Topology Analysis of Vector Fields and Application Prospect

Topology analysis is an important method to visualize vector field. Topological structure is the most significant and useful feature of vector fields which can help researchers focus on key regions and reduce the occlusion and visual cluster. Topology analysis is a frontier research of flow field visualization, while it's still difficult and complex to extract topology of vector fields. Based on some mathematical foundations related to vector fields, methods of topology analysis on both steady fields and dynamic fields are introduced with their advantages and shortcomings, and a knowledge system on topology analysis of vector fields is established. Besides, the applications and significance of topology analysis were explored to play a greater role. Finally, the combination of topology analysis with other visualization techniques were discussed.