Paco,
After looking at your hand-drawn curves, it occurs to me that perhaps you should implement it exactly as they described, i.e. linear until 0.75 and then
curving upwards to maximum. (I had wanted to make the top end curve down!) This can be implemented with a [ warning math follows ] curve called a cubic Bezier curve, the formula for which is:
http://www.moshplant.com/direct-or/bezier/math.html
The attached image uses 3 instead of 4 control points for the curve section after the up to 75% linear part. (I made point 1 and point 2 the same, and both at x = 1).
This greatly simplifies calculating the 6 coefficients ax, bx, cx and ay, by, cy
See if this is what you/they want.
Interestingly, it lends itself to implementation only with the lookup table, since as parametric functions of 't', you don't plug in X and get Y, or plug in Y and get X. Rather,
you plug in values of 't' from 0 to 1.0 and get any number of points in between. You make the increment small enough so it gives you all the values in the lookup table
from 3/4 (index 192) through full (index 255).
It's not simple math, but once you get it, it's very powerful and it's easy to implement. Your setup code can take any arbitrary point to be the transition point from linear to curve, and then compute the curve part of the lookup table with the two parametric equations. For example you might want the first 80% of control position to give you linear control from 0 to 60% power, and then curve to max fr the last 20%
You would make the X0, Y0 point then be (0.8, 0.6) and compute the table.
This is the math behind the curves in postscript, PDF and drawing packages (like google doc)
