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

本研究的长期目标是系统地开拓一种基于连续多项式表示的新的几何流形理论，并将这种严格的理论应用于形状几何和高维多属性数据建模，分析和可视化，特别强调可视化计算应用。该研究小组正在探索新的几何流形理论在微分几何，数值逼近理论，计算拓扑学和线性代数的接口。几何流形理论的研究使得对具有复杂几何、任意拓扑结构和丰富几何特征的高维多属性体数据集进行精确有效的建模成为可能。该研究为快速数据建模和数据分析提供了良好的理论基础。它有可能简化整个虚拟原型过程的数字工程在未来与长期的研究工作，通过加快数据转换从离散样本连续流形和样条为中心的可视化数据表示。

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.