First, a symmetric version of the polygon tessellating program, ugtese [Gigus '85], has been developed. It splits faces of a polygon into bilaterally symmetric convex parts. Second, uci has been extended to include quadrilateral Gregory patches; this reduces the occurrence of asymmetric creases in the interpolating surfaces. Third, several new approaches are discussed to represent the surface with Bezier and Gregory patches and to determine the corresponding control vertices. Fourth, a method for subdivision of triangular Gregory patches into Bezier patches is described.