Question

According to the documentation AbsoluteOptions[expr,name] “gives the absolute setting for the option name”.

“AbsoluteOptions gives the actual settings for options used internally by Mathematica when the setting given is Automatic or All.”

Here is an example they show:

<< AbsoluteOptions[Plot[Sin[x], {x, 0, 2 Pi}, 
     PlotRange -> Automatic], PlotRange]
>> {PlotRange -> {{0., 6.28319}, {-1., 1.}}}

Here I use << to denote Input and >> to denote output.

This seems to work fine. However, when I try to obtain the AspectRatio of a plot it simply gives me Automatic. Try this,

AbsoluteOptions[
 ListPlot3D[{{1, 1, 1, 1}, {1, 2, 1, 2}, {1, 1, 3, 1}, {1, 2, 1, 4}}, 
  AspectRatio -> Automatic],
  AspectRatio
 ]

Similar format as the example they show but the output I get is simply

{AspectRatio->Automatic}

Does this mean that the argument expr can only be a Graphics object and not Graphics3D? This doesn’t make sense because it works fine if I try to obtain the PlotRange of a Graphics3D object. Is this a bug or my mathematica is broken? Another thing could be that the documentation is not being very specific. Which one is it?
Here is a link to the documentation:

http://reference.wolfram.com/mathematica/ref/AbsoluteOptions.html

I’m using Mathematica 7.0.1.0.

Answer 1

You can apply ImageDimensions directly to Graphics3D to get its ImageSize.

It seems that AbsoluteOptions just was not modified since Mathematica 4 (see bottom of the corresponding documentation page). This function is very buggy (often gives wrong value for PlotRange for 2D graphics generated by Show, for example) and sometimes does not work at all as you pointed in your question. Compare it with FullOptions and FullGraphics those are seemed to be not modified since version 2… Sometimes FullOptions gives right value when AbsoluteOptions gives wrong or does not work at all.