Optical flow from given affine transformations

Dear community,

In my simulation, foreground images(fg) move on background images(bg) along a continuous trajectory (polynomial, Bezier parametrized with time ) while being continuously scaled and rotated. It means that at any given time I have access to the 2D position of any point on the fg. To calculate the optical flow for each pixel in the reference time, I just calculate vector that connects the center of the pixel at the reference time and final time.

My questions are:

  1. Is optical flow calculated with respect to the center of each pixel?
  2. Is my approach described above correct?
  3. How can I visualize the optical flow vectors calculated?