三维扫描仪与逆向工程关键技术研究
|
摘要
随着计算机技术的发展,工业生产、影视制作、服装设计、医疗诊断和军事训练等领域提出了一个越来越迫切的要求:快速获取物体的三维模型。三维扫描仪就是一种能够直接得到物体的原始三维信息的计算机输入设备。这种从实物样件获取产品数学模型的技术,称之为逆向工程。我们研制的三维扫描仪系列产品集光学、机械、电子、自动控制、数据采集、图像处理等诸多领域的知识为一体,是具有重大应用价值的高科技产品。
本文在国家自然科学基金(69775022)和“863”高技术研究发展计划(863-306-ZT04-06-3)的资助下,对三维扫描仪系统进行了理论研究和技术实现,重点研究了三维信息获取和逆向工程中的几个关键技术:系统定标、数据修补、点云压缩、三维重建、网格简化等。
本文首先系统总结了现有三维信息获取技术,简要介绍了常见的几种三维扫描仪产品和今后的发展趋势,提出了三维数字化基本流程和关键技术。
三维扫描仪按照信息获取方式的不同可分为接触式和非接触式两大类。接触式使用测头直接触碰物体表面,根据测量装置的空间几何结构得到测头的坐标; 非接触式主要基于计算机视觉原理,从摄像机拍摄的图像中获取目标的三维信息。考虑到不同的应用场合,我们分别研制了接触式多关节机械臂三维扫描仪(3DLCS-400)和非接触式结构光彩色三维扫描仪(3DLCS-200)。本文简要介绍了这两种三维扫描仪的系统原理、系统构成以及工作流程。
系统结构参数偏差会导致坐标测量误差,为提高测量精度,对三维扫描仪进行定标,以获得尽可能准确的实际结构参数是非常必要的。本文针对非线性系统的多参数定标问题,结合最小二乘法和遗传算法各自优点,提出了一种收敛速度快,又有较高精度的混合智能算法。首先通过改进的最小二乘法计算得到问题的次优解,以此作为遗传算法的基因中心值,并将基因范围动态缩小进行进化计算,从而获得最优解。该算法解决了传统方法遇到奇异阵无法求逆的困难,克服了一般遗传算法效率太低的缺点,大大提高了定标的速度和精度。
在三维扫描仪对物体扫描过程中,由于各种因素的限制,可能导致物体某些
Along with the development of computer technology, an urgent request, that is how to obtain 3D model of objects, is put forward in industrial production, movie making, apparel design, medical diagnosis and military training etc. 3D scanner is a kind of input equipment which can acquire the 3D data of an object directly. This technology comes to be known as Reverse Engineering. 3D scanner realtes to such subjects as optics, mechanics, electronics, automatic control, image process etc and has much significance on many applications.
In this dissertation, some key technology used in 3D scanner are developed including 3D acquiring, system calibration, data repairing, point cloud compression, 3D reconstruction and triangle mesh simplification. My work has been supported by National Natural Science Fundation (69775022) and National 863 Project (863-306-ZT04-06-3).
First, to the fields of 3D acquiring, it systematically concludes the popular 3D acquiring methods and some products of 3D scanner. The basic process and key technology are also presented.
3D scanner can be divided into two types according to its acquiring method: contact and non-contact. The former uses probe to touch the surface of objects and obtain the coordination from geometry structure. The latter gets 3D information from a series of photographs of video camera based on computer vision theory. Considering different applications, we developped contact multi-joint 3D scanner(3dlcs-400) and non-contact constructed lighting 3D scanner(3dlcs-200). The theory, constitute and work process are introduced.
System parameter errors will result in the coordination errors. In order to improve measuring accuracy, it is necessary to calibrate the structure parameters. Combined with fast convergence and high accuracy, a hybrid intelligent algorithm is proprosed to solve the parameter calibration of the nonlinear system. The results that computed through the improved least-square algorithm become the the original values
of the genetic algorithm where gene range could be dynamically changed. The experiment shows that the hybrid algorithm is valid in practical application. Because of some restrictions, incomplete data is possible to appear in the scanning process. Data repairing based on genetic algorithm and BP neural network is investigated to solve the problem. With the improvement of accuracy, the number of point cloud increases quickly and needs to be compressed. The simplest method uses sampling at the cost of quality, so it is not fit for complex object’s surface. In this dissertation, an adaptive 3D Splitting method for compressing of the data on the spacial contours is presented. Triangle mesh model is selected to build boundary representation. The reconstruction methods with orderliness data and scattered data are discussed. The new way uses a set of multilayer parallel planes to bed the set of scattered points. First, we regulate the scattered points into a serial of contour lines. Seconed, we sort the points in the same of contour lines in anticlockwise. Final, we reconstruct the object with the way of parallel contour lines. Nowadays, the quantity of triangle mesh becomes more and more to meet the demand of reality sensation. But complex mesh model is adverse to storage, transfer and render. Progressive mesh is a good method to simplify meshes. In PM form, an arbitrary mesh is stored as a much coarser mesh together with a sequence of detail records that indicate how to incrementally refine exactly back into the original mesh. The PM representation naturally supports progressive transmission, offers a concise encoding of itself, and permits selective refinement. On the basis of PM, a new method which collaspe half edge and keep the color attributes is given. It not only avoids the complexity of computing new vertex, but also embodys the effect of color. The practical results appear perfect.
