Broad spectrum diffusion model for room acoustics ray-tracing algorithms

Geometrical acoustics methods have already been transformed to account for diffusely reflecting boundaries. In randomized ray-tracing algorithms, the sound rays are either specularly reflected or scattered, according to the value of a random number which is compared with the diffusion factor. However, this method becomes inefficient if this factor depends on frequency, since the process must then be repeated for each frequency band. A method is proposed in this paper to compute all frequency components simultaneously in a single pass. The diffuse reflection model is based on the definition of a new concept: the "splitting coefficient," which can differ from the diffusion factor. First, the randomized ray-tracing method is described and the diffusion model is applied to a single diffusing surface in free field. It is shown that the results computed by the program are in accordance with theoretical results. Then, the method is shown to work properly when it is applied to more realistic enclosures: This is proved in theory and illustrated by some examples. A particular problem is the increase of the statistical error which has been solved by an appropriate control of the splitting coefficient.