Circle approximation using LN Bézier curves of even degree and its application

We present an approximation method of circular arcs using linear-normal (LN) Bézier curves of even degree, four and higher. Our method achieves G m continuity for endpoint interpolation of a circular arc by a LN Bézier curve of degree 2m, for m = 2 , 3 . We also present the exact Hausdorff distance between the circular arc and the approximating LN Bézier curve. We show that the LN curve has an approximation order of 2 m + 2 , for m = 2 , 3 . Our approximation method can be applied to offset approximation, so obtaining a rational Bézier curve as an offset approximant. We derive an algorithm for offset approximation based on the LN circle approximation and illustrate our method with some numerical examples.