面向快速原型制造的反求工程关键技术研究
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摘要
快速原型制造（RP＆M）是当代制造业的新兴技术，属前沿课题。反求
工程与快速原型制造结合，将从根本上改变传统的产品设计、制造模式。
但是，当前的反求技术还无法达到与快速制造技术的匹配。本文在探讨了
面向RP＆M的反求工程的科学体系与框架的基础上，从数据预处理、网格
划分、光滑曲面构造、STL文件信息处理等方面进行了系统、深入地研究，
以期实现RE/RP＆M的有机集成，从而提高快速产品开发的能力。
首先，根据RP技术中STL文件的特点，有针对性地提出了离散数据的
预处理和网格划分的具体方法。基于神经网络的数据修补，自动数据分块、
以及自适应卡尔曼滤波等多种技术手段的使用，解决了当前在数据预处理
方面存在的难点问题。云状数据的基于物理的网格划分和选点三角剖分等
方法的提出，进一步丰富和发展了网格划分的内容，显著地提高了网格的
生成质量。
其次，以现代微分几何学为工具，系统研究了光滑曲面的C~1和G~1构造
方法：指出了初始网格的细分标准，并就此给出了均匀细分和选择性细分
两种方式；指明了细分中细分数与反求容差的量化关系，提高了细分的科
学性和合理性；运用优化理论，提出了曲面质量迭代提高以达到准C~2连续
曲面的方法，极大地改善了曲面的光顺效果。
此外，通过对现有的多分辨率造型方法的分析，首次在反求工程中引
入同心超面、星形邻域等概念，并提出了一种基于局部拓扑结构识别的网
格简化新算法。这不仅有效地消除了网格模型中存在大量的冗余网格，减
少了STL文件的长度，也使RP＆M中的造型显示、支撑添加、切片等后续
处理更为方便、快捷。
最后，对反求技术和快速原型技术的集成问题进行了深入研究；指出
了表面模型用于RP＆M中存在的问题；给出了STL文件拓扑重建的方法和
数据结构；讨论了STL文件的错误校验和修复技术；在此基础上，进行了
快速成型机的接口文件生成和实体成型加工实验，验证了本文所提技术路
线的正确性和科学性，为实现RE/RPM的一体化起到了积极地推动作用。
RP&M (Rapid Prototyping Manufacturing) is a newly developing technology in the
field of manufacturing industry of the time. Reverse Engineering (RE), combined with
RPM, may fundamentally change the traditional mode of production design and
manufacturing. But, the present technology of RE doesn match the rapid prototyping
technology at all. In this paper, the system configuration of RE based on RP&M (RERP) is
proposed. It is expounded comprehensively from the aspect of data preprocessing,
triangulation, smooth surface construction, STL file information processing , etc. Once
realizing the organic integration of RE/RPM, it can greatly improve the ability of Rapid
Product Development (RPD).
Firstly, according to the characteristic of STL file, the scattered data preprocessing
and methods of triangulation are presented. Data repairing based on neural network,
automatic boundary point recognition, adaptive kalman filtering, etc, various kinds of
technical means are utilitied for solving the difficult problems in data preprocessing. Some
methods, such as physically-based triangulation and selective triangulation, are investigated
enriching and developing the content of triangulation and improving the grid quality
greatly.
Secondly, by means of differential geometry, some methods of smooth surface
construction are studied systematically. Given the subdivision criterion of initial grid, two
techniques of averaged subdivision and selective subdivision are discussed. Resort to the
quantitative relationship between subdivision number and allowed error of RE, subdivision
becomes more scientific and reasonable. Using the optimum theory. an iterative method of
improving surface quality so as to gain quasi-C2 surface is proposed. This scheme is capable
of yielding smoother surfaces, if the fairing algorithm is applied one after the other.
In addition, there are lots of redundant grids in polyhedral model gained from RE. It is
unbeneficial for later treatment of RP&M. Through analyzing all kinds of methods of
multi-resolution model, concepts of concentric superface and star neighbourhood are first
presented in RE. A new model simplification algorithm, based on local geometry and
topology recognition. is developed. It is not only reduce the length of STL file, but also
bring convenience for displaying graphics and adding support.
Finally, the integration of RP technology and RE is deep investigated. Some problems
related with surface model and RP technology is pointed out. The method and data structure
of reconsfructing the topology information of STL file are proposed. Also addressed in the
paper are issues of the mistake check methods and repairing techniques of STL file. Then
an experimental procedure of creating interface file and making the seat prototype of a bike
is summarized in detail. The result testifies the feasibility and practicability of the technical
line presented in this paper. All of the above-mentioned measures, impact the development
for realizing the integration of RE/RPM.
工程与快速原型制造结合，将从根本上改变传统的产品设计、制造模式。
但是，当前的反求技术还无法达到与快速制造技术的匹配。本文在探讨了
面向RP＆M的反求工程的科学体系与框架的基础上，从数据预处理、网格
划分、光滑曲面构造、STL文件信息处理等方面进行了系统、深入地研究，
以期实现RE/RP＆M的有机集成，从而提高快速产品开发的能力。
首先，根据RP技术中STL文件的特点，有针对性地提出了离散数据的
预处理和网格划分的具体方法。基于神经网络的数据修补，自动数据分块、
以及自适应卡尔曼滤波等多种技术手段的使用，解决了当前在数据预处理
方面存在的难点问题。云状数据的基于物理的网格划分和选点三角剖分等
方法的提出，进一步丰富和发展了网格划分的内容，显著地提高了网格的
生成质量。
其次，以现代微分几何学为工具，系统研究了光滑曲面的C~1和G~1构造
方法：指出了初始网格的细分标准，并就此给出了均匀细分和选择性细分
两种方式；指明了细分中细分数与反求容差的量化关系，提高了细分的科
学性和合理性；运用优化理论，提出了曲面质量迭代提高以达到准C~2连续
曲面的方法，极大地改善了曲面的光顺效果。
此外，通过对现有的多分辨率造型方法的分析，首次在反求工程中引
入同心超面、星形邻域等概念，并提出了一种基于局部拓扑结构识别的网
格简化新算法。这不仅有效地消除了网格模型中存在大量的冗余网格，减
少了STL文件的长度，也使RP＆M中的造型显示、支撑添加、切片等后续
处理更为方便、快捷。
最后，对反求技术和快速原型技术的集成问题进行了深入研究；指出
了表面模型用于RP＆M中存在的问题；给出了STL文件拓扑重建的方法和
数据结构；讨论了STL文件的错误校验和修复技术；在此基础上，进行了
快速成型机的接口文件生成和实体成型加工实验，验证了本文所提技术路
线的正确性和科学性，为实现RE/RPM的一体化起到了积极地推动作用。
RP&M (Rapid Prototyping Manufacturing) is a newly developing technology in the
field of manufacturing industry of the time. Reverse Engineering (RE), combined with
RPM, may fundamentally change the traditional mode of production design and
manufacturing. But, the present technology of RE doesn match the rapid prototyping
technology at all. In this paper, the system configuration of RE based on RP&M (RERP) is
proposed. It is expounded comprehensively from the aspect of data preprocessing,
triangulation, smooth surface construction, STL file information processing , etc. Once
realizing the organic integration of RE/RPM, it can greatly improve the ability of Rapid
Product Development (RPD).
