III.6.2 Bidirectional reflectance distribution function (BRDF)
The basic radiosity assumes ideal diffuse reflections, but it is quite straightforward to extend this model to cover other types of reflections as well. The basic tool for that is the acoustic bidirectional reflectance distribution function (BRDF). Those are functions that have their background in computer graphics and in investigation of how light is reflected from a material.

There are different ways to represent BRDFs. Below you can see a straightforward implementation in which the solid angle around the reflector is discretized to sectors of the same size, and for each incident-reflection angle pair there is a reflection factor.

- Move the source to note that the reflection is invariant with respect to the source location.
- Reduce diffusion to make the reflection to be more specular, and see that now the reflection depends on the source location.
- Increasing the BRDF discretization enables more accurate representation of reflection properties.

Absorption: Diffusion:
BRDF discretization:

The approach presented above can describe the reflection properties more precisely than what can be achieve by assuming just ideal diffuse or specular reflections. This approximation is still quite crude but sufficient for practical room acoustic modeling purposes. More complex representations are possible as well. For example, use of a decomposition having spherical harmonics as the basis functions would enable more accurate representations with smooth transition over the whole hemi-sphere.

Representation of ideally specular reflections with the BRDFs is impossible in practice. This is since their reproduction would require the BRDFs to be discretized in infinitely small angles. More and more accurate simulation of specular reflections can be achieved by increasing the discretization such that it tends to resemble a specular reflection.

One practical limitation with BRDFs is that typically there is no measured data available that would describe the reflection properties even in this accuracy, as it is most common to have data only of material absorption and diffusion coefficients in given frequency bands.