Sequence of Gn LN polynomial curves approximating circular arcs

In this paper we derive a sequence of linear normal (LN) curves b2n of degree 2n which are Gn endpoint interpolations of a circular arc and have approximation order 2n+2. This is an extension of the circle approximation method by LN Bézier curves given in Ahn and Hoffmann (2014) to all even degrees. We also extend the circle approximation to an ellipse approximation by Gn LN curves of degree 2n. An upper bound of the Hausdorff distance between the ellipse and its LN approximation is obtained. We illustrate our results through an LN approximation of convolution curves of ellipses and a spline curve.