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Analyzing midpoint subdivision. (English) Zbl 1236.65017
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.

65D18Computer graphics, image analysis, and computational geometry
Full Text: DOI arXiv
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