Iirc, triangulation iterations can replace previous cuts. So A and B might not have any meaning in the next iteration if you triangulate properly. That's why it's okay to cut at random, because it only affects outcome indirectly.
Yes. After checking Wikipedia I was referring to the edge flipping operation which is described in the “flip algorithms” section. So there's also a divide and conquer algorithm in the article, but it needs extra steps to fix the divide edge. Was that what you were talking about?
