| 三次Hermite插值曲线的细化优化 |
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| 引用本文： | 裴芳,韩旭里.三次Hermite插值曲线的细化优化[J].计算技术与自动化,2009,28(4):68-71. |
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| 作者姓名： | 裴芳 韩旭里 |
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| 作者单位： | 中南大学,数学科学与计算技术学院,湖南,长沙,410083 |
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| 基金项目： | 国家自然科学基金项目，湖南省自然科学基金项目 |
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| 摘 要： | 在给定端点及其切矢方向的条件下，通过在相邻两节点之间插入一个中间节点，研究三次Hermite插值曲线的优化问题．如果以与曲率有关的二阶导数为目标，证明插入节点与不插入节点的情形是一样的，体现三次Hermite插值曲线的一种特性．如果以与挠率有关的三阶导数为目标，给出优化三次Hermite曲线的计算公式，从而提出一种新的曲线构造方法．实例表明了方法的有效性．
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| 关 键 词： | 三次Hermite插值 能量优化 曲线表示 计算机辅助几何设计 |
Thinning and Optimization of Cubic Hermit Curves |
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| PEI Fang,HAN Xu-li.Thinning and Optimization of Cubic Hermit Curves[J].Computing Technology and Automation,2009,28(4):68-71. |
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| Authors: | PEI Fang HAN Xu-li |
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| Affiliation: | (The School of Mathematics and Computing Teehnology, Central--South university, Changsha, 410083, China) |
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| Abstract: | Given .some points and their tangent vectors, this paper studies the problem of the optimization of cubic Hermite interpolation curves. According to the objective of second--order derivative related to curvatures, it is proved that there is no difference whether we insert a knot or not. And it presents a characteristic of cubic Hermite interpolation curves. According to the objective of third--order derivative related to torsions, the formula to calculate the cubic optimized Hermite interpolation curves is given. And then we propose a new method to construct curves. The results show the effectiveness of this method. |
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| Keywords: | cubic hermite interpolation energy optimization the representation of curves computer aided geometric design |
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