In my opinion, triangle 1 definitely doesn't cover the pixel and triangle 4 definitely covers it. If we assume a pixel is covered when there is a intersection with the triangle, then both triangle 2 & 3 cover the pixel. If we assume a pixel is covered only when the triangle includes the middle point of the pixel, then triangle 2 doesn't cover the pixel while triangle 3 does.

To add to the point above, other than only looking at the center point of the pixels maybe it would be advantageous to include more points of the pixel to have a better approximation of the area of the triangle within the pixel.

We briefly mentioned in class that pixels aren't actually square. While 4 seems triangle seems to contain the whole pixel, it would seem like over-kill (large margins on all sides) if pixels were actually more like circles with blurred edges.

I agree with @weiren and believe that we should color the pixel when the midpoint of the pixel is within the triangle. An example that makes me doubt this hypothesis is the question of what would happen if we had a very small but visible triangle right at the center of the pixel. If this triangle is very very small, it might not make sense to alter the color of the pixel to match it. This is assuming that a pixel is either fully lit or not lit.

Intuitively, another metric for determining whether the pixel is covered or not can be the percentage of the surface that is covered. If that percentage exceeds 70%, for example, we could consider the pixel covered. By that logic, triangles 3 and 4 cover, and 1 and 2 do not (although 3 barely makes the cut).

Similar to tarajones99's comment, I wonder what happens if a triangle doesn't pass through the center of any pixel. Say, if we had a grid of such pixels, triangle 2 would not cover any center. Would it make sense for it to disappear or should its color be blended (based on percentage of area it covers)?

Motivated by combining the midpoint idea and percent coverage, I wonder if it makes sense to have something similar to line rasterization, but with a shape that doesn't intersect with the pixel square (like a small circle).

Assuming that more than one of these triangles cover the pixel, and that the pixel can only be one color, how do we indicate that? How do we decide which triangle the pixel "belongs to"?

Perhaps, we could inscribe a circle in the triangle and see if that overlaps the pixel?

I guess first question is which one of these 4 triangle is on top (closest to camera) and whether they are opaque or transparent.

If we treat them separately, Triangle 1 will not be rasterized as it doesn't cover the pixel at all. For 2,3,4 we will have to consider how many samples per pixel using to render. If it's jus 1 sample/pixel and it's at the center of the pixel, 3,4 will be rendered.

I guess there are lots of ways to render this pixel. The more accurate it represents the final color, the more efforts hardware need to do, but you also get better image. It's a trade off between image quality and hardware processing time.