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Christian Dick, Joachim Georgii, Rüdiger Westermann, "A Hexahedral Multigrid Approach for Simulating Cuts in Deformable Objects," IEEE Transactions on Visualization and Computer Graphics, vol. 17, no. 11, pp. 16631675, November, 2011.  
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@article{ 10.1109/TVCG.2010.268, author = {Christian Dick and Joachim Georgii and Rüdiger Westermann}, title = {A Hexahedral Multigrid Approach for Simulating Cuts in Deformable Objects}, journal ={IEEE Transactions on Visualization and Computer Graphics}, volume = {17}, number = {11}, issn = {10772626}, year = {2011}, pages = {16631675}, doi = {http://doi.ieeecomputersociety.org/10.1109/TVCG.2010.268}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
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TY  JOUR JO  IEEE Transactions on Visualization and Computer Graphics TI  A Hexahedral Multigrid Approach for Simulating Cuts in Deformable Objects IS  11 SN  10772626 SP1663 EP1675 EPD  16631675 A1  Christian Dick, A1  Joachim Georgii, A1  Rüdiger Westermann, PY  2011 KW  Deformable objects KW  cutting KW  finite elements KW  multigrid KW  octree meshes. VL  17 JA  IEEE Transactions on Visualization and Computer Graphics ER   
[1] A. Brandt, “MultiLevel Adaptive Solutions to BoundaryValue Problems,” Math. of Computation, vol. 31, no. 138, pp. 333390, 1977.
[2] W. Hackbusch, MultiGrid Methods and Applications: Springer Series in Computational Mathematics. Springer, 1985.
[3] W.L. Briggs, V.E. Henson, and S.F. McCormick, A Multigrid Tutorial, second ed. SIAM, 2000.
[4] D. Bielser, V.A. Maiwald, and M.H. Gross, “Interactive Cuts through 3Dimensional Soft Tissue,” Computer Graphics Forum, vol. 18, no. 3, pp. 3138, 1999.
[5] D. Bielser and M.H. Gross, “Interactive Simulation of Surgical Cuts,” Proc. Pacific Graphics, pp. 116125, 2000.
[6] A.B. Mor and T. Kanade, “Modifying Soft Tissue Models: Progressive Cutting with Minimal New Element Creation,” Proc. Int'l Conf. Medical Image Computing and Computer Assisted Intervention (MICCAI), pp. 598608, 2000.
[7] M. Wicke, M. Botsch, and M. Gross, “A Finite Element Method on Convex Polyhedra,” Computer Graphics Forum, vol. 26, no. 3, pp. 355364, 2007.
[8] I. Babuška and J.M. Melenk, “The Partition of Unity Method,” Int'l J. Numerical Methods in Eng., vol. 40, no. 4, pp. 727758, 1997.
[9] T. Strouboulis, K. Copps, and I. Babuška, “The Generalized Finite Element Method,” Computer Methods in Applied Mechanics and Eng., vol. 190, nos. 32/33, pp. 40814193, 2001.
[10] T. Belytschko and T. Black, “Elastic Crack Growth in Finite Elements with Minimal Remeshing,” Int'l J. Numerical Methods in Eng., vol. 45, no. 5, pp. 601620, 1999.
[11] N. Moës, J. Dolbow, and T. Belytschko, “A Finite Element Method for Crack Growth without Remeshing,” Int'l J. Numerical Methods in Eng., vol. 46, no. 1, pp. 131150, 1999.
[12] N. Sukumar, N. Moës, B. Moran, and T. Belytschko, “Extended Finite Element Method for Threedimensional Crack Modelling,” Int'l J. Numerical Methods in Eng., vol. 48, no. 11, pp. 15491570, 2000.
[13] Y. Abdelaziz and A. Hamouine, “A Survey of the Extended Finite Element,” Computers and Structures, vol. 86, nos. 11/12, pp. 11411151, 2008.
[14] L. Jeřábková and T. Kuhlen, “Stable Cutting of Deformable Objects in Virtual Environments Using XFEM,” IEEE Computer Graphics and Applications, vol. 29, no. 2, pp. 6171, Mar./Apr. 2009.
[15] P. Kaufmann, S. Martin, M. Botsch, E. Grinspun, and M. Gross, “Enrichment Textures for Detailed Cutting of Shells,” ACM Trans. Graphics, vol. 28, no. 3, pp. 50:150:10, 2009.
