Non-stationary subdivision schemes for surface interpolation based on exponential polynomials

This paper is concerned with non-stationary interpolatory subdivision schemes that can reproduce a large class of (complex) exponential polynomials. It enables our scheme to exactly reproduce the parametric surfaces such as torus and spheres. The subdivision rules are obtained by using the reproducing property of exponential polynomials which constitute a shift-invariant space S. In this study, we are particularly interested in the schemes based on the known butterfly-shaped stencils, proving that these schemes have the same smoothness and approximation order as the classical Butterfly interpolatory scheme.