forum.alglib.net

Can you use the radial basis functions in ALGlib to interpolate spherical coordinates on the unit sphere

I have a bunch of theta, phi coordinates with a density value.

If I sample a new data point, not captured in the data but on the sphere, can I use the RBF2d or 3d to give me what the interpolated density value should be?

Yes you can do this. The sphere is just another 2D parameter space.
Just input the samples as regular 2D coordinates into ALGLIB with 0 < elevation < PI/2 and 0 < inclination < PI.

An alternative approach is just to stick in the flat 2D cartesian space and parameterize it (http://research.microsoft.com/en-us/um/people/hoppe/sphereparam.pdf).