本文在国家自然科学基金(69775022)和“863”高技术研究发展计划(863-306-ZT04-06-3)的资助下,对三维扫描仪系统进行了理论研究和技术实现,重点研究了三维信息获取和逆向工程中的几个关键技术:系统定标、数据修补、点云压缩、三维重建、网格简化等。
本文首先系统总结了现有三维信息获取技术,简要介绍了常见的几种三维扫描仪产品和今后的发展趋势,提出了三维数字化基本流程和关键技术。
三维扫描仪按照信息获取方式的不同可分为接触式和非接触式两大类。接触式使用测头直接触碰物体表面,根据测量装置的空间几何结构得到测头的坐标; 非接触式主要基于计算机视觉原理,从摄像机拍摄的图像中获取目标的三维信息。考虑到不同的应用场合,我们分别研制了接触式多关节机械臂三维扫描仪(3DLCS-400)和非接触式结构光彩色三维扫描仪(3DLCS-200)。本文简要介绍了这两种三维扫描仪的系统原理、系统构成以及工作流程。
系统结构参数偏差会导致坐标测量误差,为提高测量精度,对三维扫描仪进行定标,以获得尽可能准确的实际结构参数是非常必要的。本文针对非线性系统的多参数定标问题,结合最小二乘法和遗传算法各自优点,提出了一种收敛速度快,又有较高精度的混合智能算法。首先通过改进的最小二乘法计算得到问题的次优解,以此作为遗传算法的基因中心值,并将基因范围动态缩小进行进化计算,从而获得最优解。该算法解决了传统方法遇到奇异阵无法求逆的困难,克服了一般遗传算法效率太低的缺点,大大提高了定标的速度和精度。
在三维扫描仪对物体扫描过程中,由于各种因素的限制,可能导致物体某些
Along with the development of computer technology, an urgent request, that is how to obtain 3D model of objects, is put forward in industrial production, movie making, apparel design, medical diagnosis and military training etc. 3D scanner is a kind of input equipment which can acquire the 3D data of an object directly. This technology comes to be known as Reverse Engineering. 3D scanner realtes to such subjects as optics, mechanics, electronics, automatic control, image process etc and has much significance on many applications.
In this dissertation, some key technology used in 3D scanner are developed including 3D acquiring, system calibration, data repairing, point cloud compression, 3D reconstruction and triangle mesh simplification. My work has been supported by National Natural Science Fundation (69775022) and National 863 Project (863-306-ZT04-06-3).
First, to the fields of 3D acquiring, it systematically concludes the popular 3D acquiring methods and some products of 3D scanner. The basic process and key technology are also presented.
3D scanner can be divided into two types according to its acquiring method: contact and non-contact. The former uses probe to touch the surface of objects and obtain the coordination from geometry structure. The latter gets 3D information from a series of photographs of video camera based on computer vision theory. Considering different applications, we developped contact multi-joint 3D scanner(3dlcs-400) and non-contact constructed lighting 3D scanner(3dlcs-200). The theory, constitute and work process are introduced.
System parameter errors will result in the coordination errors. In order to improve measuring accuracy, it is necessary to calibrate the structure parameters. Combined with fast convergence and high accuracy, a hybrid intelligent algorithm is proprosed to solve the parameter calibration of the nonlinear system. The results that computed through the improved least-square algorithm become the the original values
of the genetic algorithm where gene range could be dynamically changed. The experiment shows that the hybrid algorithm is valid in practical application. Because of some restrictions, incomplete data is possible to appear in the scanning process. Data repairing based on genetic algorithm and BP neural network is investigated to solve the problem. With the improvement of accuracy, the number of point cloud increases quickly and needs to be compressed. The simplest method uses sampling at the cost of quality, so it is not fit for complex object’s surface. In this dissertation, an adaptive 3D Splitting method for compressing of the data on the spacial contours is presented. Triangle mesh model is selected to build boundary representation. The reconstruction methods with orderliness data and scattered data are discussed. The new way uses a set of multilayer parallel planes to bed the set of scattered points. First, we regulate the scattered points into a serial of contour lines. Seconed, we sort the points in the same of contour lines in anticlockwise. Final, we reconstruct the object with the way of parallel contour lines. Nowadays, the quantity of triangle mesh becomes more and more to meet the demand of reality sensation. But complex mesh model is adverse to storage, transfer and render. Progressive mesh is a good method to simplify meshes. In PM form, an arbitrary mesh is stored as a much coarser mesh together with a sequence of detail records that indicate how to incrementally refine exactly back into the original mesh. The PM representation naturally supports progressive transmission, offers a concise encoding of itself, and permits selective refinement. On the basis of PM, a new method which collaspe half edge and keep the color attributes is given. It not only avoids the complexity of computing new vertex, but also embodys the effect of color. The practical results appear perfect.
引文
[1] M. Levoy, K. Pulli, B. Curless, S. Rusinkiewicz. The Digital Michelangelo Project: 3D scanning of large statues. Computer Graphics (SIGGRAPH’00 Proceedings), 2000:131-144
[2] 韩涛.激光三角法三维轮廓测量技术的研究[硕士学位论文].西安交通大学,2002
[3] 刘影,杭九全,万耀青.反求工程与现代设计.机械设计,1998,12:1-4
[4] 田晓冬,史桂蓉,阮雪榆.复杂曲面实物的逆向工程及其关键技术.机械设计与制造工程,2000,29(4):l-6
[5] 雷刚,邹昌平.快速逆向工程研究进展.机械工艺师,2000,10:32-38
[6] 王先逵.制造技术的历史回顾与面临的机遇挑战.机械工程学报,2002, 38(8):1-8
[7] 李德华,胡汉平,金刚. 从平面到立体--三维扫描技术. 计算机世界,C3,1999.7.26
[8] 金刚,周学泳,李德华. 三维扫描技术的应用. 计算机世界,C7,1999.7.26
[9] 金刚,陈振羽,宋昆. 几种三维扫描设备. 计算机世界,C12,1999.7.26
[10] 金刚,吴晓刚,李德华. 三维扫描系统中的关键技术. 计算机世界,C1,1999.7.26
[11] 金刚,李泽宇,李德华. 常用的三维信息获取技术. 计算机世界,C8,1999.7.26
