2009/11/26 by Hartmut Prautzsch, Qi Chen, Prautzsch, Hartmut +1
Computer Science · #Computational Geometry (cs.CG) #FOS: Computer and information sciences #Graphics (cs.GR) #I.3.5 #cs.CG #cs.GR
paper · pdf · doi:10.48550/arxiv.0911.5157
The paper was improved by adding more explanations and by adding an illustration of how the statements depend on each other. We combined a few theorems to simplify the structure of the paper and better described the meaning of the statements and how they fit into the overall proof. 24 pages, 10 figures
arxiv created 2011/04/27 · arxiv updated 2011/04/28
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 Schroeder were able to prove C1-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 C1-continuous at their extraordinary points.