How to obtain surface shading data from a 3D plot?

Question

Suppose I have a graphical output like this:

Is it possible to obtain the shading data (generated by lighting simulation) at each point on the surface with respect to the local co-ordinate chart of each surface?

The code for each surface part:

Spherical part:

ParametricPlot3D[{2 Sqrt[1 - u^2 Sin[v]^2 (1 + Cos[v]^2)], u Sin[2 v],
   2 u Sin[v]}, {u, 0, 1}, {v, -\[Pi], \[Pi]}, PlotRange -> Full, 
 Mesh -> None]

Cylindrical part:

ParametricPlot3D[{1 + Cos[u], 
  Sin[u], (1 + Floor[-v/(Abs[-v] + 1)] - 
      Floor[v/(Abs[v] + 1)]) Max[-Sqrt[4 - 2 (1 + Cos[u])], v]/
    2 + (1 + Floor[v/(Abs[v] + 1)] - Floor[-v/(Abs[-v] + 1)]) Min[
     Sqrt[4 - 2 (1 + Cos[u])], v]/2}, {u, -2, 2}, {v, -4 \[Pi], 
  4 \[Pi]}, PlotRange -> Full, PlotPoints -> 100, Exclusions -> None, 
 Mesh -> None]

Note: I am primarily after the shading data of the spherical part, as the cylindrical part is extremely easy to guess (the shading is constant along the vertical)