A Review of a B-spline based Volumetric Representation: Design, Analysis and Fabrication of Porous and/or Heterogeneous Geometries

The needs of modern (additive) manufacturing (AM) technologies can no longer be satisfied by geometric modeling tools that are based on boundary representations (B-reps) - AM requires the representation and manipulation of interior heterogeneous fields and materials. Further, while the need for a tight coupling between design and analysis has been recognized as crucial almost since geometric modeling (GM) was conceived, contemporary GM systems only offer a loose link between the two, if at all. For more than half a century, the (trimmed) Non-Uniform Rational B-spline (NURBs) surface representation has been the B-rep of choice for virtually all the GM industry. Fundamentally, B-rep GM has evolved little during this period. In this work, we review almost a decade of research and development in extending this boundary representation to a B-spline based, volumetric representation (V-rep) that successfully confronts the existing and anticipated design, analysis, and manufacturing foreseen challenges. We have extended all fundamental B-rep GM operations, such as primitive and surface constructors, and Boolean operations, to trimmed trivariate V-reps. This enables the much-needed tight link between the designed geometry and (iso-geometric) analysis on one hand and the full support of (additive) manufacturing of porous, (graded-) heterogeneous and anisotropic geometries, on the other. Examples and applications of V-rep GM, that span design, analysis and optimization, and AM, of lattice- and micro-structure synthesis as well as graded-heterogeneity, are demonstrated, with emphasis on AM.