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

职业：用于计算机辅助设计的分部实体几何：原理、算法、工作流程、

• 批准号: 2048182
• 负责人: Vinayak Krishnamurthy
• 金额: $ 55.46万
• 依托单位: Texas A&M Engineering Experiment Station
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2021
• 资助国家: 美国
• 起止时间: 2021-08-01 至 2026-07-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2048182&HistoricalAwards=false
• 关键词: CAREER; Partitive; Solid; Geometry; Computer

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.

该学院早期职业发展计划（CAREER）资助将为新的几何建模框架（部分实体几何）奠定基础，用于设计复杂的二维和三维几何图案。建模复杂的图案（例如细胞结构）是固有的。使更多设计师和工程师能够使用复杂的几何建模是促进许多工程学科（包括汽车、航空航天）颠覆性创新的关键。建造，增材制造、力学、热流体和声学领域的当前生成设计和建模工具是高度自动化的，这使得设计师很难探索新想法并提出“假设”问题。这种表示形式还应同时支持计算高效的机械评估，例如有限元模拟，这将使设计人员能够应用他们的专业知识、想法和创造力。交互时间长且直观，对于认真的人很有用因此，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应用中。学习机制，年轻观众将能够轻松生成复杂的形状，通过 3D 打印将其原型化为拼图，并通过玩拼图来发现几何的基本原理，这将从根本上改变孩子们通过双手发展空间推理能力的方式。 - 设计和原型制作这项研究将引入空间填充形状作为部分实体几何的基础新颖形状表示，这将使正向设计工作流程能够为生成和程序设计创建复杂的形状和结构。目前，该赠款将整合这种表示。将开发高效且稳健的形状表示方法，并将其嵌入到交互式软件工作流程中，使用户能够直接直观地创建作为算法的形状。将进行人体研究，以研究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部分实体几何，以设计各种互锁形状、功能分级的细胞结构。和拉胀材料。将对用户生成的几何模型进行数值评估并通过机械测试来发现用户提供的输入几何形状与所得形状的行为之间的关系。综合教育和推广计划将包括本科生实习和培训。新的研究生课程将。该研究还将向研究人员和公众分发免费的网络建模工具，创建一个大型的复杂几何模型在线百科全书供公众使用，该赠款将通过夏令营向 K-12 学生介绍交互式生成设计。通过基于游戏的有形学习促进空间推理。该奖项反映了 NSF 的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。

项目成果

LayerLock: Layer-Wise Collision-Free Multi-Robot Additive Manufacturing Using Topologically Interlocked Space-Filling Shapes

LayerLock：使用拓扑互锁空间填充形状的分层无碰撞多机器人增材制造

• DOI: 10.1016/j.cad.2022.103392
• 发表时间: 2022-08-01
• 期刊: Comput. Aided Des.
• 作者: Vinayak R. Krishnamurthy;Laxmi Poudel;M. Ebert;Daniel H. Weber;Rencheng Wu;Wenchao Zhou;E. Akleman;Zhenghui Sha
• 通讯作者: Zhenghui Sha

Voronoi Spaghetti & VoroNoodles: Topologically Interlocked, Space-Filling, Corrugated & Congruent Tiles

沃罗诺伊意大利面

• DOI: 10.1145/3550340.3564229
• 发表时间: 2022-11
• 期刊: SA '22: SIGGRAPH Asia 2022 Technical Communications
• 作者: Mullins, Cassie;Ebert, Matthew;Akleman, Ergun;Krishnamurthy, Vinayak
• 通讯作者: Krishnamurthy, Vinayak

SplitCode: Voronoi-based error exaggeration for authentication of manufactured parts

SplitCode：基于 Voronoi 的错误夸大，用于制造零件的验证

• DOI: 10.1016/j.jmsy.2022.10.005
• 发表时间: 2022-10
• 期刊: Journal of Manufacturing Systems
• 影响因子: 12.1
• 作者: Adhikari, Riddhi R.;ElSayed, Karim A.;Akleman, Ergun;Panchal, Jitesh H.;Krishnamurthy, Vinayak
• 通讯作者: Krishnamurthy, Vinayak