Convergence and normal continuity analysis of non-stationary subdivision schemes near extraordinary vertices and faces
Provides theoretical guarantees for non-stationary subdivision schemes, which are widely used in geometric modeling and computer graphics.
The paper derives new sufficient conditions for convergence and normal continuity of non-stationary subdivision schemes on 2-manifold meshes with arbitrary topology, addressing a previously open problem.
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.