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 Schröder were able to prove C1C1-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 C1C1-continuous at their extraordinary points.

► Midpoint subdivision surfaces of any degree are smooth at their extraordinary points.
► C1C1 analysis tools for infinite classes of subdivision schemes for arbitrary meshes.
► New spectral properties of subdivision matrices.