Getting a list of accurate coordinates from a plot

Question

I have encountered this problem of getting a list of accurate coordinates from a plot. Upon searching online, the best method of doing so is to right-click on the plot and select "Get Coordinates". After which, I will have to use my mouse to probe and move along the plot as accurately and steadily as I can, but it was rather inaccurate.

Hence, I will like to ask if there are any other methods to get the list of accurate coordinates from a plot?

Thank you!

Answer 1

I would not suggest using Table as VF1 suggested, as it is very easy to miss critical regions because of the regular sampling that Table uses. Bumping up the sampling rate is not always a wise idea.

Instead, I suggest using EvaluationMonitor, which is an option for Plot. This allows you to make use of Plot's adaptive algorithms for the sampling and get the points that end up being plotted. For example:

With[{f = Sin@#^2 &}, Reap@Plot[f@x, {x, 0, 10}, EvaluationMonitor :> Sow@{x, f@x}]][[2, 1]]

An alternative to this would be to simply get the coordinates from the FullForm of the plot object as:

With[{fig = Plot[Sin[x^2], {x, 0, 10}]}, First@Cases[fig, Line[x_] :> x, Infinity]]

but this becomes messy to handle when you have several lines plotted at once.

Answer 2

My impression was that you might want a point-and-click interface to select points, after generating a plot like so:

f[x_] = x^3 - x;
plot = Plot[f[x], {x, -1.3, 1.3}]

Now, the following code sets up a graphic that allows you to click and drag to get points on the graph.

p = {0, f[0]};
bag = Internal`Bag[];
Labeled[EventHandler[
  Show[plot, Epilog -> {PointSize[Large], Red, 
    Point[Dynamic[{p[[1]], f[p[[1]]]}]]}],
  "MouseDragged" :> (pt = MousePosition["Graphics"];
    If[Abs[pt[[2]] - f[pt[[1]]]] < 0.1, p = pt; 
      Internal`StuffBag[bag, p]])],
  Dynamic[p]]

The label is dynamically updated to reflect the value of the point on the graph near the mouse position. The results are stored in the bag, which you can access as follows.

Internal`BagPart[bag, All]

(* Out: {{0.618387, -0.341731}, {0.623414, -0.341731}, 
        {0.623414, -0.330505}, {0.628442, -0.330505}, 
        {0.633469, -0.330505}, {0.643525, -0.330505}, 
        {0.648552, -0.330505}, {0.65358, -0.330505}} *)

Answer 3

As mentioned in the comments above, you are looking for a table of values rather than all of the values of the coordinates in a plot of your function. Look at Table in the docs for an extensive description of how to use it.

Here's an example:

Table[{x, x^2}, {x, 0, 4, .1}]

Returns a list of pairs of $(x, y)$ coordinates where $y(x) = x^2$ for $x$ values between $0$ and $4$ with a step size of $0.1$.

Answer 4

If the plot is as follows:

pl = Plot[x^2, {x, -1, 1}]

then the list out of which the plot is built takes the form:

pl[[1, 1, 3, 2, 1]]

The output is, however, very long.

Answer 5

This is my code, inspired by Mr. Mark McClure,

curve = Plot[1/(1 + 4 \[Pi]^2 x^2), {x, -2, 2}, PlotRange -> All];

DynamicModule[{p = Undefined},
 EventHandler[
  Show[curve, Frame -> True, 
   Epilog ->
    Text[Style[Dynamic@p, Red, FontFamily -> "Arial", 15], 
     Scaled@{0.1, 0.15}, {-1, 0}]], 
  "MouseClicked" :> (p = MousePosition["Graphics"])
  ]
 ]