# Thorough, accessible material about Fourier basis functions and Spherical Harmonics?

Spherical harmonics appear in several computer graphics techniques. I feel that in order to be a better computer graphics developer, I need to have a deep understanding of what they are and how they are used.

It seems that the reference most often recommended to understand Spherical Harmonics is "Stupid Spherical Harmonics Tricks" by Peter-Pike Sloan.

I started reading it but did not find a "satisfying" definition of SH, it seems like the document mostly relies on other references for the "basics". Other references introduce the Fourier Basis functions as a "simpler version" of SH, but once again it seems hard to find good material explaining them.

What are thorough, accessible references to understand Fourier basis functions and Spherical Harmonics ?

• What is missing for you from the SH wikipedia page ? en.wikipedia.org/wiki/Spherical_harmonics Oct 15, 2015 at 13:20
• Fourier basis functions are simply sines (or sines.x * sines.y). Like sound can decompose in spectrums (i.e. set of sines), so is it for a 1D drawing. For 2D data, you simply do that in x then y (but I find quite intuitive to extrapolate the notion of wavelength to 2D). Maybe you should tell what is your background in maths ? (which school level ?) Oct 15, 2015 at 13:23
• @FabriceNEYRET Thank you for the link. While I don't think this information will benefit other users, my background in maths is prépa(MP*) + engineering school (Master Degree) ; the program did not have in-depth covering of SH. I am indeed looking for material as rigorous as what I was used to study, although I now have less time to do so, so brevity is also important.
– wip
Oct 16, 2015 at 3:02
• I read the paper you linked, it seems pretty solid. Oct 16, 2015 at 5:10