基于特征与约束识别的点云曲线参数化建模研究
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摘要
作为先进制造技术的一个重要组成部分,反求工程已从最初的原型复制技术逐步发展成为支持产品创新设计和新产品开发的重要技术手段。与这一趋势相对应,反求工程重建的CAD模型已不再是传统的实体模型,而是更具创新设计能力、支持产品全生命周期的特征模型。在面向特征造型的反求工程技术背景下,本文以产品设计意图与测量意图理解为着眼点,以重建支持产品创新的参数化特征模型为目标,围绕反求工程CAD建模中的特征识别、约束识别、全局优化及参数化等关键技术展开研究。
点云截面曲线的成功参数化建模对于提高反求工程模型重建的精度和效率,实现逆向创新设计都有很好的应用价值；同时,对于丰富计算机图形学研究具有理论价值。本文所做的工作主要有以下几个方面：
(1)系统研究了常见曲线特征的数学表达和性质以及曲线特征在几何约束条件下的拟合技术。给出了截面点云特征识别的基本含义,并且提出了一种新的特征识别准则,能够实现一段点云数据的基本特征的识别。
(2)本文给出了常见曲线之间各种约束的表达形式,并在此基础之上建立了一种约束识别准则,可以实现各平面几何特征之间的约束识别。
(3)在进行截面形状特征约束重构时,可以将由点云数据拟合得到的各段曲线,在满足各段之间的约束条件下进行整体约束逼近,从而构造整个截面形状特征。本文通过建立一通用的全局优化模型,来解决满足各段之间的约束下进行整体约束逼近的问题。并且尝试了利用MATLAB提供的最优化计算工具箱中的fmincon函数进行最优化计算,可以得到较理想的结果。并且从逼近误差和约束误差分析了全局优化的结果。
(4)本文研究了基于曲线的参数化设计方法,给出了Bezier曲线的参数化表达形式,并对自由曲线的等距偏移进行了一定的研究。
(5)最后在总结全文工作的基础上,指出了有待进一步研究的内容和方向。
As an important component of advanced manufacturing technology, reverse engineering gradually developed into an important technical means of product innov-ation and new product development from the initial prototype support replication technology. Corresponding to this trend, Reverse Engineering CAD model recon-struction of the entity is no longer a traditional model, but more innovative design capabilities, supporting for product lifecycle feature model. In the context of reverse engineering technology for feature modeling, this paper start the study to focus the understanding of the product design intent and the measurement intent, to rebuild the parametric feature model supporting for product innovation, to focus the key technologies in reverse engineering CAD modeling, such as feature recognition, constraint recognition, global optimization, parametric modeling and so on.
Unorganized point cloud curve parametric modeling is very valuable both for improving the accuracy and efficiency of reconstruction and innovative design and for enriching computer graphics research. This major work done mainly in the following areas.
Firstly, both the nature and the mathematical expression of the common curve characteristics and the fitting techniques of Curves by the numbers was researched. The basic meaning of point cloud feature recognition and a new feature recognition criteria was introduced. Basic characteristics of point cloud data can be identified successfully by this method. Rebulided parameters was keeped consistent with the original design parameters as much as possible.
Secondly, in this paper, the expression of various constraints between common curveis was introduced. On this basis, a constraint recognition criteria was established in this paper, which can identify the constraints between the various geometry characteristics.
Thirdly, rebuilding constraints of the cross section, each curve which point cloud data can be fitted to can have an overall constraint approximation to construct the shape of cross section in the conditions of meeting the constraint between paragraphs. A general the global optimization model was given to solve the problems of an overall constraint approximation in this article. The fmincon function of MATLAB Optimization Toolbox was used of solving optimization calculation. That can get effective results. The results of global optimization from approximation error and constraint error was analysed.
Fourthly, in this paper, parameter design method based on the curve was researched. The parameters expression of Bezier curves and the approach to satisfy the constraint relations were given. Equidistant offset of the free curve has been researched in this paper.
Finally, on the basis of summarizing the work, the content and direction of the further research were given.
