A Highly Accurate Approximation of Conic Sections by Quartic Bézier Curves

A new approximation method for conic section by quartic Bezier curves is proposed. This method is based on the quartic Bezier approximation of circular arcs. We give the upper bound of Hausdorff distance between the conic section and the quartic Bezier curve, and also show that the approximation order is eight. And we prove that our approximation method has a smaller upper bound than previous quartic Bezier approximation methods. A quartic G 2 -continuous spline approximation of conic sections is obtained by using the subdivision scheme at the shoulder point of the conic section.