[Bf-committers] BRDF conversion - Was Farsthary anouncement

[Yves Poissant]

From: "Brecht Van Lommel" <brecht at blender.org>
Sent: Thursday, February 05, 2009 2:03 AM

> Heh, the thing I thought may be difficult is turning the physical ones 
> into legacy ones, so they would still give reasonable results when using 
> algorithms that rely on splitting things up (for example irradiance 
> caching, SSS, baking GI for games, .. ). I have never tried this though so 
> I wouldn't know.
>
> The other way around seem quite doable to me _if_ you don't expect those 
> things to give physically correct results, which I think is reasonable.

Let's examine material properties that are related to reflections and not 
bother with transparency and transmission for now. We will already have 
enough for now.

Legacy material parameters are many :
ka - controls the amount of ambience component contribution
kd - controls the amount of diffuse component contribution
ks - controls the amount of specular component contribution
es - controls the tightness of the specular component
kr - controls the amount of reflection component contribution
dr - controls the distance at which the reflections are no more visible

And let's not care about the material color for now. Compared to that, a 
simple BRDF is controled by one single parameter :
r - controls the material microscopic roughness.

The only control you have on a BRDF is the distribution of orientation of 
the microfacets of the material's surface. That is admitedly not much. But 
like I mentioned earlier, the power of physically plausible materials is 
that the BRDF (in that case BSDF) can be stacked (or layered).

The problem, then, is finding a reliable function that will map those 6 
legacy parameters into that single physical one. So let's examine each one 
of those legacy parameters and see if we can make any intelligent deduction 
from their values.

ka - This parameter is supposed to control the amount of ambient light 
hiting the material. Essentially, that would be all the indirect 
illumination coming from the environment excluding the explicitly placed 
lights in the scene. All this parameter value can tell us, is essentially 
how much indirect illumination we assume we have in the environment. And 
this indirect illumination is assumed to be perfectly uniformly distributed 
all over (except when AO is used but AO is not a material property). 
Whatever its setting, the "quality" of the ambience shading is always that 
of a perfectly rough (lambertian) surface so if we were to use this 
parameter to set the BRDF roughness, we would have to conclude that the 
material roughness is always 100%. Clearly, this is generally not the case.

kd - This parameter is supposed to control the amount of diffuse reflection 
of the lights only. Whatever the setting of this variable, the shading 
falloff of the diffuse part always follows the lambertian (cosine) law 
(Oren-Nayar and Minaert shaders modify that though) so if we only had the 
diffuse contribution parameter to rely onto, we would have to conclude that 
the material is perfectly rough but absorbs more or less the light that it 
receive. In fact, this parameters comes multiplying the material color but 
it does not modify its surface roughness. Diffuse roughness is constant at 
100%.

ks - This parameter is supposed to control the strength of the reflection 
coming from the lights in the scene. Notice already, that we now have two 
parameters that are both supposed to control the amount of reflection from 
the lights in the scene: kd and ks. Except that ks is assumed to be related 
to a smooth material. Not a perfectly smooth not a perfectly rough material 
but a controlable smoothness of the material. Like kd, this parameter does 
not control the apparent roughness or smoothness of the surface though. Only 
its absorption of the light that hits the surface. According to physically 
plausible prrinciples, kd and ks should be interdependent and should both be 
controled by one single parameter even though they are related to two 
different material roughness properties. This seemingly contradiction is 
solved with double layer BSDF.

