MULTIDIMENSIONAL INTERPOLATORY SUBDIVISION SCHEMES

This paper presents a general construction of multidimensional interpo latory subdivision schemes. In particular, we provide a concrete metho d for the construction of bivariate interpolatory subdivision schemes of increasing smoothness by finding an appropriate mask to convolve wi th the mask of a three-direction box spline B-r,B-r,B-r of equal multi plicities. The resulting mask for the interpolatory subdivision exhibi ts all the symmetries of the three-direction box spline and with this increased symmetry comes increased smoothness. Several examples are co mputed (for r = 2,...,8). Regularity criteria in terms of the refineme nt mask are established and applied to the examples to estimate their smoothness.