I have a set of data for a number point points on a sphere. How do I create or use a function to linearly interpolate this data for other points on the sphere?

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Hello,
For something I'm working on I have a number of sampled points on a sphere. I know the value of some function at these points but I need to be able to "linearly,"(no spline) interpolate the value of this function at a number of different points also on this sphere.
I have the data as vectors containing the coordinates (both spherical and cartesian) of the sampled points and the points I need to interpolate as well as a vector containing the values of the function at the sampled points.
I've tried using griddata() but that yields a large number of NaN values. Is there some function that I can use to aid me in calculating this or will I have to "manually," calculate the value at each interpolated point by finding the nearest neighbors and using slerp() (or something similar)?

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