[12] Will P.M., Pennington K.S., Grid coding: Preprocessing technique for robot and machine vision. Artificial Intelligence, 1971; 2(3): 319-329
[13] Will P.M., Pennington K.S., Norel technique for image processing. Proc. IEEE, 1972; 60(6): 669-680
[14] Popplestone R.J., Brown C.M., Ambler A.P., Crawford G.F., Forming models of plane and cylinder faceted bollies from light stripes. In: Proc. 4th Intern, Joint Conf. Artif. Intell. 1975: 664-668
[15] Agin G.J. Binford T.O. Computer description of curved objects. In: Proc. 3rd Intern Conf. Artif. Intell. , Stanford, CA, 1973: 629-640
[16] Potmesil M., Generating models of solid objects by matching 3D surface segments. In: Proc 8th Intern Joint Conf Artif Intell, Karlsruhe, 1983: 1089-1093
[17] Sato Y., Kitagawa H., Fujita H. Shape Measurement of Curved Objects Using Multiple Slit Ray Projections. IEEE Trans Patt Anal Mach Intell, 1982: 641-646
[18] Tio J. B. K., McPherson C.A., Hall E.L., Curved Surface Measurement for Robot Vision. Proc RPIP, 1983: 52-96
[19] Tsai R.Y., A versatile camera calibration technique for high accuracy 3D machine vision metrology using of the shelf TV cameras and lenses. IEEE J Robotics Autom, 1987; RA-3 (4): 323-344
[20] Mansbach P., Calibration of a camera and light source by fitting to a physical model. Comput Vis Graph Image Process, 1986; 35: 200-219
[21] 蒋向前,李柱,谢铁邦. 全息光栅干涉法测量曲面形貌的理论研究. 华中理工大学学报,1994,22(2):316-320
[22] 孙龙祥.深度图像分析.北京:电子工业出版社,1996.62-87
[23] 强玉俊,蒋大真,盛康龙. 工业CT 研制进展. 核物理动态,1994,11(4):214-218
[24] P.Saint-Marc, G.Medioni. Adaptive Smoothing for Feature Extraction in Proceeding of the Image Understanding workshop, 1988. 1100-1113
[25] 肖贵福.对发展坐标测量机测头的新思考.现代计量测试,1995,4:21-23
[26] 黄真,孔令富.并联机器人机构学理论及控制.北京:机械工业出版社,1997. 45-67
[27] Denavit J, Hartenberg R. A kinematic notation for lower pair mechanism based on matrices. ASME Journal of Applied Mechanics, 1955, Vol 22(6), 215-221
[28] 王福瑞.单片微机测控系统设计大全.北京:北航出版社,1999.125-138
[29] 长春第一光学仪器厂.旋转编码器手册.吉林:吉林大学出版社,2000.3-9
[30] 王化祥,张淑英.传感器原理及应用.天津:天津大学出版社,1999.21-72
[31] 陈宝林.最优化理论与算法.北京:清华大学出版社,1989.83-116
[32] 邓乃扬.无约束最优化方法.北京:科学出版社,1982.142-173
[33] 叶东,黄庆成,车仁生.多关节坐标测量机的误差模型.光学精密工程,1999,7(2):91-96
[34] 叶东,黄庆成,车仁生.多关节坐标测量机的结构参数校准.宇航计测技术,1999,9(6):12-15
[35] 叶东,黄庆成,车仁生.六自由度关节式坐标测量机关节零位偏差的标定算法.工具技术,1999,33:34-36
[36] 邹璇,李德华.多关节机械臂的坐标模型和参数标定.光学精密工程,2001, 9(3):252-256.
[37] 席少霖.非线性最优化方法. 北京:高等教育出版社, 1992. 187-212.
[38] Nirwan Ansari,Edwin Hou.用于最优化的计算智能.李军,边肇祺译. 北京:清华大学出版社,1999.141-150
[39] 焦李成.神经网络计算.西安:电子科技大学出版社,1995.32-44
[40] Hopfield.J.J.,“Neural computation of decision in optimaization problems”, Biological Cybernetics, vol.52, 1985, 141-152
[41] Hopfield.J.J.,“Neural networks and physical systems with emergent collective computational abilities”, PNAS, Vol.79, 2554-2558, 1982
[42] Hopfield.J.J.,“Neurons with graded response have collective computation properties like those of two state neurons”PNAS, Vol. 81, 3088-3092, 1984
[43] Metropolis,N.A.,A.Rosenbluth,M.Rosenbluth,A.Teller and E.Teller,“Equation of state calculations by fast computing machines”,Journal of Chemical Physics, Vol.21, 1953, 1087-1092
[44] Leong,H.W.,D.G.Wong and C.L.Liu,“A simulated annealing channel router”Proc.IEEE international Conference on Computer Aided Design,Santa Clara,CA,November 1985,226-229
[45] Tan,H.L., S.B.Gelfand and E.J.Delp,“A cost minimization approach to edge detection using simulated annealing”, IEEE Trans. On Pattern Analysis and Machine Intelligence, vol.14, no.1, January 1992, 3-18
[46] Lin, F.T.,C.Y.Kao and C.C hsu,“Applying the genetic approach to simulated annealing in solving some NP-hard problems”, IEEE Trans. On System, Man, and Cybernetics, vol.23, no.6, November 1993, 1752-1767
[47] 焦李成.进化计算与进化神经网络-计算智能的新方向.电子科技,1995,1:9-19
[48] 周明,孙淑栋.遗传算法原理及应用.北京:国防工业出版社,1999.6-24
[49] Zbiginiew Michalewicz.演化程序-遗传算法与数据编码的结合.周家驹,何险峰译.北京:科学出版社,2000.34-57
[50] 陈国良.遗传算法原理及其应用.北京:人民邮电出版社,1996. 12-28
[51] 张文修,梁怡.遗传算法的数学基础.西安:西安交通大学出版社,2000.3-9
[52] D J Weir, M J Milroy et al.Reverse engineering physical models employing wrap-around B-spline surfaces and quadrics. 'Proc Instn Mech Engrs, Part B: Journal of Engineering Manufacture,1995, 210(2): 147-157
[53] Gu P,Yan X. Neural network approach to the reconstruction of free form surfaces for reverseengineering. CAD,1995,27(1):54-64
[54] 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
[55] 马小虎等. 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):492-498
[56] Garland M et al. Surface simplification using quadric error metrics. In:ACM SIGGRAPH,Los Angeles,1997. 209-216
[57] Chen Y H, Liu C Y. Quadric surface extract ion using genetic algorithms [J]. Computer Aided Design,1999, 31 (2) : 101-110.
[58] Sapidis N, and Perucchio. Delaunary triangulation of arbitrarily shaped planar Domains, Computer Aided Geometric Design,1991,Vol.8:421-437
[59] Lai J Y,Ueng W D and YAO CY. Registration and data merging for muiltiple sets of scan data.Advances Manufacturing Technilogy,1999,Vol,15(1):54-63
[60] Tamas varady,Ralph R Martin et al. Reverse engineering of geometric models-an introduction. Computer Aided Design,1997, 29(4): 255-268.
[61] 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
[62] Marshall S J, Harrison R F. Optimization and training of 15eed forward Neural Networks byGenetic Algorithms. 2nd IEEE Int Conf on ANN,1991:34-43.
