面向不规则点消除的四边形网格优化方法
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摘要
为了改善四边形网格的拓扑连接关系,针对Liu等提出的优化方法[1](Liu Jianfei,Sun Shuli,Chen Yongqiang.A new method of quality improvement for quadrilateral mesh based on small polygon reconnection).Acta Mechanica Sinica,2012,28(1):140-145),提出了面向不规则点消除的四边形网格优化方法.首先引入了一个加速策略,使每次操作可以处理的区域更大,从而提高了消除不规则点的能力;其次将方法拓展至曲面网格的优化.数值实验结果表明,该方法既能够大幅度改善ANSYS等数值模拟软件生成的四边形网格,也能进一步提高使用图形学领域方法得出的四边形网格的质量.
For improving topological connection of quadrilateral mesh, we presented a optimization method based on irregular node removal by upgrading and adapting the method of Liu et al. [1]( Liu Jianfei, Sun Shuli, Chen Yongqiang. A new method of quality improvement for quadrilateral mesh based on small polygon reconnection. Acta Mechanica Sinica, 2012, 28(1): 140-145). First, we used a strategy to speed up the original method, so it is able to treat bigger polygons and is more powerful to remove irregular nodes. Second, we recast the method to the curved surface. The testing results demonstrate that the upgraded method can greatly improve topological connectivity of meshes generated by finite element analysis packages including ANSYS. Meshes generated by the current state of art techniques in computer graphics can also be improved by our method.
For improving topological connection of quadrilateral mesh, we presented a optimization method based on irregular node removal by upgrading and adapting the method of Liu et al. [1]( Liu Jianfei, Sun Shuli, Chen Yongqiang. A new method of quality improvement for quadrilateral mesh based on small polygon reconnection. Acta Mechanica Sinica, 2012, 28(1): 140-145). First, we used a strategy to speed up the original method, so it is able to treat bigger polygons and is more powerful to remove irregular nodes. Second, we recast the method to the curved surface. The testing results demonstrate that the upgraded method can greatly improve topological connectivity of meshes generated by finite element analysis packages including ANSYS. Meshes generated by the current state of art techniques in computer graphics can also be improved by our method.
引文
[1]Liu J F,Sun S L,Chen Y Q.A new method of quality improvement for quadrilateral mesh based on small polygon reconnection[J].Acta Mechanica Sinica,2012,28(1):140-145
[2]Lin Tianjun,Guan Zhenqun,Chang Jihai,et al.An efficient method for unstructured dynamic mesh deformation-vertex-ball spring smoothing[J].Journal of Computer-Aided Design&Computer Graphics,2013,25(11):1651-1657(in Chinese)(林天军,关振群,昌继海,等.高效的非结构动网格变形方法——点球弹簧修匀法[J].计算机辅助设计与图形学学报,2013,25(11):1651-1657)
[3]Xiao Zhoufang,Chen Jianjun,Cao Jian,et al.Automatic hexahedral mesh generation algorithm for many-to-many sweep volumes[J].Journal of Computer-Aided Design&Computer Graphics,2012,24(8):989-996(in Chinese)(肖周芳,陈建军,曹建,等.多源多目标扫掠体的全六面体网格自动生成算法[J].计算机辅助设计与图形学学报,2012,24(8):989-996)
[4]Huang Jin,Jiang Tengfei,Bao Hujun.Research progress on automatic quadrilateral and hexahedral remeshing[J].Journal of Computer-Aided Design&Computer Graphics,2015,27(8):1354-1362(in Chinese)(黄劲,江腾飞,鲍虎军.四边形与六面体自动重网格化技术研究综述[J].计算机辅助设计与图形学学报,2015,27(8):1354-1362)
