基于非均匀B样条小波分解的NURBS曲线光顺

NURBS curve fairing based on non-uniform B-spline wavelet decomposition

利用非均匀B样条小波的正交性、局部性和振动性,研究基于非均匀B样条小波分解的有理曲线的光顺算法.第一步,通过不同的节点选取方法,实现非均匀有理B样本(non-uniformrationalBspline,NURBS)曲线的小波分解;第二步,通过曲线逼近实现NURBS曲线的整体光顺和局部光顺.通过施加约束解决曲线光顺前后端点位置和切矢不变的问题.该算法在反求工程CAD软件RE-SOFT中的实际应用效果表明,基于非均匀B样条小波分解的NURBS曲线光顺算法能够有效地去除曲线上的坏点,改善曲线的品质.

Taking advantage of orthogonality, locality and oscillation of non-uniform B-spline wavelets, a new fairing algorithm for rational B-spline curve was studied. Various knots selection methods were used to decompose the non-uniform rational B-spline （NURBS） curve. The global and local fairing for the NURBS curve were implemented through approximation. The problem of position and tangent preserving at end points were dealt with by adding constraints. The applications in RE-SOFT,a reverse engineering software developed by Zhejiang University, showed that the fairing algorithm based on non-uniform Bspline wavelets decomposition can efficiently remove the bad points and improve the quality of the curve.