Convergence Analysis of Regular Dynamic Loop-Like Subdivision Scheme

Abstract

This paper is concerned with the regular dynamic loop-like subdivision scheme based on the extension of Box-Spline method. The purpose of the addressed problem is to prove the convergence of the subdivision scheme and verify the $C^0$ and $C^1$ continuity by calculating the eigenvalues of the 2-neighbor subdivision matrix. Compared with the loop subdivision scheme in previous references, the designed scheme can generate exact revolving surfaces and hold a stronger modeling capability because the subdivision matrix can update regularly with the iteration procedure. Finally, some examples are given to illustrate the effectiveness of the proposed method.