平面参数三次样条曲线的优化光顺算法

An Optimal Fairing Algorithm for Planar Cubic Spline Curves

给出了基于Kjellander和离散曲率的平面参数三次样条曲线的一种优化光顺算法。首先介绍了离散曲率和Kjellander的光顺法,进而给出了一个带有修改因子λ的目标函数,并通过求解得到λ值和光顺后的型值点,最后得到光顺后的曲线。此法使曲线的曲率变化均匀,使光顺后的曲线与原曲线的偏差小,并且算法简单易行,计算量较小。

An optimal fairing algorithm based on Kjellander and discrete curvature for planar parametric cubic spline curves is presented. Firstly, discrete curvature and fairing algorithm based on Kjellander is introduced and an objective function of having modification factor λ is presented. Then the value of λ and faired points are obtained by solving this function. Finally, fairing curves is acquired. This method makes the change of curvature of faired curves more uniformly and the deviation from the initial curves more small.