Problem using Rotation in Show

Question

I would like to have an animation of rotating box and displayed it with other elements (not rotated) using Show. The first step to do that is to have all the elements working properly. So I did the following:

1. Created a box:

   myBox = Cuboid[{-40, 40, 0}, {40, 60, 10}];
   

   and make a Graphics3D out of it:

   Graphics3D[myBox]
   

2. Rotated it:

   Rotate[Graphics3D[myBox], Pi/2, {0, 0}]
   

3. Used Show:

   Show[Rotate[Graphics3D[myBox], Pi/2, {0, 0}]]
   

And the strange things started to happen.

I've got "Show::gtype: Rotate is not a type of graphics.". So I googled and found the following: link1, link2, link3

I tried most of the suggestions from those threads and the only one that helped was halirutan's from the first one:

    Show[Graphics@First@Rotate[Graphics3D[myBox], Pi/2, {0, 0}]]

There was no error, but also no rotation, so the problem was still not solved.

Then I tried:

    First@Show[Graphics@Rotate[Graphics3D[myBox], Pi/2, {0, 0}]]

The image was rotated, but it wasn't Graphics, so I couldn't use Show on it.

I suppose that answer is somewhere in the threads I quoted, but either I missed it or I can't use it.

Answer 1

myBox = Cuboid[{-40, 40, 0}, {40, 60, 10}];
Show@MapAt[Rotate[#, Pi/4, {0, 0, 1}, {0, 0, 0}] &, Graphics3D[myBox], {1}]

Manipulate[Table[Show[Graphics3D[{Red, Sphere[{0, 0, 0}, 30],
    Green, Cylinder[{{30, 30, 30}, {40, 50, 40}}, 30]}],
    MapAt[Rotate[#, k, v, {0, 0, 0}] &, Graphics3D[myBox], {1}],
    Boxed -> False, PlotRange -> {{-100, 100}, {-100, 100}, {-100, 100}}],
   {k, 0, 2 Pi, Pi/12}] // ListAnimate,
 {{v, {1, 0, 0}}, {{1, 0, 0}, {0, 1, 0}, {0, 0, 1}}}]

Answer 2

My understanding of the question is that you are not interested in doing a rotation of the 3D object inside the 3D scene, but instead want to do a 2D rotation of the displayed Graphics3D, as if the latter were just another 2D Graphics element.Then you want to combine the result with additional 2D Graphics using Show.

For this task, the right tool is simply to use Inset. Here is an example:

Show[
 Graphics[
  Inset[
   Rotate[
    Graphics3D[myBox, ImageSize -> 300], Pi/4, {0, 0}] ]
  ],
 ImageSize -> 300
 ]

Here I used the same commands as in the question, except to change the rotation angle to something more obviously "rotated". Then I specified ImageSize options for both the Graphics3D and the final Show. This, together with the options for Inset and the choice of PlotRange in Graphics, can be used to place the rotated object arbitrarily. Here I didn't include that because there were no other objects to be displayed. But the Show framework is all you needed, and from there everything works as it always does in Show.

In principle, you can also do away with Rotate completely and use the options of Inset directly to rotate the content in 2D.

Answer 3

The answer:

myBox = Cuboid[{-40, 40, 0}, {40, 60, 10}];

Show@MapAt[Rotate[#, Pi/4, {0, 0, 1}, {0, 0, 0}] &, Graphics3D[myBox], {1}]

is a good method.

I have an another way to solve this problem.

myBox = Graphics3D[Cuboid[{-40, 40, 0}, {40, 60, 10}]];

Graphics3D[Rotate[myBox[[1]], Pi/4, {0, 0, 1}, {0, 0, 0}]]

Compare with the above method, it is simpler and easier to understand.