Tech-OrNay2

Here, σ (sigma) is the roughness parameter. If this value is zero, B = 0, A = 1, and we’re left with the original Lambertian model. The cosine of the difference between viewing and incident angle is at its max when those two angles are the same, and is restricted to positive values (it wouldn’t make sense for this term to subtract from the luminance).

Spheres rendered with increasing roughness parameter (from left to right) using Oren-Nayar model

At greater distances, more facets within the rough surface contribute to the luminance detected by a single photoreceptor

References:

Oren, M. & Nayar, S. K. (1992). Generalization of the Lambertian Model and Implications for Machine Vision. International Journal of Computer Vision, Vol 14:3.

Fosner, R. (2003, May 14). Implementing Modular HLSL with RenderMonkey. Gamasutra. Retrieved May 9, 2009, from http://www.gamasutra.com/features/20030514/fosner_03.shtml

http://en.wikipedia.org/wiki/Oren%E2%80%93Nayar_diffuse_model

What is it that makes the moon look the way it does?

A rough surface can be modeled as a collection of many micro-facets that each behave as a simple Lambertian surface. When viewed from a distance, the light received by a single photoreceptor (in either a digital camera or biological eye) is the sum of light reflected by multiple facets. Each facet has a normal angle that deviates by some amount from the normal of the surface, and a Gaussian function is commonly used to describe the distribution of these deviations. The variance of this distribution works well as a measure roughness; zero variance corresponds to a perfectly smooth surface where all of the facets are in the same plane and the surface exhibits perfectly Lambertian diffuse reflection.