Approximate merging of a pair of quartic Bézier curve with shape parameters

Computer Engineering and Applications ›› 2011, Vol. 47 ›› Issue (14): 160-163.

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Approximate merging of a pair of quartic Bézier curve with shape parameters

YUE Li，QIN Xinqiang，HU Gang，LI Kai

School of Science，Xi’an University of Technology，Xi’an 710054，China

Received:1900-01-01 Revised:1900-01-01 Online:2011-05-11 Published:2011-05-11

两相邻带参四次Bézier曲线的近似合并

岳丽，秦新强，胡钢，李凯

西安理工大学理学院，西安 710054

Abstract

Abstract: A class of polynomial basis function of 5th degree with four shape control parameters is presented.It is an extension of cubic Bernstein basis functions.Properties of the basis function are analyzed and the corresponding polynomial curve with four sharp parameters is defined.QE-Bézier curve is extension of quartic Bézier curve，so the QE-Bézier curve not only inherits the outstanding properties of the quartic Bézier curve，but also is adjustable in sharp and fit close to the control polygon.The question about approximate merging a pair of QE-Bézier is researched.The explicit formula of control points of the merged QE-Bézier curve can be given directly by combining the fitting method of curves with the theory of general inverse matrix and the error is given.Finally，the examples are presented，which show the effectiveness of the presented method.

Key words: quartic Bézier curve, shape parameter, extension, approximate merging

摘要： 给出了带有4个形状参数的5次多项式基函数，分析了这组基函数的性质，并由此基函数构造了带4个形状控制参数的四次扩展Bézier曲线（简称QE-Bézier曲线）。QE-Bézier曲线是对四次Bézier曲线的扩展，它不仅具有与四次Bézier曲线类似的性质，而且具有灵活的形状可调性和更好的逼近性。进一步研究了两相邻QE-Bézier曲线的合并问题，通过曲线拟合方法与广义逆矩阵理论相结合，直接得到了合并曲线控制顶点的显示表达式，并给出了误差分析，数值实例显示逼近效果较好。

关键词: 四次Bézier曲线, 形状参数, 扩展, 近似合并

YUE Li，QIN Xinqiang，HU Gang，LI Kai. Approximate merging of a pair of quartic Bézier curve with shape parameters[J]. Computer Engineering and Applications, 2011, 47(14): 160-163.

岳丽，秦新强，胡钢，李凯. 两相邻带参四次Bézier曲线的近似合并[J]. 计算机工程与应用, 2011, 47(14): 160-163.

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Approximate merging of a pair of quartic Bézier curve with shape parameters

两相邻带参四次Bézier曲线的近似合并

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