Exploration of 3D motorcycle complexes from hexahedral meshes

Shape decompositions that are guided by a motorcycle graph endow topological properties that are relevant for many engineering applications, such as T-spline fitting, shape compression and structured mesh generation. While for the surface case this is a widely studied and well-established construction, the concept of motorcycle graph was lifted to volumes only recently (Brückler et al., 2021). Due to this recent introduction, the generation of volumetric motorcycle graphs that fulfill application dependent criteria, such as minimal number of blocks or high approximation capabilities, is still an open problem. In this article we study and compare two alternative approaches to the computation of volume shape decompositions guided by a motorcycle graph. The proposed methodologies are designed to optimize alternative application-dependent quality criteria and, overall, perform better than prior art in most of the cases.