CRII: III: Topology-Driven, Multi-Scale Tensor Field Visualization

Oregon State University, Corvallis OR

Investigators

Abstract

Multi-dimensional modeling has enabled and is enabling breakthroughs in many research fields such as science, engineering and art, and is constantly producing high dimensional data that requires analyzing, mining and visualization. The size of the data is often big as the fine resolution of the modeling warrants accuracy in the theories developed. The stress and strain tensors in fluid and solid mechanics, the diffusion tensor in medical imaging, the curvature tensor in shape modeling, and the deformation gradient tensor in earthquake engineering are just a few examples. These tensors appear in the form of data arrays, and having the capability of visualizing the topological structures and their dynamics can potentially empower domain scientists with new insights and possibly new fundamental understandings of the physical and biological phenomena. In addition to sharing the knowledge and tools created through this research among scientific communities, the investigator will incorporate the work into teaching materials for undergraduate and graduate students and into summer programs for K-12 students. Due to the complexity and extensiveness of the data, any visualization has to be mindful of occlusion and cluttering. In particular, this project will investigate theories and algorithms that support topology-driven, multi-scale visualization of three-dimensional, second-order tensor fields. One focus will be on the smooth transition of these tensor quantities from one scale to another to ensure consistency in the topological structures and preservation of topological features. The other focus is on defining all possible topologies and developing visualization algorithms that represent the dynamics of the field topology at one scale.