The NURBS book
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
A simple method for approximating rational Bézier curve using Bézier curves
Computer Aided Geometric Design
Approximating rational triangular Bézier surfaces by polynomial triangular Bézier surfaces
Journal of Computational and Applied Mathematics
Sample-based polynomial approximation of rational Bézier curves
Journal of Computational and Applied Mathematics
Polynomial approximation of rational Bézier curves with constraints
Numerical Algorithms
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Approximation of rational B-spline curves by B-spline curves is an important issue in computer aided geometric design. This paper presents a method to approximate a uniform rational B-spline with B-spline curve sequence as follows. We first elevate the degree of the original rational B-spline curve and take the control points of the degree-elevated curve as new control points of the B-spline approximation curve. Next we take an extended knot vector of the original curve as a new knot vector of the approximation curve. This generates a B-spline approximation curve with the same degree as the degree-elevated curve. Based on the discrete B-spline and multiple products of B-spline functions, we finally prove that the derivatives of any given degree of the uniform B-spline approximation curve sequence converge uniformly to the corresponding derivatives of the original rational B-spline curve. This approximation method is very simple and guarantees the convergence of the approximation.