Cr rational splines over a triangulation

We propose a construction of Cr bivariate rational splines over a triangulation, via a finite element approach. For r⩾2, the usual bivariate polynomial splines require some supersmoothness at the vertices of the triangles, even when dealing with macro-elements. This is no more a requirement for our rational approach. In this paper we give a constructive method for rational Cr finite elements in R2 defined over triangles. Beside the general case, the process of construction is illustrated with two examples, namely the C1 case and the C2 case.