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I really want to know how to plot the Cartesian grid lines on a 2D plane onto a sphere in the context of stereographic projection. I found this image showing what I want to plot. Can anyone help me to obtain the code to plot this sphere using SphericalPlot3D and MeshFunctions?

Projection

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  • $\begingroup$ It would help if you provided the definition of Cartesian grid lines. $\endgroup$ – MarcoB Jun 10 '20 at 23:51
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This looks like a stereographic projection to me:

stereo[{x_, y_}] := {
  (2 x)/(1 + x^2 + y^2),
  (2 y)/(1 + x^2 + y^2),
  (-1 + x^2 + y^2)/(1 + x^2 + y^2)}
ParametricPlot3D[
 stereo[{x, y}], {x, -2 π, 2 π}, {y, -2 π, 2 π}, 
 PlotRange -> Full, PlotTheme -> "Classic"]

stereographic projection of the plane

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