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?
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