Trajectory Vorticity - Computation and Visualization of Rotational Trajectory Behavior in an Objective Way

Trajectory data consisting of a low number of smooth parametric curves are standard data sets in visualization. For a visual analysis, not only the behavior of the individual trajectories is of interest but also the relation of the trajectories to each other. Moving objects represented by the trajectories may rotate around each other or around a moving center. We present an approach to compute and visually analyze such rotational behavior in an objective way. We introduce trajectory vorticity (TRV), a measure of rotational behavior of a low number of trajectories. We show that it is objective and that it can be introduced in two independent ways: by approaches for unsteadiness minimization and by considering the relative spin tensor. We compare TRV against single-trajectory methods and apply it to a number of constructed and real trajectory data sets, including drifting buoys in the Atlantic, midge swarm tracking data, pedestrian tracking data, pigeon flocks, and a simulated vortex street.