EAGER: Foundations of robust surface parametrization and resampling

有效地处理3D形状信息（几何）对于许多领域至关重要：例如，计算机辅助设计，科学计算，城市规划和文化遗产保护。生成和存储的几何数据量正在迅速增加。表示几何数据的最常用方法是使用非结构化网格。非结构化网格具有许多吸引人的特性，但与图像处理算法相比，非结构化网格固有地限制了许多几何处理和物理模拟算法的效率和精度，以及表示的紧凑性。网格参数化是基本的几何处理技术，用于将曲面转换为类似图像的表示，以及将数据映射到曲面。虽然已经取得了显着的进展，在高品质的全球参数化算法的一些重要的问题还没有得到解决，限制了潜在的广泛适用性，这些techniques.This探索性的项目是开发数学和算法的基础，控制全球参数化的质量，以及限制可能的本地失真量。正在开发的技术，准共形映射理论和高效的贪婪优化算法的基础上，将作为未来工作的基础上强大的，高品质的和可扩展的全球参数化。

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.