Applying transformation to the plot as well as the GridLines?

Questions
1

Given a simple Plot[x, {x, -1, 1} GridLines->Automatic]

is there a way to apply transformation to the plot as well as the GridLines? For example

Plot[x, {x, -1, 1}, GridLines->Automatic]/.L_Line:>GeometricTransformation[L, ShearingTransform[Pi/4, {1,0}, {0,1}]]

will transform the plot but not the GridLines. Can the GridLines also be transformed?

2

Here is an attempt with FullGraphics, a very old function:

fg = FullGraphics[Plot[x, {x, -1, 1},
    GridLines -> Automatic]]
Graphics[GeometricTransformation[fg[[1]],
  ShearingTransform[Pi/4, {1, 0}, {0, 1}]]]
3

Try this:

p = Plot[x, {x, -1, 1}, GridLines -> Automatic];

ImageForwardTransformation[p,ShearingTransform[Pi/4,{1,0},{0,1}],PlotRange->All]

Shearedplot.png
Shearedplot.png544Ă—218 16 KB

4

Thanks to both. Never heard of either of those functions.