Hierarchical Box Splines

Box splines are considered as a natural generalization of univariate uniform B-splines. Box splines have local support and are positive in the interior of its support. The translates of box splines form a partition of unity. In this paper we extend the hierarchical paradigm of tensor product B-splines to box splines, which are called hierarchical box splines. We take the application of quartic smooth hierarchical box splines in surface fitting as an example to demonstrate the adaptivity and flexibility of hierarchical box splines.