反求工程曲面重构技术研究
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摘要
目前，激烈的市场竞争使产品更新换代频繁，要求企业做出快速反应。工业产品中自由曲线曲面设计由于三视图表达不清而难以进行CAD建模。利用反求工程技术，可以有效缩短产品开发时间，提高市场竞争力，解决CAD建模中的难题。本文在全面分析国内外反求工程领域研究现状的基础上，把反求工程CAD建模中三维表面重构作为研究重点，并对三维重构中交互建模进行了深入研究。
本文提出网格法进行三维散乱点曲面重构，并对网格法中的网格规划问题提出统筹规划的方法。网格线的构建采用低次、少控制点的方法，使生成的曲面简洁光顺。网格骨架线间以及骨架线与曲面间至少要施加一阶连续性约束，实现曲面间光滑过渡。对散乱点曲面拟合分为两种基本类型：由点直接生成面以及由点—线—面的方式生成面，并对各类型曲面拟合的特点及适用场合进行了归纳总结。
对曲面重构中的曲面拼接，提出实现光顺拼接的关键因素是曲面边界的选择及曲面变化趋势，并给出如何确定边界和怎样判断曲面变化趋势的检测手段。对曲面拟合及拼接的数学方法进行了初步探讨，尝试如何对曲线、曲面的控制点、节点向量以及次数进行优化。
对工程中的渐消面、三边域曲面以及Y型曲面等特殊形状的曲面重构给出了解决方案，对蒙皮法中出现的曲面畸变现象进行了具体分析，并通过边界规范化、数据延拓以及曲面裁剪几个步骤使曲面畸变得到控制。
最后，本文将所述三维重构方法应用于“佳宝”汽车外形改型设计，经过再设计实现创新，取得工程应用的较好效果。
Presently, the drastic competitiveness in market, which make the products life cycles shorter and shorter, requires rapidly responding for enterprise. In industry design, the free-form shapes cannot be properly described in 3-D views so that the CAD models cannot be created. But reverse engineering (RE) technology can shorter the product development time, improve competitiveness, and overcome the special difficulties in industry design for free-form shapes. Based on the full analysis of the fields of the present research on the reverse engineering with home and foreign documents this paper take 3-D surface reconstruction for the key and crucial technology of CAD modelling of RE and accordingly do some in-depth research about interactive modelling of 3-D surface reconstruction.
In this paper, the network method of surface reconstruction, in which how to program the framework line, is proposed. The framework line should created in lower degree and a small number of control points so that the created surfaces from them are smoothness. It should be throw G1 continuity at least between framework lines in order to realize fairness connection. For the random scatter point's surface fitting this paper classified it as two types: surface approximated directly from point clouds and surface interpolated from curves that created from selected points, and further more how to perform surface reconstruction by each kind of surface fitting method and in which situation it should be used are outlined.
A new method of surfaces connection is introduced, and the key factor about surface connection is how to select the surface boundary line and the tendency of the connected surface. And then how to diagnose the quality of final surface models and what method is applied are outlined. Furthermore this paper tries to optimize parameter, control point, knots vector and degree that controlled the free-form shapes fitting or interpolation.
How to solve general difficulties in engineer, such as disappeared surface reconstruction, triangle surface reconstruction and Y shape surface reconstruction are also outlined. And the distortion in lofting surface is analyzed, and how to solve the problem is also outlined.
In the end all stated in this paper was applied to "JiaBao" automobile body out surface reconstruction, by further forward designing realize technology innovation. It is proved that the application is performed efficiently and practicality.
