基于分数阶傅里叶变换的NURBS曲面拟合

孔德明; 黄紫双; 王书涛; 史慧超

doi:10.3969/j.issn.1000-1158.2021.03.06

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计量学报 ›› 2021, Vol. 42 ›› Issue (3) : 294-300. DOI: 10.3969/j.issn.1000-1158.2021.03.06

几何量计量

基于分数阶傅里叶变换的NURBS曲面拟合

孔德明¹,黄紫双¹,王书涛¹,史慧超²

作者信息 +

NURBS Surface Fitting Based on Fractional Fourier Transform

KONG De-ming¹,HUANG Zi-shuang¹,WANG Shu-tao¹,SHI Hui-chao²

Author information +

文章历史 +

摘要

为了实现对自由曲面模型的高精度非均匀有理B样条(NURBS)曲面拟合,提出了一种基于分数阶傅里叶变换的NURBS曲面拟合方法。首先,借助分数阶傅里叶变换对自由曲面模型点云数据的高程图像展开分析,从中提取出表征自由曲面表面三维结构的特征点;然后,利用外切圆取点法结合提取的特征点选取用于NURBS曲面拟合的数据点;最后,利用分数阶傅里叶变换滤波及反插节点法对拟合曲面形状进行优化,提高拟合精度。实验结果表明:该方法与传统NURBS拟合方法相比,在不同调整次数下拟合结果的均方根误差降低了28%,取得了更好的拟合效果。

Abstract

In order to realize high quality non-uniform rational B-splines (NURBS) fitting surface of free-form surface model, a NURBS surface fitting method based on fractional Fourier transform is proposed. Firstly, the elevation image of the point cloud data of the free-form surface model is analyzed by means of fractional Fourier transform, and the feature points representing the three-dimensional structure of the free-form surface are extracted from the elevation image of the point cloud data of the free-form surface model. Then, the data points for NURBS surface fitting are selected by using the outer tangent circle extraction method combined with the extracted feature points. Finally, the fractional Fourier transform filtering and inverse interpolation node method are used to optimize the shape of the fitting surface to improve the fitting accuracy. The experimental results show that compared with the traditional NURBS fitting method, the root-mean-square error of the fitting results is reduced by 28% under different adjustment times, and the fitting effect is better.

导出引用

孔德明,黄紫双,王书涛,史慧超. 基于分数阶傅里叶变换的NURBS曲面拟合[J]. 计量学报. 2021, 42(3): 294-300 https://doi.org/10.3969/j.issn.1000-1158.2021.03.06

KONG De-ming,HUANG Zi-shuang,WANG Shu-tao,SHI Hui-chao. NURBS Surface Fitting Based on Fractional Fourier Transform[J]. Acta Metrologica Sinica. 2021, 42(3): 294-300 https://doi.org/10.3969/j.issn.1000-1158.2021.03.06

中图分类号： TB92

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