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Bounds on partial derivatives of NURBS surfaces

Bounds on partial derivatives of NURBS surfaces
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摘要 In this paper, we estimate the partial derivative bounds for Non-Uniform Rational B-spline(NURBS) surfaces. Firstly, based on the formula of translating the product into sum of B-spline functions, discrete B-spline theory and Dir function, some derivative bounds on NURBS curves are provided. Then, the derivative bounds on the magnitudes of NURBS surfaces are proposed by regarding a rational surface as the locus of a rational curve. Finally, some numerical examples are provided to elucidate how tight the bounds are. In this paper, we estimate the partial derivative bounds for Non-Uniform Rational B-spline(NURBS) surfaces. Firstly, based on the formula of translating the product into sum of B-spline functions, discrete B-spline theory and Dir function, some derivative bounds on NURBS curves are provided. Then, the derivative bounds on the magnitudes of NURBS surfaces are proposed by regarding a rational surface as the locus of a rational curve. Finally, some numerical examples are provided to elucidate how tight the bounds are.
作者 WANG Guo-jin XU Hui-xia HU Qian-qian
机构地区 School of Mathematical Sciences Institute of Mathematics Department of Mathematics
出处 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2017年第3期281-293,共13页 高校应用数学学报（英文版）（B辑）
基金 Supported by the National Natural Science Foundation of China(61572430,61303144) the Natural Science Foundation of Zhejiang Province(LY15F020002,LY16F020020) the Ningbo Natural Science Foundation(2016A610223)
关键词 NURBS curve NURBS surface derivative bound Dir function discrete B-spline NURBS curve NURBS surface derivative bound Dir function discrete B-spline
分类号 TP391.7 [自动化与计算机技术—计算机应用技术]
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Applied Mathematics(A Journal of Chinese Universities)
2017年 第3期

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