EAGER: Bridging Geometric Manifold Theory and Higher-Dimensional Data Modeling for Visual Computing

这项研究的长期目标是系统地开创一种基于连续多项式表示的新的几何流形理论，并将这一数学严谨的理论应用于形状几何和高维、多属性数据的建模、分析和可视化，特别是视觉计算应用。研究小组正在探索新的几何流形理论，涉及微分几何、数值逼近理论、计算拓扑和线性代数。新的重要几何流形理论的研究使得对几何形状复杂、拓扑任意、几何特征丰富的高维、多属性体数据集的精确有效建模成为可能。这一以理论为中心的研究为快速数据建模和数据分析提供了坚实的理论基础。通过加快从离散样本到连续流形和以样条线为中心的可视数据表示的数据转换，它有可能通过更长期的研究努力来简化未来数字工程的整个虚拟原型过程。

The long-term goal of this research aims to systematically trailblaze a novel geometric manifold theory founded upon continuous polynomial representations, and to apply this mathematically-rigorous theory to both shape geometry and higher-dimensional, multi-attribute data modeling, analysis and visualization, with a special emphasis on visual computing applications. The research team is exploring new geometric manifold theory at the interface of differential geometry, numerical approximation theory, computational topology, and linear algebra. The study of new and important geometric manifold theory enables the accurate and effective modeling of higher-dimensional, multi-attribute volumetric datasets which are of complicated geometry, arbitrary topology, and with rich geometric features. This theory-centered research provides a sound theoretical foundation for rapid data modeling and data analysis. It has a potential to streamline the entire virtual prototyping processes for digital engineering in the future with longer-term research efforts by expediting data transformation from discrete samples to continuous manifold and spline-centric visual data representations.