Firstly, according to the characteristic of STL file, the scattered data preprocessing
and methods of triangulation are presented. Data repairing based on neural network,
automatic boundary point recognition, adaptive kalman filtering, etc, various kinds of
technical means are utilitied for solving the difficult problems in data preprocessing. Some
methods, such as physically-based triangulation and selective triangulation, are investigated
enriching and developing the content of triangulation and improving the grid quality
greatly.
Secondly, by means of differential geometry, some methods of smooth surface
construction are studied systematically. Given the subdivision criterion of initial grid, two
techniques of averaged subdivision and selective subdivision are discussed. Resort to the
quantitative relationship between subdivision number and allowed error of RE, subdivision
becomes more scientific and reasonable. Using the optimum theory. an iterative method of
improving surface quality so as to gain quasi-C2 surface is proposed. This scheme is capable
of yielding smoother surfaces, if the fairing algorithm is applied one after the other.
In addition, there are lots of redundant grids in polyhedral model gained from RE. It is
unbeneficial for later treatment of RP&M. Through analyzing all kinds of methods of
multi-resolution model, concepts of concentric superface and star neighbourhood are first
presented in RE. A new model simplification algorithm, based on local geometry and
topology recognition. is developed. It is not only reduce the length of STL file, but also
bring convenience for displaying graphics and adding support.
Finally, the integration of RP technology and RE is deep investigated. Some problems
related with surface model and RP technology is pointed out. The method and data structure
of reconsfructing the topology information of STL file are proposed. Also addressed in the
paper are issues of the mistake check methods and repairing techniques of STL file. Then
an experimental procedure of creating interface file and making the seat prototype of a bike
is summarized in detail. The result testifies the feasibility and practicability of the technical
line presented in this paper. All of the above-mentioned measures, impact the development
for realizing the integration of RE/RPM.
引文
1．吴锡英．信息时代的全球制造策略—兼议我国制造业的发展．中国机械工程，1998，9(7)：1-3．
2.Bohn J H, Michael J Wonzy. Automatic CAD-model repair: shell-closure, Proc. SFF symposium 1992, The Univ Of Texas at Austin, 86-94.
3.Albano L D, Sub N P. Automatic Design and Concurrent Engineering, CAD, 1994, 26(7):499-504.
4.Bullinger H, Jorg K F et al. RPD-A multi-disciplinary approach for design of innovative products. 3~(rd) Int Conf On Mfg Tech, 1995, 11-19.
5.B Wiedemann, H A Jantzen. Strategies and applications for rapid product and process development in Daimler-Benz AG. Computers in Industry 39, 1999, 11-25.
6．颜永年，张伟，卢清萍等．基于离散／堆积成型概念的RPM原理和发展．中国机械工程，1994，5(4)：64-66．
7．赵一毅，李占利，卢秉恒．激光快速成型中激光扫描路径的快速生成算法．计算机辅助设计与图形学学报，1998，10(3)：260-265．
8．刘斌，黄树槐．快速原型制造技术中实时切片算法的研究与实现．计算机辅助设计与图形学学报，1997，9(6)：488-493．
9．柯映林，钱应璋．散乱点曲面测量造型技术及其在飞机曲面工装模具设计与制造中的应用研究．航空学报，1996，17(6)：760-763．
10．种永民，杨海成．测量造型技术中的数据处理方法．西北工业大学学报，1997，15(4)：624-628．
11．周利民，赵万华，卢秉恒．自由曲面的快速逆求工程及实现技术．中国机械工程，1997，8(4)：62-64．
12．张畅，张祥林，黄树槐．快速造型技术中的反求工程．中国机械工程，1997，8(5)：60-62．
13.Tamas varady, Ralph R Martin et al. Reverse engineering of geometric models-an introduction.Computer Aided Design, 1997, 29(4): 255-268.
14.Bopaya B, Yasser A Hosni. Reverse Engineering and its relevance to Industrial Engineering: A Critical Review. Computers ind Engng, 1994, 26(2): 343-348.
15.J P Kruth. Matherial incress manufacturing by rapid prototyping techniques. Annals of the CIRP,1991, 40(2): 603-614.
16.D Kochan. Solid free-form manufacturing-possibilities and restrictions. Computers in Industry,1992, 133-140.
17.J H Stanley. CT-assisted solid freeform fabrication. Sixth Int Conf On RP, 1995, 267-274.
18.D Sims. New reality in aircraft design and manufacture. IEEE CG&A, 1994, 16(1): 91-91.
19.Zollikofer P, Leon E. A tools for rapid prototying in the biosciences. IEEE CG&A, 1995, 11(2):48-95.
20.D J Walton, M Yeung. Geometric modelling from CT scans for stereolithography appartus. In Tang, Z(Ed.) New Advances in CAD&Computer Graphics(Proc. Cad/Graphics'93)Intemational Academic Publishers, Beijing(1993)417-422.
21.T Whohlers, Rapid prototyping in Japan and Europe. RPA/SME's Rapid Prototyping Newsletter, Vol. 1, No.2, Second Quarter 1995.
