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A sharp degree bound on G 2-refinable multi-sided surfaces
Kȩstutis Karčiauskas1, Jörg Peters2
1Department CISE, University of Florida, Vilnius University, Lithuania.
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.
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