Abstract
Computer-aided geometric design combines mathematical concepts and computing skills that smooth curves through subdivision schemes. Subdivision schemes perform smoothing by turning the control polygon into a limit curve under a refinement rule, a prime example of which is improving the signal-to-noise ratio in modern devices. Because of the importance and location of subdivision schemes, mathematicians use them in CAD, computer graphics and advanced simulation methods. In this research, a family of 3-point Quaternary approximating subdivision scheme $R_{\zeta}$ is presented with its properties and analysis, including necessary conditions for convergence, Laurent polynomial, degree of the generation and polynomial reproduction, continuity analysis, Hölder regularity, and limit stencils. The visual performance of the proposed scheme is also presented to highlight the importance of this research and to validate the scheme.
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