基于法矢比率的样条曲线光顺

Normal Vector Ratio Based Smoothing of B-Spline Curves

论文提出了一种新的基于曲线法矢比率分析的B样条曲线光顺方法。一条曲线一般由若干凹凸分段顺序相连组成。设计人员按设计意图对各曲线段指定其上各点处的目标法矢分量比率图,比较目标法矢分量比率图与实际法矢分量比率图,即可判断出各曲线段的光顺性。对光顺性较差的曲线段,通过最小二乘逼近优化过程调整其控制顶点,从而达到光顺目的。该优化过程的目标函数兼顾光顺性及光顺前后曲线的偏差,可通过调节相应参数来达到设计要求。实例表明,该文方法灵活方便,可行有效,为曲线光顺问题的解决提供了一种新的选择。

A novel normal vector ratio based method for smoothing of B-spline curves is presented,A B-spline curve is generally composed of several convex or concave segments,According to the design intent,target normal vector ratio plots of these segements,which are provided by the designer,are compared to actual normal vector ratio plots,so the smoothness of every curve segment can be identified,For segments with poor smoothness,their control points are modified in a process of least-squares approximation optimization,In the process,the importance of smoothness versus coherence to the original design can be adjusted by the designer, Experimental results are given to show the validity of this method.