Adaptive Polynomial Approximation to Circular Arcs
We present a new adaptive method for approximating circular arcs in polynomial form by using the s-power series. Circular arcs can be expressed in infinite series form, we obtain the order-k Hermite interpolant by truncating at the kth term. An upper bound on the error of the interpolant is available, so we can obtain the lowest degree polynomial curve that approximates a circular arc within any user-prescribed tolerance. And this degree can be further reduced through subdivision, which generates a spline approximation with Ck continuity at the joints.
Shaobo Zhong, Yimin Cheng and Xilong Qu
L. Z. Lu "Adaptive Polynomial Approximation to Circular Arcs", Applied Mechanics and Materials, Vols. 50-51, pp. 678-682, 2011