Implicit Visualization of 2D Vector Field Topology for Periodic Orbit Detection

We present implicit visualization of 2D vector field topology, and show its utility for validating and guiding approaches for periodic orbit extraction. Instead of following the traditional approach by explicit extraction of the topological skeleton, we investigate its implicit visualization by approaches that label the regions that are separated by the skeleton. While such approaches perform well for gradient fields, they fail, in particular, to visualize periodic orbits. This motivates us to complement the label-based approach with a closely related distance-based metric. We show that our approach is able to reveal periodic orbits, also in configurations in which the state-of-the-art techniques for periodic orbit extraction fail, and demonstrate their utility for interactive extraction of all periodic orbits of a 2D vector field.