This was a test in having an AI (google-cli) write almost everything on this page. I resorted to writing some code myself when I just couldn't figure out how to ask it to do what I wanted. This is the closest I've come to "vibe coding".
Barycentric Coordinates for Triangle Rasterization
Symmetric Polynomial
Adjust u, w so that the lines are perpendicular to the triangle sides. (TODO: calculate automatically). Set s1, t1, s2, t2 as desired.