Re: [Algorithms] Lighting (HDR)

[Fabian G. <f.g...@49...>]

Joe Meenaghan wrote:
> Hey All,
>  
> Just a few random questions pertaining primarily to HDR lighting that 
> I'm hoping to get some insight on.
>  
> 1. I have differing information about the normalization term for the 
> Blinn-Phong BRDF and I'd like to know which is correct. In Real-Time 
> Rendering the authors suggest (m + 8) / (8 * pi) based on a 
> derivation from Sloan and Hoffman. However, in Pharr and Humphrey 
> (Physically Based Rendering, p.446) they calculate (m + 2) / (2 * pi). 
> The definite integral solution demonstrated in the 
> latter appears reasonable to me, so I'm uncertain. Normally I've 
> associated the m+2 version as the normalization term for plain Phong, 
> yet, Pharr and Humphrey are very explicitly referring to the Blinn BRDF 
> and are using the half vector rather than the reflection vector in their 
> discussion, and they are convincing. Is there something I'm missing?    

I went through the same thing a few months ago. See the discussion in 
the comments here:

   http://www.rorydriscoll.com/2009/01/25/energy-conservation-in-games/

(Including a comment from Naty Hoffman who did the derivation mentioned 
in RTR). The exact normalization factor obviously depends on what 
variant of the BRDF you use. I did the computation for typical variants 
of Phong and Blinn-Phong here:

   http://www.farbrausch.de/~fg/articles/phong.pdf

(also referenced in the discussion above). Hope that helps!

Cheers,
-Fabian "ryg" Giesen