Interactive Tensor Field Visualization

这个项目解决了科学可视化中一个公认的研究挑战--如何可视化张量场。张量场广泛存在于各种科学和工程学科中，例如流体动力学、力学、材料科学和地球科学，在这些学科中，张量场可以量化各种材料上的反作用力。张量场特别难以可视化，因为(A)大量的变量(例如，对于3D二阶张量为9)及其相互作用，以及(B)所涉及的大数据集，特别是对于时变张量场。目前，用于理解张量的可视化方法非常有限。该项目将提供一套新颖直观的基于形变和智能代理的可视化方法，帮助科学家和工程师交互探索和了解张量场的性质和结构。从概念上讲，张量对它们周围的空间施加力。这个项目的方法是允许张量场通过使代表该空间的理想化元素变形来显示自己。目标是以交互方式进行这些变形，以便用户可以检查可能感兴趣的数据的不同区域和属性。该项目将探索变形的不同实现，以及使用不同的张量分解方法来创建更直观的有意义的变形。该项目还将研究智能代理，这些代理将在张量场中寻找感兴趣的特征，以便更好地展示它们。这个项目的想法和方法将使技术能够理解整个科学和工程中的基本问题，并将在真实的数据集上进行测试。

This project addresses a well-recognized research challenge in scientific visualization - how to visualize tensor fields. Tensor fields are prevalent in a variety of scientific and engineering disciplines such as fluid dynamics, mechanics, material science, and earth sciences, where they quantify the opposing forces on various materials. Tensor fields are particularly hard to visualize because of (a) the large number of variables (e.g. 9 for 3D second order tensors) and their interplay, and (b) the large data sets involved, particularly for time varying tensor fields. Currently, there are a very limited number of visualization methods for understanding tensors. This project will provide a suite of novel and intuitive visualization methods, based on deformation and intelligent agents, to help scientists and engineers interactively explore and understand the nature and structure of tensor fields. Conceptually, tensors exert force on the space around them. This project's approach is to allow the tensor field to manifest itself by deforming idealized elements representing that space. The goal is to do these deformations interactively so users can examine different regions and properties of the data that may be of interest. The project will explore different implementations of the deformations, as well as the use of different methods of tensor decomposition to create more intuitively meaningful deformations. The project will also investigate intelligent agents that will seek out features of interest in the tensor field, so that they may be better displayed. Ideas and methods from this project will be enabling technologies towards understanding fundamental problems throughout science and engineering, and will be tested against real data sets.