Mixed trigonometric and hyperbolic subdivision scheme with two tension and one shape parameters

In this paper, we propose a new family of non-stationary subdivision scheme, based on mixed trigonometric hyperbolic B-spline basis functions with two tension and one shape parameters. We prove that the proposed subdivision scheme of order k produces Ck-2-continuous limit curves. By assigning appropriate values to the two tension and shape parameters, many known subdivision schemes are special cases of our approach. Several variants of non-stationary subdivision schemes are discussed, and numerical examples illustrate their performances.