On C2 triangle/quad subdivision

In this article, we present a subdivision scheme for mixed triangle/quad meshes that is C-2 everywhere except for isolated, extraordinary points. The rules that we describe are the same as Stam and Loop's scheme [2003] except that we perform an unzipping pass prior to subdivision. This simple modification improves the smoothness along the ordinary triangle/quad boundary from C-1 to C-2, and creates a scheme capable of subdividing arbitrary meshes. Finally, we end with a proof based on Levin and Levin's [2003] joint spectral radius calculation to show our scheme is indeed C2 along the triangle/quad boundary.