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arXiv · 1605.04156

Rational B\'ezier Curves Approximated by Bernstein-Jacobi Hybrid Polynomial Curves

Mao Shi
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Abstract

In this paper, we propose a linear method for $C^{(r,s)}$ 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.

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Mao Shi. 2016-05-13. Rational B\'ezier Curves Approximated by Bernstein-Jacobi Hybrid Polynomial Curves. https://doi.org/10.1007/s40314-020-01291-8

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