Convexity Preservation of the Ternary 6-point Interpolating Subdivision Scheme

Abstract

AbstractThe frequent use of subdivision schemes (SSs) for curve sketching can be seen in various papers published during recent years. These SSs provides efficient method for producing curves and surfaces. Further, these SSs can be divide in various categories but we focused only one of the type of SS called interpolating SS. Here, we have discussed some properties of the “ternary 6-point interpolating subdivision scheme” introduced by Faheem and Mustafa [1] in 2008. The aim of this paper is to discuss about a geometric property called “Convexity” with the tension parameter \(\mu \) and its effect on curve sketching. The scheme is analyzed and its convexity preserving property is proved using mathematical induction. Strictly convex initial data is used for the evaluation of the condition on the tension parameter \(\mu \). This condition shows that our scheme is more efficient than other schemes in terms of lower value of tension parameter \(\mu \) . The significance of the condition is displayed through numerical applications.