GOALI: Toward Super-Robust Geometric Computation for Complex Component Design

该奖项的研究目标是为复杂部件设计所需的稳健几何计算开发理论基础、算法基础和计算框架。新方法基于点表示，通过将连续曲面转换为一组点来表示层深度法线图像。基于层的加法制造将是本项目中加工几何形状的主要目标制造方法。主要的研究活动包括：(1)研究基于点的几何计算理论和相关技术，以提高其健壮性；(2)开发一套有效和高效的基于点的几何运算和相关计算方法；(3)研究基于点的几何运算的并行计算策略和相关算法；(4)通过航空航天和生物医学测试案例验证所开发的原型软件。通过与工业合作伙伴的密切合作，这项研究将产生用于设计复杂产品组件的原型软件，以及将从项目网站公开获得的几何操作和测试用例的库。如果成功，这项研究的结果将提供一个机会，以创建具有显著更复杂的形状的组件设计，以实现更好的性能，如多功能和最低材料和能源的使用。应用实例包括生物工程、航空航天和工具。这种复杂的形状设计也可能给直接数字制造的应用带来革命性的突破，直接数字制造可能是一种颠覆性的制造技术。这项工作还将通过构建软件系统、教材、实验室项目和案例研究来加强研究和教育的基础设施。工程专业的研究生和本科生以及职业生涯中期的专业人士将从课堂教学和参与研究中受益。将利用面向高中生的外展计划来增加少数族裔的参与。设计的实践学习体验和接触真实世界的应用程序将提高国内学生对科学和工程的兴趣，从而增强我们在全球劳动力市场的竞争力。

The research objective of this GOALI award is to develop theoretical foundations, algorithmic infrastructure, and computational framework for robust geometric computation required by complex component design. The new approach is based on a point representation, layer-depth normal image, by converting a continuous surface into a set of points. Layer-based additive manufacturing will be the primary target fabrication approach for the processed geometric forms in this project. Key research activities will include: (1) investigating a point-based geometric computation theory and related techniques for improving its robustness; (2) developing a set of point-based geometric operations and related computational approaches that are effective and efficient; (3) investigating a parallel computing strategy and related algorithms for point-based geometric operations; and (4) verifying the developed prototype software by using aerospace and biomedical test cases. By working closely with an industrial partner, the research will result in prototype software for designing complex product components and a library of geometric operations and test cases that will be publicly available from a project website.If successful, the results of this research will provide an opportunity to create a component design with dramatically more complex shapes for achieving better performance such as multi-functionality and the minimum usage of material and energy. Example applications include bioengineering, aerospace, and tooling. Such complex shape design could also bring about a transformational breakthrough to the applications of direct digital manufacturing, which can be a disruptive manufacturing technology. This work will also enhance the infrastructure for research and education by building software systems, teaching materials, lab projects, and case studies. Graduate and undergraduate engineering students and mid-career professionals will benefit through classroom instruction and involvement in the research. Outreach programs to high school students will be utilized to increase minority participation. The designed hands-on learning experience and exposure to real world applications will increase domestic students' interest in science and engineering and, therefore, strengthen our competitiveness in the global workforce.