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Journal of Applied Mathematics
Volume 2014, Article ID 628285, 7 pages
Research Article

A Six-Point Variant on the Lane-Riesenfeld Algorithm

1Department of Mathematics, The Islamia University of Bahawalpur, Bahawalpur 63100, Pakistan
2Department of Mathematics, University of Science and Technology of China, Hefei 230026, China

Received 30 November 2013; Accepted 15 April 2014; Published 8 May 2014

Academic Editor: Mohamad Alwash

Copyright © 2014 Pakeeza Ashraf 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.


We apply six-point variant on the Lane-Riesenfeld algorithm to obtain a new family of subdivision schemes. We also determine the support, smoothness, Hölder regularity, magnitude of the artifact, and the shrinkage effect due to the change of integer smoothing parameter that characterizes the members of the family. The degree of polynomial reproduction also has been discussed. It is observed that the proposed schemes have less shrinkage effect and as a result better preserve the shape of control polygon.