Journal of Applied Mathematics
- J. Appl. Math.
- Volume 2014 (2014), Article ID 857840, 18 pages.
Quartic Rational Said-Ball-Like Basis with Tension Shape Parameters and Its Application
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.
J. Appl. Math., Volume 2014 (2014), Article ID 857840, 18 pages.
First available in Project Euclid: 2 March 2015
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Zhu, Yuanpeng; Han, Xuli; Liu, Shengjun. Quartic Rational Said-Ball-Like Basis with Tension Shape Parameters and Its Application. J. Appl. Math. 2014 (2014), Article ID 857840, 18 pages. doi:10.1155/2014/857840. https://projecteuclid.org/euclid.jam/1425305856