Abstract
The Room Acoustic Rendering Equation introduced in [1] formalizes a variety of room acoustics modeling algorithms. One key concept in the equation is the Acoustic Bidirectional Reflectance Distribution Function (A-BRDF) which is the term that models sound reflections. In this paper, we present a method to compute analytically the A-BRDF in cases with diffuse reflections parametrized by random variables. As an example, analytical A-BRDFs are obtained for the Vector Based Scattering Model, and are validated against numerical Monte Carlo experiments. The analytical computation of A-BRDFs can be added to a standard acoustic ray tracing engine to obtain valuable data from each ray collision thus reducing significantly the computational cost of generating impulse responses.
Highlights
Computers have been used for over thirty years to model room acoustics
We develop a method to compute the analytical solution for the Acoustic Bidirectional Reflectance Distribution Function (A-BRDF) in cases where sound reflections are diffuse, and diffusion is parametrized by one random variables
Let us briefly review the Room Acoustic Rendering Equation (RARE) introduced in [1], which models the propagation of acoustic energy through the environment both in diffusive and general non-diffusive conditions
Summary
Computers have been used for over thirty years to model room acoustics. Nowadays, computational acoustics modeling has become a common practice in many different disciplines: the acoustic design of buildings such as auditoria or concert halls [2] [3], outdoor acoustics [4], audio post-production in Digital Cinema [5] or audio for video-games and other interactive applications [6]-[8]. The most important geometrical methods that have been applied to acoustics are: image source method [10] [11], ray tracing [12], beam tracing [13]-[15] and radiosity [16]-[18]. Siltanen et al introduce the Room Acoustic Rendering Equation [1] which is a model for acoustic energy propagation This approach, borrowed from computer graphics, integrates several geometrical methods within the same theoretical framework. We develop a method to compute the analytical solution for the A-BRDF in cases where sound reflections are diffuse, and diffusion is parametrized by one (or more) random variables.
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