Preconditioned progressive iterative approximation for tensor product Bezier patches

Based on the diagonally compensated reduction, the preconditioned progressive iterative approximation (PPIA) for tensor product Bezier 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 Bezier patches is presented. Several numerical examples are presented to illustrate the effectiveness of the proposed methods. (C) 2021 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.

Automated summary

This paper presents the preconditioned progressive iterative approximation (PPIA) based on diagonally compensated reduction for tensor product Bezier patches, which significantly accelerates the convergence rate of progressive iterative approximation (PIA). An inexact PPIA format is introduced to enhance the robustness and reduce the computational complexity. Several numerical examples are provided to demonstrate the effectiveness of the proposed methods.