The Best Uniform Cubic Approximation of Circular Arcs with High Accuracy

Abstract

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 circular arc is given in explicit form. The approximation is constructed so that the error function is the Chebyshev polynomial of degree 6; the error function equioscillates 7 times; the approximation order is 6. The numerical examples demonstrate the efficiency and simplicity of the approximation method as well as satisfying the properties of the best uniform approximation and yielding the best approximation of least deviation and the highest possible accuracy.