Constructing a transfer function

Question

How would I go about creating the below transfer function?

It would take two parameters:

• position of bulge in range (-1.0, +1.0)
• sharpness of bump

That picture only demonstrates movement in the first parameter.

I can think of a few possible approaches:

• figure out a formula
• Bezier curves?
• start with a few points and do some kind of chain-links type physics dynamical simulation, where each link exerts a force of its neighbours, and the end links are held low, a particular link is held high
• something like the above but starting out with a crude shape and filtering out high frequencies

However I can't see any simple way to set out on any of the above approaches.

Can anyone see a clean way to crack it?

Answer 1

Looks like a normal distribution with variable skew to me. I would look for something like that before I'd go for Bezier curves.