I've been trying to get a basic understanding of this topic for awhile now (as
far as it concerns lighting for CGI) and WOW is it tough-going, basically
because of the maths involved.

What sparked my interest was reading of its use (apparently to GREAT effect) in
AVATAR.

I'm *beginning* to understand some of the basics-- mainly that it's a
render-time-and-memory-saving technique for use in *real-time* rendering of
games. But I'm wondering if it has any advantages for our usual raytracing, or
how it's even applicable to non-real-time rendering. (In some ways, it seems to
be a kind of environment-mapping technique that uses GPU power to emulate(?)
what we get from raytracing/radiosity and/or HDRI lighting. But is it baked into
textures? I haven't a clue.) The 'overall' mechanism of what it does makes
*some* sense-- it creates a blurry environment map for lighting a scene. (That's
my simpleton's understanding of it!) And with a low-overhead as far as
computation goes, which I guess makes a lot of sense in the gaming world.

Here's a good intro to the subject, as good as any other; the page has links to
some of the original academic papers as well...

http://imdoingitwrong.wordpress.com/2011/04/14/spherical-harmonics-wtf/

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> I'm *beginning* to understand some of the basics-- mainly that it's a
> render-time-and-memory-saving technique for use in *real-time* rendering of
> games. But I'm wondering if it has any advantages for our usual raytracing, or
> how it's even applicable to non-real-time rendering. (In some ways, it seems to
> be a kind of environment-mapping technique that uses GPU power to emulate(?)
> what we get from raytracing/radiosity and/or HDRI lighting. But is it baked into
> textures? I haven't a clue.) The 'overall' mechanism of what it does makes
> *some* sense-- it creates a blurry environment map for lighting a scene. (That's
> my simpleton's understanding of it!) And with a low-overhead as far as
> computation goes, which I guess makes a lot of sense in the gaming world.

I played about with this a bit back in the DirectX 6/7(?) days when it 
was first included. From what I remember it helps with lighting diffuse 
surfaces and blurred reflections in real time. Without SH you'd need to 
sample the environment at a number of points and do a weighted average 
to come up with the result which is very costly and noisy. SH is a way 
to perform a (costly) one-off transformation of the environment map so 
that smooth "realistic-looking" diffuse lighting can be created without 
much overhead per frame. It might be a good speedup for rendering 
animations in POV if you can approximate your background as a texture 
mapped sphere, it might even give similar/smoother results than 
radiosity for a given render time.

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