Trigonometric Splines , Trigonometric B-Splines , Partition of Unity , Convex-Hull Property , Integral Representation , Recursion Formula
Abstract:
In this paper we investigate some properties of trigonometric B-splines, which form a finitely-supported basis of the space of trigonometric spline functions. We establish a complex integral representation for trigonometric B-splines, which is in certain analogy to the polynomial case, but the proof of which has to be done in a different and more complicated way. Using this integral representation, we can prove some identities concerning the evaluation of a trigonometric B-spline, its derivative and its partial derivative w.r.t. the knots. As a corollary of the last mentioned identity, we obtain a result on the tangent space of a trigonometric spline function. Finally we show that - in the case of equidistant knots - the trigonometric B-splines of odd order form a partition of a constant, and therefore the corresponding B-spline curve possesses the convex-hull property. This is also illustrated by a numerical example.
Additional information:
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