| 一种新的带参数双三次有理插值样条的有界性与点控制 |
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| 引用本文： | 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). |
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| 作者姓名： | 邓四清 方逵 谢进 陈福来 陆海波 |
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| 作者单位： | 韶关学院数学与信息科学学院;湖南农业大学信息科学技术学院;合肥学院数理系;湘南学院数学系; |
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| 基金项目： | 国家自然科学基金资助项目，湖南省教育厅科研资助项目，湖南省科技计划项目，安徽省教育厅自然科研项目，韶关学院校级重点扶持学科建设项目，湖南省重点学科建设项目资助，湖南省高校科技创新团队支持计划资助 |
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| 摘 要： | 文19]中,作者构造了一种基于函数值的带参数的分子为双三次、分母为双二次的二元有理插值样条.本文进一步研究该种二元有理插值样条的有界性,给出插值的逼近表达式,讨论插值曲面形状的点控制问题.在插值条件不变的情况下,插值区域内任一点插值函数的值可以根据设计的需要通过对参数的选取修改,从而达到插值曲面局部修改的目的.
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| 关 键 词： | 插值 有理样条 有界性 点控制 计算机辅助几何设计 |
BOUNDED PROPERTY AND POINT CONTROL OF A NEW BIVARIATE RATIONAL BICUBIC INTERPOLATING SPLINE WITH PARAMETERS |
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| Deng Siqing,Fang Kui,Xie Jin,Chen Fulai,Lu Haibo.BOUNDED PROPERTY AND POINT CONTROL OF A NEW BIVARIATE RATIONAL BICUBIC INTERPOLATING SPLINE WITH PARAMETERS[J].Mathematica Numerica Sinica,2010,32(4). |
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| Authors: | Deng Siqing Fang Kui Xie Jin Chen Fulai Lu Haibo |
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| Institution: | Deng Siqing (School of Mathematics and Information Science,Shaoguan University,Shaoguan 512005,Guangdong,China) Fang Kui (School of Information Science and Technology,Hunan Agricultural University,Changsha 410128,China) Xie Jin (Department of Mathematics and Physics,Hefei University,Hefei 230601,China) Chen Fulai Lu Haibo (Department of Mathematics,Xiangnan University,Chenzhou 423000,Hunan,China) |
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| Abstract: | A bivariate rational interpolation method with parameters was created in an earlier work which was based on function values only,and this spline is with bicubic numerator and biquadratic denominators.This paper will deal with the bounded property,approximation property and the point control method of the interpolating surface.It is proved that the values of the interpolating function in the interpolation region are bounded no matter what the parameters might be.Also,the approximation expression of the inter... |
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| Keywords: | interpolation rational spline bounded property point control computer aided geometric design |
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