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.

这个教师早期职业发展计划（CAREER）赠款将建立一个新的几何建模框架的基础-部分立体几何-复杂的二维和三维几何图案的设计。模拟复杂的图案，如细胞结构，是国家利益的几个领域所固有的，包括消费品，体育和军事保护装备，以及弯曲的小型化电子产品。让更多的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颠覆性创新的关键，包括汽车，航空航天，建筑，增材制造，机械，热流体和声学领域。目前用于生成式设计和建模的工具是高度自动化的，这使得设计师很难探索新的想法并提出“假设”问题。需要一种新的几何实体表示法，使设计人员能够在设计细胞结构时运用他们的专业知识、想法和创造力。这种表示还应同时支持计算效率高的机械评估，例如有限元模拟。这项研究将使复杂的几何建模提供给所有人，实时和直观的互动，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应用他们的知识，从新材料的设计到新的建筑形式和安全产品。这笔赠款将进一步实现一种新型的学习机制，年轻的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动手设计和原型活动来发展他们的空间推理能力的方式。这项研究将引入空间填充形状作为部分立体几何的基础新形状表示，这将使向前的设计工作流程能够创建复杂的形状和结构，用于生成和程序设计。有了这种表示，赠款将整合目前不同的方法，如隐式建模，中轴表示，和Voronoi镶嵌成一个单一的统一的方法，形状表示。将开发高效和强大的算法，并嵌入交互式软件工作流程中，使用户能够直接直观地创建以前不可能的形状。将进行人类受试者研究，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。一个假设驱动的方法将采取调查partitive立体几何设计各种各样的联锁形状，功能梯度细胞结构，和拉胀材料。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形状与结果形状的行为之间的关系。一个全面的教育和推广计划将包括本科生实习和一个新的研究生课程。该项目将向研究人员和公众免费传播一个基于网络的建模工具。这项研究还将创建一个大型的复杂几何模型在线百科全书，供公众使用。通过夏令营，该基金会将向K-12学生介绍互动生成设计，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

• DOI: 10.1016/j.cad.2022.103392
• 发表时间: 2022-08-19
• 期刊: COMPUTER-AIDED DESIGN
• 影响因子: 4.3
• 作者: Krishnamurthy, Vinayak;Poudel, Laxmi;Sha, Zhenghui
• 通讯作者: Sha, Zhenghui

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
• 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
• 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