Journal Article10.1137/S0036142995294310
Multidimensional Interpolatory Subdivision Schemes
TL;DR: In this article, a general construction of multidimensional interpolatory subdivision schemes is presented, in particular, a concrete method for finding an appropriate mask to convolve with the mask of a three-direction box spline Br,r,r of equal multiplicities.
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Abstract: This paper presents a general construction of multidimensional interpolatory subdivision schemes. In particular, we provide a concrete method for the construction of bivariate interpolatory subdivision schemes of increasing smoothness by finding an appropriate mask to convolve with the mask of a three-direction box spline Br,r,r of equal multiplicities. The resulting mask for the interpolatory subdivision exhibits all the symmetries of the three-direction box spline and with this increased symmetry comes increased smoothness. Several examples are computed (for r = 2,...,8). Regularity criteria in terms of the refinement mask are established and applied to the examples to estimate their smoothness.
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