The best quintic Chebyshev approximation of circular arcs of order ten

Abedallah M. Rababah (United Arab Emirates University)

International Journal of Electrical and Computer Engineering
Vol 9, No 5: October 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 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.