Abstract
We present a unified approach to subdivision algorithms for meshes with arbitrary topology which admits a rigorous analysis of the generated surface and give a sufficient condition for the regularity of the surface, i.e. for the existence of a regular smooth parametrization near the extraordinary point. The criterion is easily applicable to all known algorithms such as those of Doo-Sabin and Catmull-Clark, but will also be useful to construct new algorithms like interpolatory subdivision schemes.
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