III.8 Hybrid models


All the room acoustic modeling techniques have their pros and cons. At the moment, there is no single method that could cover the whole frequency band and the whole temporal span of an impulse response with sufficient accuracy and efficiency. For this reason, it is common to build hybrids that combine strengths of different methods and at the same time avoid their weaknesses. Here we present a couple of such proposal.

Note that in this section the term image-source technique can be thought to cover both the actual image-source technique and the beam-tracing that is based on the image-source principle. In this sense they are identical and the beam-tracing can be seen just as an accelerated way to get to the same result as with the original image-source technique.

III.8.1 Multi-pass ray-tracing
The ray-tracing technique covered earlier is a single-pass technique, but it is possible to turn it into a two-pass technique, and after that it starts to get closer to the acoustic radiance transfer. In this approach each hit of a ray on a surface is registered instead of registering hits with a receiver. By this means each surface will finally have a similar response than what acoustic radiance transfer would provide. After that, it is possible to use exactly the same final gathering pass as with the other two-pass techniques.

This is a very attractive approach for practical implementations as it is possible to carry out energy propagation spatially in more accurate directions than what discretized responses of acoustic radiance transfer would enable. In this approach the spatial discretization has a role only in the intermediate storage at patches and in the final gathering, but not at the level of individual rays that can be traced with higher accuracy.

III.8.2 Time-division hybrids
One natural pair of techniques that can be used to complement each is formed by the image-source method and radiosity (or acoustic radiance transfer). This would work best for a time-division hybrid, in which the early reflections are computed with the image-source technique, and the computation of later reflections is trusted for the radiosity method. By that means the early specular reflections would be as accurate as possible while the computation of late reverberation would still be efficient and it would have enough of diffused sound energy - both of those would be challenges for the plain image-source method.

III.8.3 Frequency-division hybrids
A main challenge in all the GA methods is their inability to model all the wave phenomena such as edge diffraction. For this reason, it is reasonable to construct hybrids that use some wave-based methods for the computation of the low frequencies while the higher end should be computed with some GA method.

One such complete hybrid that has been proposed uses the finite-difference time-domain simulation for the low frequencies, beam-tracing for the early specular reflections, and acoustic radiance transfer for the later reflections, at higher frequencies. This combination is able to cover efficiently the whole duration of the impulse response and the whole audible frequency band.

The proper cross-over frequency from the wave-based methods to GA methods is still under discussion. In principle, the wave-equation gives the ground truth here and it should be used as high as possible. However, it is worth remembering that the normal wave-equation does not contain terms that model air absorption and at higher frequencies it has an essential role. For this reason, if any wave-based model is to be used at those higher frequencies the air absorption should be either incorporated in the equation to be solved, or implemented as post-processing operation.