Abstract: A subdivision algorithm is presented for the computation and representation of a smooth surface of arbitrary topological type interpolating a given net of smooth curves. The algorithm belongs to a new class of subdivision schemes called combined subdivision schemes. These schemes can exactly interpolate a net of curves given in any parametric representation. The surfaces generated by our algorithm are G² except at a finite number of points, where the surface is G¹ and has bounded curvature. The algorithm is simple and easy to implement, and is based on a variant of the famous Catmull-Clark subdivision scheme.