基于点云边界和曲率特征的车身A级曲面光顺方法
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摘要
光滑流畅的车身外型是汽车产品在激烈市场竞争中胜出的法宝,这就要求车身A级曲面光顺技术具有更高的效率。国内外学者对曲面光顺理论进行了广泛研究,但在车身A级曲面光顺实践过程中的应用性不强。因此,如何高效的光顺车身A级曲面是光顺工程师亟待解决的难题。
针对上述问题,对基于点云边界和曲率特征的车身A级曲面光顺方法进行研究。研究具体工作如下：
(1)对插值曲面的型值点按照其u,v两个方向的参数值是否为0进行分类,并推导出不同类型的型值点对应的反求公式,改进了一种利用插值法反求Bezier曲面控制顶点的算法,提高算法的稳定性,使其便于编程实现。
(2)为了解决从点云直接拟合的曲面不能满足点云边界特征的问题,给出了提取点云边界点的算法。为了提高点云边界点提取算法的效率,将空间点云数据投影到平面,建立平面点云的包围盒,根据点云的密度将其划分为若干个小网格,利用最值算法提取边界网格内的点作为点云的边界点。
(3)给出一种符合点云曲率特征的基于均分弦长准则的插值曲面型值点搜索算法。建立平面网格点阵与空间点云上型值点的对应关系,根据均分弦长准则调整平面网格点阵的位置,使得搜索到的型值点按照点云的曲率变化趋势均匀分布。
(4)利用VC++编程实现基于点云边界和曲率特征的车身A级曲面光顺模块,通过VC++与UG软件的接口技术将该模块集成到UG软件中,提高车身A级曲面光顺的自动化程度。
最后对曲面光顺模块进行实例验证,得出下面结论：对于曲率变化较平缓的点云,光顺后的曲面基本可以满足车身A级曲面的要求；对于曲率变化较大的点云或过渡曲面的点云,该模块也可以方便快捷的进行曲面重构,为后期的人工交互光顺操作节约了时间,提高了车身A级曲面光顺的质量和效率。
Smooth and fluent contour is the key factor for automotive products to survive in the fierce market competition, so smoothing technologies of class A surfaces for Auto-body are supposed to be more efficient. Although much theoretical research on surfaces smoothing has been done by domestic and foreign scholars, the practical application on smoothing for Auto-body was still at a low level. Therefore, how to smooth class A surfaces efficiently and high-quality is a difficult problem that smoothing engineers have to face.
Aiming at the above problems, research on the smoothing method based on boundary and curvature of cloud points has been presented in the paper. Specific research contents are as follows:
(1) An reverse algorithm for control vertex of Bezier surface has been improved through classifying the parameter values of characteristic points that used to construct interpolation surfaces according to whether the parameter values in u, v direction is equal to zero, which improved the stability of reverse algorithm and made it easily programmed.
(2) An algorithm of extracting boundary points from the cloud points has been presented in order to overcome the problem that the surface fitted from cloud points directly can not satisfy the border characteristics of the cloud points. In order to increase the efficiency of the boundary points extraction algorithm, the space points have been projected on a plane and the bounding box of the plane points which will be divided into several small grids has been built, then a magnitude algorithm can be used to extract the boundary points from the boundary grid.
(3) An algorithm that can make the searched characteristic points distributed evenly according to the curvature of cloud points has been given. Plane mesh intersections have been built and the relation between space cloud points and plane mesh intersections have also been built, then the plane mesh intersections can be moved to adjust the position of characteristic points that used to construct interpolation surfaces. A method that can divide string lengths between characteristic points in each row or column has been used to adjust the position of plane mesh intersections in order to make the characteristic points selected satisfy the curvature feature of the cloud points.
(4) An algorithm that used to smooth Class A surfaces for Auto-body based on boundary and curvature of cloud points has been realized in VC++language, and the smoothing module has been integrated into the UG software with the help of Interface Techniques between VC++and UG software, which can improve the automation level for Auto-body Class A surface.
Through the examples validating for the smoothing module, conclusions as follows have been drawn:Surfaces smoothed by this smoothing module satisfy the requirements of Auto-body Class A surface for the cloud points with gentle curvature; For cloud points with large curvature changes or transitional surfaces, this module can reconstruct surface easily and conveniently, and save time for later artificial interactive operation and improve the smoothing quality and efficiency for Auto-body Class A surface.
