I am thinking about the best ways to render two dimensional objects in the highest detail possible using modern graphics technology and it occurred to me that when I simplify a situation enough, I ought to be able to calculate the exact percentage of coverage of a triangle over a pixel, at least for the cases where an edge spans a pixel. This is, after all, the primary issue that multisampling and supersampling are dealing with, the issue of coverage.
I now realize that the question of how to exactly produce the coverage of the pixel that the vertices lie on is a much more difficult one.
Is it fair for me to say that it is theoretically possible to perform such a calculation on programmable shaders? After all, it's quite possible to compute the area covered by an arbitrary triangle which lies over a grid, on all the grid cells.
I guess I seem to have already come up with an explanation of why not do antialiasing this way: the corners.