This is true for quite a few graphic algorithms today. Certain terms in the equations used are pre-computed, and you can generalize all of them in a sense to be “probes”, “queries”, “function inversions”, “look up tables” or whatever. The only real way to know what can be computed on the fly vs what can be stored is to go ahead, try to implement it, think really fucking hard, and then see what you can do in real time. That’s basically how the field has advanced the formulas used into something that can run in real time, or can run in screen space complexity rather than scene complexity, and so on.

An equation given to you will be one of 2 forms usually; the raw equation that may come from optics, in which case expect an ass load of calculus and diff equations with arcane terms not seen outside of Maxwell’s equations. Or, in the likely case, the presenter is a PhD ubermensch nerd who has already pulled the terms out, rewritten them, is presenting them, and you need to be really paying close attention to every single word during their talk to figure it out. It’s at your discretion to determine which of the two forms is easier for you to deal with.