Basically I'm currently using a software that edit curve and I was wondering which kind of interpolation it was using.
You have on point at (0,0) and another at (1,1).
The middle point never changes x position but y changes when grabbing the point.
If you grab the middle point all the way up you get something like this.
It looks like an exponential function but I'm not sure about that because when you put the middle point at (0.5,0.5). You get a perfect linear line from (0,0) to (1,1)
One possibility is $f(t)=t^\alpha$, with $\alpha=\frac{\log y}{\log x}$.