Progressive-Iterative Approximation by Extension of Cubic Uniform B-spline Curves

In order to obtain faster convergence rate, we proposed the (weighted) progressive-iterative ap- proximation by the extension of the cubic uniform B-spline curves with shape parameters. Firstly, we pre- sented the (weighted) progressive-iterative approximation expression, and then studied the optimal shape parameters and the optimal weight by analyzing the spectral radius of the iterative matrix of the progres- sive-iterative approximation. Finally, we also proposed the (weighted) progressive-iterative approximation by the extension of bicubic uniform B-spline surfaces, and pointed out that the initial surface also has the (weighted) progressive iteration approximation property. Numerical results show that the optimal shape pa- rameters and the optimal weight make the iterative methods have the fastest convergence rate.