Problem with MousePosition after rotating a graphic

Question

I've been doing a dynamic matrix plot using MousePosition but I need to rotate the plot 45°. but when I do that the MousePosition lose coordinates.

Any idea of how to do the rotation keeping MousePosition working?.

This is the code I´ve been using:

rowNumber[rowdim_] := 
  If[# === None, #, 
    If[MatchQ[#, _?(1 <= # <= rowdim &)], #, None] &[
          1 + rowdim - Last@Ceiling[#]]] &@MousePosition["Graphics"];
colNumber[coldim_] := 
  If[# === None, #, 
   If[MatchQ[#, _?(1 <= # <= coldim &)], #, None] &[
          First@Ceiling[#]]] &@MousePosition["Graphics"];

DynamicModule[{x = {}}, EventHandler[
  Dynamic@MatrixPlot[
     SparseArray[
     Append[Map[# -> If[EvenQ@Count[x, #], 1, 0] &, x], {i_, j_} ->       
       1], {7, 7}],
  Mesh -> All],
 {"MouseClicked" :> 
    (x = 
       DeleteCases[
         Append[x, {rowNumber[7],colNumber[7]}], 
         {a_, b_} /; a == None || b == None])}]]

Answer 1

You can apply RotationTransform[θ] to the graphics primitives produced by MatrixPlot and RotationTransform[-θ] to theMousePosition coordinates:

θ = π/4;
rowNumber[rowdim_] := If[# === None, #, If[MatchQ[#, _?(1 <= # <= rowdim &)], #, None] &[
      1 + rowdim - Last@Ceiling[RotationTransform[-θ]@#]]] &[MousePosition["Graphics"]];
colNumber[coldim_] := If[# === None, #, If[MatchQ[#, _?(1 <= # <= coldim &)], #, None] &[
      First@Ceiling[RotationTransform[-θ]@#]]] &@ MousePosition["Graphics"];
DynamicModule[{x = {}}, 
 EventHandler[Dynamic@MapAt[GeometricTransformation[#, RotationTransform[θ]] &,
     MatrixPlot[SparseArray[Append[Map[# -> If[EvenQ@Count[x, #], 1, 0] &, x], 
      {i_, j_} -> 1], {7, 7}], Mesh -> All, Frame -> False, 
     ImageSize -> 1 -> 50], {1}], 
  {"MouseClicked" :> (x = DeleteCases[Append[x, {rowNumber[7], colNumber[7]}], {a_, b_} /; 
     a == None || b == None])}]]

If you need the frame and frame ticks, you can overlay a rotated empty plot with the same image size setting:

DynamicModule[{x = {}}, EventHandler[Dynamic@Overlay[{Rotate[#, θ] &@
    MatrixPlot[ConstantArray[0, {7, 7}], ImageSize -> 1 -> 50], 
   MapAt[GeometricTransformation[#, RotationTransform[θ]] &, 
    MatrixPlot[SparseArray[Append[Map[# -> If[EvenQ@Count[x, #], 1, 0] &, x], 
       {i_, j_} -> 1], {7, 7}], Mesh -> All, Frame -> False, ImageSize -> 1 -> 50], {1}]}, 
    All, 2, Alignment -> Center], 
    {"MouseClicked" :> (x = DeleteCases[Append[x, {rowNumber[7], colNumber[7]}], 
      {a_, b_} /; a == None || b == None])}]]

Use θ = π/6 to get