Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
Browse
5 results
Search Results
Article Citation - WoS: 9Citation - Scopus: 13Positivity Preserving Interpolation by Using Rational Quartic Spline(Amer inst Mathematical Sciences-aims, 2020) Karim, Samsul Ariffin Abdul; Othman, Mahmod; Saaban, Azizan; Ghaffar, Abdul; Nisar, Kottakkaran Sooppy; Baleanu, Dumitru; Harim, Noor AdillaIn this study, a new scheme for positivity preserving interpolation is proposed by using C-1 rational quartic spline of (quartic/quadratic) with three parameters. The sufficient condition for the positivity rational quartic interpolant is derived on one parameter meanwhile the other two are free parameters for shape modification. These conditions will guarantee to provide positive interpolating curve everywhere. We tested the proposed positive preserving scheme with four positive data and compared the results with other established schemes. Based on the graphical and numerical results, we found that the proposed scheme is better than existing schemes, since it has extra free parameter to control the positive interpolating curve.Article Citation - WoS: 13Citation - Scopus: 14Generalized 5-Point Approximating Subdivision Scheme of Varying Arity(Mdpi, 2020) Rehman, Aziz Ur; Baleanu, Dumitru; Nisar, Kottakkaran Sooppy; Ghaffar, Abdul; Abdul Karim, Samsul Ariffin; Hussain, Sardar Muhammad; Karim, Samsul Ariffin Abdul; Ur Rehman, AzizThe 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.Article Citation - WoS: 16Citation - Scopus: 23Construction of New Cubic Bezier-Like Triangular Patches With Application in Scattered Data Interpolation(Springer, 2020) Saaban, Azizan; Skala, Vaclav; Ghaffar, Abdul; Nisar, Kottakkaran Sooppy; Baleanu, Dumitru; Karim, Samsul Ariffin AbdulThis paper discusses the functional scattered data interpolation to interpolate the general scattered data. Compared with the previous works, we construct a new cubic Bezier-like triangular basis function controlled by three shape parameters. This is an advantage compared with the existing schemes since it gives more flexibility for the shape design in geometric modeling. By choosing some suitable value of the parameters, this new triangular basis is reduced to the cubic Ball and cubic Bezier triangular patches, respectively. In order to apply the proposed bases to general scattered data, firstly the data is triangulated using Delaunay triangulation. Then the sufficient condition for C-1 continuity using cubic precision method on each adjacent triangle is implemented. Finally, the interpolation scheme is constructed based on a convex combination between three local schemes of the cubic Bezier-like triangular patches. The detail comparison in terms of maximum error and coefficient of determination r(2) with some existing meshfree methods i.e. radial basis function (RBF) such as linear, thin plate spline (TPS), Gaussian, and multiquadric are presented. From graphical results, the proposed scheme gives more visually pleasing interpolating surfaces compared with all RBF methods. Based on error analysis, for all four functions, the proposed scheme is better than RBFs except for data from the third function. Overall, the proposed scheme gives r(2) value between 0.99920443 and 0.99999994. This is very good for surface fitting for a large scattered data set.Article Citation - WoS: 5Citation - Scopus: 17A New Class of 2q-Point Nonstationary Subdivision Schemes and Their Applications(Mdpi, 2019) Bari, Mehwish; Ullah, Zafar; Iqbal, Mudassar; Nisar, Kottakkaran Sooppy; Baleanu, Dumitru; Ghaffar, AbdulThe 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.Article Citation - WoS: 14Citation - Scopus: 26Construction 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, DumitruIn 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.