Abstract
The Subdivision Schemes (SSs) have been the heart of Computer Aided Geometric Design (CAGD) almost from its origin, and various analyses of SSs have been conducted. SSs are commonly used in CAGD and several methods have been invented to design curves/surfaces produced by SSs to applied geometry. In this article, we consider an algorithm that generates the 5-point approximating subdivision scheme with varying arity. By applying the algorithm, we further discuss several properties: continuity, Hölder regularity, limit stencils, error bound, and shape of limit curves. The efficiency of the scheme is also depicted with assuming different values of shape parameter along with its application.
Highlights
Computer Aided Geometric Design (CAGD) deals with studies of curves and surfaces used in computer graphics, data structure, and computational algebra
We present the error between control polygon and limit curve after kth subdivision level of 5-point binary, ternary, and quaternary subdivision schemes using different values mentioned in Tables 1–3 by applying the approach of Hashmi [31]
Our experiments show that higher arity scheme are better than the lower arity schemes in the sense of computational cost and error bounds
Summary
Computer Aided Geometric Design (CAGD) deals with studies of curves and surfaces used in computer graphics, data structure, and computational algebra. Mustafa et al [17] further worked on odd-point ternary approximating subdivision schemes and developed a formula to generalize them. Ghaffar et al [19] introduced a general formula for 4-point a-ary approximating subdivision scheme for curve designing for any arity a ≥ 2. Mustafa et al [20] worked over odd point ternary families of approximating subdivision schemes and showed that their schemes have high smoothness. They worked on subdivision regularization, in which they showed that unified frame work can work well for both curve fitting and noise removal.
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