In the physically based Blinn-Phong equation presented by my own company, tri-Ace, the specular is multiplied by the Fresnel term and the diffuse is thus multiplied by (1 - Fresnel) in order to maintain energy conservation.

It is the first equation in this paper: http://research.tri-ace.com/Data/s2012_beyond_CourseNotes.pdf

Oren-Nayar by itself is energy-conservative when considering only the diffuse term, so logically if you want to add some specular you have to somehow modify the diffuse.

I am adding the specular component of Blinn-Phong from that paper and am not sure how to correctly adjust the diffuse term.

My initial thought was to do the same as before, by multiplying it by (1 - Fresnel). But Oren-Nayar is already view-dependent and that is like doubling its view-dependence.

Is it as simple as I thought or is it more complicated to normalize the combination of specular and diffuse here?

What do I need to know in order to balance speculars and diffuses of other models on my own without having to run online every time?

Looking at Cook-Torrance here, the diffuse term is just Lambert. That is not physically plausible, is it?

How do you make it so?

L. Spiro

To check if your formula is energy conserving, you have to do the integral of your formula just like Fabian Giesen did in this blog (check comments, quick link: http://www.farbrausch.de/~fg/stuff/phong.pdf).

That's a looooot of math and has the risk of making your head explode, but it will make you be 100% sure.

Thank you for the replies.

I spoke to a coworker at tri-Ace and it seems Chris_F and I made the same mistake. The diffuse is not multiplied by (1 - Fresnel), it’s (1 - F0), where F0 is the specular reflectance for the normal direction for the Fresnel, which is Fspec(F0). We both had assumed that F0 was the Fresnel term and Fspec was the specular color. At tri-Ace, the specular color is always assumed to be white, and is therefore not present in that equation (or is present only as a magnitude). It makes more sense now.

When combining the Blinn-Phong specular from that equation with Oren-Nayar, it makes much more sense now to apply (1 - F0) to the diffuse rather than (1 - Fresnel).

L. Spiro

We both had assumed that F0 was the Fresnel term and Fspec was the specular color.

If you want to check your assumptions, but without computing the integrals by hand, you can always resort to numeric integration using monte carlo sampling. I'm pretty sure, boost comes with a random number generator the produces evenly distributed random directions.

If you want to check your assumptions, but without computing the integrals by hand, you can always resort to numeric integration using monte carlo sampling. I'm pretty sure, boost comes with a random number generator the produces evenly distributed random directions.

No need for random directions - just use spherical coordinates (and if your BRDF is isotropic, you only need the elevation). Every time you use dot(L, N) in your shader, use cos(theta), and so on. And then you can just integrate it numerically in Mathematica or something.

I don't have a source for this, but I *think* using this approach actually introduces a bias towards the poles. Assuming an unstratified sampling pattern.