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

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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.