gdalgorithms-list

[Algorithms] Stupid SH Question

[Dan G. <dan...@gm...>]

Dear List,
  I have a stupid question about Spherical Harmonics.  I am reading your
Peter-Pike Sloan's "Stupid Spherical Harmonics Tricks" (
http://www.ppsloan.org/publications/StupidSH36.pdf).

In the appendix on recurrence rules, he state that P{0,0} is 0, but looking
at the definition for P{m,m} = (1 -
2m)P{m-1,m-1} this would mean that all results are 0.

Shouldn't P{0,0} = 1 instead?

thanks
DanG
(I tried posting this question to Peter-Pike, but Microsoft rejected my
email)
-- 
Dan Glastonbury, Dan dot Glastonbury at gmail dot com
`Pour encourjay lays ortras'

Re: [Algorithms] Stupid SH Question

[<wi...@wh...>]

Quoting Dan Glastonbury <dan...@gm...>:

> Dear List,
>   I have a stupid question about Spherical Harmonics.  I am reading your
> Peter-Pike Sloan's "Stupid Spherical Harmonics Tricks" (
> http://www.ppsloan.org/publications/StupidSH36.pdf).
>
> In the appendix on recurrence rules, he state that P{0,0} is 0, but looking
> at the definition for P{m,m} = (1 -
> 2m)P{m-1,m-1} this would mean that all results are 0.
>
> Shouldn't P{0,0} = 1 instead?

Looks like an error. P{0,0} is the 0th Legendre function which should
be everywhere 1 as you state.

Cheers,
Willem

Re: [Algorithms] Stupid SH Question

[Dan G. <dan...@gm...>]

>
> Looks like an error. P{0,0} is the 0th Legendre function which should
> be everywhere 1 as you state.


Thanks Willem.

Now to decode his fast implementation of cos(m.phi) and sin(|m|.phi)...

cheers
DanG
-- 
Dan Glastonbury, Dan dot Glastonbury at gmail dot com
`Pour encourjay lays ortras'