The Mask of Odd Points n-Ary Interpolating Subdivision Scheme. (7th November 2012)

• Record Type: Journal Article
• Authors: Mustafa, Ghulam; Deng, Jiansong; Ashraf, Pakeeza; Abdul Rehman, Najma
• Other Names: Roy Debasish Academic Editor.
• Is Part Of: Journal of applied mathematics. Volume 2012(2012)
• Publication Date: 2012-11-07
• Subjects: Mathematics -- Periodicals; 519.05
• DOI: 10.1155/2012/205863
• Languages: English
• ISSNs: 1110-757X

Abstract

Abstract : We present an explicit formula for the mask of odd pointsn -ary, for any oddn ⩾ 3, interpolating subdivision schemes. This formula provides the mask of lower and higher arity schemes. The 3-point and 5-pointa -ary schemes introduced by Lian, 2008, and (2 m + 1 )-pointa -ary schemes introduced by, Lian, 2009, are special cases of our explicit formula. Moreover, other well-known existing odd pointn -ary schemes including the schemes introduced by Zheng et al., 2009, can easily be generated by our formula. In addition, error bounds between subdivision curves and control polygons of schemes are computed. It has been noticed that error bounds decrease when the complexity of the scheme decreases and vice versa. Also, as we increase arity of the schemes the error bounds decrease. Furthermore, we present brief comparison of total absolute curvature of subdivision schemes having different arity with different complexity. Convexity preservation property of scheme is also presented.