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Re: Rotating Spherical Harmonics

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"Nicolas Bonneel" <nicolas.bonneel@wwwwwwwwanadoo.fr> wrote in message 
news:jsoivg$ei0$1@speranza.aioe.org...

> But I don't find the exact method that slow (for a given rotation, you 
> just have a b*b matrix to build for each band of order b). The maths (for 
> the exact formula) are here:
> http://www.cs.columbia.edu/~cs4162/slides/spherical-harmonic-lighting.pdf
> (actually, if I remember well there might be a typo in the formula which 
> can be easily corrected by looking at the references).

Hello again.

I tried implementing the recursion formulae from the above "Gritty Details" 
paper and I find that, as written, the formula for band b specify indices 
into the matrix for band (b-1) which are clearly out of bounds.

For example, the Umn term for m>0 equates to 0_P^b_mn which indexes into the 
(m,n) term of the matrix for the previous band when abs(n)<b. But m can run 
from -b to +b whereas the matrix from the previous band has a dimension 
which runs only from -(b-1) to +(b-1) - something is wrong somwhere. I also 
suspect that the conditions for the W matrix are the wrong way round.

I did try comparing the tables with the original paper of Ivanic & 
Ruedenberg, but this seems to be the same apart from some minor symbol 
changes.

Maybe I'm misinterpretting something here?

Can you recall the errors that you found when you implemented this method?

Thanks
Thomas

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Rotating Spherical Harmonics "Thomas" <someone@somewhere.com> - 2012-06-29 12:22 +0100
  Re: Rotating Spherical Harmonics Nicolas Bonneel <nicolas.bonneel@wwwwwwwwanadoo.fr> - 2012-07-01 00:16 -0400
    Re: Rotating Spherical Harmonics "Thomas" <someone@somewhere.com> - 2012-07-02 12:56 +0100
    Re: Rotating Spherical Harmonics "Thomas" <someone@somewhere.com> - 2012-07-05 14:04 +0100

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