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

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.