Getting vertex data from a transformed surface

I'm building a tool for visualizing satellite coverage swaths. They start as a variably sized equatorial band of a sphere that's then rotated by a specified amount.

To use the result with the rest of our system, we need the rotated swath defined in terms of lat, lon, elevation. I have a solution for converting the cartesian coordinates of the swath to lat, lon, elevation, but can't seem to extract it's rotated x,y,z values. Is there a MATLAB function that pushes a transform (translate, rotate, scale) down to the verticies of the transformed object so that those (rotated) values can be accessed?

Thanks!

Mike