Convergence and normal continuity analysis of non-stationary subdivision schemes near extraordinary vertices and faces

TL;DR

This paper develops new conditions to analyze the convergence and normal continuity of non-stationary subdivision schemes on complex 2-manifold meshes, especially near extraordinary vertices and faces.

Contribution

It introduces novel sufficient conditions for convergence and normal continuity of rotationally symmetric, non-stationary subdivision schemes near extraordinary features.

Findings

Derived new sufficient conditions for convergence.

Established criteria for normal continuity near extraordinary vertices.

Applicable to arbitrary topology meshes.

Abstract

Convergence and normal continuity analysis of a bivariate non-stationary (level-dependent) subdivision scheme for 2-manifold meshes with arbitrary topology is still an open issue. Exploiting ideas from the theory of asymptotically equivalent subdivision schemes, in this paper we derive new sufficient conditions for establishing convergence and normal continuity of any rotationally symmetric, non-stationary, subdivision scheme near an extraordinary vertex/face.