[63] 钟纲.曲线曲面重建方法研究[博士学位论文].浙江大学,2002
[64] C.L. Bajaj, F. Bernardini and G. Xu, Automatic reconstruction of surfaces and scalar fields form 3D scans, SIGGRAPH’95,109-118
[65] M. Eck and H. Hoppe,Automatic reconstruction of B-spline surfaces of arbitrary topological type,SIGGRAPH, 1996, 335-342
[66] B.Guo, Design, Surface reconstruction: from points to splines, Computer-Aided 1997, 29(4): 269-277
[67] S .Lee, G. Wolberg and S.Y. Shin, Scattered data interpolation with multilevel B-spline, IEEE Transactions on Visualization and Computer Graphics, 1997,3(3):228-244
[68] M. Yang and E. Lee, Segmentation of measured point data using a parametric quadric surface approximation, Computer-Aided Design, 1999, 31,499-457
[69] L.A. Piegl and W. Tiller, Parameterization for surface fitting in reverse engineering, Computer-Aided Design, 2001,33,593-603
[70] M.S. Floater, Meshless parameterization and B-spline surface approximation, The Mathematics of Surfaces, 2000,1-18
[71] Shigeru Muraki, Volumetric Shape Description of Range Data Using `Blobby Model’,Proceedings of SIGGRAPH 91 (Las Vegas, Nevada, Jul. 28-Aug. 2,1991). In Computer Graphics, 25, 4 (Jul. 1991) ACM SIGGRAPH, New York,1991,227-235
[72] C. Bajaj and I. Ihm, C1 smoothing of polyhedral with implicit algebraic splines. SIGGRAPH’92, 1992, 79-86
[73] C. Bajaj and I. Ihm, Algebraic surface design with Hermite interpolation.ACM Transactions on Graphics,1992, 11(1):61-91
[74] N.S .Sapidis and P.J. Besl, Direct construction of polynomial surfaces from dense range images through region growing, ACM Transactions on Graphics,1995,14(2):171-200
[75] H.K. Zhao, S. Osher, B.Merriman and M. Kang, Implicit and nonparametric shape reconstruction from unorganized data using a variational level set method, Computer Vision and Image Understanding, 2000, 80,295-314
[76] Carr J. C., R. K. Beatson, J. B.Cherrie, T. J. Mitchell, W. R. Fright, B.C.McCallum, T. R. Evans, Reconstruction and Representation of 3D Objects with Radial Basis Functions, SIGGRAPH'2001,2001
[77] L. Zhou and C. Kambhamettu, Extending superquadrics with exponent functions: modeling and reconstruction, Graphical Models, 2001,63,1-20
[78] Turk G, O'Brien J. Shape Transformation Using Variational Implicit Functions.InRockwood A ed. SIGGRAPH'99 Conference Proceedings. Los Angeles:ACM Press,1999, 335-342
[79] D.E. Breen and R.T. Whitaker, A Level-Set Approach for the Metamorphosis of Solid Models, IEEE Transactions on Visualization and Computer Graphics,7(2):173-192
[80] H. Hoppe, T. DeRose, T. Duchamp, J. McDonald and W. Stuetzle, Surface reconstruction from unorganized points, Computer Graphics, 1992,26(2):71-76
[81] N. Amenta,M. Bern,M. Kamvysselis, A new Voronoi-based surface reconstruction algorithm,SIGGRAPH’98, 415-421
[82] C. Bradley, Rapid prototyping models generated from machine vision data Computers in Industry, 2001,41,159-173
[83] M.S. Floater and M. Riemers, Meshless parameterization and surface reconstruction, Computer Aided Geometric Design, 2001,18,77-92
[84] H. Hoppe, T. DeRose, T. Duchamp and M. Halstead, Piecewise smooth surface reconstruction, SIGGRAPH, 1994, 295-302
[85] H.Fuchs, Z.Kedem, etal. Optimal Surface Reconstruction from Planar Contours, Communications of the ACM, Vol. 20, 1977
[86] E. Keppel. Approximating Complex Surface by Triangulation of Contour Lines, IBM J. R&D,Vol. 19, 1975
[87] D. Meyers, S. Skinner. Surfaces from Contours, ACM Transactions on Graphics, 11(3), 1992
[88] Barequet, Gill, Daniel Shapiro, Ayellet Tal. History Consideration in Reconstructing Polyhedral Surface from Parallel Slices, Proceeding of Visualization '96, San Francisco, California,Oct. 27-Nov. 1,1996
[89] H. N.Ghristiansen, T. W.Sederberg. Conversion of Complex Contours Line Definition into Polygonal Element Mosaics, Computer Graphics, 12(2), 1978
[90] W. Schroeder, Jonathan A. Zarge, and William E. Lorensen. Decimation of triangle meshes. SIGGRAPH ’92 (26): 65-70, 1992
[91] W. Schroeder. Polygon reduction techniques. Siggraph’95, Course Notes.30 1.1-1.14, 1995
[92] Marc Soucy and Denis Laurendeau. Multiresolution surface modeling based on hierarchical triangulation. Computer Vision and Image Understanding, 63(1):1-14, 1996.
[93] Marc Soucy, Guy Godin, and Marc Rioux. A texture-mappping approach for the compression of colored 3d triangulation. The Visual Computer 1996, 12:503-514
[94] http://www.innovmetric.com
[95] C. L. Bajaj and D.R. Schikore. Error bounded reduction of triangle meshes with multivariate data. SPIE,2656:34-45, 1996.