22．周利民．自由曲面快速反求技术与应用研究．西安交通大学博士学位论文，1997年5月．
23．王建国．快速反馈设计系统．第一届中国RP&M会议论文集，清华大学，北京．
24.Luo Feilu et al. Vision-based Measurement of Free-Form Surfaces. Journal of National University of Defense Technology, 1995, 17(3): 13-19
25．邢渊，周雄辉等．集成反向工程系统研究．机械工程学报，1998，34(3)：1-5．
26．梁任，伍正祥．坐标测量的抽样点数、分布与精度．机械工程学报，1994，30(4)：29-34．
27．柯映林，李维诗．复杂曲面离散测量布点理论和算法研究．计算机辅助设计与图形学学报，1998，10(Suppl.).57-60．
28．高国军，陈康宁等．用CMM检测自由曲面时检测点和路径的规划方法研究．西安交通大学学报，1996，30(7)：57-63．
29.D J Weir, M J Milroy et al. Reverse engineering physical models employing wrap-around B-spline surfaces and quadrics. Proc Inet(?) Mech Engrs, Part B: Journal of Engineering Manufacture,1996, 210(2): 147-157.
30.Gu P,Yan X. Neural network approach to the reconstruction of free form surfaces for reverse engineering. CAD, 1995, 27(1):54-64.
31.Alan C L, Shou-Yee Lin et al. Automated sequence arrangement of 3D point data for surface fitting in reverse engineering. Computers in Industry, 1998, 35(2): 149-173.
32.B Sarkar, C H Menq. Smooth-surface approximation and reverse engineering, CAD, 1991,23(9): 623-626.
33.D R Smith, Kanade. Autonomous scene description with range image. CVGIP, 1985, 31(3):322-334.
34.M J Milroy, Bradley et al. Segmentation of a wrap-around model using an active contour. CAD,1997, 29(4): 299-320.
35.P J Besl, R C Jain. Three dimensional object recognition. ACM Computing Surveys, 1985,17(1): 75-145.
36.H Yasser, F Labiche. Laser based system for reverse engineering. Computers ind Engng, 1994,26(2): 387-394.
37.J A Robert, M D James. Reverse engineering industrial applications. Computers ind Engng,1994, 26(2): 381-385.
38．李江雄，柯映要．基于实物的复杂曲面产品反求工程中的CAD建模技术．中国机械工程，1999， 10(4)： 390-393．
39.P N Chivate, A G Jablokow. Solid-Model Generation from Measured Point Data. CAD, 1993, 25(9): 587-600.
40.Wen-Der Ueng. Asweep-surface fitting algorithm for reverse engineering. Computers in Industry, 1998, 35(3): 261-273.
41.Gill Barequet, Yuval Kaplan. A data front-end for layered manufacturing. CAD, 1998, 30(4):231-243.
42.Colin Bradley, G W Vickers. Free-form surface reconstruction for machine vision rapid prototyping, Optical Engineering, 1993, 32(9): 2191-2200.
43.Cindy M G, John F Hughes. Modeling surfaces of arbitrary topology using manifolds. Computer Graphics29, 1995, 359-367.
44.William, Andrew Witkin. Free-form shape design using triangulated surfaces. Computers Graphics28, 1994, 247-256.
45.Herbert E, Ernst P M. Three-dimension alpha shapes. ACM Trans on Graphics, 1994, 13(1):43-72.
46.Leila D F, Enrico Puppo. Hierarchical triangulation for multiresolution surface description. ACM Trans on Graphics, 1995, 14(4): 363-411.
47.Hoppe H, DeRose T et al. Mesh optimization. Computer Graphics, 1993, 27(1): 19-26.
48.Biplab Sarkar, Chia-Hsiang Menq. Parameter optimization in approximating curves and surfaces to measurement data. Computer Aided Geometric Design8, 1991, 267-290.
49.L H T Chang, H B Said. A c~2 triangular patch for the interpolation of functional scattered data. CAD, 1997, 29(6): 407-412.
50.P N Chivate, A G Jablokow. Extending surfaces for reverse engineering solid model generation. Computers in Industry 38, 1999: 265-294.
51.Y H Chen, C Y Liu. Quadric surface extraction using genetic algorthms. CAD 31, 1999, 101-110.
52.Paul W F, William C K. Efficient multiresolution counterparts to variational methods for surface reconstruction. Computer Vision and Image Understanding, 1998, 70(2): 157-176.
53.B K Choi, H Y Shin et al. Triangulation of scattered data in 3D space. CAD, 1988, 20(5): 239-248.
54．崔汉国，胡瑞安等．三维任意区域中点集的三角剖分算法．计算机辅助设计与图形学学报，1995，7(2)：103-107．
55．姜寿山，杨海成等．用空间形状优化标准完成散乱数据的三角剖分．计算机辅助设计与图形学学报，1995，7(4)：241-249．
56．李琼砚，陆际联．空间离散点曲面的疏密三角划分．北京理工大学学报，1997，17(5)：634-638．
57．卢朝阳，吴成柯等．满足全局Delaunay特性的带特征约束的散乱数据最优三角剖分．计算机学报，1997，20(2)：118-124．
58.William E Lorensen, Harvey E Cline. Marching cubes: a high resolution 3D surface construction algorithm. Computer Graphics, 1987, 21(4): 163-169.
59.Hugues Hoppe, Tony Derose. Surface reconstruction from unorganized points. Computer Graphics, 1992, 26(2): 71-78.
60.Baining Guo. Surface reconstruction: from points to splines. CAD, 1997, 29(4): 269-277.
61．王平江，黄雪梅等．曲面激光密集测量三维数据的三角片逼近方法．工程图学学报，1998，No．1：17-27．
62.M J Miroy et al. G~1 continuity of B-spline surface patches in reverse engineering. CAD, 1995, 27(6): 471-478.
63．宁涛，经玲等．优化技术在B样条曲面拼接中的应用．计算机辅助设计与图形学学报，1997，9(2)：136-142．
64.Jensen T. Assembling triangular and rectangular patches and multivariate splines, in: Frain, ed.,Geometric Modelling: Algorithms and new trends. SIAM, Philadelphia, PA, 1987, 203-220
65．柯映林，谭建荣等．参数Bezier三角曲面的VC~1构造及其在复杂曲面产品测量造型中的应用．浙江大学学报，1995，29(3)：355-360．
66．柯映林，应道宁．参数Bezier三角曲面的GC~1设计．工程图学学报，1995，No．2，51-59．
67.T N T Goodman, H B Said. A C~1 triangular interpolant suitable for scattered data interpolation. Communications in Applied Numerical Methods7, 1991, 479-485.
