The Mask of Odd Points n-Ary Interpolating Subdivision Scheme
Joint Authors
Abdul Rehman, Najma
Ashraf, Pakeeza
Mustafa, Ghulam
Deng, Jiansong
Source
Journal of Applied Mathematics
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-20, 20 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-11-07
Country of Publication
Egypt
No. of Pages
20
Main Subjects
Abstract EN
We present an explicit formula for the mask of odd points n-ary, for any odd n⩾3, interpolating subdivision schemes.
This formula provides the mask of lower and higher arity schemes.
The 3-point and 5-point a-ary schemes introduced by Lian, 2008, and (2m+1)-point a-ary schemes introduced by, Lian, 2009, are special cases of our explicit formula.
Moreover, other well-known existing odd point n-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.
American Psychological Association (APA)
Mustafa, Ghulam& Deng, Jiansong& Ashraf, Pakeeza& Abdul Rehman, Najma. 2012. The Mask of Odd Points n-Ary Interpolating Subdivision Scheme. Journal of Applied Mathematics،Vol. 2012, no. 2012, pp.1-20.
https://search.emarefa.net/detail/BIM-1028763
Modern Language Association (MLA)
Mustafa, Ghulam…[et al.]. The Mask of Odd Points n-Ary Interpolating Subdivision Scheme. Journal of Applied Mathematics No. 2012 (2012), pp.1-20.
https://search.emarefa.net/detail/BIM-1028763
American Medical Association (AMA)
Mustafa, Ghulam& Deng, Jiansong& Ashraf, Pakeeza& Abdul Rehman, Najma. The Mask of Odd Points n-Ary Interpolating Subdivision Scheme. Journal of Applied Mathematics. 2012. Vol. 2012, no. 2012, pp.1-20.
https://search.emarefa.net/detail/BIM-1028763
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1028763