[16] G. Debunne, M. Desbrun, A.H. Barr, and M.P. Cani, “Interactive Multiresolution Animation of Deformable Models,” Proc. Eurographics Workshop Computer Animation and Simulation, pp. 133144, 1999.
[17] M. Müller and M. Gross, “Interactive Virtual Materials,” Proc. Graphics Interface, pp. 239246, 2004.
[18] J. Georgii and R. Westermann, “Interactive Simulation and Rendering of Heterogeneous Deformable Bodies,” Proc. Vision, Modeling and Visualization, pp. 383390, 2005.
[19] M. Botsch, M. Pauly, M. Wicke, and M. Gross, “Adaptive Space Deformations Based on Rigid Cells,” Computer Graphics Forum, vol. 26, no. 3, pp. 339347, 2007.
[20] N. Pietroni, F. Ganovelli, P. Cignoni, and R. Scopigno, “Splitting Cubes: A Fast and Robust Technique for Virtual Cutting,” The Visual Computer, vol. 25, no. 3, pp. 227239, 2009.
[21] D. Terzopoulos, J. Platt, A. Barr, and K. Fleischer, “Elastically Deformable Models,” Proc. ACM SIGGRAPH, pp. 205214, 1987.
[22] D. Terzopoulos and K. Fleischer, “Modeling Inelastic Deformation: Viscoelasticity, Plasticity, Fracture,” Proc. ACM SIGGRAPH, pp. 269278, 1988.
[23] A. Nealen, M. Müller, R. Keiser, E. Boxerman, and M. Carlson, “Physically Based Deformable Models in Computer Graphics,” Computer Graphics Forum, vol. 25, no. 4, pp. 809836, 2006.
[24] D.L. James and D.K. Pai, “ArtDefo: Accurate Real Time Deformable Objects,” Proc. ACM SIGGRAPH, pp. 6572, 1999.
[25] G. Debunne, M. Desbrun, M.P. Cani, and A.H. Barr, “Dynamic RealTime Deformations Using Space and Time Adaptive Sampling,” Proc. ACM SIGGRAPH, pp. 3136, 2001.
[26] S. Capell, S. Green, B. Curless, T. Duchamp, and Z. Popović, “A Multiresolution Framework for Dynamic Deformations,” Proc. ACM SIGGRAPH/Eurographics Symp. Computer Animation, pp. 4147, 2002.
[27] E. Grinspun, P. Krysl, and P. Schröder, “CHARMS: A Simple Framework for Adaptive Simulation,” ACM Trans. Graphics, vol. 21, no. 3, pp. 281290, 2002.
[28] M. Müller, B. Heidelberger, M. Teschner, and M. Gross, “Meshless Deformations Based on Shape Matching,” ACM Trans. Graphics, vol. 24, no. 3, pp. 471478, 2005.
[29] E. Sifakis, T. Shinar, G. Irving, and R. Fedkiw, “Hybrid Simulation of Deformable Solids,” Proc. ACM SIGGRAPH/Eurographics Symp. Computer Animation, pp. 8190, 2007.
[30] M. BroNielsen and S. Cotin, “RealTime Volumetric Deformable Models for Surgery Simulation Using Finite Elements and Condensation,” Computer Graphics Forum, vol. 15, no. 3, pp. 5766, 1996.
[31] X. Wu, M.S. Downes, T. Goktekin, and F. Tendick, “Adaptive Nonlinear Finite Elements for Deformable Body Simulation Using Dynamic Progressive Meshes,” Computer Graphics Forum, vol. 20, no. 3, pp. 349358, 2001.
[32] J.F. O'Brien and J.K. Hodgins, “Graphical Modeling and Animation of Brittle Fracture,” Proc. ACM SIGGRAPH, pp. 137146, 1999.
[33] J.F. O'Brien, A.W. Bargteil, and J.K. Hodgins, “Graphical Modeling and Animation of Ductile Fracture,” ACM Trans. Graphics, vol. 21, no. 3, pp. 291294, 2002.
[34] M. Nesme, P.G. Kry, L. Jeřábková, and F. Faure, “Preserving Topology and Elasticity for Embedded Deformable Models,” ACM Trans. Graphics, vol. 28, no. 3, pp. 52:152:9, 2009.
[35] H.W. Nienhuys and A.F. van der Stappen, “Combining Finite Element Deformation with Cutting for Surgery Simulations,” Proc. Eurographics—Short Presentations, pp. 4352, 2000.
