EAGER: Foundations of robust surface parametrization and resampling

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Processing 3D shape information (geometry) efficiently is crucial for many domains: for example, computer-aided design, scientific computing, urban planning and cultural heritage preservation. The amount of geometric data generated and stored is rapidly increasing. The most common way to represent geometric data is with unstructured meshes. Unstructured meshes enjoy many attractive features, but inherently limit the efficiency and accuracy of many algorithms for geometry processing and physical simulation, as well as compactness of representations, compared to image processing algorithms. Mesh parametrization is the fundamental geometric processing technique used both in the context of converting surfaces to image-like representations, and for mapping data to surfaces. While significant progress has been made in the development of high-quality global parametrization algorithms a number of important questions are unresolved, limiting the potentially broad applicability of these techniques.This exploratory project is developing mathematical and algorithmic bases for controlling global parametrization quality as well as limiting the possible amount of local distortion. The techniques being developed, based on the theory of quasiconformal maps and efficient greedy optimization algorithms, will serve as a foundation for future work on robust, high-quality and scalable global parametrization.