68.Claudia Cottin, Ruud van Damme. Construction of a VC~1interpolant over triangles via edge deletion. Computer Aided Geometric Design11, 1994, 675-686.
69.Gerald Farin. A modified clough-tocher interpolant. Computer Aided Geometric Design2, 1985,19-27.
70.Stephen Mann.Cubic precision clough-tocher interpolation.Computer Aided Geometric Design16, 1999, 85-88.
71.Montana D J, Davis L. Training feedforward network using genetic algorithm. Int Joint Conf on AI, 1989: 762-767.
72.Marshall S J, Harrison R F. Optimization and training of Feed forward Neural Networks by Genetic Algorithms. 2nd IEEE Int Conf on ANN, 1991: 34-43.
73．周利民，胡德州等．激光扫描三角法测量精度因素的分析和研究．计量学报，1998，19(2)：130-135．
74．周辉，李涛等．数字曲线的线性逼近和分段识别．大连理工大学学报，1997，37(5)：576-580．
75.JianMing HU, Hong YAN. Polygonal approximation of digital curves based on the principles of conceptual organization. Pattern Recognition, 1997, 30(5): 701-718.
76.Wani M A, Batchelor B G. Edge-region-based segmention of range images. IEEE Trans. on Pattern Analysis and Machine Intelligence. 1994, 16(3): 314-319.
77.Kass M, Witkin A. Snakes: Active contour models. Proceedings of the 1rt International Conference on Computer Vision, 1987, 1, 259-269.
78.Cohen L D, Cohen I. Finite-element methods for active contour models and balloons for 2D and 3D images. IEEE Trans on Pattern Analysis and Machine Intelligence. 1993, 15(11): 1131-1147.
79.Donna J W, Mubarak ShaH. A fast algorithm for active contours and curvature estimation. CVGIP: Image Understanding. 1992, 55(1): 14-26.
80．刘国庆．一维自适应Kalman滤波的一种最优算法．高等学校计算数学学报，1997，No．1，48-53．
81．刘国庆，郭金吉．Kalman滤波的自适应算法．高等学校计算数学学报，1997，No．4，337-345．
82．L.雍，T.索德斯图姆．递推辨识的理论与实践．北京，科学出版社，1989．
83．吴大任编．微分几何讲义．北京，人民教育出版社，1981．
84.Gan G K Jacob, Chua Chee Kai et al. Development of a new prototyping interface. Computers in Industry, 1999(39): 61-70.
85.Stereolithography Interface Specification. 3D systems, Inc. June 1988.
86.Roscoe L E et al. Living with STL files. 6th Int Conf On Rapid Prototyping, Dayton, Ohio,USA, June 4-7, 1995, pp.145-151.
87．徐利治，周蕴时，孙玉柏编著．逼近论．北京：国防工业出版社，1985，249-273．
88．孙家广编著．计算机图形学(新版)．北京，清华大学出版社，1998．
89.Breen D E, House D H. A physically-based particle model of woven cloth. Visual Computer,1992, 8(5-6): 264-277.
90.Eberhardt B, Weber A. A fast, flexible, particle-system model for cloth draping. IEEE Compute Graphics and Application, 1996, 16(5): 52-59.
91.Kenji Shimada, David C Gossard, Automatic triangular mesh generation of trimmed parametri(?) surfaces for finite element analysis. Computer Aide Geometric Design, 1998, 15(2): 199-222
92.Brenen K,Campbell S, Pctzold L. Numerical Solution of Initial-Value Problems in Differential/Algebraic Equation, New York: North-Holland, 1989.
93.Jeng Yen. Constrained equations of motion in multibody dynamics as ODEs on manifolds. SIAN Journal for Numerical Analysis, 1993, 30(2): 553-568.
94．费景高．微分代数问题的一类数值算法．计算数学，1994，No．1，47-58．
95．高望东，刘淑珍编著．数值计算方法．大连，大连理工大学出版社，1992．
96．钟万勰．弹性力学求解新体系．大连，大连理工大学出版社，1995．
97.Potra F A, Rheinbolt W C. Different-geometric techniques for solving differential/algebraic equations.NATO-ASI Series, Vol, 69, Springer-Verlag, 1991.
98.Farin G. Triangular Bernstein-Bezierpatches. CAGD, 1986, 3(1): 83-127.
99.Barnhill R, Farin G. C~1quintic interpolation over triangles: two explicit representations. Int J Number Methods in Eng17, 1981, 1763-1778.
100.Nielson G M, Ramaraj R. Interpolation over a sphere based upon a minimum norm network. Comput Aided Geometric Des4, 1987, 41-57.
101.Chang G, Davis P J. The convexity of Bernstein polynomials over triangles. J Appro Theory, 1984, 40(1):11-28.
102．施法中编著．计算机辅助几何设计与非均匀有理B样条．北京，北京航空航天大学，1994，479-495．
103.Goldman R N. Subdivision algorithms for Bezier triangles. CAD, 1983, 15(3): 159-166.
104.D Liu, J Hoschek. GC~1 continuity conditions between adjacent rectangular and triangular Bezier surface patches. CAD, 1989, 194-200.
105.C L Lawson. Software for C~1 surface interpolation. In Mathematical Software Ⅲ, J R Rice,(ed.), Academic Press, New York, 1977, 161-194.
106.Cendes Z J, Wong S H. C~1 quadratic interpolation over arbitrary points sets. IEEE Comput Graph & App 1989: 18-26.
107.Reinhold Klass. Correction of local surface irregularities using reflection lines. CAD, 1980,12(2): 73-77.
108.DeRose T, Mann S. An approximately G~1 cubic surface interpolation. In Lyche T and Schumaker L L(Eds.) Mathematical Methods in Computer Aided Geometric Design Ⅱ Academic Press(1992)pp: 185-196.
109.B Piper. Visually smooth interpolation with triangular Bezier patches, in: Frain, ed., Geometric Modelling: Algorithms and new trends. SIAM, Philadelphia, PA, 1987, 220-232.
