三角网格模型的特征保持混合折叠简化
|
摘要
在增材制造、逆向工程等领域,广泛存在包含大量甚至海量数据的三角网格模型。为便于存储并提高处理效率,经常需要进行网格模型简化。但在网格简化过程中存在特征保持、简化率和简化效率冲突的问题,为更好地平衡简化结果和简化效率,提出了特征保持的混合折叠算法。在基于曲度精确计算新顶点、最大距离高效计算折叠代价的基础上,对边界特征区域和非边界特征区域采用边折叠方式进行保特征简化,对非特征区域则采用三角形折叠方法进行高效简化,最后通过偏差和网格正则度对简化结果作出误差评价。算法实例表明:混合折叠算法的模型细节特征保持较好,简化前后变形较小且效率适中。
In additive manufacturing,reverse engineering,and other fields,many triangular mesh models were used to process big data.To facilitate storage and improve processing efficiency,simplifying the mesh model was necessary.However,conflicts existed among feature preservation,simplification rate,and simplification efficiency in mesh simplification.For improved balancing of results and efficiency of simplification,a method based on curvedness was proposed to compute new vertices more precisely.In addition,a method based on the max distance was proposed to compute collapse cost efficiently.The edge collapse was adopted for preserving the features of boundary and non-boundary feature regions,and the triangle collapse was applied to simplify the non-feature areas efficiently.The mesh regularity of the simplified model and the deviation between the original and simplified models were used as evaluation criteria for mesh simplification.Extensive experiments demonstrate that the mesh simplification algorithm with hybrid collapse can effectively preserve the features of a complicated mesh model with fewer errors and moderate efficiency.
In additive manufacturing,reverse engineering,and other fields,many triangular mesh models were used to process big data.To facilitate storage and improve processing efficiency,simplifying the mesh model was necessary.However,conflicts existed among feature preservation,simplification rate,and simplification efficiency in mesh simplification.For improved balancing of results and efficiency of simplification,a method based on curvedness was proposed to compute new vertices more precisely.In addition,a method based on the max distance was proposed to compute collapse cost efficiently.The edge collapse was adopted for preserving the features of boundary and non-boundary feature regions,and the triangle collapse was applied to simplify the non-feature areas efficiently.The mesh regularity of the simplified model and the deviation between the original and simplified models were used as evaluation criteria for mesh simplification.Extensive experiments demonstrate that the mesh simplification algorithm with hybrid collapse can effectively preserve the features of a complicated mesh model with fewer errors and moderate efficiency.
引文
[1]耿国华,石晨晨,魏潇然,等.3D打印中的模型分割与打包[J].光学精密工程,2016,24(6):1439-1447.KENG G H,SHI CH CH,WEI X R,et al..Model segmentation and packaging in 3Dprinting[J].Opt.Precision Eng.,2016,24(6):1439-1447.(in Chinese)
[2]DASSI F,ETTINGER B,PEROTTO S,et al..Amesh simplification strategy for a spatial regression analysis over the cortical surface of the brain[J].Applied Numerical Mathematics,2015,90:111-131.
[3]袁小翠,吴禄镇,陈华伟,等.特征保持点云数据精简[J].光学精密工程,2015,23(9):2666-2676.YUAN X C,WU L ZH,CHEN H W,et al..Point cloud adaptive simplification of feature extraction[J].Opt.Precision Eng.,2015,23(9):2666-2676.(in Chinese)
[4]MICHAUD C,MELLADO N,PAULIN M.Mesh simplification with curvature error metric[C].Eurographics 2017,Lyon,France:Posters,2017.
[5]LEE H,KYUNG M H.Parallel mesh simplification using embedded tree collapsing[J].Visual Computer,2016,32(6-8):967-976.
[6]CABIDDU D,ATTENE M.Large mesh simplification for distributed environments[J].Computers&Graphics,2015,51:81-89.
[7]LI Y B,ZHU Q.A new mesh simplification algorithm based on quadric error metrics[C].International Conference on Advanced Computer Theory and Engineering,Phuket,Thailand:ICACTE,2008:528-532.
