反求工程中基于混合过渡特征的三角网格模型数据处理技术研究
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摘要
三角网格模型具有简单、直观的特性使之成为当前模型显示中最常用的格式。特征建模因其能同时面向设计和制造过程，被广泛应用于模型重建过程。特征对产品的几何外形具有极为重要的控制作用，因而特征处理技术成为当前反求工程领域的关键技术，而最核心的部分是特征提取，它是后续处理技术的基础和前提。由于过渡特征特别是混合过渡特征无法采用单一的法矢或曲率信息进行有效提取，因此过渡特征提取技术研究是目前研究的难点和热点。
根据三角网格模型混合过渡特征的不规则性和拓扑结构原理，提出了一种多法矢夹角阈值特征提取算法进行混合过渡特征提取研究。首先用一组能对模型进行区域分割的法矢夹角阈值进行特征提取，通过区域分割确定每个非特征区域的点集；对非特征区域进行最小二乘拟合精度比较，确定各个区域法矢夹角阈值；用各区域的最佳法矢夹角阈值确定整个模型的特征，实现混合过渡特征的准确提取并对三角网格模型进行区域分割。
研究了一种空间生长填充三角网格孔洞修补改进算法，进行混合过渡特征区域和跨区域的孔洞修补。首先对网格模型孔洞边界进行自动识别，用空间网格生长法对孔洞区域进行网格填充；选择孔洞边界相关顶点作为采样点对新增孔洞顶点进行最小二乘位置调整；引入区域分割和特征边界曲线拟合方法进行混合过渡特征及跨区域的孔洞修补，为提高多区域孔洞的修补精度提供一种可行方案。
针对模型简化过程中特征保护问题，采取基于区域分割的模型简化方法。根据简化需要，结合区域面片数量比例和区域曲率值，合理调整分配各个区域的简化量，减少曲率较大的特征区域简化量；采用加入面积权值的QEM模型简化算法对各个区域进行独立简化，实现模型简化的同时有效地保护特征。
在以上研究的基础上，构建了“基于混合过渡特征的三维模型重建系统原型”，该系统可将各研究算法转化为三维模型相关可视化处理过程中。
Triangular mesh model possesses the simple and intuitive characteristics,whichmakes it the most popular format of model shows.Feature reconstruction is widelyused in reverse engineering model reconstruction process,for it can faces bothdesign and manufacturing process. Feature has very important control effect ofgeometrical shape of products, thus feature treatment technologies are the keyfield technology in reverse engineering, and the core part is feature extractiontechnique because this process is the foundation and prerequisite of follow-upprocessing. As the blend features especially mixed blend feature can not beextracted effectively by using single vector or curvature information, therefore, theblend feature extraction technology is a hotspot and quite difficult in currentresearch.
According to irregularities and topological structure of mixed blend feature intriangular mesh model, this paper presents a new multi threshold of vector anglefeature extraction algorithm to hybrid blend feature extraction. Firstly，mixedblend feature is extracted by a group threshold angles of normal vector which cansegment the model preliminary, and point set with different threshold angles ofeach non-feature region are determined; then each region least-square fittingprecision of different threshold angles are compared in order to choose the bestthreshold angle of normal vector;Finally, mixed blend features are extractedaccurately by the best threshold angle of different regions, in this way trianglemesh model segmentation based on features is taken out.
An improved space mesh growing hole filling algorithm is proposed aiming attriangular mesh holes in mixed blend feature region and cross regions. Firstly, allboundary feature is recognized and hole boundaries are automaticly identified byhole boundary properties; then the hole area is filled by meshes through spatialmesh growth method; finally, new added vertex positions are adjusted byleast-square method according to the boundary area vertex. Introducing region segmentation and boundary features curve fitted into mixed blend feature andcross regions hole filling algorithm, provides a feasible scheme for improvingfilling precision in multi-regions hole filling problem.
For the purpose of feature regions protection in triangular mesh simplificationprocess, a mesh simplification algorithm based on region segmentation is adopted.According to the needs of simplification, regions simplified quantity distributionsare rationally adjusted by region mesh quantity ratios and region curvature values,and as a result, the simplified quantities of feature regions with large curvature arereduced. Each region is simplified independently by a QEM model simplificationalgorithm with added area weights of relevant triangle meshes; realize effectivelyfeature region protection in the triangle mesh model simplification processing.
"Processing prototype system based on mixed blend features of3D modelreconstruction" is constructed based on above studies.This system can transfereach algorithm into visualization in correlation model processing process.
根据三角网格模型混合过渡特征的不规则性和拓扑结构原理，提出了一种多法矢夹角阈值特征提取算法进行混合过渡特征提取研究。首先用一组能对模型进行区域分割的法矢夹角阈值进行特征提取，通过区域分割确定每个非特征区域的点集；对非特征区域进行最小二乘拟合精度比较，确定各个区域法矢夹角阈值；用各区域的最佳法矢夹角阈值确定整个模型的特征，实现混合过渡特征的准确提取并对三角网格模型进行区域分割。
研究了一种空间生长填充三角网格孔洞修补改进算法，进行混合过渡特征区域和跨区域的孔洞修补。首先对网格模型孔洞边界进行自动识别，用空间网格生长法对孔洞区域进行网格填充；选择孔洞边界相关顶点作为采样点对新增孔洞顶点进行最小二乘位置调整；引入区域分割和特征边界曲线拟合方法进行混合过渡特征及跨区域的孔洞修补，为提高多区域孔洞的修补精度提供一种可行方案。
针对模型简化过程中特征保护问题，采取基于区域分割的模型简化方法。根据简化需要，结合区域面片数量比例和区域曲率值，合理调整分配各个区域的简化量，减少曲率较大的特征区域简化量；采用加入面积权值的QEM模型简化算法对各个区域进行独立简化，实现模型简化的同时有效地保护特征。
在以上研究的基础上，构建了“基于混合过渡特征的三维模型重建系统原型”，该系统可将各研究算法转化为三维模型相关可视化处理过程中。
Triangular mesh model possesses the simple and intuitive characteristics,whichmakes it the most popular format of model shows.Feature reconstruction is widelyused in reverse engineering model reconstruction process,for it can faces bothdesign and manufacturing process. Feature has very important control effect ofgeometrical shape of products, thus feature treatment technologies are the keyfield technology in reverse engineering, and the core part is feature extractiontechnique because this process is the foundation and prerequisite of follow-upprocessing. As the blend features especially mixed blend feature can not beextracted effectively by using single vector or curvature information, therefore, theblend feature extraction technology is a hotspot and quite difficult in currentresearch.
