基于差分进化算法的B 样条曲线曲面拟合

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。

B-Spline Curve and Surface Fitting Using Differential Evolution Algorithm

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.