Shape preservation of 4-point interpolating non-stationary subdivision scheme

In this paper, the shape preserving properties of the binary four-point interpolating non-stationary scheme (Beccari et al., 2007) are analyzed, which we obtain for the hyperbolic case of the scheme, when ν0>1. Sufficient conditions on the original control points are developed that allow to generate positivity, monotonicity and convexity preserving curves after a finite number of subdivision steps. Moreover, the results are generalized to derive conditions for the shape preservation of the limit curves. Also the limit curves with specific shape preserving properties are depicted by significant application of derived conditions on the initial data.