针对上述问题,对基于点云边界和曲率特征的车身A级曲面光顺方法进行研究。研究具体工作如下：
(1)对插值曲面的型值点按照其u,v两个方向的参数值是否为0进行分类,并推导出不同类型的型值点对应的反求公式,改进了一种利用插值法反求Bezier曲面控制顶点的算法,提高算法的稳定性,使其便于编程实现。
(2)为了解决从点云直接拟合的曲面不能满足点云边界特征的问题,给出了提取点云边界点的算法。为了提高点云边界点提取算法的效率,将空间点云数据投影到平面,建立平面点云的包围盒,根据点云的密度将其划分为若干个小网格,利用最值算法提取边界网格内的点作为点云的边界点。
(3)给出一种符合点云曲率特征的基于均分弦长准则的插值曲面型值点搜索算法。建立平面网格点阵与空间点云上型值点的对应关系,根据均分弦长准则调整平面网格点阵的位置,使得搜索到的型值点按照点云的曲率变化趋势均匀分布。
(4)利用VC++编程实现基于点云边界和曲率特征的车身A级曲面光顺模块,通过VC++与UG软件的接口技术将该模块集成到UG软件中,提高车身A级曲面光顺的自动化程度。
最后对曲面光顺模块进行实例验证,得出下面结论：对于曲率变化较平缓的点云,光顺后的曲面基本可以满足车身A级曲面的要求；对于曲率变化较大的点云或过渡曲面的点云,该模块也可以方便快捷的进行曲面重构,为后期的人工交互光顺操作节约了时间,提高了车身A级曲面光顺的质量和效率。
Smooth and fluent contour is the key factor for automotive products to survive in the fierce market competition, so smoothing technologies of class A surfaces for Auto-body are supposed to be more efficient. Although much theoretical research on surfaces smoothing has been done by domestic and foreign scholars, the practical application on smoothing for Auto-body was still at a low level. Therefore, how to smooth class A surfaces efficiently and high-quality is a difficult problem that smoothing engineers have to face.
Aiming at the above problems, research on the smoothing method based on boundary and curvature of cloud points has been presented in the paper. Specific research contents are as follows:
(1) An reverse algorithm for control vertex of Bezier surface has been improved through classifying the parameter values of characteristic points that used to construct interpolation surfaces according to whether the parameter values in u, v direction is equal to zero, which improved the stability of reverse algorithm and made it easily programmed.
(2) An algorithm of extracting boundary points from the cloud points has been presented in order to overcome the problem that the surface fitted from cloud points directly can not satisfy the border characteristics of the cloud points. In order to increase the efficiency of the boundary points extraction algorithm, the space points have been projected on a plane and the bounding box of the plane points which will be divided into several small grids has been built, then a magnitude algorithm can be used to extract the boundary points from the boundary grid.
(3) An algorithm that can make the searched characteristic points distributed evenly according to the curvature of cloud points has been given. Plane mesh intersections have been built and the relation between space cloud points and plane mesh intersections have also been built, then the plane mesh intersections can be moved to adjust the position of characteristic points that used to construct interpolation surfaces. A method that can divide string lengths between characteristic points in each row or column has been used to adjust the position of plane mesh intersections in order to make the characteristic points selected satisfy the curvature feature of the cloud points.
(4) An algorithm that used to smooth Class A surfaces for Auto-body based on boundary and curvature of cloud points has been realized in VC++language, and the smoothing module has been integrated into the UG software with the help of Interface Techniques between VC++and UG software, which can improve the automation level for Auto-body Class A surface.
Through the examples validating for the smoothing module, conclusions as follows have been drawn:Surfaces smoothed by this smoothing module satisfy the requirements of Auto-body Class A surface for the cloud points with gentle curvature; For cloud points with large curvature changes or transitional surfaces, this module can reconstruct surface easily and conveniently, and save time for later artificial interactive operation and improve the smoothing quality and efficiency for Auto-body Class A surface.
引文
[1]徐家川,雷雨成,洪英武等.汽车A级曲面的光顺方法[J].汽车技术,2008,2：17-20.
