CAREER: Partitive Solid Geometry for Computer-Aided Design: Principles, Algorithms, Workflows, & Applications

这项学院早期职业发展计划(Career)赠款将为设计复杂的二维和三维几何图案奠定新的几何建模框架-分区立体几何-的基础。对复杂的图案进行建模，如细胞结构，是几个涉及国家利益的领域的固有问题，包括消费品、运动和军事防护装备，以及曲面微型化电子产品。使更多的设计师和工程师能够使用复杂的几何建模，对于促进汽车、航空航天、建筑、添加剂制造、机械、热流体和声学领域等许多工程领域的颠覆性创新至关重要。目前用于生成性设计和建模的工具都是高度自动化的，这使得设计师很难探索新的想法和提出“假设”问题。需要一种新的几何实体表示法，使设计者能够在设计蜂窝结构时应用他们的专业知识、想法和创造力。这样的表示还应该同时支持计算效率高的机械评估，例如有限元模拟。这项研究将使所有人都可以使用复杂的几何建模，实时和直观地与之交互，对严肃的工程设计有用，并可用于娱乐学习。因此，新手和专家设计师将能够创造性地将他们的知识应用于从新材料设计到新建筑形式和安全产品的各种应用。这笔赠款将进一步支持一种新型的学习机制，在这种机制下，年轻观众将能够轻松地生成复杂的形状，通过3D打印将其作为拼图的原型，并通过玩拼图来发现几何的基本原理。这将从根本上改变儿童通过动手设计和原型活动发展空间推理能力的方式。本研究将引入空间填充形状作为分区立体几何的潜在新形状表征，这将使前向设计工作流程能够创建用于生成性和程序性设计的复杂形状和结构。有了这个表示，赠款将把目前不同的方法，如隐式建模、中轴表示和Voronoi镶嵌到一个单一的统一形状表示方法中。将开发高效和强大的算法，并将其嵌入交互式软件工作流中，使用户能够直接和直观地创建以前不可能实现的形状。将进行人类主题研究，以调查这些新的工作流程如何促进工程设计中的创造性思维。将采用假设驱动的方法来研究用于设计各种连锁形状、功能梯度蜂窝结构和伸展材料的分割固体几何。用户生成的几何模型将通过数值和机械测试进行评估，以发现用户提供的输入几何与结果形状的行为之间的关系。一项全面的教育和推广计划将包括本科生实习和一门新的研究生课程。该项目将向研究人员和公众分发免费的基于网络的建模工具。这项研究还将创建一个大型在线百科全书，其中包括复杂的几何模型，供公众使用。通过夏令营，奖助金将向K-12年级的学生介绍交互式生成设计，通过基于游戏的有形学习来促进空间推理。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 Faculty Early Career Development Program (CAREER) grant will establish the foundations of a new geometric modeling framework – partitive solid geometry – for the design of complex two- and three-dimensional geometric patterns. Modeling complex patterns, such as cellular structures, is intrinsic to several areas of national interest, including consumer products, protective gear for sports and the military, and curved miniaturized electronics. Making complex geometric modeling accessible to more designers and engineers is key to facilitating disruptive innovations in many engineering disciplines, including the automotive, aerospace, construction, additive manufacturing, mechanics, thermo-fluids, and acoustics fields. Current tools for generative design and modeling are highly automated, which makes it difficult for designers to explore new ideas and ask “what-if” questions. A new representation of geometric solids is needed that will allow designers to apply their expertise, ideas, and creativity in designing cellular structures. Such a representation should also simultaneously support computationally efficient mechanical evaluation, such as finite element simulation. This research will make complex geometric modeling available to all, real-time and intuitive to interact with, useful for serious engineering design, and usable for recreational learning. As a result, novice and expert designers will be able to creatively apply their knowledge in applications ranging from the design of new materials to new architectural forms and safe products. This grant will further enable a new type of learning mechanism, where younger audiences will be able to easily generate complex shapes, prototype them as puzzles through 3D printing, and play with the puzzles to discover basic principles of geometry. This will fundamentally transform the way children develop their spatial reasoning ability through hands-on design and prototyping activities.This research will introduce space-filling shapes as the underlying novel shape representation for partitive solid geometry, which will enable forward design workflows for the creation of complex shapes and structures for generative and procedural design. With this representation, the grant will integrate currently disparate methods such as implicit modeling, medial axis representations, and Voronoi tessellations into a single unified methodology for shape representation. Efficient and robust algorithms will be developed and embedded within interactive software workflows that will allow users to directly and intuitively create shapes that were not possible before. Human subject studies will be conducted to investigate how these new workflows can promote creative thinking in engineering design. A hypothesis-driven approach will be taken to investigate partitive solid geometry for designing a wide variety of interlocking shapes, functionally graded cellular structures, and auxetic materials. User-generated geometric models will be evaluated numerically and through mechanical tests to discover the relationship between the input geometry provided by the user and the behavior of the resulting shapes. A comprehensive education and outreach plan will include undergraduate internships and a new graduate course. The project will disseminate a free web-based modeling tool to researchers and the public. The research will also create a large online encyclopedia of complex geometric models for the public to use. Through summer camps, the grant will introduce interactive generative design to K-12 students to promote spatial reasoning through play-based tangible learning.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.