[ssp]

> If we assumed a radially symmetric kernel, then coverage would just be some monotonic function of the distance from the pixel center to the edge

I don't think that's true. Consider a simple case where the shape is a square and you are sampling in such a way that the closest edge point is closer to a corner of the square than the filter width. Using a function of distance you will get the same result as when sampling far from the corner. But the coverage is different in the two cases.

[jacobolus]

I’m just talking about rendering one edge (infinite line) separating the plane into two regions.

If you want to deal with pixels near multiple edges, it needs to be more complicated.