[2]Hosaka.M.Theory of Curve and Surface Synthesis and Their Smooth Fitting [M].Japan:Information Processing in Japan,1969,9:60-80.
[3]Kjellander.Smoothing of Cubic Parametric Spline[J].Computer aided Design,1983,15(3):175-179.
[4]Kjellander.Smoothing of Cubic Parametric surface[J].Computer-Aided Design,1983,15(5):288-293.
[5]Nowaki.H,Resse.D.Design and fairing of ship surface[J].in:Barnhill and Boehmeds, Surface in CAGD. North Holland, amsterdem,1983,3():121-134.
[6]Farin. GREIN.G, Sapidis.N, A.J. Worsey Fairing cubic B-spline curves[J].CAGD.1987,4():91-103.
[7]Lott. NJ,Pullin. DI.Method for fairing B-spline surfaces[J].Computer-Aided Design,1988, 20(10):597-604.
[8]Rando.T,Roulier.J.Designing faired parametric surface [J].CAD,1991,23():429-497.
[9]Stefaine H S.Shape Improvement of Surfaces[J].Journal of computing,1998,13:135-152.
[10]Zhang C,Cheng F.Removing local irregularities of NURBS surfaces by modifying highlight lines[J].Computer-aided Design,1998,30(11):923-930.
[11]Lyche T,Mrken K,Quak E.Theory and Algorithm of Non-uniform Splines Wavelets [EB/OL].2001.
[12]苏步青,刘鼎元.计算几何[M].上海科学技术出版社,1981.
[13]复旦大学数学系,江南造船厂.单根曲线光顺的基样条法[J].江南造船厂技术资料,1974,7.
[14]齐东旭等.曲线拟合的数值磨光方法[J].数学学报,1975,18(3)：173-184.
[15]忻元龙.双三次样条曲线及其在曲面光顺中的应用[J].复旦学报,自然科学版,1977：63-68.
[16]董光昌.船体数学放样—回弹法[M].北京：科学出版社,1978.
[17]彭国华.有理曲面光滑拼接和曲面光顺理论及应用[D]：[博士学位论文].西北工业大学,1992.
[18]穆国旺,朱心雄,涂侯杰等.曲面光顺的分片能量法[J].工程图学学报,1999(1)：29-34.
[19]彭芳瑜,周云飞,周艳红等.基于能量法的截面曲线自动形状修改算法[J].华中理工大学学报,1999,27(6)：60-62.
[20]龙小平.局部能量最优法与曲线曲面的光顺[J].计算机辅助设计与图形学学报,2002,14(12)：1109-1113.
[21]Yulin Wang, et. al.Shape control of Bezier surfaces with iso-parametric monotone curvature constraints.Computer Aided Geometric Design,2003,20(6):383-394.
[22]Yulin Wang, et. al.Designing fair curves using monotone curvature pieces. Computer Aided Geometric Design,2004,21(5):515-527.
[23]张军,彭国华,戴霞.基于图像的曲面光顺方法[J].工程图学学报,2005,26(1)：45-49.
[24]王秀丽,宁正元.基于高斯曲率的曲面光顺方法研究[J].计算机工程.2006,32(16)：207-209.
[25]盛柯芳.基于EMD的离散数字曲线曲面光顺方法研究[D].浙江工业大学.2008.
[26]张美玉,秦绪佳,刘世双等.基于EMD的四边域曲面光顺算法[J].中国图像图形报.2009,14(5)：984-985.
[27]刘光帅,李柏林.曲面处理的曲率域能量优化方法研究[J].2011,28(2)：763-765.
[28]孙延奎,朱心雄.任意B样条曲面的多分辨率表示及光顺[J].工程图学学报,999,(3)：49-54.
[29]孙延奎,朱心雄.B样条曲线的小波光顺法[J].工程图学学报,1998,(4)：51-58
[30]孙延奎,朱心雄,唐龙等.准均匀B样条曲面小波分解的快速算法[J].清华大学学报(自然科学版),2001,4(4)：51-55.
[31]纪小刚,龚光容.半正交B样条小波及其在曲线曲面光顺中的应用[J].机械工程学报,2006,42(9)：54-60.
[32]李奇敏,柯映林.基于非均匀B样条小波的NURBS曲面光顺[J].中国机械工程,2007,(3月上半月)：577-582.
