The Mask of Odd Points n-Ary Interpolating Subdivision Scheme
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, 2...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/205863 |
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| author | Ghulam Mustafa Jiansong Deng Pakeeza Ashraf Najma Abdul Rehman |
| author_facet | Ghulam Mustafa Jiansong Deng Pakeeza Ashraf Najma Abdul Rehman |
| author_sort | Ghulam Mustafa |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-6d790bd5d1fb45688fe0dd5b4d54de88 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-6d790bd5d1fb45688fe0dd5b4d54de882025-02-03T05:57:46ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/205863205863The Mask of Odd Points n-Ary Interpolating Subdivision SchemeGhulam Mustafa0Jiansong Deng1Pakeeza Ashraf2Najma Abdul Rehman3Department of Mathematics, The Islamia University of Bahawalpur, Bahawalpur 63100, PakistanDepartment of Mathematics, University of Science and Technology of China, Hefei 230026, ChinaDepartment of Mathematics, The Islamia University of Bahawalpur, Bahawalpur 63100, PakistanDepartment of Mathematics, The Islamia University of Bahawalpur, Bahawalpur 63100, PakistanWe 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.http://dx.doi.org/10.1155/2012/205863 |
| spellingShingle | Ghulam Mustafa Jiansong Deng Pakeeza Ashraf Najma Abdul Rehman The Mask of Odd Points n-Ary Interpolating Subdivision Scheme Journal of Applied Mathematics |
| title | The Mask of Odd Points n-Ary Interpolating Subdivision Scheme |
| title_full | The Mask of Odd Points n-Ary Interpolating Subdivision Scheme |
| title_fullStr | The Mask of Odd Points n-Ary Interpolating Subdivision Scheme |
| title_full_unstemmed | The Mask of Odd Points n-Ary Interpolating Subdivision Scheme |
| title_short | The Mask of Odd Points n-Ary Interpolating Subdivision Scheme |
| title_sort | mask of odd points n ary interpolating subdivision scheme |
| url | http://dx.doi.org/10.1155/2012/205863 |
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