Region control of rational quartic interpolating spline curve based on function values

doi:10.3778/j.issn.1002-8331.2008.20.058

Computer Engineering and Applications ›› 2008, Vol. 44 ›› Issue (20): 192-195.DOI: 10.3778/j.issn.1002-8331.2008.20.058

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Region control of rational quartic interpolating spline curve based on function values

DENG Si-qing¹,FANG Kui^2,3,XIE Jin⁴

1.Department of Mathematics，Xiangnan University，Chenzhou，Hunan 423000，China
2.School of Information Science and Technology，Hunan Agricultural University，Changsha 410128，China
3.School of Mathematics and Computer，Hunan Normal University，Changsha 410081，China
4.Department of Mathematics and Physics，Hefei University，Hefei 230601，China

Received:2007-10-09 Revised:2007-12-24 Online:2008-07-11 Published:2008-07-11
Contact: DENG Si-qing

基于函数值的有理四次样条曲线的区域控制

邓四清¹,方逵^2,3,谢进⁴

1.湘南学院数学系，湖南郴州 423000
2.湖南农业大学信息科学技术学院，长沙 410128
3.湖南师范大学数学与计算机科学学院，长沙 410081
4.合肥学院数理系，合肥 230601

通讯作者: 邓四清

Abstract

Abstract: To constrain the interpolating curves to be bounded in the given region is an important problem in curve design.A rational quartic interpolating spline based on function values with linear denominator is constructed.The sufficient conditions for the interpolating curves to be above，below or between the given broken lines or piecewise quadratic curves are derived.An example is given in the end of this paper.

Key words: computer application, rational interpolation, quartic spline, region control

摘要： 将插值曲线约束于给定的区域之内是曲线形状控制中的重要问题。构造了一种分母为线性的基于函数值的C¹连续有理四次插值样条。这种有理四次插值样条中含有参数，因而可以在插值条件不变的情况下通过对参数的选择进行曲线的局部修改，给约束控制带来了方便。对该种插值曲线的区域控制问题进行了研究，给出了将其约束于给定的折线，二次曲线之上、之下或之间的充分条件.最后给出了数值例子。

关键词: 计算机应用, 有理插值, 四次样条, 区域控制

DENG Si-qing¹,FANG Kui^2,3,XIE Jin⁴. Region control of rational quartic interpolating spline curve based on function values[J]. Computer Engineering and Applications, 2008, 44(20): 192-195.

邓四清¹,方逵^2,3,谢进⁴. 基于函数值的有理四次样条曲线的区域控制[J]. 计算机工程与应用, 2008, 44(20): 192-195.

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Region control of rational quartic interpolating spline curve based on function values

基于函数值的有理四次样条曲线的区域控制

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