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The Ray-Radiosity Method

The traditional method of acoustic ray tracing is to trace rays around the space while looking for intersections between the rays and a small sphere. This method is straightforward and intuitive, but it can require a fairly high amount of rays to generate enough hits to produce a meaningful energy histogram. To limit the amount of rays needed, Treble GA solver uses a Ray-Radiosity (RR) approach to raytracing the scattered and the late part of the response. This method generally assumes that the sound field is diffuse, which is considered fair for the scattered and the late part of the response. It is also known as "Diffuse rain" or "Secondary Source", and is related to radiosity methods.

In Treble's RR solver, a ray is traced from the source like in traditional acoustic raytracing, but at every reflection a small part of the energy is traced back to each receiver under the assumption that the sound field and the reflection is diffuse. The energy that the ray carries is only decrease when a ray is reflected off an absorbing surface. Here the random-incidence absorption coefficient is used. The decay over distance is handled by the fact that the rays spread out as they propagate though the space.

When the ray is reflected off a surface there are multiple factors that decide in which direction the new ray will travel. The specular vector is computed along with a scattered vector. The resulting vector will be a new vector based on a weighted average between the two vectors.

v^resulting=(1s)v^specular+sv^scattered\hat{v}_{resulting}=(1-s) \hat{v}_{specular} + s \hat{v}_{scattered}

The energy at a receiver is calculated by estimating how much energy would be probably to hit receiver in the case of a complete diffusion of the incoming wave. The scattering coefficient is taken into account in this step as well.