It's done the same way that antialiased lines are done. There are many algorithms for doing this task with the simplest being to rasterize the image at higher resolution then sampling down (which is what most graphics cards do for their full-screen AA). There are also algorithms for directly performing antialiasing, with the quick google search http://www.google.com/search?hl=en&q...ed-area+sample turning up a number of good discussions.

My point on the document was that the screen/image representation samples a continuous function and the sampling function determines the minimum visible item.