Algebraic reflections in geometric acoustics

Stochastic Ray tracing is one of the most widely used geometric acoustic algorithms, and excels primarily for modelling the late room response in high frequencies. A significant bottleneck of the algorithm is the high computational cost of testing rays for intersection with geometry, and the high amount of rays required for convergence. Several methods exist to reduce this cost by means of reducing geometric complexity. This paper instead proposes using bidirectional reflectance distribution functions (BRDF) to algebraically compute transmission paths between receivers and sources, thereby decreasing the amount of total rays needed. For each ray-geometry intersection, transmissions paths are calculated recursively, and several transmission paths can thereby be taken into account for each intersection test, while allowing for point-like transmitters and receivers. The method has been implemented on a graphics processor, and calculated room acoustic parameters are comparable to commercial geometric acoustic software, as well as measurements in the high frequency limit.