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    We introduce trajectory vorticity (TRV), a new objective measure for analyzing rotational behavior in multiple moving object trajectories. This method enhances visual analysis by quantifying collective rotation, applicable to diverse datasets.

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    Area of Science:

    • Data Visualization
    • Computational Geometry
    • Fluid Dynamics

    Background:

    • Trajectory data analysis is crucial for understanding object interactions.
    • Existing methods often focus on individual trajectories, neglecting collective rotational dynamics.
    • Visualizing the relationship between multiple moving objects, such as rotation, is challenging.

    Purpose of the Study:

    • To develop an objective computational method for analyzing the rotational behavior of multiple trajectories.
    • To introduce a novel metric, trajectory vorticity (TRV), for quantifying collective rotation.
    • To validate TRV's objectivity and applicability across various real-world and simulated datasets.

    Main Methods:

    • Introduced trajectory vorticity (TRV) as a measure of rotational behavior for multiple trajectories.
    • Developed two independent approaches to compute TRV: unsteadiness minimization and relative spin tensor.
    • Compared TRV with single-trajectory analysis methods.

    Main Results:

    • Trajectory vorticity (TRV) provides an objective measure of collective rotational behavior.
    • TRV was successfully applied to diverse datasets, including drifting buoys, midge swarms, pedestrian tracking, pigeon flocks, and simulated vortex streets.
    • The method effectively captures and quantifies rotational dynamics previously difficult to analyze.

    Conclusions:

    • Trajectory vorticity (TRV) offers a robust and objective approach for analyzing the rotational dynamics of multiple moving objects.
    • This new metric enhances the visual analysis of complex trajectory datasets.
    • TRV has broad applicability in fields requiring the study of collective motion and rotation.