Approximating rational Bezier curves by constrained Bezier curves of arbitrary degree
Provides a practical approximation technique for computer-aided geometric design, but is incremental in nature.
The paper proposes a method to approximate rational Bézier curves with polynomial Bézier curves of arbitrary degree using weighted least-squares, achieving constrained approximation. Tested on examples with weight functions ω(t) and ω(t)^2.
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.