Progressive iterative approximation for regularized least square bivariate B-spline surface fitting

Recently, the use of progressive iterative approximation (PIA) to fit data points has received a deal of attention benefitting from its simplicity, flexibility, and generality. In this paper, we present a novel progressive iterative approximation for regularized least square bivariate B-spline surface fitting (RLSPIA). RLSPIA extends the PIA property of univariate NTP (normalized totally positive) bases to linear dependent non-tensor product bivariate B-spline bases, which leads to a lower order fitting result than common tensor product B-spline surface. During each iteration, the weights for generating fairing updating surface are obtained by solving an energy minimization problem with box constraints iteratively. Furthermore, an accelerating term is introduced to speed up the convergence rate of RLSPIA, which is comparable favourably with the theoretical optimal one. Several examples are provided to illustrate the efficiency and effectiveness of the proposed method.