基于平面轮廓的实体模型重建
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摘要
随着全球化竞争的日益激烈和买方市场的迅速形成，制造业的快速产品创新设计能力已成为决定企业兴衰成败的首要因素。逆向工程技术作为实现快速创新设计的重要途径，已经受到越来越多的关注。
基于约束的结构类零件特征模型重建是逆向工程中一个新的研究方向，具有很强的理论意义和实用价值。当前主流的3D CAD软件如CATIA、Pro/Engineer等在实体建模时主要是基于草图设计的。本文在特征数据分割的基础上，结合正向设计的思路，着重研究结构件中的拉伸、旋转等基于草图的特征模型重建问题。本文研究的主要内容如下：
1) 根据平面轮廓数据点处的近似曲率变化识别出特征点，并确定特征点类型；
2) 利用“非均匀原点距离法”对二维数据点精减；
3) 采用“正负偏差累加法”判断各段数据点确定的曲线类型，基于约束对分段的平面轮廓曲线进行整体拟合；
4) 研究并推导无约束直线段和圆弧段的拟合方法及有约束圆弧段的拟合方法；
5) 结合Pro/ENGINEERING的逆向工程专用模块，实现了旋转实体、拉伸实体及从文件混合高级曲面模型的生成。
With the forming of the buyers' market, the trend of global competition has been intensified much more than before. The ability of developing new product rapidly for manufacturing enterprise already becomes the chief factor, which determines the enterprise's fortune. As an important approach of rapid creative design, Reverse Engineering has got more attention.
The research on constraints based structural feature model reconstruction method is a new aspect in reversing engineering, which can be used to reconstruct more reliable model. Modeling in current 3D CAD software such as CATIA、pro/Engineer are mainly based on sketch design. According to the idea of modeling and on the basis of segmenting 3D data with feature design intention, this thesis studies the reconstruction methods of model sketch-based feature such as extruded and rotational features in structural part models. The main contents of this thesis are as follows:
1) According to the approximate curvature of each contour point, the feature points are recognized from the point-data; the styles of them are confirmed.
2) The unsymmetrical origin-distance approach is adopted to reduce the 2D point-data.
3) After confirming the segments types (line or circle) we call that approach as "Sign Error Accumulative Total". The contour is globally constructed through determining the constraints with the neighbor segments.
4) Studying and deducing the reconstruction methods of unconstraint beeline segments, unconstraint circle segments, and constraint circle segments.
Applying the reverse engineering tools of Pro/ENGINEERING to realize model generation of the rotational entity, extruded entity, and advanced surface of Blend from File.
基于约束的结构类零件特征模型重建是逆向工程中一个新的研究方向，具有很强的理论意义和实用价值。当前主流的3D CAD软件如CATIA、Pro/Engineer等在实体建模时主要是基于草图设计的。本文在特征数据分割的基础上，结合正向设计的思路，着重研究结构件中的拉伸、旋转等基于草图的特征模型重建问题。本文研究的主要内容如下：
1) 根据平面轮廓数据点处的近似曲率变化识别出特征点，并确定特征点类型；
2) 利用“非均匀原点距离法”对二维数据点精减；
3) 采用“正负偏差累加法”判断各段数据点确定的曲线类型，基于约束对分段的平面轮廓曲线进行整体拟合；
4) 研究并推导无约束直线段和圆弧段的拟合方法及有约束圆弧段的拟合方法；
5) 结合Pro/ENGINEERING的逆向工程专用模块，实现了旋转实体、拉伸实体及从文件混合高级曲面模型的生成。
With the forming of the buyers' market, the trend of global competition has been intensified much more than before. The ability of developing new product rapidly for manufacturing enterprise already becomes the chief factor, which determines the enterprise's fortune. As an important approach of rapid creative design, Reverse Engineering has got more attention.
The research on constraints based structural feature model reconstruction method is a new aspect in reversing engineering, which can be used to reconstruct more reliable model. Modeling in current 3D CAD software such as CATIA、pro/Engineer are mainly based on sketch design. According to the idea of modeling and on the basis of segmenting 3D data with feature design intention, this thesis studies the reconstruction methods of model sketch-based feature such as extruded and rotational features in structural part models. The main contents of this thesis are as follows:
1) According to the approximate curvature of each contour point, the feature points are recognized from the point-data; the styles of them are confirmed.
