[Bf-committers] BRDF conversion - Was Farsthary anouncement

Yves Poissant ypoissant2 at videotron.ca
Thu Feb 12 16:09:28 CET 2009

From: "Arne Schmitz" <arne.schmitz at gmx.net>
Sent: Thursday, February 12, 2009 5:08 AM

>> The mathematical definition of a BRDF is simple enough, that it seems
>> you could wrap specular and diffuse legacy shaders into a blackbox,
>> with all the parameters stored internally, not visible to the outside
>> world. Sure, it'd suck quite a lot, but what I'm wondering is if
>> that'd work better then trying to mathematically map legacy shaders to
>> valid BRDF's.
> The problem with many legacy materials / BRDFs is, that they are not
> true BRDFs. That is they violate some conditions of being a physically
> valid BRDF. For example the traditional Phong model is not energy
> conserving, i.e. it might create more reflected radiance, than
> incoming radiance is produced. With this in mind, I figure you /could/
> for example map a legacy BRDF to a 6-dimensional function defined on
> spherical harmonics, and make a least squares approximation to a
> valid, modern BRDF that is physically sound. You will notice
> differences, but it would still be nice. Anyone want to write a paper
> about that? :) I think SIGGRAPH Asia deadline is coming up...

I like your post Arne. You make it look just scary enough ;-)

Indeed, the mathematical definition of a BRDF looks simple enough. However, 
the implications of this apparent simplicity are quite complex. One only 
need to read Robert Lewis paper "Making Shaders More Physically Plausible", 
one of the first papers to attempt to tweak the Phong shader into an energy 
conserving and reciprocal sort of BRDF, to understand the mathematical 
wizardness and deep BRDF understanding required to do that. Today, the 
mathematical formula for normalizing the Phong model is known and its 
simplicity is stunning. But coming to that required quite some mathematical 

Today, we know that the trick is to figure the integral of the volume 
occupied by the reflection distribution lobe and find a way to normalize 
that volume to unity. The Phong lobe is itself mathematically simple and 
integrating that is also quite simple and once analytically integrated, the 
normalizing is also relatively trivial.

But there are other shader models that are much more complex and it is quite 
difficult to figure the integral of the distribution lobe. Some shaders 
cannot be analytically integrated and I'm not aware of any researcher who 
have spent time trying to convert those difficult shaders into a form of 
BRDF while there are already very good and flexible BRDF models that can 
flexibly replace them. So indeed, if someone from the Blender developers 
community was to figure that, it could be worth a paper for some SIGGRAPH.

On the research front, the recent efforts are rather into developing some 
empirical BRDF models based on accumulating some basis functions that are 
weighted through least-square fitting such that any measured BRDF can be 
mimicked with a procedural model. Along the same line, your suggestion, 
Arne, does fit nicely into recent efforts.


I found this 3D World page from reading february issue of 3D World yesterday 
concerning "Technoloogies to watch during 2009" among them is BRDF =).


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