I am learning about color spaces in digital images, and while researching the precise definition of the sRGB space on wikipedia, found what seemed to me as an unnecessarily complex, full of (to me) arbitrary details. The explanation on wikipedia, in the link given below, had a lot of constants which I did not know the meaning, purpose or choice of - it all seemed to add arbitrary complexity. What is K-zero? What is the meaning of the phi value, 12.92? And so on.
The mathematics has been tailored to suit computers, where numerical issues arise, especially with the low 8-bit format of sRGB, so I understand the need for a piecewise function - but can someone explain to me the practical value of the added complexity, and the reasoning behind each constant? I graphed the formulae C^(1/2.4) (which is what I used to think sRGB essentially was) and A*C^(1/2.4) - (1 - A) on Desmos, and the curves were extremely similar. I do not understand why there there was a need for the alpha value and the "- (1 - a)" in the first place, nor do I understand the choice of A = 1.055.
The piecewise transfer function from CIEXYZ space to sRGB space is defined as follows:
C' = 12.92 * C when C ≤ 0.0031308
C' = 1.055 * C^(1/2.4)-0.055 when C > 0.0031308
And here is the same definition, along with an explanation (which seems to me is based on unexplained, arbitrary formulae), with greater detail: https://en.wikipedia.org/wiki/SRGB#Theory_of_the_transformation
Many of the standardized colorimetric systems are crippled with numerical constants and weird functions that can be piecewise. This is because they are essentially empirical and try to capture the behavior of the human visual system.
An additional source of complexity is the definition of the white reference color to be used, in order to account for the type of light source - natural or artificial - and described by a color temperature associated to Plank's law.
Don't expect easy explanations, you need to dive deep in the layers of colorimetry. Not counting some remains of television technology standards, analog and later digital.
Among some other niceties,
https://en.wikipedia.org/wiki/CIELAB_color_space#Forward_transformation
and
https://en.wikipedia.org/wiki/Color_difference#CIEDE2000.