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

Abstract

Abstract-In this paper, weighted G 1 -multi-degree reduction of Bézier curves is considered. The degree reduction of a given Bézier curve of degree n is used to write it as a Bézier curve of degree m, m < n. Exact degree reduction is not possible, and, therefore, approximation methods are used. The weight function w(t) = 2t(1 − t), t ∈ [0, 1] is used with the L2-norm in multidegree reduction with G 1 -continuity at the end points of the curve. Since we consider boundary conditions this weight function improves approximation in the middle of the curve. Numerical results and comparisons show that the proposed method produces fewer errors and outperform all existing methods.

Quartic approximation of circular arcs using equioscillating error function

“…The Bézier curve p(t) of degree 4 is given by, see [11] Since it is intended to represent the arc with a polynomial curve with minimum error, it is not important if the errors occur at the endpoints or anywhere else; it is important to maintain this disruption as low as possible there where the error occurs. In some other schemes, it is necessary that the approximating Bézier curve is G k -continuous at the end points, see [20]. To represent a circular arc, the Bézier points are selected to take advantage of the symmetry properties of the circle.…”

Application of Lagrange Interpolation Method to Solve First-Order Differential Equation Using Newton Interpolation Approach

“…The authors in (Ibrahim, & Koksal, 2021a) studied the commutativity with non-zero initial conditions (ICs) and their effects on the sensitivity was studied in [Salisu, I, 2022a;Salisu, I, 2022c] while the realization and decomposition of a fourth-order LTVSs with nonzero ICs by cascaded two Second-Order commutative pairs was introduced by (Ibrahim, & Koksal, 2021b;Salisu, & Rababah, 2022). The authors in (Rababah, & Ibrahim, 2016a;Rababah, & Ibrahim, 2016b;Rababah, & Ibrahim, 2018) come up with a numerical approximative process for degree reduction of curves and surface which approaches can be used to solve complex ODES, PDEs, and FDEs.…”

Explicit Solution of First-Order Differential Equation Using Aitken’s and Newton’s Interpolation Methods

“…The authors (Ibrahim, & Koksal, 2021a) studied the commutativity with non-zero initial conditions (ICs), and their effects on the sensitivity were studied (Salisu, 2022a;Salisu, 2022c) while the realization and decomposition of a fourth-order LTVSs with nonzero ICs by cascaded two Second-Order commutative pairs was introduced by (Ibrahim, & Koksal, 2021b;Salisu, & Rababah, 2022). The authors (Rababah, & Ibrahim, 2016a;Rababah, & Ibrahim, 2016b;Rababah, & Ibrahim, 2018) come up with a numerical approximative process for degree reduction of curves and surfaces which approaches can be used to solve complex ODES, PDEs, and FDEs.…”