Oren-Nayar

Diffuse Lighting

We’ll start out with a couple of fundamental definitions:

Illuminance: The amount of visible light energy received by a surface per unit area. We assume the incoming light rays are parallel with each other - a reasonable approximation when the light source is very far away.

The diffuse model is called Lambertian reflectance and works well for matte surfaces. This model reflects equally in all directions, whereas rough surfaces tend to reflect light back in the direction of the source even at high incidence angles (known as backscattering). A sphere rendered with Lambertian reflectance where the incident angle is near the viewing angle will result in a central bright spot that darkens towards the edge. A full moon is a familiar example of a rough spherical object that clearly does not exhibit Lambertian reflectance - the moon appears flat and equally lit from center to edge.

Luminance: The amount of visible light energy that is reflected by a surface (emitted + transmitted + reflected). For simplicity’s sake, we’ll consider a surface that only reflects (and neither emits nor transmits) light. Reflectance is determined by the illuminance and sometimes the viewing angle.

Here, E0 is the intensity of the incident light, and θi (theta) is the angle between the light vector and the surface normal.

Pure Lambertian reflectance

Clearly non-Lambertian reflectance

Ii = E0 cos(θi)