Gauss-Seidel Progressive Iterative Approximation (GS-PIA) for Loop Surface Interpolation

Abstract

We propose a Gauss-Seidel progressive iterative approximation (GS-PIA) method for Loop subdivision surface interpolation by combining classical Gauss-Seidel iterative method for linear system and progressive iterative approximation (PIA) for data interpolation. We prove that GS-PIA is convergent by applying matrix theory. GS-PIA algorithm retains the good features of the classical PIA method, such as the resemblance with the given mesh and the advantages of both a local method and a global method. Compared with some existed interpolation methods of subdivision surfaces, GS-PIA algorithm has advantages in three aspects. First, it has a faster convergence rate compared with the PIA and WPIA algorithms. Second, compared with WPIA algorithm, GS-PIA algorithm need not to choose weights. Third, GS-PIA need not to modify the mesh topology compared with other methods with fairness measures. Numerical examples for Loop subdivision surfaces interpolation illustrated in this paper show the efficiency and effectiveness of GS-PIA algorithm. CCS Concepts •Computing methodologies → Parametric curve and surface models;