Trigonometric B-spline curves have gained a remarkable attention in computer-aided geometric design (CAGD). This paper presents the cubic and rational cubic trigonometric B-spline curves using new trigonometric functions and shape parameter η ∈ (1/2, 2]. The proposed curves inherit the basic properties of classical B-spline and have been proved. For uniform knots, both curves are C 2 continuous. On non-uniform knots, cubic trigonometric curves are C 3 and C 5 continuous, whereas rational trigonometric curves are C 3 continuous and have been derived. The applicability of proposed curves has been checked by constructing open and closed curves. Different models like glass, kettle, human hand, and vase have been designed by both schemes and compared.

Trigonometric B-spline curves with shape parameters are equally important and useful for modeling in Computer-Aided Geometric Design (CAGD) like classical B-spline curves. This paper introduces the cubic polynomial and rational cubic B-spline curves using new cubic basis functions with shape parameter ξ∈[0,4]. All geometric characteristics of the proposed Trigonometric B-spline curves are similar to the classical B-spline, but the shape-adjustable is additional quality that the classical B-spline curves does not hold. The properties of these bases are similar to classical B-spline basis and have been delineated. Furthermore, uniform and non-uniform rational B-spline basis are also presented. C3 and C5 continuities for trigonometric B-spline basis and C3 continuities for rational basis are derived. In order to legitimize our proposed scheme for both basis, floating and periodic curves are constructed. 2D and 3D models are also constructed using proposed curves.