A. Agudo and B. Calvo, Finite Element based sequential Bayesian Non-Rigid Structure from Motion, 2012 IEEE Conference on Computer Vision and Pattern Recognition, pp.1418-1425, 2012.
DOI : 10.1109/CVPR.2012.6247829

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=

J. Allard, S. Cotin, F. Faure, P. Bensoussan, F. Poyer et al., Sofa-an open source framework for medical simulation, MMVR 15- Medicine Meets Virtual Reality, pp.13-18, 2007.
URL : https://hal.archives-ouvertes.fr/inria-00319416

D. Baraff and A. Witkin, Large steps in cloth simulation, Proceedings of the 25th annual conference on Computer graphics and interactive techniques , SIGGRAPH '98, pp.43-54, 1998.
DOI : 10.1145/280814.280821

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=

R. Barrett, W. Michael, . Berry, F. Tony, J. D. Chan et al., Roldan Pozo, Charles Romine, and Henk Van der Vorst. Templates for the solution of linear systems: building blocks for iterative methods, Siam, vol.43, 1994.

A. Bartoli and A. Zisserman, Direct Estimation of Non-Rigid Registration, Procedings of the British Machine Vision Conference 2004, pp.899-908, 2004.
DOI : 10.5244/C.18.92

K. Bathe, Finite Element Procedures in Engineering Analysis, Journal of Pressure Vessel Technology, vol.106, issue.4, 1982.
DOI : 10.1115/1.3264375

H. Bay, A. Ess, T. Tuytelaars, and L. Van-gool, Speeded-Up Robust Features (SURF), Computer Vision and Image Understanding, vol.110, issue.3, pp.346-359, 2008.
DOI : 10.1016/j.cviu.2007.09.014

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=

T. Belytschko and T. Black, Elastic crack growth in finite elements with minimal remeshing, International Journal for Numerical Methods in Engineering, vol.55, issue.5, pp.601-620, 1999.
DOI : 10.1115/1.3656897

T. Belytschko, Y. Krongauz, D. Organ, M. Fleming, and P. Krysl, Meshless methods: An overview and recent developments, Computer Methods in Applied Mechanics and Engineering, vol.139, issue.1-4, pp.3-47, 1996.
DOI : 10.1016/S0045-7825(96)01078-X

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=

T. Belytschko, Y. Y. Lu, and L. Gu, Element-free Galerkin methods, International Journal for Numerical Methods in Engineering, vol.95, issue.2, pp.229-256, 1994.
DOI : 10.1093/mnras/181.3.375

J. Bender, M. Müller, A. Miguel, M. Otaduy, M. Teschner et al., A Survey on Position-Based Simulation Methods in Computer Graphics, Computer graphics forum, pp.228-251, 2014.
DOI : 10.1109/TVCG.2012.79

J. Bey, Verfeinerung von Tetraeder-Gittern, Computing, vol.10, issue.4, pp.355-378, 1995.
DOI : 10.1007/978-3-662-02427-0

D. Bielser, P. Glardon, M. Teschner, and M. Gross, A state machine for real-time cutting of tetrahedral meshes, Graphical Models, vol.66, issue.6, pp.398-417, 2004.
DOI : 10.1016/j.gmod.2004.05.009

D. Bielser, A. Volker, M. H. Maiwald, and . Gross, Interactive Cuts through 3-Dimensional Soft Tissue, Computer Graphics Forum, vol.18, issue.3, pp.31-38, 1999.
DOI : 10.1111/1467-8659.00325

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=

Y. Jean and . Bouguet, Pyramidal Implementation of the Lucas Kanade Feature Tracker: Description of the algorithm, 2002.

D. Cynthia, S. Bruyns, A. Senger, K. Menon, S. Montgomery et al., A survey of interactive meshcutting techniques and a new method for implementing generalized interactive mesh cutting using virtual tools. The journal of visualization and computer animation, pp.21-42, 2002.

S. Huu-phuoc-bui, H. Tomar, S. Courtecuisse, S. P. Cotin, D. Bordas et al., Real-time error controlled adaptive mesh refinement: Application to needle insertion simulation Adaptive and featurepreserving subdivision for high-quality tetrahedral meshes, Computer Graphics Forum, vol.29, issue.1, pp.117-127, 2010.

