A new insight into the Gn continuity of polynomial surfaces Original Research Article

A theorem of Degen describes the structure of G1 and G2 connection between two polynomial surfaces. This is based on common vector polynomials and an irreducibility condition of one of these vector functions related to the common boundary. In this paper Degenʹs results are reformulated, a new proof and a new interpretation is given which makes it possible to generalize the previous results to Gn continuity. Surprisingly, in case of Gn continuity, there is no need to add further conditions than for the G1G2 cases, still exists a common Gn continuous polynomial virtual patch with polynomial reparametrizations.