No, they are the boundaries of the dynamic range.
That’s where, before talking film curves, understanding film could prove itself useful.
Black relative exposure is Dmax. White relative exposure is Dmin. Contrast is the slope of the film sensitometry curve, aka the gamma of the film. Hardness is the slope of the paper sensitometry curve, aka the gamma or hardness of the paper. The latitude is the area of the dynamic range where the sensitivity is roughly linear. What we do in filmic is modeling a virtual print of a virtual positive we create on a virtual paper we define.
See https://www.kodak.com/uploadedfiles/motion/US_plugins_acrobat_en_motion_education_sensitometry_workbook.pdf
Log-logistic is great as long as you don’t mind your mid-tones contrast imposing the rate of transition in toe and shoulder as well.
Filmic lets you manage the 3 separately to define more than a blind curve : it defines a virtual film emulsion. Is it good, is it bad ? I don’t care, we know how to handle that, it’s a known territory.
So yeah it’s more parameters, but it’s also more control… Also the spline has an option to use cubic or quadric toe and shoulder such that you can control precisely how fast you converge to white and black. And if you set the latitude to 0, then you remove the linear central part to keep only the quadric/cubic toe and shoulder with slope continuity.
If your grip is with how filmic deals internally with parameter covariance… That can be fixed. We ultimately just need to put 4 nodes in a log2/log_something space, ensure we intercept middle grey, draw a 3 parts S curve with a linear middle part to connect those dots, and bring back everything to linear. Everything in-between is to help users, if it goes in the way, it can be changed.
But removing all parameters for a solution where everything is tied together, pull one thread and the whole sweater comes with it, I don’t call that progress. Perhaps it will appeal to the 2-clicks-magic crowd. But you don’t create a virtual emulsion + print anymore, that’s something else. And at very least, I want to be able to control the transition rate of shadows and highlights aside from the midtones contrast, thank you very much. I have no doubt you can come with a nicer and more elegant solution if you ditch that ability, but that’s kind of important to shape the curve.
And, yes… like any spline, not all parameters give a correct curve. Oscillations happen, overshoot and undershoot too, over-constraining a spline is never a good idea. Take any tone curve, go wild with it, and you will make it unstable just as well. But we are still using them because, so far, it’s the only way to interpolate smoothly a collection of sparse points.
Maybe we could add extra checks, for example ensuring the second order derivative of shoulder and toe is never == 0 and do something about it, but what ?