Some improvements on the derivative bounds of rational Bézier curves and surfaces
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Cited by (16)
Improved derivative bounds of the rational quadratic Bézier curves
2015, Applied Mathematics and ComputationDerivative bound estimations on rational conic Bézier curves
2014, Applied Mathematics and ComputationCitation 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 DesignCitation Excerpt :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.
New minimal bounds for the derivatives of rational Bézier paths and rational rectangular Bézier surfaces
2013, Applied Mathematics and ComputationOn the bounds of the derivative of rational Bézier curves
2013, Applied Mathematics and ComputationOn derivative bounds for the rational quadratic Bézier paths
2013, Computer Aided Geometric Design