In this video, we show the example data sets included in the paper, animated over time.
These are four example data sets of three trajectories rotating around a central point on a circle in different manners.
We show the motion of the particles in a fixed global reference system.
The trajectories are the result of a super- position of two rotational movements:
a rotation of the local reference system with the angular speed p
and a rotation of the particles in this local reference system with the angular speed q.
When observed in this optimal reference system, their objective rotations become clear: we can see their varying direction and speed.
In another, non-optimal reference system though (here taken from the top left example) their behavior becomes more obscure.
We now show our new measure, TRV, on a number of data sets.
These trajectories show drifter buoys advected by ocean currents in the North Atlantic Ocean.
They are sparsely distributed, their nearest neighbors several hundred kilometers away.
Still, our new method, TRV, is able to pick up objective rotational behavior.
High rotation can be observed on a few trajectories in the North Atlantic Gyre, around Iceland and Greenland.
As a second example, we applied TRV on insect trajectories.
These 3D trajectories were reconstructed from videos of midges in a large translucent box.
While their behavior seems erratic, TRV highlights some insects of especially high and low rotational behavior
These TRV values can change rapidly when the set of neighbors changes.
This happens as midges disappear from the tracked set, or move too far away.
With this data set, the movement of socially distancing pedestrian crowds has been studied.
Here, 32 study participants move quickly within an enclosed space, while attempting to keep a social distance of 1.5m from each other.
The group at large tends to move in a counterclockwise rotation, but only six individuals show high objective rotation.
Finally, we show the changing objective rotation over time in a simulation of bird-like agents (boids).
In an initial chaotic phase, the boids all show strong rotational behavior.
To simulate emergent behavior found in bird flocks or fish swarms, each individual agent follows a simple set of rules.
Swarms form as the boids align with their neighbors, showing a decrease in their rate of rotation by TRV.
At this point, all boids find themselves as part of established swarms, and seize to rotate.
Only intermittent rotational behavior can be observed in single individuals.