[pcwalton]

Mathematically, what you want to do here is to calculate the area of the pixel square (or circle; however you want to approximate it) that the shape covers. In this case a linear ramp actually approximates the true value better than smoothstep does. (I had the derivation worked out at some point; I don't have it handy, unfortunately.) Of course, beauty is in the eye of the beholder, and aesthetically one might prefer smoothstep.

By the way, since the article mentions ellipse distance approximations, the fastest way to approximate distance to an ellipse is to use a trick I came up with based on a paper from 1994 [1]: https://github.com/servo/webrender/blob/c4bd5b47d8f5cd684334... Unless it's changed recently, this is what Firefox uses for border radius.

[1]: http://mesh.brown.edu/taubin/pdfs/Taubin-tog94.pdf