JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2021, Vol. 56 ›› Issue (6): 81-94.doi: 10.6040/j.issn.1671-9352.0.2021.136

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Progressive-iterative approximation by the triangular β-B curves with shape parameter

WANG Zeng-zhen, LIU Hua-yong*, ZHA Dong-dong   

  1. Anhui Jianzhu University, Hefei 230601, Anhui, China
  • Published:2021-06-03

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Abstract: In order to accelerate the convergence speed of the progressive-iterative approximation method and overcome the defect that the general B-spline curves cannot represent curves such as circles or ellipses, this paper discusses its(weighted)progressive-iterative approximation based on β-B curves. Compared with general cubic uniform polynomial B-spline curve, the former has better continuity. The iterative matrix of the(weighted)progressive-iterative approximation is obtained according to the selected β-B basis function. Based on the conclusion that the spectral radius is the smallest and the convergence speed is the fastest,the optimal shape parameters of the(weighted)progressive-iterative approximation and the optimal weight w of the weighted progressive-pterative approximation method are derived. Then this paper does convergence analysis on them respectively. Finally, numerical examples are given to analyze the iteration speed and iteration error when the shape parameters are different. The experimental results show that the convergence speed is the fastest when the shape parameter and weight are optimal.

Key words: β-B curve, progressive-iterative approximation, spectral radius, convergence rate

CLC Number: 

  • O241.5
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