[Sharlin]

It literally means that you take a box-shaped piece of the polygon, ie. the intersection of the polygon and a box (a square, in this case the size of one pixel). And do this for each pixel as they’re processed by the rasterizer. If you think of a polygon as a function from R^2 to {0, 1}, where every point inside the polygon maps to 1, then it’s just a signal that you can apply filters to.

[blauditore]

But as I understand it, the article is about rasterization, so if we filter after rasterization, the sampling has already happened, no? In other words: Isn't this about using the intersection of polygon x square instead of single sample per pixel rasterization?

[dahart]

This is about taking an analytic sample of the scene with an expression that includes and accounts for the choice of filter, instead of integrating some number of point samples of the scene within a pixel.

In this case, the filtering and the sampling of the scene are both wrapped into the operation of intersection of the square with polygons. The filtering and the sampling are happening during rasterization, not before or after.

Keep in mind a pixel is an image sample, which is different from taking one or many point-samples of the scene in order to compute the pixel color.

[yorwba]

It is applying the filter before rasterization, and then taking a single sample of the filtered signal per pixel.

[Sharlin]

The problem is determining the coverage, the contribution of the polygon to a pixel's final color, weighted by a filter. This is relevant at polygon edges, where a pixel straddles one or more edges, and some sort of anti-aliasing is required to prevent jaggies[1] and similar aliasing artifacts, such as moiré, which would result from naive discretization (where each pixel is either 100% or 0% covered by a polygon, typically based on whether the polygon covers the pixel center).

[1] https://en.wikipedia.org/wiki/Jaggies