For the math behind beziers, see 'Bezier.pas'. Here I just say a bit about where some relevant Python code is.

The routines for Face-Bezier texture projections are in quarkpy\b2utils, texPlaneFromCph and texcpFromFace. The former is rather complicated; I think it might be possible to clean it up using the Axis Base idea, but anway the code as some comments.