I am trying to create a nice ease-in-out function that given values from 0 - 1 produces an output of 0 - 1 which accelerates slowly up to full speed then slows down again as it nears 1.
I currently have a function using sine, in the form...
$$y = (\sin(πx/2))^2$$
This works ok, and gives me results in the range I require however it is too quick to reach the terminal velocity, I am looking for something which has a more gradual start / end and a steeper center (if that makes sense).
Any help would be appreciated!