测量数据点的高精度B样条曲线拟合算法

High precision B-spline curve fitting algorithm of measure points

为提高曲线重构的效率,提出了关键点提取算法,用于三维测量型值点的B样条曲线逼近。根据离散曲率分析提取具有曲率极值的型值点作为初始关键点,再根据初始关键点和型值点的参数值构建的节点矢量,确保最小二乘矩阵满秩,用最小二乘法反算控制顶点。通过Hausdorff距离衡量逼近曲线与型值点间的逼近偏差,设定偏差阈值和多点调整算法,确定新增关键点的位置区间,根据形状指数分析找到新增关键点的精确位置,通过不断迭代找到满足逼近允差要求的最终关键点和控制顶点。实例验证表明,同一逼近允差前提下,新算法在迭代计算时间、迭代次数及最终所得控制顶点个数等方面优于其他方法。

To improve curve reconfiguration efficiency,the key points selection algorithm was proposed and applied in B-spline curve approximation of 3Dmeasure points.The measure points with curvature extrema were selected as ini-tial key points according to the analysis of discrete curvature.The knot vector established by the key points and the parameter values of the measure points which guaranteed a full-rank interpolation matrix.The unknown control points of the B-spline curve were determined by the least squared method.Hausdorff distance was used to measure the deviation between the given points set and the approximated curve.New key points were selected by the devia-tion and multi-point adjusting algorithm according to the analysis of shape index.Final key points and control points meeting the specified tolerance requirement were acquired through iterations.Experimental results demonstrated that the new algorithm was superior comparing to other methods in the aspects of the number of the control points,the number of iterations and the computation time.