PBR Frensel effect

Question

I'm read Real-Time Rendering and the Radiometry section was too hard for me to understand, so I googled PBR and found this article.

Can someone explain the next sentence?

The second observation about Fresnel properties is that the curve or gradient between the angles does not vary much from material to material. Metals are the most divergent, but they too can be accounted for analytically.

Secondly, I'm really new to PBR. Can you recommend other good articles about this subject, with a focus on coding?

Answer 1

By "gradient between the angles" the author is talking about a a simple 2D function: Reflectivity(theta). As mentioned in the previous paragraph, for ALL materials, Reflectivity(theta) tends towards 100% as the theta tends towards 90 degrees. That is, ALL materials behave like a perfect mirror when the grazing angle is 90 degrees.

However, the in-between values of Reflectivity(theta) may be different for wood, metal, concrete, etc. Again, think of the 2D graph mapping theta to reflectivity. They would have different ease-in and ease-out behaviors, to use an animation analogy.

See the graph below that sentence, and replace "Center" and "Edge" with 0 and 90.

What the author means by "accounted for analytically" is that we don't need to store the exact curve (either in a lookup texture or array) -- we can compute Fresnel with a formula ("analytically") using other values in the material.

Here is an article about Fresnel by John Hable. He writes good articles with shader codes, especially about color correction and skin:

http://filmicgames.com/archives/557

This is not about PBR, but about storing your 1D falloff functions instead of computing analytically (the opposite of above). Maybe it will be interesting:

http://c0de517e.blogspot.com/2013/12/never-again-point-lights.html

Answer 2

As per the answer above, the sentence refer to the function representing the behavior of the energy bounce (due to reflection) as a function of the angle. This curve is shared between many materials and starts gradually at a linear slope before starting to converge toward 1.0 (hence complete reflection) as it approaches 90 degrees - typically the curve will start to converge aroun 60-70 degrees.

Note that for metals this function is more diverse and does expose different behavior - this is very evident for iron which in effect reflects less around 70 degrees before converging back again - google fresnel reflection or IOR for metallic materials to inspect this behavior.

Good references will be the Siggraph 2010 / 2012 and 2015 presented by Brent Burley of Disney - here is 2012 which gives a good summary of the subject - notice that some of Burley's equations are artistically chosen (diffuse approximation near the rims) as he mentions:

https://disney-animation.s3.amazonaws.com/library/s2012_pbs_disney_brdf_notes_v2.pdf