Numerical checking of C1 for arbitrary degree quadrilateral subdivision schemes

Abstract

We derive a numerical method to confirm that a subdivision scheme based on quadrilateral meshes is C 1 at the extraordinary points. We base our work on Theorem 5.25 in Peters and Reif's book "Subdivision Surfaces", which expresses it as a condition on the derivatives within the characteristic ring around the EV. This note identifies instead a sufficient condition on the control points in the natural configuration from which the conditions of Theorem 5.25 can be established. © 2009 Springer Berlin Heidelberg.