Hermite subdivision with shape constraints on a rectangular mesh
In 1999 [Adv. Comput. Math. 10, No. 3-4, 343--365 (1999; Zbl 0934.65009)], \textit{S. Dubuc} and \textit{J.-L. Merrien} introduced a Hermite subdivision scheme which gives \((C^1)\)-interpolants on a rectangular mesh. In this paper a two parameter version of this scheme is analyzed, and \((C^1)\)-convergence is proved for a range of the two parameters. By introducing a control grid the parameters in the scheme can be chosen so that the interpolant inherits positivity and/or directional monotonicity from the initial data. Several examples are given showing that a desired shape can be achieved even if only very crude estimates for the initial slopes are used. The bibliography contains 22 items.
scientific article; zbMATH DE number 5081852
scientific article