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

Abstract

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 ${\mathcal{C}}^{k-2}$-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.

Keywords:

• Non-stationary subdivision scheme
• tension parameter
• hyperbolic trigonometric B-splines

2010 AMS Subject Classifications:

• 41A15
• 42A10
• 65D10
• 65D17

Acknowledgments

We would like to thank anonymous reviewers for their invaluable comments.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by Toubkal/20/101-Campus France under [grant number [43594NB].