ABSTRACT
A bstrac t. In order to define the smoothness of a piecewise polynomial surface, the domains of adjacent pieces must be related to one another by connecting maps; such maps reparametrize the surface pieces by mapping the domains of adjacent pieces to a joint domain. We characterize the subclass of connecting maps that can be used to surround a point by three or more pieces. The characterization of connecting maps for second order continuity suggests a lower bound on the degree of any curvature continuous surface assembled from polynomial pieces.
