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Journal of Graphics ›› 2021, Vol. 42 ›› Issue (5): 790-800.DOI: 10.11996/JG.j.2095-302X.2021050790

• Computer Graphics and Virtual Reality • Previous Articles     Next Articles

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)

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. 

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