É. Chamberland, A. Fortin, and M. Fortin, Comparison of the performance of some finite element discretizations for large deformation elasticity problems, Computers & Structures, vol.88, issue.11-12, pp.664-673, 2010.
DOI : 10.1016/j.compstruc.2010.02.007

I. Chowdhury, P. Shambhu, and . Dasgupta, Computation of rayleigh damping coefficients for large systems, The Electronic Journal of Geotechnical Engineering, vol.8, issue.0, 2003.

G. Philippe, S. Ciarlet, and . Kesavan, Lectures on three-dimensional elasticity, 1983.

L. ?í?ková and P. ?í?ek, Numerical linear algebra, Handbook of Computational Statistics, pp.105-137, 2012.

O. Comas, A. Zeike, J. Taylor, S. Allard, S. Ourselin et al., Efficient Nonlinear FEM for Soft Tissue Modelling and Its GPU Implementation within the Open Source Framework SOFA, International Symposium on Biomedical Simulation, pp.28-39, 2008.
DOI : 10.1007/978-3-540-70521-5_4

URL : https://hal.archives-ouvertes.fr/hal-00841568

S. Cotin, H. Delingette, and N. Ayache, A hybrid elastic model for real-time cutting, deformations, and force feedback for surgery training and simulation. The Visual Computer, pp.437-452, 2000.
DOI : 10.1007/pl00007215

URL : https://hal.archives-ouvertes.fr/hal-01386233

M. Diana, P. Halvax, D. Mertz, A. Legner, J. Brulé et al., Improving Echo-Guided Procedures Using an Ultrasound-CT Image Fusion System, Surgical Innovation, vol.42, issue.3, pp.217-222, 2015.
DOI : 10.1002/jcu.22141

C. Dick, J. Georgii, and R. Westermann, A hexahedral multigrid approach for simulating cuts in deformable objects. Visualization and Computer Graphics, IEEE Transactions on, vol.17, issue.11, pp.1663-1675, 2011.

J. Edmonds, A combinatorial representation of polyhedral surfaces. Notices of the, 1960.

F. Faure, C. Duriez, H. Delingette, J. Allard, B. Gilles et al., SOFA: A Multi-Model Framework for Interactive Physical Simulation, 2012.
DOI : 10.1007/8415_2012_125

URL : https://hal.archives-ouvertes.fr/hal-00681539

F. Faure, C. Duriez, H. Delingette, J. Allard, B. Gilles et al., SOFA: A Multi-Model Framework for Interactive Physical Simulation, Soft Tissue Biomechanical Modeling for Computer Assisted Surgery, pp.283-321, 2012.
DOI : 10.1007/8415_2012_125

URL : https://hal.archives-ouvertes.fr/hal-00681539

M. Ferrant, A. Nabavi, B. Macq, M. Peter, . Black et al., Serial registration of intraoperative MR images of the brain, Medical Image Analysis, vol.6, issue.4, pp.337-359, 2002.
DOI : 10.1016/S1361-8415(02)00060-9

E. Fléchon, F. Zara, G. Damiand, and F. Jaillet, A unified topological-physical model for adaptive refinement, Workshop on Virtual Reality Interaction and Physical Simulation, pp.39-48, 2014.

I. Fried, Condition of finite element matrices generated from nonuniform meshes., AIAA Journal, vol.1971, issue.2, pp.219-221, 1972.
DOI : 10.1007/BF02162515

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, issue.3, pp.271-281, 2000.
DOI : 10.1111/1467-8659.00419

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=

R. Michael and . Gosz, Finite element method: Applications in solids, structures , and heat transfer, 2005.

K. Hartmut, . Gumprecht, C. Darius, . Widenka, B. Christianto et al., Brainlab vectorvision neuronavigation system: technology and clinical experiences in 131 cases, Neurosurgery, vol.44, issue.1, pp.97-104, 1999.

