Browsing by Author "Hussain, Sardar Muhammad"

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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: Hussain, Sardar Muhammad...et al. (2020). "Generalized 5-Point Approximating Subdivision Scheme of Varying Arity", Mathematics, Vol. 8, No. 4.
Generalized 5-Point Approximating Subdivision Scheme of Varying Arity
(2020) Hussain, Sardar Muhammad; Rehman, Aziz Ur; Baleanu, Dumitru; Nisar, Kottakkaran Sooppy; Ghaffar, Abdul; Abdul Karim, Samsul Ariffin; 56389
The Subdivision Schemes (SSs) have been the heart of Computer Aided Geometric Design (CAGD) almost from its origin, and various analyses of SSs have been conducted. SSs are commonly used in CAGD and several methods have been invented to design curves/surfaces produced by SSs to applied geometry. In this article, we consider an algorithm that generates the 5-point approximating subdivision scheme with varying arity. By applying the algorithm, we further discuss several properties: continuity, Holder regularity, limit stencils, error bound, and shape of limit curves. The efficiency of the scheme is also depicted with assuming different values of shape parameter along with its application.