汽车后视镜的理论建模与应用技术研究
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摘要
汽车后视镜是汽车上一个非常重要的部件,如果后视镜有盲区和图像变形,势必给安全行车带来隐患。研究出一种大视野低失真的后视镜对减少交通事故带来的损失有重要意义,而且现在汽车越来越普及,后视镜市场也有巨大潜力,在这种情况下出现了许多新型后视镜的设计,最具代表性的是渐变曲率后视镜,但这些新型后视镜都缺乏数学模型支持和可靠的理论分析,缺乏能够量化的评估方法。本文将通过分析某新型后视镜的特点,提出一种数学建模方法,建立该新型后视镜的数学模型,并通过该模型对这类后视镜进行理论分析和数值仿真,从而对这类后视镜的性能进行量化评估。
本文主要由理论研究和应用仿真两部分组成。第一部分是理论研究:在最小二乘法基础上引入了一种改进的算法——移动最小二乘法,并介绍了反求工程的应用方法。将移动最小二乘法应用于汽车后视镜拟合问题中,并与传统的最小二乘法的结果进行对照,展示该方法的优越性。第二部分是应用仿真:利用移动最小二乘法建立的数学模型,设计了相应的仿真算法,直观展现后视镜的视野范围。本文的具体研究内容如下:
第一章介绍了研究背景,指出本文研究要解决的关键技术问题及研究内容。
第二章介绍曲面拟合的传统方法——最小二乘法的理论,在此基础上,采用了一种改进的曲面拟合方法——移动最小二乘法。并对移动最小二乘法的权函数的选取、A矩阵的可逆性、影响域半径的确定以及插值函数的性质等关键性问题都进行了详细的分析。
第三章介绍了反求工程的基本理论,研究了基于特征的反求工程,并指出了其优势。提出了把反求技术应用于求汽车后视镜参数问题的思想方法。
第四章是将数学建模和仿真技术应用于后视镜问题中。首先利用反求技术得到后视镜上大量点的坐标。然后分别利用最小二乘法和改进的算法——移动最小二乘法对汽车后视镜进行曲面拟合,建立后视镜的数学模型。进而将仿真技术应用于后视镜中,设计相应的仿真算法,对前面建立的数学模型进行数值仿真分析,仿真结果直观展现后视镜的视野范围,为下一步工作打下基础。
最后总揽全文,得出结论。
Rearview mirror is a quite important part of an automobile. If there are blind domains and distorted image on the rearview mirror of an automobile that may increase the probability of danger to driver. It is very significant to design a kind of rearview mirror with wide eyeshot and little distortion. Nowadays automobile is more and more popular, and the market of rearview mirror is quite large. So people have designed a lot of new rearview mirrors, of which the most typical type is gradual change curvature rearview mirror. However, these new types are short of the support of mathematical models and dependable theoretical analysis. In this paper we will present a new method and establish a mathematical model of new rearview mirror by analyzing its characteristic. Moreover, we will evaluate the quality of this rearview mirror by theoretical analysis and numerical simulation.The paper consists of two parts: in the first part we study the theory of rearviewmirror. On the basis of Least Squares, we present an improved algorithm ------Moving Least Squares. Moreover, we introduce the applied method of reverse engineer. We will apply Moving Least Squares to rearview mirror. Compared with the method of Least Squares, Moving Least Squares is more predominant. In the second part, we talk about the application of rearview mirror. And we establish the model of rearview mirror by Moving Least Squares and design corresponding algorithm. We apply simulation technique to mathematical model, which can display intuitionally field of vision of rearview mirror. The main research work is listed as follows:In the first chapter, we give research background. Then we point out the key problem and research content that may be solved in our research work.In the second chapter, we present the traditional way of surface fitting ------LeastSquares. We present a kind of amendatory algorithm------Moving Least Squaresbased on Least Squares. Moreover, we analyze explicitly selection of weighted function, reversibility of A matrix, confirm of radius of influencing domain and characteristic of interpolating function and so on.In the third chapter, we present the basis theory of reverse engineer and discuss
reverse engineering based on characteristic and point out its merit. Moreover, we present an ideology way that will apply reverse technology to seek the parameter of rearview mirror.In the fourth chapter, we apply mathematical model and simulation technique to rearview mirror. Firstly, we get a lot of coordinates of points of rearview mirror. Secondly, we apply surface fitting on rearview mirror by least squares and moving least squares and establish corresponding mathematical models. Finally, we apply simulation technique to rearview mirror and design corresponding simulation algorithm and make out numerical analysis to established mathematical model. The simulation result shows distinctly field of vision of rearview mirror.At last, the research work in the paper is summarized.
