11.4.2 Acoustic modeling

Figure 11.13: An audio model is much simpler. (From Pelzer, Aspock, Schroder, and Vorlander, 2014, [252])
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(a) & (b)

The geometric modeling concepts from Section 3.1 apply to the auditory side of VR, in addition to the visual side. In fact, the same models could be used for both. Walls that reflect light in the virtual world also reflect sound waves. Therefore, both could be represented by the same triangular mesh. This is fine in theory, but fine levels of detail or spatial resolution do not matter as much for audio. Due to high visual acuity, geometric models designed for visual rendering may have a high level of detail. Recall from Section 5.4 that humans can distinguish $ 30$ stripes or more per degree of viewing angle. In the case of sound waves, small structures are essentially invisible to sound. One recommendation is that the acoustic model needs to have a spatial resolution of only $ 0.5$m [341]. Figure 11.13 shows an example. Thus, any small corrugations, door knobs, or other fine structures can be simplified away. It remains an open challenge to automatically convert a 3D model designed for visual rendering into one optimized for auditory rendering.

Now consider a sound source in the virtual environment. This could, for example, be a ``magical'' point that emits sound waves or a vibrating planar surface. The equivalent of white light is called white noise, which in theory contains equal weight of all frequencies in the audible spectrum. Pure static from an analog TV or radio is an approximate example of this. In practical settings, the sound of interest has a high concentration among specific frequencies, rather than being uniformly distributed.

How does the sound interact with the surface? This is analogous to the shading problem from Section 7.1. In the case of light, diffuse and specular reflections occur with a dependency on color. In the case of sound, the same two possibilities exist, again with a dependency on the wavelength (or equivalently, the frequency). For a large, smooth, flat surface, a specular reflection of sound waves occurs, with the outgoing angle being equal to the incoming angle. The reflected sound usually has a different amplitude and phase. The amplitude may be decreased by a constant factor due to absorption of sound into the material. The factor usually depends on the wavelength (or frequency). The back of [341] contains coefficients of absorption, given with different frequencies, for many common materials.

In the case of smaller objects, or surfaces with repeated structures, such as bricks or corrugations, the sound waves may scatter in a way that is difficult to characterize. This is similar to diffuse reflection of light, but the scattering pattern for sound may be hard to model and calculate. One unfortunate problem is that the scattering behavior depends on the wavelength. If the wavelength is much smaller or much larger than the size of the structure (entire object or corrugation), then the sound waves will mainly reflect. If the wavelength is close to the structure size, then significant, complicated scattering may occur.

At the extreme end of modeling burdens, a bidirectional scattering distribution function (BSDF) could be constructed. The BSDF could be estimated from equivalent materials in the real world by a combination of a speaker placed in different locations and a microphone array to measure the scattering in a particular direction. This might work well for flat materials that are large with respect to the wavelength, but it will still not handle the vast variety of complicated structures and patterns that can appear on a surface.

Steven M LaValle 2020-01-06