Is the BRDF just a function of the material objects, or are there other things to consider externally from the object itself?
@YoungNathan In most cases, the BRDF is a function determined by the surface. Though like any other function, you can use other things to pamaterize it in a given frame (e.g. player location).
Why is it significant that Wi points away from the surface rather than into the surface? Would the latter cause a change in the sign? Is there another purpose behind this?
One interesting thing to note on this slide is the cosine term in BRDF. This term (https://en.wikipedia.org/wiki/Lambert%27s_cosine_law) for reference, is Lambert's Cosine Law. All this tells us is that the angle, given a fixed intensity of light, is inversely correlated with the amount of light that will be reflected.
I think it's significant that Wi points away from the surface because as the diagram shows, and as our intuition would tell us the incoming light ray should go into the surface. However since we're defining the ray by a point and direction, and our point is on the surface, we can either go further into the surface, or point opposite the surface, and convention tells us its the latter.
I wanted more insight on how BRDFs are derived, and found this useful resource that talks about how to derive these functions from metallic rough surfaces. It goes super in depth and is pretty interesting: https://docs.lib.purdue.edu/cgi/viewcontent.cgi?article=2524&context=cstech