Refinable bi-quartics for design and analysis. (September 2018) - Karčiauskas, Kȩstutis; Peters, Jörg
Abstract: 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. Graphical abstract: Highlights: The construction converts quad meshes with irregularities to a bi-4 surface. The surface consists of subdivision rings completed by a tiny G 1 cap. The rings join C 1 or, at the cost of more pieces, C 2 . The surface is compatible with CAD, yields good highlight distributions. A refinable space of functions on the surface.