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Re: Range of "Spherical Coordinates" in SPHER_HARM [message #62851 is a reply to message #62846]

Thu, 09 October 2008 10:18

jameskuyper
Messages: 79
Registered: October 2007

Member

Karlo Janos wrote:
> Hello all!
>
> I am a little bit confused about the usage of spherical coordinates in
> the function SPHER_HARM.
> The first parameter should be the azimuthal angle theta (in the help
> document named 'polar' or 'colatitudinal') and the second parameter the
> polar angle phi (in the help document named 'azimuthal' or
> 'longitudinal').
> According to the example code at the end of the help page the range for
> theta seems to be [0; pi] as I would have presumed. But what is the
> range for phi? [0; 2pi] or [-pi; pi]? In some functions (where the
> keyword '/DEGREES' is possible) it must be the latter, relating to the
> coordinate system of the earth. But what about SPHER_HARM? I did not
> find any explanation about the definition of theta and phi there.

It is a fundamental feature of the spherical coordinate system that
theta and theta+2*!PI represent the same location, and similarly for
phi and phi+2*!PI. For this reason, the spherical harmonic functions
must show these same symmetries. It is no coincidence that that the
spherical harmonics are calculated by first calculating cos() and
sin() of theta and phi (or integer multiples thereof), and then using
those values for all subsequent calculations. There is therefore no
reason for SPHERE_HARM to impose any arbitrary limits on either theta
or phi, whether or not the /DEGREES option is turned on. I don't
believe that it imposes any such limits, my tests reveal none.

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[Message index]

		Re: Range of "Spherical Coordinates" in SPHER_HARM By: jameskuyper on Sun, 12 October 2008 11:45
		Re: Range of "Spherical Coordinates" in SPHER_HARM By: Karlo Janos on Sun, 12 October 2008 04:41
		Re: Range of "Spherical Coordinates" in SPHER_HARM By: Kenneth P. Bowman on Thu, 09 October 2008 06:22
		Re: Range of "Spherical Coordinates" in SPHER_HARM By: jameskuyper on Thu, 09 October 2008 10:18
		Re: Range of "Spherical Coordinates" in SPHER_HARM By: Karlo Janos on Mon, 13 October 2008 00:22

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