Ck (geometrically continuous surface) constructions were developed to create surfaces that are smooth also at irregular points where, in a quad-mesh, three or more than four elements come together. Isogeometricâ€…elements were developed to unify the representation of geometry and of engineering analysis. We show how matched constructions for geometry and analysis automatically yield isogeometric elements. This provides a formal framework for the existing and any future isogeometric elements based on geometric continuity. 
Matched G k -constructions always yield C k -continuous isogeometric elements