二次曲面的NURBS最优化表示方法研究  

Research on NURBS Optimization Expression Method of Quadric Surfaces

作　　者：孔德明[1,2] 黄紫双 杨丹 KONG De-ming;HUANG Zi-shuang;YANG Dan(School of Electrical Engineering,Yanshan University,Qinhuangdao,Hebei 066004,China;Department of Telecommunications and Information Processing,Ghent University,Ghent B-9000,Belgium)

机构地区：[1]燕山大学电气工程学院,河北秦皇岛066004 [2]根特大学通信与信息处理系,比利时根特B-9000

出　　处：《计量学报》2020年第8期909-917,共9页Acta Metrologica Sinica

基　　金：国家自然科学基金(61501394);河北省自然科学基金(F2016203155)。

摘　　要：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。In order to solve the problem of the low accuracy and complicated process of quadric surface fitting on nonuniform 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 

分 类 号：TB92[一般工业技术—计量学]