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Rational Bézier Curves Approximated by Bernstein-Jacobi Hybrid Polynomial Curves (1605.04156v2)
Published 13 May 2016 in cs.CG
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.