Volumetric Modeling

The needs of modern (additive) manufacturing (AM) technologies can be satisfied no longer by B-reps, as AM requires the representation and manipulation of interior fields as well. Further, while the need for a tight coupling between the 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 about half a century, (trimmed) Non Uniform Rational B-spline (NURBs) surfaces has been the representation of choice for virtually all the GM industry. Fundamentally, B-rep GM has evolved little during this period. In this talk, we seek to examine an extended volumetric representation (V-rep) that will successfully confront the existing and anticipated design, analysis, and manufacturing foreseen challenges.  We extend 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 to (Isogeometric) analysis on one hand and the full support of additive manufacturing on the other.
Further, special capabilities in supporting Isogeometric analysis will also be presented, that enable robust queries over the V-reps, including precise contact analysis, maximal penetration depth, and accurate integration over trimmed domains. Examples and other applications of V-rep GM, including AM and lattice- and micro-structure synthesis will also be demonstrated.
In collaboration with many others, including Ben Ezair, Fady Massarwi, Boris van Sosin, Annalisa Buffa, Giancarlo Sangalli, Pablo Antolin and Massimiliano Martinelli.