Progressive Iterative Approximation of SOR for Non-uniform Cubic B-spline Curve and Surface Interpolation.

Progressive iterative approximation (PIA) is an efficient data fitting technique which makes the initial curve or surface approximate the data points to be processed by successive iterations. However, since the spectral radius of iterative matrix in traditional PIA is relatively large, the iterative convergence rate is relatively slow, which results in poor efficiency of data fitting. In this paper, we develop a successive over-relaxation progressive iterative approximation (SOR-PIA) for non-uniform cubic B-splines to overcome the defect. Besides, we employ the equidistant search strategy to estimate the relaxation factor, which greatly accelerates the convergence speed of the iterative process. Experimental results show that SOR-PIA iterative interpolation can achieve a higher accuracy within the equivalent number of iterations compared with the standard PIA and weighted PIA (WPIA) iterative interpolation.