Analysis of Geometric Properties of Ternary Four-Point Rational Interpolating Subdivision Scheme
Shape preservation has been the heart of subdivision schemes (SSs) almost from its origin, and several analyses of SSs have been established. Shape preservation properties are commonly used in SSs and various ways have been discovered to connect smooth curves/surfaces generated by SSs to applied geo...
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| Format: | Article |
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MDPI AG
2020-03-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/8/3/338 |
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| author | Pakeeza Ashraf Bushra Nawaz Dumitru Baleanu Kottakkaran Sooppy Nisar Abdul Ghaffar Muhammad Aqeel Ahmed Khan Saima Akram |
| author_facet | Pakeeza Ashraf Bushra Nawaz Dumitru Baleanu Kottakkaran Sooppy Nisar Abdul Ghaffar Muhammad Aqeel Ahmed Khan Saima Akram |
| author_sort | Pakeeza Ashraf |
| collection | DOAJ |
| description | Shape preservation has been the heart of subdivision schemes (SSs) almost from its origin, and several analyses of SSs have been established. Shape preservation properties are commonly used in SSs and various ways have been discovered to connect smooth curves/surfaces generated by SSs to applied geometry. With an eye on connecting the link between SSs and applied geometry, this paper analyzes the geometric properties of a ternary four-point rational interpolating subdivision scheme. These geometric properties include monotonicity-preservation, convexity-preservation, and curvature of the limit curve. Necessary conditions are derived on parameter and initial control points to ensure monotonicity and convexity preservation of the limit curve of the scheme. Furthermore, we analyze the curvature of the limit curve of the scheme for various choices of the parameter. To support our findings, we also present some examples and their graphical representation. |
| first_indexed | 2024-04-13T11:35:11Z |
| format | Article |
| id | doaj.art-7d4acf3c8ad145adbfe4221eb5b5740a |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-04-13T11:35:11Z |
| publishDate | 2020-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-7d4acf3c8ad145adbfe4221eb5b5740a2022-12-22T02:48:27ZengMDPI AGMathematics2227-73902020-03-018333810.3390/math8030338math8030338Analysis of Geometric Properties of Ternary Four-Point Rational Interpolating Subdivision SchemePakeeza Ashraf0Bushra Nawaz1Dumitru Baleanu2Kottakkaran Sooppy Nisar3Abdul Ghaffar4Muhammad Aqeel Ahmed Khan5Saima Akram6Department of Mathematics, Government Sadiq College Women University, Bahawalpur 63100, PakistanDepartment of Mathematics, Government Sadiq College Women University, Bahawalpur 63100, PakistanDepartment of Mathematics, Cankaya University, 06790 Ankara, TurkeyDepartment of Mathematics, College of Arts and Sciences, Prince Sattam bin Abdulaziz University, Wadi Aldawaser 11991, Saudi ArabiaInformetrics Research Group, Ton Duc Thang University, Ho Chi Minh City 700000, VietnamDepartment of Mathematics, COMSATS University Islamabad, Lahore Campus, Lahore 54000, PakistanCentre for Advanced Studies in Pure and Applied Mathematics Bahauddin Zakariya University Multan, Multan 66000, PakistanShape preservation has been the heart of subdivision schemes (SSs) almost from its origin, and several analyses of SSs have been established. Shape preservation properties are commonly used in SSs and various ways have been discovered to connect smooth curves/surfaces generated by SSs to applied geometry. With an eye on connecting the link between SSs and applied geometry, this paper analyzes the geometric properties of a ternary four-point rational interpolating subdivision scheme. These geometric properties include monotonicity-preservation, convexity-preservation, and curvature of the limit curve. Necessary conditions are derived on parameter and initial control points to ensure monotonicity and convexity preservation of the limit curve of the scheme. Furthermore, we analyze the curvature of the limit curve of the scheme for various choices of the parameter. To support our findings, we also present some examples and their graphical representation.https://www.mdpi.com/2227-7390/8/3/338monotonicity-preservationconvexity-preservationcurvaturerational interpolatingsubdivision schemes |
| spellingShingle | Pakeeza Ashraf Bushra Nawaz Dumitru Baleanu Kottakkaran Sooppy Nisar Abdul Ghaffar Muhammad Aqeel Ahmed Khan Saima Akram Analysis of Geometric Properties of Ternary Four-Point Rational Interpolating Subdivision Scheme Mathematics monotonicity-preservation convexity-preservation curvature rational interpolating subdivision schemes |
| title | Analysis of Geometric Properties of Ternary Four-Point Rational Interpolating Subdivision Scheme |
| title_full | Analysis of Geometric Properties of Ternary Four-Point Rational Interpolating Subdivision Scheme |
| title_fullStr | Analysis of Geometric Properties of Ternary Four-Point Rational Interpolating Subdivision Scheme |
| title_full_unstemmed | Analysis of Geometric Properties of Ternary Four-Point Rational Interpolating Subdivision Scheme |
| title_short | Analysis of Geometric Properties of Ternary Four-Point Rational Interpolating Subdivision Scheme |
| title_sort | analysis of geometric properties of ternary four point rational interpolating subdivision scheme |
| topic | monotonicity-preservation convexity-preservation curvature rational interpolating subdivision schemes |
| url | https://www.mdpi.com/2227-7390/8/3/338 |
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