The needs of modern additive manufacturing (AM) technologies can no longer be satisfied by boundary representations (B-reps), as AM requires the representation and manipulation of interior fields and materials. 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 about half a century, trimmed Non Uniform Rational B-spline (NURBs) surfaces have 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 trimmed NURBs 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 to Isogeometric analysis on one hand and the full support of heterogeneous and anisotropic additive manufacturing on the other.
Time permitting, special capabilities toward the support of Isogeometric analysis will 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 with heterogeneous materials also will be demonstrated.
In collaboration with many others, including Ben Ezair, Fady Massarwi, Boris van Sosin, Jinesh Machchhar, Annalisa Buffa, Giancarlo Sangalli, Pablo Antolin, and Massimiliano Martinelli.
Gershon Elber is a professor in the Computer Science Department at the Israel Institute of Technology (the Technion). His research interests span computer-aided geometric designs and computer graphics. Elber received a BSc in computer engineering and an MSc in computer science from the Technion in 1986 and 1987, respectively, and a PhD in computer science from the University of Utah in 1992. He is a member of SIAM and the ACM. He was a Visiting Professor at the University of Washington and at Boeing (2006-2007) and MIT (2018). He founded GeomCore, a geometry-related company, in his sabbatical in 2000.
Elber has served on the editorial board of the Computer Aided Design, Computer Graphics Forum, The Visual Computer, Graphical Models, and the International Journal of Computational Geometry & Applications and has served in many conference program committees including Solid Modeling, Shape Modeling, Geometric Modeling and Processing, Pacific Graphics, Computer Graphics International, and Siggraph. Elber was one of the paper chairs of Solid Modeling 2003 and Solid Modeling 2004, one of the conference chairs of Solid and Physical Modeling 2010, the chair of GDM 2014, the conference co-chair of SIAM GD/SPM 2015, and the conference co-chair of SPM 2018.
He has published over 200 papers in international conferences and journals, presented 10 keynote invited talks, and is one of the authors of “Geometric Modeling with Splines—An Introduction.” Elber received the Ray and Miriam Klein Technion Research Award in 1998; the Hershel Rich Technion Innovation Award in both 2002 for “Virtual Marionettes—Remote Collaboration Animation and Interaction,” and in 2019 for “Volumetric Modeling Solutions”; the CodeArt award in 2003 (National Art in Computing Contest, third place); the John Gregory Memorial Award in 2011, for “Appreciation for Outstanding Contributions in Geometric Modeling”; and the Solid Modeling Association Pioneers Award in 2016.
Elber was the vice dean for computing and the vice dean for teaching in the Computer Science Department at the Technion from 1997-1999 and 2002-2004, respectively, and was the deputy vice president for computing for the Technion from 2010-2013. Elber can be reached at the Technion, Israel Institute of Technology, Department of Computer Science, Haifa 32000, ISRAEL. Email: firstname.lastname@example.org, Fax: 972-4-829-5538.