'Sub-pixel' movement is achieved by moving an over-sized image and then scaling the image. When the image is scaled down, the antialising effect creates the impression of movement within a pixel. For example, to move the small circle 0.25 pixels, the large circle image (which is 4 times bigger) is moved 1 pixel and then shrunk back down. If you download the Source Movie you can view the effect by zooming in on the leading edge of the circle in the paint window and playing the movie.
First published 16/12/2005