A Universal Framework for Geometric Information in Product Development

This award supports research which aims to establish a universal theoretical and computational framework aimed at breaking down key barriers that negatively affect the flow of 3D geometric information from engineering design into analysis and manufacturing, while supporting modern machine learning algorithms. The expected results will pave the way for long-term societal impacts by eliminating specific inefficiencies in 3D shape modeling and processing throughout the engineering product development cycle of complex engineered systems. The research developed through this project will also directly impact diversity initiatives for incoming underrepresented and minority engineering undergraduate and graduate students at the University of Connecticut. Through its integrated educational plan, this project will lead to the creation of new educational content for engineering curricula, and its targeted outreach will focus on K-12 students, teachers, and the local school district, serving groups that have traditionally been underrepresented in the engineering disciplines. The project framework uses the observation that any and all valid geometric models must be based on a valid notion of distance and must therefore fully support distance computations and queries. The new framework is based on a novel spherical decomposition of the 3D domain of interest in terms of maximal and mutually tangent spheres. The uniquely defined decomposition, denoted as the Maximal Disjoint Ball Decomposition (MDBD), has several key theoretical and computational attributes, including: (1) the ability to describe the geometry in a hierarchical manner and with a level of detail that can be adjusted on demand; and (2) its intrinsic support for modern geometric machine learning algorithms. Moreover, the framework naturally interfaces with all existing valid geometric representations without requiring representation conversions and integrates with recent powerful advances in CAD that represent shapes as implicitly and hierarchically defined 3D signals. Consequently, the framework has the potential to have a broad impact throughout the computational design and manufacturing process and is an ideal candidate for wide industry adoption. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.