According to irregularities and topological structure of mixed blend feature intriangular mesh model, this paper presents a new multi threshold of vector anglefeature extraction algorithm to hybrid blend feature extraction. Firstly，mixedblend feature is extracted by a group threshold angles of normal vector which cansegment the model preliminary, and point set with different threshold angles ofeach non-feature region are determined; then each region least-square fittingprecision of different threshold angles are compared in order to choose the bestthreshold angle of normal vector;Finally, mixed blend features are extractedaccurately by the best threshold angle of different regions, in this way trianglemesh model segmentation based on features is taken out.
An improved space mesh growing hole filling algorithm is proposed aiming attriangular mesh holes in mixed blend feature region and cross regions. Firstly, allboundary feature is recognized and hole boundaries are automaticly identified byhole boundary properties; then the hole area is filled by meshes through spatialmesh growth method; finally, new added vertex positions are adjusted byleast-square method according to the boundary area vertex. Introducing region segmentation and boundary features curve fitted into mixed blend feature andcross regions hole filling algorithm, provides a feasible scheme for improvingfilling precision in multi-regions hole filling problem.
For the purpose of feature regions protection in triangular mesh simplificationprocess, a mesh simplification algorithm based on region segmentation is adopted.According to the needs of simplification, regions simplified quantity distributionsare rationally adjusted by region mesh quantity ratios and region curvature values,and as a result, the simplified quantities of feature regions with large curvature arereduced. Each region is simplified independently by a QEM model simplificationalgorithm with added area weights of relevant triangle meshes; realize effectivelyfeature region protection in the triangle mesh model simplification processing.
"Processing prototype system based on mixed blend features of3D modelreconstruction" is constructed based on above studies.This system can transfereach algorithm into visualization in correlation model processing process.
引文
[1] Chikofsky E. J., Cross J. H.Reverse Engineering and Design Recovery: ATaxonomy.IEEE Software,1990,7(1):13-17
[2]刘之生．反求工程技术．北京：机械工业出版社，1996
[3] Varady T,Ralph R M.,Jordan C.Reverse engineering of geometric models-anintroduction.Computer-Aided Design,1997,29(4):255-268
[4] Pal B., Ralph R M.,Varady T.Algorithms for reverse engineering boundaryrepresentation models.Computer-Aided Design,2001,33;839-851
[5] Lee K. H., Woo H.Use of reverse engineering method for rapid product development.Computer&Industrial Engineering,1998,35(1-2):21-24
[6]金涛，童水光．逆向工程技术．北京：机械工业出版社，2003
[7] Huang J. B.Geometric feature extraction and model reconstruction from unorganizedpoints for reverse engineering of mechanical parts with arbitrary topology:[Ph.D.dissertation]. Ohio State: The Ohio State University,2001
[8] Zhu G. S., Zhou T. R,Zhou J. Fourier-Mellin matching method application to revolvedsurface extraction in reverse engineering. In: The38th International Conference onComputers and Industrial Engineering,Beijin,2008
[9] Thompson W B,Owen J C, Stark S R,et al.Feature based reverse engineering ofmechanical parts.IEEE Transactions on Robotics and Automation,1999,15(1):57-66
[10] Au C K, Yuen M M F.Feature-based reverse engineering of mannequin for garmentdesign. Computer-Aided Design,1999,31(12):751-759
[11]柯映林，刘云峰，范树迁，等．基于特征的反求工程建模系统RE-SOFT．计算辅助设计与图形学学报，2004，16(6)：799-811；
[12]柯映林，李岸，王军文．过渡特征提取中的概率统计理论和方法．机械工程学报，2003，39(6)：140-144
[13] Lu Z.,Ke Y. L.,Sun Q.,et al.Method to extract blend surface feature in reverseengineering. Chinese Journal of Mechanical Engineering (English Edition),2003,16(3):248-251
[14] Ke Y. L., Sun Q., Lu Z.Least-square method based feature fitting and extraction inreverse engineering.Chinese Journal of Mechanical Engineering(English edition),2003,16(2):163-166
[15]柯映林，单东日．基于区分割与约束逼近的二次曲面重建．浙江大学学报(工学版)，2004，38(10)：1274-1279
[16]金涛，陈建良，童水光．三维模型对称平面重建的特征匹配方法．计算机辅助设计与图形学学报，2003，15(5)：616-620
[17]王丽敏，周天瑞．基于特征的反求工程建模技术研究进展．南方金属，2009(171)：1-4
[18] Benk P, Varady T.Segmentation methods for smooth point regions of conventionalengineering objects. Computer-Aided Design,2004,36(6);511-523
[19] Huang J,Menq C H.Automatic data segmentation for geometric feature extraction fromunorganized3-D coordinate points.IEEE Transitions on Robotics and Automation,2001,17(3):268-279
