with a two dimensional surface, if we take (2,1) as the center point and consider a transformation with a rotation angle of 45º, the point (3,3) is transformed into point...
Start by translating the pivot point, $(2,1)$, to the origin, $(0,0)$, which in turn translates the point to be rotated, $(3,3)$, to $(1,2)$
Rotation of the point $(x,y) = (1,2)$ about the origin may now be accomplished by the equations
$x' = x\cos{\theta}-y\sin{\theta}$
$y' = y\cos{\theta}+x\sin{\theta}$
where $\theta = 45^\circ$
Finish by translating $(x',y')$ back to its position relative to $(2,1)$