A plot with labeled points in one plotting command?

Question

For my work, I am examining the values of a complex function as I vary the input according to a real parameter, and I want to both give the general plot and the plot of specific points, with labels (so one sees the direction of increase).

I knew from the documentation that Point and Epilog together allow you to label points on graphs; e.g.,

ourF[z_] := z^2;
parts[z_] := {Re[z], Im[z]}
ParametricPlot[parts[ourF[x + I/4]], {x, -3 , 3}, 
 Epilog -> {{PointSize[Medium], 
    Point[Table[parts[ourF[ j + I/4]], {j, -3, 3}]]}}]

This produces:

A plot with labeled points, just as in the documentation

Looking at the answers to this site's Question 1854 (especially Jacob Jurmain's), Listplot in newer versions of Mathematica has a Labeled option that labels the points in the Listplot. Indeed, I can get what I want by making a Plot and Listplot separately and then Showing them together. e.g.

ourF[z_] := z^2;
parts[z_] := {Re[z], Im[z]}
plotOne = ParametricPlot[parts[ourF[x + I/4]], {x, -3 , 3}];
plotTwo = ListPlot[Table[Labeled[parts[ourF[ j + I/4]],
     Row[{"x = ", j}], Right
     ], {j, -3, 3}]];
Show[plotOne, plotTwo]

which yields

A plot with labeled points

as required.

My first attempt, however, was to simply put the ListPlot in the Epilog, e.g.

ourF[z_] := z^2;
parts[z_] := {Re[z], Im[z]}
ParametricPlot[parts[ourF[x + I/4]], {x, -3 , 3}, 
 Epilog -> {ListPlot[Table[Labeled[parts[ourF[ j + I/4]],
      Row[{"x = ", 13/10 + j/10}], Right
      ], {j, -3, 3}]]}]

This yields the error:

Graphics is not a Graphics primitive or directive.

I guess ParametricPlot calls Graphics, and Listplot is now calling Graphics inside the other Graphics, hence the issue.

I also tried putting Labeled in the Point variation, but Point doesn't know what to do with the label, and the error message becomes

Coordinate Labeled[{8.9375, -1.5}, Row[{"x = ", 1}], Right] should be a pair of numbers, or a Scaled or Offset form.

Q: Is there any way of putting it all in one plotting command?

P.S.: An answer in the vein of, "You have acceptable output, stop worrying about it" would also be reasonable. I am new to Mathematica, but it seems to the newcomer as though Mathematica puts in one line what I would use 5-10 lines in MATLAB to set up, and [after having debugged] the fewest number of lines is the best.

Add First on ListPlot. Related: 73402, because Epilog essentially accepts the same what Graphics does. — Kuba, Feb 12 '15 at 19:39
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score 5 · Accepted Answer · answered Feb 12 '15 at 21:27

Just to show you can readily do this directly with graphics primitives:

ourF[z_] := z^2;
parts[z_] := {Re[z], Im[z]}
ParametricPlot[parts[ourF[x + I/4]], {x, -3, 3},
    Epilog -> Table[{ {PointSize[.01], Red, Point@#},
        Text[Row[{"x = ", 13/10 + j/10}], #, {-2, 0}]} &@
        parts[ourF[j + I/4]], {j, -3, 3}],
          PlotRangePadding -> {{0, 1}, {1, 1}}]

enter image description here

score 3 · Answer 2 · edited Apr 13 '17 at 12:55

You are five keystrokes ([[1]]) close to something that works (See also: this and this)

ParametricPlot[parts[ourF[x + I/4]], {x, -3, 3}, PlotRangeClipping -> False, ImagePadding -> 30,
 Epilog -> ListPlot[Table[Labeled[parts[ourF[j + I/4]], Row[{"x = ", 13/10 + j/10}], Right], 
                    {j, -3, 3}]][[1]]]

enter image description here

Alternatively, you can use ParametricPlot[...][[1]] as the Epilog setting in ListPlot:

ListPlot[Table[Labeled[parts[ourF[j + I/4]], Row[{"x = ", 13/10 + j/10}], Right], {j, -3, 3}], 
 Epilog -> ParametricPlot[parts[ourF[x + I/4]], {x, -3, 3}][[1]]]

Update: Using MeshFunctions and Mesh:

ParametricPlot[parts[ourF[x + I/4]], {x, -3, 3},
 PlotRangePadding -> {{0, 1}, {1, 1}}, ImageSize -> 500,
 BaseStyle -> {PointSize[Large], Blue}, MeshFunctions -> {#2 &}, 
 Mesh -> {Table[{Im[ourF[j + I/4]], 
            Text[Style[Row[{"x = ", 13/10 + j/10}], 12, Black], parts[ourF[j + I/4]], {-2, 0}]}, 
          {j, -3, 3}]}]

Text[] also has the reference point option after the position. It would make the lables not intersect the line - looks better. — Alexey Bobrick, Feb 16 '15 at 16:23

A plot with labeled points in one plotting command?

2 Answers2