The Ray-Radiosity Method
The traditional method of acoustic ray tracing involves tracing rays throughout the environment while detecting intersections with a small detection sphere. While this method is conceptually straightforward and intuitive, it typically requires a large number of rays to generate a sufficient number of hits for constructing a meaningful energy histogram.
To reduce the number of required rays, the Treble GA solver employs a Ray-Radiosity (RR) approach for modeling scattered reflections and the late part of the impulse response. This method operates under the assumption that the sound field is diffuse, which is generally a reasonable approximation for these late-stage reflections. It is also referred to as the "Secondary Source" method and is related to radiosity-based techniques.
In Treble's RR solver, rays are traced from the source similarly to traditional acoustic ray tracing. However, at each ray-surface intersection, a portion of the energy is immediately propagated back to each receiver, assuming that the sound field and reflections are diffuse. The energy carried by a ray is only reduced when it encounters an absorptive surface, where the random-incidence absorption coefficient is applied. The natural decay of energy over distance is inherently accounted for by the spatial dispersion of rays as they propagate through the environment.
When a ray is reflected off a surface, multiple factors determine its new direction. The specular reflection vector is computed alongside a scattered reflection vector. The final reflection direction is then determined by a weighted combination of these two vectors, balancing specular and scattered components.
The energy at a receiver is estimated by determining the probable energy contribution under the assumption of complete diffusion of the incoming wave. During this process, the scattering coefficient is also taken into account to accurately model the distribution of reflected energy.
Impulse Response (RR)
As mentioned above, the energy of each ray is accumulated into a histogram, which is subsequently converted into the Ray Radiosity Impulse Response (RR-IR). Due to the histogram's limited temporal resolution, the fine structure of the RR-IR is synthesized using a Poisson-distributed noise process [1]. This ensures a realistic temporal distribution of energy and prevents potential audible artifacts.
Each reflection is represented by a pulse, with its time of arrival estimated based on the reflection density specific to the given source-receiver pair. A pulse is then generated and time-shifted accordingly. Its energy is assigned to preserve the total energy of the histogram, while its phase is randomized within the range assuming a diffuse sound field. Finally, the IR is synthesized by accumulating all pulses into a single waveform.
References
[1] Dirk Schroder. Physically Based Real-Time Auralization of Interactive Virtual Environments. PhD thesis, RWTH Aachen University, Aachen, Germany, 2011.