How can we model a function for this staircase curve?
I would like to model the curve shown below and I see four essential parameters for this:
- $a$ represents the bend downwards
- $b$ is the height of the stairs
- $c$ is the length of the stairs (to keep it simple we can use $2\pi$)
- $d$ represents the angle of the stairs
The picture is a schematic representation and the function I am looking for does not have to produce exactly this curve shape and it might be the case that the suggested parameters $a,b,c,d$ are thought too short. How the curvature of the bend is formed, there I am open as well, since a rough approximation of the illustration in the picture below is enough for me.
I have already looked at some approaches, for example Equation for a smooth staircase function. I already like these curve representations very much, but they do not include this downward bend. Therefore I would be very grateful for any suggestion.