[codeflo]

The opening statement makes it out that this exact calculation is supposed to be superior to multisampling, but the opposite is the case. Computing the exact mathematical coverage of a single polygon against a background is useless for animations if you can't seamlessly stitch multiple polygons together. And that's why GPUs use multisampling: Each sample is an exact mathematical point that's covered by either polygon at the seam, without the background bleeding through.

[dahart]

You might be making some incorrect assumptions about what this article is describing. It’s not limited to a single polygon against a background.

Analytic integration is always superior to multisampling, assuming the same choice of filter, and as long as the analytic integration is correct. Your comment is making an assumption that the analytic integration is incorrect in the presence of multiple polygons. This isn’t true though, the article is using multiple polygons, though the demo is limited in multiple ways for simplicity, it doesn’t appear to handle any arbitrary situation.

The limitations of the demo (whether it handles overlapping polygons, stitched meshes, textures, etc.) does not have any bearing on the conceptual point that computing the pixel analytically is better than taking multiple point samples. GPUs use multisampling because it’s easy and finite to compute, not because it’s higher quality. Multisampling is lower quality than analytic, but it’s far, far easier to productize, and it’s good enough for most things (especially games).

[muyyatin2]

This is correct! My CPU implementation of this code can handle the overlapping polygons / meshes / textures. https://phetsims.github.io/alpenglow/#depthSort (takes forever to load, sorry!) is an example of using the analytic approach to render a phong-shaded teapot, where it splits things into adjacent but non-overlapping polygons (from a source of VERY overlapping polygons).

[blauditore]

If you can't stitch polygons together seamlessly, how can you be sure the background doesn't bleed through with sampling? Isn't computing the exact coverage the same as having infinitely many point samples? The bleed-through of the background would then also be proportional to the gap between polygons, so if that one's small, the bleeding would be minor as well.

[codeflo]

No, in animated models, there is no gap between polygons. And if you only compute single-polygon coverage, you can’t determine whether for two polygons that each cover 50% of a pixel, they both cover the same 50%, or complementary 50%, or anything in between. In practice, systems like that tend to show something like 25% background, 25% polygon A and 50% polygon B for the seam pixels, depending on draw order. That is, you get 25% background bleed.