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In this thesis I show that midpoint subdivision of any degree = 2 generates subdivision surfaces which are C1-continuous at their extraordinary points. This extends the result by Zorin and Schröder for midpoint subdivision of degree up to 9 [ZS01]. To the best of my knowledge this is the first analysis for an entire class of (infinitely many) subdivision algorithms. Moreover, in this thesis I extend the result to an even wider class of subdivision algorithms that can be factored into midpoint operators and simplest subdivision [PR97].
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Techniques for analyzing classes of subdivision algorithms at extraordinary points, Qi Chen
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- 2010
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