Abstract: For the self-intersection of Non-Uniform Rational B-Splines (NURBS) equidistance curves,a new method of generating NURBS equidistance curves was put forward.Based on the control point,the NURBS curve was generated,and a method of generating NURBS equidistance curves with backtracking and regulable fairing was given.The contour curve was traced through the cutting method,the self-intersection line segment in the equidistance curve is removed,and the smooth processing was carried out at the self-intersection point of the curve.In the case of a given outline error,the NURBS equidistance curve of the fairing processing could be opted in the light of the actual demand.The method was applied in practical system based on Qt development environment,and the excellent performance had been achieved.

Key words: self-intersection, non-uniform rational B-splines curve, equidistance curve, cutting, fairing

摘要： 针对CAD/CAM中非均匀有理B样条(NURBS)等距曲线经常产生自交的问题,提出一种新的NURBS等距曲线生成方法。基于带权重的控制点生成NURBS曲线,给出一种具有回溯可调节光顺的NURBS等距曲线生成方法。通过裁剪对等距曲线进行回溯,去除等距曲线中自交的线段,并对曲线的自交点处进行光顺处理。光顺处理的NURBS等距曲线在给定轮廓偏差下,可以根据实际需求实现过渡范围的可调节。在Qt的开发环境下对该方法进行了验证,取得了较好的效果。

关键词: 自交, 非均匀有理B样条曲线, 等距曲线, 裁剪, 光顺