You can do something like this,
SetAttributes[verbosePlot, HoldAll]
verbosePlot[plotcommand_] := Module[{plot, pp, mr},
{pp, mr} = {PlotPoints,
MaxRecursion} /. (Trace[plot = plotcommand,
HoldPattern[(MaxRecursion -> _Integer) | (PlotPoints -> _Integer)],
TraceInternal -> True] // Flatten // Reverse //
ReleaseHold);
Print@*Row /@ {{"MaxRecursions \[Rule] ",
mr}, {"PlotPoints \[Rule] ", pp}, {"PlotRange \[Rule] ",
Charting`get2DPlotRange@plotcommand}};
plot
]
Here we are using Trace
to find the actual values of MaxRecursion
and PlotPoints
used, and the undocumented function Charting`get2DPlotRange@plotcommand
to get the PlotRange
(a different method is needed for this option since Trace
will return PlotRange->All
if that is the option given).
Thanks to Simon Woods for this method, and thanks to J.M. for the tips on improving it. This will plot the command and give the values for the requested option.
verbosePlot[Plot[{Sin[x], Sin[2 x], Sin[3 x]}, {x, 0, 2 Pi}]]

another example,
verbosePlot[
ParametricPlot[
r^2 { Sqrt[t] Cos[t], Sin[t]}, {t, 0, 3 Pi/2}, {r, 1, 2}]]

If you want to extract the option values from an already created plot, I don't know how to do that. The only information available in the FullForm
of the plot would be the number of mesh points, not the algorithm used to generate them.
Note that you can also bypass this user-defined function and go straight to TracePrint
,
TracePrint[
ParametricPlot[
r^2 {Sqrt[t] Cos[t], Sin[t]}, {t, 0, 3 Pi/2}, {r, 1,
2}], (MaxRecursion -> _Integer) | (PlotPoints -> _Integer),
TraceInternal -> True]
Charting`get2DPlotRange@%

if you don't mind the duplicated results from TracePrint
AbsoluteOptions
can help a little.You can get the value ofPlotRange
like thisAbsoluteOptions[a, PlotRange]
But the value ofPlotPoints
andMaxRecursion
Maybe be vanished after you get thea
. $\endgroup$PlotLabel
too. Or you could pass them to a combinedText
graphic as shown in the 3rd example on howTo/MakeASmootherOrRougherPlot. This shows a dynamic example with labels forMaxRecursion
andPlotPoints
. $\endgroup$MaxRecursion
orPlotPoints
from the result of evaluating aPlot
expression. $\endgroup$