In this case it is the inversion of a circular paraboloid on a sphere that may or may not be at the origin. Example is the sphere: x^2 + y^2 + z^2 = R^2, the coordinates of the new points after the the inversion are: (x, y, z) -> R^2.(x, y, z) / (x^2 + y^2 + z^2).
