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.
Bibliographical noteFunding Information:
✩ Yeon Ju Lee was supported by the Korea Research Foundation Grant funded by the Korean Government (MOEHRD) (KRF-2007-357-C00007). Jungho Yoon was supported by Priority Research Centers Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2009-0093827). * Corresponding author. E-mail addresses: email@example.com (Y.J. Lee), firstname.lastname@example.org (J. Yoon).
- Approximation order
- Asymptotical equivalence
- Exponential polynomial
- Non-stationary subdivision