Hermite subdivision with shape constraints on a rectangular mesh

In 1999, Dubuc and Merrien introduced a Hermite subdivision scheme which gives C1-interpolants on a rectangular mesh. In this paper a two parameter version of this scheme is analyzed, and C1-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.

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