Oren–Nayar reflectance model
[1] It has been shown to accurately predict the appearance of a wide range of natural surfaces, such as concrete, plaster, sand, etc.
The appearance of various materials are determined to a large extent by their reflectance properties.
Most reflectance models can be broadly classified into two categories: diffuse and specular.
A surface that obeys Lambert's Law appears equally bright from all viewing directions.
For a large number of real-world surfaces, such as concrete, plaster, sand, etc., however, the Lambertian model is an inadequate approximation of the diffuse component.
This is primarily because the Lambertian model does not take the roughness of the surface into account.
Since photo receptors of the retina and pixels in a camera are both finite-area detectors, substantial macroscopic (much larger than the wavelength of incident light) surface roughness is often projected onto a single detection element, which in turn produces an aggregate brightness value over many facets.
The primary reason for this is that the foreshortened facet areas will change for different viewing directions, and thus the surface appearance will be view-dependent.
Analysis of this phenomenon has a long history and can be traced back almost a century.
The Oren–Nayar reflectance model, developed by Michael Oren and Shree K. Nayar in 1993,[1] predicts reflectance from rough diffuse surfaces for the entire hemisphere of source and sensor directions.
The model takes into account complex physical phenomena such as masking, shadowing and interreflections between points on the surface facets.
Today, it is widely used in computer graphics and animation for rendering rough surfaces.
The roughness of the surface is specified using a probability function for the distribution of facet slopes.
The standard deviation of the facet slopes (gradient of the surface elevation),
of the light reflected by the faceted surface, according to the Oren-Nayar model, is where the direct illumination term
Here are rendered images of a sphere using the Oren-Nayar model, corresponding to different surface roughnesses (i.e. different
