基于样条函数改进的傅里叶积分重建算法研究  

Research on Improved Fourier Integral Reconstruction Algorithm Based on Spline Function

作　　者：于雪 孙兴伟[1,2] 董祉序 刘寅 杨赫然 吴翔恂[3] YU Xue;SUN Xing-wei;DONG Zhi-xu;LIU Yin;YANG He-ran;WU Xiang-xun(School of Mechanical Engineering,Shenyang University of Technology,Shenyang 110870,China;Key Laboratory of Numerical Control Manufacturing Technology for Complex Surfaces of Liaoning Province,Shenyang 110870,China;School of Software,Shenyang University of Technology,Shenyang 110870,China)

机构地区：[1]沈阳工业大学机械工程学院,辽宁沈阳110870 [2]辽宁省复杂曲面数控制造技术重点实验室,辽宁沈阳110870 [3]沈阳工业大学软件学院,辽宁沈阳110870

出　　处：《机械工程与自动化》2022年第5期39-41,共3页Mechanical Engineering & Automation

基　　金：辽宁省“兴辽英才计划”项目(XLYC1905003)。

摘　　要：为提高曲面物体三维廓形的重建精度,提出了一种基于样条函数曲线拟合改进的傅里叶梯度积分算法。通过使用样条函数表示曲面梯度改进算法中的southwell模型来提高模型精度,改进后对曲面梯度计算的southwell模型进行反对称周期性扩展,对扩展后的southwell模型进行二维离散傅里叶变换,模型与频域中曲面展开系数形成傅里叶变换对,以此计算出频域中曲面展开系数;对频域中曲面展开系数进行傅里叶逆变换,进而得到曲面高度分布。通过与传统southwell模型的傅里叶积分重建及差分采样模型积分重建进行精度对比分析,结果表明,相较于使用southwell模型及差分采样模型等传统傅里叶梯度积分法,本文提出的基于样条函数改进的傅里叶积分重建算法可显著提高重建精度。In order to improve the reconstruction accuracy of the 3 D profile of curved objects, an improved Fourier gradient integration algorithm based on spline function curve fitting is proposed. Improve model accuracy by using splines to represent surface gradients in the southwell model in the improved algorithm. After the improvement, the antisymmetric periodic expansion of the southwell model for surface gradient calculation is performed, and the two-dimensional discrete Fourier transform is performed on the expanded southwell model. The model and the surface expansion coefficients in the frequency domain form a Fourier transform pair, so as to calculate the surface expansion coefficients in the frequency domain, perform inverse Fourier transform on the surface expansion coefficients in the frequency domain, and then obtain the surface height distribution. The accuracy is compared with the Fourier integral reconstruction of the traditional southwell model and the integral reconstruction of the differential sampling model. The results show that the algorithm proposed in this paper can significantly improve the reconstruction accuracy compared with the traditional Fourier gradient integration methods such as the southwell model and the differential sampling model.

关 键 词：傅里叶积分法 样条函数曲线拟合 southwell模型 

分 类 号：TB115[理学—数学] TP391.7[理学—应用数学]