[8]李现民,李桂清,张小玲,等.基于子分规则的边折叠简化方法[J].计算机辅助设计与图形学学报,2002,14(1):8-13.LI X M,LI G Q,ZHANG X L,et al..Edge collapse simplification based on subdivision[J].Journal of Computer-Aided Design Computer Graphics,2002,14(1):8-13.(in Chinese)
[9]段黎明,杨尚朋,张霞,等.基于遗传算法的三角网格折叠简化[J].光学精密工程,2018,26(6):1489-1496.DUAN L M,YANG SH P,ZHANG X,et al..Collapsing simplification of triangular mesh based on genetic algorithm[J].Opt.Precision Eng.,2018,26(6):1489-1496.(in Chinese)
[10]段黎明,邵辉,李中明,等.高效率的三角网格模型保特征简化方法[J].光学精密工程,2017,25(2):460-468.DUAN L M,SHAO H,LI ZH M,et al..Simplification method for feature preserving of efficient triangular mesh model[J].Opt.Precision Eng.,2017,25(2):460-468.(in Chinese)
[11]裴艳云,陈飞翔.一种基于不平滑度的网格简化算法[J].计算机工程与应用,2013,49(14):174-177.PEI Y Y,CHEN F X.Mesh simplification algorithm based on non-smoothness[J].Computer Engineering and Applications,2013,49(14):174-177.(in Chinese)
[12]张欣,秦茂玲,谢堂龙.基于特征保持的三角形折叠网格简化算法[J].计算机技术与发展,2012,22(1):94-97.ZHANG X,QIN M L,XIE L T.Mesh simplification algorithm of triangle collapse based on feature preserving[J].Computer Technology and Development,2012,22(1):94-97.(in Chinese)
[13]佟玉斌,王辉.基于曲面拟合的三角形网格简化[J].计算机工程,2012,38(8):242-245.TONG Y B,WANG H.Triangular mesh simplification based on surface fitting[J].Computer Engineering,2012,38(8):242-245.(in Chinese)
[14]WEI J,LOU Y.Feature preserving mesh simplification using feature sensitive metric[J].Computer Science and Technology,2010,25(3):595-605.
[15]王爱霖,刘弘,张桂娟.基于谷脊线特征的三维网格模型简化方法[J].计算机辅助设计与图形学学报,2014,26(5):788-793.WANG A L,LIU H,ZHANG G J.A mesh simplification method based on ridge-valley lines[J].Journal of Computer-Aided Design Computer Graphics,2014,26(5):788-793.(in Chinese)
[16]周继来,周明全,耿国华,等.基于曲度特征的三维模型检索算法[J].计算机应用,2016,36(7):1914-1917.ZHOU J L,ZHOU M Q,GENG G H.3D model retrieval algorithm based on curvedness feature[J].Journal of Computer Applications,2016,36(7):1914-1917.(in Chinese)
[17]WANG J,YU Z.Surface feature based mesh segmentation[J].Computers&Graphics,2011,35(3):661-667.
[18]ARHID K,ZAKANI F R,BOUKSIM M,et al..An Efficient Hierarchical 3D Mesh Segmentation Using Negative Curvature and Dihedral Angle[J].International Journal of Intelligent Engineering&Systems,2017,10(5):143-152.
[19]崔鑫,闫秀天,李世鹏.保持特征的散乱点云数据去噪[J].光学精密工程,2017,25(12):3169-3178.CUI X,YAN X T,LI SH P.Feature preserving scattered point cloud denoising[J].Opt.Precision Eng.,2017,25(12):3169-3178.(in Chinese)
[20]DING Y,DWIVEDI R,KOVACEVIC R.Process planning for 8-axis robotized laser-based direct metal deposition system:A case on building revolved part[J].Robotics and Computer-Integrated Manufacturing,2017,44:67-76.
[2]DASSI F,ETTINGER B,PEROTTO S,et al..Amesh simplification strategy for a spatial regression analysis over the cortical surface of the brain[J].Applied Numerical Mathematics,2015,90:111-131.
[3]袁小翠,吴禄镇,陈华伟,等.特征保持点云数据精简[J].光学精密工程,2015,23(9):2666-2676.YUAN X C,WU L ZH,CHEN H W,et al..Point cloud adaptive simplification of feature extraction[J].Opt.Precision Eng.,2015,23(9):2666-2676.(in Chinese)
[4]MICHAUD C,MELLADO N,PAULIN M.Mesh simplification with curvature error metric[C].Eurographics 2017,Lyon,France:Posters,2017.
