Hemisphere vertices projection onto a ground plane from center

Hi all,

I'm not sure how to search for existing scripts that can do the following.

I need to project every vertex of a hemisphere into a plane located at its bottom or "south pole" (from the center of the corresponding full sphere to a plane located at the pole). See images please.

If I need to do this manually, I trace lines from the center of the sphere to each vertex, and extend them to the plane. Then I select and scale uniformly every section or ring of the hemisphere and move the selected ring to the point on the plane where the corresponding line intersects the ground plane.

Please see the images attached (Front view, perspective and top view)

If anyone can remember seeing this or wants to create a script, it would be great.

Thanks!