wolfram mathematica - How to determine PlotRange to include all of graphics?

Question

Given Graphics object, how do I determine the range of coordinates needed to include all of graphics? Basically I need something like what Show does by default, but I want to specify PlotRange,PlotRangePadding and ImagePadding explicitly.

Example, two Shows below should render the same

g = Graphics[{Thickness[1], CapForm["Round"], Line[{{0, 0}, {1, 1}}]}];
Show[g]
Show[g, PlotRange -> getPlotRange[g], PlotRangePadding->getPlotRangePadding[g], ImagePadding->getImagePadding[g]]

Motivation: fixing diagrams in this question

Update: AbsoluteOptions gives me PlotRange but not the other two options. Explicitly specifying ImagePadding->Automatic changes appearance though it's supposedly Automatic by default.

Two images below show differently and I don't understand why

g = Graphics[{Thickness[1], CapForm["Round"], Line[{{0, 0}, {1, 1}}]}];
Show[g]
Show[g, Sequence @@ AbsoluteOptions[Show[g]]]

Update 2: A similar problem was brought up a year ago, with no solutions proposed, and not fixed as of Mathematica 8.0. To summarize

1. There's no way to reproduce Show[g] above with explicit setting of PlotRange
2. There's no way to get absolute ImagePadding used by Show[g]
3. Show[g,PlotRange->Automatic] looks different from Show[g]
4. AbsoluteOptions can give the wrong result for PlotRange

Answer 1

I can suggest the following Ticks hack:

pl = Plot[Sin[x], {x, 0, 10}];
Reap[Rasterize[Show[pl, Ticks -> {Sow[{##}] &, Sow[{##}] &}, ImageSize -> 0], 
   ImageResolution -> 1]][[2, 1]]

=> {{-0.208333, 10.2083}, {-1.04167, 1.04167}} 

The trick is that real PlotRange is determined by the FrontEnd, not by the Kernel. So we must force the FrontEnd to render the graphics in order to get tick functions evaluated. This hack gives the complete PlotRange with explicit value of PlotRangePadding added.

More general solution taking into account a possibility that pl has non-standard value of DisplayFinction option and that it may have Axes option set to False:

completePlotRange[plot:(_Graphics|_Graphics3D|_Graph)] := 
 Quiet@Last@
   Last@Reap[
     Rasterize[
      Show[plot, Axes -> True, Frame -> False, Ticks -> (Sow[{##}] &), 
       DisplayFunction -> Identity, ImageSize -> 0], ImageResolution -> 1]]

One can get the exact PlotRange (without the PlotRangePadding added) with the following function:

plotRange[plot : (_Graphics | _Graphics3D | _Graph)] := 
 Quiet@Last@
   Last@Reap[
     Rasterize[
      Show[plot, PlotRangePadding -> None, Axes -> True, Frame -> False, 
       Ticks -> (Sow[{##}] &), DisplayFunction -> Identity, ImageSize -> 0], 
      ImageResolution -> 1]]

---

P.S. On the Documentation page for PlotRange under the "More information" one can read: "AbsoluteOptions gives the actual settings for options used internally by Mathematica when the setting given is Automatic or All. " (emphasis mine). So it seems that the Documentation does not even guarantee that AbsoluteOptions will give correct values for PlotRange when it is not Automatic or All.