Good approximation of circles by curvature-continuous Be´zier curves
Computer Aided Geometric Design
Mathematical methods in computer aided geometric design
Best approximation of circle segments by quadratic Be´zier curves
Curves and surfaces
Approximation of circular arcs by cubic polynomials
Computer Aided Geometric Design
High-order approximation of conic sections by quadratic splines
Computer Aided Geometric Design
An O(h2n) Hermite approximation for conic sections
Computer Aided Geometric Design
Approximation of circular arcs by Bézier curves
Journal of Computational and Applied Mathematics
Circular arc approximation by quintic polynomial curves
Computer Aided Geometric Design
G3 approximation of conic sections by quintic polynomial curves
Computer Aided Geometric Design
Curves and surfaces for CAGD: a practical guide
Curves and surfaces for CAGD: a practical guide
A rational quartic Bézier representation for conics
Computer Aided Geometric Design
Approximation of circular arcs and offset curves by Bézier curves of high degree
Journal of Computational and Applied Mathematics
Necessary and sufficient conditions for rational quartic representation of conic sections
Journal of Computational and Applied Mathematics
An approximation of circular arcs by quartic Bézier curves
Computer-Aided Design
High order approximation of rational curves by polynomial curves
Computer Aided Geometric Design
The definition and computation of a metric on plane curves
Computer-Aided Design
High accuracy geometric Hermite interpolation
Computer Aided Geometric Design
Approximating conic sections by constrained Bézier curves of arbitrary degree
Journal of Computational and Applied Mathematics
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In this paper we propose two approximation methods of conic section by quartic Bezier curves. These are the extensions of the quartic Bezier approximations of circular arcs presented in Ahn and Kim (1997) [1] and Kim and Ahn (2007) [10] to conic cases. We also give the error bounds of the Hausdorff distances between the conic section and the approximation curves, and show that the error bounds have the approximation order eight. Our methods yield quartic G^2 (curvature) continuous spline approximations of conic sections using the subdivision scheme stated in Floater (1995, 1997) [5,11]. We illustrate our results by some numerical examples.