English

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 C(r,s)C^{(r,s)} 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}
}