2) The unsymmetrical origin-distance approach is adopted to reduce the 2D point-data.
3) After confirming the segments types (line or circle) we call that approach as "Sign Error Accumulative Total". The contour is globally constructed through determining the constraints with the neighbor segments.
4) Studying and deducing the reconstruction methods of unconstraint beeline segments, unconstraint circle segments, and constraint circle segments.
Applying the reverse engineering tools of Pro/ENGINEERING to realize model generation of the rotational entity, extruded entity, and advanced surface of Blend from File.
引文
[1] 陈贤杰等．RP&M技术在中国的发展．国家生产力促进中心网，2001．
[2] 刘之生．反求工程技术．北京：机械工业出版社，1996．
[3] Tamas Varady, RalPh R Martin, Jordan Cox. Reverse engineering of geometric models-an introduction Computer-Aided Design. 1997, 29(4): 255～268.
[4] Alain Bemard. Reverse engineering for rapid product development: a state of the art. SPIE: 1999: 3835: 5～63.
[5] 刘利．三维测量技术新动态．机电一体化，1997，1：20～23．
[6] Wohler T. 3D digitizing for engineering. Computer Graphics World, 1995, 18(2): S1-S2.
[7] Jarvis R A. A Perspective on range finding techniques for computer vision, IEEE Transactions on Pattern Analysis and Machine Intelligence, 1983, 5(2): 122～119.
[8] 王广等．数据采集与处理．2001，16(21)：235-238．
[9] Butler C. Investigation into the Performance of probes on coordinate measuring machines. Industrial Metrology. 1991, 2(1): 59～70.
[10] Digitrek user manual-version 3.1. Italy Coord3 Company, 1999.
[11] Halioua M, Liu H C. Optical Three-dimensional Sensing by Phase Measuring Profilemetry. Optics and Laser in Engineering, 1989, 11(3): 185～215.
[12] Takeda M, Mutoh K, Fourier. Transform Profilemetry for the Automatic Measurement of 3D Object Shapes. APPI. Opt, 1983, 22: 3977～39820.
[13] Toyooka S, lwaasa Y., Automatic Profilemetry of 3D Difftlse Objects by Spatial Phase Detection. APPI. Opt, 1986, 25: 1630～1633.
[14] Jacques Lewandowski, Bruno Menard, Daniel Hennequin, Ligh. Sectioning with Large Depth of Focus by Means of Fresnel Diffraction of an Edge. Optical Engineering, 1993, 32(9): 2181～2184.
[15] 王晓林等．光切法三维轮廓测量的原理及其应用．光学技术，1992，2：39～43．
[16] K Kobayashi, K Akiyama, et al. Laser-scanning imaging system for real-time measurement of 3D object problem. Optics Communications, 1989, 74(4): 165～170.
[17] 张舜德．面向快速原型制造的反求工程若干关键技术研究：[博士学位论文]．西安：西安交通大学，2001．
[18] 王广等．数据采集与处理．2001，16(21)：235-238．
[19] 周剑等．层析三维数字化测量原理及层析图象边缘精度分析与标定．西安交通大学学报，1999，33(7)：84～88．
[20] 唐朝伟等．三维曲面激光精密测量技术．计量学报，1995，15(2)：99～103．
[21] 张畅等．快速造形技术中的反求工程．中国机械工程，1997，第8卷第5期：60～62．
[22] 孙立建等．反求技术在RPM中的应用．河北工业大学学报，1999，第28卷第6期：22～24．
[23] 苏海等．昆明理工大学学报．2001，第26卷第4期：68～71．
[24] 滕功勇等．新技术新工艺，2002，1：26～27．
[25] Honghin Zha, et al. Surface Reconstruction in Overlapping Range Images for Generating Close-Surface 3-D Object models. Proceedings of the 1998 IEEE International Conference on Systems, Man and Cybernetics, 4530～4535.
[26] 李江雄．复杂曲面反求工程CAD建模系统和技术研究：[博士学位论文]．杭州：浙江大学，1998．
[27] 贾彦君．反求工程CAD建模系统RE-SOFT中高级几何处理与多视拼合技术研究．[硕士学位论文]．杭州： 浙江大学，2001．
[28] Xunnan Yang, Guozhao Wang. Planar point set fairing and fitting by arc splines. Computer-Aided Design, 2001, 33: 35～43.
