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基于正则渐进迭代逼近的自适应B 样条曲线拟合

  

  1. 大连理工大学盘锦校区基础教学部,辽宁 盘锦 124221
  • 出版日期:2018-04-30 发布日期:2018-04-30
  • 基金资助:
    国家自然科学基金项目(11601064);中央高校基本科研业务专项资金项目(DUT14RC(3)024,DUT16RC(4)67,DUT17LK09)

Adaptive B-spline Curve Fitting Based on Regularized Progressive Iterative Approximation

  1. School of Mathematics and Physics Science, Dalian University of Technology, Panjin Liaoning 124221, China
  • Online:2018-04-30 Published:2018-04-30

摘要: 基于渐进迭代逼近(PIA)的数据拟合方法以其简单和灵活的特性获得了广泛的关
注。为了获得高保真度的拟合曲线,提出了一种基于主导点选取和正则渐进迭代逼近(RPIA)的
自适应B 样条曲线拟合算法。首先根据数据点的曲率估计选取初始主导点并生成初始PIA 曲线。
然后,借助于拟合误差和数据点集的曲率分布选取加细的主导点及实现PIA 曲线的更新。得益
于基于曲率分布的主导点选取,使得拟合曲线在复杂区域分布较多的控制顶点,而在平坦区域
则较少。通过正则参数的引入构造了一种RPIA 格式,提升了渐进迭代控制的灵活性。最后,
数值算例表明相比于传统最小二乘曲线拟合该算法在使用较少数量的控制顶点时可实现较高的
拟合精度。

关键词: B 样条曲线拟合, 正则渐进迭代逼近, 自适应加细, 曲率估计

Abstract: The use of progressive iterative approximation (PIA) to fit data points has received a deal of
attention benefitting from its simplicity and flexibility. To obtain a fitting curve satisfying the shape
high fidelity, we present an adaptive B-spline curve fitting algorithm based on regularized progressive
iterative approximation (RPIA) and the selection of dominant points. Firstly, the initial dominant points
are selected from the given points in terms of curvature estimates and an initial progressive iterative
approximation curve is constructed. Then the fitting curve based on RPIA is updated by means of the
fitting error and the selection of refinement dominant points according to the curvature distribution of
given points. The fitting curve possesses fewer control points at flat regions but more at complex
regions. By the use of a regular parameter, progressive iterative approximation is generalized and the
flexibility of PIA is promoted. Finally, numerical examples are provided to demonstrate that compared
with the conventional least square approaches the proposed method can achieve a higher fitting
precision with far fewer control points.

Key words: B-spline curve fitting, regularized progressive iterative approximation, adaptive refinement;
curvature estimation