Explanipedia

Recurrence Relations for Jacobi Orthogonal Polynomials on the Triangular Domain Open

Iqbal M. Batiha, Wala’a Ahmad Alkasasbeh, Abedallah Rababah, Hamzah O. Al-Khawaldeh, Iqbal H. Jebril · 2025

In this paper, we present recurrence relations for the Jacobi weighted orthogonal polynomials Pn,r(α,β,γ) (u, v, w) with r = 0, 1, . . . , n, where n ≥ 0, defined on the triangular domain T = {(u, v, w) : u, v, w ≥ 0, u + v + w = 1} for va…

HSS-progressive interpolation for Loop and Catmull–Clark Subdivision Surfaces Open

Yusuf Fatihu Hamza, Mukhtar Fatihu Hamza, Abedallah Rababah, Sadiya Ali Rano · 2024

Loop and Catmull–Clark subdivision schemes are the most popular and commonly employed approximation subdivision schemes. However, some features of the given mesh are lost in their refinement process. Thus, the subdivision surfaces of Loop …

Rate of Convergence of Hermite-Fejér Interpolation over Roots of Chebyshev-IV Polynomials Open

Abedallah Rababah, A.N. Vall, Amima AlGheily, Reem Ghazal · 2024

Geometric Degree Reduction of Wang–Ball Curves Open

Yusuf Fatihu Hamza, Mukhtar Fatihu Hamza, Abedallah Rababah, Salisu Ibrahim · 2023

There are substantial methods of degree reduction in the literature. Existing methods share some common limitations, such as lack of geometric continuity, complex computations, and one-degree reduction at a time. In this paper, an approxim…

Some Operations on the Rational Bezier Curves Open

Abedallah Rababah, Mashael Ashraf, Dana El Haddad · 2022

Decomposition of Fourth‐Order Euler‐Type Linear Time‐Varying Differential System into Cascaded Two Second‐Order Euler Commutative Pairs Open

Salisu Ibrahim, Abedallah Rababah · 2022

This paper presents decomposition of the fourth‐order Euler‐type linear time‐varying system (LTVS) as a commutative pair of two second‐order Euler‐type systems. All necessary and sufficient conditions for the decomposition are deployed to …

Conformable chebyshev differential Equation of first kind Open

Abedallah Rababah · 2020

In this paper, the Chebyshev-I conformable differential equation is considered. A proper power series is examined; there are two solutions, the even solution and the odd solution. The Rodrigues’ type formula is also allocated for the confo…

The best sextic approximation of hyperbola with order twelve Open

Abedallah Rababah, Esra’a Rababah · 2020

In this article, the best uniform approximation for the hyperbola of degree 6 that has approximation order 12 is found. The associated error function vanishes 12 times and equioscillates 13 times. For an arc of the hyperbola, the error is …

Approximating offset Curves using Bezier curves with high accuracy Open

Abedallah Rababah, Moath Jaradat · 2020

In this paper, a new method for the approximation of offset curves is presented using the idea of the parallel derivative curves. The best uniform approximation of degree 3 with order 6 is used to construct a method to find the approximati…

RateofConvergenceofHermite-Fej´erPolynomialsfor Functions with Derivatives of Bounded Variation Open

Abedallah Rababah · 2020

In this paper, the behavior of the Hermite-Fej´er interpolation for functionswithderivativesofboundedvariationon[−1,1]isstudiedbytakingtheinterpolation over the zeros of Chebyshev polynomials of the second kind. An estimate for the rate of…

Properties of the Differentiation Matrices of the Bezier Curves and Surfaces Open

Abedallah Rababah, Lamyaa Almobaiyed, Eman Ibrahim, Amira Kassar · 2020

The best quintic Chebyshev approximation of circular arcs of order ten Open

Abedallah Rababah · 2019

Mathematically, circles are represented by trigonometric parametric equations and implicit equations. Both forms are not proper for computer applications and CAD systems. In this paper, a quintic polynomial approximation for a circular arc…

High order approximation of degree nine and order eighteen Open

Abedallah Rababah · 2019

In this paper, a method to approximate curves by polynomials of degree nine is presented. The resulting approximation has order eighteen. The method is applied to approximate a circular arc, and the error function is studied and characteri…

Change of Basis Transformation from the Bernstein Polynomials to the Chebyshev Polynomials of the Fourth Kind Open

Abedallah Rababah, Esraa Hijazi · 2019

In this paper, the change of bases transformations between the Bernstein polynomial basis and the Chebyshev polynomial basis of the fourth kind are studied and the matrices of transformation among these bases are constructed. Some examples…

Quadratic quadrature formula for curves with third degree of exactness Open

Abedallah Rababah · 2019

In this article, a quadrature formula of degree 2 is given that has degree of exactness 3 and order 5. The formula is valid for any planar curve given in parametric form unlike existing Gaussian quadrature formulas that are valid only for …

The Best Uniform Cubic Approximation of Circular Arcs with High Accuracy Open

Abedallah Rababah · 2017

In this article, the issue of the best uniform cubic approximation of circular arcs with parametrically defined polynomial curves is considered. By a proper choice of the Bezier points, the best uniform approximation of degree 3 to a circu…

Convergence of Hermite-Fejér interpolation over roots of third-kind Chebyshev polynomials Open

Abedallah Rababah · 2016

This paper considers the Hermite-Fejér interpolation to functions of bounded variation.This interpolation is considered when the nodes of interpolation are taken to be the roots of the third-kind Chebyshev polynomials.An estimate for the r…

Weighted $G^0$- and $G^1$-Degree Reduction of Disk Bezier Curves Open

Abedallah Rababah, Yusuf Fatihu Hamza · 2016

A Bezier curve in the plane whose control points are disks is called a disk Bezier curve. In this paper we introduce a novel approach to find weighted degree reduction of disk Bezier curve with $G^0$- and $G^1$ continuity at the bounda…

Recurrence Relations for Orthogonal Polynomials on Triangular Domains Open

Abedallah Rababah · 2016

In Farouki et al, 2003, Legendre-weighted orthogonal polynomials P n , r ( u , v , w ) , r = 0 , 1 , … , n , n ≥ 0 on the triangular domain T = { ( u , v , w ) : u , v , w ≥ 0 , u + v + w = 1 } are constructed, where u , v , w are the bary…

Quartic approximation of circular arcs using equioscillating error function Open

Abedallah Rababah · 2016

A high accuracy quartic approximation for circular arc is given in this article. The approximation is constructed so that the error function is of degree 8 with the least deviation from the x-axis; the error function equioscillates 9 times…

Weighted G1-Multi-Degree Reduction of B´ezier Curves Open

Abedallah Rababah, Salisu Ibrahim · 2016

In this paper, weighted G1-multi-degree reduction of B´ezier curves is considered. The degree reduction of a given B´ezier curve of degree n is used to write it as a B´ezier curve of degree m,m < n. Exact degree reduction is not possible, …

The best uniform quadratic approximation of circular arcs with high accuracy Open

Abedallah Rababah · 2016

In this article, the issue of the best uniform approximation of circular arcs with parametrically defined polynomial curves is considered. The best uniform approximation of degree 2 to a circular arc is given in explicit form. The approxim…

Multi-degree reduction of disk Bézier curves with G 0 $G^{0}$ - and G 1 $G^{1}$ -continuity Open

Abedallah Rababah, Yusuf Fatihu Hamza · 2015

In this paper, we propose methods to find a $G^{k}$ -multi-degree reduction of disk Bézier curves for $k=0,1$ . The methods are based on degree reducing the center and radius curves using $G^{k}$ -continuity and minimizing the correspondin…

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