Browsing by Author "Ashraf, Pakeeza"

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Citation - WoS: 13
Citation - Scopus: 18
Analysis of Geometric Properties of Ternary Four-Point Rational Interpolating Subdivision Scheme
(Mdpi, 2020) Nawaz, Bushra; Baleanu, Dumitru; Nisar, Kottakkaran Sooppy; Ghaffar, Abdul; Khan, Muhammad Aqeel Ahmed; Akram, Saima; Ashraf, Pakeeza; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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.
Citation - WoS: 8
Citation - Scopus: 14
Shape-Preserving Properties of a Relaxed Four-Point Interpolating Subdivision Scheme
(Mdpi, 2020) Ghaffar, Abdul; Baleanu, Dumitru; Sehar, Irem; Nisar, Kottakkaran Sooppy; Khan, Faheem; Ashraf, Pakeeza; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this paper, we analyze shape-preserving behavior of a relaxed four-point binary interpolating subdivision scheme. These shape-preserving properties include positivity-preserving, monotonicity-preserving and convexity-preserving. We establish the conditions on the initial control points that allow the generation of shape-preserving limit curves by the four-point scheme. Some numerical examples are given to illustrate the graphical representation of shape-preserving properties of the relaxed scheme.
Citation - WoS: 4
Citation - Scopus: 5
A Shape-Preserving Variant of Lane-Riesenfeld Algorithm
(Amer inst Mathematical Sciences-aims, 2021) Mustafa, Ghulam; Khan, Husna A.; Baleanu, Dumitru; Ghaffar, Abdul; Nisar, Kottakkaran Sooppy; Ashraf, Pakeeza; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
This paper introduces a family of shape-preserving binary approximating subdivision schemes by applying a shape-preserving variant on the Lane-Riesenfeld algorithm. Using the symbols of subdivision schemes, we determine convergence and smoothness, Holder continuity, and support size of the limit curves. Furthermore, these schemes produce monotonic and convex curves under the certain conditions imposed on the initial data.