On the evaluation of box splines
The topic of multivariate \(B\)-splines really took off after the appearance of nice recurrence relations for simplex splines due to \textit{C. A. Micchelli} [Rocky Mt. J. Math. 10, 485-497 (1980; Zbl 0456.41003)]. The present paper outlines the procedures to meet the difficulties that arise in evaluation of box splines [for definition and other details see \textit{C. de Boor}, \textit{K. Höllig} and \textit{S. D. Riemenschneider}, Box splines, Springer, Berlin (1993)], when a straightforward use of the simple recurrence relation for such splines is made. It is mentioned that the difficulty is essentially due to the fact that step functions are not computable. A MATLAB program for the (correct) evaluation of a box spline is also given. Since use of the recurrence relation is very time-consuming, various alternative approaches involving use of the idea of subdivision [see \textit{E. Cohen}, \textit{T. Lyche} and \textit{R. Riesenfeld}: Comput. Aided Geom. Des. 1, 131-148 (1984; Zbl 0567.65004) and \textit{W. Dahmen} and \textit{C. A. Micchelli}, ibid. 1, 115- 129 (1984; Zbl 0581.65011)] are also given.
scientific article; zbMATH DE number 510186