[96] A. Ciampalini, P. Cignoni, C. Montani, and R. Scopigno. Multiresolution decimation based on global error. The Visual Computer, 13(5):228-246, June 1997
[97] R.Klein, G.Liebic, and W.Straber. Mesh Reduction with Error Control. In proceedings of Visulization’96, 1996: 311-317
[98] Klein. Multiresolution representations for surfaces meshes based on the vertex decimation method. Computer &Graphics,1998,22(1):13-26
[99] J. Cohen, A. Varshney, D. Manocha, G. Turk, H.Weber, P. Agarwal, F. Brooks, andW. Wright. Simplification envelopes. Siggraph ’96, 119-128,1996
[100] K.J. Renze and J.H. Oliver. Generalized unstructured decimation. IEEE C.G.&A., 16(6):24-32, 1996
[101] Greg Turk. Re-tiling polygonal surfaces. SIGGRAPH’92 26(55-64), July 1992
[102] J. Rossignac and P. Borrel. Multi-resolution3D approximation for rendering complex scenes. In B. Falcidieno and T.L. Kunii, editors, Geometric Modeling in Computer Graphics, 455-465
[103] http://www.research.ibm.com/3dix
[104] B. Hamann. A data reduction scheme for triangulated surfaces. Computer Aided Geometric Design,11(2):197-214, 1994
[105] M.J. De Haemer and M.J. Zyda. Simplification of objects rendered by polygonal approximations. Computers& Graphics, 15(2):175-184, 1991
[106] A.D. Kalvin, C.B. Cutting, B. Haddad, and M.E. Noz. Constructing topologically connected surfaces for the comprehensive analysis of 3D medical structures. SPIE Vol. 1445 Image Processing, 247-259, 1991
[107] A. D. Kalvin and R.H. Taylor. Superfaces: Poligonal mesh simplification with bounded error. IEEE C.G.&A.,16(3):64-77, 1996
[108] 唐泽圣.三维数据场可视化.北京:清华大学出版社,1999.12-34
[109] Hugues Hoppe, Tony DeRose, Tom Duchamp, John McDonald, and Werner Stuetzle. Mesh optimization. Siggraph ’93, 19-26, 1993
[110] 周昆.基于三角形折叠的网格简化算法. 计算机学报,1998,21(6): 506-513
[111] H. Hoppe. Progressive meshes. Siggraph’96, 99-108, 1996
[112] H.Hoppe. View-Dependent Refinement of Progressive Meshes, Computer Graphics, Siggraph ’97 189-198
[113] Hoppe. Efficient Implementation of Progressive Meshes. Technical Report, MSR-TR-98-02, 1998
[114] J. Popovic and H. Hoppe. Progressive simplicial complexes. Siggraph ’97, 217-224, 1997
[115] 陶志良,潘志庚,石教英. 支持快速恢复的可逆递进网格及其生成方法. 计算机学报,1999,5:503-507
[116] M.E. Algorri and F. Schmitt. Mesh simplification. Eurographics’96 15(3):78-86, 1996.
[117] R. Ronfard and J. Rossignac. Full-range approximation of triangulated polyhedra. Eurographics’96 ,15(3):67-76, 1996
[118] M. Reddy. Scrooge: Perceptually-driven polygon reduction. Computer Graphics Forum, 15(4):191-203,1996
[119] M Garland and P.S. Heckbert. Surface simplification using quadric error metrics Siggraph ’97 31
[120] Schmalstieg Detal. Smooth of levels of detail. IEEE Proceedings of Virtual Reality Annual International Symposium , LosAlamitos,1997.12-19
[121] M. Eck, T. De Rose, T. Duchamp, H. Hoppe, M. Lounsbery, and W. Stuetzle. Multiresolution analysis of arbitrary meshes. Siggraph ’95, 173-181, 1995
[122] A. Certain, J. Popovic, T. DeRose, T. Duchamp, D. Salesin, and W. Stuetzle. Interactive multiresolution surface viewing. Siggraph ’96, 91-98,1996
[123] C. Andujar, D. Ayala, P. Brunet, R. Joan-Arinyo, and J. Sole’. Automatic generation of multiresolutionboundary Eurographics’96 ,15(3):87-96, 1996
[124] T. He, L. Hong, A. Kaufman, A. Varshney, and S. Wang. Voxel-based object simplification. In IEEE Visualization ’95 Proceedings, pages 296–303. IEEE Comp. Soc. Press, 1995
[125] Cohen J, Olano M, Manocha D. Appearance-preserving simplification . Siggraph’98 32:115-122
[126] P. Cignoni1, C.Montani1. A general method for preserving attribute values on simplified meshes. Proceedings of the IEEE Visualization 1998,59-66
[127] M. Garland and P. Heckbert Simplifying surfaces with color and texture using quadric error metrics. Proceedings of the IEEE Visualization ,1998
[128] H.Hoppe . New quadric metric for simplifying meshes with appearance attributes. Proceedings of the IEEE Visualization ,1999
[129] Hoppe H, Pedro V. Sander. Texture-Mapping Progressive Meshes, SIGGRAPH’2001, 409-416
[130] Mann Y, Cohen D. Selective pixel transmission for navigating in remote virtual environments. Eurographics’96. 201-206
[131] P.Rigiroli et al. Computers &Graphics 25:449-461,2001
[132] 潘志庚,马小虎,石教英.虚拟环境中多细节层次模型自动生成算法. 软件学报,1996,7(9):526-531.
[133] 周晓云,刘慎权.基于特征角准则的多面体模型简化方法.计算机学报,1996,19(增刊):217-223
[134] 马小虎, 潘志庚,石教英. 基于三角形移去准则的多边体模型简化方法.计算机学报,1998,21(6):492-498
[135] 周昆潘志庚石教英. 多细节层次模型间的平滑过渡. 计算机辅助设计与图形学学报, 2000,12(6):463-467
[136] 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):481-491
[137] P. Heckbert and M. Garland. Survey of surface simplification algorithms. Technical report, Carnegie Mellon University -Dept. of Computer Science, 1997
[138] P.Cignoni1,C.Montani1.A Comparison of mesh simplification algorithms. Computer&Graphics , 22(1):33-54,1998
[2] 韩涛.激光三角法三维轮廓测量技术的研究[硕士学位论文].西安交通大学,2002
[3] 刘影,杭九全,万耀青.反求工程与现代设计.机械设计,1998,12:1-4
[4] 田晓冬,史桂蓉,阮雪榆.复杂曲面实物的逆向工程及其关键技术.机械设计与制造工程,2000,29(4):l-6
