Open AccessThe best quintic Chebyshev approximation of circular arcs of order ten
Author(s) -
Abedallah Rababah
Publication year - 2019
Publication title -
international journal of power electronics and drive systems/international journal of electrical and computer engineering
Language(s) - English
Resource type - Journals
eISSN - 2722-2578
pISSN - 2722-256X
DOI - 10.11591/ijece.v9i5.pp3779-3785
Subject(s) - minimax approximation algorithm , mathematics , chebyshev polynomials , approximation error , quintic function , equioscillation theorem , chebyshev filter , chebyshev nodes , approximation theory , spline (mechanical) , parametric statistics , trigonometric functions , polynomial , trigonometric polynomial , mathematical analysis , function (biology) , trigonometry , nonlinear system , geometry , orthogonal polynomials , gegenbauer polynomials , classical orthogonal polynomials , physics , statistics , quantum mechanics , thermodynamics , evolutionary biology , biology
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 is presented. This approximation is set so that the error function is of degree $10$ rather than $6$; the Chebyshev error function equioscillates $11$ times rather than $7$; the approximation order is $10$ rather than $6$. The method approximates more than the full circle with Chebyshev uniform error of $1/2^{9}$. The examples show the competence and simplicity of the proposed approximation, and that it can not be improved.