Browsing by Author "Karim, Samsul Ariffin Abdul"

Now showing 1 - 4 of 4

Citation Count: Ali, F.A.M...et al. (2020). "Construction of Cubic Timmer Triangular Patches and Its Application in Scattered Data Interpolation", Mathematics, Vol. 8, No. 2.
Construction of Cubic Timmer Triangular Patches and Its Application in Scattered Data Interpolation
(MDPI AG, 2020) Ali, Fatin Amani Mohd; Karim, Samsul Ariffin Abdul; Saaban, Azizan; Hasan, Mohammad Khatim; Ghaffar, Abdul; Nisar, Kottakkaran Sooppy; Baleanu, Dumitru; 56389
This paper discusses scattered data interpolation by using cubic Timmer triangular patches. In order to achieve C1 continuity everywhere, we impose a rational corrected scheme that results from convex combination between three local schemes. The final interpolant has the form quintic numerator and quadratic denominator. We test the scheme by considering the established dataset as well as visualizing the rainfall data and digital elevation in Malaysia. We compare the performance between the proposed scheme and some well-known schemes. Numerical and graphical results are presented by using Mathematica and MATLAB. From all numerical results, the proposed scheme is better in terms of smaller root mean square error (RMSE) and higher coefficient of determination (R2). The higher R2 value indicates that the proposed scheme can reconstruct the surface with excellent fit that is in line with the standard set by Renka and Brown's validation.
Citation Count: Karim, S.A.A...et al. (2020). "Construction of New Cubic Bézier-Like Triangular Patches With Application in Scattered Data İnterpolation", Advances in Difference Equations, Vol. 2020, No. 1.
Construction of New Cubic Bézier-Like Triangular Patches With Application in Scattered Data İnterpolation
(Springer, 2020) Karim, Samsul Ariffin Abdul; Saaban, Azizan; Skala, Vaclav; Ghaffar, Abdul; Nisar, Kottakkaran Sooppy; Baleanu, Dumitru; 56389
This paper discusses the functional scattered data interpolation to interpolate the general scattered data. Compared with the previous works, we construct a new cubic Bézier-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 Bézier 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 C1 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 Bézier-like triangular patches. The detail comparison in terms of maximum error and coefficient of determination r2 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 r2 value between 0.99920443 and 0.99999994. This is very good for surface fitting for a large scattered data set.
Citation Count: Harim, Noor Adilla...et al. (2020). "Positivity preserving interpolation by using rational quartic spline", AIMS Mathematics, Vol. 5, No. 4, pp. 3762-3782.
Positivity preserving interpolation by using rational quartic spline
(2020) Harim, Noor Adilla; Karim, Samsul Ariffin Abdul; Othman, Mahmod; Saaban, Azizan; Ghaffar, Abdul; Nisar, Kottakkaran Sooppy; Baleanu, Dumitru; 56389
In 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.
Citation Count: Hashim, Ishak...at all (2021). "Scattered data interpolation using cubic trigonometric bézier triangular patch", Computers, Materials and Continua, Vol. 69, No. 1, pp. 221-236.
Scattered data interpolation using cubic trigonometric bézier triangular patch
(2021) Hashim, Ishak; Draman, Nur Nabilah Che; Karim, Samsul Ariffin Abdul; Yeo, Wee Ping; Baleanu, Dumitru; 56389
This paper discusses scattered data interpolation using cubic trigonometric Bézier triangular patches with C1 continuity everywhere. We derive the C1 condition on each adjacent triangle. On each triangular patch, we employ convex combination method between three local schemes. The final interpolant with the rational corrected scheme is suitable for regular and irregular scattered data sets. We tested the proposed scheme with 36,65, and 100 data points for some well-known test functions. The scheme is also applied to interpolate the data for the electric potential. We compared the performance between our proposed method and existing scattered data interpolation schemes such as Powell–Sabin (PS) and Clough–Tocher (CT) by measuring the maximum error, root mean square error (RMSE) and coefficient of determination (R2). From the results obtained, our proposed method is competent with cubic Bézier, cubic Ball, PS and CT triangles splitting schemes to interpolate scattered data surface. This is very significant since PS and CT requires that each triangle be splitting into several micro triangles.