本文提出网格法进行三维散乱点曲面重构，并对网格法中的网格规划问题提出统筹规划的方法。网格线的构建采用低次、少控制点的方法，使生成的曲面简洁光顺。网格骨架线间以及骨架线与曲面间至少要施加一阶连续性约束，实现曲面间光滑过渡。对散乱点曲面拟合分为两种基本类型：由点直接生成面以及由点—线—面的方式生成面，并对各类型曲面拟合的特点及适用场合进行了归纳总结。
对曲面重构中的曲面拼接，提出实现光顺拼接的关键因素是曲面边界的选择及曲面变化趋势，并给出如何确定边界和怎样判断曲面变化趋势的检测手段。对曲面拟合及拼接的数学方法进行了初步探讨，尝试如何对曲线、曲面的控制点、节点向量以及次数进行优化。
对工程中的渐消面、三边域曲面以及Y型曲面等特殊形状的曲面重构给出了解决方案，对蒙皮法中出现的曲面畸变现象进行了具体分析，并通过边界规范化、数据延拓以及曲面裁剪几个步骤使曲面畸变得到控制。
最后，本文将所述三维重构方法应用于“佳宝”汽车外形改型设计，经过再设计实现创新，取得工程应用的较好效果。
Presently, the drastic competitiveness in market, which make the products life cycles shorter and shorter, requires rapidly responding for enterprise. In industry design, the free-form shapes cannot be properly described in 3-D views so that the CAD models cannot be created. But reverse engineering (RE) technology can shorter the product development time, improve competitiveness, and overcome the special difficulties in industry design for free-form shapes. Based on the full analysis of the fields of the present research on the reverse engineering with home and foreign documents this paper take 3-D surface reconstruction for the key and crucial technology of CAD modelling of RE and accordingly do some in-depth research about interactive modelling of 3-D surface reconstruction.
In this paper, the network method of surface reconstruction, in which how to program the framework line, is proposed. The framework line should created in lower degree and a small number of control points so that the created surfaces from them are smoothness. It should be throw G1 continuity at least between framework lines in order to realize fairness connection. For the random scatter point's surface fitting this paper classified it as two types: surface approximated directly from point clouds and surface interpolated from curves that created from selected points, and further more how to perform surface reconstruction by each kind of surface fitting method and in which situation it should be used are outlined.
A new method of surfaces connection is introduced, and the key factor about surface connection is how to select the surface boundary line and the tendency of the connected surface. And then how to diagnose the quality of final surface models and what method is applied are outlined. Furthermore this paper tries to optimize parameter, control point, knots vector and degree that controlled the free-form shapes fitting or interpolation.
How to solve general difficulties in engineer, such as disappeared surface reconstruction, triangle surface reconstruction and Y shape surface reconstruction are also outlined. And the distortion in lofting surface is analyzed, and how to solve the problem is also outlined.
