|
|
NURBS Surface Fitting Based on Fractional Fourier Transform |
KONG De-ming1,HUANG Zi-shuang1,WANG Shu-tao1,SHI Hui-chao2 |
1. School of Electrical Engineering, Yanshan University, Qinhuangdao, Hebei 066004, China
2. School of Information Science and Technology, Beijing University of Chemical Technology, Beijing 100029, China |
|
|
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.
|
Received: 08 January 2020
Published: 23 March 2021
|
|
|
|
|
[1]鞠华, 王文, 谢金, 等. 逆向工程中自由曲面的自适应数字化算法研究[J]. 计量学报, 2003(2): 99-102.
Jü H, Wang W, Xie J, et al. Research on Adaptive Digitization Algorithm for Free Surface in Reverse Engineering [J]. Acta Metrologica Sinica, 2003(2): 99-102.
[2]孙迎兵, 吴凤和, 郭保苏, 等. 基于MKSA算法的曲面自适应采样[J]. 计量学报, 2018, 39(5): 622-627.
Sun Y b, Wu F H Guo B S, et al. Adaptive sampling of surfaces based on MKSA algorithm [J]. Acta Metrologica Sinica, 2018, 39(5): 622-627.
[3]Wu F F, Li J, Yang H M, et al. Research of pavement topography based on NURBS reconstruction for 3D structured light[J]. Optik, 2019, 163074.
[4]张礼林, 王国瑾. 带B样条曲率线的NURBS曲面设计[J]. 计算机辅助设计与图形学学报, 2018, 30(9): 1692-1698.
Zhang L L, Wang G J. Design of NURBS surfaces with B-spline curvature[J]. Computer-Aided Design & Computer Graphic, 2018, 30(9): 1692-1698.
[5]张翠翠, 黄海松, 吕健. 基于三角网格的民族工艺品曲面重构技术[J]. 计算机应用研究, 2014, 31(6): 1906-1908,1917.
Zhang C C, Huang H S, Lü J. Surface reconstruction technology of ethnic handicrafts based on triangular mesh[J]. Journal of Computer Applications, 2014, 31(6): 1906-1908,1917.
[6]张娟, 侯进, 吴婷婷, 等. 三维散乱点云模型的快速曲面重建算法[J]. 计算机辅助设计与图形学学报, 2018, 30(2): 235-243.
Zhang J, Hou J, Wu T T, et al. Fast surface reconstruction algorithm for 3D scattered point cloud model[J]. Journal of Computer-Aided Design & Computer Graphics, 2018, 30(2): 235-243.
[7]杨征宇, 夏庆观, 缪德建. 基于小波变换和NURBS的自由曲面重构的去噪处理[J]. 模具技术, 2009,(4): 5-9.
Yang Z Y, Xia Q G, Miao DJ. Denoising of free surface reconstruction based on wavelet transform and NURBS [J]. Mould Technology, 2009,(4): 5-9.
[8]张立峰, 周雷. 基于小波融合的电容层析成像图像重建[J]. 计量学报, 2019, 40(2): 285-288.
Zhang L F, Zhou L. Image Reconstruction of Capacitive Imaging Based on Wavelet Fusion[J]. Acta Metrologica Sinica, 2019, 40(2): 285-288.
[9]马金铭, 苗红霞, 苏新华, 等. 分数傅里叶变换理论及其应用研究进展[J]. 光电工程, 2018, 45(6): 5-28.
Ma J M, Miao H X, Su X H, et al. Progress in fractional Fourier transform theory and its application[J]. Opto-Electronic Engineering, 2018, 45(6): 5-28.
[10]陶然, 邓兵, 王越. 分数阶傅里叶变换及其应用[M]. 北京: 清华大学出版社, 2009.
[11]徐小军, 王友仁, 陈帅. 基于下采样分数阶小波变换的图像融合新方法[J]. 仪器仪表学报, 2014, 35(9): 2061-2069.
Xu X J, Wang Y R, Chen S. A new image fusion method based on down sampling fractional wavelet transform [J]. Chinese Journal of Scientific Instrument, 2014, 35(9): 2061-2069.
[12]郭学卫, 申永军, 杨绍普. 基于样本熵和分数阶傅里叶变换的滚动轴承故障特征提取[J]. 振动与冲击, 2017, (18): 65-69.
Guo X W, Shen Y J, Yang S P. Fault feature extraction of rolling bearing based on sample entropy and fractional Fourier transform[J]. Journal of Vibration and Shock, 2017, (18): 65-69.
[13]酒明远, 陈恩庆, 齐林, 等. 基于多核学习的多阶次分数阶傅里叶变换域人脸识别[J]. 光电工程, 2018, 45(6): 134-142.
JIU M Y, CHEN E Q, QI L, et al. Multi-order fractional Fourier transform domain face recognition based on multi-core learning[J]. Opto-Electronic Engineering, 2018, 45(6): 134-142.
[14]步衍瀚, 王平波. 基于分数阶傅里叶变换的滤波[J]. 舰船电子工程, 2016, 36(4): 38-40.
Bu Y H, WANG P B. Filtering based on fractional Fourier transform[J]. Ship Electronic Engineering, 2016, 36(4): 38-40.
[15]Piegl L A, Tiller W. The NURBS book [M]. Berlin, Germany: Springer, 1996: 236-247.
[16]施法中. 计算机辅助几何设计与非均匀有理B样条[M]. 北京: 高等教育出版社, 2001: 446-452.
[17]孔德明,黄紫双,杨丹. 二次曲面的NURBS最优化表示方法研究[J]. 计量学报, 2020, 41(8): 909-917.
Kong D M, Huang z S, Yang D. Research on NURBS Optimization Expression Method of Quadric Surfaces[J]. Acta Metrologica Sinica, 2020, 41(8): 909-917.
[18]王恒奎, 边耐欣, 王文, 等. 基于Trimmed NURBS曲面几何特征的数字化自适应采样[J]. 计量学报, 2002, 23(4): 271-275.
Wang H K, Bian N X, Wang W, et al. Digital Adaptive Sampling Based on Geometric Features of Trimmed NURBS Surface [J]. Acta Metrologica Sinica, 2002, 23(4): 271-275.
[19]田小强, 孔令富,孔德明, 等. 利用离散平稳小波变换改进NURBS二次曲面拟合方法[J]. 计量学报, 2020, 41(6): 662-668.
Tian X Q, Kong L F, Kong D M, et al. An Improved Method for NURBS Quadric Surface Based on Discrete Stationary Wavelet Transform[J]. Acta Metrologica Sinica, 2020, 41(6): 662-668. |
|
|
|