Classification and Construction of Bivariate Subdivision Schemes

Bin Han


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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