better ContourLabels for ContourPlot

Question

When I use the ContourPlot I prefer to use ContourLabels rather than using the PlotLegends. However the labels are often displayed very close to the frame so it sometimes can be hard to read them.
Example:
 ContourPlot[
    Sin[x^2 + 2 y],
    {x, 0, 2}, {y, 0, 2},
    Contours -> 5,
    ContourLabels -> True
 ]

As you can see some numbers are placed very close to the axes. Since there is enough space in the plot where they could be placed instead I would prefer to have them a little further away from the frame.
Is there a way of achieving this? Or would I need to place those labels manually?

Bob Hanlon · Accepted Answer

Clear["Global`*"]

f[x_, y_] = Sin[x^2 + 2 y];

cp = ContourPlot[
   f[x, y], {x, 0, 2}, {y, 0, 2}, Contours -> 5];

Get the data points used for the contours in cp
data = Cases[cp, GraphicsComplex[data_List, __] :> data, Infinity][[1]];

Every time the following is executed it will randomly choose a placement for the labels (excluding values very near the edges). If the labels are still too close to the edges or those for adjacent contours overlap, you can execute again to get a different placement.
Show[cp,
 Epilog ->
  {Text[Style[Round[f @@ #, 0.01] /. (0.) :> 0,
       12, Bold], #] & /@ 
    data[[Cases[cp, Line[pts__] :> RandomChoice[pts[[5 ;; -5]]], Infinity]]]}]

tad · Answer

This placement problem of contour labels goes back at least to version 9. A comment I received from WRI in 2014:
The problem with ContourLabels is an existing one, it is currently being worked on by our developers. I understand that this is an inconvenience and the workarounds that you suggested are also some of the tricks that we suggest users to do to avoid labels being truncated. Other than these workarounds you can try the value of ContourLabels to be functions of the form f[x,y,z], that is, make custom labels. See under Details section of documentation: http://reference.wolfram.com/mathematica/ref/ContourLabels.html
The two workarounds suggested are

increase PlotRangePadding, to give space around the plot for labels at the edges, and
manually position the labels at the edge using the ContourLabels option with functions, as WRI suggested

better ContourLabels for ContourPlot

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