[20]胡鑫，习俊通，金烨．反求工程中散乱点云数据的自动分割与曲面重构．上海交通大学学报，2004，38(1)：62-65
[21]马骊溟，徐毅，李泽湘．基于高斯曲率极值点的散乱点云数据特征点提取．系统仿真学报，2008，20(9)：2341-2344
[22] Carr J. C.,Beatson R. K.,Cherrie J. B.,et al. Reconstruction and representation of3Dobjects with radial basis functions. Proceedings of the ACM SIGGRAPH Conferenceon Computer Graphics.Los Angeles:ACM,2001:67-76
[23] Guennebaud G, Gross M.Algebraic point set surfaces. Proceedings of the ACMSIGGRAPH Conference on Computer Graphics. San Diego: ACM,2007,26(23):23-31
[24]陈志杨．基于三角曲面的逆向工程CAD建模方法．中国机械工程，2003，14(8)：698-701
[25]邱泽阳，肖双九，宋晓字，等．基于三角Bezier曲面局部逼近的3D点插补算法．西北工业大学学报，2002，20(3)：497-501
[26]柯映林，贾明．带边界约束的B样条曲面逼近．计算机辅助设计与图形学学报，2003，15(12)：1549-155
[27] Wen S. H.,Chuang J. C.A reverse engineering based approach for product formdesign.Design Studies,2003,24(2):155-131
[28] Sterolithography Interface Specification.3D systems,Inc. June1988
[29] Hoppe H, Derose T, Duchamp T,et al.Surface reconstruction from unorganizedpoints.Proceedings of ACM SIGGRAPH’92.Chicago,1992:71-78
[30] Amenta M, Bern M, Kamvysselis M. A new Voronoi-based surface reconstructionalgorithm. Proceedings of ACM SIGGRAPH’98. Orlando,1998:415-421
[31]王青，王融清，鲍虎军，等．散乱数据点的增量快速曲面重建算法．软件学报,2000，11(9)：83-89
[32] Lawson C L. Software for C1surface interpolation. Rice J.Mathematical Software III.Pasadena, California: California Institute of Technology,1977:161-194
[33] Bowyer A. Computing dirichlet tessellations. Computer Journal,1981,24(2):162-166
[34] Watson D F. Computing the n-dimension Delaunay tessellation with application toVoronoi polytypic. Computer Journal,1981,24(2):167-172
[35] Sloan SW. A fast algorithm for constructing Delaunay triangulation in the plane.Advances Engineering Software,1987,9(1):34-55
[36]余杰，吕品，郑昌文．Delaunay三角网构建方法比较研究．中国图像图形学报，2010，15(8)：1158-1167
[37]吕震，贾明，柯映林．三角曲面数字样品的特征提取与再现技术．计算机辅助设计与图形学学报，2002，14(8)：768-771
[38] Girod B., Greiner G., Niemann H.Principles of3D image analysis and synthesis.Norwell：Kluwer Academic Publishers,2000:166-180
[39] Lee Y., Park S., Jun Y.,et al.A robust approach to edge detection of scanned pointdata.International Journal of Advanced Manufacturing Technology,2004,23(3-4):263-271
[40]董方敏，肖人彬，钟毅芳，等．机械CAD三角网格模型的特征表面分割混合算法．中国机械工程，2007，18(4)：382-387
[41]钱锦锋，陈志杨，张三元，等．点云数据压缩中的边界特征检测．中国图像图形学报，2005，10(2)：164-169
[42]李根，陈志杨，张三元，等．网格曲面中复杂孔洞的自动修补算法．浙江大学学报，2007，3(3)：407－411
[43]张丽艳，周儒荣，周来水．三角网格模型孔洞修补算法研究．应用科学学报，2002，20(3)：221-224
[44] Vieira M., Shimada K.Surface mesh segmentation and smooth surface extractionthrough region.Computer-aided geometric design,2005,22:771-792
[45]邱彦杰，周雄辉．反向工程中三角网格的加工特征识别．计算机辅助设计与图形学学报，2010，22(04)：711-716
[46] Razdan A, Bae M. A Hybrid Approach to Feature Segmentation of Triangle Meshes.Computer-aided Design,2003,35(9):783-789
[47] Sunil V. B., Pande S. S．Automatic recognition of features from freeform surface CADmodels.Computer-aided design,2008,40(4):502-517
[48] Yang S. Y.,Shu S.Robust feature extraction for the composite surface mesh from STLfile.The9thInternational Conference for Young Computer Scientists,2008:1373-1378
[49] Peng Y. H.,Gao C.H. A novel boundary extraction algorithm on triangular meshes ofSTL model.Advance Advanced Materials Research,2010(97-101):2929-2934
[50]汪俊，周来水，安鲁陵，等．基于网格模型的一种新的区域分割算法．中国机械工程，2005，16(9)：796-801
[51] Charlie C. L.W.,Tang K.Pattern computation for compression garment by a physical/geometric approach.Computer-Aided Design,2010,42(2):78-86
[52] Kim H. S.,Choi H. K.,Lee K. H.,et al．Feature detection of triangular meshes based ontensor voting theory.Computer-aided design，2009(41)：47-58
[53]张慧娟，耿博，汪国平。采用张量投票理论的三角网格模型特征边提取算法．计算机辅助设计与图形学学报，2011，23(01)：62-70
[54]何荣，李际军．逆向工程中特征曲面的识别方法．计算机应用，2007，27(8)：2018-2021
[55] Vida J.,Matin R. R,Varady T.A survey of blending methods that use parametricsurfaces．Computer aided design,1994,26(5):341-365
[56] Geza K. S.,Matin R. R,Varady T.Methods to recover constant radius rolling ball blendsin reverse engineering.Computer Aided Geometric Design,2000,17:127-160
[57] Ke Y. L., Fan S. Q., Zhu W. D., et al.Feature-based reverse modeling strategies.Computer-Aided Design,2006,(38):485-506
[58]李鲜花，周来水，陈文亮．有限元网格的圆角过渡特征提取及网格修改．中国机械工程，2006，17(18)：1920-1923
[59] Garland M, Heckbert P. S. Surface simplification using quadric error metrics.Proceedings of SIGGRAPH97,Computer Graphics Proceedings, Annual ConferenceSeries.NY, USA: Addison Wesley,1997:209-216
[60] Hoppe H. Progressive meshes. In:Proceedings of the SIGGRAPH’96.Held in NewOrleans,Louisiana,1996:99-108
[61] Kalvin A. P., Taylor R.H.Surfaces:polygonal mesh simplification with boundederror.IEEE Computer Graghics Application,1996,16(3):64-77
