一种C1连续的二元有理三次插值样条

doi:10.3969/j.issn.0253-2778.2017.03.002

中国科学技术大学学报 ›› 2017, Vol. 47 ›› Issue (3): 204-213.DOI: 10.3969/j.issn.0253-2778.2017.03.002

一种C¹连续的二元有理三次插值样条

王冬银，陶有田

1. 巢湖学院应用数学学院，安徽巢湖 238000；2.中国科学技术大学数学科学学院，安徽合肥 230026； 3.安徽富煌钢构，安徽合肥 238076

收稿日期:2015-04-04 修回日期:2015-09-30 接受日期:2015-09-30 出版日期:2023-03-27 发布日期:2015-09-30

A C¹ bivariate rational cubic interpolating spline

WANG Dongyin, TAO Youtian

1. College of Applied Mathematics, Chaohu University, Chaohu 238000, China; 2. School of Mathematical Sciences, University of Science and Technology of China, Hefei 230026, China; 3. Anhui Fuhuang Steel Structure, Chaohu 238076, China

Received:2015-04-04 Revised:2015-09-30 Accepted:2015-09-30 Online:2023-03-27 Published:2015-09-30
Contact: TAO Youtian
About author:WANG Dongyin, female, born in 1978, master/associate Prof. Research field: Applied mathematics. E-mail: chaohuwdy@163.com.
Supported by:
Supported by the Nation Natural Science Foundation of China(11472063), the Provincial Natural Science Research Program of Higher Education Institutions of Anhui Province(KJ2013A194, KJ2013Z230), Anhui Province Colleges and Universities Outstanding Youth Talent Support Program(gxyqZD2016285).

摘要/Abstract

摘要： 利用矩形域上的函数值及偏导数值作为插值数据，构造了一种带6个形状参数、分母为双二次的二元有理三次插值样条，讨论了其C¹ 连续条件，给出了诸如对称性的一些性质，证明了其有界性并作了误差分析．最后给出了一个数值例子说明了形状参数对于曲面构造的有效性．

关键词: 二元有理三次插值样条, 形状参数, 有界性, 误差估计, 对称性

Abstract: A bivariate rational bicubic interpolating spline(BRIS) with biquadratic denominator and six shape parameters was constructed using both function values and partial derivatives of the function as the interpolation data in a rectangular domain. The C¹ continuous condition of BRIS was discussed. Some properties of BRIS such as symmetry were given. BRIS was proved to be bounded and its error was estimated. In the end, a numerical example was given to illustrate the effect of the shape parameters on the shape of BRIS surface.

Key words: bivariate rational interpolating spline, shape parameter, bounded property, error estimate, symmetry

中图分类号:

O241.5

王冬银, 陶有田. 一种C¹连续的二元有理三次插值样条[J]. 中国科学技术大学学报, 2017, 47(3): 204-213.

WANG Dongyin, TAO Youtian. A C¹ bivariate rational cubic interpolating spline[J]. Journal of University of Science and Technology of China, 2017, 47(3): 204-213.

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一种C¹连续的二元有理三次插值样条

A C¹ bivariate rational cubic interpolating spline

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