A New Paradigm to Design a Class of Combined Ternary Subdivision Schemes
Subdivision schemes play a vital role in curve modeling. The curves produced by the class of 2n+2-point ternary scheme (Deslauriers and Dubuc (1989)) interpolate the given data while the curves produced by a class of 2n+2-point ternary B-spline schemes approximate the given data. In this research, w...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/6679201 |
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| author | Humaira Mustanira Tariq Rabia Hameed Ghulam Mustafa |
| author_facet | Humaira Mustanira Tariq Rabia Hameed Ghulam Mustafa |
| author_sort | Humaira Mustanira Tariq |
| collection | DOAJ |
| description | Subdivision schemes play a vital role in curve modeling. The curves produced by the class of 2n+2-point ternary scheme (Deslauriers and Dubuc (1989)) interpolate the given data while the curves produced by a class of 2n+2-point ternary B-spline schemes approximate the given data. In this research, we merge these two classes to introduce a consolidated and unified class of combined subdivision schemes with two shape control parameters in order to grow versatility for overseeing valuable necessities. However, the proposed class of subdivision schemes gives optimal smoothness in the final shapes, yet we can increase its smoothness by using a proposed general formula in form of its Laurent polynomial. The theoretical analysis of the class of subdivision schemes is done by using various mathematical tools and using their coding in the Maple environment. The graphical analysis of the class of schemes is done in the Maple environment by writing the codes based on the recursive mathematical expressions of the class of subdivision schemes. |
| format | Article |
| id | doaj-art-de9adee23bf24f04bcbc0d9f53013bbb |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-de9adee23bf24f04bcbc0d9f53013bbb2025-08-20T03:26:16ZengWileyJournal of Mathematics2314-46292314-47852021-01-01202110.1155/2021/66792016679201A New Paradigm to Design a Class of Combined Ternary Subdivision SchemesHumaira Mustanira Tariq0Rabia Hameed1Ghulam Mustafa2Department of Mathematics, The Islamia University of Bahawalpur, Bahawalpur 63100, PakistanDepartment of Mathematics, The Government Sadiq College Women University Bahawalpur, Bahawalpur 63100, PakistanDepartment of Mathematics, The Islamia University of Bahawalpur, Bahawalpur 63100, PakistanSubdivision schemes play a vital role in curve modeling. The curves produced by the class of 2n+2-point ternary scheme (Deslauriers and Dubuc (1989)) interpolate the given data while the curves produced by a class of 2n+2-point ternary B-spline schemes approximate the given data. In this research, we merge these two classes to introduce a consolidated and unified class of combined subdivision schemes with two shape control parameters in order to grow versatility for overseeing valuable necessities. However, the proposed class of subdivision schemes gives optimal smoothness in the final shapes, yet we can increase its smoothness by using a proposed general formula in form of its Laurent polynomial. The theoretical analysis of the class of subdivision schemes is done by using various mathematical tools and using their coding in the Maple environment. The graphical analysis of the class of schemes is done in the Maple environment by writing the codes based on the recursive mathematical expressions of the class of subdivision schemes.http://dx.doi.org/10.1155/2021/6679201 |
| spellingShingle | Humaira Mustanira Tariq Rabia Hameed Ghulam Mustafa A New Paradigm to Design a Class of Combined Ternary Subdivision Schemes Journal of Mathematics |
| title | A New Paradigm to Design a Class of Combined Ternary Subdivision Schemes |
| title_full | A New Paradigm to Design a Class of Combined Ternary Subdivision Schemes |
| title_fullStr | A New Paradigm to Design a Class of Combined Ternary Subdivision Schemes |
| title_full_unstemmed | A New Paradigm to Design a Class of Combined Ternary Subdivision Schemes |
| title_short | A New Paradigm to Design a Class of Combined Ternary Subdivision Schemes |
| title_sort | new paradigm to design a class of combined ternary subdivision schemes |
| url | http://dx.doi.org/10.1155/2021/6679201 |
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