[62] Yun I. D., Choo K. W., Lee S.U.Mesh simplification using the edge attributes.EURASIP Journal on Applied Signal Processing,2002(10):1102–1115
[63] Kim D. H., Yun I. D., Lee S. U.Boundary-trimmed3D triangular mesh segmentationbased on iterative merging strategy.Pattern Recognition,2006(39):827-838
[64] Mangan A, Whitaker R. Partitioning3D surface meshes using watershed segmentation.IEEE Transactions on Visualization and Computer Graphics,1999,5(4):308-321
[65] Besl P J,McKay N D.A method for registration of3-D shapes.IEEE Transaction onPattern Analysis and Machine Intelligence,1992,14(2):239-256
[66] Woo H,Kang E,Wang S,et al.A new segmentation method for point clouddata.International Journal of Machine Tools&Manufacture,2002,42(2):167-178
[67]张旭，王青，柯映林．基于模板的点云边特征提取技术．计算机集成制造系统，2008，14(6)：1175-1181
[68] Yang M,Lee E.Segmentation of measured point data using a parametric quadricsurface approximation. Computer Aided Design,1999,31(7):449-457
[69]李江雄，柯映林．基于特征的复杂曲面反求建模技术研究．机械工程学报，2000，36(5)：18-22
[70] Lavoue G.,Dupont F.,Baskurt A.Constant Curvature Region Decomposition of3D-Meshes by a Mixed Approach Vertex-triangle. Journal of WSCG,2004,12(2):245-252
[71] Lee Y,Lee S,Shamir A,et al．Intelligent mesh scissoring using3D snakes. Proceedingsof the12th Pacific Conference on Computer Graphics and Applications.WashingtonDC,USA:IEEE Computer Society,2004:279-287
[72] Zhang Y.,Paik J. K.,Koschan A.,et al.A Simple and Efficient Algorithm for PartDecomposition of3-d Triangulated Models Based on Curvature Analysis.InternationalConference on Image Processing, Rochester,NY,USA,2002:273-276
[73]王宏涛，张丽艳，李忠文，等．基于RBF神经网络的三角网格曲面孔洞修补．中国机械工程，2005，16(23)：2072-2075
[74] Branch J., Prieto F., Boulanger P.Automatic hole-filling algorithm for triangularmeshes using local radial function.Third International Symposium on3D DataProcessing, Visualization and Transmission,Chapel Hill,NC,2006:727-734
[75] Liepa P.Filling holes in meshes． Proceedings of the2003Eurographics/ACMSIGGRAPH Symposium on Geometry Processing.Aire-la-Vile,Switzerland:Eurographics Association,2003:200-205
[76] Pernot J. P., Moraru G., Veron P.Filling holes in meshes using a mechanical model tosimulate the curvature variation minimization.Computers&Graphics,2006(30):892-902
[77] Zhao W., Gao S., Lin H.A robust hole-filling algorithm for triangular mesh.VisualCompute,2007,(23):987-997
[78]张丽艳，周儒荣，周来水．三角网格模型孔洞修补算法研究．应用科学学报，2002，20(3)：221-224
[79]韦争亮，钟约先，袁朝龙，等．三角网格大面积孔洞光顺修补算法研究．中国机械工程，2008，19(8)：949-954
[80]刘德平，余水晶，陈建军，等．基于最小二乘支持微量机的三角网格修补算法．计算机集成制造系统，2009，15(9)：1867-1871
[81] Kraevoy V., Sheffer A.Template Based Mesh Completion．Symposium on GeometryProcessing,2005:13-22
[82] Chen C. Y., Cheng K. Y., Liao H. Y. M.A sharpness dependent approach to3D polygonmesh hole filling.Proceeding of2005Eurographics．Dublin,Ireland,2005:13-16
[83]钱归平，潘瑞芳，童若锋．保持特征的网格修补．中国图象图形学报，2010，5(2)：334-339
[84] Yongtae J.A piecewise hole filling algorithm in reverse engineering.Computer-aidedDesign,2005(37):263-272
[85] Rossignac J,Borrel P.Multi-resolution3D approximation for rendering complex scenesIn Falcidieno B. and Kunii T.L.(eds),Geometric Modeling in Computer graphics. NewYork,USA:Springer Verlag,1993:455-465
[86] Low K. L., Tan T. S.Model Simplification Using Vertex-Clustering．In Proceedings ofthe1997Symposium on ACM Symposium on Interactive3D Graphics,New York,USA,1997:75-82
[87]周昆，潘志庚，石教英．一种新的基于顶点聚类的网格简化算法．自动化学报，1999，25(1)：1-8
[88] Derose T,Lounsbery M,Warren J.Multi-resolution Analysis for Surfaces of ArbitraryTopological Type.ACM Transactions on Graphics,1997,16(1):34-73
[89] Matthias E,Derose T,Lounsbery M,et al.Multi-Resolution analysis of arbitrarymeshes.In:Proceedings of the Computer Graphics,Annual Conference Series,SIGGRAPH. Losangeles,1995:71-78
[90] Markus H G.,Roger G.Efficient triangular surface approximations using wavelets andquadtree data structure．IEEE Transactions on Visualization and Computer Graphics,Jun.1996,2(2):130-143
[91] Hoppe H.View-dependent refinement of progressive meshes. Computer Graphics(SIGGRAPH'97),1997,31(3):189-198
[92]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．软件学报，1999，10(5)：503-507
[93] Schroeder W J,Zarge J A,et al.Decimation of triangle meshes.Computer Graphics,1992,26(2):65-70
[94] William J. S.A Toplogy Modifying Progressive Decimation Algorithm.In:Proceedingsof the8th conference on Visualization '97,CA,USA:IEEE Computer Society Press LosAlamitos,1997:205-212
[95] Hoppe H.New Quadric Metric for Simplification Meshes with AppearanceAttributes.In：IEEE Visualization1999,1999:59-66
