The best quintic Chebyshev approximation of circular arcs of order ten - Abedallah M. Rababah (Institute of Advanced Engineering and Science, 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.