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Design, Analysis, Optimization, and Fabrication of Heterogeneous Lattices via Spline-based Volumetric Representations

19 Nov 2025

Boundary representations (B-reps) can no longer satisfy the needs of modern (additive) manufacturing (AM) technologies. AM requires the representation and manipulation of interior fields and materials. Further, while the need for a tight coupling between design and analysis has been recognized as crucial almost since geometric modelling (GM) has been conceived, contemporary GM systems only offer loose links between the two.

For more than half a century, the (trimmed NURBs) surface representation has been the B-rep of choice for the GM industry. Fundamentally, B-rep GM has evolved little during this period. Herein, we present a, B-spline based, volumetric representation (V-rep) that successfully confronts existing and anticipated design, analysis, and manufacturing foreseen challenges.  Among others, full support of AM of porous (lattice) and/or heterogeneous artifacts is offered, as well as direct compatibility with the B-rep contemporary representation as well as iso-geometric analysis (IGA).

Examples and applications of V-rep GM, that span design, analysis and optimization, and AM, of (heterogeneous) lattice- and micro-structures, including compliant functional lattice mechanisms, will be demonstrated.

Keywords: Trivariate splines, Functionally graded materials, Micro-structures

Work in collaboration with many others, including Ben Ezair, Fady Massarwi, Boris van Sosin, Jinesh Machchhar, Q Youn Hong, Sumita Dahiya, Annalisa Buffa, Giancarlo Sangalli, Pablo Antolin, Massimiliano Martinelli, Bob Haimes, and Stefanie Elgeti.

Speaker: Gershon Elber, Professor, Computer Science, Technion, IIT