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Least Degree G 1-refinable Multi-sided Surfaces Suitable for Inclusion into C 1 bi-2 Splines
Kȩstutis Karčiauskas1, Jörg Peters2
1Vilnius University, Lithuania.
Abstract:
Geometrically smooth spline surfaces, generalized to include n-sided facets or configurations of n ≠ 4 quads, can exhibit a curious lack of additional degrees of freedom for modelling or engineering analysis when refined. This paper establishes a minimal polynomial degree for smooth constructions of multi-sided surfaces that guarantees more flexibility in all directions under refinement. Degree bi-4 is both necessary and sufficient for flexibility-increasing G 1-refinability within a bi-quadratic C 1 spline complex. Sufficiency is proven by two alternative flexibly G 1-refinable constructions exhibiting good highlight line distributions.
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