Trigonometric generalized T-splines

Abstract

The paper’s main aim consists of extending the T-spline approach to trigonometric generalized B-splines, a particularly relevant case of non-polynomial splines. Such goal can be achieved by a careful revision of some results concerning the basic properties of the trigonometric generalized B-splines and by a formalization of the concept of T-splines in the trigonometric setting. Moreover, fundamental for the use of this new tool is the study of the noteworthy case with constant frequencies and of the linear independence of the corresponding blending functions, which can be proved to be strongly linked to the linear independence of the polynomial blending functions associated to the same T-mesh.