, and we choose one that leads to the hyperbolic splines in the first reduced Chebyshev system. We construct a de\thinspace Boor type algorithm for such splines, which reduces to the well known one in the limit cases of cubic ($p=0$) and linear ($p\rightarrow \infty$) splines. The knot insertion matrices involved behave nicely with respect to the change in tension parameter within range $0<p<\infty$, but also with respect to the knot sequence.

Knot insertion; Chebyshev systems; Tension splines

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