[29] G H Liu, Y 5 Wong, Y F Zhang, H T Loh. Adaptive fairing of digitized point data with discrete curvature. Computer-Aided Design, 2002, 34: 309～320.
[30] S Karbacher, G Hausler. A new approach for modeling and smoothing of scattered 3D data. SPIE, 1998, 3313: 168～177.
[31] S Karbacher, X Laboureux, N Schon, G Hausler. Processing Range Data for Reverse Engineering and Virtual Reality. In: Proceedings of Third International Conference on 3D Digital Imaging and Modeling, 2001, 314 321.
[32] Rudiger Dillmann, Stefan Vogt, Andreas Zilker. Data Reduction for Optical 3D-Inspection in Automotive Application. Proceeding of IEEE International Conference on Multisensor Fusion and Integrationfor Intelligent Systems, TaiPei, Taiwan: August 1999.
[33] K H Lee, H Woo, T Suk. Data Reduction Methods for Reverse Engineering. International Journal of Advanced Manufacturing Technology, 2001, 17: 735～743.
[34] K H Lee, H Woo, T Suk. Point Data Reduction Using 3D Grids. International Journal of Advanced Manufacturing Technology, 2001, 18: 201～210.
[35] M Yang, E Lee. Segmentation of measured point data using a parametric quadric surface approximation. Computer-Aided Design, 1999, 31 : 449～457.
[36] M J Milroy, C Bradley, G W Vickers. Segmentation of a wrap-around model using an active contour. Computer-Aided Design, 1997, 29(4): 299～320.
[37] Paul J Besl, Ramesh C Jain. Segmentation Through Variable-Order Surface Fitting. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1988, 10(2): 167～192.
[38] Andrew W Fitzgibbon, David W Eggert, Robert B Fisher. High-level CAD model acquisition from range images. Computer-Aided Design, 1997, 29(4): 321～330.
[39] Gosh, Pal N, Pal S. Image Segmentation using Neural Networks. Biological Cybernetics,1991,66: 151～158.
[40] Chen C, Tsao E, Lin W. Medical Image Segmentation by a Constraint Satisfaction Neural Networks. IEEE Transactions on Nuclear Science, 1991, 38: 678～686.
[41] Yokoya N, Levine M. Range Image Segmentation Based on Differential Geometry:hybrid approach. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1989,11: 643～694.
[42] Abdalla Alrashdan, Saeid Motavalli, Behrooz Fallahi. Automatic segmentation of digitized data for reverse engineering applications. IIE Transactions, 2000, 320: 59～69.
[43] Weiyin Ma, J P Kruth. Parameterization of randomly measured points for least squares fitting of B-spline curves and surfaces. Computer-Aided Design, 1995, 27(9): 663～675.
[44] M J Milroy, C Bradle, G W vickers, D J weir. G1 continuity of B-spline surface patches in reverse engineering. Computer-Aided Design, 1995, 27(6): 471～478.
[45] Piegl L A, Tiller W. Surface approximation to scanned data. The Visual Computer, 2000,6: 386～395.
[46] Lin C Y, Liou C S, Lai J Y. A surface-lofting approach for smooth-surface reconstruction from 3D measurement data. Computers In Indust, 1997, 34(1): 73-85.
[47] Kruth J P, Kerstens A. Reverse engineering modeling of free-form surfaces from Point clouds subject to boundary conditions.Joumal of Materials Processing Technology, 1998,76: 120-127.
[48] Lai J Y, Ueng W D. G2 continuity for multiple surfaces fitting. The International Journal of Advanced Manufacturing Technology, 2001, 17: 575～585.
[49] Choi B K. Surface Modeling for CAD/CAM. New York: Elsevier Science Publishers,1991.
[50] Hoppe H, DeRose T, Duchanmp T, et al. Mesh Optimization. SIGRAPH-Computer Graphics Proceeding, Annual conference Series, 1993: 19～26.
[51] Hoppe H. Generate of 3D geometric models from unstructured 3D points. SPIE, 1995,2410: 424～431.
[52] Hoppe H, DeRose T, Cuchamp T, et al. Surface Reconstruction from Unorganized Points.Computer Graphics, 1992, 26(2): 71～78.
[53] Hoppe H. Progressive Meshes. Computer Graphics Proceedings, Annual Conference Series. 1996: 99～108.
