In general this is a tween, as you know, but its shape is distinctive of both in and out "easing" ... I think the Tween library allows you control easing. If not, this is log of values from beginning or back from the end, with a threshold, that is placed on top of the original curve. Hope this helps?

f(0) = 0
f(1) = 1
f'(0) = 0
f'(1) = 0

i think there's a clue in the name... quintic equation. although i'm pretty sure you can do it with a cubic, but not less...

if
f(x) = ax^3 + bx^2 + cx + d
then f'(x) = 3ax^2 + 2bx + c

so given f(0) = 0 then d = 0
and f(1) = 1 so a + b + c + 0 = 1
and f'(0) = 0 so c = 0
and f'(1) = 0 so 3a + 2b = 0

so
a + b = 1
3a + 2b = 0

a = -2
b = 3

f(x) = -2x^3 + 3x^2

were a bunch of posts about this stuff on the old forum. comes under many different names thought so it's hard to know what to search for - tweening, easing, lerp...

http://processing.org/discourse/yabb2/YaBB.pl?num=1191032076

ah, this is the one i remember:

http://processing.org/discourse/yabb2/YaBB.pl?num=1265917089/1

You might find what you need in the animation libraries ;)

wolfram graph

that's very shallow though, the quintic version probably helps make it steeper. a standard sine wave would also work, i think.

Thanks for the help!!
Kooogy, I put the function in my app and it works fine.
Next  time I will have a look to the library before beginning that kind of app !!!

Thanks