Porting the discussion from the other thread–I remember having a couple objections to the Gaussian model, and would appreciate hearing your take.
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As before–angle-space is bounded, so the Gaussian distribution is quite literally ill-defined on this space. To overcome this ill-definedness, some sort of modification like truncation (e.g., Gaussian distribution conditioned on a disk of radius 90 degrees) or projection is necessary. -
I see on the site that you’re truncating at 90 degrees. That, to me, seems to introduce another issue: when the truncation is fixed, Gaussians with different variances look completely different after truncation. A very narrow Gaussian is almost unchanged, while a very wide Gaussian almost turns into the uniform distribution on the interval:
In particular, this means that very floody lights are modeled as having a very sharp, discontinuous cutoff at the boundary, which does not match what we observe–even mules have a Lambertian profile with a continuous dropoff. Is there a part of the model that I missed which addresses this? Or should we exclude very floody lights from your model? -
Reflector beams have very distinct regions known as hotspot, corona, and spill, and so do many TIRs. A Gaussian beam profile does not meaningfully capture these distinct regions.(I see that this is just part of the tradeoff between simplicity/generality and accuracy.)
