Rational cubic trigonometric Hermite interpolation spline curves and applications

doi:10.3778/j.issn.1002-8331.2010.05.003

Computer Engineering and Applications ›› 2010, Vol. 46 ›› Issue (5): 7-9.DOI: 10.3778/j.issn.1002-8331.2010.05.003

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Rational cubic trigonometric Hermite interpolation spline curves and applications

XIE Jin^1，2，TAN Jie-qing²，LI Sheng-feng^1，3，DENG Si-qing⁴

1.Department of Mathematics and Physics，Hefei University，Hefei 230601，China
2.School of Computer ＆ Information，Hefei University of Technology，Hefei 230009，China
3.Department of Mathematics and Physics，Bengbu College，Bengbu，Anhui 233000，China
4.School of Mathematics and Information Science，Shaoguan University，Shaoguan，Guangdong 512005，China

Received:2009-07-22 Revised:2009-11-27 Online:2010-02-11 Published:2010-02-11
Contact: XIE Jin

有理三次三角Hermite插值样条曲线及其应用

谢进^1，2，檀结庆²，李声锋^1，3，邓四清⁴

1.合肥学院数学与物理系，合肥 230601
2.合肥工业大学计算机与信息学院，合肥 230009
3.蚌埠学院数学与物理系，安徽蚌埠 233000
4.韶关学院数学与信息科学学院，广东韶关 512005

通讯作者: 谢进

Abstract

Abstract: A class of rational cubic trigonometric spline curves is presented，which shares the same properties of normal cubic Hermite interpolation spline and contains trigonometric polynomials and shape parameters.Without solving system of equations，the shape of interpolation curves can be adjusted and C2 continuous by taking different values of parameters.Moreover，by selecting proper control points and shape parameters，the spline curves can represent transcendental curves exactly，such as tetracuspid and quadrifolium.

Key words: cubic interpolation spline, rational cubic trigonometric interpolation spline, transcendental curve, tetracuspid, quadrifolium

摘要： 给出一种有理三次三角Hermite插值样条曲线，具有三次Hermite插值样条相似的性质。该样条含有三角函数和形状参数，利用形状参数的不同取值可以调控插值曲线的形状，甚至不用解方程组，就能使曲线达到C2连续。此外，选择合适的控制点和形状参数，这种样条可以精确表示星形线和四叶玫瑰线等超越曲线。

关键词: 三次插值样条, 有理三次三角插值样条, 超越曲线, 星形线, 四叶玫瑰线

CLC Number:

TP391

XIE Jin^1，2，TAN Jie-qing²，LI Sheng-feng^1，3，DENG Si-qing⁴. Rational cubic trigonometric Hermite interpolation spline curves and applications[J]. Computer Engineering and Applications, 2010, 46(5): 7-9.

谢进^1，2，檀结庆²，李声锋^1，3，邓四清⁴. 有理三次三角Hermite插值样条曲线及其应用[J]. 计算机工程与应用, 2010, 46(5): 7-9.

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Rational cubic trigonometric Hermite interpolation spline curves and applications

有理三次三角Hermite插值样条曲线及其应用

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