两相邻CEBézier曲线的近似合并

doi:10.13190/jbupt.201006.76.hug

北京邮电大学学报 ›› 2010, Vol. 33 ›› Issue (6): 76-80.doi: 10.13190/jbupt.201006.76.hug

两相邻CEBézier曲线的近似合并

胡钢¹,秦新强¹,岳丽¹,刘哲²

1西安理工大学理学院, 西安 710054; 2西北工业大学理学院, 西安 710072

收稿日期:2009-08-03 修回日期:2010-05-07 出版日期:2010-12-28 发布日期:2011-01-07
通讯作者: 胡钢 E-mail:huhui_xauot@163.com
基金资助:
国家自然科学基金项目（60971127,10926152）; 陕西省教育厅基金项目(09JK613); 西安理工大学校青年基金项目(108210817); 西北工业大学基础研究基金项目(JC200949)

Approximate Merging of a Pair of CEBézier Curves

Received:2009-08-03 Revised:2010-05-07 Online:2010-12-28 Published:2011-01-07

摘要/Abstract

摘要：

为了进一步丰富和发展CEBézier曲线的相关理论，针对该曲线的近似合并问题，提出了一种将两相邻CEBézier曲线合并成1条CEBézier曲线的方法. 该方法通过将曲线拟合方法与广义逆矩阵理论相结合，直接得到合并后CEBézier曲线控制顶点的显示表达式，同时给出了具体的合并误差. 实验结果表明，新方法不仅可获得较好的合并效果，而且具有易于实现、误差计算简单的特点，可广泛应用于计算机辅助设计中对曲线的近似合并.

关键词: 三次扩展Bé, zier曲线；形状参数；近似合并；曲线拟合；广义逆矩阵

Abstract:

Cubic extension Bézier (CEBézier) curve with multiple shape parameters is one of the most important extensions of the cubic Bézier curve. It not only inherits the outstanding properties of the cubic Bézier curve, but with a good performance on adjusting their local shapes by changing the shape control parameters. In order to develop the basic theory of CEBézier curve, a new method to deal with approximating two adjacent CEBézier curves by one CEBézier curve is presented for the approximate merging of existing curve design. By combining the fitting method of curves and the theory of the general inverse matrix, the explicit formula of control points of the merged CEBézier curve can be given directly. Eventually, some merging examples are discussed and the errors of approximate merging are given as well. Experiments illustrate that the proposed method not only has a good merging effect, but is easy to implement and simple to error estimation.

Key words: cubic extension Bézier curve, shape parameter, approximate merging, curve fitting, general inverse matrix

中图分类号:

TP391.4

胡钢,秦新强,岳丽,刘哲. 两相邻CEBézier曲线的近似合并[J]. 北京邮电大学学报, 2010, 33(6): 76-80.

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两相邻CEBézier曲线的近似合并

Approximate Merging of a Pair of CEBézier Curves

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