This was incredibly hard to achieve (for me). It uses Loop-Blinn with earclipping triangulator. In the case of one (or more) vertices intersecting a bezier "triangle" (control point + 2 polygon neighbours) the bezier triangle must be split in two (or more) "wings" (but for rendering each of the wings still has the original triangle as control points of course). There are so many things that can go wrong with this basic fix that I almost went insane. In the end of the video there is a tiny glitch but that one is acceptable for me since I made the polygon self-intersecting (looking at just the polygon vertices; the concave bezier curve is just added as an extra with absolutely no bearing on the rest of the process)