110.Gary Herron. Smooth closed surfaces with discrete triangular interpolants. Computer Aided Geometric Design2, 1985, 297-306.
111.Loop C. A G~1 triangular surface of arbitrary topologicat type. Comput Aided Geom Desll,1994, 303-330.
112.Chiyokura H, Kimura F. Localized surface interpolation method for irregular meshes. Comput Graph, 1993, 17(3): 289-298.
113.D J Walton, D S Meek. A triangular G~1 patch from boundary curves. CAD, 1996, 28(2):113-123.
114.C Y Wang. Shape classification of the parametric cubic curve and parametric B-spline cubic curve. CAD, 1981, 13(4): 199-206.
115.D S Meek, D J Walton. Shape determination of planar uniform cubic B-spline segments. CAD,1990, 22(7): 434-441.
116.Chiyokura H. Localized surface interpolation method for irregular meshes. In Kunii T L(Ed.)Advanced Computer Graphics, Springer-Verlag, Tokyo(1986)pp3-19.
117.B Pham. Offset curves and surfaces: a brief survey. CAD, 24(4): 223-229.
118．韩西安．基于仿射变换的等距线逼近方法．计算机辅助设计与图形学学报，1999，11(1)：8-10
119.Schroeder W J, Zarge J A et al. Decimation of triangle meshes. Computer Graphics, 1995,29(2): 171-182.
120.Veron P, Leon J C. Static polyhedron simplification using error measurements. Computer Aided Design, 1997, 29(4): 287-298.
121.Hamann B. A data reduction scheme for triangulated surfaces. Computer Aided Geometric Design, 1994, 11(2): 197-214.
122.Hoppe H. Progressive meshes. Computer Graphics, 1996, 30(2): 119-128.
123.Isler V, Lau R W H. Real-time multi-resolution modeling for complex virtual environments. In:Proc of VRST'96, Hong Kong, 1996, 11-19.
124.Eck M, Rossignac J R et al..Multi-resolution analysis of arbitrary meshes. Computer Graphics, 1995, 29(2): 171-182.
125.DeHamer J M , Zyda M J . Simplification of objects rendered by polygonal approximations. Computers Graphics, 1991, 25(2): 175-184.
126.Garland M, Heckbert P S. Surface simplification using quadric error metrics. Computer Graphics, 1997, 31(3): 209-216.
127．周昆，潘志庚，石教英．基于三角形折叠的网格简化算法．计算机学报，1998，21 (6)： 506-513．
128．李捷，唐泽圣．三维复杂模型的实时连续多分辨率绘制．计算机学报，1998，21(6)：482-491．
129．马小虎，潘志庚，石教英．基于三角形移去准则的多面体模型简化方法．计算机学报，1998，21(6)：492-499．
130．李捷，唐洋圣．改进的基于区域生长的模型简化算法．计算机辅助设计与图形学学报，1998，10(增刊)：14-19．
131.Alan D K, Raussel H T. Superfaces: Polygonal mesh simplification with bounded error. IEEE Computer Graphics and Application, 1996, 64-77.
132.Miller J F. CAD Requirements for Rapid Prototyping Tutorial. Rapid Prototyping & Manufacturing94, Detroit: Soc of Manufacturing Engineers, 1994.
133.Rock S J, Michael J Wozny. Generating Topological Information from a Bucket of Facet. Proceedings of Solid Freeform Fabrication Symposuim. 1992, The Univ Of Texas at Austin. Pp: 251-259.
134.Makela, I, Polenc A. Some Efficient Procedures for Correcting Triangulated Models. Proc SFF Symposium, Austin, Texas, USA, 1993, pp: 126-134.
135.Sheng Xuejun, Meler I F. Generating topological structures for surface models. IEEE Computer Graphics and Applications, 1995, 15(11): 35-41.
136．陈永府，张华等．任意曲面的三角形网格划分．计算机辅助设计与图形学学报，1997，9(5)：396-401．
137．刘斌，黄树槐．快速成型技术中数据模型的自动诊断与修复．华中理中大学学报，1996，24(9)：61-63．
138.D Kochan, Chua Chee Kai, Du Zhaohui. Rapid prototyping issues in the 21~(st) century. Computers in Industry 39, 1999, 3-10.
139.Sub Y S, Wozny M J. Adaptive Slicing of SFF Processes. 5~(th) Int. Conf. On RP, Dayton, Ohio,USA, 1994, pp: 404-411.
140.Gan G K Jacob, Chua Chee Kai, Tong Mei. Development of a new rapid prototyping interface. Computers in Industry 39, 1999, 61-70.
141．M-RPMS-Ⅱ多功能快速成型系统用户手册．清华大学激光快速成形中心，1999年5月．
2.Bohn J H, Michael J Wonzy. Automatic CAD-model repair: shell-closure, Proc. SFF symposium 1992, The Univ Of Texas at Austin, 86-94.
3.Albano L D, Sub N P. Automatic Design and Concurrent Engineering, CAD, 1994, 26(7):499-504.
4.Bullinger H, Jorg K F et al. RPD-A multi-disciplinary approach for design of innovative products. 3~(rd) Int Conf On Mfg Tech, 1995, 11-19.
5.B Wiedemann, H A Jantzen. Strategies and applications for rapid product and process development in Daimler-Benz AG. Computers in Industry 39, 1999, 11-25.
6．颜永年，张伟，卢清萍等．基于离散／堆积成型概念的RPM原理和发展．中国机械工程，1994，5(4)：64-66．
7．赵一毅，李占利，卢秉恒．激光快速成型中激光扫描路径的快速生成算法．计算机辅助设计与图形学学报，1998，10(3)：260-265．
8．刘斌，黄树槐．快速原型制造技术中实时切片算法的研究与实现．计算机辅助设计与图形学学报，1997，9(6)：488-493．
9．柯映林，钱应璋．散乱点曲面测量造型技术及其在飞机曲面工装模具设计与制造中的应用研究．航空学报，1996，17(6)：760-763．
10．种永民，杨海成．测量造型技术中的数据处理方法．西北工业大学学报，1997，15(4)：624-628．
11．周利民，赵万华，卢秉恒．自由曲面的快速逆求工程及实现技术．中国机械工程，1997，8(4)：62-64．
12．张畅，张祥林，黄树槐．快速造型技术中的反求工程．中国机械工程，1997，8(5)：60-62．
13.Tamas varady, Ralph R Martin et al. Reverse engineering of geometric models-an introduction.Computer Aided Design, 1997, 29(4): 255-268.
