Cheap Lights with Spherical Harmonics

There's another great application of spherical harmonics in (non-real-time) lighting, used by Weta for Avatar. Instead of precomputing the terms for a particular lighting setup as above, they use SH to store an environment map for every point on an object, including the effect of occluding geometry. This is independent of the camera and light positions. At render time it's then cheap to rotate the environment or move the lights, and still get correctly occluded diffuse lighting. They won a technical Academy award for it.

Easy-ish overview: https://www.fxguide.com/featured/the-science-of-spherical-ha...

SIGGRAPH 2010 paper, focusing more on the creation of the SH cache than it's use: http://dbonline.igroupnet.com/ACM.FT/1780000/1778774/037-pan...

Slides about same: http://wwwcg.in.tum.de/fileadmin/user_upload/Lehrstuehle/Leh...

Similarly, circular harmonics [0] allows you to project a function onto coefficients of a single angle instead of two.

[0] - http://www.blackpawn.com/texts/ch/default.html

Ah, interesting. I was familiar with spherical harmonics for Ambisonics [1], a technology for representing the directional sound field at point (or perhaps a head-sized sphere), using the spherical harmonic decomposition to approximate the sound field in a reasonably small number of discrete channels.

[1] http://en.wikipedia.org/wiki/Ambisonics

spherical harmonics! Cool to know that aren't only used in quantum mechanics :)