If anyone is curious about applications - these can be used to approximate low-frequency components of a point's surroundings. They were used in Halo 3 to do real-time HDRI lighting and shadowing (see "Lighting and Material of Halo 3" from Siggraph 2008).
After the success of this method, there was a fairly long stretch of researchers looking for a better orthonormal basis (such as 2D Haar wavelents, as spherical harmonics is basically a Fourier Transform on a spherical basis). I think the pinnacle of this direction was Anisotropic Spherical Gaussians from 2013.
These days though, you'd at least use a neural net to learn a basis (or use a neural net to learn something else entirely). And of course, Gaussian Splats are the technique du jour for realtime relighting.
After the success of this method, there was a fairly long stretch of researchers looking for a better orthonormal basis (such as 2D Haar wavelents, as spherical harmonics is basically a Fourier Transform on a spherical basis). I think the pinnacle of this direction was Anisotropic Spherical Gaussians from 2013.
These days though, you'd at least use a neural net to learn a basis (or use a neural net to learn something else entirely). And of course, Gaussian Splats are the technique du jour for realtime relighting.