Communications of the
Korean Mathematical Society CKMS

In this paper we present an error bound for cubic spline approximation of conic section curve. We compare it to the error bound proposed by Floater \cite{ACM96_Floater}. The error estimating function proposed in this paper is sharper than Floater's at the mid-point of parameter, which means the overall error bound is sharper than Floater's if the estimating function has the maximum at the mid-point.

Keywords: conic section, spline approximation, cubic Be\'zier curve, error analysis, geometric Hermite interpolation

MSC numbers: 41A50, 41A52, 65D05, 64D07