Extract boundary values in a specific order

I have a circular domain and I need to extract the boundary values of the solution, ordered by angle. I can extract the boundary values manually:

u.vector().get_local()[ boundary_indecies ]

However, I don’t know the coordinates of these indices on the mesh. Anyone knows how I can extract the mesh coordinates according to these boundary values?

Use tabulate_dof_coordinates
X = u.function_space.tabulate_dof_coordinates()