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Ulrich Neumann
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With pic=ListLinePlot[...] (your plot) you get the points from

pts=Cases[pic, Line[p_] :> p, -1][[1]] y=Interpolation[pts,InterpolationOrder->1] xy=Map[{#,y[#]}&,{1,1.1Range[1,1.210,...1](* your gridpoints x *)}] 

With pic=ListLinePlot[...] (your plot) you get the points from

pts=Cases[pic, Line[p_] :> p, -1][[1]] y=Interpolation[pts,InterpolationOrder->1] xy=Map[{#,y[#]}&,{1,1.1,1.2,...(* your gridpoints *)}] 

With pic=ListLinePlot[...] (your plot) you get the points from

pts=Cases[pic, Line[p_] :> p, -1][[1]] y=Interpolation[pts,InterpolationOrder->1] xy=Map[{#,y[#]}&,Range[1,10,.1](* your gridpoints x *)] 
Source Link
Ulrich Neumann
  • 61.8k
  • 2
  • 29
  • 66

With pic=ListLinePlot[...] (your plot) you get the points from

pts=Cases[pic, Line[p_] :> p, -1][[1]] y=Interpolation[pts,InterpolationOrder->1] xy=Map[{#,y[#]}&,{1,1.1,1.2,...(* your gridpoints *)}]