基于最少控制点的非均匀有理B样条曲线拟合

Non-Uniform Rational B-Splines Curve Fitting Based on the Least Control Points

针对叶片型线的优化设计,提出采用自适应方法提取合适的节点来插值非均匀有理B样条(NURBS)曲线的算法,实现了满足一定精度要求的数据点云拟合以及控制点的计算.该方法首先通过点云外形特征提取主特征点,把主特征点作为节点插值NURBS曲线,通过德布尔递推公式求解控制点,然后根据误差及曲率信息自适应地增加节点反复迭代,直到达到要求的拟合误差精度,从而简洁有效地实现了大量数据点云的拟合.相比传统方法,该方法能够更快地达到要求的逼近精度,同时将误差与曲率信息结合起来调整节点,不仅适合于有局部大曲率及有噪声点的数据点云的曲率计算,而且可用于估计插值节点的数量和工业逆向设计中空间曲面控制点的提取,为优化设计奠定了良好的基础.

Aiming at the optimizing design of vane curve, a novel algorithm of adaptively choosing appropriate nodes is proposed to interpolate non-uniform rational B-splines （NURBS） curve, and the error-bounded curve fitting is carried out and the control points are determined. The dominant points are identified and extracted with the curvature information, and serve as nodes to interpo- late NURBS curve, then the control points are evaluated via de Boor iterative equation. Simultaneously, a new node is adaptively added according to the error and curvature properties of fitting curve to iterate procedure until the required accuracy is met. Several experiments are performed to validate this method.