rotate a plane around a diagonal

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 ve开发者_如何学运维rtical 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.

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.

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.