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

该研究项目的目标是开发一种新的统一计算框架，用于数据表示，多尺度材料建模和异构数据集的可视化，以支持信息集成，访问和分析。该技术解决方案独特地建立在多元单纯形样条的数学严格理论基础上，该理论迄今为止在数据建模和可视化方面仍然严重不足。研究活动有以下四个主要主题：（1）全面研究多元单纯形样条和关键数值算法的新的重要理论性质，重点是数学的严谨性，效率，准确性和鲁棒性;（2）开发新的，鲁棒的技术，用于模拟复杂的几何/拓扑结构，并表示任何四面体域上的体积多维材料分布;（3）单纯形样条数据可视化技术的发展;（4）通过算法设计和工具包实现，将单纯形样条应用于建模和可视化中的广泛问题。所有这些活动预计将使我们更接近我们的最终，长期目标，普遍促进体积样条作为强大的，一般的，和惊人的强大的数据建模方法，用于信息集成和相关的应用程序。该项目的研究成果将通过该项目的网站（http：//www.cs.sunysb.edu/jiangqin/research.html）传播。

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).