A new class of subdivision schemes is presented. Each scheme in this class is a quasi-interpolatory scheme with a tension parameter, which reproduces polynomials up to a certain degree. We find that these schemes extend and unify not only the well-known Deslauriers-Dubuc interpolatory schemes but the quadratic and cubic B-spline schemes. This paper analyzes their convergence, smoothness and accuracy. It is proved that the proposed schemes provide at least the same or better smoothness and accuracy than the aforementioned schemes, when all the schemes are based on the same polynomial space. We also observe with some numerical examples that, by choosing an appropriate tension parameter, our new scheme can remove undesirable artifacts which usually appear in interpolatory schemes with irregularly distributed control points.
Bibliographical noteFunding Information:
We would like to thank the anonymous reviewers and associate editor for many useful comments and suggestions. Jungho Yoon has been supported in part by KRF-2004-015-C00057 and Sung Woo Choi has been supported by R01-2005-000-10120-0 from Korea Science and Engineering Foundation in Ministry of Science & Technology. Byung-Gook Lee has been supported by R05-2004-000-10968-0 from Ministry of Science and Technology.
- Approximation order
- Polynomial reproduction
- Subdivision scheme