Good approximation of circles by curvature-continuous Be´zier curves
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
The rational cubic Be´zier representation of conics
Computer Aided Geometric Design
High-order approximation of conic sections by quadratic splines
Computer Aided Geometric Design
Geometric Hermite interpolation with maximal order and smoothness
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
Approximation of conic sections by curvature continuous quartic Bézier curves
Computers & Mathematics with Applications
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In this paper, an algorithm for approximating conic sections by constrained Bezier curves of arbitrary degree is proposed. First, using the eigenvalues of recurrence equations and the method of undetermined coefficients, some exact integral formulas for the product of two Bernstein basis functions and the denominator of rational quadratic form expressing conic section are given. Then, using the least squares method, a matrix-based representation of the control points of the optimal Bezier approximation curve is deduced. This algorithm yields an explicit, arbitrary-degree Bezier approximation of conic sections which has function value and derivatives at the endpoints that match the function value and the derivatives of the conic section up to second order and is optimal in the L"2 norm. To reduce error, the method can be combined with a curve subdivision scheme. Computational examples are presented to validate the feasibility and effectiveness of the algorithm for a whole curve or its part generated by a subdivision.