I'm currently working on a synth, and many of the knobs are not linear in nature. Often, knobs will have a simple algorithm by which they transform linear changes into curved ones (such as volume or frequency). In other cases, the curve is a bit more arbitrary, and this is one of those cases.
I know what values I want to hit (roughly), and have a pretty large degree of relative tolerance for some of the values. Here are the values and their tolerances:
(0, 1) //no tolerance
(0.25, 1.75194 +- .00001)
(0.5, 3.5 +- .5)
(0.75, 11 +- 1)
(1, 500 +- 100)
They end up creating a pretty hard curve, and I've been attempting to match it by plugging values into a somewhat similar curve equation:
I know there must be a better way, but I have no idea how to solve a multiple variable equation for multiple known values which each have tolerances. Further, it has to (in my case) be computationally simple.
How can one create an simple equation to approximate a curve of known values which each have tolerances?
So far my steps are:
- Find a simple equation that's already fairly similar.
- Graph the points and equation
- Start messing with the increment rate of x, and any other variables and hope you get close.
But I'm certain there are much better approaches.
Edit: for anyone interested, here's where the values of y and their tolerances were derived from. It is an equation which can go from a triangle wave, to roughly a sine wave, to roughly a square wave. I think it's pretty neat!
