基于能量优化G2连续插值三次样条曲线

计算机工程与应用 ›› 2007, Vol. 43 ›› Issue (16): 64-66.

基于能量优化G²连续插值三次样条曲线

王洪申^1,3，张树生¹，张仪哲²，赵传阳³

1.西北工业大学现代设计与集成制造技术教育部重点实验室，西安 710072
2.武汉理工大学机电工程学院，武汉 430070
3.兰州电力学校，兰州 730070

收稿日期:1900-01-01 修回日期:1900-01-01 出版日期:2007-06-01 发布日期:2007-06-01
通讯作者: 王洪申

Optimization of energy-based parametric cubic spline curves with G²-continuity

WANG Hong-shen^1,3，ZHANG Shu-sheng¹，ZHANG Yi-zhe²，ZHAO Chuan-yang³

1.The Key Laboratory of Contemporary Designing and Integrated Manufacturing Technology，Ministry of Education，Northwestern
Polytechnical University，Xi’an 710072，China
2.School of Mechanical and Electronic Engineering，Wuhan University of Technology，Wuhan 430070，China
3.Lanzhou Electric Power School，Lanzhou 730070，China

Received:1900-01-01 Revised:1900-01-01 Online:2007-06-01 Published:2007-06-01
Contact: WANG Hong-shen

摘要/Abstract

摘要： 给出了一种在能量优化意义下构造G²连续保形插值三次参数样条曲线的方法。具体步骤如下：（1）以曲线应变能最小为目标构造目标函数，通过解线性方程组，求出优化意义下的每个插值点处的最优切矢方向；（2）用文中给出的简易公式求出各插值点的曲率，进而计算出插值点处的切矢模长，使曲线满足G²连续、保形插值的条件；（3）用Hermite插值方法求出相邻两插值点间的曲线。实验结果显示了方法的有效性。

Abstract: Given a way of constructing a shape preserving and interpolatory spline with G²-continuity by using parametric cubic segments.The process consists of three step：（1）Computing the optimal tangent directions for interpolation spline so that the energy of curve is a minimum.（2）Using the formula of curvature which is given in this paper，computed the curvature of every interpolation data point，then the module of tangent vectors were obtained on the condition that the curve is G²-continuity and shape preserving.（3）Then each segment is determined by Hermite interpolation satisfying given endpoint（position and tangent） conditions.Numerical examples are given to show the efficiency of this method.

王洪申^1,3，张树生¹，张仪哲²，赵传阳³. 基于能量优化G²连续插值三次样条曲线[J]. 计算机工程与应用, 2007, 43(16): 64-66.

WANG Hong-shen^1,3，ZHANG Shu-sheng¹，ZHANG Yi-zhe²，ZHAO Chuan-yang³. Optimization of energy-based parametric cubic spline curves with G²-continuity[J]. Computer Engineering and Applications, 2007, 43(16): 64-66.

基于能量优化G²连续插值三次样条曲线

Optimization of energy-based parametric cubic spline curves with G²-continuity

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