[36] S. Cotin, H. Delingette, and N. Ayache, “A Hybrid Elastic Model for RealTime Cutting, Deformations, and Force Feedback for Surgery Training and Simulation,” The Visual Computer, vol. 16, no. 8, pp. 437452, 2000.
[37] C. Forest, H. Delingette, and N. Ayache, “Removing Tetrahedra from a Manifold Mesh,” Proc. Computer Animation, pp. 225229, 2002.
[38] H.W. Nienhuys and A.F. van der Stappen, “A Surgery Simulation Supporting Cuts and Finite Element Deformation,” Proc. Int'l Conf. Medical Image Computing and Computer Assisted Intervention (MICCAI), pp. 145152, 2001.
[39] D. Serby, M. Harders, and G. Székely, “A New Approach to Cutting into Finite Element Models,” Proc. Int'l Conf. Medical Image Computing and Computer Assisted Intervention (MICCAI), pp. 425433, 2001.
[40] D. Steinemann, M.A. Otaduy, and M. Gross, “Fast Arbitrary Splitting of Deforming Objects,” Proc. ACM SIGGRAPH/Eurographics Symp. Computer Animation, pp. 6372, 2006.
[41] D. Bielser, P. Glardon, M. Teschner, and M. Gross, “A State Machine for RealTime Cutting of Tetrahedral Meshes,” Proc. Pacific Graphics, pp. 377386, 2003.
[42] F. Ganovelli, P. Cignoni, C. Montani, and R. Scopigno, “A Multiresolution Model for Soft Objects Supporting Interactive Cuts and Lacerations,” Computer Graphics Forum, vol. 19, no. 3, pp. 271281, 2000.
[43] N. Molino, Z. Bao, and R. Fedkiw, “A Virtual Node Algorithm for Changing Mesh Topology During Simulation,” ACM Trans. Graphics, vol. 23, no. 3, pp. 385392, 2004.
[44] S. Martin, P. Kaufmann, M. Botsch, M. Wicke, and M. Gross, “Polyhedral Finite Elements Using Harmonic Basis Functions,” Computer Graphics Forum, vol. 27, no. 5, pp. 15211529, 2008.
[45] E. Sifakis, K.G. Der, and R. Fedkiw, “Arbitrary Cutting of Deformable Tetrahedralized Objects,” Proc. ACM SIGGRAPH/Eurographics Symp. Computer Animation, pp. 7380, 2007.
[46] S. Popinet, “Gerris: A TreeBased Adaptive Solver for the Incompressible Euler Equations in Complex Geometries,” J. Computational Physics, vol. 190, no. 2, pp. 572600, 2003.
[47] L. Shi and Y. Yu, “Visual Smoke Simulation with Adaptive Octree Refinement,” Proc. Computer Graphics and Imaging, pp. 1319, 2004.
[48] F. Losasso, F. Gibou, and R. Fedkiw, “Simulating Water and Smoke with an Octree Data Structure,” ACM Trans. Graphics, vol. 23, no. 3, pp. 457462, 2004.
[49] E. Haber and S. Heldmann, “An Octree Multigrid Method for QuasiStatic Maxwell's Equations with Highly Discontinuous Coefficients,” J. Computational Physics, vol. 223, no. 2, pp. 783796, 2007.
[50] R.S. Sampath and G. Biros, “A Parallel Geometric Multigrid Method for Finite Elements on Octree Meshes,” SIAM J. Scientific Computing, vol. 32, no. 3, pp. 13611392, 2010.
[51] J. Bolz, I. Farmer, E. Grinspun, and P. Schröder, “Sparse Matrix Solvers on the GPU: Conjugate Gradients and Multigrid,” ACM Trans. Graphics, vol. 22, no. 3, pp. 917924, 2003.
[52] X. Wu and F. Tendick, “Multigrid Integration for Interactive Deformable Body Simulation,” Proc. Int'l Symp. Medical Simulation, pp. 92104, 2004.
[53] J. Georgii and R. Westermann, “A Multigrid Framework for RealTime Simulation of Deformable Bodies,” Computer and Graphics, vol. 30, no. 3, pp. 408415, 2006.
[54] L. Shi, Y. Yu, N. Bell, and W.W. Feng, “A Fast Multigrid Algorithm for Mesh Deformation,” ACM Trans. Graphics, vol. 25, no. 3, pp. 11081117, 2006.
