为了提高二次曲面的拟合精度,提出了一种基于离散平稳小波变换的NURBS二次曲面的拟合方法。 首先利用格网化方法得到二次曲面模型点云数据的高程图像及其高程序列,其次对此高程序列进行离散平稳小波变换提取出二次曲面模型表面的特征点,最后利用提取的特征点实现高精度NURBS二次曲面拟合。实验结果表明,该方法与NURBS拟合方法相比,球面和圆锥面拟合结果的均方根误差分别降低了55.79%和50.47%,具有较高的拟合精度。
Abstract
In order to improve fitting accuracy of quadric surface,an improved method for the currently recognized NURBS quadric surface method based on discrete stationary wavelet transform was proposed. At first, elevation image of the quadric surface point cloud and elevation sequence were obtained by using the grid method. Then feature points of the quadric surface were extracted from the discrete stationary wavelet transform results of the elevation sequence of the elevation image. Finally, high accuracy NURBS quadric surface was realized by using the extracted feature points. The experimental results showed that compared with NURBS method, the root mean squared errors of fitting results of sphere and cone surface were reduced 55.79% and 50.47% respectively, and it had satisfactory fitting precision.
关键词
计量学 /
曲面拟合 /
离散平稳小波变换 /
NURBS二次曲面 /
逆向工程
Key words
metrology /
surface fitting /
discrete stationary wavelet transform /
NURBS quadric surface /
reverse engineering
{{custom_sec.title}}
{{custom_sec.title}}
{{custom_sec.content}}
参考文献
［1］王慧, 朱春钢, 李彩云. 插值有理Bézier渐近四边形的有理Bézier曲面 ［J］. 计算机辅助设计与图形学学报, 2017, 29(8): 1497-1504.
Wang H, Zhu C G, Li C Y. Rational Bézier surfaces with interpolation rational Bézier asymptotic quadrilateral ［J］. Journal of Computer-Aided Design & Computer Graphics, 2017, 29(8): 1497-1504.
［2］史建华, 刘盼. 大尺寸航空发动机叶片的高效型面检测方法 ［J］. 计量学报, 2018, 39(5): 605-608.
Shi J H, Liu P. High Efficiency Measurement Method for Large-size Aeroengine Blade Profile ［J］. Acta Metrologica Sinica, 2018, 39(5): 605-608.
［3］皮格,特莱尔. 非均匀有理B样条［M］. 2版.赵罡,等译.北京:清华大学出版社, 2010.
［4］Piegl L, Tiller W. The NURBS book［M］. 2nd ed. New York: Springer 1997: 236-247.
［5］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.
［6］徐平, 薛凌云, 常英杰. 汽车发动机进气歧管高精度亚像素边缘检测 ［J］. 计量学报, 2018, 39(3): 35-39.
Xu P, Xue L Y, Chang J J. Subpixel Edge Detection with High Precision for Vehicle Engine Intake Manifolds ［J］. Acta Metrologica Sinica, 2018, 39(3): 35-39.
［7］郑旭. 基于离散小波变换的特征提取和故障分类方法研究［D］. 北京: 北京化工大学, 2017.
［8］马平, 司志宁. 基于小波变换的CT/ECT图像融合方法 ［J］. 计量学报, 2018, 39 (4): 90-94.
Ma P, Si Z N. A Method of CT/ECT Image Fusion Based on Wavelet Transform ［J］. Acta Metrologica Sinica, 2018, 39(4): 90-94.
［9］Xu L J, Kong D M, Li X L. On-the-fly extraction of polyhedral buildings from airborne LiDAR data ［J］. IEEE Geoscience and Remote Sensing Letters, 2014, 11(11): 1946-1950.
［10］张玉燕, 渠文涵, 郭全丽, 等. 基于3D点云平均曲率估算的损伤参数计算 ［J］. 计量学报, 2018, 39(5): 609-614.
Zhang Y Y, Qu W H, Guo Q L, et al. Damage Parameter Calculation Based on 3D Point Cloud Mean Curvature Estimation ［J］. Acta Metrologica Sinica, 2018, 39(5): 609-614.
［11］Kong D M, Xu L J, Li X L, et al. K-plane-based classification of airborne LiDAR data for accurate building roof measurement ［J］. IEEE Trans Instrument Meas, 2014, 63(5): 1200-1214.
［12］徐阳, 刘强. 考虑流线场约束的NURBS曲线拟合方法 ［J］. 计算机辅助设计与图形学学报, 2017, 29(1): 137-144.
Xu Y, Liu Q. NURBS Curve Fitting Method Considering Constraint of Streamline Field ［J］. Journal of Computer-Aided Design & Computer Graphics, 2017, 29(1): 137-144.
［13］Dong H, Chen B, Chen Y, et al. An accurate NURBS curve interpolation algorithm with short spline interpolation capacity ［J］. International Journal of Advanced Manufacturing Technology, 2012, 63(9-12): 1257-1270.
［14］Jalel S, Naouai M, Hamouda A, et al. NURBS parameterization: A new method of parameterization using the correlation relationship between nodes［M］. Springer, 2012: 216－225.
［15］叶丽, 谢明红. 采用积累弦长法拟合3次NURBS曲线 ［J］. 华侨大学学报(自然版), 2010, 31(4): 383－387.
Ye L, Xie M H. The accumulated chord length method was used to fit the Nurbs curve of order 3 ［J］. Journal of overseas Chinese University (Nature Edition), 2010, 31(4): 383－387.
［16］Tao S. Reverse calculating the control points of cubic B-spline curves ［J］. Bulletin of Science & Technology, 2014, (3): 23－25.
基金
国家自然科学基金(61501394);国家科技重大专项(2017ZX05019001-011);河北省自然科学基金(F2016203155)
PDF(2377 KB)
