Oren-Nayar diffuse model

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The Oren-Nayar model is a microfacet model of diffuse lighting due to Michael Oren and Shree K. Nayar. It is a more accurate but more complicated model of diffuse lighting than the Lambertian model. Unlike the Lambertian model it takes into account the roughness of the surface.

Let σ be the roughness of the surface. Let (θi,φi) be the direction of incoming light and let (θr,φr) be the direction of the reflected light(ie. the direction to the eye). Then if

A=1-0.5\frac{\sigma^2}{\sigma^2+0.33} and
B=0.45\frac{\sigma^2}{\sigma^2+0.09},

the diffuse term is

\frac{\rho}{\pi}I \cos \theta_i (A+B \sin \alpha \tan \beta \max(0,\cos(\phi_i-\phi_r)))

where I is the intensity of the light source,

α = max(θi,θr)
β = min(θi,θr).

Here ρ is a parameter related to the microfacet distribution, which can be absorbed into the surfaces diffuse color.

In the limit of a perfectly smooth surface (σ goes to 0), A goes to 1, and B goes to 0, so the model becomes that of Lambert, as expected.

[edit] References

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