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.
Highlights
Subdivision schemes (SSs) have become one of the most essential tools for the generation of curve/surfaces and have been appreciated in many fields such as computer aided geometric design (CAGD), image processing, animation industry, computer graphics, etc.Several univariate subdivision schemes (SSs) studied in the literature are stationary
It seems that stationary SSs cannot generate circles; on the other hand, non-stationary SSs are capable of reproducing conic sections, spirals, trigonometric and hyperbolic functions of great interest in graphical and engineering applications
The results show that the binary approximating schemes developed by the proposed algorithm have the ability to reproduce or regenerate the conic sections and trigonometric polynomials as well
Summary
Several univariate SSs studied in the literature are stationary. It seems that stationary SSs cannot generate circles; on the other hand, non-stationary SSs are capable of reproducing conic sections, spirals, trigonometric and hyperbolic functions of great interest in graphical and engineering applications. In 2003 Jena et al [24] proposed a binary fourpoint interpolating non-stationary SSs which can generate C1 limit curve. Recent proposals of non-stationary SSs have been presented by Daniel and Shunmugaraj [10,11,12], Conti and Romani [8, 9], Siddiqi et al [30, 31], Bari and Mustafa [2], and Tan et al [32] who have constructed new attractive artifacts in the subdivision museum
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