Crossing knot lines in composition of freeform B-spline geometry

摘要

Since the first publications on composition of splines (), it was clear that the composition,T(S), of a tensor product B-spline functionSwith another B-spline functionTis no longer a tensor product B-spline ifScrosses a knot line in the domain ofT. The reason can be easily explained for the fact that the new functionT(S)has a finite continuity that is governed by the knot line ofTthat is not, in general, an iso-parametric direction of the resulting compositionT(S).In this work, we propose two approaches to circumvent this long standing difficulty and reconstruct precise representations forT(S)that are either tensor products or trimmed geometry. We focus our discussion on surface-trivariate compositions,T(S), while we present examples and results, for both reconstruction approaches, for microstructure surfaces and trivariates embedded in surface and trivariate deformation functions.