Iterative Least Square Optimization for the Weights of NURBS Curve

NURBS curves have been widely applied in the field of data points approximation, and their fitting accuracy can be improved by adjusting the values of their weights. When applying the NURBS curve, it is difficult to obtain the optimal weights values due to the nonlinearity of the curve fitting problem with NURBS. In this paper, a weights iterative optimization method for NURBS curve fitting is proposed, where the geometric property of weight has been adopted to iteratively obtain the adjusting values of the weights with the least square method. The effectiveness and convergence of the proposed method are demonstrated by numerical experiments. The results show that the proposed method can obtain higher fitting accuracy than other iterative optimization methods. Meanwhile, it has the merits of data noise robustness, high accuracy with small-scale knots, and flexibility. Hence, the proposed method is suitable for applications including noisy data approximation and skinned surface generation.