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 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. © 2014 yuanpeng zhu et al.