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

这项教师早期职业发展计划（Career）资助将为设计复杂的二维和三维几何图案建立一个新的几何建模框架——分形立体几何——的基础。建模复杂的模式，如细胞结构，是内在的几个领域的国家利益，包括消费品，运动和军事防护装备，弯曲的微型电子产品。使更多的设计师和工程师能够使用复杂的几何建模是促进许多工程学科突破性创新的关键，包括汽车、航空航天、建筑、增材制造、机械、热流体和声学领域。当前用于生成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想法并提出“假设”问题。我们需要一种新的几何实体的表现形式，使设计师能够在设计细胞结构时运用他们的专业知识、思想和创造力。这种表示还应同时支持计算效率高的力学评估，如有限元模拟。这项研究将使复杂的几何建模对所有人都可用，实时和直观的交互，对严肃的工程设计有用，也可用于娱乐学习。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。这笔拨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地生成复杂的形状，通过3D打印将它们作为谜题的原型，并通过谜题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制作活动来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颖形状表示，这将为生成和程序设计的复杂形状和结构的创建提供正向设计工作流程。有了这种表示，该基金将把目前不同的方法，如隐式建模、中轴表示和Voronoi镶嵌，整合到一个统一的形状表示方法中。高效和强大的算法将被开发并嵌入到交互式软件工作流中，这将允许用户直接和直观地创建以前不可能实现的形状。将进行人体研究，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。一个假设驱动的方法将采取研究分割固体几何设计各种各样的互锁形状，功能梯度的细胞结构，和辅助材料。用户生成的几何模型将通过数值和力学测试进行评估，以发现用户提供的输入几何形状与最终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实习和一个新的研究生课程。该项目将向研究人员和公众传播一个免费的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，赠款将向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。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值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.