Family of odd point non-stationary subdivision schemes and their applications
Abstract The (2s−1) $(2s-1)$-point non-stationary binary subdivision schemes (SSs) for curve design are introduced for any integer s≥2 $s\geq 2$. The Lagrange polynomials are used to construct a new family of schemes that can reproduce polynomials of degree (2s−2) $(2s-2)$. The usefulness of the sch...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2019-05-01
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| Series: | Advances in Difference Equations |
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| Online Access: | http://link.springer.com/article/10.1186/s13662-019-2105-5 |
| _version_ | 1828842012948824064 |
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| author | Abdul Ghaffar Zafar Ullah Mehwish Bari Kottakkaran Sooppy Nisar Dumitru Baleanu |
| author_facet | Abdul Ghaffar Zafar Ullah Mehwish Bari Kottakkaran Sooppy Nisar Dumitru Baleanu |
| author_sort | Abdul Ghaffar |
| collection | DOAJ |
| description | Abstract The (2s−1) $(2s-1)$-point non-stationary binary subdivision schemes (SSs) for curve design are introduced for any integer s≥2 $s\geq 2$. The Lagrange polynomials are used to construct a new family of schemes that can reproduce polynomials of degree (2s−2) $(2s-2)$. The usefulness of the schemes is illustrated in the examples. Moreover, the new schemes are the non-stationary counterparts of the stationary schemes of (Daniel and Shunmugaraj in 3rd International Conference on Geometric Modeling and Imaging, pp. 3–8, 2008; Hassan and Dodgson in Curve and Surface Fitting: Sant-Malo 2002, pp. 199–208, 2003; Hormann and Sabin in Comput. Aided Geom. Des. 25:41–52, 2008; Mustafa et al. in Lobachevskii J. Math. 30(2):138–145, 2009; Siddiqi and Ahmad in Appl. Math. Lett. 20:707–711, 2007; Siddiqi and Rehan in Appl. Math. Comput. 216:970–982, 2010; Siddiqi and Rehan in Eur. J. Sci. Res. 32(4):553–561, 2009). Furthermore, it is concluded that the basic shapes in terms of limiting curves produced by the proposed schemes with fewer initial control points have less tendency to depart from their tangent as well as their osculating plane compared to the limiting curves produced by existing non-stationary subdivision schemes. |
| first_indexed | 2024-12-12T20:14:27Z |
| format | Article |
| id | doaj.art-e13a37f8a61f4e9095cfb06d26578ce2 |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-12-12T20:14:27Z |
| publishDate | 2019-05-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-e13a37f8a61f4e9095cfb06d26578ce22022-12-22T00:13:25ZengSpringerOpenAdvances in Difference Equations1687-18472019-05-012019112010.1186/s13662-019-2105-5Family of odd point non-stationary subdivision schemes and their applicationsAbdul Ghaffar0Zafar Ullah1Mehwish Bari2Kottakkaran Sooppy Nisar3Dumitru Baleanu4Department of Mathematical Sciences, BUITEMSDepartment of Mathematics, University of EducationDepartment of Mathematics, NCBA&EDepartment of Mathematics, College of Arts and Sciences, Prince Sattam bin Abdulaziz UniversityDepartment of Mathematics, Cankaya UniversityAbstract The (2s−1) $(2s-1)$-point non-stationary binary subdivision schemes (SSs) for curve design are introduced for any integer s≥2 $s\geq 2$. The Lagrange polynomials are used to construct a new family of schemes that can reproduce polynomials of degree (2s−2) $(2s-2)$. The usefulness of the schemes is illustrated in the examples. Moreover, the new schemes are the non-stationary counterparts of the stationary schemes of (Daniel and Shunmugaraj in 3rd International Conference on Geometric Modeling and Imaging, pp. 3–8, 2008; Hassan and Dodgson in Curve and Surface Fitting: Sant-Malo 2002, pp. 199–208, 2003; Hormann and Sabin in Comput. Aided Geom. Des. 25:41–52, 2008; Mustafa et al. in Lobachevskii J. Math. 30(2):138–145, 2009; Siddiqi and Ahmad in Appl. Math. Lett. 20:707–711, 2007; Siddiqi and Rehan in Appl. Math. Comput. 216:970–982, 2010; Siddiqi and Rehan in Eur. J. Sci. Res. 32(4):553–561, 2009). Furthermore, it is concluded that the basic shapes in terms of limiting curves produced by the proposed schemes with fewer initial control points have less tendency to depart from their tangent as well as their osculating plane compared to the limiting curves produced by existing non-stationary subdivision schemes.http://link.springer.com/article/10.1186/s13662-019-2105-5Lagrange polynomialNon-stationaryBinary approximating schemesConvergenceShape preservationCurvature and torsion |
| spellingShingle | Abdul Ghaffar Zafar Ullah Mehwish Bari Kottakkaran Sooppy Nisar Dumitru Baleanu Family of odd point non-stationary subdivision schemes and their applications Advances in Difference Equations Lagrange polynomial Non-stationary Binary approximating schemes Convergence Shape preservation Curvature and torsion |
| title | Family of odd point non-stationary subdivision schemes and their applications |
| title_full | Family of odd point non-stationary subdivision schemes and their applications |
| title_fullStr | Family of odd point non-stationary subdivision schemes and their applications |
| title_full_unstemmed | Family of odd point non-stationary subdivision schemes and their applications |
| title_short | Family of odd point non-stationary subdivision schemes and their applications |
| title_sort | family of odd point non stationary subdivision schemes and their applications |
| topic | Lagrange polynomial Non-stationary Binary approximating schemes Convergence Shape preservation Curvature and torsion |
| url | http://link.springer.com/article/10.1186/s13662-019-2105-5 |
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