[5]LEE H,KYUNG M H.Parallel mesh simplification using embedded tree collapsing[J].Visual Computer,2016,32(6-8):967-976.
[6]CABIDDU D,ATTENE M.Large mesh simplification for distributed environments[J].Computers&Graphics,2015,51:81-89.
[7]LI Y B,ZHU Q.A new mesh simplification algorithm based on quadric error metrics[C].International Conference on Advanced Computer Theory and Engineering,Phuket,Thailand:ICACTE,2008:528-532.
[8]李现民,李桂清,张小玲,等.基于子分规则的边折叠简化方法[J].计算机辅助设计与图形学学报,2002,14(1):8-13.LI X M,LI G Q,ZHANG X L,et al..Edge collapse simplification based on subdivision[J].Journal of Computer-Aided Design Computer Graphics,2002,14(1):8-13.(in Chinese)
[9]段黎明,杨尚朋,张霞,等.基于遗传算法的三角网格折叠简化[J].光学精密工程,2018,26(6):1489-1496.DUAN L M,YANG SH P,ZHANG X,et al..Collapsing simplification of triangular mesh based on genetic algorithm[J].Opt.Precision Eng.,2018,26(6):1489-1496.(in Chinese)
[10]段黎明,邵辉,李中明,等.高效率的三角网格模型保特征简化方法[J].光学精密工程,2017,25(2):460-468.DUAN L M,SHAO H,LI ZH M,et al..Simplification method for feature preserving of efficient triangular mesh model[J].Opt.Precision Eng.,2017,25(2):460-468.(in Chinese)
[11]裴艳云,陈飞翔.一种基于不平滑度的网格简化算法[J].计算机工程与应用,2013,49(14):174-177.PEI Y Y,CHEN F X.Mesh simplification algorithm based on non-smoothness[J].Computer Engineering and Applications,2013,49(14):174-177.(in Chinese)
[12]张欣,秦茂玲,谢堂龙.基于特征保持的三角形折叠网格简化算法[J].计算机技术与发展,2012,22(1):94-97.ZHANG X,QIN M L,XIE L T.Mesh simplification algorithm of triangle collapse based on feature preserving[J].Computer Technology and Development,2012,22(1):94-97.(in Chinese)
[13]佟玉斌,王辉.基于曲面拟合的三角形网格简化[J].计算机工程,2012,38(8):242-245.TONG Y B,WANG H.Triangular mesh simplification based on surface fitting[J].Computer Engineering,2012,38(8):242-245.(in Chinese)
[14]WEI J,LOU Y.Feature preserving mesh simplification using feature sensitive metric[J].Computer Science and Technology,2010,25(3):595-605.
[15]王爱霖,刘弘,张桂娟.基于谷脊线特征的三维网格模型简化方法[J].计算机辅助设计与图形学学报,2014,26(5):788-793.WANG A L,LIU H,ZHANG G J.A mesh simplification method based on ridge-valley lines[J].Journal of Computer-Aided Design Computer Graphics,2014,26(5):788-793.(in Chinese)
[16]周继来,周明全,耿国华,等.基于曲度特征的三维模型检索算法[J].计算机应用,2016,36(7):1914-1917.ZHOU J L,ZHOU M Q,GENG G H.3D model retrieval algorithm based on curvedness feature[J].Journal of Computer Applications,2016,36(7):1914-1917.(in Chinese)
[17]WANG J,YU Z.Surface feature based mesh segmentation[J].Computers&Graphics,2011,35(3):661-667.
[18]ARHID K,ZAKANI F R,BOUKSIM M,et al..An Efficient Hierarchical 3D Mesh Segmentation Using Negative Curvature and Dihedral Angle[J].International Journal of Intelligent Engineering&Systems,2017,10(5):143-152.
[19]崔鑫,闫秀天,李世鹏.保持特征的散乱点云数据去噪[J].光学精密工程,2017,25(12):3169-3178.CUI X,YAN X T,LI SH P.Feature preserving scattered point cloud denoising[J].Opt.Precision Eng.,2017,25(12):3169-3178.(in Chinese)
[20]DING Y,DWIVEDI R,KOVACEVIC R.Process planning for 8-axis robotized laser-based direct metal deposition system:A case on building revolved part[J].Robotics and Computer-Integrated Manufacturing,2017,44:67-76.