X. Guo, X. Li, Y. Bao, X. Gu, and H. Qin, Meshless thin-shell simulation based on global conformal parameterization, IEEE transactions on visualization and computer graphics, vol.12, issue.3, pp.375-385, 2006.

W. Hackbusch and S. A. Sauter, Composite finite elements for the approximation of PDEs on domains with complicated micro-structures, Numerische Mathematik, vol.75, issue.4, pp.447-472, 1997.
DOI : 10.1007/s002110050248

N. Haouchine, J. Dequidt, M. Berger, and S. Cotin, Single view augmentation of 3d elastic objects Stéphane Cotin. Physics-based Augmented Reality for 3D Deformable Object, Mixed and Augmented Reality (ISMAR) VRIPHYS -Virtual Reality Interaction and Physical Simulation, pp.229-236, 2012.
DOI : 10.1109/ismar.2014.6948432

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=

N. Haouchine, J. Dequidt, I. Peterlik, E. Kerrien, M. Berger et al., Image-guided simulation of heterogeneous tissue deformation for augmented reality during hepatic surgery, 2013 IEEE International Symposium on Mixed and Augmented Reality (ISMAR), pp.199-208, 2013.
DOI : 10.1109/ISMAR.2013.6671780

URL : https://hal.archives-ouvertes.fr/hal-00842855

S. Hartmann and P. Neff, Polyconvexity of generalized polynomial-type hyperelastic strain energy functions for near-incompressibility, International Journal of Solids and Structures, vol.40, issue.11, pp.2767-2791, 2003.
DOI : 10.1016/S0020-7683(03)00086-6

A. Gerhard and . Holzapfel, Nonlinear solid mechanics, Wiley Chichester, vol.24, 2000.

S. Jia, W. Zhang, X. Yu, and Z. Pan, CPU???GPU mixed implementation of virtual node method for real-time interactive cutting of deformable objects using OpenCL, International Journal of Computer Assisted Radiology and Surgery, vol.9, issue.2, pp.1477-1491, 2015.
DOI : 10.1016/j.media.2004.11.002

A. Grand-roman-joldes, M. Wittek, . Couton, K. Simon, K. Warfield et al., Real-time prediction of brain shift using nonlinear finite element algorithms, International Conference on Medical Image Computing and Computer-Assisted Intervention, pp.300-307, 2009.

A. Grand-roman-joldes, K. Wittek, and . Miller, Suite of finite element algorithms for accurate computation of soft tissue deformation for surgical simulation, Medical Image Analysis, vol.13, issue.6, pp.912-919, 2009.
DOI : 10.1016/j.media.2008.12.001

M. Kass, A. Witkin, and D. Terzopoulos, Snakes: Active contour models, International Journal of Computer Vision, vol.5, issue.6035, pp.321-331, 1988.
DOI : 10.1007/BF00133570

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=

P. Kaufmann, S. Martin, M. Botsch, E. Grinspun, and M. Gross, Enrichment textures for detailed cutting of shells, In ACM Transactions on Graphics, vol.28, p.50, 2009.

N. Kim, Introduction to nonlinear finite element analysis, 2014.
DOI : 10.1007/978-1-4419-1746-1

T. Linda, J. M. Kohn, . Corrigan, S. Molla, and . Donaldson, To err is human: building a safer health system, 2000.

D. Koschier, S. Lipponer, and J. Bender, Adaptive tetrahedral meshes for brittle fracture simulation, Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation, pp.57-66, 2014.

P. Kraemer, L. Untereiner, T. Jund, S. Thery, and D. Cazier, CGoGN: n-dimensional Meshes with Combinatorial Maps, 22nd International Meshing Roundtable, pp.485-503, 2013.
DOI : 10.1007/978-3-319-02335-9_27

URL : https://hal.archives-ouvertes.fr/hal-01162100

I. Leizea, H. Álvarez, I. Aguinaga, and D. Borro, Real-time deformation, registration and tracking of solids based on physical simulation, 2014 IEEE International Symposium on Mixed and Augmented Reality (ISMAR), pp.165-170, 2014.
DOI : 10.1109/ISMAR.2014.6948423

D. Bruce, T. Lucas, and . Kanade, An iterative image registration technique with an application to stereo vision, Proceedings of the 7th international joint conference on Artificial intelligence, pp.674-679, 1981.

