A Universal Framework for Geometric Information in Product Development

该奖项支持旨在建立通用理论和计算框架的研究，旨在打破对3D几何信息流从工程设计到分析和制造产生负面影响的关键障碍，同时支持现代机器学习算法。预期结果将通过在复杂工程系统的工程产品开发周期中消除3D形状建模和处理的具体低效，为长期的社会影响铺平道路。通过该项目开展的研究还将直接影响康涅狄格大学新生、代表性不足和少数族裔工科本科生和研究生的多样性倡议。通过其综合教育计划，该项目将导致为工程课程创建新的教育内容，其有针对性的外联活动将侧重于K-12学生、教师和当地学区，服务于传统上在工程学科中代表性不足的群体。项目框架采用这样的观点，即任何和所有有效的几何模型都必须基于有效的距离概念，因此必须完全支持距离计算和查询。新的框架基于3D感兴趣区域的最大球面和相切球面的一种新的球面分解。唯一定义的分解，称为最大不相交Ball分解(MDBD)，具有几个关键的理论和计算属性，包括：(1)能够以分层的方式和可以根据需要调整的细节级别来描述几何；(2)它对现代几何机器学习算法的内在支持。此外，该框架自然地与所有现有的有效几何表示相接口，而不需要表示转换，并与CAD中最新的强大进展相集成，该CAD将形状表示为隐式和分层定义的3D信号。因此，该框架有可能在整个计算设计和制造过程中产生广泛的影响，是广泛采用行业的理想候选者。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

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.