I need to apply the PCA at different points of a spherical cap, but I don’t know how to build these sets of different points, I need at least 2 sets.

Here is a picture with the idea of what I need.

I need to apply the PCA at different points of a spherical cap, but I don’t know how to build these sets of different points, I need at least 2 sets.

Here is a picture with the idea of what I need.