遗传算法求解B样条曲线最小二乘拟合问题
Least Squares Fitting with B-Spline by Genetic Algorithm
DOI: 10.12677/AAM.2014.34024, PDF, HTML,  被引量 下载: 3,519  浏览: 10,082  国家自然科学基金支持
作者: 刘 莲, 冯仁忠:北京航空航天大学,数学与系统科学学院,北京
关键词: B样条曲线最小二乘拟合遗传算法B-Spline Curve The Least Squares Fitting Genetic Algorithm
摘要: 本文提出利用遗传算法对四组不同的二维翼型数据进行线性及非线性B样条曲线最小二乘拟合,发现遗传算法解决这类问题是有效可行的。
Abstract: In this paper, we propose genetic algorithm to obtain a good approximation for least squares fitting with linear and nonlinear B-spline, and four different two-dimensional airfoil data fittings are given to show that genetic algorithm solves this kind of problem feasibly and effectively.
文章引用:刘莲, 冯仁忠. 遗传算法求解B样条曲线最小二乘拟合问题[J]. 应用数学进展, 2014, 3(4): 160-168. http://dx.doi.org/10.12677/AAM.2014.34024

参考文献

[1] 施法中 (2001) 计算机辅助几何设计与非均匀有理B样条. 高等教育出版社, 北京.
[2] Ma, W. and Kruth, J.P. (1995) Parametrization of randomly measured points for least squares fitting of B-spline curves and surfaces. Comput-er-Aided Design, 27, 663-675.
[3] 王晓鹏 (2001) 遗传算法及其在气动优化设计中的应用研究. 博士论文, 西北工业大学, 西安.
[4] 潘立登 (2009) 遗传算法及其工程应用. 机械工业出版社, 北京.
[5] Dierckx, P. (1993) Curve and surface fitting with splines. Oxford University Press, Oxford.
[6] 蒋尔雄, 赵风光, 苏仰峰 (2007) 数值逼近. 复旦大学出版社, 上海.
[7] Powell, M.J.D. (1970) Curve fitting by splines in one variable. In: Hayes, J.G., Ed., Numerical approximation to functions and data, Athlone Press, London.
[8] Anthony, H.M., Cox, M.G. and Harris, P.M. (1989) The use of local polynomial approximations in a knot-placement strategy for least-squares spline fitting. NPL Report, DITC, 148/89.