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Zbl 0872.65007
Reif, Ulrich
A unified approach to subdivision algorithms near extraordinary vertices. (English)
[J] Comput. Aided Geom. Des. 12, No.2, 153-174 (1995). ISSN 0167-8396

Summary: 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.

MSC 2000:: *65D17 Computer aided design (modeling of curves and surfaces)
68U07 Computer aided design

Keywords: subdivision; arbitrary topology; regular surface; characteristic map; extraordinary vertex

Cited in: Zbl 1247.65018 Zbl 1094.65016 Zbl 0959.65021 Zbl 0913.65011

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