Rotation of the spherical harmonics

[KrazyHorse]

Any good references out there?

Basically, my problem is that I have the coefficients of the spherical harmonic decompositon of a function defined on the sphere. The only way I was able to write these down was to define my z axis such that the function was properly azimuthally symmetric.

My decomposition therefore has Clm = 0 if m is not 0.

What I want to be able to do is transform this decomposition into another basis with new z axis pointing in arbitrary theta, phi direction

What I remember of this is that the transformation involves only a sum over m's (not l's) therefore it shouldn't take too much computer time to do (which is good, because I have to transform the bases approximately 3 million times, before doing some other manipulations)

this has something to do with the wigner-eckart theorem, but I don't want to think too hard about it. Therefore, the more cookbooky the reference gets the better.

[KrazyHorse]

I'm already getting way too clever for my own good right now.

I used Rodrigues' formula today. That wasn't something I expected to do.

[Hueij]

[Richelieu]

Re: Rotation of the spherical harmonics

Originally posted by KrazyHorse
Any good references out there?

Basically, my problem is that I have the coefficients of the spherical harmonic decompositon of a function defined on the sphere. The only way I was able to write these down was to define my z axis such that the function was properly azimuthally symmetric.

My decomposition therefore has Clm = 0 if m is not 0.

What I want to be able to do is transform this decomposition into another basis with new z axis pointing in arbitrary theta, phi direction

What I remember of this is that the transformation involves only a sum over m's (not l's) therefore it shouldn't take too much computer time to do (which is good, because I have to transform the bases approximately 3 million times, before doing some other manipulations)

this has something to do with the wigner-eckart theorem, but I don't want to think too hard about it. Therefore, the more cookbooky the reference gets the better.

This is another one of your drunk threads right? You're actually asking for the recipe for a martini, but you're too drunk to type, right?

[Atahualpa]

Du musst erst den Nippel durch die Lasche ziehen...

[KrazyHorse]

Not drunk yet. Might be soon.

Not on martinis, though. Time for more bloody marys

Last night I had a litre and a half of wine but that only kept me buzzing for about 2 hours.

7 or 8 bloody marys ought to do a better job.

[Kuciwalker]

Probably useless, but couldn't you substitute in x-y-z coordinates, do a normal rotation, and then translate back into spherical?

[KrazyHorse]

Uh. Yeah. Extremely useless. That computation takes too long.

In the end IIRC it would be of order (n^3)logn

My way should be n^2

That's the difference between 12 hours on these machines and ~1000 years.

If I was willing to accept a (n^3)logn method then I could have just done it the dumb, straightforward way. (point by point addition)

[KrazyHorse]

The dude who I'm doing work for this summer is going to get his socks blown off tomorrow when I tell him what I'm up to.

[Asher]

Have you considered a bottom-up approach?

[KrazyHorse]

huh?

[KrazyHorse]

Man, these marys are strong.

Two knocked back and I'm starting to really feel it.

[KrazyHorse]

Anybody who's supposed to be a computer scientist should know this. It seems way to useful for 3-D graphics not to be a standard problem

[Asher]

In that case maybe I should read it.

[KrazyHorse]

I also had to write my own goddamn sphercial harmonic decomposition program because it doesn't seem to be a standard fpart of an liberary i can find.

bastards.

I used to shudder every time I saw the spherical harmonics in a classas.