Weighted polynomial approximation of rational B\'ezier curves

TL;DR

This paper introduces an efficient algorithm for approximating rational Bézier curves with polynomial Bézier curves using dual constrained Bernstein basis polynomials, demonstrating effectiveness through examples.

Contribution

The paper develops a novel method leveraging dual constrained Bernstein basis polynomials and their recursive properties for constrained least squares approximation of rational Bézier curves.

Findings

Algorithm effectively approximates rational Bézier curves with polynomial Bézier curves.

Uses dual constrained Bernstein basis polynomials associated with Jacobi scalar product.

Examples demonstrate the efficiency and accuracy of the proposed method.

Abstract

We present an efficient method to solve the problem of the constrained least squares approximation of the rational B\'{e}zier curve by the B\'{e}zier curve. The presented algorithm uses the dual constrained Bernstein basis polynomials, associated with the Jacobi scalar product, and exploits their recursive properties. Examples are given, showing the effectiveness of the algorithm.