Extracting Lighting specs used in a Graphics3D object

Question

I'm getting a plot which is mostly fine with Lighting->Automatic, but a bit too dark. How do I go about getting the Lighting specification used in the plot so I could make it explicit and tweak it?

IE, need a utility which extracts lighting and related specs from a Graphics3D object.

f1[x_, y_] = 
  x (3/16 (9 - Sqrt[17]) x + 1/8 (9 - Sqrt[17]) y) + 
   y (1/8 (9 - Sqrt[17]) x + 3/4 (9 - Sqrt[17]) y);
f2[x_, y_] = 2 x^2 + 4 y^2;
Plot3D[{f1[x, y], f2[x, y]}, {x, -2, 2}, {y, -2, 2}, 
 BoxRatios -> {1, 1, 1}]

Answer 1

Due to this bug, setting Lighting for Graphics3D as an option directly (e.g. via Show) doesn't work, and we must specify it individually for every object (or a group of objects) on the scene like a usual graphics directive. Starting at least from Mathematica 10 the built-in 3D plotting functions like Plot3D take the Lighting specifications from the absolute/resolved value of the PlotStyle option (which they generate from your input), and then build them into the list of graphics primitives (the first argument of Graphics3D). One can turn on verbose logging for this process by setting the system option "VisualizationOptions" -> {"Verbose" -> True}.

We can obtain the default styles with Lighting specifications included, as the value of "DefaultPlotStyle" suboption of Method option, via Charting`ResolvePlotTheme:

defaultplotstyle = "DefaultPlotStyle" /. 
   (Method /. Charting`ResolvePlotTheme[$PlotTheme, Plot3D])

We can obtain the actual (absolute) value of PlotStyle (generated by Plot3D for your particular input) from the output generated during evaluation of Plot3D after setting the system option "VisualizationOptions" -> {"Verbose" -> True} as Domen recommends in the comments. The code below automatizes this:

f1[x_, y_] = x (3/16 (9 - Sqrt[17]) x + 1/8 (9 - Sqrt[17]) y) + 
             y (1/8 (9 - Sqrt[17]) x + 3/4 (9 - Sqrt[17]) y);
f2[x_, y_] = 2 x^2 + 4 y^2;

Internal`WithLocalSettings[
  SetSystemOptions["VisualizationOptions" -> {"Verbose" -> True}],
  reap = Reap[Block[{Print = (Sow[{##}] &)},
      Plot3D[{f1[x, y], f2[x, y]}, {x, -2, 2}, {y, -2, 2}, 
       BoxRatios -> {1, 1, 1}]]];,
  SetSystemOptions["VisualizationOptions" -> {"Verbose" -> False}] 
  ];

Cases[reap, HoldPattern[PlotStyle -> _], {1, Infinity}] /. x_Real :> Round[x, .01]

{PlotStyle -> {Directive[Specularity[GrayLevel[1], 3], RGBColor[0.88, 0.61, 0.14], 
    Lighting -> {{"Ambient", RGBColor[0.3, 0.22, 0.09]},
       {"Directional", RGBColor[0.26, 0.18, 0.04], ImageScaled[{0, 2, 2}]}, 
       {"Directional", RGBColor[0.26, 0.18, 0.04], ImageScaled[{2, 2, 2}]}, 
       {"Directional", RGBColor[0.26, 0.18, 0.04], ImageScaled[{2, 0, 2}]}}], 
   Directive[Specularity[GrayLevel[1], 3], RGBColor[0.37, 0.51, 0.71],
     Lighting -> {{"Ambient", RGBColor[0.2, 0.25, 0.33]}, 
       {"Directional", RGBColor[0.15, 0.21, 0.3], ImageScaled[{0, 2, 2}]}, 
       {"Directional", RGBColor[0.15, 0.21, 0.3], ImageScaled[{2, 2, 2}]}, 
       {"Directional", RGBColor[0.15, 0.21, 0.3], ImageScaled[{2, 0, 2}]}}]}}

Having this, you can play with the directives to get the lighting you wish.