Crossing knot lines in composition of freeform B-spline geometry

In this work, we propose two approaches to circumvent this long standing difficulty and reconstruct precise representations for T(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.