Triangular sqrt(3)-Subdivision Schemes: The Regular Case

The paper deals with the theoretical investigation of sqrt(3)-subdivision schemes in the shift-invariant setting. In Section 2 we collect the available theory on refinable functions (subdivision surfaces), with emphasis on their Sobolev and Holder smoothness. There we also discuss the computational tools and Matlab routines used for numerically estimating smoothness exponents. Families of interpolatory and approximating sqrt(3)-subdivision schemes are investigated in Section 3. Some face-based sqrt(3)-subdivision schemes which are related to vector-valued refinable functions are also analyzed.