A Study of Form, Function, and Fabrication of 3D Shapes

我们建议研究三维形状的形式、功能和制造及其相关性。形状形式包括局部几何测量、零件组成和形状零件的高级结构组织。最近，计算机图形学研究的一个明显趋势是对几何数据的高级分析和处理越来越感兴趣，更多地关注形状结构而不是几何细节。形状的功能分析就属于这一类；这是一个新兴的领域，分析的重点是整个形状的预期功能，它的组成部分，或部分组装。越来越多的研究人员将注意力从几何分析转向结构分析，最终转向功能分析。这是在最后一条战线取得重大进展的关键时刻。最后，3D制造正在成为技术发展最热门的领域之一，导致许多人和公司重新思考制造过程。随着3D打印技术的快速发展，旨在改善制造过程和结果的新的几何问题出现了。显然，对形式或功能的分析将在形成此类问题的任何解决方案方面发挥关键作用。当我们研究两个概念之间的关系时，例如形式和功能，我们经常对跨越概念但方向相反的分析和综合问题感兴趣。例如，从表单推断函数是一个分析问题。如果我们能够理解功能，那么就有可能创造出新颖的（形状）形式，受到现有形式的启发，服务于预期的功能——这是一个综合或设计问题。通过对3D形状的形式和功能的分析，本研究旨在为有效的3D内容创作和改进3D产品的设计和制造提出新的问题和解决方案。我们希望这项研究的结果能够对设计和工程实践以及娱乐行业（如电脑游戏或视觉效果公司）产生兴趣，这些行业对自动化3D内容创建有迫切的需求。在这两个应用领域，将有大量机会将这项研究产生的新技术商业化。

We propose to study form, function, and fabrication of 3D shapes and their correlations. Shape form encompasses local geometric measurements, part composition, and high-level structural organization of shape parts. Recently, an apparent trend in computer graphics research has seen growing interests in high-level analysis and process of geometry data, focusing more on shape structures than geometric details. Functional analysis of shapes falls into this category; it is an emerging area where the analysis places emphases on the intended functions of an entire shape, its constituent parts, or part assemblies. More and more researchers are shifting their attention from geometry analysis, to structural analysis, and ultimately to functional analysis. It is a critical time to make significant advances in the last front. Finally, 3D fabrication is becoming one of the hottest areas for technology developments, leading many people and firms to rethink the manufacturing process. With the rapid advances in 3D printing technologies, new geometry problems aimed at improving the process and results of fabrication are appearing. Obviously, analyses of form or function would play a key role in shaping any solution of such problems. As we study the relationship between two concepts, e.g., form and function, we are often interested in both analysis and synthesis problems which span the concepts but work in opposite directions. For example, to infer functions from forms is an analysis problem. If we are able to understand functionality, then it is possible to create novel (shape) forms, inspired by existing forms, that serve an intended function — that is a synthesis or design problem. Through analysis of form and function of 3D shapes, the proposed research aims to develop novel problems and solutions for effective 3D content creation and improved design and fabrication of 3D products. We expect the outcome of this research to be of interests to design and engineering practices, as well as the entertainment industry such as computer game or visual effect companies, where there is a critical need for automated 3D content creation. There will be plenty of opportunities, in both application domains, for commercialization of new techniques emerging from this research.