A new class of 2m-point binary non-stationary subdivision schemes

Abstract

Abstract A new class of 2m-point non-stationary subdivision schemes (SSs) is presented, including some of their important properties, such as continuity, curvature, torsion monotonicity, and convexity preservation. The multivariate analysis of subdivision schemes is extended to a class of non-stationary schemes which are asymptotically equivalent to converging stationary or non-stationary schemes. A comparison between the proposed schemes, their stationary counterparts and some existing non-stationary schemes has been depicted through examples. It is observed that the proposed SSs give better approximation and more effective results.

Keywords

• Binary approximating schemes
• Convergence
• Shape preservation
• Curvature and torsion
• Lagrange polynomials