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Zbl 1236.65017
Prautzsch, Hartmut; Chen, Qi
Analyzing midpoint subdivision. (English)
[J] Comput. Aided Geom. Des. 28, No. 7, 407-419 (2011). ISSN 0167-8396

The midpoint subdivision schemes form a class of subdivision schemes for arbitrary two-manifold meshes. It is observed that the midpoint subdivision surfaces are spline surfaces except for finitely many extraordinary points, which make the analysis of smoothness more difficult. {\it D. Zorin} and {\it P. Schröder} [Comput. Aided Geom. Des. 18, No. 5, 429--454 (2001; Zbl 0969.68155)] proved $C^1$ smoothness of midpoint subdivision surfaces of degree 2 to 9. The authors develop here a geometric framework, which enables them to prove $C^1$ continuity of midpoint subdivision surfaces of any degree greater than 1.
[H. P. Dikshit (Bhopal)]

MSC 2000:: *65D18 Computer graphics and computational geometry

Keywords: midpoint subdivision; smoothness at extraordinary points; special properties of subdivision matrices; characteristic map; spline surface; $C^{1}$ continuity

Citations: Zbl 0969.68155

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