A weighted bivariate blending rational interpolation based on function values

作者：Huang, Wei-Xian; Wang, Guo-Jin^*

来源：Applied Mathematics and Computation, 2011, 217(9): 4644-4653.

DOI：10.1016/j.amc.2010.11.016

• Computer aided geometric design
• Rational spline interpolation
• C-1-continuous
• Bivariate interpolation
• Cubic spline

This paper presents a new weighted bivariate blending rational spline interpolation based on function values. This spline interpolation has the following advantages: firstly, it can modify the shape of the interpolating surface by changing the parameters under the condition that the values of the interpolating nodes are fixed; secondly, the interpolating function is C-1-continuous for any positive parameters; thirdly, the interpolating function has a simple and explicit mathematical representation; fourthly, the interpolating function only depends on the values of the function being interpolated, so the computation is simple. In addition, this paper discusses some properties of the interpolating function, such as the bases of the interpolating function, the matrix representation, the bounded property, the error between the interpolating function and the function being interpolated.

• 出版日期2011-1-1
• 单位浙江大学