Keep on improving, still rebuilding a lot of things, and extending. This image uses a new splitter operator, which takes a surface (made of four bezier curves forming a close area), and splits it according to one orientation (two are available given the two possible opposite curve pa) and one ratio. Computation of the boundary is then done by computing the two new points on the 'base" curves, and aggregating control vectors of the "untouched" two other curves.
The previous curve corresponds to a splitter recursion on a simple pic bezier, alternating "horizontal" and "vertival" splitting. Chase the red ...