A. Malti, R. Hartley, A. Bartoli, and J. Kim, Monocular Template-Based 3D Reconstruction of Extensible Surfaces with Local Linear Elasticity, 2013 IEEE Conference on Computer Vision and Pattern Recognition, pp.1522-1529, 2013.
DOI : 10.1109/CVPR.2013.200

B. Marques, N. Haouchine, R. Plantefeve, and S. Cotin, Improving depth perception during surgical augmented reality, ACM SIGGRAPH 2015 Posters on, SIGGRAPH '15, p.24, 2015.
DOI : 10.1145/2787626.2792654

URL : https://hal.archives-ouvertes.fr/hal-01191101

E. Jerrold, . Marsden, J. Thomas, and . Hughes, Mathematical foundations of elasticity, Courier Corporation, 1994.

S. Martin, P. Kaufmann, M. Botsch, M. Wicke, and M. Gross, Polyhedral Finite Elements Using Harmonic Basis Functions, Computer Graphics Forum, vol.6, issue.4, pp.1521-1529, 2008.
DOI : 10.1111/j.1467-8659.2008.01293.x

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=

A. Mendizabal, R. Bessard-duparc, H. P. Bui, C. J. Paulus, I. Peterlik et al., Towards a face-based smoothed finite element method for real-time simulation of the brain shift Adaptive resolution for topology modifications in physicallybased animation, 2014.

J. Mezger, B. Thomaszewski, S. Pabst, and W. Straßer, Interactive physically-based shape editing, Proceedings of the 2008 ACM symposium on Solid and physical modeling, pp.79-89, 2008.
DOI : 10.1145/1364901.1364915

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=

B. Mirtich, Fast and accurate computation of polyhedral mass properties, 1996.
DOI : 10.1201/b10628-17

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=

N. Molino, Z. Bao, and R. Fedkiw, A virtual node algorithm for changing mesh topology during simulation, ACM SIGGRAPH 2005 Courses, SIGGRAPH '05, 2005.
DOI : 10.1145/1015706.1015734

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=

. Andrewb, T. Mor, and . Kanade, Modifying soft tissue models: Progressive cutting with minimal new element creation, Medical Image Computing and Computer-Assisted Intervention (MICCAI), pp.598-607, 1935.

F. Moreno-noguer, M. Salzmann, V. Lepetit, and P. Fua, Capturing 3D stretchable surfaces from single images in closed form, 2009 IEEE Conference on Computer Vision and Pattern Recognition, pp.1842-1849, 2009.
DOI : 10.1109/CVPR.2009.5206758

M. Müller, R. Keiser, A. Nealen, M. Pauly, M. Gross et al., Point based animation of elastic, plastic and melting objects, Proceedings of the 2004 ACM SIG- GRAPH/Eurographics symposium on Computer animation, pp.141-151, 2004.

A. Nealen, M. Müller, R. Keiser, E. Boxerman, and M. Carlson, Physically Based Deformable Models in Computer Graphics, Computer graphics forum, pp.809-836, 2006.
DOI : 10.1145/1015706.1015733

S. Nicolau, L. Soler, D. Mutter, and J. Marescaux, Augmented reality in laparoscopic surgical oncology, Surgical Oncology, vol.20, issue.3, pp.189-201, 2011.
DOI : 10.1016/j.suronc.2011.07.002

H. Nienhuys and A. Frank-van-der-stappen, A Surgery Simulation Supporting Cuts and Finite Element Deformation, International Conference on Medical Image Computing and Computer-Assisted Intervention, pp.145-152, 2001.
DOI : 10.1007/3-540-45468-3_18

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=

F. James, J. K. O-'brien, and . Hodgins, Graphical modeling and animation of brittle fracture, Proceedings of the 26th Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH '99, pp.137-146, 1999.