es - This is a parameter that truely changes the apparent roughness of the 
surface and this is our most reliable parameter for determining material 
roughness. In fact, several 3D application convert the specular exponent to 
roughness when they want to use legacy material properties in a physically 
plausible rendering engine. Jim Blinn was the first, AFAIK, to publish a 
function to convert Phong exponents to roughness. I've seen all kind of 
conversions, some quite complex and some very simple like just taking the 
reciprocal of the exponent as the roughness. At work, I have my own. None of 
all those conversion functions are better than the other and the perfect 
conversion does not exist. The reason is that although it seems a good 
candidate for judging the intended roughness, in practice it is not that 
reliable for several reasons:
-- The strength of kd vs ks comes modifying the apparent roughness given by 
es. Since the material parameters were tweaked so the render looks 
acceptable, there is no way telling from es alone what was the intended 
roughness.
-- Legacy material designers used to force the width of the specular 
component and increase ks to compensate for the lack of area lights in the 
scene. Larger highlights would simulate the reflection of a larger light 
instead of the point light that was actually placed in the scene.
-- Legacy material designer were designing their material with non gamma 
corrected displays and the resulting highlight width is usually much larger 
than it should have been.
-- The actual material look that was seeked for was impossible to obtain 
with the parameters at hand and the end result is something that just looked 
acceptable and workable.

kr - This parameter is supposed to control the amount of reflection coming 
from the environment but not from the lights in the scene. Notice how this 
is similar to ka. The difference is that kr addresses the reflection from a 
perfectly smooth material while ka addresses the reflection from a perfectly 
rough material. Of course, a material cannot be perfectly smooth and 
perfectly rough at the same time but having both a ka and a kr on legacy 
materials is not uncommon. What deduction can we make about the roughness of 
the material in face of this contradiction? Not much.

dr - This parameter controls the reflection falloff distance. That is the 
distance of the object being reflected at which its image is 
undistinguishable anymore. This actually can tell us a lot about the surface 
roughness. In human vision, there is a solid angle of bluriness where the 
observed objects become so blurry that we cannot make sense of them anymore. 
As this solid angle increases, the distance at which objects are too blurry 
decrease. This solid angle represent the spread of the reflection pattern 
from semi smooth surfaces. This could be a relatively reliable parameter to 
decide on the equivalent roughness. The problem is that this parameter is 
very rarely set. And even when it is set, it is usually set to compensate 
for lack of HDR in the surrounding objects and as a result, this distance is 
usually set too long. Here again, lack of gamma correction makes this 
parameter miss the mark even further.

So we end up with a lot of parameters that gives us contradictory 
information about the intended roughness of the material. The reliable 
conversion from legacy parameters to hpysical parameter is hard. Very hard 
and unreliable.

Now, let's turn to the reverse conversion, that is converting roughness to 
legacy properties.

I already mentioned that the parameters kd and ks are interdependent and 
related and should be controled by one single parameter. But it is less 
obvious that the parameters ks and es are related. They are related by the 
law of conservation of energy. As the reflection pattern become tighter (the 
highlight narrower), the same light energy is reflected in a narrower solid 
angle and become very bright. Conversely, as the material becomes less 
smooth, the reflection pattern solid angle spreads wider and the reflected 
energy also spread wider so the highlight brightness becomes duller. The 
equation that links ks and es in the Phong or Blinn-Phong shaders are called 
BRDF normalization (see "Real-Time Rendering", 3rd Edition, page 260). So we 
now have 3 legacy parameters: kd, ks and es that could and should be 
controled by one single parameter. And since we already know how to convert 
roughness to specular exponent, we could choose the roughness parameter to 
control all those 3 parameters.

If you look at it, dr and es are also directly related. They are both 
directly related to the reflection pattern solid angle spread. So that makes 
4 legacy parameters that could be controled by the single roughness 
parameter.

We are left with ka and kr. I think that anyone who have worked with legacy 
renderer know well enough that in most cases, ka should always just be left 
at zero or at least to a very low value. Inside a physically plausible 
rendering engine, there is no interpretation for ka anyways so this 
parameter should be ignored entirely.

As for kr, the perfectly smooth reflection from a surface that also have 
partially smooth properties and perfectly diffuse properties seems like an 
aberration. But it is not so. In fact, there are materials that act exactly 
like that. Those materials can be modeled with double layer of BSDF. And in 
fact, double layer materials can much better mimick other seemingly 
incongruities or contradictions of legacy materials. But that is another 
story.

Yves