14.Bopaya B, Yasser A Hosni. Reverse Engineering and its relevance to Industrial Engineering: A Critical Review. Computers ind Engng, 1994, 26(2): 343-348.
15.J P Kruth. Matherial incress manufacturing by rapid prototyping techniques. Annals of the CIRP,1991, 40(2): 603-614.
16.D Kochan. Solid free-form manufacturing-possibilities and restrictions. Computers in Industry,1992, 133-140.
17.J H Stanley. CT-assisted solid freeform fabrication. Sixth Int Conf On RP, 1995, 267-274.
18.D Sims. New reality in aircraft design and manufacture. IEEE CG&A, 1994, 16(1): 91-91.
19.Zollikofer P, Leon E. A tools for rapid prototying in the biosciences. IEEE CG&A, 1995, 11(2):48-95.
20.D J Walton, M Yeung. Geometric modelling from CT scans for stereolithography appartus. In Tang, Z(Ed.) New Advances in CAD&Computer Graphics(Proc. Cad/Graphics'93)Intemational Academic Publishers, Beijing(1993)417-422.
21.T Whohlers, Rapid prototyping in Japan and Europe. RPA/SME's Rapid Prototyping Newsletter, Vol. 1, No.2, Second Quarter 1995.
22．周利民．自由曲面快速反求技术与应用研究．西安交通大学博士学位论文，1997年5月．
23．王建国．快速反馈设计系统．第一届中国RP&M会议论文集，清华大学，北京．
24.Luo Feilu et al. Vision-based Measurement of Free-Form Surfaces. Journal of National University of Defense Technology, 1995, 17(3): 13-19
25．邢渊，周雄辉等．集成反向工程系统研究．机械工程学报，1998，34(3)：1-5．
26．梁任，伍正祥．坐标测量的抽样点数、分布与精度．机械工程学报，1994，30(4)：29-34．
27．柯映林，李维诗．复杂曲面离散测量布点理论和算法研究．计算机辅助设计与图形学学报，1998，10(Suppl.).57-60．
28．高国军，陈康宁等．用CMM检测自由曲面时检测点和路径的规划方法研究．西安交通大学学报，1996，30(7)：57-63．
29.D J Weir, M J Milroy et al. Reverse engineering physical models employing wrap-around B-spline surfaces and quadrics. Proc Inet(?) Mech Engrs, Part B: Journal of Engineering Manufacture,1996, 210(2): 147-157.
30.Gu P,Yan X. Neural network approach to the reconstruction of free form surfaces for reverse engineering. CAD, 1995, 27(1):54-64.
31.Alan C L, Shou-Yee Lin et al. Automated sequence arrangement of 3D point data for surface fitting in reverse engineering. Computers in Industry, 1998, 35(2): 149-173.
32.B Sarkar, C H Menq. Smooth-surface approximation and reverse engineering, CAD, 1991,23(9): 623-626.
33.D R Smith, Kanade. Autonomous scene description with range image. CVGIP, 1985, 31(3):322-334.
34.M J Milroy, Bradley et al. Segmentation of a wrap-around model using an active contour. CAD,1997, 29(4): 299-320.
35.P J Besl, R C Jain. Three dimensional object recognition. ACM Computing Surveys, 1985,17(1): 75-145.
36.H Yasser, F Labiche. Laser based system for reverse engineering. Computers ind Engng, 1994,26(2): 387-394.
37.J A Robert, M D James. Reverse engineering industrial applications. Computers ind Engng,1994, 26(2): 381-385.
38．李江雄，柯映要．基于实物的复杂曲面产品反求工程中的CAD建模技术．中国机械工程，1999， 10(4)： 390-393．
39.P N Chivate, A G Jablokow. Solid-Model Generation from Measured Point Data. CAD, 1993, 25(9): 587-600.
40.Wen-Der Ueng. Asweep-surface fitting algorithm for reverse engineering. Computers in Industry, 1998, 35(3): 261-273.
41.Gill Barequet, Yuval Kaplan. A data front-end for layered manufacturing. CAD, 1998, 30(4):231-243.
42.Colin Bradley, G W Vickers. Free-form surface reconstruction for machine vision rapid prototyping, Optical Engineering, 1993, 32(9): 2191-2200.
43.Cindy M G, John F Hughes. Modeling surfaces of arbitrary topology using manifolds. Computer Graphics29, 1995, 359-367.
44.William, Andrew Witkin. Free-form shape design using triangulated surfaces. Computers Graphics28, 1994, 247-256.
45.Herbert E, Ernst P M. Three-dimension alpha shapes. ACM Trans on Graphics, 1994, 13(1):43-72.
46.Leila D F, Enrico Puppo. Hierarchical triangulation for multiresolution surface description. ACM Trans on Graphics, 1995, 14(4): 363-411.
47.Hoppe H, DeRose T et al. Mesh optimization. Computer Graphics, 1993, 27(1): 19-26.
48.Biplab Sarkar, Chia-Hsiang Menq. Parameter optimization in approximating curves and surfaces to measurement data. Computer Aided Geometric Design8, 1991, 267-290.
49.L H T Chang, H B Said. A c~2 triangular patch for the interpolation of functional scattered data. CAD, 1997, 29(6): 407-412.
50.P N Chivate, A G Jablokow. Extending surfaces for reverse engineering solid model generation. Computers in Industry 38, 1999: 265-294.
51.Y H Chen, C Y Liu. Quadric surface extraction using genetic algorthms. CAD 31, 1999, 101-110.
52.Paul W F, William C K. Efficient multiresolution counterparts to variational methods for surface reconstruction. Computer Vision and Image Understanding, 1998, 70(2): 157-176.
53.B K Choi, H Y Shin et al. Triangulation of scattered data in 3D space. CAD, 1988, 20(5): 239-248.