W. Raymond and . Ogden, Non-linear elastic deformations, Courier Corporation, 1997.

D. Organ, M. Fleming, T. Terry, and . Belytschko, Continuous meshless approximations for nonconvex bodies by diffraction and transparency. Computational mechanics, pp.225-235, 1996.
DOI : 10.1007/s004660050142

M. James and . Ortega, Scientific Computing: eine Einführung in das wissenschaftliche Rechnen und parallele Numerik, 2013.

J. Pan, J. Bai, X. Zhao, A. Hao, and H. Qin, Dissection of hybrid soft tissue models using position-based dynamics, Proceedings of the 20th ACM Symposium on Virtual Reality Software and Technology, VRST '14, pp.219-220, 2014.
DOI : 10.1145/2503713.2503743

J. Pan, J. Bai, X. Zhao, A. Hao, and H. Qin, Realtime haptic manipulation and cutting of hybrid soft tissue models by extended position-based dynamics, Computer Animation and Virtual Worlds, vol.26, pp.3-4321, 2015.

J. Pan, S. Yan, H. Qin, and A. Hao, Real-time dissection of organs via hybrid coupling of geometric metaballs and physicscentric mesh-free method. The Visual Computer, pp.1-12, 2016.

J. Pan, C. Zhao, X. Zhao, A. Hao, and H. Qin, Metaballs-based physical modeling and deformation of organs for virtual surgery. The Visual Computer, pp.31-37, 2015.

C. Paulus, S. Suwelack, N. Schoch, S. Speidel, R. Dillmann et al., Simulation of complex cuts in soft tissue with the extended finite element method (x-fem), Preprint Series of the Engineering Mathematics and Computing Lab, p.2014

J. Christoph, N. Paulus, D. Haouchine, S. Cazier, and . Cotin, Augmented reality during cutting and tearing of deformable objects, Mixed and Augmented Reality (ISMAR), pp.54-59, 2015.

J. Christoph, N. Paulus, D. Haouchine, S. Cazier, and . Cotin, Surgical augmented reality with topological changes, International Conference on Medical Image Computing and Computer-Assisted Intervention, 2015.

C. J. Paulus, L. Untereiner, H. Courtecuisse, S. Cotin, and D. Cazier, Virtual cutting of deformable objects based on efficient topological operations. The Visual Computer, pp.31-37, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01208546

C. J. Paulus, L. Untereiner, H. Courtecuisse, S. Cotin, and D. Cazier, Virtual cutting of deformable objects based on efficient topological operations, Computer Graphics International (CGI), 2015.
DOI : 10.1016/j.cma.2009.06.007

URL : https://hal.archives-ouvertes.fr/hal-01208546

C. Paulus, N. Haouchine, S. Kong, R. V. Soares, D. Cazier et al., Handling topological changes during elastic registration, International Journal of Computer Assisted Radiology and Surgery, vol.196, issue.11, p.2016
DOI : 10.1118/1.4896021

URL : https://hal.archives-ouvertes.fr/hal-01397409

M. Pauly, R. Keiser, B. Adams, P. Dutré, M. Gross et al., Meshless animation of fracturing solids, ACM Transactions on Graphics, vol.24, issue.3, pp.957-964, 2005.
DOI : 10.1145/1073204.1073296

URL : https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3001686/pdf

M. Pauly, R. Keiser, B. Adams, P. Dutré, M. Gross et al., Meshless animation of fracturing solids, ACM Transactions on Graphics, vol.24, issue.3, pp.957-964, 2005.
DOI : 10.1145/1073204.1073296

M. Perriollat, R. Hartley, and A. Bartoli, Monocular Template-based Reconstruction of Inextensible Surfaces, International Journal of Computer Vision, vol.67, issue.2, pp.124-137, 2011.
DOI : 10.1007/s11263-005-3962-9

URL : https://hal.archives-ouvertes.fr/hal-00344576

A. Petit, V. Lippiello, and B. Siciliano, Real-time tracking of 3D elastic objects with an RGB-D sensor, 2015 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp.3914-3921, 2015.
DOI : 10.1109/IROS.2015.7353928

