A geometric approach for Hermite subdivision
A new approach for the construction of non-uniform and non-stationary Hermite \(C^1\) subdivision schemes is presented. This new approach lies in the geometric interpretation of the subdivision steps using Bernstein-Bézier bases and the related results for general families of spaces. The Hermite interpolating function is expressed in the Bernstein basis and replaced by two new functions from the space of the same family. The subdivision is then described in terms of the transformation matrix which maps the initial four Bézier points in the final set of seven control points corresponding to the two new functions. The presented approach can be considered as the natural extension of the cubic de Casteljau algorithm for more general function spaces. The analytic formulation of the subdivision formulas for Hermite subdivision is a consequence of the geometric constructions. The subdivision scheme for rational functions is described in detail. Numerical and graphical examples are shown in the article, too.
scientific article; zbMATH DE number 5710584