| 三次Hermite插值曲线的能量优化 |
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| 引用本文： | 裴芳,高屾,韩旭里.三次Hermite插值曲线的能量优化[J].计算机工程与应用,2014(12):184-187. |
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| 作者姓名： | 裴芳 高屾 韩旭里 |
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| 作者单位： | [1]山西财经大学应用数学学院,太原030006 [2]中南大学数学科学与计算技术学院,长沙410083 |
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| 基金项目： | 国家自然科学基金（No.10871208）;湖南省自然科学基金（No.08JJ3009）. |
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| 摘 要： | 在给定插值点的位置矢量及切矢量的情况下,通过在两相邻节点引入两个新的节点,提出了一类保持C1连续的三次Hermite插值曲线的构造方法,分别通过基于曲率、挠率的能量函数对其进行优化,给出了能量最小化的参数取值公式。讨论了参数对曲线形状的影响,实例表明了方法的有效性。
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| 关 键 词： | 三次Hermite插值曲线 曲率 挠率 能量函数 曲线形状 |
Cubic Hermite curves interpolation based on energy optimization |
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| PEI Fang,GAO Shen,HAN Xuli.Cubic Hermite curves interpolation based on energy optimization[J].Computer Engineering and Applications,2014(12):184-187. |
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| Authors: | PEI Fang GAO Shen HAN Xuli |
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| Affiliation: | 1.College of Applied Mathematics, Shanxi University of Finance ＆ Economics, Taiyuan 030006, China 2.School of Mathematics and Computing Technology, Central-South University, Changsha 410083, China) |
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| Abstract: | On condition that position vectors and tangent vectors of interpolation points are given, this paper gives a new method of generating C1 Hermite interpolation curves by introducing two new points to adjacent points. Then the curves are optimized on account of energy function related to curvatures and torsions. The value of the parameters of the formula with minimum energy is given, and whether the parameters have influence on curves is discussed. Examples show the effec-tiveness of this method. |
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| Keywords: | cubic Hermite interpolation curves curvature torsion energy function shape of curves |
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