GPU conversion of quad meshes to smooth surfaces

Abstract

We convert any quad manifold mesh into an at least C1 surface consisting of bi-cubic tensor-product splines with localized perturbations of degree bi-5 near non-4-valent vertices. There is one polynomial piece per quad facet, regardless of the valence of the vertices. Particular care is taken to derive simple formulas so that the surfaces are computed efficiently in parallel and match up precisely when computed independently on the GPU.