Derivatives of rational Be´zier curves
Computer Aided Geometric Design
Fundamentals of computer aided geometric design
Fundamentals of computer aided geometric design
Hodographs and normals of rational curves and surfaces
Computer Aided Geometric Design
On the convergence of polynomial approximation of rational functions
Journal of Approximation Theory
Bounds on the moving control points of hybrid curves
Graphical Models and Image Processing
Recursive Formulae for Hermite Polynomial Approximations to Rational Bézier Curves
GMP '00 Proceedings of the Geometric Modeling and Processing 2000
Short communication: Rational hodographs
Computer Aided Geometric Design
Minimizing the maximal ratio of weights of rational Bézier curves and surfaces
Computer Aided Geometric Design
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In this paper, we derive the bounds on the magnitude of lth (l=2,3) order derivatives of rational Bezier curves, estimate the error, in the L"~ norm sense, for the hybrid polynomial approximation of the lth (l=1,2,3) order derivatives of rational Bezier curves. We then prove that when the hybrid polynomial approximation converges to a given rational Bezier curve, the lth (l=1,2,3) derivatives of the hybrid polynomial approximation curve also uniformly converge to the corresponding derivatives of the rational curve. These results are useful for designing simpler algorithms for computing tangent vector, curvature vector and torsion vector of rational Bezier curves.