## Journal of Applied Mathematics

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

#### Abstract

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 ${C}^{1}$ 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 ${C}^{1}$ 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 ${G}^{1}$ continuous conditions are deduced for the joining of two patches.

#### Article information

Source
J. Appl. Math., Volume 2014 (2014), Article ID 857840, 18 pages.

Dates
First available in Project Euclid: 2 March 2015

Permanent link to this document
https://projecteuclid.org/euclid.jam/1425305856

Digital Object Identifier
doi:10.1155/2014/857840

#### Citation

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

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