为了解决非均匀有理B样条(NURBS)拟合二次曲面精度低、过程复杂的问题,提出了一种u、v参数化方向选择及求解出最优控制点个数选取范围的高效拟合二次曲面的方法。首先,根据二次曲面的形状特征确定u、v的参数化方向;然后,利用差值绝对值和均方根误差对不同控制点个数拟合出的各个重构曲面进行误差定量分析,根据定量分析的结果曲线求解拟合二次曲面的最优控制点个数的最小取值;最后,结合程序运行时间的关系曲线求解拟合二次曲面的最优控制点个数的最大取值。实例表明:较为常见的二次曲面的NURBS最优控制点个数的合理选取范围为201~541。该分析结果为NURBS标准分析表面的拟合过程中遇到的问题提供了理论支持和技术参考。
Abstract
In order to solve the problem of the low accuracy and complicated process of quadric surface fitting on non-uniform rational B-spline(NURBS), an efficient method is proposed to select the u, v parametric directions and calculate the selection range of optimal number of control points. Firstly, the u, v parametric directions are determined according to the shape characteristics of quadric surface. Then, the reconstructed surface fitted by different number of control points are quantitatively analyzed by using the absolute value of the differences and the RMSE. According to the quantitative analysis curves, the minimum value of the optimal number of control points of quadric surface is calculated. Finally, the maximum value of the optimal number of control points of quadric surface is calculated by the relationship between the program runtime and the number of control points. Examples showed that the reasonable selection range of NURBS optimal control points for common quadric surfaces is 201~541. The analysis result provides theoretical support and technical reference for the problems encountered in the NURBS fitting process for standard analytic surface.
关键词
计量学 /
NURBS曲面重构 /
二次曲面 /
u、v参数化方向选择 /
最优控制点个数
Key words
metrology /
NURBS surface reconstruction /
quadric surfaces;u, v parametric directions selection /
optimal number of control points
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参考文献
［1］Ravari A N, Taghirad H D. Reconstruction of B-spline curves and surfaces by adaptive group testing ［J］. [WTBX][STBX]Computer-Aided Design[STBZ][WTBZ], 2016, 74: 32-44.
［2］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］. [WTBX][STBX]Journal of Computer-Aided Design & Computer Graphics[STBZ][WTBZ], 2017, 29(8): 1497-1504.
［3］姚悦, 丁永红, 裴东兴, 等. 空气中爆炸冲击波曲线重建方法 ［J］. 计量学报, 2019, 40(4): 636-641.
Yao Y, Ding Y H, Pei D X, et al. Method for reconstructing explosion shock wave curve in air ［J］. [WTBX][STBX]Acta Metrologica Sinica[STBZ][WTBZ], 2019, 40(4): 636-641.
［4］Piegl L, Tiller W. The NURBS book［M］. New York: Springer, 1997, 236-247.
［5］潘俊超. 整椭圆的NURBS表示及其在曲面造型中的应用［D］. 芜湖:安徽师范大学, 2016.
［6］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.
［7］马力全, 蒋占四, 蒋玉龙,等. 二次NURBS曲线及曲面权重系数的研究 ［J］. 计算机应用研究, 2015, 32(4): 1253-1256.
Ma L Q, Jiang Z S, Jiang Y L et al. Study on the weight coefficients of quadratic NURBS curves and surfaces ［J］. [WTBX][STBX]Computer Application Research[STBZ][WTBZ], 2015, 32(4): 1253-1256.
［8］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］. [WTBX][STBX]Computer-Aided Design & Computer Graphic[STBZ][WTBZ], 2018, 30(9): 1692-1698.
［9］周煜, 王昊尘, 杜发荣. 航空发动机直纹叶片的线形特征点云构造算法 ［J］. 航空动力学报, 2014, 29(8): 1832-1837.
Zhou Y, Wang H Z, Du F R. An algorithm for constructing Linear feature point cloud of aeroengine straight Blade ［J］. [WTBX][STBX]Journal of Aerospace Power, [STBZ][WTBZ], 2014, 29(8): 1832-1837.
［10］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 surfaces ［J］. [WTBX][STBX]Acta Metrologica Sinica[STBZ][WTBZ], 2002, 23(4): 271-275.
［11］Dong H, Chen B, Chen Y, et al. An accurate NURBS curve interpolation algorithm with short spline interpolation capacity ［J］. [WTBX][STBX]International Journal of Advanced Manufacturing Technology[STBZ][WTBZ], 2012, 63(9-12): 1257-1270.
［12］Jalel S, Naouai M, Hamouda A, et al. NURBS parameterization: a new method of parameterization using the correlation relationship between nodes ［C］// Mexican Conference on Pattern Recognition, Springer Berlin Heidelberg, 2012: 216-225.
［13］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］. [WTBX][STBX]Journal of Huaqiao University (Nature Science)[STBZ][WTBZ], 2010, 31(4): 383-387.
［14］李新颖, 刘凯, 黄海燕. 多线函数法在曲线拟合中的应用研究 ［J］. 计量学报, 2018, 39(5): 716-719.
Li X Y, Liu K, Huang H Y. Application of multiline function method in curve fitting ［J］. [WTBX][STBX]Acta Metrologica Sinica[STBZ][WTBZ], 2018, 39 (5): 716-719.
基金
国家自然科学基金(61501394);河北省自然科学基金(F2016203155)
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