Identities for trigonometric B-splines with an application to curve design

In this paper we investigate some properties of trigonometric B-splines. We establish a complex integral representation for these functions, 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. 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 illustrated by a numerical example.