What if an edge falls on a sample point exactly at one of the vertices? I realize that some pixels are covered while sometimes not under this circumstance. For example, the top-right and bottom-left pixels for the bottom-right square pattern aren't covered, though I think they should according to the edge rules. I have an idea but not sure whether it's correct: The sample point is classified as within triangle if the point is on a strict top edge or a strict left edge. Open to any comments!

I was also curious about why the vertices of some of the triangles are not covered. Weiren, could you explain more about what you mean by “strict” top or left edge?

@acz Take the bottom-right square pattern for example. The top-left point is classified within the triangle because the two edges it's located are a top edge and a left edge. The bottom-left point and the top-right point are not classified within the triangle because there exists an edge for the point that is neither a top edge or a left edge. "Strict" means that for all edges the point is on, they must be a left edge or a top edge.