Refinable smooth surfaces for locally quad-dominant meshes with T-gons

Multi-sided facets in polyhedral models and meshes serve to connect regular submeshes (star-configurations) and to start or end quad-strips (T-configurations). Using the polyhedral mesh as control net, recursive subdivision algorithms often yield poor shape for these non-quad configurations. Polynomial surface constructions such as geometrically smooth splines (G-splines) do better, but lack subdivision-like refinability. Such refinability is useful for hierarchical modeling and engineering analysis. This paper introduces a new class of G-splines that generalizes bi-quadratic C ¹ splines to polyhedral control nets with star- and T-configurations and that is refinable.