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plotting - Extracting data values from a plot


I found that the fact is very useful that a plot sometimes contains all the original data needed to reconstruct that plot. This is very helpful for me because sometimes I need to retrieve and analysis the numerical data in plots I produced in the past. It's much easier for me(in the sense of organization of projects) to just save the plots in notebooks rather than save the numerical data in some separated files.


For example:


data1 = {{1., 2.}, {2., 3.}, {3., 1.}};
pic1 = ListPlot[data1, Joined -> True]

enter image description here


I can get the data back using


Cases[pic1, Line[x__] -> x, ∞]

(* {{{1., 2.}, {2., 3.}, {3., 1.}}} *)

This works great most of the time, but sometimes when I specified a plot range, some data are lost:


data2 = Table[{x, Cos[x]^2}, {x, -π/2, π/2, π/8}] // N;
ListPlot[data2, Joined -> True]
pic2 = ListPlot[data2, PlotRange -> {{0, 1.5}, {0, 0.5}}, Joined -> True]

enter image description here enter image description here


Graphics[Cases[pic2, _Line, ∞], AspectRatio -> 1/GoldenRatio, Axes -> True]


enter image description here


Note that the data are lost only at the vertical direction. So are there ways to tell Mathematica to save all the data into the plot?



Answer



Use Show to impose PlotRange:


data2 = Table[{x, Cos[x]^2}, {x, -π/2, π/2, π/8}];
ListPlot[data2, Joined -> True]
pic2 = Show[ListPlot[data2, Joined -> True], PlotRange -> {{0, 1.5}, {0, 0.5}}]

Then this will give you everything:


Graphics[Cases[pic2, _Line, ∞], AspectRatio -> 1/GoldenRatio, Axes -> True]

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