[54] 柯映林．离散数据几何造型技术及其应用研究：[博士学位论文]．南京：南京航空航天大学，1992．
[55] 孙家广等．计算机图形学(第三版)．北京： 清华大学出版社，1998．
[56] Imageware软件介绍．http://www.plmsolutions-eds.com.
[57] Paraform软件介绍．http：//www.paraform.com.
[58] CopyCAD软件介绍．http://www.delcam.com.cn.
[59] Strim软件曲面重建技术与逆向工程．计算机辅助设计与制造，1996，7：30．
[60] ICEM Surf软件介绍．http//www.icem.com.
[61] 姜元庆，刘配军等．UG／Imageware逆向工程培训教程．北京：清华大学出版社，2003．
[62] RE-SOFT软件介绍．http://www.super-re.com.
[63] 反求工程软件RE-SOFT5．O用户手册．浙江大学，2002，4．
[64] http: //www.fzu.edu.cn/h58/corrdinat measuring.htm.
[65] http: //www.zhizhou.com/sm3.htm.
[66] Lee KH, Woo H, Suk T. Data reduction methods for reverse engineering. International Journal of Advanced Manufacturing Technology, 2001, 17(10): 735～743.
[67] 张丽艳．逆向工程中模型重建关键技术研究： [学位论文]．南京：南京航空航天大学博士学位论文，2001．
[68] Hsin-Teng sheu, Wu-chih Hu. Muliprimitive Segmentation of Planar Cruve-A Two-Level Breakpoint Classification and Tuning Approach. IEEE Trans. Pattern Analysis and Machine Intelligence, 1999, 21: 791～797.
[69] Q.M. Wu, M.G Rodd. Boundary Segmentation and Parameter Estimation for Industrial Inspection. Proc, IEEE Computers and Digital Techniques, 1999, 137:319～327.
[70] HSIN-TENG SHEU, WU. A Rotationally Invariant Two-Phase Scheme for Corner Detection. Pattern Recognition, 1996, 29: 819～828.
[71] H sin, Teng Sheu, Wu Chih Hu. Multiprimitive segmentation of planar curves--A two-level breakpoint classification and tuning approach[J]」 .IEEE Transactions on Pattern Analysis and Machine Intelligence, 1999, 21(8): 791～797.
[72] 武仲科等．一种线段和圆弧的逼近方法及其在工程图矢量化中的应用[J]．计算机辅助设计与图形学学报，1998，10(4)： 328～332．
[73] 谢红．基于ICT的CAD建模技术研究[D]．西安：西北工业大学，1997．
[2] 刘之生．反求工程技术．北京：机械工业出版社，1996．
[3] Tamas Varady, RalPh R Martin, Jordan Cox. Reverse engineering of geometric models-an introduction Computer-Aided Design. 1997, 29(4): 255～268.
[4] Alain Bemard. Reverse engineering for rapid product development: a state of the art. SPIE: 1999: 3835: 5～63.
[5] 刘利．三维测量技术新动态．机电一体化，1997，1：20～23．
[6] Wohler T. 3D digitizing for engineering. Computer Graphics World, 1995, 18(2): S1-S2.
[7] Jarvis R A. A Perspective on range finding techniques for computer vision, IEEE Transactions on Pattern Analysis and Machine Intelligence, 1983, 5(2): 122～119.
[8] 王广等．数据采集与处理．2001，16(21)：235-238．
[9] Butler C. Investigation into the Performance of probes on coordinate measuring machines. Industrial Metrology. 1991, 2(1): 59～70.
[10] Digitrek user manual-version 3.1. Italy Coord3 Company, 1999.
[11] Halioua M, Liu H C. Optical Three-dimensional Sensing by Phase Measuring Profilemetry. Optics and Laser in Engineering, 1989, 11(3): 185～215.
[12] Takeda M, Mutoh K, Fourier. Transform Profilemetry for the Automatic Measurement of 3D Object Shapes. APPI. Opt, 1983, 22: 3977～39820.
[13] Toyooka S, lwaasa Y., Automatic Profilemetry of 3D Difftlse Objects by Spatial Phase Detection. APPI. Opt, 1986, 25: 1630～1633.
[14] Jacques Lewandowski, Bruno Menard, Daniel Hennequin, Ligh. Sectioning with Large Depth of Focus by Means of Fresnel Diffraction of an Edge. Optical Engineering, 1993, 32(9): 2181～2184.
