As in visual rendering, there are two main ways to handle the propagation of waves. The most expensive way is based on simulating the physics as accurately as possible, which involves computing numerical solutions to partial differential equations that precisely model wave propagation. The cheaper way is to shoot visibility rays and characterize the dominant interactions between sound sources, surfaces, and ears. The choice between the two methods also depends on the particular setting; some systems involve both kinds of computations [208,334]. If the waves are large relative to the objects in the environment, then numerical methods are preferred. In other words, the frequencies are low and the geometric models have a high level of detail. At higher frequencies or with larger, simpler models, visibility-based methods are preferable.