本文主要由理论研究和应用仿真两部分组成。第一部分是理论研究:在最小二乘法基础上引入了一种改进的算法——移动最小二乘法,并介绍了反求工程的应用方法。将移动最小二乘法应用于汽车后视镜拟合问题中,并与传统的最小二乘法的结果进行对照,展示该方法的优越性。第二部分是应用仿真:利用移动最小二乘法建立的数学模型,设计了相应的仿真算法,直观展现后视镜的视野范围。本文的具体研究内容如下:
第一章介绍了研究背景,指出本文研究要解决的关键技术问题及研究内容。
第二章介绍曲面拟合的传统方法——最小二乘法的理论,在此基础上,采用了一种改进的曲面拟合方法——移动最小二乘法。并对移动最小二乘法的权函数的选取、A矩阵的可逆性、影响域半径的确定以及插值函数的性质等关键性问题都进行了详细的分析。
第三章介绍了反求工程的基本理论,研究了基于特征的反求工程,并指出了其优势。提出了把反求技术应用于求汽车后视镜参数问题的思想方法。
第四章是将数学建模和仿真技术应用于后视镜问题中。首先利用反求技术得到后视镜上大量点的坐标。然后分别利用最小二乘法和改进的算法——移动最小二乘法对汽车后视镜进行曲面拟合,建立后视镜的数学模型。进而将仿真技术应用于后视镜中,设计相应的仿真算法,对前面建立的数学模型进行数值仿真分析,仿真结果直观展现后视镜的视野范围,为下一步工作打下基础。
最后总揽全文,得出结论。
Rearview mirror is a quite important part of an automobile. If there are blind domains and distorted image on the rearview mirror of an automobile that may increase the probability of danger to driver. It is very significant to design a kind of rearview mirror with wide eyeshot and little distortion. Nowadays automobile is more and more popular, and the market of rearview mirror is quite large. So people have designed a lot of new rearview mirrors, of which the most typical type is gradual change curvature rearview mirror. However, these new types are short of the support of mathematical models and dependable theoretical analysis. In this paper we will present a new method and establish a mathematical model of new rearview mirror by analyzing its characteristic. Moreover, we will evaluate the quality of this rearview mirror by theoretical analysis and numerical simulation.The paper consists of two parts: in the first part we study the theory of rearviewmirror. On the basis of Least Squares, we present an improved algorithm ------Moving Least Squares. Moreover, we introduce the applied method of reverse engineer. We will apply Moving Least Squares to rearview mirror. Compared with the method of Least Squares, Moving Least Squares is more predominant. In the second part, we talk about the application of rearview mirror. And we establish the model of rearview mirror by Moving Least Squares and design corresponding algorithm. We apply simulation technique to mathematical model, which can display intuitionally field of vision of rearview mirror. The main research work is listed as follows:In the first chapter, we give research background. Then we point out the key problem and research content that may be solved in our research work.In the second chapter, we present the traditional way of surface fitting ------LeastSquares. We present a kind of amendatory algorithm------Moving Least Squaresbased on Least Squares. Moreover, we analyze explicitly selection of weighted function, reversibility of A matrix, confirm of radius of influencing domain and characteristic of interpolating function and so on.In the third chapter, we present the basis theory of reverse engineer and discuss
reverse engineering based on characteristic and point out its merit. Moreover, we present an ideology way that will apply reverse technology to seek the parameter of rearview mirror.In the fourth chapter, we apply mathematical model and simulation technique to rearview mirror. Firstly, we get a lot of coordinates of points of rearview mirror. Secondly, we apply surface fitting on rearview mirror by least squares and moving least squares and establish corresponding mathematical models. Finally, we apply simulation technique to rearview mirror and design corresponding simulation algorithm and make out numerical analysis to established mathematical model. The simulation result shows distinctly field of vision of rearview mirror.At last, the research work in the paper is summarized.
引文
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[3] 寿纪麟.数学建模——方法与范例[M].西安:西安交通大学出版社,1996
[4] 庞作会,葛修润,郑宏等.一种新的数值方法——无网格伽辽金法(EFGM)[J].计算力学学报,1999,16(3):320～329
[5] 王建雄,沈忙作.散乱有限元镜面数据曲面拟合法[J].数值计算与计算机应用,1996,9(3):170～173
[6] P.M.普伦特著.柴家振,江伯南译.样条函数与变分方法[M].上海:上海科学技术出版社,1972.
