欢迎访问《图学学报》 分享到：
图学学报

图学学报 ›› 2021, Vol. 42 ›› Issue (5): 790-800.DOI: 10.11996/JG.j.2095-302X.2021050790

• 计算机图形学与虚拟现实 • 上一篇    下一篇

基于GIMT和弧长参数化的QG-Ball曲线近似合并

  

  1. 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
  • 出版日期:2021-10-31 发布日期:2021-11-03
  • 基金资助:
    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) 

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

  1. 1. Division of Informationize Management, Xi’an University of Technology, Xi’an Shaanxi 710048, China;  2. School of Electronics and Information Engineering, Xi’an Jiaotong University, Xi’an Shaanxi 710049, China;  3. School of Technology, Xi’an Siyuan University, Xi’an Shaanxi 710038, China;  4. School of Science, Xi’an University of Technology, Xi’an Shaanxi 710054, China
  • Online:2021-10-31 Published:2021-11-03
  • Supported by:
    National Natural Science Foundation of China (51875454); Special Scientific Research Project of Shaanxi Provincial Department of Education (19JK0686)

PDF (PC)

56

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。

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

Abstract: 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. 

中图分类号: