rotate a plane around a diagonal

Question

I would like to rotate a plane, not around a single (X or Y) axis, but around the diagonal (45 degrees between X and Y). How do I calculate the Rx and Ry given the Rdiagonal?

(Rdiagonal is the amount of rotation I would like to achieve around the diagonal axis).

To clarify: just take a yellow PostIt and draw cross on it (a horizonal and a vertical line). These are the X and Y axes. Rotating around these axes is easy (assuming you can just specify Rx and Ry). But I would like to rotate around the diagonal axis. What are the Rx and Ry in that case?

I think it's something like Rx = Rdiagonal / sqrt(2). But I'm not sure.

Answer 1

This is probably more of a mathoverflow question, but I found some information here about rotation around an arbitrary axis. It provides the derivation for the translation and rotation matrices.

Answer 2

Your plane will most certainly given by some points (depending on the dimensionality). You can then use a rotation matrix to transform these points: new = R * old. Afterwards, construct your plane from these points.

To get the right rotation matrix, see the entry at wikipedia.

Answer 3

See HERE.