Here’s an idea I came up inspired by the logistic curve in this thread.
Creating a curve with a knee and shoulder using two logisitic functions.
I basically use two scaled logistic curves. The scaling factor L scales both the functions and is the point where the two curves meet. Furthermore you can change the parameter c (let’s call this contrast) which set the steepness of the middle part.
[Sorry found some typo in the transition limit and forgot to give ranges for L and c. Now it should be correct]
Here’s the formulas:
The ranges are:
- for L: 0-2, these limits have to be.
- for c: 1-10, these limit can be changed. Smaller than one doesn’t reach 0 and 1 anymore and 10 is already very steep.
And here’s an example plot:
