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Say I have a database with x and y coordinates (30 times per second) for some objects in a 2d plane.

Is there a way to extract patterns from these coordinates?

If so, is there a way to visualize these patterns using for example vectors?

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You could take the difference between coordinates occuring consecutively. This gives your displacement vector. Then create two plots one indicating the magnitude of displacement( $((\delta x_{t})^{2}+(\delta y_{t})^{2})^{1/2}$) vs time and another plot of the direction indicated by the angle of the vector from the x axis; given by $\theta_{t} = tan^{-1}(\delta y/\delta x)$.

Hence you could visualize the magnitude and direction with respect to time.

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