Approximating rational Bezier curves by constrained Bezier curves of arbitrary degree

TL;DR

This paper introduces a method to approximate rational Bezier curves with constrained polynomial Bezier curves of any degree using weighted least-squares, demonstrating its effectiveness through examples.

Contribution

It presents a novel approach to approximate rational Bezier curves with polynomial ones under constraints, using weighted least-squares with different weight functions.

Findings

Effective approximation demonstrated through examples

Weighted least-squares method with specific weights improves accuracy

Method applicable to arbitrary degree polynomial Bezier curves

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.