| 一类加权有理四次插值样条曲线的形状控制 |
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| 引用本文： | 邓四清.一类加权有理四次插值样条曲线的形状控制[J].计算机工程与应用,2014,50(2):137-141. |
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| 作者姓名： | 邓四清 |
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| 作者单位： | 韶关学院 数学与信息科学学院，广东 韶关 512005 |
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| 基金项目： | 国家自然科学基金（No.60773110）;广东省自然科学基金（No.S2012010010069）;中山大学广东省计算数学重点实验室开放基金项目（No.201206015）;湖南省教育厅科研资助项目（No.06C791）;韶关市科技计划项目（No.2011CX/K20）. |
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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。利用带导数的和不带导数的分母为线性的有理四次插值样条构造了一类新的加权有理四次插值样条函数，插值函数具有简单的显示表示，这类新的插值样条中含有权系数，因而增加了处理问题的灵活性，给约束控制带来了方便。给出了将该种插值曲线约束于给定的折线、二次曲线之上、之下或之间的充分条件。证明了满足约束条件的加权有理样条的存在性。
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| 关 键 词： | 计算机应用 有理样条 加权插值 约束插值 形状控制 |
Shape control of weighted rational quartic interpolating spline curve. |
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| DENG Siqing.Shape control of weighted rational quartic interpolating spline curve.[J].Computer Engineering and Applications,2014,50(2):137-141. |
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| Authors: | DENG Siqing |
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| Affiliation: | School of Mathematics and Information Sciences, Shaoguan University, Shaoguan, Guangdong 512005, China |
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| Abstract: | To constrain the interpolating curves to be bounded in the given region is an important problem in curve design. A kind of weighted rational quartic spline interpolation is constructed using the rational quartic spline with linear polynomial denominator and the rational quartic spline based on function values. The interpolation function has a simple and explicit mathematical representation. The sufficient conditions for the interpolating curves to be above, below or between the given broken lines or piecewise quadratic curves are derived. |
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| Keywords: | computer application rational spline weighted interpolation constrained interpolation shape control |
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