The alternative to numerical computations, which gradually propagate the pressure numbers through the space, is visibility-based methods, which consider the paths of sound rays that emanate from the source and bounce between obstacles. The methods involve determining ray intersections with the geometric model primitives, which is analogous to ray tracing operations from Section 7.1.

It is insightful to look at the impulse response of a sound source in a virtual world. If the environment is considered as a linear filter, then the impulse response provides a complete characterization for any other sound signal [212,252,262]. Figure 11.15 shows the simple case of the impulse response for reflections in a rectangular room. Visibility-based methods are particularly good at simulating the reverberations, which are important to reproduce for perceptual reasons. More generally, visibility-based methods may consider rays that correspond to all of the cases of reflection, absorption, scattering, and diffraction. Due to the high computational cost of characterizing all rays, *stochastic ray tracing* offers a practical alternative by randomly sampling rays and their interactions with materials [341]; this falls under the general family of Monte Carlo methods, which are used, for example, to approximate solutions to high-dimensional integration and optimization problems.

Steven M LaValle 2020-01-06