Having a dataset/timeseries consisting of $x,y$ and time for n people I need to determine whether one person was close to another for more than m minutes.
Consider that $x,y$ are Real numbers, so if we choose a point $(x,y,t)$ we would need to "draw" a circle around that point. Any other point that it's inside the circle should be considered as one person that has been near the first person in time $t$.
In the end we have for each person points in the shape of $(x,y,t)$. So maybe there's a chance to fit those points into a $3$d shape and to calculate intersection between the different $3$d shapes.
Anyways, I'm open to different approaches to solve this. It also needs to be programmable.
What, precisely, do you consider close? If, by close, you mean "the distance between them is less than $\epsilon$" for some given number, $\epsilon> 0$, then, for A with (x, y) position given by x= p(t), y= q(t), and B with (x, y) position given by x= u(t), y= v(t), the distance between them is $\sqrt{(p(t)- u(t))^2+ (q(t)- v(t))^2}$ so you want $\sqrt{(p(t)- u(t))^2+ (q(t)- v(t))^2}< \epsilon$. If you don't like square roots, since $\epsilon$ is positive, this is the same as $(p(t)- u(t))^2+ (q(t)- v(t))^2< \epsilon$.