Hermite Subdivision with Shape Constraints on a Rectangular Mesh
Résumé
We study a two parameter version of the Hermite subdivision scheme introduced in [7], wish gives $C^1$ interpolants on rectangular meshes. We prove $C^1$-convergence for a range of the two parameters. By introducing a control grid we can choose the parameters in the scheme 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 we use only very crude estimates for the initial slopes.