## Hybrid Models and the Reverberant Tail

Every ray tracer has to deal with the transition between the early direct reflections, and the late reverberant field, and the limits imposed by computation time. Some programs (e.g., ODEON; Rindel, 2000), called hybrid models, use scattering coefficients in the normal way for the first two or three reflections, after which they abandon specular reflections and treat subsequent impacts as diffuse. The direction of the diffuse reflection can be selected at random by choosing an angle whose probability is based on Lambert's cosine law. This simplifies the calculations required and saves time but can miss multiple reflections.

Other programs (e.g., RAMSETE; Farina, 2000) remove a portion of the diffuse energy at each reflection, calculate its contribution at the receiver, and follow it no further. This simplification underestimates the diffuse-field energy, which might partake in multiple reflections after the initial one, but offsets the overestimation from the edge calculation. In this system all the energy remaining in a beam pyramid is assumed to be reflected specularly from the surface struck by the center ray even when the area of the beam pyramid is much greater than the reflecting area. The error introduced by this assumption overestimates the amount of specular energy reflected, but significantly reduces the computation time.

When the beam area is larger than the reflecting surface as in Fig. 22.21, not all the energy associated with a ray hits the surface, and a decision must be made as to how to treat the reflection. One approach is to clip the beam using the edges of the area struck, generating new beams, which continue on (Funkhouser et al., 1996). This approach is quite accurate but requires more computing power. Another approach is to reduce the specular energy by the ratio of the struck surface area to the beam area (when the beam area exceeds

Figure 22.21 Pyramid Beam Impacting a Small Surface

Figure 22.21 Pyramid Beam Impacting a Small Surface

the surface area). The struck surface area would replace the beam area in Eq. 22.54 for the diffuse scattering component from the surface. The energy not striking the surface would be considered diffuse and could continue on a random or a diffused path. This would limit the specularly reflected energy to that actually hitting the surface.

The computation problem is a difficult one and is a topic of considerable interest. It may be possible some day to solve the room modeling problem exactly, but in the meantime clever models can give useful results with relatively simple approximations.

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