A NEW INSIGHT INTO THE G(N) CONTINUITY OF POLYNOMIAL SURFACES

A theorem of Degen describes the structure of G(1) and G(2) connection between two polynomial surfaces. This is based on common vector polyn omials and an irreducibility condition of one of these vector function s related to the common boundary. In this paper Degen's results are re formulated, a new proof and a new interpretation is given which makes it possible to generalize the previous results to G(n) continuity. Sur prisingly, in case of G(n) continuity, there is no need to add further conditions than for the G(1)/G(2) cases, still exists a common G(n) c ontinuous polynomial virtual patch with polynomial reparametrizations.