[33]吴福鸣,潘日晶.基于能量优化与非均匀B样条小波的曲面光顺[J].计算机工程与应用,2011,47(18)：176-178.
[34]蔡中义.C(?)1连续曲面重构与光顺的有限元算法[J].工程图学学报,2002,(4)：79-86.
[35]蔡中义,李明哲.散乱分布数据曲面重构的光顺-有限元方法[J].软件学报,2003,14(4)：838-844.
[36]蔡中义.基于能量极小准则的曲面再现与光顺[J].计算机辅助设计与图形学学报2002,14(8)：758-762.
[37]甘屹,齐从谦,陈亚洲.基于遗传算法的曲线曲面光顺[J].同济大学学报,2002,20(3)：322-325.
[38]刘华勇.用遗传算法光顺基于点表示的曲线曲面[J].机械科学与技术,2006,25(7)：826-830.
[39]赵卫国,周燕,李小龙.基于能量法的曲线曲面优化设计方法研究[J].机械设计与制造,2009,(6)：208-210.
[40]李小伟,逆向工程关键技术的研究[D].[硕士学位论文].安徽：合肥工业大学.2007.
[41]王宏涛,周儒荣,张丽艳.现代测量方法在逆向工程数据采集技术中的应用[J].航空计测技术,2003,23(4).
[42]高晓辉,蔡鹤皋.3维数字化测量系统研究[J].中国机械工程,2006,11(10)：1161-1164.
[43]周士侃,娄臻亮,刘冰.反向工程中的光栅扫描技术[J].工具技术,2004,10：69-71.
[44]FiliP D,Magedson R,Markot R.Surface algorithms using bounds on derivatives[J].1986,3(2):295-311.
[45]Sun W, Bradley C,Zhang Y F.Cloud data modeling employing a unified non-redundant triangle meshes [J]. Computer Aided Geometric Design,2001,33(2):183-193.
[46]Weir DJ, Milroy M, Bradley C, Vickers GW.Reverse engineering physical models employing wrap-aroud B-spline surfaces and quadrics[A].Pro Introduction MechEngrs-PartB[C].1996,210:147-157.
[47]欧阳黎健.反求工程中数据预处理及模型修正[D]：[硕士学位论文].大连交通大学,2006.
[48]戴静兰.海量点云预处理算法研究[D]：[硕士学位论文].浙江大学,2006.
[49]谢小刚..基于数字化设计的客车车身造型技术研究[D]:[硕士学位论文].南京航空航天大学,2007.
[50]张新香.UG软件二次开发工具的使用[J].计算机光盘软件与应用,2010,(1)：41-43.
[51]刘定伟,薛澄岐.UG二次开发接口技术研究[J].机械制造与自动化,2005,34(1)：80-83.
[52]范志先,孙殿柱,李延瑞等.采用MFC开发用户交互界面的新方法[J].工程图学学报,2008,29(4)：160-163.
[53]马晓丽,孙殿柱.基于UG二次开发的菜单制作技术[J].山东理工大学学报：自然科学版,2004,18(5)：33-36.
[54]徐家川,雷雨成.汽车车身A级曲面光顺方法[J].汽车技术,2008,(2)：17-20.
[55]席平,刘勇.反向工程中的曲面光顺算法[J].北京航空航天大学学报,2002,(02)：125-128.
[56]夏卫群.车身曲面质量的评价指标研究[J].汽车科技,2005,(5)：9-11
[57]王承翔,颜运昌,黄天泽.汽车车身表面测量数据光顺方法研究[J].机械科学与技术,1996,(06)：1003-1006.
[58]朱心雄.自由曲线曲面造型技术[M].北京：科学出版社,2000.
[59]施法中.计算机辅助设计与非均匀有理B样条[M].北京：北京航空航天大学出版社,1994.
[60]徐家川,李迪,李旭.汽车车身A级曲面的表示与次数选择[J].汽车技术,2009,(9)：58-61.
[61]王天军.一个反求B6zier曲面控制点的算法[J].计算机辅助设计与图形学报,1992,4(3)：36-40.
[62]李江雄.反求工程中复杂曲面边界线的自动提取技术[J].机械设计与制造工程,2000,29(2)：26-28.