[5]Guan Zhenqun,Song Chao,Gu Yuanxian,et al.Recent advances of research on finite element mesh generation methods[J].Journal of Computer-Aided Design&Computer Graphics,2003,15(1):1-14(in Chinese)(关振群,宋超,顾元宪,等.有限元网格生成方法研究的新进展[J].计算机辅助设计与图形学学报,2003,15(1):1-14)
[6]Yin Mengxiao,Xian Chuhua,Xiong Yunhui,et al.Properties of helical strips in quad mesh optimization[J].Journal of Computer-Aided Design&Computer Graphics,2014,26(12):2107-2114(in Chinese)(尹梦晓,冼楚华,熊赟晖,等.四边形网格优化中的螺旋条带生成[J].计算机辅助设计与图形学学报,2014,26(12):2107-2114)
[7]Chen Z J,Tristano J R,Kwok W.Construction of an objective function for optimization-based smoothing[J].Engineering with Computers,2004,20(3):184-192
[8]Brewer M,Diachin L F,Knupp P,et al.The mesquite mesh quality improvement toolkit[OL].[2016-01-28].http://www.imr.sandia.gov/papers/abstracts/Br280.html
[9]Leordeanu M,Hebert M.Smoothing-based optimization[C]//Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition.Los Alamitos:IEEE Computer Society Press,2008:1-8
[10]Levi Z,Zorin D.Strict minimizers for geometric optimization[J].ACM Transactions on Graphics,2014,33(6):Article No.185
[11]Knupp P,Freitag-Diachin L,Tidwell B.Mesquite mesh quality improvement toolkit user's guide[OL].[2016-01-28].https://software.sandia.gov/mesquite/
[12]Peng C H,Zhang E,Kobayashi Y,et al.Connectivity editing for quadrilateral meshes[J].ACM Transactions on Graphics,2011,30(6):Article No.141
[13]Peng C H,Barton M,Jiang C G,et al.Exploring quadrangulations[J].ACM Transactions on Graphics,2014,33(1):Article No.12
[14]Liu Y,Xu W W,Wang J,et al.General planar quadrilateral mesh design using conjugate direction field[J].ACM Transactions on Graphics,2011,30(6):Article No.140
[15]Bunin G.Non-local topological clean-up[C]//Proceedings of the 15th International Meshing Roundtable.Heidelberg:Springer,2006:3-20
[16]Canann S A,Muthukrishnan S N,Phillips R K.Topological improvement procedures for quadrilateral finite element meshes[J].Engineering with Computers,1998,14(2):168-177
[17]Chen Ligang,Zheng Yao,Chen Jianjun.Topological improvement for quadrilateral finite element meshes[J].Journal of Computer-Aided Design&Computer Graphics,2007,19(1):78-83(in Chinese)(陈立岗,郑耀,陈建军.全四边形有限元网格的拓扑优化策略[J].计算机辅助设计与图形学学报,2007,19(1):78-83)
[18]Shi Feng,Zhang Minglei,Sun Shuli.Topological improvement for planar quadrilateral mesh based on“case-operations”[OL].[2016-01-28].http://cpfd.cnki.com.cn/Article/CPFDTOTAL-BJLH201201001201.htm(in Chinese)(施峰,张明磊,孙树立.基于“型-操作”的平面四边形网格的拓扑优化[OL].[2016-01-28].http://cpfd.cnki.com.cn/Article/CPFDTOTAL-BJLH201201001201.htm)
[19]Cao Hongmei,Guo Yan.Grid quality assessment methods[J].Journal of Taiyuan Normal University:Natural Science Edition,2008,7(4):41-43(in Chinese)(曹红梅,郭彦.计算网格质量评估方法[J].太原师范学院学报:自然科学版,2008,7(4):41-43)
[20]Bommes D,Zimmer H,Kobbelt L.Mixed-integer quadrangulation[J].ACM Transactions on Graphics,2009,28(3):Article No.77
[2]Lin Tianjun,Guan Zhenqun,Chang Jihai,et al.An efficient method for unstructured dynamic mesh deformation-vertex-ball spring smoothing[J].Journal of Computer-Aided Design&Computer Graphics,2013,25(11):1651-1657(in Chinese)(林天军,关振群,昌继海,等.高效的非结构动网格变形方法——点球弹簧修匀法[J].计算机辅助设计与图形学学报,2013,25(11):1651-1657)
[3]Xiao Zhoufang,Chen Jianjun,Cao Jian,et al.Automatic hexahedral mesh generation algorithm for many-to-many sweep volumes[J].Journal of Computer-Aided Design&Computer Graphics,2012,24(8):989-996(in Chinese)(肖周芳,陈建军,曹建,等.多源多目标扫掠体的全六面体网格自动生成算法[J].计算机辅助设计与图形学学报,2012,24(8):989-996)
