I have what I thought was a simple matter. I have a square rectangle that I want to transpose. To make obvious the fact that the square is now on its “side” and not its “bottom” one needs to have the color variegated or otherwise such that it is obvious the square has rotated 90 degrees. I tried A LOT of things but, here is the last one that did not work
Graphics[{LightGreen,Texture[sample swatch],Parallelogram[{0, 0}, IdentityMatrix[2]]}, Axes -> True, PlotRange -> {{-3, 3}, {-3, 3}}]
maybe this is usefull, using polygon you could add colors to the square, that way when you rotate it the change is notorious
Graphics[{Rotate[
Polygon[{{0, 0}, {1, 0}, {1, 1}, {0, 1}},
VertexColors -> {Red, Red, Blue, Blue}], 45 Degree]}
, Axes -> True, PlotRange -> {{-3, 3}, {-3, 3}}]
Ah, yes, I should have said why that does not work at this stage. This is a matrix algebra classroom example so that is the reason for having a Parallelogram in the present case is so there are vertex points to transform. My workaround is to use a non-square rectangle, but that is sub-optimal in this case for pedagogical reasons.
I should also mention, this exercise, fully elaborated, needs to end up in 3D with a “house” made from placing a pyramid on a cube and rotating it using RotationTransform to complete the illustration. Following the Documentation and mixing PolyhedronData with GeometricTransform to do this is not straightforward and I am struggling with that at present.
For 3D maybe you can experiment with the CSG functions.
pyramid = Pyramid[{{0, 0, 2}, {2, 0, 2}, {2, 2, 2}, {0, 2, 2}, {1, 1, 4}}];
cube = Cube[{1, 1, 1}, 2];
house = CSGRegion["Union", {pyramid, cube}]
Graphics3D[house, Boxed -> False]
Coloring to match your needs may be a bit challenging. I don’t know how to do it.
Slick. In this case once I get the shape the color does not matter. But also in this case using the Wolfram built in functions defeats the classroom matrix transform example.