二次曲面的NURBS最优化表示方法研究

doi:10.3969/j.issn.1000-1158.2020.08.03

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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。

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	孔德明
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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

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.

Key words： metrology NURBS surface reconstruction quadric surfaces;u, v parametric directions selection optimal number of control points

收稿日期: 2018-12-26 发布日期: 2020-08-13

PACS:

TB92

基金资助:国家自然科学基金(61501394);河北省自然科学基金(F2016203155)

作者简介: 孔德明(1983-),男,吉林公主岭人,燕山大学副教授,博士,主要从事高精度三维形状检测技术方面的研究。 Email: demingkong@ysu.edu.cn

引用本文:

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 De-ming,HUANG Zi-shuang,YANG Dan. Research on NURBS Optimization Expression Method of Quadric Surfaces. Acta Metrologica Sinica, 2020, 41(8): 909-917.

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