GPU smoothing of quad meshes

We present a fast algorithm for converting quad meshes on the GPU to smooth surfaces. Meshes with 12,000 input quads, of which 60% have one or more non-4-valent vertices, are converted, evaluated and rendered with 9times9 resolution per quad at 50 frames per second. The conversion reproduces bi-cubic splines wherever possible and closely mimics the shape of the Catmull-Clark subdivision surface by c-patches where a vertex has a valence different from 4. The smooth surface is piecewise polynomial and has well-defined normals everywhere. The evaluation avoids pixel dropout.