Analyzing midpoint subdivision
H Prautzsch, Q Chen - Computer Aided Geometric Design, 2011 - Elsevier
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 Schröder 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 …
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 Schröder 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 …