[7] Farim G. Triangular Bernstein-Bezier Patches [J]. CAGD, 1986, 3: 83～127
[8] 庞作会,葛修润,王水林等.对无网格伽辽金法(EFGM)的两点补充[J].岩石力学与工程学报,1999,18(5):581～584
[9] 兰凤崇,陈吉清,郑世红.散乱数据的曲面拟合及其在汽车车身外表面造型设计中的应用[J].吉林工业大学学报,1996,(3):6～10
[10] 周晚林,吴亚新,施慰连.Bezier曲面拟合方法在影像云纹测量三维物体形状中的应用[J].实验力学,1997,12(2):323～328
[11] 谭莹,漆兰芬.一种曲面拟合方法在电磁散射计算中的应用[J].华中理工大学学报,2000,28(12):16～17
[12] Aoyama. Animation and Control of Non rigid Structures [J]. Computer Graphics, 1998, 24(4): 243～252
[13] 丛伟,刘丰,李仁杰.拟合任意空间曲面的B3样条方法及其实现[J].沈阳航空工业学院学报,1999,16(1):22～28
[14] 丛伟,程云阶.B3样条曲线曲面拟合法及其在拱坝形体设计中的应用[J].小型微型计算机系统,1999,20(7):543～545
[15] 朱仁芝,程谟嵩.拟合任意空问曲面的三角函数方法[J].计算机辅助设计与图形学学报,1996,8(2):108～114
[16] 刘素贞,杨庆新,陈海燕.无单元法和有限元法的比较研究[J].河北工业大学学报,2000,29(5):66～68
[17] Lee S, Walberg G, Shin S Y. Scattered data interpolation with multilevel B-splines [J]. IEEE Trans on Visualization and Computer Graphics, 1997, 3(3): 228～244
[18] 刘安伟,肖永明,刘慎权.NURBS曲面生成及拼接[J].计算机工程,1992,8(2):29～33
[19] 刘鼎元,胡康生.Bezier曲面拟合[J].应用数学学报,1984,7(2):250～256
[20] Forsey D R, Bartels R H. Hierarchical B-spline refinement [J]. Computer Graphics, 1988, 22(4): 205～212
[21] H Hoppe, T DeRose, T Duchamp, etal. Surface reconstruction from unorganized points[J]. Computer Graphics, 1992, 26(20: 71～78
[22] Hu P, Yan X. Neural network approach to the reconstruction of freeform surfaces for reverse engineering [J]. Computer-Aided Design, 1995, 27(1): 59～64
[23] 刘志明.基于曲面重构技术的塑料异型材挤出模具制造技术研究:[硕士学位论文].大连:大连理工大学,2005
[24] 刘云峰.基于截面特征的反求工程CAD建模关键技术研究:[博士学位论文].杭州:浙江大学机械与能源工程学院,2004
[25] Na W, Kruth J P. Parameterization of randomly measured points for least squares fitting of B-spline curves and surfaces[J]. Computer-Aided Design, 1995, 27(9): 663～675
[26] Au C K, Yuen M M F. Feature-based reverse engineering of mannequin for garment design [J]. Computer-Aided Design, 1999, 31(12): 751～759
[27] Varady T, Martin R R, Cox J. Special Issue: Reverse engineering of geometric models[J]. Computer-Aided Design, 1997, 29(4): 253～254
[28] Gregory T D, Warren N W J, Henry J L. Feature based models for anatomical data fitting [J]. Computer-Aided Design, 1995, 27(12): 139～146
[29] 曹新明.反求工程中散乱数据拓扑和三角曲面重建关键技术研究:[硕士学位论文].长沙:湖南大学机械与汽车工程学院,2004
[30] 俞庆.工业缝纫机圆柱凸轮的反求制造:[硕士学位论文].西安:西安理工大学,2004
[31] H su W M, Hughes J F, Kaufman H. Direct manipulation of free-form deformations[J]. Computer Graphics, 1992, 26(2): 177～184
[32] Floater M S. Parameterization and smooth approximation of surface triangulations [J]. Computer-Aided Geometric Design, 1997, 14(3): 231～250
[33] Mayer, Ralph Martin, Jordan Cox. Reverse Engineering of Geometric models-an introduction [J]. Computer Aided Design, 1997, 29(4): 253～268
[34] Shuh-Renx Liang, Allan C. lin. Probe-radius compensation for 3D data points in reverse engineering [J]. Computer in Industry, 2002(48): 241～251
[35] John H.mathews,Kurtis D.Fink.数值方法[M].北京:电子工业出版社,2002
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