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 Bézier curve by a polynomial Bézier curve. This problem is reformulated as an approximation problem between two polynomial Bézier curves based on weighted least-squares method, where weight functions $ρ(t)=ω(t)$ and $ρ(t)=ω(t)^{2}$ are studied respectively. The efficiency of the proposed method is tested using some examples.