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

• Published in: Journal of Applied Mathematics Vol. 2014; no. 2014; pp. 618 - 635-858
• Main Authors: Zhu, Yuanpeng, Han, Xuli, Liu, Shengjun
• Format: Journal Article
• Language: English
• Published: Cairo, Egypt Hindawi Limiteds 01.01.2014; Hindawi Puplishing Corporation; Hindawi Publishing Corporation; John Wiley & Sons, Inc; Hindawi Limited; Wiley
• Subjects: Algorithms; Basis functions; Construction; Design; Error analysis (Mathematics); Estimates; Finite element analysis; Functional equations; Functions; Industrial design; Interpolation; Joining; Mathematical analysis; Spline theory; Splines
• ISSN: 1110-757X; 1687-0042
• DOI: 10.1155/2014/857840

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 C1 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 C1 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 G1 continuous conditions are deduced for the joining of two patches.