# Why is spherical harmonics used in low frequency graphics data instead of a spherical Fourier transform?

I'm curious why spherical harmonics are commonly used in real time graphics instead of a spherical Fourier transform.

I get that spherical harmonics are in a sort of frequency space (like FT is) so you can do convolution very efficiently.

I also get that SH is an approximation of a function on a sphere, using up to an infinite series to perfectly reconstruct the original data, but often using only the first few items in the series.

This sounds a lot like a spherical Fourier transform, but the math uses different functions entirely.

What is the benefit of the SH representation over spherical FT?

• Can you clarify what you mean by a "spherical Fourier transform"? I googled, but didn't turn up anything that sounds like it would match this question. Oct 27, 2016 at 4:24
• I'm thinking like taking a unit sphere, breaking it into the two angles that parameterize it, so you have a 2d function, then using 2d DFT on that. Oct 27, 2016 at 4:30
• Oct 27, 2016 at 5:39