CAREER: Vector and Tensor Field Design for Graphics and Visualization

矢量场和张量场是许多科学和工程学科的基础。本研究探讨了设计和控制的时间相关的矢量和张量场的变形域，这有可能有利于各种各样的应用程序内外的计算机图形学和科学可视化。这些应用包括：天气预测和海啸模拟、建筑和飞机设计和测试、电磁模拟、指纹分析、电影和游戏特效、计算机生成艺术、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，以支持时间依赖域上的时间依赖矢量和张量场的设计和控制。通过使用一些图形和可视化任务作为测试平台来识别常见的设计操作，例如矢量场可视化和流体模拟。提供了用于跟踪和控制矢量场或张量场随时间的结构变化的有效算法，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是基于纤维束和分叉的概念，分别从微分几何和动力系统。此外，研究人员探索新的可视化技术，以解决时间依赖的矢量和张量场的变形域。作为研究的结果，核心设计操作集成到一个系统中，这些算法的实现被编译成库，以支持直接集成到主机应用程序。设计系统及其支持图书馆将向公众传播。就其对教育的影响而言，设计系统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.