[96] Hamann B.A Data Reduction Scheme for Triangulated Surfaces.Computer AidedGeometric Design,1994,11(3):197-214
[97] Gieng T S,Hamann B,Joy K L,et al.Constructing Hierarchies for TriangleMeshes.IEEE Transactions on Visualization and Computer Graphics,1998,4(2):145-161
[98] Hoppe H, Derose T,DuchampT.,et al.Mesh optimization. Computer Graphics(SIGGRAPH'93),1993,27:19-26
[99]陆国栋，许鹏，温星.基于向量夹角的三角网格模型简化算法．工程设计学报，2005，12(2)：124-128
[100] Wu Y.,He Y. J.,Cai H.M.QEM-based mesh simplification with global geometryfeatures preserved.In：Proceedings of the2nd international conference on Computergraphics and interactive techniques in Australasia and South East Asia,2004:50-57
[101]刘晓利，刘则毅，高朋东，等．基于尖特征度的边折叠简化算法．软件学报，2005，16(5)：669-675
[102]杜晓晕，尹宝才，孔德慧.基于加权二次误差测度的边折叠简化算法．北京工业大学学报，2007，33(7)：731-736
[103]张丽艳，周儒荣，唐杰，等．带属性的三角网格模型简化算法研究．计算机辅助设计与图形学学报，2002，14(3)：199-204
[104] Chen J. X.,Hu H. H.One mesh model simplification method based on shape transformof triangles.Proceedings of the16th International Conference on Artificial Reality andTelexistence Workshops.Washington DC:IEEE Computer Society,2006:74-79
[105]彭育辉，高诚辉，何炳蔚．基于内角加权及二次误差度量的三角形折叠算法．中国图像图形学报，2008(4)：115-119
[106]全红艳，张田文，董宇欣．一种基于区域分割的几何模型简化方法．计算机学报，2006，29(10)：1834-1842
[107]吴韦力，王博亮，黄绍辉．一种改进的基于二次误差测度的网格简化算法．厦门大学学报(自然科学版)，2007，46(3)：337-341
[108]董方敏，刘勇，肖人彬．一种改进的基于形状特征保持的QEM简化算法．计算机应用，2008，28(8)：2040-2043
[109]刘晓东，董显法，郭威，等．保持特征的三角形有限元网格简化方法．计算力学学报，2010，27(4)：682-687
[110] Cui X.F., Gao S.M., Zhou G.P. An effective algorithm for recognizing and suppressingblend features, Computer-Aided Design and Applications,2004:24-28
[111]催秀芳，高曙明，周广平．一种高效的过渡特征识别和抑制算法．计算机集成制造系统，2004，10(1)：77-82
[112] Hoffman R., Jain A. K. Segmentation and classification of range images. IEEE TransPattern,1997,9(5):608-620
[113]陈志扬，钱锦锋，叶修梓．基于STL模型的逆向工程实体建模技术．中国机械工程，2003，14(20)：1760-1763
[114] Dai M., Newman T. S., Cao C. G.Least-squares-based fitting of paraboloids.PatternRecognition,2007,40(2):504-515
[115] Armin G.,Devrim A．Least squares3D surface and curve matching．ISPRS Journal ofPhotogrammetry and Remote Sensing,2005,59(3):151-174
[116] Varady T., Facellob M. A., Tereka Z.Automatic extraction of surface structures indigital shape reconstruction. Computer-aided design,2007(39):379-388
[117]陈杰，高诚辉，何炳蔚．三角网格模型的混合过渡特征提取方法研究，机械科学与技术，2011，30(1)：81-85
[118]陈杰，高诚辉，何炳蔚．反求工程三维特征提取技术的研究进展，中国工程机械学报，2009，7(2)：239-244
[119] Magid E., Soldea O., Rivlin E.A comparison of Gaussian and mean curvatureestimation methods on triangular meshes of range image data.Computer Vision andImage Understanding2007(107):139-157
[120] Besl P J,Jain R C.Segmentation throuth variable order surface fitting.IEEETransactions on Pattern Analysis and Machine Intelligence,1988,29(2):167-192
[121] Barrera D., Fortex M. A., Gonzalez P.,et al.Filling polygonal holes with minimalenergy surfaces on Powell-Sabin type triangulations. Journal of Computational andApplied Mathematics,2010,234(4):1058-1068
[122] Chen J.,Gao C. H.,He B. W.Regions Segmentation Algorithm of Triangle MeshesBased on Normal Vector. Advanced Materials Research,2010,(102-104):111-115
[123] Sun W. J., Martyn H., John W. M.An investigation of the robustness of the nonlinearleast-squares sphere fitting method to small segment angle surfaces.Original ResearchArticle Precision Engineering,2008,32(1):55-62
[124]唐慧，罗立民，周正东．基于曲线曲率的网格简化方法．中国图像图形学报，2008，13(11)：2224-2230
[125] Cignoniy P, Rocchiniz C, Scopigno R.Metro:measuring error on simplifiedsurfaces.Computer Graphics Forum,1998,17(2):167-174
[2]刘之生．反求工程技术．北京：机械工业出版社，1996
[3] Varady T,Ralph R M.,Jordan C.Reverse engineering of geometric models-anintroduction.Computer-Aided Design,1997,29(4):255-268
[4] Pal B., Ralph R M.,Varady T.Algorithms for reverse engineering boundaryrepresentation models.Computer-Aided Design,2001,33;839-851
[5] Lee K. H., Woo H.Use of reverse engineering method for rapid product development.Computer&Industrial Engineering,1998,35(1-2):21-24
[6]金涛，童水光．逆向工程技术．北京：机械工业出版社，2003
[7] Huang J. B.Geometric feature extraction and model reconstruction from unorganizedpoints for reverse engineering of mechanical parts with arbitrary topology:[Ph.D.dissertation]. Ohio State: The Ohio State University,2001
[8] Zhu G. S., Zhou T. R,Zhou J. Fourier-Mellin matching method application to revolvedsurface extraction in reverse engineering. In: The38th International Conference onComputers and Industrial Engineering,Beijin,2008
[9] Thompson W B,Owen J C, Stark S R,et al.Feature based reverse engineering ofmechanical parts.IEEE Transactions on Robotics and Automation,1999,15(1):57-66
