G1G1 approximation of conic sections by quartic Bézier curves

This paper proposes a new approximation method for conic sections by quartic Bézier curves with G1G1 end-point continuity. We give an upper bound on the Hausdorff distance between the conic section and the quartic Bézier approximation curve, and also show that the approximation order is eight. Moreover, using the subdivision scheme at the shoulder point of the conic section, the resulting approximation curve has G2G2 (curvature)-continuity with the conic section at the endpoints. Finally, we prove that our approximation has a smaller error bound than previous quartic Bézier approximations, and also present some numerical examples to demonstrate the validity and effectiveness of our method.