Analyzing midpoint subdivision
Midpoint subdivision generalizes the Lane-Riesenfeld algorithm for uniform tensor product splines and can also be applied to non-regular meshes. For example, midpoint subdivision of degree 2 is a specific Doo-Sabin algorithm and midpoint subdivision of degree 3 is a specific Catmull-Clark algorithm. In 2001, Zorin and Schroder were able to prove C(1)-continuity for midpoint subdivision surfaces analytically up to degree 9. Here, we develop general analysis tools to show that the limiting surfaces under midpoint subdivision of any degree >= 2 are C(1)-continuous at their extraordinary points. (C) 2011 Elsevier B.V. All rights reserved.
midpoint subdivision smoothness at extraordinary points spectral properties of subdivision matrices characteristic map