Conditions for geometric continuity between polynomial and rational surface patches Original Research Article

Necessary and sufficient conditions for geometric continuity of arbitrary order between surface patches are derived and discussed. An analogy between the continuity conditions for curves and for patches is used to interpret these conditions. The paper presents a procedure of finding the order of continuity between two polynomial or rational patches, and describes two possible approaches to constructing patches joined smoothly via constructing their cross derivatives. One of these approaches leads to a costly numerical procedure based on the necessary and sufficient conditions, the other uses explicit formulae corresponding to stronger sufficient conditions. The results presented here are based on the algebraic results obtained in (Kiciak, 1995).