A. Petit, V. Lippiello, and B. Siciliano, Tracking Fractures of Deformable Objects in Real-Time with an RGB-D Sensor, 2015 International Conference on 3D Vision, pp.632-639, 2015.
DOI : 10.1109/3DV.2015.78

N. Pietroni, F. Ganovelli, P. Cignoni, and R. Scopigno, Splitting cubes: a fast and robust technique for virtual cutting. The Visual Computer, pp.227-239, 2009.
DOI : 10.1007/s00371-008-0216-1

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=

J. Pilet, V. Lepetit, and P. Fua, Fast Non-Rigid Surface Detection, Registration and Realistic Augmentation, International Journal of Computer Vision, vol.20, issue.2, pp.109-122, 2008.
DOI : 10.1007/s11263-006-0017-9

URL : https://infoscience.epfl.ch/record/128417/files/PiletLF07.pdf

R. Plantefeve, I. Peterlik, H. Courtecuisse, R. Trivisonne, J. Radoux et al., Atlas-Based Transfer of Boundary Conditions for Biomechanical Simulation, Medical Image Computing and Computer-Assisted Intervention (MICCAI), pp.33-40, 2014.
DOI : 10.1007/978-3-319-10470-6_5

URL : https://hal.archives-ouvertes.fr/hal-01070339

P. Pratt, D. Stoyanov, M. Visentini-scarzanella, and G. Yang, Dynamic guidance for robotic surgery using imageconstrained biomechanical models, Medical Image Computing and Computer-Assisted Intervention (MICCAI), pp.77-85, 2010.
DOI : 10.1007/978-3-642-15705-9_10

J. Kun-qian, X. Bai, J. Yang, J. Pan, and . Zhang, Virtual reality based laparoscopic surgery simulation, Proceedings of the 21st ACM Symposium on Virtual Reality Software and Technology, pp.69-78, 2015.

J. Kun-qian, X. Bai, and . Yang, Junjun Pan, and Jianjun Zhang. Essential techniques for laparoscopic surgery simulation, Computer Animation and Virtual Worlds, 2016.

M. Rivara, Local modification of meshes for adaptive and/or multigrid finite-element methods, Journal of Computational and Applied Mathematics, vol.36, issue.1, pp.79-89, 1991.
DOI : 10.1016/0377-0427(91)90227-B

M. Salzmann and P. Fua, Linear local models for monocular reconstruction of deformable surfaces. Pattern Analysis and Machine Intelligence, pp.931-944, 2011.

J. Mathieu-salzmann, S. Pilet, P. Ilic, and . Fua, Surface Deformation Models for Nonrigid 3D Shape Recovery, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.29, issue.8, pp.1481-1487, 2007.
DOI : 10.1109/TPAMI.2007.1080

S. A. Sauter and R. Warnke, Composite Finite Elements for Elliptic Boundary Value Problems with Discontinuous Coefficients, Computing, vol.7, issue.1, pp.29-55, 2006.
DOI : 10.1007/978-3-642-84659-5

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=

S. Schaefer, J. P. Hakenberg, and J. Warren, Smooth subdivision of tetrahedral meshes, Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing , SGP '04, pp.147-154, 2004.
DOI : 10.1145/1057432.1057452

O. Schenk and K. Gärtner, Solving unsymmetric sparse systems of linear equations with PARDISO, Future Generation Computer Systems, vol.20, issue.3, pp.475-487, 2004.
DOI : 10.1016/j.future.2003.07.011

]. N. Schoch, S. Suwelack, R. Dillmann, and V. Heuveline, Simulation of surgical cutting of soft tissue using the x-fem, Preprint Series of the Engineering Mathematics and Computing Lab, p.2013

M. Seiler, D. Steinemann, J. Spillmann, and M. Harders, Robust interactive cutting based on an adaptive octree simulation mesh. The Visual Computer, pp.519-529, 2011.
DOI : 10.1007/s00371-011-0561-3

J. Shewchuk, What is a good linear finite element? interpolation, conditioning , anisotropy, and quality measures (preprint), p.73, 2002.

