rational splines over a triangulation

We propose a construction of C r 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 C r finite elements in R 2 defined over triangles. Beside the general case, the process of construction is illustrated with two examples, namely the C 1 case and the C 2 case.