基于GIMT和弧长参数化的QG-Ball曲线近似合并  

Approximate merging of QG-Ball curves using GIMT and arc-length parameterization

作　　者：胡先智[1] 梁艳 吕丹[4] 胡钢 HU Xian-zhi;LIANG Yan;LYU Dan;HU Gang(Division of Informationize Management,Xi’an University of Technology,Xi’an Shaanxi 710048,China;School of Electronics and Information Engineering,Xi’an Jiaotong University,Xi’an Shaanxi 710049,China;School of Technology,Xi’an Siyuan University,Xi’an Shaanxi 710038,China;School of Science,Xi’an University of Technology,Xi’an Shaanxi 710054,China)

机构地区：[1]西安理工大学信息化管理处,陕西西安710048 [2]西安交通大学电子与信息工程学院,陕西西安710049 [3]西安思源学院理工学院,陕西西安710038 [4]西安理工大学理学院,陕西西安710054

出　　处：《图学学报》2021年第5期790-800,共11页Journal of Graphics

基　　金：国家自然科学基金项目(51875454);陕西省教育厅专项科学研究计划项目(19JK0686)。

摘　　要：曲线近似合并作为CAGD中复杂曲线设计的一种有效技术,一直备受学者们的关注,并在CAD/CAM领域得到了广泛的应用。针对现有带形状参数的广义Ball曲线难以合并的问题,提出了一种基于广义逆矩阵理论(GIMT)和弧长参数化的QG-Ball曲线近似合并方法。首先,利用曲线近似弧长参数化算法计算出QG-Ball曲线弧长等分对应的配置点列(亦称等分点)和配置点参数值;其次,基于所得等弧长配置点列及其参数值,再结合广义逆矩阵理论和曲线拟合方法,便可以直接得到计算合并后QG-Ball曲线控制顶点的一个显式表达式;最后,利用连续函数的L2范数定义了一个度量曲线合并效果的误差计算公式,并给出了一些具有代表性的数值算例及其合并误差。实例结果表明,所提出的方法可以高效地实现QG-Ball曲线的近似合并,不仅易于操作、误差计算简单,而且能方便地推广到其他曲线的近似合并。As an effective technique for the design of complex curve,approximate merging has generated much attention from scholars and been in wide use in CAD/CAM.To address the difficulty in merging generalized Ball curves with parameters,this paper proposed a new method for the approximate merging of QG-Ball curves based on generalized inverse matrix theory(GIMT)and arc-length parameterization.Given two QG-Ball curves,we first calculate a sequence of equal arc-length parameters of the QG-Ball curves by using approximate arc-length parameterization algorithm;Based on the sequence of parameters GIMT,and curve fitting algorithm,an explicit expression was presented to calculate the control points of approximate merged QG-Ball curve.To verify the effectiveness of the method,numerical examples were provided and the merging errors were discussed.The experimental results show that the proposed method not only can efficiently realize the approximate merging of QG-Ball curves,which is of high operability and easy for error calculation,but also can be extended to other curves conveniently.

关 键 词：QG-Ball曲线 形状参数 近似合并 广义逆矩阵 弧长参数化 

分 类 号：TP391.4[自动化与计算机技术—计算机应用技术]