点云截面曲线的成功参数化建模对于提高反求工程模型重建的精度和效率,实现逆向创新设计都有很好的应用价值；同时,对于丰富计算机图形学研究具有理论价值。本文所做的工作主要有以下几个方面：
(1)系统研究了常见曲线特征的数学表达和性质以及曲线特征在几何约束条件下的拟合技术。给出了截面点云特征识别的基本含义,并且提出了一种新的特征识别准则,能够实现一段点云数据的基本特征的识别。
(2)本文给出了常见曲线之间各种约束的表达形式,并在此基础之上建立了一种约束识别准则,可以实现各平面几何特征之间的约束识别。
(3)在进行截面形状特征约束重构时,可以将由点云数据拟合得到的各段曲线,在满足各段之间的约束条件下进行整体约束逼近,从而构造整个截面形状特征。本文通过建立一通用的全局优化模型,来解决满足各段之间的约束下进行整体约束逼近的问题。并且尝试了利用MATLAB提供的最优化计算工具箱中的fmincon函数进行最优化计算,可以得到较理想的结果。并且从逼近误差和约束误差分析了全局优化的结果。
(4)本文研究了基于曲线的参数化设计方法,给出了Bezier曲线的参数化表达形式,并对自由曲线的等距偏移进行了一定的研究。
(5)最后在总结全文工作的基础上,指出了有待进一步研究的内容和方向。
As an important component of advanced manufacturing technology, reverse engineering gradually developed into an important technical means of product innov-ation and new product development from the initial prototype support replication technology. Corresponding to this trend, Reverse Engineering CAD model recon-struction of the entity is no longer a traditional model, but more innovative design capabilities, supporting for product lifecycle feature model. In the context of reverse engineering technology for feature modeling, this paper start the study to focus the understanding of the product design intent and the measurement intent, to rebuild the parametric feature model supporting for product innovation, to focus the key technologies in reverse engineering CAD modeling, such as feature recognition, constraint recognition, global optimization, parametric modeling and so on.
Unorganized point cloud curve parametric modeling is very valuable both for improving the accuracy and efficiency of reconstruction and innovative design and for enriching computer graphics research. This major work done mainly in the following areas.
Firstly, both the nature and the mathematical expression of the common curve characteristics and the fitting techniques of Curves by the numbers was researched. The basic meaning of point cloud feature recognition and a new feature recognition criteria was introduced. Basic characteristics of point cloud data can be identified successfully by this method. Rebulided parameters was keeped consistent with the original design parameters as much as possible.
Secondly, in this paper, the expression of various constraints between common curveis was introduced. On this basis, a constraint recognition criteria was established in this paper, which can identify the constraints between the various geometry characteristics.
Thirdly, rebuilding constraints of the cross section, each curve which point cloud data can be fitted to can have an overall constraint approximation to construct the shape of cross section in the conditions of meeting the constraint between paragraphs. A general the global optimization model was given to solve the problems of an overall constraint approximation in this article. The fmincon function of MATLAB Optimization Toolbox was used of solving optimization calculation. That can get effective results. The results of global optimization from approximation error and constraint error was analysed.
Fourthly, in this paper, parameter design method based on the curve was researched. The parameters expression of Bezier curves and the approach to satisfy the constraint relations were given. Equidistant offset of the free curve has been researched in this paper.
Finally, on the basis of summarizing the work, the content and direction of the further research were given.
引文
1.柯映林.反求工程CAD建模理论、方法和系统[M],北京：机械工业出版社,2005,30-50.
2.陈曦.反求工程中基于点云的特征挖掘技术研究[D],杭州：浙江大学,2005.
3.单东日.反求工程CAD建模中特征与约束技术研究[D],杭州：浙江大学,2003.
4.余览梅.多项式约束优化问题的一种新方法[J],温州大学学报,2009,30(3),1-5.
5.栾世超.求解线性约束优化问题的一种全局优化算法[J],山东农业大学学报,2009,40(2),277-279.
6.殷明.Bezier曲线的矩阵形式及其应用[J],工科数学,1994,10(2),1-5.
7.王家纯. Bezier曲线反求参数算法的研究[J],控制工程,2007,14(10),76-79.
8.郑厚生.关于Bezier曲线性质及曲线拟合问题[J],华侨大学学报自然科学版,1994,13(4),1-7.
9.沈海鸥,陈淑珍,孙晓安.曲线的二次有理Bezier曲线拟合[J],武汉大学学报,1997,43(1),391-400.
10.王新和,程世洲.曲线拟合的最小二乘法[J],新疆职业大学学报,2004,12(2),84-87.
11.施法中.权因子、参数变换与有理二次Bezier曲线参数化[J],航空学报,1994,15(9),29-33.
12.李安平,井爱雯.有理Bezier曲线的光顺拟合法[J],陕西师范大学学报,1999,27(10),96-98.
13.陈光,任志良,孙海柱.最小二乘曲线拟合及Matlab实现[J],软件技术,2005,24(3),107-109.
14.郭凤华,杨兴强.Bezier曲线最优参数化研究[J],计算机科学,2005,23(5),61-64.
15.吕震.反求工程CAD建模中的特征技术研究[D],杭州：浙江大学,2002.
16.刘云峰.基于截面特征的反求工程CAD建模关键技术研究[D],杭州：浙江大学,2004.
17.朱伟东.反求工程中基于几何约束的模型重建理论及应用研究[D],杭州：浙江大学,2007.
18.梁锡坤.B样条类曲线及其在曲线参数化中的应用[J],计算机应用与软件,2009,26(4),18-24.
19.郭凤华.参数曲线的最优参数化[J],计算机辅助设计与图形学学 报,2007,19(4),61-65.
20.施法中.反求标准型有理二次Bezier曲线的参数与内权因子[J],计算机辅助设计与图形学学报,1995,7(2),83-88.
21.赵恒,张永华,金建国.基于Bezier曲线的参数化设计方法[J],科技通报,2000,16(6),455-512.
22.张旭,曹健,刘玉树.基于二维非参数化判别分析的人脸识别[J],北京理工大学学报,2009,29(9),753-756.
23.董明晓,郑康平,姚斌.曲面重构中点云数据的区域分割研究[J],中国图象图形学报,2005,10(5),575-579.
24.金建国,包晔,缪永伟.曲线参数化技术研究与分析[J],浙江工业大学学报,2003,31(5),580-586.
25.殷国富,陈永华.计算机辅助设计技术与应用[M],北京：北京科学出版社,2000,20-40.
26.李际军.反求工程CAD建模关键技术研究[D],杭州：浙江大学,1999.
27.王正林,何倩.精通MATLAB科学计算[M],北京：电子工业出版社,2007,60-90.
28.栗塔山.最优化计算原理与算法程序设计[M],北京：国防科技大学出版社,2001,30-100.
29.谭浩强.C程序设计[M],北京：清华大学出版社,1999,20-80.
30.徐士良.数值方法(C++描述)[M],北京：清华大学出版社,2008,10-90.
31.徐士良.C常用算法程序集[M],北京：清华大学出版社,1996,10-60.
32.金涛,童水光.逆向工程技术[M],北京：机械工业出版社,2003,40-60.
33.单岩,谢斌飞.Image ware逆向造型技术基础[M],北京：清华大学出版社2006,1-40.
34.I. Choi and K. Lee. Efficient generation of reflection lines to evaluate car body surfaces [J], Mathematical Engineering in Industry,1998,7(2),233-250.
35.Lennings A F, Peters J G, Vergeest J S M. An efficient integration of algorithms to evaluate the quality of free-form surfaces [J], Computer & Graphics,1995,19 (6), 861-872..
36.朱心雄.自由曲线曲面造型技术[M],北京：科学技术出版社,2000,348-375.
37. Au Ck, Yuen MMF. Unified approach to NURBS curve shape modification [J], Computer-Aided Design,1995,27(20),85-93.
38.施法中.计算机辅助几何设计及NURBS[M],北京：北京航空航天大学出版社,1994,96-105.
39.I. D. Faux and M. J. Pratt. Computational Geometry for Design and Manufacture[J], Ellis Horwood, Chichester, England,1981.
40.高复先.科学计算[M],大连：大连海运学院出版社,1987,41-68.
41.丁晓庆.工科数学分析.上册[M],北京：科学出版社,2002,120-200.
42.丁晓庆.工科数学分析.下册[M],北京：科学出版社,2002,47-82.
43.张铁,阎家斌.数值分析[M],北京：冶金工业出版社,2007,30-70.
44.钱汉臣.计算机实用图形学与CAD技术[M],重庆：西南师范大学出版社,1995,28-30.
45.谭浩强.C程序设计(第二版)[M],北京：清华大学出版社,2002,10-80.
46.席庆,张春林. Visual C++6.0实用编程技术[M],北京：中国水利水电出版社,1999,10-30.
2.陈曦.反求工程中基于点云的特征挖掘技术研究[D],杭州：浙江大学,2005.
3.单东日.反求工程CAD建模中特征与约束技术研究[D],杭州：浙江大学,2003.
4.余览梅.多项式约束优化问题的一种新方法[J],温州大学学报,2009,30(3),1-5.
5.栾世超.求解线性约束优化问题的一种全局优化算法[J],山东农业大学学报,2009,40(2),277-279.
6.殷明.Bezier曲线的矩阵形式及其应用[J],工科数学,1994,10(2),1-5.
7.王家纯. Bezier曲线反求参数算法的研究[J],控制工程,2007,14(10),76-79.
8.郑厚生.关于Bezier曲线性质及曲线拟合问题[J],华侨大学学报自然科学版,1994,13(4),1-7.