[2]Hosaka.M.Theory of Curve and Surface Synthesis and Their Smooth Fitting [M].Japan:Information Processing in Japan,1969,9:60-80.
[3]Kjellander.Smoothing of Cubic Parametric Spline[J].Computer aided Design,1983,15(3):175-179.
[4]Kjellander.Smoothing of Cubic Parametric surface[J].Computer-Aided Design,1983,15(5):288-293.
[5]Nowaki.H,Resse.D.Design and fairing of ship surface[J].in:Barnhill and Boehmeds, Surface in CAGD. North Holland, amsterdem,1983,3():121-134.
[6]Farin. GREIN.G, Sapidis.N, A.J. Worsey Fairing cubic B-spline curves[J].CAGD.1987,4():91-103.
[7]Lott. NJ,Pullin. DI.Method for fairing B-spline surfaces[J].Computer-Aided Design,1988, 20(10):597-604.
[8]Rando.T,Roulier.J.Designing faired parametric surface [J].CAD,1991,23():429-497.
[9]Stefaine H S.Shape Improvement of Surfaces[J].Journal of computing,1998,13:135-152.
[10]Zhang C,Cheng F.Removing local irregularities of NURBS surfaces by modifying highlight lines[J].Computer-aided Design,1998,30(11):923-930.
[11]Lyche T,Mrken K,Quak E.Theory and Algorithm of Non-uniform Splines Wavelets [EB/OL].2001.
[12]苏步青,刘鼎元.计算几何[M].上海科学技术出版社,1981.
[13]复旦大学数学系,江南造船厂.单根曲线光顺的基样条法[J].江南造船厂技术资料,1974,7.
[14]齐东旭等.曲线拟合的数值磨光方法[J].数学学报,1975,18(3)：173-184.
[15]忻元龙.双三次样条曲线及其在曲面光顺中的应用[J].复旦学报,自然科学版,1977：63-68.
[16]董光昌.船体数学放样—回弹法[M].北京：科学出版社,1978.
[17]彭国华.有理曲面光滑拼接和曲面光顺理论及应用[D]：[博士学位论文].西北工业大学,1992.
[18]穆国旺,朱心雄,涂侯杰等.曲面光顺的分片能量法[J].工程图学学报,1999(1)：29-34.
[19]彭芳瑜,周云飞,周艳红等.基于能量法的截面曲线自动形状修改算法[J].华中理工大学学报,1999,27(6)：60-62.
[20]龙小平.局部能量最优法与曲线曲面的光顺[J].计算机辅助设计与图形学学报,2002,14(12)：1109-1113.
[21]Yulin Wang, et. al.Shape control of Bezier surfaces with iso-parametric monotone curvature constraints.Computer Aided Geometric Design,2003,20(6):383-394.
[22]Yulin Wang, et. al.Designing fair curves using monotone curvature pieces. Computer Aided Geometric Design,2004,21(5):515-527.
[23]张军,彭国华,戴霞.基于图像的曲面光顺方法[J].工程图学学报,2005,26(1)：45-49.
[24]王秀丽,宁正元.基于高斯曲率的曲面光顺方法研究[J].计算机工程.2006,32(16)：207-209.
[25]盛柯芳.基于EMD的离散数字曲线曲面光顺方法研究[D].浙江工业大学.2008.
[26]张美玉,秦绪佳,刘世双等.基于EMD的四边域曲面光顺算法[J].中国图像图形报.2009,14(5)：984-985.
[27]刘光帅,李柏林.曲面处理的曲率域能量优化方法研究[J].2011,28(2)：763-765.
[28]孙延奎,朱心雄.任意B样条曲面的多分辨率表示及光顺[J].工程图学学报,999,(3)：49-54.
[29]孙延奎,朱心雄.B样条曲线的小波光顺法[J].工程图学学报,1998,(4)：51-58
[30]孙延奎,朱心雄,唐龙等.准均匀B样条曲面小波分解的快速算法[J].清华大学学报(自然科学版),2001,4(4)：51-55.
[31]纪小刚,龚光容.半正交B样条小波及其在曲线曲面光顺中的应用[J].机械工程学报,2006,42(9)：54-60.
[32]李奇敏,柯映林.基于非均匀B样条小波的NURBS曲面光顺[J].中国机械工程,2007,(3月上半月)：577-582.
