The Topology Voronoi Graph of Visualizing Local Vector Field

Topology visualization methods are very important for discovering the topology structure of the fluid fields. Among them, topology graph is a primary means, which can describe the topology relation among the critical points clearly. However, it is incapable of depicting the scope of the topology feature in the fluid field. As a basic property of topology feature, the scope property is important to investigate the fluid field and its time-dependent transformation. This paper presents a new method named topology Voronoi graph which is able to define the scope and describe the trend of one topology feature in the time-dependent vector field. First, we introduce the streamline distance to describe the mutual influence between any two points in the vector field. Then we can calculate the streamline distance of each point, with respect to the critical point it crossed, to define the feature region for the critical points in the vector field. Finally, we design an efficient topology Voronoi graph generation algorithm. The experiments on the wind field and the synthetic function data show that this method can enhance the structure visualization effects on the fluid field.