[5] 雷刚,邹昌平.快速逆向工程研究进展.机械工艺师,2000,10:32-38
[6] 王先逵.制造技术的历史回顾与面临的机遇挑战.机械工程学报,2002, 38(8):1-8
[7] 李德华,胡汉平,金刚. 从平面到立体--三维扫描技术. 计算机世界,C3,1999.7.26
[8] 金刚,周学泳,李德华. 三维扫描技术的应用. 计算机世界,C7,1999.7.26
[9] 金刚,陈振羽,宋昆. 几种三维扫描设备. 计算机世界,C12,1999.7.26
[10] 金刚,吴晓刚,李德华. 三维扫描系统中的关键技术. 计算机世界,C1,1999.7.26
[11] 金刚,李泽宇,李德华. 常用的三维信息获取技术. 计算机世界,C8,1999.7.26
[12] Will P.M., Pennington K.S., Grid coding: Preprocessing technique for robot and machine vision. Artificial Intelligence, 1971; 2(3): 319-329
[13] Will P.M., Pennington K.S., Norel technique for image processing. Proc. IEEE, 1972; 60(6): 669-680
[14] Popplestone R.J., Brown C.M., Ambler A.P., Crawford G.F., Forming models of plane and cylinder faceted bollies from light stripes. In: Proc. 4th Intern, Joint Conf. Artif. Intell. 1975: 664-668
[15] Agin G.J. Binford T.O. Computer description of curved objects. In: Proc. 3rd Intern Conf. Artif. Intell. , Stanford, CA, 1973: 629-640
[16] Potmesil M., Generating models of solid objects by matching 3D surface segments. In: Proc 8th Intern Joint Conf Artif Intell, Karlsruhe, 1983: 1089-1093
[17] Sato Y., Kitagawa H., Fujita H. Shape Measurement of Curved Objects Using Multiple Slit Ray Projections. IEEE Trans Patt Anal Mach Intell, 1982: 641-646
[18] Tio J. B. K., McPherson C.A., Hall E.L., Curved Surface Measurement for Robot Vision. Proc RPIP, 1983: 52-96
[19] Tsai R.Y., A versatile camera calibration technique for high accuracy 3D machine vision metrology using of the shelf TV cameras and lenses. IEEE J Robotics Autom, 1987; RA-3 (4): 323-344
[20] Mansbach P., Calibration of a camera and light source by fitting to a physical model. Comput Vis Graph Image Process, 1986; 35: 200-219
[21] 蒋向前,李柱,谢铁邦. 全息光栅干涉法测量曲面形貌的理论研究. 华中理工大学学报,1994,22(2):316-320
[22] 孙龙祥.深度图像分析.北京:电子工业出版社,1996.62-87
[23] 强玉俊,蒋大真,盛康龙. 工业CT 研制进展. 核物理动态,1994,11(4):214-218
[24] P.Saint-Marc, G.Medioni. Adaptive Smoothing for Feature Extraction in Proceeding of the Image Understanding workshop, 1988. 1100-1113
[25] 肖贵福.对发展坐标测量机测头的新思考.现代计量测试,1995,4:21-23
[26] 黄真,孔令富.并联机器人机构学理论及控制.北京:机械工业出版社,1997. 45-67
[27] Denavit J, Hartenberg R. A kinematic notation for lower pair mechanism based on matrices. ASME Journal of Applied Mechanics, 1955, Vol 22(6), 215-221
[28] 王福瑞.单片微机测控系统设计大全.北京:北航出版社,1999.125-138
[29] 长春第一光学仪器厂.旋转编码器手册.吉林:吉林大学出版社,2000.3-9
[30] 王化祥,张淑英.传感器原理及应用.天津:天津大学出版社,1999.21-72
[31] 陈宝林.最优化理论与算法.北京:清华大学出版社,1989.83-116
[32] 邓乃扬.无约束最优化方法.北京:科学出版社,1982.142-173
[33] 叶东,黄庆成,车仁生.多关节坐标测量机的误差模型.光学精密工程,1999,7(2):91-96
[34] 叶东,黄庆成,车仁生.多关节坐标测量机的结构参数校准.宇航计测技术,1999,9(6):12-15
[35] 叶东,黄庆成,车仁生.六自由度关节式坐标测量机关节零位偏差的标定算法.工具技术,1999,33:34-36
[36] 邹璇,李德华.多关节机械臂的坐标模型和参数标定.光学精密工程,2001, 9(3):252-256.
[37] 席少霖.非线性最优化方法. 北京:高等教育出版社, 1992. 187-212.
[38] Nirwan Ansari,Edwin Hou.用于最优化的计算智能.李军,边肇祺译. 北京:清华大学出版社,1999.141-150
[39] 焦李成.神经网络计算.西安:电子科技大学出版社,1995.32-44
[40] Hopfield.J.J.,“Neural computation of decision in optimaization problems”, Biological Cybernetics, vol.52, 1985, 141-152
[41] Hopfield.J.J.,“Neural networks and physical systems with emergent collective computational abilities”, PNAS, Vol.79, 2554-2558, 1982
[42] Hopfield.J.J.,“Neurons with graded response have collective computation properties like those of two state neurons”PNAS, Vol. 81, 3088-3092, 1984
[43] Metropolis,N.A.,A.Rosenbluth,M.Rosenbluth,A.Teller and E.Teller,“Equation of state calculations by fast computing machines”,Journal of Chemical Physics, Vol.21, 1953, 1087-1092
[44] Leong,H.W.,D.G.Wong and C.L.Liu,“A simulated annealing channel router”Proc.IEEE international Conference on Computer Aided Design,Santa Clara,CA,November 1985,226-229
[45] Tan,H.L., S.B.Gelfand and E.J.Delp,“A cost minimization approach to edge detection using simulated annealing”, IEEE Trans. On Pattern Analysis and Machine Intelligence, vol.14, no.1, January 1992, 3-18
[46] Lin, F.T.,C.Y.Kao and C.C hsu,“Applying the genetic approach to simulated annealing in solving some NP-hard problems”, IEEE Trans. On System, Man, and Cybernetics, vol.23, no.6, November 1993, 1752-1767
[47] 焦李成.进化计算与进化神经网络-计算智能的新方向.电子科技,1995,1:9-19
[48] 周明,孙淑栋.遗传算法原理及应用.北京:国防工业出版社,1999.6-24
[49] Zbiginiew Michalewicz.演化程序-遗传算法与数据编码的结合.周家驹,何险峰译.北京:科学出版社,2000.34-57
[50] 陈国良.遗传算法原理及其应用.北京:人民邮电出版社,1996. 12-28
[51] 张文修,梁怡.遗传算法的数学基础.西安:西安交通大学出版社,2000.3-9
[52] D J Weir, M J Milroy et al.Reverse engineering physical models employing wrap-around B-spline surfaces and quadrics. 'Proc Instn Mech Engrs, Part B: Journal of Engineering Manufacture,1995, 210(2): 147-157
[53] Gu P,Yan X. Neural network approach to the reconstruction of free form surfaces for reverseengineering. CAD,1995,27(1):54-64
[54] 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
[55] 马小虎等. 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):492-498
[56] Garland M et al. Surface simplification using quadric error metrics. In:ACM SIGGRAPH,Los Angeles,1997. 209-216
[57] Chen Y H, Liu C Y. Quadric surface extract ion using genetic algorithms [J]. Computer Aided Design,1999, 31 (2) : 101-110.
