Refinable bi-quartics for design and analysis

To be directly useful both for shape design and a thin shell analysis, a surface representation has to satisfy three properties: (1) be compatible with CAD surface representations, (2) yield generically a good highlight distribution, and (3) offer a refinable space of functions on the surface. Here we propose a new construction, based on a number of recently-developed techniques, that satisfies all three criteria. The construction converts quad meshes with irregularities, where more or fewer than four quads meet, to C ¹ (or, at the cost of more pieces, C ²) bi-4 surface consisting of subdivision rings for the main body completed by a tiny G ¹ cap.