Re: fft in spherical coordinates

Henrietta Denoue <henrietta@xxxxxxxxxxxx> wrote:

< I have a set of data in spherical coordinates (phi, theta, r) and I need
< to subject these to a fft operation.

Why do you want to subject them to an fft? (It matters)

< When I search the literature, I am
< being warned of regular FFT since the spherical data are not defined on
< a regular grid having well-defined equidistant grid cells (uniformely
< sampled), but an irregular grid where (to simplify take a 2-dim. polar
< grid) those with smaller 'r' are clustered together more densely than
< those with higher 'r'.

(snip)

What are the boundary conditions on the data?

My first thought would be to expand in spherical harmonics for
the theta and phi part.

I know for cylindrical coordinates there is a Fourier-Bessel
transform, with sine/cos on the Z axis and theta axis, and
bessel functions on the R axis.

As with a recent discussion here, it depends on the problem
you are trying to solve. If you want to find the vibrational
modes for a solid or hollow sphere, you have to have the right
boundary conditions.

-- glen
.

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