9.沈海鸥,陈淑珍,孙晓安.曲线的二次有理Bezier曲线拟合[J],武汉大学学报,1997,43(1),391-400.
10.王新和,程世洲.曲线拟合的最小二乘法[J],新疆职业大学学报,2004,12(2),84-87.
11.施法中.权因子、参数变换与有理二次Bezier曲线参数化[J],航空学报,1994,15(9),29-33.
12.李安平,井爱雯.有理Bezier曲线的光顺拟合法[J],陕西师范大学学报,1999,27(10),96-98.
13.陈光,任志良,孙海柱.最小二乘曲线拟合及Matlab实现[J],软件技术,2005,24(3),107-109.
14.郭凤华,杨兴强.Bezier曲线最优参数化研究[J],计算机科学,2005,23(5),61-64.
15.吕震.反求工程CAD建模中的特征技术研究[D],杭州：浙江大学,2002.
16.刘云峰.基于截面特征的反求工程CAD建模关键技术研究[D],杭州：浙江大学,2004.
17.朱伟东.反求工程中基于几何约束的模型重建理论及应用研究[D],杭州：浙江大学,2007.
18.梁锡坤.B样条类曲线及其在曲线参数化中的应用[J],计算机应用与软件,2009,26(4),18-24.
19.郭凤华.参数曲线的最优参数化[J],计算机辅助设计与图形学学 报,2007,19(4),61-65.
20.施法中.反求标准型有理二次Bezier曲线的参数与内权因子[J],计算机辅助设计与图形学学报,1995,7(2),83-88.
21.赵恒,张永华,金建国.基于Bezier曲线的参数化设计方法[J],科技通报,2000,16(6),455-512.
22.张旭,曹健,刘玉树.基于二维非参数化判别分析的人脸识别[J],北京理工大学学报,2009,29(9),753-756.
23.董明晓,郑康平,姚斌.曲面重构中点云数据的区域分割研究[J],中国图象图形学报,2005,10(5),575-579.
24.金建国,包晔,缪永伟.曲线参数化技术研究与分析[J],浙江工业大学学报,2003,31(5),580-586.
25.殷国富,陈永华.计算机辅助设计技术与应用[M],北京：北京科学出版社,2000,20-40.
26.李际军.反求工程CAD建模关键技术研究[D],杭州：浙江大学,1999.
27.王正林,何倩.精通MATLAB科学计算[M],北京：电子工业出版社,2007,60-90.
28.栗塔山.最优化计算原理与算法程序设计[M],北京：国防科技大学出版社,2001,30-100.
29.谭浩强.C程序设计[M],北京：清华大学出版社,1999,20-80.
30.徐士良.数值方法(C++描述)[M],北京：清华大学出版社,2008,10-90.
31.徐士良.C常用算法程序集[M],北京：清华大学出版社,1996,10-60.
32.金涛,童水光.逆向工程技术[M],北京：机械工业出版社,2003,40-60.
33.单岩,谢斌飞.Image ware逆向造型技术基础[M],北京：清华大学出版社2006,1-40.
34.I. Choi and K. Lee. Efficient generation of reflection lines to evaluate car body surfaces [J], Mathematical Engineering in Industry,1998,7(2),233-250.
35.Lennings A F, Peters J G, Vergeest J S M. An efficient integration of algorithms to evaluate the quality of free-form surfaces [J], Computer & Graphics,1995,19 (6), 861-872..
36.朱心雄.自由曲线曲面造型技术[M],北京：科学技术出版社,2000,348-375.
37. Au Ck, Yuen MMF. Unified approach to NURBS curve shape modification [J], Computer-Aided Design,1995,27(20),85-93.
38.施法中.计算机辅助几何设计及NURBS[M],北京：北京航空航天大学出版社,1994,96-105.
39.I. D. Faux and M. J. Pratt. Computational Geometry for Design and Manufacture[J], Ellis Horwood, Chichester, England,1981.
40.高复先.科学计算[M],大连：大连海运学院出版社,1987,41-68.
41.丁晓庆.工科数学分析.上册[M],北京：科学出版社,2002,120-200.
42.丁晓庆.工科数学分析.下册[M],北京：科学出版社,2002,47-82.
43.张铁,阎家斌.数值分析[M],北京：冶金工业出版社,2007,30-70.
44.钱汉臣.计算机实用图形学与CAD技术[M],重庆：西南师范大学出版社,1995,28-30.
45.谭浩强.C程序设计(第二版)[M],北京：清华大学出版社,2002,10-80.
46.席庆,张春林. Visual C++6.0实用编程技术[M],北京：中国水利水电出版社,1999,10-30.