Surface Flattening based on Linear-Elastic Finite Element Method
This paper presents a linear-elastic finite element method based flattening algorithm for three dimensional triangular surfaces. First, an intrinsic characteristic preserving method is used to obtain the initial developing graph, which preserves the angles and length ratios between two adjacent edges. Then, an iterative equation is established based on linear-elastic finite element method and the flattening result with an equilibrium state of internal force is obtained by solving this iterative equation. The results show that complex surfaces can be dealt with this proposed method, which is an efficient tool for the applications in computer aided design, such as mould design.
[1] McCartney J, Hinds BK, Seow BL. The flattening of triangulated surfaces
incorporating darts and gussets. Computer Aided Design 1999,
31(4):249-260.
[2] Wang CCL, Kai T, Benjamin ML. Freeform surface flattening based on
fitting a woven mesh model. Computer Aided Design 2005, 37(8):
799-814.
[3] Wang CCL, Chen SSF, Yuen MMF. Surface flattening based on energy
model. Computer Aided Design 2002, 34(11): 823-833.
[4] Yueqi Zhong, Bugao Xu. A physically based method for triangulated
surface flattening. Computer Aided Design, 2006, 38(10): 1062-1073.
[5] Parida L, Mudur SP. Constraint-satisfying planar development of
complex surfaces. Comput Aided Des 1993, 25(4): 225-32.
[6] Floater MS. Parameterization and smooth approximation of surface
triangulations. Computer Aided Geometry Design 1997, 14(3): 231-250.
[7] Sheffer A, Lévy B, Mogilnitsky M,et al. ABF++: fast and robust angle
based flattening. ACM Trans Graph 2005, 24(2):311-330.
[8] L'evy B, Petitjean S, Ray N, et al. Least squares conformal maps for
automatic texture atlas generation. ACM Transactions on Graphics, 2002,
21(3): 362-371.
[9] Liu LG, Zhang L, Xu Y, et al. A local/global approach to mesh
parameterization [J]. Computer Graphics Forum, 2008, 27(5): 495-504.
[10] Chen WL, Zhang S, Jin XB. Research on the algorithm of hole repairing
of finite element mesh. Chinese journal of computers, 2005, 28(6):
1068-1071.
[11] Sederberg T W, Gao P, Wang G J, et al. 2-D shape blending: an intrinsic
solution to the vertex path problem. Proceedings of SIGGRAPH. Los
Angeles: ACM, 1993: 15-18.
[12] Toledo S. Taucs: a library of sparse linear solvers [EB/PL]. (2003-9-4)
[2010-3-10]. http://www.tau.ac.il- /~stoledo/taucs/.
[13] Wang XC. Finite element method [M]. Beijing: Tsinghua University
Press, 2003.
[14] Bao YD. Research on one step inverse forming fem and crash simulation
of auto body part. Ph.D. thesis. Changchun: Jilin University; 2005.
[1] McCartney J, Hinds BK, Seow BL. The flattening of triangulated surfaces
incorporating darts and gussets. Computer Aided Design 1999,
31(4):249-260.
[2] Wang CCL, Kai T, Benjamin ML. Freeform surface flattening based on
fitting a woven mesh model. Computer Aided Design 2005, 37(8):
799-814.
[3] Wang CCL, Chen SSF, Yuen MMF. Surface flattening based on energy
model. Computer Aided Design 2002, 34(11): 823-833.
[4] Yueqi Zhong, Bugao Xu. A physically based method for triangulated
surface flattening. Computer Aided Design, 2006, 38(10): 1062-1073.
[5] Parida L, Mudur SP. Constraint-satisfying planar development of
complex surfaces. Comput Aided Des 1993, 25(4): 225-32.
[6] Floater MS. Parameterization and smooth approximation of surface
triangulations. Computer Aided Geometry Design 1997, 14(3): 231-250.
[7] Sheffer A, Lévy B, Mogilnitsky M,et al. ABF++: fast and robust angle
based flattening. ACM Trans Graph 2005, 24(2):311-330.
[8] L'evy B, Petitjean S, Ray N, et al. Least squares conformal maps for
automatic texture atlas generation. ACM Transactions on Graphics, 2002,
21(3): 362-371.
[9] Liu LG, Zhang L, Xu Y, et al. A local/global approach to mesh
parameterization [J]. Computer Graphics Forum, 2008, 27(5): 495-504.
[10] Chen WL, Zhang S, Jin XB. Research on the algorithm of hole repairing
of finite element mesh. Chinese journal of computers, 2005, 28(6):
1068-1071.
[11] Sederberg T W, Gao P, Wang G J, et al. 2-D shape blending: an intrinsic
solution to the vertex path problem. Proceedings of SIGGRAPH. Los
Angeles: ACM, 1993: 15-18.
[12] Toledo S. Taucs: a library of sparse linear solvers [EB/PL]. (2003-9-4)
[2010-3-10]. http://www.tau.ac.il- /~stoledo/taucs/.
[13] Wang XC. Finite element method [M]. Beijing: Tsinghua University
Press, 2003.
[14] Bao YD. Research on one step inverse forming fem and crash simulation
of auto body part. Ph.D. thesis. Changchun: Jilin University; 2005.
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:56615", author = "Wen-liang Chen and Peng Wei and Yidong Bao", title = "Surface Flattening based on Linear-Elastic Finite Element Method", abstract = "This paper presents a linear-elastic finite element method based flattening algorithm for three dimensional triangular surfaces. First, an intrinsic characteristic preserving method is used to obtain the initial developing graph, which preserves the angles and length ratios between two adjacent edges. Then, an iterative equation is established based on linear-elastic finite element method and the flattening result with an equilibrium state of internal force is obtained by solving this iterative equation. The results show that complex surfaces can be dealt with this proposed method, which is an efficient tool for the applications in computer aided design, such as mould design.
", keywords = "Triangular mesh, surface flattening, finite elementmethod, linear-elastic deformation.", volume = "5", number = "7", pages = "1360-6", }
