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Journal of Applied Mathematics
Volume 2014 (2014), Article ID 857840, 18 pages
Research Article

Quartic Rational Said-Ball-Like Basis with Tension Shape Parameters and Its Application

School of Mathematics and Statistics, Central South University, Changsha 410083, China

Received 22 March 2014; Accepted 5 June 2014; Published 26 June 2014

Academic Editor: Fernando Simões

Copyright © 2014 Yuanpeng Zhu 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.


Four new quartic rational Said-Ball-like basis functions, which include the cubic Said-Ball basis functions as a special case, are constructed in this paper. The new basis is applied to generate a class of continuous quartic rational Hermite interpolation splines with local tension shape parameters. The error estimate expression of the proposed interpolant is given and the sufficient conditions are derived for constructing a positivity- or monotonicity- preserving interpolation spline. In addition, we extend the quartic rational Said-Ball-like basis to a triangular domain which has three tension shape parameters and includes the cubic triangular Said-Ball basis as a special case. In order to compute the corresponding patch stably and efficiently, a new de Casteljau-type algorithm is developed. Moreover, the continuous conditions are deduced for the joining of two patches.