Computational and Algorithmic Representations of Geonetric Objects - CARGO: Computational Topology for Exploring Time-varying Volume Data

DMS-0138426Jack S. Snoeyink科学测量和计算机模拟的现象，如空气湍流，核爆炸，或在发动机燃烧，当在高性能计算设施进行，产生大量的四维数据表示变量，如温度和压力如何随时间变化。这个孵化项目汇集了格鲁吉亚理工学院查佩尔山的研究人员，和劳伦斯利弗莫尔国家实验室开发一个原型可视化工具，既可以快速计算这样的等值面从这样的数据集，也提供了一个全球性的摘要，可以指出用户应该在哪里寻找数据集，以找到有趣的现象。采取的方法是扩展工作的轮廓树“参数化函数族的莫尔斯理论”，这足以从2D等值面或切片可视化4D数据。 当科学家、工程师和学生可以探索来自模拟的数据时，他们对模拟过程的理解只会提高。这不仅增加了国家在高性能计算中心的投资回报，而且还可以产生更清洁的发动机。

DMS-0138426Jack S. SnoeyinkScientific measurements and computer simulations of phenomena like air turbulence, nuclear explosions, or combustion in an engine, when conducted at high-performance computing facilities, produce vast amounts of four-dimensional data representing how variables such as temperature andpressure change over time. This incubation project brings together researchers at UNC Chapel Hill, Georgia Tech, and Lawrence Livermore National Labs to develop a prototype visualization tool that can both quickly compute such iso-surfaces from such data sets and also provide a global summary that can indicate where a user should look in the data set to find interesting phenomena.The approach to be taken is to extend work on contour trees to a "Morse theory for a parameterized family of functions" that is sufficient to visualize 4D data from 2D iso-surfaces or slices. When scientists, engineers, and students can explore the data that comes from simulation, their understanding of the process that is being simulated can only improve.This not only increases the return from the national investment in high-performance computing centers, but can also result in, for example, cleaner-burning engines.