Rotating x,y points 45 degrees I have a two dimensional data set that I would like to rotate 45 degrees such that a 45 degree line from the points (0,0 and 10,10) becomes the x-axis. For example, the x,y points (1,1), (2,2), and (3,3) would be transformed to the points (0,1), (0,2), and (0,3), respectively, such that they now lie on the x-axis. The points (1,0), (2,0), and (3,0) would be rotated to the points  (1,1), (2,2), and (3,3). How can I calculate how to rotate a series of x,y point 45 degrees?

I don't think you have defined things properly, at least not with the usual mathematical definition of the $x$ axis going positive left and the $y$ axis going positive up.  If you rotate the $x$ axis as you say, $(1,1)$ should go to $(1,0)$, not to $(0,1)$.  Also note that your vectors change in length, which may or may not be a problem.
You seem to be trying to rotate the plane of lattice points by $45^\circ$.  The problem is that many lattice points are no longer lattice points after the rotation.  Your definition is not linear:  given $(1,1) \to (1,0), (0,1) \to (1,1)$ we should have $(1,0) \to (0,-1)$ which is clearly not what you want.
