Numerical Checking of C1 for Arbitrary Degree Quadrilateral Subdivision Schemes

Authors:
U. H. Augsdörfer;T. J. Cashman;N. A. Dodgson;M. A. Sabin
Affiliations:
The Computer Laboratory, University of Cambridge, UK;The Computer Laboratory, University of Cambridge, UK;The Computer Laboratory, University of Cambridge, UK;Numerical Geometry Ltd., UK
Venue:
Proceedings of the 13th IMA International Conference on Mathematics of Surfaces XIII
Year:
2009

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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.