This paper presents a method for approximating conic sections using quintic polynomial curves. The constructed quintic polynomial curve has G~3 -continuity with the conic section at the end points and G~1 -continuity at the parametric mid-point. It is found that for any conic section, there exist three quintic polynomial curves satisfying the mentioned geometric continuity. One of them is the geometric Hermite interpolate proposed in (Floater ,1997) and one of the others is shown to have much smaller error and better shape-preserving property.
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