Bézier Award

Gershon Elber, CS, Technion*


Volumetric Representations (V-reps): the Geometric Modeling of the Next Generation

The needs of modern (additive) manufacturing (AM) technologies can no longer be satisfied by boundary representations (B-reps). AM requires the representation and manipulation of interior fields and materials as well. Further, while the need for a tight coupling between design and analysis has been recognized as crucial almost since geometric modeling (GM) has been conceived, contemporary GM systems only offer a loose link between the two, if at all.

For about half a century, the (trimmed) Non Uniform Rational B-spline (NURBs) 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 talk, we seek to examine an extended volumetric representation (V-rep) that successfully confronts 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 between the designed geometry and (Isogeometric) analysis on one hand and the full support of (heterogeneous and anisotropic) additive manufacturing on the other.

Examples and other applications of V-rep GM, including AM and lattice-and micro-structure synthesis and heterogeneous materials, will also be demonstrated.

* This work is in collaboration with many others, including Ben Ezair, Fady Massarwi, Boris van Sosin, Jinesh Machchhar, Annalisa Buffa, Giancarlo Sangalli, Pablo Antolin, Massimiliano Martinelli, Bob Haimes and Stefanie Elgeti.

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