| 插值曲线区域控制的加权有理插值方法 |
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| 引用本文： | 刘爱奎,段奇,杜世田,曹庆杰,Twizell E H.插值曲线区域控制的加权有理插值方法[J].计算机辅助设计与图形学学报,2000,12(7):497-501. |
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| 作者姓名： | 刘爱奎 段奇 杜世田 曹庆杰 Twizell E H |
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| 作者单位： | 1. 山东工业大学数理系,济南,250061
2. 英国Brunel大学数学与统计系,伦敦,UB8 3PH |
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| 基金项目： | 国家自然科学基金!( 19872 0 41)，山东省自然科学基金!( Y99A0 1)，英国皇家基金资助 |
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| 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，文中利用分母为线性的有理三次插值样条和仅基于函数值的有理三次插值样条构造了一种加权有理三次插值样条，由于这种有理三次插值样条中含有新的参数，给约束控制带来了方便，给出了将插值曲线约束于给定的折线、二次曲线之上（下）或之间的条件，最后给出了数值例子。
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| 关 键 词： | 有理插值 三次样条 插值曲线 区域控制 加权 CAD |
Region Controlling of the Interpolating Curve by Weighted Rational Interpolation |
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| LIU Ai-Kui,DUAN Qi,DU Shi-Tian,CAO Qing-Jie,Twizell E H.Region Controlling of the Interpolating Curve by Weighted Rational Interpolation[J].Journal of Computer-Aided Design & Computer Graphics,2000,12(7):497-501. |
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| Authors: | LIU Ai-Kui DUAN Qi DU Shi-Tian CAO Qing-Jie Twizell E H |
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| Abstract: | To constrain the interpolating curves to be bounded in the given region is an important problem in curve design. In this paper, the weighted rational cubic spline interpolation has been constructed using the rational cubic spline with linear denominator and the rational cubic spline based on function values. Because of the new parameters in the interpolating functions, the problems to constrain the weighted rational interpolating curves to lie strictly above or below the given piecewise linear curves (or quadratic curves) and even between them can be solved. |
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| Keywords: | curve design rational interpolation cubic spline constrained interpolation |
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