Drawing outside of 3D plot area

Question

I have some grid-lines I want to extend outside of the bounding box of 3D plot BarChart3D. I do want to keep the bounding box small, as I want the automatic axes on the bounding box edge remain next to data.

In case of 2D plots ImagePadding does the trick. In Plot3D it does not. Here is an example.

ρ = 1/2 ({{1, 0, 0, -1}, {0, 0, 0, 0}, {0, 0, 0, 0}, {-1, 0, 0, 1}});
Show[{
  BarChart3D[ρ, BarSpacing -> {1, 1}, ChartLayout -> "Grid", 
   FaceGrids -> None, Method -> {"Canvas" -> None}, 
   PlotRange -> {{-1, 8}, {-1, 8}, {-0.5, 0.5}}, Boxed -> True, 
   FaceGrids -> None, Axes -> {True, True, True}, 
   ViewPoint -> {1, -5, 3}, 
   Ticks -> {Range[-10, 10, 2], Range[-10, 10, 2], 
     Range[-10, 10, 2]}], 
  Graphics3D[{Table[Text[y, {10, y 2 - 1.5, 0}], {y, 1, 4}], 
    Table[Line[{{-4, y 2 - 1.5, 0}, {20, y 2 - 1.5, 0}}], {y, 1, 
      4}]}]}, PlotRangeClipping -> False, ImagePadding -> All
 ]

If I add PlotRange->All I see, that the manual grid lines were clipped. I want the long lines, but BoundingBox tightly around the bars.

There exists a trivial solution for same problem for 2D plots: Drawing outside Plot area

I do expect, there is a solution, which does not require re-implementation of axes, face grids and other features.

Answer 1

Here is one way to do it. The strategy is to create our own bounding box Graphics3D object, and then give all the important options to Show instead of BarChart3D

Module[{barchart, linesandlabels, box},
 barchart =  BarChart3D[\[Rho], BarSpacing -> {1, 1},
    ChartLayout -> "Grid", 
    FaceGrids -> None,
    Method -> {"Canvas" -> None} ];
 linesandlabels = Graphics3D[{
    Table[Text[y, {10, y 2 - 1.5, 0}], {y, 1, 4}], 
    Table[Line[{{-4, y 2 - 1.5, 0}, {20, y 2 - 1.5, 0}}], {y, 1, 4}]}];
 box = Graphics3D[{Directive[
     FaceForm[None],
     EdgeForm[Black]],
    Cuboid[{-1, -1, -.5}, {8, 8, .5}]}];
 Show[barchart, linesandlabels, box,
  Boxed -> False,
  Axes -> True,
   Ticks -> {Range[-10, 8, 2], Range[-10, 8, 2], 
         Range[-10, 10, 2]},
  PlotRange -> {{-1, 20}, {-1, 8}, {-0.5, 0.5}},
  AxesOrigin -> {-1, -1, -.5},
  AxesStyle -> Opacity[0],
  TicksStyle -> Opacity[1]
  ]
 ]

This feels like a bit of a kludge, but works for this situation. If you want to do it more generally, we could possibly make a plotting function out of it.