In the end all stated in this paper was applied to "JiaBao" automobile body out surface reconstruction, by further forward designing realize technology innovation. It is proved that the application is performed efficiently and practicality.
引文
[1]孙玉文．面向快速原型制造的反求工程关键技术研究．[博士学位论文]．大连：大连理工大学，2001．
[2]田晓东，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)1-6
[3]Tamas Varady, Ralph Martin, Jordan Cox. Reverse Engineering of Geometric models-an introduction. Computer Aided Design, 1997,29(4):253-268
[4]栗全庆，，王宏，，张英杰，，赵汝嘉．实物反求工程的关键技术分析，机械设计．1999，6：4-6
[5]冯涛，吴晓林，王亚，陈先．反求工程与快速成型．机械工艺师．1998，10：4-6
[6]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
[7]王文深，狄文辉。反求工程技术及其应用．河南机电高等专科学校学报．2001，9(2)：6-9．
[8]刘之升，黄纯主编．反求工程技术．北京：机械工业出版社．1992．4
[9]金涛，陈建良，童水光．逆向工程技术研究进展．中国机械工程．2002，13(16)1430-1436
[10]高晓辉，蔡鹤皋．三维数字化测量系统．中国机械工程．2000，11(10)：1161-1164
[11]雷刚，邹昌平，黄剑鸣．快速逆向工程研究进展．机械工艺师．2000，10：54-56
[12]Wohler T. 3D Digitizing for Engineering. Computer Graphics World. 1995,18(2):s1-s3
[13]CHAN V H, Bradley C, Vickers G W. A Multi-sensor Approach to Automating Co-ordinate Measuring Machine-based Reverse Engineering. Computer in Industry, 2001,44(2):105-115
[14]SONG C K, Kim S W. Reverse Engineering Autonomous Digitization of Free-formed Surface on a CNC Coordinate Measuring Machine. International Journal of Machine Tools & Manufacture, 1997,37(7):1041-1051
[15]Anon. High-speed Optical Measuring Boosts Reverse Engineering. Professional Engineering, 1997,10(9):32-41
[16]Milroy M J, Bradley C, Vickers G W. Segmentation of Wrap-around Model Using an Active Contour. Computer Aided Design, 1997,29(4):299-320
[17]史桂蓉，邢渊，张永清，金红．基于曲率半径的数据分割．计算机工程与应用．2001，15：93-95
[18]Sarkar B, Meng C H, Smooth-surface Approximation and Reverse Engineering. Computer Aided Design, 1991,23(9):623-628
[19]Vida J, Martin RP, Varady T. A surface Blending Methods that Use Parametric Surface. Computer Aided Design, 1994,26(5):287-298
[20]MA W, Kruth J P, Parameterization of Randomly Measured Points for Least Square Fitting of B-spline Curves and Surface. Computer Aided Design, 1995,27(9):663-675
[21]Fast Animation and Control of Nonrigid Structures. Computer Graphics. 1990,24(4):243-252
[22]张舜德，朱东波，卢秉恒．反求工程中三维几何形状测量及数据处理机电工程技术2001 1：7～10
[23]金涛，单岩，童水光．产品反求工程中基于几何特征及约束的模型重建．计算机辅助设计与图形学学报．2001，13(3)：202-207
[24]阳道善，陈吉红，周济，孙德保．测量数据云中规则表面的自动识别．计算机工程．2001，27(5)：22-24
[25]LIN CY, LIOU C S, LAI J Y. Surface-lofting Approach for Smooth-surface reconstruction From 3D Measurement data. Computer In Industry , 1997,34(1):73-85
[26]王文深，狄文辉。反求工程技术及其应用．河南机电高等专科学校学报．2001，9(2)：6-9．
[27]史桂蓉，邢渊，张永清．反向工程几何建模自动化系统．上海交通大学学报．2000，34(3)：392-395．
[28]刑渊．集成反向工程系统及其关键技术的研究：[博士学位论文]，上海：上海交通大学，1998
[29]SHI Guirong, XING Yuan, ZHANG Yongqing. Reverse-Engineering Automatic Geometry Modelling System. Journal of Shanghai Jiaotong University, 2000.34(3):392-395
