中文摘要：

几何逆向工程中的光顺曲线重构问题本质上属于回归问题。支持向量回归机是求解回归问题的新的十分有效的方法。论文研究用支持向量回归机处理光顺曲线的重构问题。鉴于后者有着对于光顺性的特殊要求，已有的支持向量机并不适用。通过修正惩罚因子对支持向量机加以改造，即根据测量数据点的分布情况，利用各测量点圆率的特性确定对应的惩罚因子，从而实现了自由曲线的光顺重构。数值试验表明新方法可以剔除输入数据中不光顺点的影响，并在给定的精度条件下有效地逼近曲线，达到较好的拟合效果。

英文摘要：

The problem of construction of smoothing curve is actually regression problem.The support vector machine （SVM） is a very effective method for regression issue.How to use SVM to solve the problem of curve smoothing reconstruction in reverse engineering is discussed in this paper.Whereas SVM is not suitable for the smoothing regression,a modified support vector regression model is proposed.The optimization problem and its dual formula are described.The parameter C of every point is redefined by the character of round curvature.Through an example,the robust is compared among different methods.The results show that the smoothness of curves fitted by modified method is better than by the former SVM model,when there are some bad measure points in the datum.