Derivatives of rational Be´zier curves
Computer Aided Geometric Design
On the convergence of polynomial approximation of rational functions
Journal of Approximation Theory
Curves and surfaces for CAGD: a practical guide
Curves and surfaces for CAGD: a practical guide
Approximation with Active B-Spline Curves and Surfaces
PG '02 Proceedings of the 10th Pacific Conference on Computer Graphics and Applications
Shape-preserving properties of univariate cubic L1 splines
Journal of Computational and Applied Mathematics
Geometric Hermite interpolation: in memoriam Josef Hoschek
Computer Aided Geometric Design - Special issue: Geometric modelling and differential geometry
Progressive iterative approximation and bases with the fastest convergence rates
Computer Aided Geometric Design
High order approximation of rational curves by polynomial curves
Computer Aided Geometric Design
A simple method for approximating rational Bézier curve using Bézier curves
Computer Aided Geometric Design
Computer Aided Geometric Design
Multi-degree reduction of Bézier curves with constraints, using dual Bernstein basis polynomials
Computer Aided Geometric Design
Computer Aided Geometric Design
Totally positive bases and progressive iteration approximation
Computers & Mathematics with Applications
Weighted progressive iteration approximation and convergence analysis
Computer Aided Geometric Design
High accuracy geometric Hermite interpolation
Computer Aided Geometric Design
Polynomial approximation of rational Bézier curves with constraints
Numerical Algorithms
Approximating uniform rational B-spline curves by polynomial B-spline curves
Journal of Computational and Applied Mathematics
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We present an iteration method for the polynomial approximation of rational Bezier curves. Starting with an initial Bezier curve, we adjust its control points gradually by the scheme of weighted progressive iteration approximations. The L"p-error calculated by the trapezoidal rule using sampled points is used to guide the iteration approximation. We reduce the L"p-error by a predefined factor at every iteration so as to obtain the best approximation with a minimum error. Numerical examples demonstrate the fast convergence of our method and indicate that results obtained using the L"1-error criterion are better than those obtained using the L"2-error and L"~-error criteria.