Bivariate spline interpolation at grid points (Q1899125)

The feasibility of Lagrange interpolation at point sets including the grid points of rectangular partitions adding one or two diagonals to each rectangle by bivariate splines of arbitrary degreee and smoothness, is shown. In order to achieve this, the authors generate a net of line segments and choose point sets in these segments which satisfy the Schoenberg-Whitney condition for certain univariate spline spaces such that a principle of degree reduction can be applied. It may be observed that this approach is completely different from those contained in some earlier papers on bivariate splines of degree at most three [cf. \textit{C. K. Chui, T. X. He, R. H. Wang}, Colloq. Math. Soc. Janos Bolyai 49, 247-255 (1987; Zbl 0622.41003)].