[15] 王晓林等．光切法三维轮廓测量的原理及其应用．光学技术，1992，2：39～43．
[16] K Kobayashi, K Akiyama, et al. Laser-scanning imaging system for real-time measurement of 3D object problem. Optics Communications, 1989, 74(4): 165～170.
[17] 张舜德．面向快速原型制造的反求工程若干关键技术研究：[博士学位论文]．西安：西安交通大学，2001．
[18] 王广等．数据采集与处理．2001，16(21)：235-238．
[19] 周剑等．层析三维数字化测量原理及层析图象边缘精度分析与标定．西安交通大学学报，1999，33(7)：84～88．
[20] 唐朝伟等．三维曲面激光精密测量技术．计量学报，1995，15(2)：99～103．
[21] 张畅等．快速造形技术中的反求工程．中国机械工程，1997，第8卷第5期：60～62．
[22] 孙立建等．反求技术在RPM中的应用．河北工业大学学报，1999，第28卷第6期：22～24．
[23] 苏海等．昆明理工大学学报．2001，第26卷第4期：68～71．
[24] 滕功勇等．新技术新工艺，2002，1：26～27．
[25] Honghin Zha, et al. Surface Reconstruction in Overlapping Range Images for Generating Close-Surface 3-D Object models. Proceedings of the 1998 IEEE International Conference on Systems, Man and Cybernetics, 4530～4535.
[26] 李江雄．复杂曲面反求工程CAD建模系统和技术研究：[博士学位论文]．杭州：浙江大学，1998．
[27] 贾彦君．反求工程CAD建模系统RE-SOFT中高级几何处理与多视拼合技术研究．[硕士学位论文]．杭州： 浙江大学，2001．
[28] Xunnan Yang, Guozhao Wang. Planar point set fairing and fitting by arc splines. Computer-Aided Design, 2001, 33: 35～43.
[29] G H Liu, Y 5 Wong, Y F Zhang, H T Loh. Adaptive fairing of digitized point data with discrete curvature. Computer-Aided Design, 2002, 34: 309～320.
[30] S Karbacher, G Hausler. A new approach for modeling and smoothing of scattered 3D data. SPIE, 1998, 3313: 168～177.
[31] S Karbacher, X Laboureux, N Schon, G Hausler. Processing Range Data for Reverse Engineering and Virtual Reality. In: Proceedings of Third International Conference on 3D Digital Imaging and Modeling, 2001, 314 321.
[32] Rudiger Dillmann, Stefan Vogt, Andreas Zilker. Data Reduction for Optical 3D-Inspection in Automotive Application. Proceeding of IEEE International Conference on Multisensor Fusion and Integrationfor Intelligent Systems, TaiPei, Taiwan: August 1999.
[33] K H Lee, H Woo, T Suk. Data Reduction Methods for Reverse Engineering. International Journal of Advanced Manufacturing Technology, 2001, 17: 735～743.
[34] K H Lee, H Woo, T Suk. Point Data Reduction Using 3D Grids. International Journal of Advanced Manufacturing Technology, 2001, 18: 201～210.
[35] M Yang, E Lee. Segmentation of measured point data using a parametric quadric surface approximation. Computer-Aided Design, 1999, 31 : 449～457.
[36] M J Milroy, C Bradley, G W Vickers. Segmentation of a wrap-around model using an active contour. Computer-Aided Design, 1997, 29(4): 299～320.
[37] Paul J Besl, Ramesh C Jain. Segmentation Through Variable-Order Surface Fitting. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1988, 10(2): 167～192.
[38] Andrew W Fitzgibbon, David W Eggert, Robert B Fisher. High-level CAD model acquisition from range images. Computer-Aided Design, 1997, 29(4): 321～330.
[39] Gosh, Pal N, Pal S. Image Segmentation using Neural Networks. Biological Cybernetics,1991,66: 151～158.
[40] Chen C, Tsao E, Lin W. Medical Image Segmentation by a Constraint Satisfaction Neural Networks. IEEE Transactions on Nuclear Science, 1991, 38: 678～686.
[41] Yokoya N, Levine M. Range Image Segmentation Based on Differential Geometry:hybrid approach. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1989,11: 643～694.
[42] Abdalla Alrashdan, Saeid Motavalli, Behrooz Fallahi. Automatic segmentation of digitized data for reverse engineering applications. IIE Transactions, 2000, 320: 59～69.
