Rational B\'ezier Curves Approximated by Bernstein-Jacobi Hybrid Polynomial Curves
Computational Geometry
2023-03-30 v2
Abstract
In this paper, we propose a linear method for approximation of rational B\'{e}zier curve with arbitrary degree polynomial curve. Based on weighted least-squares, the problem be converted to an approximation between two polynomial curves. Then applying Bernstein-Jacobi hybrid polynomials, we obtain the resulting curve. In order to reduce error, degree reduction method for B\'{e}zier curve is used. A error bound between rational B\'{e}zier curve and B\'{e}zier curve is presented. Finally, some examples and figures were offered to demonstrate the efficiency, simplicity, and stability of our methods.
Keywords
Cite
@article{arxiv.1605.04156,
title = {Rational B\'ezier Curves Approximated by Bernstein-Jacobi Hybrid Polynomial Curves},
author = {Mao Shi},
journal= {arXiv preprint arXiv:1605.04156},
year = {2023}
}