The final gathering is a computationally fast operation, much faster than the sound propagation performed in the first phase. It is possible to move the listener and the gather response in real-time even in very complex geometries.
The gathering algorithm goes through all the surfaces that are visible to the listener, and registers the energy accordingly. Here we again need the $1/r^2$ attenuation, as it can be thought that the energy from a surface is emitted as spherical wavefront. This corresponds to the form factors used in the actual propagation as those depend on the mutual distance of patches as well.
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