Bounds on partial derivatives of NURBS surfaces  

作　　者：WANG Guo-jin XU Hui-xia HU Qian-qian 

机构地区：[1]School of Mathematical Sciences, Zhejiang University [2]Institute of Mathematics, Zhejiang Wanli University [3]Department of Mathematics, Zhejiang Gongshang University

出　　处：《Applied Mathematics(A Journal of Chinese Universities)》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)

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.

关 键 词：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]