Browsing by Author "Hameed, Rabia"

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Citation Count: Mustafa, Ghulam...et al. (2020). "A Class of Refinement Schemes With Two Shape Control Parameters", IEEE Access, Vol. 8, pp. 98316-98329.
A Class of Refinement Schemes With Two Shape Control Parameters
(2020) Mustafa, Ghulam; Hameed, Rabia; Baleanu, Dumitru; Mahmood, Ayesha; 56389
A subdivision scheme defines a smooth curve or surface as the limit of a sequence of successive refinements of given polygon or mesh. These schemes take polygons or meshes as inputs and produce smooth curves or surfaces as outputs. In this paper, a class of combine refinement schemes with two shape control parameters is presented. These even and odd rules of these schemes have complexity three and four respectively. The even rule is designed to modify the vertices of the given polygon, whereas the odd rule is designed to insert a new point between every edge of the given polygon. These schemes can produce high order of continuous shapes than existing combine binary and ternary family of schemes. It has been observed that the schemes have interpolating and approximating behaviors depending on the values of parameters. These schemes have an interproximate behavior in the case of non-uniform setting of the parameters. These schemes can be considered as the generalized version of some of the interpolating and B-spline schemes. The theoretical as well as the numerical and graphical analysis of the shapes produced by these schemes are also presented.
Citation Count: Hameed, Rabia...et al. (2021). "A divided differences based medium to analyze smoothness of the binary bivariate refinement schemes", Advances in Difference Equations, Vol. 2021, No. 1.
A divided differences based medium to analyze smoothness of the binary bivariate refinement schemes
(2021) Hameed, Rabia; Mustafa, Ghulam; Baleanu, Dumitru; Chu, Yu-Ming; 56389
In this article, we present the continuity analysis of the 3D models produced by the tensor product scheme of (m + 1)-point binary refinement scheme. We use differences and divided differences of the bivariate refinement scheme to analyze its smoothness. The C-0, C(1 )and C-2 continuity of the general bivariate scheme is analyzed in our approach. This gives us some simple conditions in the form of arithmetic expressions and inequalities. These conditions require the mask and the complexity of the given refinement scheme to analyze its smoothness. Moreover, we perform several experiments by using these conditions on established schemes to verify the correctness of our approach. These experiments show that our results are easy to implement and are applicable for both interpolatory and approximating types of the schemes.
Citation Count: Hameed, Rabia...et al. (2020). "A New Approach to Increase the Flexibility of Curves and Regular Surfaces Produced by 4-Point Ternary Subdivision Scheme", Mathematical Problems in Engineering, Vol. 2020.
A New Approach to Increase the Flexibility of Curves and Regular Surfaces Produced by 4-Point Ternary Subdivision Scheme
(2020) Hameed, Rabia; Mustafa, Ghulam; Liaqat, Amina; Baleanu, Dumitru; Khan, Faheem; Al-Qurashi, Maysaa M.; Chu, Yu-Ming; 56389
In this article, we present a new subdivision scheme by using an interpolatory subdivision scheme and an approximating subdivision scheme. The construction of the subdivision scheme is based on translation of points of the 4-point interpolatory subdivision scheme to the new position according to three displacement vectors containing two shape parameters. We first study the characteristics of the new subdivision scheme analytically and then present numerical experiments to justify these analytical characteristics geometrically. We also extend the new derived scheme into its bivariate/tensor product version. This bivariate scheme is applicable on quadrilateral meshes to produce smooth limiting surfaces up toC3continuity.