Some improvements on the derivative bounds of rational Bézier curves and surfaces

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Abstract

Based on some existing identities and elementary inequalities, also using the method of degree elevation, this note improves the derivative bounds of rational Bézier curves and surfaces.

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Cited by (16)

  • Derivative bound estimations on rational conic Bézier curves

    2014, Applied Mathematics and Computation
    Citation Excerpt :

    Especially, the estimation of bounds on derivatives of rational Bézier curves has important applications in CAGD [2] and Computer Graphics (CG) [3]. Thus many authors gave bounds on the magnitude of the derivative of rational Bézier curves [2,3,5,4,6–12] and rational triangular Bézier surfaces [13–15]. In this paper we give a new result about the derivative bounds of rational conic Bézier curves.

  • An improvement on the upper bounds of the magnitudes of derivatives of rational triangular Bézier surfaces

    2014, Computer Aided Geometric Design
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    Hence, a priori determination of a tight bound on their derivative magnitude is nontrivial. So far, many literatures have focused on estimating or improving the bounds on the derivatives of rational curves or surfaces (Floater, 1992; Saito et al., 1995; Wang et al., 1997; Hermann, 1999; Zheng and Sederberg, 2000; Selimovic, 2005; Cao et al., 2007; Hu and Wang, 2007; Zhang and Wang, 2005; Huang and Su, 2006; Zhang and Ma, 2006; Deng, 2011; Deng and Li, 2013; Li et al., 2013). We notice that most of these papers have focused on the bounds estimation of the derivatives of Bézier curves or tensor product Bézier surfaces.

  • On the bounds of the derivative of rational Bézier curves

    2013, Applied Mathematics and Computation
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