Approximating rational Bezier curves by constrained Bezier curves of arbitrary degree

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.