[30]李江雄。复杂曲面产品反求工程的CAD建模技术：[博士学位论文]．杭州：浙江大学，1998
[31]周儒荣，张丽艳，苏旭，周来水．海量散乱点的曲面重建算法研究． 软件学报，2001，12(2)：249-255
[32]种永民，杨海成．实物测量造型软件系统．机械科学与技术．1998，17(2)：329-331
[33]种永民，杨海成．实物测量造型技术中的数据分块方法．机械科学与技术．1996，15(6)：989-992
[34]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：北京航空航天大学出版社．1994．2
[35]刘壮，张乐年．曲面造型技术综述．计算机辅助设计及制造．1997，6：20-22
[36]朱心雄等著．自由曲线曲面造型技术．北京：科学技术出版社．2000，1
[37]黄小平，杜晓明，熊有伦．逆向工程中的建模技术．中国机械工程，2001，12(5)：539-542
[38]肖尧先，王细洋，柯映林．基于实物模型的反求工程造型应用．机械设计与制造．2002，3：77-78
[39]Surfacer 9.0 Advanced Training Guide. Imageware
[40]唐朝伟，梁锡昌．三维曲面激光精密测量技术．计量学报，1994，15(2)：99-103
[41]张舜德，朱东波，卢秉恒．反求工程中三维几何形状测量及数据处理 机电工程技术2001 1：7-10
[42]SarkarB, MenqChia-Hsiang. CAGD, 1999(8):267-290
[43]VidaJ, MartinR, VaradyTetal. CAD, 1994,26(5):341-365
[44]Varady T, Rockwood A P. Vertex blending based on the setback split. In : Daehlem M, Lycle T, Schumater L L etc al ed. Mathematical Methods for Curves and Surface. Vanderbilt University Press. 1995:527-742
[45]BradleyG, VickersGW. Annalsof CIRP, 1992,41:437-440
[46]Milroy M J, Bradley C, Vichers G W et al. Machine Vision and Applications, 1996,9:106-118
[47]史桂蓉，邢渊，张永清，金红．基于曲率半径的数据分割．计算机工程与应用．2001，15：94-95
[48]Woodward C D. Cross-sectional design of B-spline surface interpolation. CAD. 20.8.1988:441-451
[49]彭芳喻，周济，周艳红，周云飞．基于最小二乘法的曲面生成算法研究．工程图学学报．1999，3：41-46
[50]朱东波，张舜德，李涤尘，卢秉恒．密集散乱测量数据点的B样条曲面拟合研究．计算机辅助设计与图形学学报．2001，13(12)：1123-1128
[2]田晓东，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)1-6
[3]Tamas Varady, Ralph Martin, Jordan Cox. Reverse Engineering of Geometric models-an introduction. Computer Aided Design, 1997,29(4):253-268
[4]栗全庆，，王宏，，张英杰，，赵汝嘉．实物反求工程的关键技术分析，机械设计．1999，6：4-6
[5]冯涛，吴晓林，王亚，陈先．反求工程与快速成型．机械工艺师．1998，10：4-6
[6]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
[7]王文深，狄文辉。反求工程技术及其应用．河南机电高等专科学校学报．2001，9(2)：6-9．
[8]刘之升，黄纯主编．反求工程技术．北京：机械工业出版社．1992．4
[9]金涛，陈建良，童水光．逆向工程技术研究进展．中国机械工程．2002，13(16)1430-1436
[10]高晓辉，蔡鹤皋．三维数字化测量系统．中国机械工程．2000，11(10)：1161-1164
[11]雷刚，邹昌平，黄剑鸣．快速逆向工程研究进展．机械工艺师．2000，10：54-56
[12]Wohler T. 3D Digitizing for Engineering. Computer Graphics World. 1995,18(2):s1-s3
[13]CHAN V H, Bradley C, Vickers G W. A Multi-sensor Approach to Automating Co-ordinate Measuring Machine-based Reverse Engineering. Computer in Industry, 2001,44(2):105-115
[14]SONG C K, Kim S W. Reverse Engineering Autonomous Digitization of Free-formed Surface on a CNC Coordinate Measuring Machine. International Journal of Machine Tools & Manufacture, 1997,37(7):1041-1051
[15]Anon. High-speed Optical Measuring Boosts Reverse Engineering. Professional Engineering, 1997,10(9):32-41
[16]Milroy M J, Bradley C, Vickers G W. Segmentation of Wrap-around Model Using an Active Contour. Computer Aided Design, 1997,29(4):299-320
