Conformal Microstructure Synthesis in Trimmed Trivariate Based V-Reps

Abstract

We present a complete microstructure tiling paradigm for V-rep models, or volumetric models consisting of trimmed trivariates. Existing methods (Massarwi et al., 2018) are employed to tile individual primitive tensor product trivariates in a conformal way, only to handle the intersection of the microstructure tiles with the trimming surfaces of the trivariates. One-to-one and two-to-one bridging tiles are then constructed along the trimmed zones, while tile-clipping is completely avoided. The Boolean operation cases of subtraction, intersection and union are considered. The result is a set of, regular in the interior, possibly heterogeneous, trivariates, that defines the whole microstructure arrangement. This result is fully compatible with iso-geometric analysis as well as heterogeneous additive manufacturing. Examples are presented, including of 3D printed heterogeneous microstructures.