This image is edge of paper book sideways. I wanna find transformation of usual free hand photo of paper book. This situation occurs in beginning of book: right part (odd page) is near linear, while left , even page has shape similar to this function.
The left side starts with a slope close to 0 degrees, then a linear 45, then 0 degrees at maximum, and begins to increase to over 45, sometimes close to 90 degrees of slope. The end of the page depends on the book, it can be close to 90 degrees and sometimes less than 45 degrees.
What family of functions could this be? More interesting for me is not y = f(x) but x = fx(p) and y = fy(p) where p is position straightened page. Next step will go from 2D case to 3D where observer can be in infinity or not, and above not necessary center of page.
This appears similar to the probability density function of the F-distribution from statistics. You will likely need to make a few tweaks to the d1 and d2 numbers from the formula for the F-distribution but you should be able to replicate something similar to this using that.
I have made a quick desmos visual chart that you can change the d1 and d2 variables to get the anticipated result you are looking for.
https://www.desmos.com/calculator/kqf4opdb3z
You can find more information on the F-distribution here as well: https://en.wikipedia.org/wiki/F-distribution