# Extracting patterns from the spatiotemporal movement of objects

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?

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 $$\theta_{t} = tan^{-1}(\delta y/\delta x)$$.