Preconditioned progressive iterative approximation for tensor product Bézier patches

Based on the diagonally compensated reduction, the preconditioned progressive iterative approximation (PPIA) for tensor product Bézier patches is presented. Due to the effectiveness of the preconditioner, the convergence rate of progressive iterative approximation (PIA) is accelerated significantly. To improve the robustness and reduce the computational complexity of PPIA, the inexact PPIA format for tensor product Bézier patches is presented. Several numerical examples are presented to illustrate the effectiveness of the proposed methods.