[55] M. Kazhdan and H. Hoppe, “Streaming Multigrid for GradientDomain Operations on Large Images,” ACM Trans. Graphics, vol. 27, no. 3, pp. 21:121:10, 2008.
[56] X. Jin, S. Chen, and X. Mao, “ComputerGenerated Marbling Textures: A GPUBased Design System,” IEEE Computer Graphics and Applications, vol. 27, no. 2, pp. 7884, Mar./Apr. 2007.
[57] C. Dick, J. Georgii, R. Burgkart, and R. Westermann, “Computational Steering for PatientSpecific Implant Planning in Orthopedics,” Proc. Eurographics Workshop Visual Computing for Biomedicine, pp. 8392, 2008.
[58] Y. Zhu, E. Sifakis, J. Teran, and A. Brandt, “An Efficient Multigrid Method for the Simulation of HighResolution Elastic Solids,” ACM Trans. Graphics, vol. 29, no. 2, pp. 16:116:18, 2010.
[59] S.A. Sauter and R. Warnke, “Composite Finite Elements for Elliptic Boundary Value Problems with Discontinuous Coefficients,” Computing, vol. 77, no. 1, pp. 2955, 2006.
[60] T. Preusser, M. Rumpf, and L.O. Schwen, “Finite Element Simulation of Bone Microstructures,” Proc. 14th Workshop the Finite Element Method in Biomedical Eng., Biomechanics and Related Fields, pp. 5266, 2007.
[61] F. Liehr, T. Preusser, M. Rumpf, S. Sauter, and L.O. Schwen, “Composite Finite Elements for 3D Image Based Computing,” Computing and Visualization in Science, vol. 12, no. 4, pp. 171188, 2009.
[62] S.F. FriskenGibson, “Using Linked Volumes to Model Object Collisions, Deformation, Cutting, Carving, and Joining,” IEEE Trans. Visualization and Computer Graphics, vol. 5, no. 4, pp. 333348, Oct.Dec. 1999.
[63] K.J. Bathe, Finite Element Procedures. Prentice Hall, 2002.
[64] C.C. Rankin and F.A. Brogan, “An Element Independent Corotational Procedure for the Treatment of Large Rotations,” ASME J. Pressure Vessel Technology, vol. 108, no. 2, pp. 165174, 1986.
[65] J. Georgii and R. Westermann, “Corotated Finite Elements Made Fast and Stable,” Proc. Workshop Virtual Reality Interactions and Physical Simulation, pp. 1119, 2008.
[66] A. Lorusso, D.W. Eggert, and R.B. Fisher, “A Comparison of Four Algorithms for Estimating 3D Rigid Transformations,” Proc. British Conf. Machine Vision, pp. 237246, 1995.
[67] M.J. Aftosmis, M.J. Berger, and G. Adomavicius, “A Parallel Multilevel Method for Adaptively Refined Cartesian Grids with Embedded Boundaries, AIAA 20000808,” Proc. 38th AIAA Aerospace Sciences Meeting and Exhibit, 2000.
[68] L. Jeřábková, T. Kuhlen, T.P. Wolter, and N. Pallua, “A Voxel Based Multiresolution Technique for Soft Tissue Deformation,” Proc. ACM Symp. Virtual Reality Software and Technology, pp. 158161, 2004.
[69] W. Wang, “Special Bilinear Quadrilateral Elements for Locally Refined Finite Element Grids,” SIAM J. Scientific Computing, vol. 22, no. 6, pp. 20292050, 2001.
[70] S. Toledo, D. Chen, V. Rotkin, and O. Meshar, “TAUCS: A Library of Sparse Linear Solvers,” http://www.tau.ac.il/~stoledotaucs, 2003.
[71] L. Kharevych, P. Mullen, H. Owhadi, and M. Desbrun, “Numerical Coarsening of Inhomogeneous Elastic Materials,” ACM Trans. Graphics, vol. 28, no. 3, pp. 51:151:8, 2009.
[72] M. Teschner, S. Kimmerle, B. Heidelberger, G. Zachmann, L. Raghupathi, A. Fuhrmann, M.P. Cani, F. Faure, N. MagnenatThalmann, W. Strasser, and P. Volino, “Collision Detection for Deformable Objects,” Computer Graphics Forum, vol. 24, no. 1, pp. 6181, 2005.