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.
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Augsdörfer, U.H., Cashman, T.J., Dodgson, N.A., Sabin, M.A. (2009). Numerical Checking of C 1 for Arbitrary Degree Quadrilateral Subdivision Schemes. In: Hancock, E.R., Martin, R.R., Sabin, M.A. (eds) Mathematics of Surfaces XIII. Mathematics of Surfaces 2009. Lecture Notes in Computer Science, vol 5654. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03596-8_3
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DOI: https://doi.org/10.1007/978-3-642-03596-8_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-03595-1
Online ISBN: 978-3-642-03596-8
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