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

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

2004-03-23

arxiv.org/abs/math/0403380v1

Mathematics

Numerical Analysis

2004-13

Scientific paper

A new global basis of B-splines is defined in the space of generalized quadratic splines (GQS) generated by Merrien subdivision algorithm. Then, refinement equations for these B-splines and the associated corner-cutting algorithm are given. Afterwards, several applications are presented. First a global construction of monotonic and/or convex generalized splines interpolating monotonic and/or convex data. Second, convergence of sequences of control polygons to the graph of a GQS. Finally, a Lagrange interpolant and a quasi-interpolant which are exact on the space of affine polynomials and whose infinite norms are uniformly bounded independently of the partition.

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