Motivated by the increasing request of surface representation techniques suitable for biomedical imaging applications, we construct a non-stationary subdivision scheme for regular 3-directional grids, which enjoys the following properties: (i) interpolation, (ii) affine invariance, (iii) C2 smoothness, (iv) approximation order 6 and (v) the capability of reproducing several trigonometric surfaces, especially ellipsoids. To study the smoothness properties of this new scheme via existing analysis tools, we also construct an auxiliary stationary subdivision scheme enjoying properties (i)-(iv). Taking into account that, when applied on regular 3-directional grids, the Modified Butterfly scheme is C1 and has approximation order 4, the subdivision schemes derived in this paper can be considered improved variants of the Modified Butterfly scheme.
Bibliographical noteFunding Information:
Lucia Romani was partially supported by MIUR-PRIN 2012, grant no. 2012MTE38N. Jungho Yoon was supported by Priority Research Centers Program 2009-0093827 through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology.
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- Approximation order
- Exponential polynomial reproduction
- Non-stationary subdivision