The estimation of bounds on derivatives of rational Bézier curves has significant application in Computer Aided Geometric Design (CAGD).This paper proposes a piecewise method to estimate the derivative bounds of the rational Bézier curves.This method applies the Bernstein basis functions' extreme value characteristics and fundamental inequalities to estimate the derivative bounds of the rational Bézier curves.Both theoretical analysis and numerical examples show that our bound is sharper than existing ones.The proposed method has an excellent convergence effect for smooth rational Bézier curves with severe weights and control points.
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Zhou et al. (2024) studied this question.