可调形三次三角Cardinal插值样条曲线

doi:10.12286/jssx.2015.1.34

计算数学 ›› 2015, Vol. 37 ›› Issue (1): 34-41.DOI: 10.12286/jssx.2015.1.34

可调形三次三角Cardinal插值样条曲线

宋爱平, 陶建明, 易旦萍, 张益汉

扬州大学机械工程学院, 江苏扬州 225127

收稿日期:2014-01-10 出版日期:2015-02-15 发布日期:2015-03-10

PDF ( 1120 ) 引用被引次数 ( 13 | 4 )

宋爱平, 陶建明, 易旦萍, 张益汉. 可调形三次三角Cardinal插值样条曲线[J]. 计算数学, 2015, 37(1): 34-41.

Song Aiping, Tao Jianming, Yi Danping, Zhang Yihan. CUBIC TRIGONOMETRIC CARDINAL INTERPOLATION SPLINE WITH ADJUSTABLE SHAPE[J]. Mathematica Numerica Sinica, 2015, 37(1): 34-41.

CUBIC TRIGONOMETRIC CARDINAL INTERPOLATION SPLINE WITH ADJUSTABLE SHAPE

Song Aiping, Tao Jianming, Yi Danping, Zhang Yihan

College of Mechanical Engineering, Yangzhou University, Yangzhou 225127, Jiangsu, China

Received:2014-01-10 Online:2015-02-15 Published:2015-03-10

在三次Cardinal插值样条曲线的基础上,引入了三角函数多项式,得到一组带调形参数的三次三角Cardinal样条基函数,以此构造一种可调形的三次三角Cardinal插值样条曲线.该插值样条可以精确表示直线、圆弧、椭圆以及自由曲线,改变调形参数可以调控插值曲线的形状.该插值样条避免了使用有理形式,其表达式较为简洁,计算量也相对较少,从而为多种线段的构造与处理提供了一种通用与简便的方法.

关键词： 插值样条曲线, 三角多项式基函数, 三次三角Cardinal插值样条, 调形参数

By introducing trigonometric polynomial functions on the basis of cubic Cardinal interpolation spline curve, a set of primary functions with shape adjustable parameter is obtained, and a new curve called cubic trigonometric Cardinal interpolation spline is constructed by it. The spline can be used to accurately represent line, arc, ellipse and free curve, and the shape of interpolation spline can be controlled by changing the adjustable parameter. The interpolation spline has a more concise expression by avoid using rational form, and it needs relatively less calculation, which provides a common and simple method for constructing and processing of curves.

Key words: Interpolation spline curve, Trigonometric polynomial basis functions, Cubic trigonometric Cardinal interpolation spline, Adjustable shape parameter

MR(2010)主题分类:

65D05
64D07

分享此文:

[1] 李成贵,王民. 超精密加工中NURBS曲面的保形插值算法[J]. 北京工业大学学报, 2008, 34(2): 133-136.

[2] 赵彤,吕强,张辉等. 三次均匀B样条曲线高速实时插补研究[J]. 计算机集成制造系统, 2008, 14(9): 1830-1836.

[3] 谢进,檀结庆,刘植,李声峰. 一类带参数的有理三次三角Hermite插值样条[J]. 计算数学, 2011, 33(2): 125-132.

[4] 吴晓勤,韩旭里,罗善明. 三次H-Cardinal样条曲线机曲面[J]. 工程图学学报, 2008, (5): 83-88.

[5] Delibasis, Konstantinos K., Kechriniotis, Aristides I., Assimakis, Nicholas D. New closed formula for the univariate hermite interpolating polynomial of total degree and its application in medical image slice interpolation[J]. Transactions on Signal Processing, 2012, 60(12): 6294-6304.

[6] Bica, Alexandru Mihai1. Fitting data using optimal Hermite type cubic interpolating splines[J]. Applied Mathematics Letters, 2012, 25(12): 2047-2051.

[7] 方逵,邓四清,谭德松,吴泉源. 三次有理插值样条曲线曲面[J]. 计算机应用与软件, 2011, 28(7): 22-24.

[8] Zhang J W, Krause F L, Zhang H Y. Extend cubic uniform B-spline by unified trigonometric and hyberolic basis[J]. Graph Models, 2005, 67(2): 100-119.

[1]	李军成, 刘成志. 带参数的C³连续拟Catmull-Rom样条函数[J]. 计算数学, 2018, 40(1): 96-106.
[2]	李军成, 刘成志. 形状可调的C²连续三次三角Hermite插值样条[J]. 计算数学, 2016, 38(2): 187-199.
[3]	樊梦, 王同科, 常慧宾. 非光滑函数的分数阶插值公式[J]. 计算数学, 2016, 38(2): 212-224.
[4]	王同科, 佘海艳, 刘志方 . 分数阶光滑函数线性和二次插值公式余项估计[J]. 计算数学, 2014, 36(4): 393-406.
[5]	谢进, 檀结庆, 刘植, 李声锋. 一类带参数的有理三次三角Hermite插值样条[J]. 计算数学, 2011, 33(2): 125-132.
[6]	邓四清, 方逵, 谢进, 陈福来, 陆海波. 一种新的带参数双三次有理插值样条的有界性与点控制[J]. 计算数学, 2010, 32(4): 337-348.
[7]	谢进, 檀结庆, 李声锋, 邓四清. 非均匀的二次三角双曲加权样条曲线[J]. 计算数学, 2010, 32(2): 147-156.
[8]	邓四清, 方逵, 谢进, 陈福来, 陆海波. 一种基于函数值的二元有理插值函数及其性质[J]. 计算数学, 2009, 31(1): 77-86.

阅读次数

全文

摘要

可调形三次三角Cardinal插值样条曲线

CUBIC TRIGONOMETRIC CARDINAL INTERPOLATION SPLINE WITH ADJUSTABLE SHAPE

扫码分享