III-COR: Multivariate Simplex Splines for Data Modeling and Visualization

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The goal of this research project is to develop a novel unified computational framework for data representation, multi-scale material modeling, and visualization of heterogeneous datasets that will support information integration, access and analysis. The technical solution is uniquely founded upon the mathematically rigorous theory of multivariate simplex splines, which have until now remained severely under-explored in data modeling and visualization. The research activities have the following four major themes: (1) the comprehensive study of new important theoretical properties of multivariate simplex splines and key numerical algorithms, with an emphasis on mathematical rigor, efficiency, accuracy, and robustness; (2) the development of new, robust techniques for modeling complex geometry/topology and representing volumetric multidimensional material distributions over any tetrahedral domains; (3) the development of data visualization technologies for simplex splines; and (4) application of simplex splines to a wide range of problems in modeling and visualization through the algorithm design and toolkit implementation. All of these activities are expected to move us one step closer to our ultimate, longer-term goal of generally promoting volumetric splines as robust, general, and strikingly powerful data modeling approaches for use in information integration and relevant applications. Research results of this project will be disseminated through the project's website (http://www.cs.sunysb.edu/~qin/research.html).