图学学报
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摘要: 应用B 样条曲线曲面拟合内在形状带有间断或者尖点的数据时,最小二乘法得到的 拟合结果往往在间断和尖点处误差较大,原因在于最小二乘法将拟合函数B 样条的节点固定。本 文在利用3 次B 样条曲线和曲面拟合数据时,应用差分进化算法设计出一种能够自适应地设置B 样条节点的方法,同时对节点的数量和位置进行优化,使得B 样条拟合曲线曲面在间断和尖点处 产生拟多重节点,实现高精度地拟合采样于带有间断或尖点的曲线和曲面数据。
关键词: 数据拟合, B 样条曲线曲面, 最小二乘法, 差分进化算法, 自适应, 拟多重节点
Abstract: To use B-spline curve and surface to fit data with an underlying function having discontinuous points and/or cusps, the fitting results obtained by least squares method are often bad in the vicinity of discontinuous points and cusps because of the fixed B-spline knots. In this paper, we propose a method for solving data fitting problem with cubic B-spline curve and surface by using differential evolution algorithm. Our method can set B-spline knots adaptively, so as to optimize the number and location of knots simultaneously and produce quasi-multiple knot in the vicinity of discontinuous points and cusps. With this, we can fit data with an underlying function having discontinuous points and/or cusps with high precision.
Key words: data fitting, B-spline curve and surface, least squares method, differential evolution algorithm, adaptation, quasi-multiple knot
何兵朋, 冯仁忠, 余胜蛟. 基于差分进化算法的B 样条曲线曲面拟合[J]. 图学学报, DOI: 10.11996/JG.j.2095-302X.2016020178.
He Bingpeng, Feng Renzhong, Yu Shengjiao. B-Spline Curve and Surface Fitting Using Differential Evolution Algorithm[J]. Journal of Graphics, DOI: 10.11996/JG.j.2095-302X.2016020178.
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链接本文: http://www.txxb.com.cn/CN/10.11996/JG.j.2095-302X.2016020178
http://www.txxb.com.cn/CN/Y2016/V37/I2/178