Approximating rational Bezier curves by constrained Bezier curves of arbitrary degree

Abstract: In this paper, we propose a method to obtain a constrained approximation of a rational B\'{e}zier curve by a polynomial B\'{e}zier curve. This problem is reformulated as an approximation problem between two polynomial B\'{e}zier curves based on weighted least-squares method, where weight functions $\rho(t)=\omega(t)$ and $\rho(t)=\omega(t)^{2}$ are studied respectively. The efficiency of the proposed method is tested using some examples.