Generalized $C^1$ quadratic B-splines generated by Merrien subdivision algorithm and some applications.

2004-13A new global basis of B-splines is defined in the space of generalizedquadratic splines (GQS)generated by Merrien subdivision algorithm. Then, refinement equations forthese B-splines andthe associated corner-cutting algorithm are given. Afterwards, severalapplications arepresented. First a global construction of monotonic and/or convexgeneralized splines interpolating monotonic and/or convex data. Second,convergence of sequencesof control polygons to the graph of a GQS. Finally, a Lagrange interpolantand a quasi-interpolant which are exact on the space of affine polynomialsand whose infinitenorms are uniformly bounded independently of the partition