Geometry Processing Approaches for Defective Discrete Surfaces

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Artists and software developers in the computer graphics field are continually modeling 3D objects as discrete surfaces (triangle and quadrilateral meshes). Modeling surfaces involves multiple routinely used procedures such as deforming, smoothing, and flattening. Such procedures rely on geometry processing operators. Often, the surfaces are not so well-behaved, and exhibit defects such as holes and disconnected components. These "defective surfaces" are problematic as they do not lend themselves to elementary operations, such as computations of derivatives, which form the basis of geometry operators. As a result, current geometry operators cannot handle most of the defective surfaces. This represents a substantial practical challenge, as defective surfaces are all over the place in computer graphics, most notably in industry and in 3D object repositories. Our long-term vision is to design a new geometry processing paradigm that can handle defective surfaces. To derive a general approach that works for all operators, we will successively examine pairs of operators and defect types. Our first objective investigates meaningful results of an operator when dealing with a specific defect. User studies will reveal what participants perceive as meaningful results. With these insights, our second objective focuses on deriving an alternative surface representation for defective surfaces. The alternative representation will be equivalent to the defective surface with respect to the meaningful results for the operator and type of defect. By design, this alternative representation will allow the robust computation of the geometry operator. The third objective is to derive an approach transferring the results of the operator back to the original defective surface, again in a way that preserves the meaningfulness identified in the user study. The long-term goal is to investigate all operators and types of defects, and to design a unified alternative representation. This research is important for academic researchers and end users in industry, as it will broaden the range of applicability of geometry processing operators. It is significant for the computer graphics field, but also more generally, for science and engineering. The outcomes of the research will provide three core benefits: (1) insights into what end users see as meaningful results of geometry operators applied to defective surfaces, (2) an alternative representation for defective surfaces, and (3) a process to apply geometry operators on defective surfaces by back-and-forth conversion through the alternative representation. Canada has a vast ecosystem of companies working in computer graphics. These companies rely on the constant advancement of theoretical approaches operating on the surfaces of 3D objects. Furthermore, the highly qualified personnel trained through this research program will have access to quality jobs here in Canada, while also increasing the expertise of Canadian companies.