[10] Au C K, Yuen M M F.Feature-based reverse engineering of mannequin for garmentdesign. Computer-Aided Design,1999,31(12):751-759
[11]柯映林，刘云峰，范树迁，等．基于特征的反求工程建模系统RE-SOFT．计算辅助设计与图形学学报，2004，16(6)：799-811；
[12]柯映林，李岸，王军文．过渡特征提取中的概率统计理论和方法．机械工程学报，2003，39(6)：140-144
[13] Lu Z.,Ke Y. L.,Sun Q.,et al.Method to extract blend surface feature in reverseengineering. Chinese Journal of Mechanical Engineering (English Edition),2003,16(3):248-251
[14] Ke Y. L., Sun Q., Lu Z.Least-square method based feature fitting and extraction inreverse engineering.Chinese Journal of Mechanical Engineering(English edition),2003,16(2):163-166
[15]柯映林，单东日．基于区分割与约束逼近的二次曲面重建．浙江大学学报(工学版)，2004，38(10)：1274-1279
[16]金涛，陈建良，童水光．三维模型对称平面重建的特征匹配方法．计算机辅助设计与图形学学报，2003，15(5)：616-620
[17]王丽敏，周天瑞．基于特征的反求工程建模技术研究进展．南方金属，2009(171)：1-4
[18] Benk P, Varady T.Segmentation methods for smooth point regions of conventionalengineering objects. Computer-Aided Design,2004,36(6);511-523
[19] Huang J,Menq C H.Automatic data segmentation for geometric feature extraction fromunorganized3-D coordinate points.IEEE Transitions on Robotics and Automation,2001,17(3):268-279
[20]胡鑫，习俊通，金烨．反求工程中散乱点云数据的自动分割与曲面重构．上海交通大学学报，2004，38(1)：62-65
[21]马骊溟，徐毅，李泽湘．基于高斯曲率极值点的散乱点云数据特征点提取．系统仿真学报，2008，20(9)：2341-2344
[22] Carr J. C.,Beatson R. K.,Cherrie J. B.,et al. Reconstruction and representation of3Dobjects with radial basis functions. Proceedings of the ACM SIGGRAPH Conferenceon Computer Graphics.Los Angeles:ACM,2001:67-76
[23] Guennebaud G, Gross M.Algebraic point set surfaces. Proceedings of the ACMSIGGRAPH Conference on Computer Graphics. San Diego: ACM,2007,26(23):23-31
[24]陈志杨．基于三角曲面的逆向工程CAD建模方法．中国机械工程，2003，14(8)：698-701
[25]邱泽阳，肖双九，宋晓字，等．基于三角Bezier曲面局部逼近的3D点插补算法．西北工业大学学报，2002，20(3)：497-501
[26]柯映林，贾明．带边界约束的B样条曲面逼近．计算机辅助设计与图形学学报，2003，15(12)：1549-155
[27] Wen S. H.,Chuang J. C.A reverse engineering based approach for product formdesign.Design Studies,2003,24(2):155-131
[28] Sterolithography Interface Specification.3D systems,Inc. June1988
[29] Hoppe H, Derose T, Duchamp T,et al.Surface reconstruction from unorganizedpoints.Proceedings of ACM SIGGRAPH’92.Chicago,1992:71-78
[30] Amenta M, Bern M, Kamvysselis M. A new Voronoi-based surface reconstructionalgorithm. Proceedings of ACM SIGGRAPH’98. Orlando,1998:415-421
[31]王青，王融清，鲍虎军，等．散乱数据点的增量快速曲面重建算法．软件学报,2000，11(9)：83-89
[32] Lawson C L. Software for C1surface interpolation. Rice J.Mathematical Software III.Pasadena, California: California Institute of Technology,1977:161-194
[33] Bowyer A. Computing dirichlet tessellations. Computer Journal,1981,24(2):162-166
[34] Watson D F. Computing the n-dimension Delaunay tessellation with application toVoronoi polytypic. Computer Journal,1981,24(2):167-172
[35] Sloan SW. A fast algorithm for constructing Delaunay triangulation in the plane.Advances Engineering Software,1987,9(1):34-55
[36]余杰，吕品，郑昌文．Delaunay三角网构建方法比较研究．中国图像图形学报，2010，15(8)：1158-1167
[37]吕震，贾明，柯映林．三角曲面数字样品的特征提取与再现技术．计算机辅助设计与图形学学报，2002，14(8)：768-771
[38] Girod B., Greiner G., Niemann H.Principles of3D image analysis and synthesis.Norwell：Kluwer Academic Publishers,2000:166-180
[39] Lee Y., Park S., Jun Y.,et al.A robust approach to edge detection of scanned pointdata.International Journal of Advanced Manufacturing Technology,2004,23(3-4):263-271
[40]董方敏，肖人彬，钟毅芳，等．机械CAD三角网格模型的特征表面分割混合算法．中国机械工程，2007，18(4)：382-387
[41]钱锦锋，陈志杨，张三元，等．点云数据压缩中的边界特征检测．中国图像图形学报，2005，10(2)：164-169
[42]李根，陈志杨，张三元，等．网格曲面中复杂孔洞的自动修补算法．浙江大学学报，2007，3(3)：407－411
[43]张丽艳，周儒荣，周来水．三角网格模型孔洞修补算法研究．应用科学学报，2002，20(3)：221-224
[44] Vieira M., Shimada K.Surface mesh segmentation and smooth surface extractionthrough region.Computer-aided geometric design,2005,22:771-792
[45]邱彦杰，周雄辉．反向工程中三角网格的加工特征识别．计算机辅助设计与图形学学报，2010，22(04)：711-716
[46] Razdan A, Bae M. A Hybrid Approach to Feature Segmentation of Triangle Meshes.Computer-aided Design,2003,35(9):783-789
[47] Sunil V. B., Pande S. S．Automatic recognition of features from freeform surface CADmodels.Computer-aided design,2008,40(4):502-517
[48] Yang S. Y.,Shu S.Robust feature extraction for the composite surface mesh from STLfile.The9thInternational Conference for Young Computer Scientists,2008:1373-1378
[49] Peng Y. H.,Gao C.H. A novel boundary extraction algorithm on triangular meshes ofSTL model.Advance Advanced Materials Research,2010(97-101):2929-2934
[50]汪俊，周来水，安鲁陵，等．基于网格模型的一种新的区域分割算法．中国机械工程，2005，16(9)：796-801
[51] Charlie C. L.W.,Tang K.Pattern computation for compression garment by a physical/geometric approach.Computer-Aided Design,2010,42(2):78-86
