I have an image, I, sampled on a uniform grid:
$\ x_i = i*\Delta x, y_j = j*\Delta y, $
I need to resample this image to a grid rotated counterclockwise by an angle $\ \theta$ around $\ (x_0,y_0)$:
$\ u_i = i*\Delta u, v_j = j*\Delta v $
$\ x(u_i,v_j) = x_0 + cos(\theta)*u_i - v_j*sin(\theta)$
$\ y(u_i,v_j) = y_0 + sin(\theta)*u_i + v_j*cos(\theta)$
How do I best do this?
I understand that I can e.g. do bilinear interpolation to find I from the 4 (x,y) corners around each $\ (u_i,v_j)$.
However I am not free to choose $\ \Delta u $ and $\ \Delta v $ as I wish.
What is the Nyquist criterion for this rotated grid?
Am I right in assuming that it will be?:
$\ \Delta u = cos(\theta)*\Delta x + sin(\theta)*\Delta y$
$\ \Delta v = -sin(\theta)*\Delta x + cos(\theta)*\Delta y$