However, performing this is computationally heavy in real cases. Below is an algorithm for that and a call for that should be added into the beam-tracing algorithm shown earlier.
The most difficult part in the algorithm above is the function differenceBeam that would clip out tmpBeam out of newBeam . This algorithm is straightforward to implement for the 2D case demonstrated here, but making it work in 3D would be much more challenging. It could end up in cases in which the beam cross-sections could have holes or will be split into several disjoint parts. Handling all those would be much more tedious when compared to the option of retaining the original cross-sectional shapes that are typically low-order polygons. For this reason, it is typically more efficient not to perform full 3D clipping in real applications, but instead, use more approximate beams. However, if those are done properly, there is no need to perform any ray validation, but it is sufficient to know if the listener is inside a beam or not, and there are no obstructions in the last section of the reflection path. To see and verify this, please, move the listener around and notice that valid paths are possible only inside the beams.
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