[4]Huang Jin,Jiang Tengfei,Bao Hujun.Research progress on automatic quadrilateral and hexahedral remeshing[J].Journal of Computer-Aided Design&Computer Graphics,2015,27(8):1354-1362(in Chinese)(黄劲,江腾飞,鲍虎军.四边形与六面体自动重网格化技术研究综述[J].计算机辅助设计与图形学学报,2015,27(8):1354-1362)
[5]Guan Zhenqun,Song Chao,Gu Yuanxian,et al.Recent advances of research on finite element mesh generation methods[J].Journal of Computer-Aided Design&Computer Graphics,2003,15(1):1-14(in Chinese)(关振群,宋超,顾元宪,等.有限元网格生成方法研究的新进展[J].计算机辅助设计与图形学学报,2003,15(1):1-14)
[6]Yin Mengxiao,Xian Chuhua,Xiong Yunhui,et al.Properties of helical strips in quad mesh optimization[J].Journal of Computer-Aided Design&Computer Graphics,2014,26(12):2107-2114(in Chinese)(尹梦晓,冼楚华,熊赟晖,等.四边形网格优化中的螺旋条带生成[J].计算机辅助设计与图形学学报,2014,26(12):2107-2114)
[7]Chen Z J,Tristano J R,Kwok W.Construction of an objective function for optimization-based smoothing[J].Engineering with Computers,2004,20(3):184-192
[8]Brewer M,Diachin L F,Knupp P,et al.The mesquite mesh quality improvement toolkit[OL].[2016-01-28].http://www.imr.sandia.gov/papers/abstracts/Br280.html
[9]Leordeanu M,Hebert M.Smoothing-based optimization[C]//Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition.Los Alamitos:IEEE Computer Society Press,2008:1-8
[10]Levi Z,Zorin D.Strict minimizers for geometric optimization[J].ACM Transactions on Graphics,2014,33(6):Article No.185
[11]Knupp P,Freitag-Diachin L,Tidwell B.Mesquite mesh quality improvement toolkit user's guide[OL].[2016-01-28].https://software.sandia.gov/mesquite/
[12]Peng C H,Zhang E,Kobayashi Y,et al.Connectivity editing for quadrilateral meshes[J].ACM Transactions on Graphics,2011,30(6):Article No.141
[13]Peng C H,Barton M,Jiang C G,et al.Exploring quadrangulations[J].ACM Transactions on Graphics,2014,33(1):Article No.12
[14]Liu Y,Xu W W,Wang J,et al.General planar quadrilateral mesh design using conjugate direction field[J].ACM Transactions on Graphics,2011,30(6):Article No.140
[15]Bunin G.Non-local topological clean-up[C]//Proceedings of the 15th International Meshing Roundtable.Heidelberg:Springer,2006:3-20
[16]Canann S A,Muthukrishnan S N,Phillips R K.Topological improvement procedures for quadrilateral finite element meshes[J].Engineering with Computers,1998,14(2):168-177
[17]Chen Ligang,Zheng Yao,Chen Jianjun.Topological improvement for quadrilateral finite element meshes[J].Journal of Computer-Aided Design&Computer Graphics,2007,19(1):78-83(in Chinese)(陈立岗,郑耀,陈建军.全四边形有限元网格的拓扑优化策略[J].计算机辅助设计与图形学学报,2007,19(1):78-83)
[18]Shi Feng,Zhang Minglei,Sun Shuli.Topological improvement for planar quadrilateral mesh based on“case-operations”[OL].[2016-01-28].http://cpfd.cnki.com.cn/Article/CPFDTOTAL-BJLH201201001201.htm(in Chinese)(施峰,张明磊,孙树立.基于“型-操作”的平面四边形网格的拓扑优化[OL].[2016-01-28].http://cpfd.cnki.com.cn/Article/CPFDTOTAL-BJLH201201001201.htm)
[19]Cao Hongmei,Guo Yan.Grid quality assessment methods[J].Journal of Taiyuan Normal University:Natural Science Edition,2008,7(4):41-43(in Chinese)(曹红梅,郭彦.计算网格质量评估方法[J].太原师范学院学报:自然科学版,2008,7(4):41-43)
[20]Bommes D,Zimmer H,Kobbelt L.Mixed-integer quadrangulation[J].ACM Transactions on Graphics,2009,28(3):Article No.77