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Mathematical Problems in Engineering
Volume 2018, Article ID 2324893, 9 pages
Research Article

Six-Point Subdivision Schemes with Cubic Precision

1School of Mathematics, Hefei University of Technology, Hefei 230009, China
2School of Computer and Information, Hefei University of Technology, Hefei 230009, China

Correspondence should be addressed to Zhi Liu; moc.621@413ihzuil

Received 10 July 2017; Revised 5 November 2017; Accepted 22 November 2017; Published 3 January 2018

Academic Editor: Dan Simon

Copyright © 2018 Jun Shi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper presents 6-point subdivision schemes with cubic precision. We first derive a relation between the 4-point interpolatory subdivision and the quintic B-spline refinement. By using the relation, we further propose the counterparts of cubic and quintic B-spline refinements based on 6-point interpolatory subdivision schemes. It is proved that the new family of 6-point combined subdivision schemes has higher smoothness and better polynomial reproduction property than the B-spline counterparts. It is also showed that, both having cubic precision, the well-known Hormann-Sabin’s family increase the degree of polynomial generation and smoothness in exchange of the increase of the support width, while the new family can keep the support width unchanged and maintain higher degree of polynomial generation and smoothness.