HCC: Medium: Robust and Accurate Modeling with Multifield Geometry

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Computer tools for creating, analyzing and modifying geometry are the core component in computer-aided design systems, indispensable for engineering and product prototyping, surgical simulation, prosthesis design, dentistry, architecture, computer animation and games. There is a considerable demand for high-level modeling tools, expressing the user?s intent directly while being capable of handling complex models robustly. Surface optimization techniques unify traditional ab initio modeling of high-quality surfaces and manipulation of existing geometric data in a single natural framework by specifying suitable optimization functionals governing the surface behavior. This framework is conceptually representation-independent: the surface can be approximated by spline patches, subdivision surfaces, meshes or in implicit form. While this framework is highly appealing for practical applications, surface optimization rarely finds its way into industrial applications, as existing interactive techniques are not sufficiently robust, while the more precise and reliable methods are too slow to be used interactively.This research project develops fundamental mathematical and algorithmic techniques essential for bringing surface optimization methods to mainstream geometric modeling applications. The research is addressing the following problems: shape representation and its accuracy, such that the modeled surfaces depend solely on the user input and not the particular choice of sampling or approximation basis; robust and efficient modeling algorithms to ensure predictable and responsive behavior in interactive applications; diverse control to allow sufficient freedom for arbitrary shape manipulation. The investigated approach has two key components: multifield geometry descriptions, building on ideas from discrete geometry, high-order geometric modeling, and finite elements and novel multiscale numerical solvers that combine robust global algorithms at coarse scales with fast and accurate algorithms at fine scales to achieve the performance and robustness needed in applications. The new methods are explored in the context of high-level modeling tasks, including modeling from two-dimensional projections or drawings, feature-based and appearance-based editing and template fitting for dental CAD.