A new 8-point binary interpolatory subdivision scheme with shape parameter and its applications

Abstract

This paper introduces a new technique for the construction of an 8-point subdivision scheme (SS) with a shape parameter mu. Some well-known SSs are particular cases of our proposed 8point binary SS. We find the parametric range in which the proposed SS generates C1-continuous limit curves. It is observed that our proposed SS is C3-continuous for mu = 5 2048 . Some important properties of the proposed SS like the symmetry of basic limit function, exactness, approximation order, and convexity preservation are discussed. We also discuss error bounds and curvature of the limit curves of the proposed SS. Further, we illustrate the effectiveness of the shape parameter of the proposed SS through various applications of the SS. It is noted that the proposed SS has the potential to generate fractal curves for suitable choices of the shape parameter.