54．崔汉国，胡瑞安等．三维任意区域中点集的三角剖分算法．计算机辅助设计与图形学学报，1995，7(2)：103-107．
55．姜寿山，杨海成等．用空间形状优化标准完成散乱数据的三角剖分．计算机辅助设计与图形学学报，1995，7(4)：241-249．
56．李琼砚，陆际联．空间离散点曲面的疏密三角划分．北京理工大学学报，1997，17(5)：634-638．
57．卢朝阳，吴成柯等．满足全局Delaunay特性的带特征约束的散乱数据最优三角剖分．计算机学报，1997，20(2)：118-124．
58.William E Lorensen, Harvey E Cline. Marching cubes: a high resolution 3D surface construction algorithm. Computer Graphics, 1987, 21(4): 163-169.
59.Hugues Hoppe, Tony Derose. Surface reconstruction from unorganized points. Computer Graphics, 1992, 26(2): 71-78.
60.Baining Guo. Surface reconstruction: from points to splines. CAD, 1997, 29(4): 269-277.
61．王平江，黄雪梅等．曲面激光密集测量三维数据的三角片逼近方法．工程图学学报，1998，No．1：17-27．
62.M J Miroy et al. G~1 continuity of B-spline surface patches in reverse engineering. CAD, 1995, 27(6): 471-478.
63．宁涛，经玲等．优化技术在B样条曲面拼接中的应用．计算机辅助设计与图形学学报，1997，9(2)：136-142．
64.Jensen T. Assembling triangular and rectangular patches and multivariate splines, in: Frain, ed.,Geometric Modelling: Algorithms and new trends. SIAM, Philadelphia, PA, 1987, 203-220
65．柯映林，谭建荣等．参数Bezier三角曲面的VC~1构造及其在复杂曲面产品测量造型中的应用．浙江大学学报，1995，29(3)：355-360．
66．柯映林，应道宁．参数Bezier三角曲面的GC~1设计．工程图学学报，1995，No．2，51-59．
67.T N T Goodman, H B Said. A C~1 triangular interpolant suitable for scattered data interpolation. Communications in Applied Numerical Methods7, 1991, 479-485.
68.Claudia Cottin, Ruud van Damme. Construction of a VC~1interpolant over triangles via edge deletion. Computer Aided Geometric Design11, 1994, 675-686.
69.Gerald Farin. A modified clough-tocher interpolant. Computer Aided Geometric Design2, 1985,19-27.
70.Stephen Mann.Cubic precision clough-tocher interpolation.Computer Aided Geometric Design16, 1999, 85-88.
71.Montana D J, Davis L. Training feedforward network using genetic algorithm. Int Joint Conf on AI, 1989: 762-767.
72.Marshall S J, Harrison R F. Optimization and training of Feed forward Neural Networks by Genetic Algorithms. 2nd IEEE Int Conf on ANN, 1991: 34-43.
73．周利民，胡德州等．激光扫描三角法测量精度因素的分析和研究．计量学报，1998，19(2)：130-135．
74．周辉，李涛等．数字曲线的线性逼近和分段识别．大连理工大学学报，1997，37(5)：576-580．
75.JianMing HU, Hong YAN. Polygonal approximation of digital curves based on the principles of conceptual organization. Pattern Recognition, 1997, 30(5): 701-718.
76.Wani M A, Batchelor B G. Edge-region-based segmention of range images. IEEE Trans. on Pattern Analysis and Machine Intelligence. 1994, 16(3): 314-319.
77.Kass M, Witkin A. Snakes: Active contour models. Proceedings of the 1rt International Conference on Computer Vision, 1987, 1, 259-269.
78.Cohen L D, Cohen I. Finite-element methods for active contour models and balloons for 2D and 3D images. IEEE Trans on Pattern Analysis and Machine Intelligence. 1993, 15(11): 1131-1147.
79.Donna J W, Mubarak ShaH. A fast algorithm for active contours and curvature estimation. CVGIP: Image Understanding. 1992, 55(1): 14-26.
80．刘国庆．一维自适应Kalman滤波的一种最优算法．高等学校计算数学学报，1997，No．1，48-53．
81．刘国庆，郭金吉．Kalman滤波的自适应算法．高等学校计算数学学报，1997，No．4，337-345．
82．L.雍，T.索德斯图姆．递推辨识的理论与实践．北京，科学出版社，1989．
83．吴大任编．微分几何讲义．北京，人民教育出版社，1981．
84.Gan G K Jacob, Chua Chee Kai et al. Development of a new prototyping interface. Computers in Industry, 1999(39): 61-70.
85.Stereolithography Interface Specification. 3D systems, Inc. June 1988.
86.Roscoe L E et al. Living with STL files. 6th Int Conf On Rapid Prototyping, Dayton, Ohio,USA, June 4-7, 1995, pp.145-151.
87．徐利治，周蕴时，孙玉柏编著．逼近论．北京：国防工业出版社，1985，249-273．
88．孙家广编著．计算机图形学(新版)．北京，清华大学出版社，1998．
89.Breen D E, House D H. A physically-based particle model of woven cloth. Visual Computer,1992, 8(5-6): 264-277.
90.Eberhardt B, Weber A. A fast, flexible, particle-system model for cloth draping. IEEE Compute Graphics and Application, 1996, 16(5): 52-59.
91.Kenji Shimada, David C Gossard, Automatic triangular mesh generation of trimmed parametri(?) surfaces for finite element analysis. Computer Aide Geometric Design, 1998, 15(2): 199-222
92.Brenen K,Campbell S, Pctzold L. Numerical Solution of Initial-Value Problems in Differential/Algebraic Equation, New York: North-Holland, 1989.
93.Jeng Yen. Constrained equations of motion in multibody dynamics as ODEs on manifolds. SIAN Journal for Numerical Analysis, 1993, 30(2): 553-568.
94．费景高．微分代数问题的一类数值算法．计算数学，1994，No．1，47-58．
95．高望东，刘淑珍编著．数值计算方法．大连，大连理工大学出版社，1992．
96．钟万勰．弹性力学求解新体系．大连，大连理工大学出版社，1995．
97.Potra F A, Rheinbolt W C. Different-geometric techniques for solving differential/algebraic equations.NATO-ASI Series, Vol, 69, Springer-Verlag, 1991.
98.Farin G. Triangular Bernstein-Bezierpatches. CAGD, 1986, 3(1): 83-127.
99.Barnhill R, Farin G. C~1quintic interpolation over triangles: two explicit representations. Int J Number Methods in Eng17, 1981, 1763-1778.
