Flow Visualization Based on A Derived Rotation Field

Abstract

We identify and investigate the Φ field – a derived flow attribute field whose value at a given spatial location is determined by the integral curve initiated at the point. Specifically, we integrate the angle difference between the velocity vectors at two consecutive points along the integral curve to get the Φ field value. Important properties of the Φ field and its gradient magnitude |∇Φ| field are studied. In particular, we show that the patterns in the derived Φ field are generally aligned with the flow direction based on an inequality property. In addition, we compare the Φ field with some other attribute fields and discuss its relation with a number of flow features, such as LCS and cusp-like seeding structures. Furthermore, we introduce a unified framework for the computation of the Φ field and its gradient field, ∇Φ, and employ the Φ field and |∇Φ| field to a number of flow visualization and exploration tasks, including integral curve filtering, seeds generation and flow domain segmentation. We show that these tasks can be conducted more efficiently based on the information encoded in the Φ field.