[58] Sapidis N, and Perucchio. Delaunary triangulation of arbitrarily shaped planar Domains, Computer Aided Geometric Design,1991,Vol.8:421-437
[59] Lai J Y,Ueng W D and YAO CY. Registration and data merging for muiltiple sets of scan data.Advances Manufacturing Technilogy,1999,Vol,15(1):54-63
[60] Tamas varady,Ralph R Martin et al. Reverse engineering of geometric models-an introduction. Computer Aided Design,1997, 29(4): 255-268.
[61] 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
[62] Marshall S J, Harrison R F. Optimization and training of 15eed forward Neural Networks byGenetic Algorithms. 2nd IEEE Int Conf on ANN,1991:34-43.
[63] 钟纲.曲线曲面重建方法研究[博士学位论文].浙江大学,2002
[64] C.L. Bajaj, F. Bernardini and G. Xu, Automatic reconstruction of surfaces and scalar fields form 3D scans, SIGGRAPH’95,109-118
[65] M. Eck and H. Hoppe,Automatic reconstruction of B-spline surfaces of arbitrary topological type,SIGGRAPH, 1996, 335-342
[66] B.Guo, Design, Surface reconstruction: from points to splines, Computer-Aided 1997, 29(4): 269-277
[67] S .Lee, G. Wolberg and S.Y. Shin, Scattered data interpolation with multilevel B-spline, IEEE Transactions on Visualization and Computer Graphics, 1997,3(3):228-244
[68] M. Yang and E. Lee, Segmentation of measured point data using a parametric quadric surface approximation, Computer-Aided Design, 1999, 31,499-457
[69] L.A. Piegl and W. Tiller, Parameterization for surface fitting in reverse engineering, Computer-Aided Design, 2001,33,593-603
[70] M.S. Floater, Meshless parameterization and B-spline surface approximation, The Mathematics of Surfaces, 2000,1-18
[71] Shigeru Muraki, Volumetric Shape Description of Range Data Using `Blobby Model’,Proceedings of SIGGRAPH 91 (Las Vegas, Nevada, Jul. 28-Aug. 2,1991). In Computer Graphics, 25, 4 (Jul. 1991) ACM SIGGRAPH, New York,1991,227-235
[72] C. Bajaj and I. Ihm, C1 smoothing of polyhedral with implicit algebraic splines. SIGGRAPH’92, 1992, 79-86
[73] C. Bajaj and I. Ihm, Algebraic surface design with Hermite interpolation.ACM Transactions on Graphics,1992, 11(1):61-91
[74] N.S .Sapidis and P.J. Besl, Direct construction of polynomial surfaces from dense range images through region growing, ACM Transactions on Graphics,1995,14(2):171-200
[75] H.K. Zhao, S. Osher, B.Merriman and M. Kang, Implicit and nonparametric shape reconstruction from unorganized data using a variational level set method, Computer Vision and Image Understanding, 2000, 80,295-314
[76] Carr J. C., R. K. Beatson, J. B.Cherrie, T. J. Mitchell, W. R. Fright, B.C.McCallum, T. R. Evans, Reconstruction and Representation of 3D Objects with Radial Basis Functions, SIGGRAPH'2001,2001
[77] L. Zhou and C. Kambhamettu, Extending superquadrics with exponent functions: modeling and reconstruction, Graphical Models, 2001,63,1-20
[78] Turk G, O'Brien J. Shape Transformation Using Variational Implicit Functions.InRockwood A ed. SIGGRAPH'99 Conference Proceedings. Los Angeles:ACM Press,1999, 335-342
[79] D.E. Breen and R.T. Whitaker, A Level-Set Approach for the Metamorphosis of Solid Models, IEEE Transactions on Visualization and Computer Graphics,7(2):173-192
[80] H. Hoppe, T. DeRose, T. Duchamp, J. McDonald and W. Stuetzle, Surface reconstruction from unorganized points, Computer Graphics, 1992,26(2):71-76
[81] N. Amenta,M. Bern,M. Kamvysselis, A new Voronoi-based surface reconstruction algorithm,SIGGRAPH’98, 415-421
[82] C. Bradley, Rapid prototyping models generated from machine vision data Computers in Industry, 2001,41,159-173
[83] M.S. Floater and M. Riemers, Meshless parameterization and surface reconstruction, Computer Aided Geometric Design, 2001,18,77-92
[84] H. Hoppe, T. DeRose, T. Duchamp and M. Halstead, Piecewise smooth surface reconstruction, SIGGRAPH, 1994, 295-302
[85] H.Fuchs, Z.Kedem, etal. Optimal Surface Reconstruction from Planar Contours, Communications of the ACM, Vol. 20, 1977
[86] E. Keppel. Approximating Complex Surface by Triangulation of Contour Lines, IBM J. R&D,Vol. 19, 1975
[87] D. Meyers, S. Skinner. Surfaces from Contours, ACM Transactions on Graphics, 11(3), 1992
[88] Barequet, Gill, Daniel Shapiro, Ayellet Tal. History Consideration in Reconstructing Polyhedral Surface from Parallel Slices, Proceeding of Visualization '96, San Francisco, California,Oct. 27-Nov. 1,1996
[89] H. N.Ghristiansen, T. W.Sederberg. Conversion of Complex Contours Line Definition into Polygonal Element Mosaics, Computer Graphics, 12(2), 1978
[90] W. Schroeder, Jonathan A. Zarge, and William E. Lorensen. Decimation of triangle meshes. SIGGRAPH ’92 (26): 65-70, 1992
[91] W. Schroeder. Polygon reduction techniques. Siggraph’95, Course Notes.30 1.1-1.14, 1995
[92] Marc Soucy and Denis Laurendeau. Multiresolution surface modeling based on hierarchical triangulation. Computer Vision and Image Understanding, 63(1):1-14, 1996.
[93] Marc Soucy, Guy Godin, and Marc Rioux. A texture-mappping approach for the compression of colored 3d triangulation. The Visual Computer 1996, 12:503-514
[94] http://www.innovmetric.com
[95] C. L. Bajaj and D.R. Schikore. Error bounded reduction of triangle meshes with multivariate data. SPIE,2656:34-45, 1996.
