• 论文 •

### 带参数的C3连续拟Catmull-Rom样条函数

1. 湖南人文科技学院数学与金融学院, 娄底 417000
• 收稿日期:2017-03-23 出版日期:2018-03-15 发布日期:2018-02-03
• 基金资助:

湖南省自然科学基金资助项目（2017JJ3124）.

Li Juncheng, Liu Chengzhi. THE C3 QUASI CATMULL-ROM SPLINE FUNCTION WITH PARAMETERS[J]. Mathematica Numerica Sinica, 2018, 40(1): 96-106.

### THE C3 QUASI CATMULL-ROM SPLINE FUNCTION WITH PARAMETERS

Li Juncheng, Liu Chengzhi

1. College of Mathematics and Finances, Hunan University of Humanities, Science and Technology, Loudi 417000, China
• Received:2017-03-23 Online:2018-03-15 Published:2018-02-03

A class of quasi Catmull-Rom spline function with parameters is presented in this paper to make the Catmull-Rom spline have shape-adjustable ability and high-order continuity. The quasi Catmull-Rom spline function can not only automatically achieve C3 continuity without solving equation systems, but also adjust the shape of the interpolation curve through the two parameters. The best quasi Catmull-Rom spline interpolation function can be obtained by determining the optimal value of the parameters.

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 [1] Derose T D, Barsky B A. Geometric continuity, shape parameters, and geometric constructions for Catmull-Rom splines[J]. ACM Transactions on Graphics, 1988, 7(1):1-41.[2] Maggini M, Melacci S, Sarti L. Representation of facial features by Catmull-Rom splines[J]. Lecture Notes in Computer Science, 2007, 4673:408-415.[3] Yuksel C, Schaefer S, Keyser J. Parameterization and applications of Catmull-Rom curves[J]. Computer-Aided Design, 2011, 43(7):747-755.[4] Yan L L, Liang J F. An extension of the Bézier model[J]. Applied Mathematics and Computation, 2011, 218(6):2863-2879.[5] Qin X Q, Hu G, Zhang N J, Shen X L, Yang Y. A novel extension to the polynomial basis functions describing Bézier curves and surfaces of degree n with multiple shape parameters[J]. Applied Mathematics and Computation, 2013, 223:1-16.[6] Han X L. Piecewise quartic polynomial curves with a local shape parameter[J]. Journal of Computational and Applied Mathematics, 2006, 23(1):34-45.[7] Juhász I, Hoffmann M. On the quartic curve of Han[J]. Journal of Computational and Applied Mathematics, 2009, 223(1):124-132.[8] Li J C, Chen S. The cubic α -Catmull-Rom spline[J]. Mathematical and Computational Applications, 2016, 21(3):33.[9] 李军成, 刘成志, 易叶青. 带形状因子的C2连续五次Cardinal样条与Catmull-Rom样条[J]. 计算机辅助设计与图形学学报, 2016, 28(11):1821-1831.[10] 杨平, 汪国昭.C3连续的7次PH样条曲线插值[J]. 计算机辅助设计与图形学学报, 2014, 26(5):731-738.
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