[52] Kim H. S.,Choi H. K.,Lee K. H.,et al．Feature detection of triangular meshes based ontensor voting theory.Computer-aided design，2009(41)：47-58
[53]张慧娟，耿博，汪国平。采用张量投票理论的三角网格模型特征边提取算法．计算机辅助设计与图形学学报，2011，23(01)：62-70
[54]何荣，李际军．逆向工程中特征曲面的识别方法．计算机应用，2007，27(8)：2018-2021
[55] Vida J.,Matin R. R,Varady T.A survey of blending methods that use parametricsurfaces．Computer aided design,1994,26(5):341-365
[56] Geza K. S.,Matin R. R,Varady T.Methods to recover constant radius rolling ball blendsin reverse engineering.Computer Aided Geometric Design,2000,17:127-160
[57] Ke Y. L., Fan S. Q., Zhu W. D., et al.Feature-based reverse modeling strategies.Computer-Aided Design,2006,(38):485-506
[58]李鲜花，周来水，陈文亮．有限元网格的圆角过渡特征提取及网格修改．中国机械工程，2006，17(18)：1920-1923
[59] Garland M, Heckbert P. S. Surface simplification using quadric error metrics.Proceedings of SIGGRAPH97,Computer Graphics Proceedings, Annual ConferenceSeries.NY, USA: Addison Wesley,1997:209-216
[60] Hoppe H. Progressive meshes. In:Proceedings of the SIGGRAPH’96.Held in NewOrleans,Louisiana,1996:99-108
[61] Kalvin A. P., Taylor R.H.Surfaces:polygonal mesh simplification with boundederror.IEEE Computer Graghics Application,1996,16(3):64-77
[62] Yun I. D., Choo K. W., Lee S.U.Mesh simplification using the edge attributes.EURASIP Journal on Applied Signal Processing,2002(10):1102–1115
[63] Kim D. H., Yun I. D., Lee S. U.Boundary-trimmed3D triangular mesh segmentationbased on iterative merging strategy.Pattern Recognition,2006(39):827-838
[64] Mangan A, Whitaker R. Partitioning3D surface meshes using watershed segmentation.IEEE Transactions on Visualization and Computer Graphics,1999,5(4):308-321
[65] Besl P J,McKay N D.A method for registration of3-D shapes.IEEE Transaction onPattern Analysis and Machine Intelligence,1992,14(2):239-256
[66] Woo H,Kang E,Wang S,et al.A new segmentation method for point clouddata.International Journal of Machine Tools&Manufacture,2002,42(2):167-178
[67]张旭，王青，柯映林．基于模板的点云边特征提取技术．计算机集成制造系统，2008，14(6)：1175-1181
[68] Yang M,Lee E.Segmentation of measured point data using a parametric quadricsurface approximation. Computer Aided Design,1999,31(7):449-457
[69]李江雄，柯映林．基于特征的复杂曲面反求建模技术研究．机械工程学报，2000，36(5)：18-22
[70] Lavoue G.,Dupont F.,Baskurt A.Constant Curvature Region Decomposition of3D-Meshes by a Mixed Approach Vertex-triangle. Journal of WSCG,2004,12(2):245-252
[71] Lee Y,Lee S,Shamir A,et al．Intelligent mesh scissoring using3D snakes. Proceedingsof the12th Pacific Conference on Computer Graphics and Applications.WashingtonDC,USA:IEEE Computer Society,2004:279-287
[72] Zhang Y.,Paik J. K.,Koschan A.,et al.A Simple and Efficient Algorithm for PartDecomposition of3-d Triangulated Models Based on Curvature Analysis.InternationalConference on Image Processing, Rochester,NY,USA,2002:273-276
[73]王宏涛，张丽艳，李忠文，等．基于RBF神经网络的三角网格曲面孔洞修补．中国机械工程，2005，16(23)：2072-2075
[74] Branch J., Prieto F., Boulanger P.Automatic hole-filling algorithm for triangularmeshes using local radial function.Third International Symposium on3D DataProcessing, Visualization and Transmission,Chapel Hill,NC,2006:727-734
[75] Liepa P.Filling holes in meshes． Proceedings of the2003Eurographics/ACMSIGGRAPH Symposium on Geometry Processing.Aire-la-Vile,Switzerland:Eurographics Association,2003:200-205
[76] Pernot J. P., Moraru G., Veron P.Filling holes in meshes using a mechanical model tosimulate the curvature variation minimization.Computers&Graphics,2006(30):892-902
[77] Zhao W., Gao S., Lin H.A robust hole-filling algorithm for triangular mesh.VisualCompute,2007,(23):987-997
[78]张丽艳，周儒荣，周来水．三角网格模型孔洞修补算法研究．应用科学学报，2002，20(3)：221-224
[79]韦争亮，钟约先，袁朝龙，等．三角网格大面积孔洞光顺修补算法研究．中国机械工程，2008，19(8)：949-954
[80]刘德平，余水晶，陈建军，等．基于最小二乘支持微量机的三角网格修补算法．计算机集成制造系统，2009，15(9)：1867-1871
[81] Kraevoy V., Sheffer A.Template Based Mesh Completion．Symposium on GeometryProcessing,2005:13-22
[82] Chen C. Y., Cheng K. Y., Liao H. Y. M.A sharpness dependent approach to3D polygonmesh hole filling.Proceeding of2005Eurographics．Dublin,Ireland,2005:13-16
[83]钱归平，潘瑞芳，童若锋．保持特征的网格修补．中国图象图形学报，2010，5(2)：334-339
[84] Yongtae J.A piecewise hole filling algorithm in reverse engineering.Computer-aidedDesign,2005(37):263-272
[85] Rossignac J,Borrel P.Multi-resolution3D approximation for rendering complex scenesIn Falcidieno B. and Kunii T.L.(eds),Geometric Modeling in Computer graphics. NewYork,USA:Springer Verlag,1993:455-465
[86] Low K. L., Tan T. S.Model Simplification Using Vertex-Clustering．In Proceedings ofthe1997Symposium on ACM Symposium on Interactive3D Graphics,New York,USA,1997:75-82
[87]周昆，潘志庚，石教英．一种新的基于顶点聚类的网格简化算法．自动化学报，1999，25(1)：1-8
