Trigonometric Generalized T-splines Cesare Bracco a,b , Dmitry Berdinsky a , Durkbin Cho c , Min-jae Oh a and Tae-wan Kim a, ∗ a Department of Naval Architecture & Ocean Engineering - Seoul National University 1, Gwanak-ro, Gwanak-gu, Seoul 151-744, Korea b Department of Mathematics - University of Turin v. Carlo Alberto 10, 10123 Torino, Italy c Department of Mathematics - Dongguk University Pil-dong 3-ga, Jung-gu, Seoul 100-715, Korea Abstract The paper’s main aim consists of extending the T-spline approach to trigono- metric 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. Keywords: T-spline, T-mesh, GB-spline, analysis-suitable, linear independence, iso- geometric analysis. 1 Introduction The piecewise polynomial functions, in particular in their B-spline representation, are basic for many computer aided design (CAD) methods. A significant advancement in their use for the modeling of surfaces and volumes has been done in the last decade with the introduction of T-splines (see [15]): while in the classical framework the control points of a spline surface lie, from the topological point of view, on a rectangular grid and then the edges of the grid intersect only at “cross junctions”, in the case of T-splines partial * Corresponding author. E-mail: taewan@snu.ac.kr, Phone: +82-2-880-1437, Fax: +82-2-888-9298. Email addresses: cesare.bracco@yahoo.it (C. Bracco), berdinsky@gmail.com (D. Berdinsky), durk- bin@dongguk.edu (D. Cho), mjoh80@snu.ac.kr (M. Oh). 1