[96] A. Ciampalini, P. Cignoni, C. Montani, and R. Scopigno. Multiresolution decimation based on global error. The Visual Computer, 13(5):228-246, June 1997
[97] R.Klein, G.Liebic, and W.Straber. Mesh Reduction with Error Control. In proceedings of Visulization’96, 1996: 311-317
[98] Klein. Multiresolution representations for surfaces meshes based on the vertex decimation method. Computer &Graphics,1998,22(1):13-26
[99] J. Cohen, A. Varshney, D. Manocha, G. Turk, H.Weber, P. Agarwal, F. Brooks, andW. Wright. Simplification envelopes. Siggraph ’96, 119-128,1996
[100] K.J. Renze and J.H. Oliver. Generalized unstructured decimation. IEEE C.G.&A., 16(6):24-32, 1996
[101] Greg Turk. Re-tiling polygonal surfaces. SIGGRAPH’92 26(55-64), July 1992
[102] J. Rossignac and P. Borrel. Multi-resolution3D approximation for rendering complex scenes. In B. Falcidieno and T.L. Kunii, editors, Geometric Modeling in Computer Graphics, 455-465
[103] http://www.research.ibm.com/3dix
[104] B. Hamann. A data reduction scheme for triangulated surfaces. Computer Aided Geometric Design,11(2):197-214, 1994
[105] M.J. De Haemer and M.J. Zyda. Simplification of objects rendered by polygonal approximations. Computers& Graphics, 15(2):175-184, 1991
[106] A.D. Kalvin, C.B. Cutting, B. Haddad, and M.E. Noz. Constructing topologically connected surfaces for the comprehensive analysis of 3D medical structures. SPIE Vol. 1445 Image Processing, 247-259, 1991
[107] A. D. Kalvin and R.H. Taylor. Superfaces: Poligonal mesh simplification with bounded error. IEEE C.G.&A.,16(3):64-77, 1996
[108] 唐泽圣.三维数据场可视化.北京:清华大学出版社,1999.12-34
[109] Hugues Hoppe, Tony DeRose, Tom Duchamp, John McDonald, and Werner Stuetzle. Mesh optimization. Siggraph ’93, 19-26, 1993
[110] 周昆.基于三角形折叠的网格简化算法. 计算机学报,1998,21(6): 506-513
[111] H. Hoppe. Progressive meshes. Siggraph’96, 99-108, 1996
[112] H.Hoppe. View-Dependent Refinement of Progressive Meshes, Computer Graphics, Siggraph ’97 189-198
[113] Hoppe. Efficient Implementation of Progressive Meshes. Technical Report, MSR-TR-98-02, 1998
[114] J. Popovic and H. Hoppe. Progressive simplicial complexes. Siggraph ’97, 217-224, 1997
[115] 陶志良,潘志庚,石教英. 支持快速恢复的可逆递进网格及其生成方法. 计算机学报,1999,5:503-507
[116] M.E. Algorri and F. Schmitt. Mesh simplification. Eurographics’96 15(3):78-86, 1996.
[117] R. Ronfard and J. Rossignac. Full-range approximation of triangulated polyhedra. Eurographics’96 ,15(3):67-76, 1996
[118] M. Reddy. Scrooge: Perceptually-driven polygon reduction. Computer Graphics Forum, 15(4):191-203,1996
[119] M Garland and P.S. Heckbert. Surface simplification using quadric error metrics Siggraph ’97 31
[120] Schmalstieg Detal. Smooth of levels of detail. IEEE Proceedings of Virtual Reality Annual International Symposium , LosAlamitos,1997.12-19
[121] M. Eck, T. De Rose, T. Duchamp, H. Hoppe, M. Lounsbery, and W. Stuetzle. Multiresolution analysis of arbitrary meshes. Siggraph ’95, 173-181, 1995
[122] A. Certain, J. Popovic, T. DeRose, T. Duchamp, D. Salesin, and W. Stuetzle. Interactive multiresolution surface viewing. Siggraph ’96, 91-98,1996
[123] C. Andujar, D. Ayala, P. Brunet, R. Joan-Arinyo, and J. Sole’. Automatic generation of multiresolutionboundary Eurographics’96 ,15(3):87-96, 1996
[124] T. He, L. Hong, A. Kaufman, A. Varshney, and S. Wang. Voxel-based object simplification. In IEEE Visualization ’95 Proceedings, pages 296–303. IEEE Comp. Soc. Press, 1995
[125] Cohen J, Olano M, Manocha D. Appearance-preserving simplification . Siggraph’98 32:115-122
[126] P. Cignoni1, C.Montani1. A general method for preserving attribute values on simplified meshes. Proceedings of the IEEE Visualization 1998,59-66
[127] M. Garland and P. Heckbert Simplifying surfaces with color and texture using quadric error metrics. Proceedings of the IEEE Visualization ,1998
[128] H.Hoppe . New quadric metric for simplifying meshes with appearance attributes. Proceedings of the IEEE Visualization ,1999
[129] Hoppe H, Pedro V. Sander. Texture-Mapping Progressive Meshes, SIGGRAPH’2001, 409-416
[130] Mann Y, Cohen D. Selective pixel transmission for navigating in remote virtual environments. Eurographics’96. 201-206
[131] P.Rigiroli et al. Computers &Graphics 25:449-461,2001
[132] 潘志庚,马小虎,石教英.虚拟环境中多细节层次模型自动生成算法. 软件学报,1996,7(9):526-531.
[133] 周晓云,刘慎权.基于特征角准则的多面体模型简化方法.计算机学报,1996,19(增刊):217-223
[134] 马小虎, 潘志庚,石教英. 基于三角形移去准则的多边体模型简化方法.计算机学报,1998,21(6):492-498
[135] 周昆潘志庚石教英. 多细节层次模型间的平滑过渡. 计算机辅助设计与图形学学报, 2000,12(6):463-467
[136] 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):481-491
[137] P. Heckbert and M. Garland. Survey of surface simplification algorithms. Technical report, Carnegie Mellon University -Dept. of Computer Science, 1997
[138] P.Cignoni1,C.Montani1.A Comparison of mesh simplification algorithms. Computer&Graphics , 22(1):33-54,1998