基于轮廓关键点的B样条曲线拟合算法

针对逆向工程中的点云切片轮廓数据点列，提出一种基于轮廓关键点的B样条曲线拟合算法.在确保扫描线点列形状保真度的前提下，首先对其进行等距重采样等预处理，并遴选出曲线轮廓关键点，生成初始插值曲线；再利用邻域点比较法求出初始曲线与各采样点间的偏差值，在超过拟合允差处增加新的关键点，并生成新的插值曲线，重复该步骤至拟合曲线满足预定精度要求.实验表明，在对稠密的二维断面数据点进行B样条逼近时，该算法能有效压缩控制顶点数目，并具有较高的计算效率.同时，由于所得控制顶点的分布能准确反映曲线的曲率变化，该方法还可作为误差约束的曲线逼近中的迭代步骤之一.

A B-Spline Curve Fitting Algorithm Based on Contour Key Points

Aimed at the sliced contour data points of point cloud in the reverse engineering, a B-spline curve fitting method based on contour key points was presented. Under the premise of keeping the shape fidelity, first, the scanned strip point set was resampled with an equidistance method and the contour key points were selected, in turn an initial interpolation curve was built. Next, the curve deviation values were calculated with a neighborhood point comparison method, and a new key point was added where the curve deviation value exceeded the specified tolerance, then a new interpolation curve was gained. The above procedure was repeated until the fitting curve reached expected accuracy. The numerical experiments show that, for the B-spline fitting of dense sectional scanned points, the proposed algorithm effectively compresses the number of key points and bears high computational efficiency. At the same time, since the distribution of key points accurately reflects the fitting curve’s curvature changes, this method also makes one promising iteration step in the curve approximation under deviation constraints.