非均匀三次B样条曲线光顺性研究

Non-Uniform Cubic B-Spline Curves Fairing Research

本文给出的光顺方法是通过节点移去，又插入，实现对Ｂ样条曲线形状控制．根据Ｂ样条曲线的性质，采用了光顺定性准则自动选择需光顺的节点．本文的研究包括节点处曲率不连续值的计算，节点移去算法，光顺一条Ｂ样条曲线算法等内容．并在计算机上实施了整个光顺过程，用实例证明了本文所给方法的有效性．

Fairing method that is presented in the paper is repeatedly removing and reinserting knots of spline, so that obtaining fairing B-spline curves. Based on theB-spline curves character, the paper adopt fairness criterion that automatically selectthe offending knot. The scheme of this paper involves new knot removal algorithm, curvature at knot discontinuity calculating and fairing B-spline curves algorithm ect.