CAREER: Vector and Tensor Field Design for Graphics and Visualization

矢量场和张量场在许多科学和工程学科中都是基本的。这项研究探索了可变形区域上随时间变化的矢量场和张量场的设计和控制，这一研究具有在计算机图形学和科学可视化内外的广泛应用的潜力。这些应用包括：天气预报和海啸模拟、建筑和飞机设计和测试、电磁模拟、指纹分析、电影和游戏的特殊效果、计算机生成的艺术、形状和运动分析和编辑以及教育。在这个项目中，研究人员确定了核心功能，并开发了有效的算法来支持依赖时间的域上依赖时间的矢量场和张量场的设计和控制。常见的设计操作是通过使用许多图形和可视化任务作为试验台来确定的，例如矢量场可视化和流体模拟。提供了有效的算法来跟踪和控制矢量场或张量场随时间的结构变化，这使得能够控制场的拓扑和分析行为。这些算法背后的思想分别基于微分几何和动力学系统中的纤维丛和分叉的概念。此外，研究人员还探索了新的可视化技术，以解决可变形区域上随时间变化的矢量场和张量场。研究的结果是，核心设计操作被集成到系统中，这些算法的实现被编译到库中，以支持直接集成到主机应用程序中。设计系统及其配套图书馆将会向公众发放。就其对教育的影响而言，设计体系被整合到理工科本科生的课程中。

Vector and tensor fields are fundamental in many science and engineering disciplines. This research explores the design and control of time-dependent vector and tensor fields over deformable domains, which have the potential of benefiting a wide variety of applications within and outside computer graphics and scientificvisualization. These applications include: weather prediction and tsunami simulation, building and aircraft design and testing, electromagnetic simulation, fingerprint analysis, special effects for movies and games, computer-generated arts, shape and motion analysis and editing, and education. In this project, the investigator identifies core functionalities and develops efficient algorithms to support the design and control of time-dependent vector and tensor fields on time-dependent domains. Common design operations are identified by using a number of graphics and visualization tasks as a testbed, such as vector field visualization and fluid simulation. Efficient algorithms are provided for tracking and controlling structural changes in a vector or tensor field over time which enable control over the topology and analytical behaviors of the field. The ideas behind these algorithms are based on the concepts of fiber bundles and bifurcations from differential geometry and dynamic systems, respectively. In addition, the investigator explores novel visualization techniques to address time-dependent vector and tensor fields over deformable domains. As a result of the research, core design operations are integrated into a system, and implementations of these algorithms are compiled into libraries to support direct integration into host applications. Both the design system and its supporting libraries will be disseminated to the public. With respect to its impacts oneducation, the design system is integrated into the curriculum forundergraduate students majoring in science and engineering.