A sharp degree bound on G2-refinable multi-sided surfaces. (August 2020) - Karčiauskas, Kȩstutis; Peters, Jörg
Abstract: Refinement of a space of splines should yield additional degrees of freedom for modeling and engineering analysis, both along boundaries and in the interior. Yet such additional flexibility fails to materialize for multi-sided G 2 surface constructions when the polynomial degree is too low. This paper establishes a tight lower bound on the polynomial degree of flexibility-increasing refinable multi-sided G 2 surface constructions within a C 2 spline complex — by ruling out bi-5 constructions and by exhibiting a multi-sided bi-6 construction that yields good highlight line and curvature distributions. The bi-6 construction consists of one 2 × 2 macro-patch for each of the n sectors that join to form the multi-sided surface. Graphical abstract: Highlights: Refinement should yield additional freedom for modeling and engineering analysis. Not so for bi-5 multi-sided G2 constructions compatible with C2 cubic splines: for bi-5 with C 2 sectors some G -edges remain a single polynomial under refinement. A bi-6 construction yields good shape and refinement increases flexibility everywhere. This characterizes flexibility-increasing refinable multi-sided G 2 constructions.