[Algorithms] Undershooting in spherical harmonics generated by cubemap convolution

[Alen L. <ale...@cr...>]

Hi all,

When generating 2nd order SHs by convolving environment cubemaps, In
some rare cases I get some strange artefacts that seem as if that is
just a limitation of 2nd order SHs, but I'm not sure, so I figured I'd
ask...

The problematic case is where there is only a handful of very bright
(~2000x the cubemap average) pixels in one narrow direction (~0.5
deg). (This example is generated by a sun disk in the skies, when seen
through a small window in a dark room).

In this case I get large undershooting (manifesting as a black spot)
in some other direction. Depending on the bright direction, the black
spot is sometimes on the opposite side, but sometimes it is e.g. 90 or
135 degrees from the bright side, etc. I was expecting to see
something like this in the exact opposite direction, but I'm a bit
surprised to see it move around. Then again, I'm not an SH expert, so
I'm probably wrong.

So to ask a concrete question: Is it normal for SH approximation
errors in such "spiky" cases to generate undershooting in directions
that are not directly opposite to the brightest point?

Thanks,
Alen