# How to find a parametric equation?

I want to find an equation for a race track, so I could get the position of a point with respect to time. Let's say I have this track and here are a few points on it:

Could it be possible to model an equation based on these points like regression does and how? Also I'm new to parametric equations and I tried googling some parametric equation tutorials but I couldn't find any good, so maybe if you know some good learning resources could you please tell me? Thanks!

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If you're given a collection of points $\{(x_{i},y_{i}\}_{i=1}^{N}$, then you must choose an appropriate parameter (which you have flexibility in doing). An obvious choice is to take $t\in[0,1]$ and assign each node equal spacing within the parameter domain. You could also weight the spacing, change the parameter domain to something larger or smaller, etc. What you end up doing is dependent on the needs of the particular problem.