Analytical derivation of a formula for the reduction of computation time by the voxel crossing technique used in room acoustical simulation

Computation times of room acoustical simulation algorithms still suffer from the time consuming search for ray-wall-intersections. Spatial subdivision may speed up ray tracing considerably. For room acoustics, where the number of surface polygons (walls) is not so high, the voxel technique appears suitable. The voxel crossing algorithm is very fast. However, its performance was not yet investigated up to now. Voxels are small cubes by which the space is subdivided periodically. The advantage: Only in the rare case a voxel intersects a wall the intersection point needs to be computed. In this paper, by estimating the probabilities of such intersections, an analytical formula is derived, by which the optimum degree of spatial subdivision and the factor of acceleration of the algorithm can be forecasted. It turns out that the computation time increases only with instead of with K₀ (the number of polygons of the room). Thus, on a modern PC, computation time for a full room acoustical simulation even for highly complicated rooms may be reduced by a factor in the order of 100, i.e. to a few seconds.