CAREER: Vector and Tensor Field Design for Graphics and Visualization

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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.