100.Nielson G M, Ramaraj R. Interpolation over a sphere based upon a minimum norm network. Comput Aided Geometric Des4, 1987, 41-57.
101.Chang G, Davis P J. The convexity of Bernstein polynomials over triangles. J Appro Theory, 1984, 40(1):11-28.
102．施法中编著．计算机辅助几何设计与非均匀有理B样条．北京，北京航空航天大学，1994，479-495．
103.Goldman R N. Subdivision algorithms for Bezier triangles. CAD, 1983, 15(3): 159-166.
104.D Liu, J Hoschek. GC~1 continuity conditions between adjacent rectangular and triangular Bezier surface patches. CAD, 1989, 194-200.
105.C L Lawson. Software for C~1 surface interpolation. In Mathematical Software Ⅲ, J R Rice,(ed.), Academic Press, New York, 1977, 161-194.
106.Cendes Z J, Wong S H. C~1 quadratic interpolation over arbitrary points sets. IEEE Comput Graph & App 1989: 18-26.
107.Reinhold Klass. Correction of local surface irregularities using reflection lines. CAD, 1980,12(2): 73-77.
108.DeRose T, Mann S. An approximately G~1 cubic surface interpolation. In Lyche T and Schumaker L L(Eds.) Mathematical Methods in Computer Aided Geometric Design Ⅱ Academic Press(1992)pp: 185-196.
109.B Piper. Visually smooth interpolation with triangular Bezier patches, in: Frain, ed., Geometric Modelling: Algorithms and new trends. SIAM, Philadelphia, PA, 1987, 220-232.
110.Gary Herron. Smooth closed surfaces with discrete triangular interpolants. Computer Aided Geometric Design2, 1985, 297-306.
111.Loop C. A G~1 triangular surface of arbitrary topologicat type. Comput Aided Geom Desll,1994, 303-330.
112.Chiyokura H, Kimura F. Localized surface interpolation method for irregular meshes. Comput Graph, 1993, 17(3): 289-298.
113.D J Walton, D S Meek. A triangular G~1 patch from boundary curves. CAD, 1996, 28(2):113-123.
114.C Y Wang. Shape classification of the parametric cubic curve and parametric B-spline cubic curve. CAD, 1981, 13(4): 199-206.
115.D S Meek, D J Walton. Shape determination of planar uniform cubic B-spline segments. CAD,1990, 22(7): 434-441.
116.Chiyokura H. Localized surface interpolation method for irregular meshes. In Kunii T L(Ed.)Advanced Computer Graphics, Springer-Verlag, Tokyo(1986)pp3-19.
117.B Pham. Offset curves and surfaces: a brief survey. CAD, 24(4): 223-229.
118．韩西安．基于仿射变换的等距线逼近方法．计算机辅助设计与图形学学报，1999，11(1)：8-10
119.Schroeder W J, Zarge J A et al. Decimation of triangle meshes. Computer Graphics, 1995,29(2): 171-182.
120.Veron P, Leon J C. Static polyhedron simplification using error measurements. Computer Aided Design, 1997, 29(4): 287-298.
121.Hamann B. A data reduction scheme for triangulated surfaces. Computer Aided Geometric Design, 1994, 11(2): 197-214.
122.Hoppe H. Progressive meshes. Computer Graphics, 1996, 30(2): 119-128.
123.Isler V, Lau R W H. Real-time multi-resolution modeling for complex virtual environments. In:Proc of VRST'96, Hong Kong, 1996, 11-19.
124.Eck M, Rossignac J R et al..Multi-resolution analysis of arbitrary meshes. Computer Graphics, 1995, 29(2): 171-182.
125.DeHamer J M , Zyda M J . Simplification of objects rendered by polygonal approximations. Computers Graphics, 1991, 25(2): 175-184.
126.Garland M, Heckbert P S. Surface simplification using quadric error metrics. Computer Graphics, 1997, 31(3): 209-216.
127．周昆，潘志庚，石教英．基于三角形折叠的网格简化算法．计算机学报，1998，21 (6)： 506-513．
128．李捷，唐泽圣．三维复杂模型的实时连续多分辨率绘制．计算机学报，1998，21(6)：482-491．
129．马小虎，潘志庚，石教英．基于三角形移去准则的多面体模型简化方法．计算机学报，1998，21(6)：492-499．
130．李捷，唐洋圣．改进的基于区域生长的模型简化算法．计算机辅助设计与图形学学报，1998，10(增刊)：14-19．
131.Alan D K, Raussel H T. Superfaces: Polygonal mesh simplification with bounded error. IEEE Computer Graphics and Application, 1996, 64-77.
132.Miller J F. CAD Requirements for Rapid Prototyping Tutorial. Rapid Prototyping & Manufacturing94, Detroit: Soc of Manufacturing Engineers, 1994.
133.Rock S J, Michael J Wozny. Generating Topological Information from a Bucket of Facet. Proceedings of Solid Freeform Fabrication Symposuim. 1992, The Univ Of Texas at Austin. Pp: 251-259.
134.Makela, I, Polenc A. Some Efficient Procedures for Correcting Triangulated Models. Proc SFF Symposium, Austin, Texas, USA, 1993, pp: 126-134.
135.Sheng Xuejun, Meler I F. Generating topological structures for surface models. IEEE Computer Graphics and Applications, 1995, 15(11): 35-41.
136．陈永府，张华等．任意曲面的三角形网格划分．计算机辅助设计与图形学学报，1997，9(5)：396-401．
137．刘斌，黄树槐．快速成型技术中数据模型的自动诊断与修复．华中理中大学学报，1996，24(9)：61-63．
138.D Kochan, Chua Chee Kai, Du Zhaohui. Rapid prototyping issues in the 21~(st) century. Computers in Industry 39, 1999, 3-10.
139.Sub Y S, Wozny M J. Adaptive Slicing of SFF Processes. 5~(th) Int. Conf. On RP, Dayton, Ohio,USA, 1994, pp: 404-411.
140.Gan G K Jacob, Chua Chee Kai, Tong Mei. Development of a new rapid prototyping interface. Computers in Industry 39, 1999, 61-70.
141．M-RPMS-Ⅱ多功能快速成型系统用户手册．清华大学激光快速成形中心，1999年5月．