Preface:
I'm just a musician, trying to understand some math. Don't blame me, please ;)
Synopsis:
Given next 5 images, calculate slope of the proportion function. Make so the highest proportion is determined by the input n
Image 1,
Image 2,
Image 3,
Image 4,
Image 5
Description:
You can see 5 screenshots from the program FabFilter C-2. I need to do exactly the same mathematically with changing max number (max right position of the knob).
My thoughts:
I tried 2 fixed number - 10 and 200 (+1 is because of starting from 1; 200 is input n):
1: f1(x) = 9x + 1
2: f2(x) = 199x + 1
3: f3(x) = f2 / f1
4: f4(x) = x * (9.95 * f3) + 1
This example works well for fixed inputs (coefficients). But for any other coefficient in f2
it's a mess. Plus the slope is more linear than it should be.
Edit:
I made a mistake. I started to describe it as 1 to 10 linear function. But it should be 0 through 1 or 1 through 2. So, for each given 0<=x<=1 we have to construct a non-linear function so that f(0)=1, f(0.5)=3, f(1)=100. But the last number (100) can be changed, so that f(0.5) has to change somehow too..
Edit 2:
I found the solution for the domain [0,1] and the f(1)=200 on this site. I choose an EXPONENTIAL USING CURVE FITTING option.
It is
f(x)≈2.32033e^(4.46319x)−1.32027
There should be an explanation)
P.S.:
I appreciate every answer! Thanks