Parametric Rational Cubic Approximation Scheme for Circular Arcs

The research paper presents a numerical method for the \({G}^{2}\) $G^2$ - approximation of circular arcs. The developed technique is worked on a quarter circle and the complete circle is formed using affine transformation. The optimal value of the free parameters is searched by reducing the approximation error to its minimum. Approximation order of the proposed scheme varies from \(O\left({\gamma }^{2}\right)\) $O\left({\gamma }^2\right)$ to \(O\left({\gamma }^{4}\right),\) $O\left({\gamma }^4\right),$ depending on the choice of free parameters. The proposed approximation scheme has an improved level of accuracy than the prevailing schemes.