A constructive algebraic strategy for interpolatory subdivision schemes induced by bivariate box splines |
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Authors: | Costanza Conti Luca Gemignani Lucia Romani |
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Institution: | 1. Dipartimento di Energetica “Sergio Stecco”, Università di Firenze, Viale Morgagni 40/44, 50134, Firenze, Italy 2. Dipartimento di Matematica, Università di Pisa, Largo Bruno Pontecorvo 5, 56127, Pisa, Italy 3. Dipartimento di Matematica e Applicazioni, Università di Milano-Bicocca, Via R. Cozzi 53, 20125, Milano, Italy
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Abstract: | This paper describes an algebraic construction of bivariate interpolatory subdivision masks induced by three-directional box spline subdivision schemes. Specifically, given a three-directional box spline, we address the problem of defining a corresponding interpolatory subdivision scheme by constructing an appropriate correction mask to convolve with the three-directional box spline mask. The proposed approach is based on the analysis of certain polynomial identities in two variables and leads to interesting new interpolatory bivariate subdivision schemes. |
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