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Classification and Construction of Bivariate
Subdivision Schemes

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Bin Han

## Abstract

In this paper, we shall classify all possible subdivision
schemes on a triangular or quadrilateral regular mesh. Then we shall
give a general procedure to construct various subdivision
schemes with certain desired properties. Finally, we shall present
some examples of $C^2$ $\sqrt{2}, \sqrt{3}$ and triadic interpolatory
subdivision schemes with small stencils which are of interest in
CAGD.

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