[17]史桂蓉，邢渊，张永清，金红．基于曲率半径的数据分割．计算机工程与应用．2001，15：93-95
[18]Sarkar B, Meng C H, Smooth-surface Approximation and Reverse Engineering. Computer Aided Design, 1991,23(9):623-628
[19]Vida J, Martin RP, Varady T. A surface Blending Methods that Use Parametric Surface. Computer Aided Design, 1994,26(5):287-298
[20]MA W, Kruth J P, Parameterization of Randomly Measured Points for Least Square Fitting of B-spline Curves and Surface. Computer Aided Design, 1995,27(9):663-675
[21]Fast Animation and Control of Nonrigid Structures. Computer Graphics. 1990,24(4):243-252
[22]张舜德，朱东波，卢秉恒．反求工程中三维几何形状测量及数据处理机电工程技术2001 1：7～10
[23]金涛，单岩，童水光．产品反求工程中基于几何特征及约束的模型重建．计算机辅助设计与图形学学报．2001，13(3)：202-207
[24]阳道善，陈吉红，周济，孙德保．测量数据云中规则表面的自动识别．计算机工程．2001，27(5)：22-24
[25]LIN CY, LIOU C S, LAI J Y. Surface-lofting Approach for Smooth-surface reconstruction From 3D Measurement data. Computer In Industry , 1997,34(1):73-85
[26]王文深，狄文辉。反求工程技术及其应用．河南机电高等专科学校学报．2001，9(2)：6-9．
[27]史桂蓉，邢渊，张永清．反向工程几何建模自动化系统．上海交通大学学报．2000，34(3)：392-395．
[28]刑渊．集成反向工程系统及其关键技术的研究：[博士学位论文]，上海：上海交通大学，1998
[29]SHI Guirong, XING Yuan, ZHANG Yongqing. Reverse-Engineering Automatic Geometry Modelling System. Journal of Shanghai Jiaotong University, 2000.34(3):392-395
[30]李江雄。复杂曲面产品反求工程的CAD建模技术：[博士学位论文]．杭州：浙江大学，1998
[31]周儒荣，张丽艳，苏旭，周来水．海量散乱点的曲面重建算法研究． 软件学报，2001，12(2)：249-255
[32]种永民，杨海成．实物测量造型软件系统．机械科学与技术．1998，17(2)：329-331
[33]种永民，杨海成．实物测量造型技术中的数据分块方法．机械科学与技术．1996，15(6)：989-992
[34]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：北京航空航天大学出版社．1994．2
[35]刘壮，张乐年．曲面造型技术综述．计算机辅助设计及制造．1997，6：20-22
[36]朱心雄等著．自由曲线曲面造型技术．北京：科学技术出版社．2000，1
[37]黄小平，杜晓明，熊有伦．逆向工程中的建模技术．中国机械工程，2001，12(5)：539-542
[38]肖尧先，王细洋，柯映林．基于实物模型的反求工程造型应用．机械设计与制造．2002，3：77-78
[39]Surfacer 9.0 Advanced Training Guide. Imageware
[40]唐朝伟，梁锡昌．三维曲面激光精密测量技术．计量学报，1994，15(2)：99-103
[41]张舜德，朱东波，卢秉恒．反求工程中三维几何形状测量及数据处理 机电工程技术2001 1：7-10
[42]SarkarB, MenqChia-Hsiang. CAGD, 1999(8):267-290
[43]VidaJ, MartinR, VaradyTetal. CAD, 1994,26(5):341-365
[44]Varady T, Rockwood A P. Vertex blending based on the setback split. In : Daehlem M, Lycle T, Schumater L L etc al ed. Mathematical Methods for Curves and Surface. Vanderbilt University Press. 1995:527-742
[45]BradleyG, VickersGW. Annalsof CIRP, 1992,41:437-440
[46]Milroy M J, Bradley C, Vichers G W et al. Machine Vision and Applications, 1996,9:106-118
[47]史桂蓉，邢渊，张永清，金红．基于曲率半径的数据分割．计算机工程与应用．2001，15：94-95
[48]Woodward C D. Cross-sectional design of B-spline surface interpolation. CAD. 20.8.1988:441-451
[49]彭芳喻，周济，周艳红，周云飞．基于最小二乘法的曲面生成算法研究．工程图学学报．1999，3：41-46
[50]朱东波，张舜德，李涤尘，卢秉恒．密集散乱测量数据点的B样条曲面拟合研究．计算机辅助设计与图形学学报．2001，13(12)：1123-1128
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