[88] Derose T,Lounsbery M,Warren J.Multi-resolution Analysis for Surfaces of ArbitraryTopological Type.ACM Transactions on Graphics,1997,16(1):34-73
[89] Matthias E,Derose T,Lounsbery M,et al.Multi-Resolution analysis of arbitrarymeshes.In:Proceedings of the Computer Graphics,Annual Conference Series,SIGGRAPH. Losangeles,1995:71-78
[90] Markus H G.,Roger G.Efficient triangular surface approximations using wavelets andquadtree data structure．IEEE Transactions on Visualization and Computer Graphics,Jun.1996,2(2):130-143
[91] Hoppe H.View-dependent refinement of progressive meshes. Computer Graphics(SIGGRAPH'97),1997,31(3):189-198
[92]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．软件学报，1999，10(5)：503-507
[93] Schroeder W J,Zarge J A,et al.Decimation of triangle meshes.Computer Graphics,1992,26(2):65-70
[94] William J. S.A Toplogy Modifying Progressive Decimation Algorithm.In:Proceedingsof the8th conference on Visualization '97,CA,USA:IEEE Computer Society Press LosAlamitos,1997:205-212
[95] Hoppe H.New Quadric Metric for Simplification Meshes with AppearanceAttributes.In：IEEE Visualization1999,1999:59-66
[96] Hamann B.A Data Reduction Scheme for Triangulated Surfaces.Computer AidedGeometric Design,1994,11(3):197-214
[97] Gieng T S,Hamann B,Joy K L,et al.Constructing Hierarchies for TriangleMeshes.IEEE Transactions on Visualization and Computer Graphics,1998,4(2):145-161
[98] Hoppe H, Derose T,DuchampT.,et al.Mesh optimization. Computer Graphics(SIGGRAPH'93),1993,27:19-26
[99]陆国栋，许鹏，温星.基于向量夹角的三角网格模型简化算法．工程设计学报，2005，12(2)：124-128
[100] Wu Y.,He Y. J.,Cai H.M.QEM-based mesh simplification with global geometryfeatures preserved.In：Proceedings of the2nd international conference on Computergraphics and interactive techniques in Australasia and South East Asia,2004:50-57
[101]刘晓利，刘则毅，高朋东，等．基于尖特征度的边折叠简化算法．软件学报，2005，16(5)：669-675
[102]杜晓晕，尹宝才，孔德慧.基于加权二次误差测度的边折叠简化算法．北京工业大学学报，2007，33(7)：731-736
[103]张丽艳，周儒荣，唐杰，等．带属性的三角网格模型简化算法研究．计算机辅助设计与图形学学报，2002，14(3)：199-204
[104] Chen J. X.,Hu H. H.One mesh model simplification method based on shape transformof triangles.Proceedings of the16th International Conference on Artificial Reality andTelexistence Workshops.Washington DC:IEEE Computer Society,2006:74-79
[105]彭育辉，高诚辉，何炳蔚．基于内角加权及二次误差度量的三角形折叠算法．中国图像图形学报，2008(4)：115-119
[106]全红艳，张田文，董宇欣．一种基于区域分割的几何模型简化方法．计算机学报，2006，29(10)：1834-1842
[107]吴韦力，王博亮，黄绍辉．一种改进的基于二次误差测度的网格简化算法．厦门大学学报(自然科学版)，2007，46(3)：337-341
[108]董方敏，刘勇，肖人彬．一种改进的基于形状特征保持的QEM简化算法．计算机应用，2008，28(8)：2040-2043
[109]刘晓东，董显法，郭威，等．保持特征的三角形有限元网格简化方法．计算力学学报，2010，27(4)：682-687
[110] Cui X.F., Gao S.M., Zhou G.P. An effective algorithm for recognizing and suppressingblend features, Computer-Aided Design and Applications,2004:24-28
[111]催秀芳，高曙明，周广平．一种高效的过渡特征识别和抑制算法．计算机集成制造系统，2004，10(1)：77-82
[112] Hoffman R., Jain A. K. Segmentation and classification of range images. IEEE TransPattern,1997,9(5):608-620
[113]陈志扬，钱锦锋，叶修梓．基于STL模型的逆向工程实体建模技术．中国机械工程，2003，14(20)：1760-1763
[114] Dai M., Newman T. S., Cao C. G.Least-squares-based fitting of paraboloids.PatternRecognition,2007,40(2):504-515
[115] Armin G.,Devrim A．Least squares3D surface and curve matching．ISPRS Journal ofPhotogrammetry and Remote Sensing,2005,59(3):151-174
[116] Varady T., Facellob M. A., Tereka Z.Automatic extraction of surface structures indigital shape reconstruction. Computer-aided design,2007(39):379-388
[117]陈杰，高诚辉，何炳蔚．三角网格模型的混合过渡特征提取方法研究，机械科学与技术，2011，30(1)：81-85
[118]陈杰，高诚辉，何炳蔚．反求工程三维特征提取技术的研究进展，中国工程机械学报，2009，7(2)：239-244
[119] Magid E., Soldea O., Rivlin E.A comparison of Gaussian and mean curvatureestimation methods on triangular meshes of range image data.Computer Vision andImage Understanding2007(107):139-157
[120] Besl P J,Jain R C.Segmentation throuth variable order surface fitting.IEEETransactions on Pattern Analysis and Machine Intelligence,1988,29(2):167-192
[121] Barrera D., Fortex M. A., Gonzalez P.,et al.Filling polygonal holes with minimalenergy surfaces on Powell-Sabin type triangulations. Journal of Computational andApplied Mathematics,2010,234(4):1058-1068
[122] Chen J.,Gao C. H.,He B. W.Regions Segmentation Algorithm of Triangle MeshesBased on Normal Vector. Advanced Materials Research,2010,(102-104):111-115
[123] Sun W. J., Martyn H., John W. M.An investigation of the robustness of the nonlinearleast-squares sphere fitting method to small segment angle surfaces.Original ResearchArticle Precision Engineering,2008,32(1):55-62
[124]唐慧，罗立民，周正东．基于曲线曲率的网格简化方法．中国图像图形学报，2008，13(11)：2224-2230
[125] Cignoniy P, Rocchiniz C, Scopigno R.Metro:measuring error on simplifiedsurfaces.Computer Graphics Forum,1998,17(2):167-174