[43] Weiyin Ma, J P Kruth. Parameterization of randomly measured points for least squares fitting of B-spline curves and surfaces. Computer-Aided Design, 1995, 27(9): 663～675.
[44] M J Milroy, C Bradle, G W vickers, D J weir. G1 continuity of B-spline surface patches in reverse engineering. Computer-Aided Design, 1995, 27(6): 471～478.
[45] Piegl L A, Tiller W. Surface approximation to scanned data. The Visual Computer, 2000,6: 386～395.
[46] Lin C Y, Liou C S, Lai J Y. A surface-lofting approach for smooth-surface reconstruction from 3D measurement data. Computers In Indust, 1997, 34(1): 73-85.
[47] Kruth J P, Kerstens A. Reverse engineering modeling of free-form surfaces from Point clouds subject to boundary conditions.Joumal of Materials Processing Technology, 1998,76: 120-127.
[48] Lai J Y, Ueng W D. G2 continuity for multiple surfaces fitting. The International Journal of Advanced Manufacturing Technology, 2001, 17: 575～585.
[49] Choi B K. Surface Modeling for CAD/CAM. New York: Elsevier Science Publishers,1991.
[50] Hoppe H, DeRose T, Duchanmp T, et al. Mesh Optimization. SIGRAPH-Computer Graphics Proceeding, Annual conference Series, 1993: 19～26.
[51] Hoppe H. Generate of 3D geometric models from unstructured 3D points. SPIE, 1995,2410: 424～431.
[52] Hoppe H, DeRose T, Cuchamp T, et al. Surface Reconstruction from Unorganized Points.Computer Graphics, 1992, 26(2): 71～78.
[53] Hoppe H. Progressive Meshes. Computer Graphics Proceedings, Annual Conference Series. 1996: 99～108.
[54] 柯映林．离散数据几何造型技术及其应用研究：[博士学位论文]．南京：南京航空航天大学，1992．
[55] 孙家广等．计算机图形学(第三版)．北京： 清华大学出版社，1998．
[56] Imageware软件介绍．http://www.plmsolutions-eds.com.
[57] Paraform软件介绍．http：//www.paraform.com.
[58] CopyCAD软件介绍．http://www.delcam.com.cn.
[59] Strim软件曲面重建技术与逆向工程．计算机辅助设计与制造，1996，7：30．
[60] ICEM Surf软件介绍．http//www.icem.com.
[61] 姜元庆，刘配军等．UG／Imageware逆向工程培训教程．北京：清华大学出版社，2003．
[62] RE-SOFT软件介绍．http://www.super-re.com.
[63] 反求工程软件RE-SOFT5．O用户手册．浙江大学，2002，4．
[64] http: //www.fzu.edu.cn/h58/corrdinat measuring.htm.
[65] http: //www.zhizhou.com/sm3.htm.
[66] Lee KH, Woo H, Suk T. Data reduction methods for reverse engineering. International Journal of Advanced Manufacturing Technology, 2001, 17(10): 735～743.
[67] 张丽艳．逆向工程中模型重建关键技术研究： [学位论文]．南京：南京航空航天大学博士学位论文，2001．
[68] Hsin-Teng sheu, Wu-chih Hu. Muliprimitive Segmentation of Planar Cruve-A Two-Level Breakpoint Classification and Tuning Approach. IEEE Trans. Pattern Analysis and Machine Intelligence, 1999, 21: 791～797.
[69] Q.M. Wu, M.G Rodd. Boundary Segmentation and Parameter Estimation for Industrial Inspection. Proc, IEEE Computers and Digital Techniques, 1999, 137:319～327.
[70] HSIN-TENG SHEU, WU. A Rotationally Invariant Two-Phase Scheme for Corner Detection. Pattern Recognition, 1996, 29: 819～828.
[71] H sin, Teng Sheu, Wu Chih Hu. Multiprimitive segmentation of planar curves--A two-level breakpoint classification and tuning approach[J]」 .IEEE Transactions on Pattern Analysis and Machine Intelligence, 1999, 21(8): 791～797.
[72] 武仲科等．一种线段和圆弧的逼近方法及其在工程图矢量化中的应用[J]．计算机辅助设计与图形学学报，1998，10(4)： 328～332．
[73] 谢红．基于ICT的CAD建模技术研究[D]．西安：西北工业大学，1997．
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