[33]吴福鸣,潘日晶.基于能量优化与非均匀B样条小波的曲面光顺[J].计算机工程与应用,2011,47(18)：176-178.
[34]蔡中义.C(?)1连续曲面重构与光顺的有限元算法[J].工程图学学报,2002,(4)：79-86.
[35]蔡中义,李明哲.散乱分布数据曲面重构的光顺-有限元方法[J].软件学报,2003,14(4)：838-844.
[36]蔡中义.基于能量极小准则的曲面再现与光顺[J].计算机辅助设计与图形学学报2002,14(8)：758-762.
[37]甘屹,齐从谦,陈亚洲.基于遗传算法的曲线曲面光顺[J].同济大学学报,2002,20(3)：322-325.
[38]刘华勇.用遗传算法光顺基于点表示的曲线曲面[J].机械科学与技术,2006,25(7)：826-830.
[39]赵卫国,周燕,李小龙.基于能量法的曲线曲面优化设计方法研究[J].机械设计与制造,2009,(6)：208-210.
[40]李小伟,逆向工程关键技术的研究[D].[硕士学位论文].安徽：合肥工业大学.2007.
[41]王宏涛,周儒荣,张丽艳.现代测量方法在逆向工程数据采集技术中的应用[J].航空计测技术,2003,23(4).
[42]高晓辉,蔡鹤皋.3维数字化测量系统研究[J].中国机械工程,2006,11(10)：1161-1164.
[43]周士侃,娄臻亮,刘冰.反向工程中的光栅扫描技术[J].工具技术,2004,10：69-71.
[44]FiliP D,Magedson R,Markot R.Surface algorithms using bounds on derivatives[J].1986,3(2):295-311.
[45]Sun W, Bradley C,Zhang Y F.Cloud data modeling employing a unified non-redundant triangle meshes [J]. Computer Aided Geometric Design,2001,33(2):183-193.
[46]Weir DJ, Milroy M, Bradley C, Vickers GW.Reverse engineering physical models employing wrap-aroud B-spline surfaces and quadrics[A].Pro Introduction MechEngrs-PartB[C].1996,210:147-157.
[47]欧阳黎健.反求工程中数据预处理及模型修正[D]：[硕士学位论文].大连交通大学,2006.
[48]戴静兰.海量点云预处理算法研究[D]：[硕士学位论文].浙江大学,2006.
[49]谢小刚..基于数字化设计的客车车身造型技术研究[D]:[硕士学位论文].南京航空航天大学,2007.
[50]张新香.UG软件二次开发工具的使用[J].计算机光盘软件与应用,2010,(1)：41-43.
[51]刘定伟,薛澄岐.UG二次开发接口技术研究[J].机械制造与自动化,2005,34(1)：80-83.
[52]范志先,孙殿柱,李延瑞等.采用MFC开发用户交互界面的新方法[J].工程图学学报,2008,29(4)：160-163.
[53]马晓丽,孙殿柱.基于UG二次开发的菜单制作技术[J].山东理工大学学报：自然科学版,2004,18(5)：33-36.
[54]徐家川,雷雨成.汽车车身A级曲面光顺方法[J].汽车技术,2008,(2)：17-20.
[55]席平,刘勇.反向工程中的曲面光顺算法[J].北京航空航天大学学报,2002,(02)：125-128.
[56]夏卫群.车身曲面质量的评价指标研究[J].汽车科技,2005,(5)：9-11
[57]王承翔,颜运昌,黄天泽.汽车车身表面测量数据光顺方法研究[J].机械科学与技术,1996,(06)：1003-1006.
[58]朱心雄.自由曲线曲面造型技术[M].北京：科学出版社,2000.
[59]施法中.计算机辅助设计与非均匀有理B样条[M].北京：北京航空航天大学出版社,1994.
[60]徐家川,李迪,李旭.汽车车身A级曲面的表示与次数选择[J].汽车技术,2009,(9)：58-61.
[61]王天军.一个反求B6zier曲面控制点的算法[J].计算机辅助设计与图形学报,1992,4(3)：36-40.
[62]李江雄.反求工程中复杂曲面边界线的自动提取技术[J].机械设计与制造工程,2000,29(2)：26-28.