Cubic Hermite curves interpolation based on energy optimization

Computer Engineering and Applications ›› 2014, Vol. 50 ›› Issue (12): 184-187.

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Cubic Hermite curves interpolation based on energy optimization

PEI Fang1, GAO Shen1, HAN Xuli2

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

Online:2014-06-15 Published:2015-05-08

三次Hermite插值曲线的能量优化

裴芳1，高屾1，韩旭里2

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

Abstract

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 effectiveness of this method.

Key words: cubic Hermite interpolation curves, curvature, torsion, energy function, shape of curves

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。

关键词: 三次Hermite插值曲线, 曲率, 挠率, 能量函数, 曲线形状

PEI Fang1, GAO Shen1, HAN Xuli2. Cubic Hermite curves interpolation based on energy optimization[J]. Computer Engineering and Applications, 2014, 50(12): 184-187.

裴芳1，高屾1，韩旭里2. 三次Hermite插值曲线的能量优化[J]. 计算机工程与应用, 2014, 50(12): 184-187.

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Cubic Hermite curves interpolation based on energy optimization

三次Hermite插值曲线的能量优化

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