Browsing by Author "Bari, Mehwish"

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Citation Count: Ghaffar, Abdul...et al. (2019). "A new class of 2m-point binary non-stationary subdivision schemes", Advances in Difference Equations, Vol. 2019, No. 1.
A new class of 2m-point binary non-stationary subdivision schemes
(Springer Open, 2019) Ghaffar, Abdul; Ullah, Zafar; Bari, Mehwish; Nisar, Kottakkaran Sooppy; Al-Qurashi, Maysaa M.; Baleanu, Dumitru; 56389
A new class of 2m-point non-stationary subdivision schemes (SSs) is presented, including some of their important properties, such as continuity, curvature, torsion monotonicity, and convexity preservation. The multivariate analysis of subdivision schemes is extended to a class of non-stationary schemes which are asymptotically equivalent to converging stationary or non-stationary schemes. A comparison between the proposed schemes, their stationary counterparts and some existing non-stationary schemes has been depicted through examples. It is observed that the proposed SSs give better approximation and more effective results.
Citation Count: Ghaffar, A...et al. (2019). "A New Class of 2Q-Point Nonstationary Subdivision Schemes and Their Applications",Mathematics, Vol. 7, No. 7.
A New Class of 2Q-Point Nonstationary Subdivision Schemes and Their Applications
(MDPI AG, 2019) Ghaffar, Abdul; Bari, Mehwish; Ullah, Zafar; Iqbal, Mudassar; Nisar, Kottakkaran Sooppy; Baleanu, Dumitru; 56389
The main objective of this study is to introduce a new class of 2q-point approximating nonstationary subdivision schemes (ANSSs) by applying Lagrange-like interpolant. The theory of asymptotic equivalence is applied to find the continuity of the ANSSs. These schemes can be nicely generalized to contain local shape parameters that allow the user to locally adjust the shape of the limit curve/surface. Moreover, many existing approximating stationary subdivision schemes (ASSSs) can be obtained as nonstationary counterparts of the proposed ANSSs
Citation Count: Bari, Mehwish...et al. (2021). "Construction and analysis of unified 4-point interpolating nonstationary subdivision surfaces", Advances in Difference Equations, Vol. 2021, No. 1.
Construction and analysis of unified 4-point interpolating nonstationary subdivision surfaces
(2021) Bari, Mehwish; Mustafa, Ghulam; Ghaffar, Abdul; Nisar, Kottakkaran Sooppy; Baleanu, Dumitru; 56389
Subdivision schemes (SSs) have been the heart of computer-aided geometric design almost from its origin, and several unifications of SSs have been established. SSs are commonly used in computer graphics, and several ways were discovered to connect smooth curves/surfaces generated by SSs to applied geometry. To construct the link between nonstationary SSs and applied geometry, in this paper, we unify the interpolating nonstationary subdivision scheme (INSS) with a tension control parameter, which is considered as a generalization of 4-point binary nonstationary SSs. The proposed scheme produces a limit surface having C1 smoothness. It generates circular images, spirals, or parts of conics, which are important requirements for practical applications in computer graphics and geometric modeling. We also establish the rules for arbitrary topology for extraordinary vertices (valence >= 3). The well-known subdivision Kobbelt scheme (Kobbelt in Comput. Graph. Forum 15(3):409-420, 1996) is a particular case. We can visualize the performance of the unified scheme by taking different values of the tension parameter. It provides an exact reproduction of parametric surfaces and is used in the processing of free-form surfaces in engineering.
Citation Count: Ghaffar, Abdul...et al. (2019). "Construction and Application of Nine-Tic B-Spline Tensor Product SS", Mathematics, Vol. 7, No. 8.
Construction and Application of Nine-Tic B-Spline Tensor Product SS
(MDPI, 2019) Ghaffar, Abdul; Iqbal, Mudassar; Bari, Mehwish; Hussain, Sardar Muhammad; Manzoor, Raheela; Nisar, Kottakkaran Sooppy; Baleanu, Dumitru; 56389
In this paper, we propose and analyze a tensor product of nine-tic B-spline subdivision scheme (SS) to reduce the execution time needed to compute the subdivision process of quad meshes. We discuss some essential features of the proposed SS such as continuity, polynomial generation, joint spectral radius, holder regularity and limit stencil. Some results of the SS using surface modeling with the help of computer programming are shown.
Citation Count: Ghaffar, Abdul...et al. (2019). "Family of odd point non-stationary subdivision schemes and their applications", Advances in Difference Equations.
Family of odd point non-stationary subdivision schemes and their applications
(Springer Open, 2019) Ghaffar, Abdul; Ullah, Zafar; Bari, Mehwish; Nisar, Kottakkaran Sooppy; Baleanu, Dumitru; 56389
The (2s-1)-point non-stationary binary subdivision schemes (SSs) for curve design are introduced for any integer s2. The Lagrange polynomials are used to construct a new family of schemes that can reproduce polynomials of degree (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.