基于光顺优化的NURBS曲线权因子估计方法

Weights Estimation for NURBS Curves Based on Fairing Optimization

摘要: 基于弹性均匀细梁的应力能和扰动能的光顺优化,提出了NURBS曲线权因子的一种估计方法:将应力能和扰动能离散化,得到一个泛函,对此泛函极小化而得权因子.同时,文中给出的极小泛函统一了目前文献中出现的一类不同光顺标准.为了减少导数的计算量,文中采用了NURBS曲线的矩阵表示,最后,通过数值算例比较了各种光顺标准的优劣.

Abstract: This paper proposes an approach of constructing planar piecewise Bézier curve of 4th or 5th degree with all edges tangent to a given control polygon and the curve segments are joined together with C² and C³ continuity．The segmented Bézier curves are all shape-preserving to their tangent polygon．Finally，a few numerical examples illustrate that the method given in this paper is effective for CAGD．