Rational Bézier Curves Approximated by Bernstein-Jacobi Hybrid Polynomial Curves

Abstract

In this paper, we propose a linear method for $C^{(r,s)}$ approximation of rational Bézier curve with arbitrary degree polynomial curve. Based on weighted least-squares, the problem be converted to an approximation between two polynomial curves. Then applying Bernstein-Jacobi hybrid polynomials, we obtain the resulting curve. In order to reduce error, degree reduction method for Bézier curve is used. A error bound between rational Bézier curve and Bézier curve is presented. Finally, some examples and figures were offered to demonstrate the efficiency, simplicity, and stability of our methods.