Techniques for analyzing classes of subdivision algorithms at extraordinary points

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].