J. R. Shewchuk, An introduction to the conjugate gradient method without the agonizing pain, 1994.

P. Shrivastava and S. Das, Particle Coding for Meshfree Cutting of Deformable Assets, Proceedings of the 2014 Indian Conference on Computer Vision Graphics and Image Processing, ICVGIP '14, p.6, 2014.
DOI : 10.1145/369028.369087

H. Si and A. Tetgen, A quality tetrahedral mesh generator and threedimensional delaunay triangulator. Weierstrass Institute for Applied Analysis and Stochastic, 2006.

E. Sifakis and J. Barbic, FEM simulation of 3D deformable solids, ACM SIGGRAPH 2012 Posters on, SIGGRAPH '12, p.20, 2012.
DOI : 10.1145/2343483.2343501

E. Sifakis, K. G. Der, and R. Fedkiw, Arbitrary cutting of deformable tetrahedralized objects, Proceedings of the 2007 ACM SIGGRAPH/Eurographics Symposium on Computer Animation, SCA '07, p.73, 2007.

E. Sifakis, T. Shinar, G. Irving, and R. Fedkiw, Hybrid simulation of deformable solids, Proceedings of the 2007 ACM SIGGRAPH/Eurographics symposium on Computer animation, pp.81-90, 2007.

A. Singh, H. Glenn, and . Strauss, High-Fidelity Cataract Surgery Simulation and Third World Blindness, Surgical Innovation, vol.38, issue.2, p.1553350614537120, 2014.
DOI : 10.1016/j.jcrs.2011.11.014

URL : http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4365142

A. Michael and . Slawinski, Waves and rays in elastic continua, World Scientific, 2010.

S. Speidel, . Kuhn, . Bodenstedt, . Röhl, . Kenngott et al., Visual tracking of da vinci instruments for laparoscopic surgery, SPIE Medical Imaging International Society for Optics and Photonics, pp.903608-903608, 2014.

D. Steinemann, M. Harders, M. Gross, and G. Szekely, Hybrid Cutting of Deformable Solids, IEEE Virtual Reality Conference (VR 2006), pp.35-42, 2006.
DOI : 10.1109/VR.2006.74

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=

D. Steinemann, A. Miguel, M. Otaduy, and . Gross, Fast arbitrary splitting of deforming objects, Proceedings of the 2006 ACM SIG- GRAPH/Eurographics symposium on Computer animation, pp.63-72, 2006.

B. Su, X. Wang, and H. Liao, Soft tissue cutting control method with surgical scalpel

E. Süli, F. David, and . Mayers, An introduction to numerical analysis, 2003.
DOI : 10.1017/CBO9780511801181

S. Suwelack, Real-Time Biomechanical Modeling for Intraoperative Soft Tissue Registration, 2013.
DOI : 10.1117/12.878228

S. Suwelack, S. Röhl, S. Bodenstedt, D. Reichard, R. Dillmann et al., Physics-based shape matching for intraoperative image guidance, Hannes Kenngott, Beat P. Müller, and Stefanie Speidel, p.41111901, 2014.
DOI : 10.1118/1.4896021.1

S. Suwelack, S. Röhl, R. Dillmann, A. Wekerle, H. Kenngott et al., Quadratic Corotated Finite Elements for Real-Time Soft Tissue Registration, Computational Biomechanics for Medicine, pp.39-50, 2012.
DOI : 10.1007/978-1-4614-3172-5_6

J. Teran, N. Molino, R. Fedkiw, and R. Bridson, Adaptive physics based tetrahedral mesh generation using level sets, Engineering with Computers, vol.100, issue.4, pp.2-18, 2005.
DOI : 10.1007/s00366-005-0308-8

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=

A. Tsoli, A. Antonis, and . Argyros, Tracking deformable surfaces that undergo topological changes using an rgb-d camera Laparoscopic liver resection: a systematic review, 3D Vision (3DV), 2016 Fourth International Conference on, pp.333-341410, 2009.
DOI : 10.1109/3dv.2016.42

E. Wang, T. Nelson, and R. Rauch, Back to elementstetrahedra vs. hexahedra, Proceedings of the 2004 International AN- SYS Conference, 2004.

Y. Wang, C. Jiang, C. Schroeder, and J. Teran, An adaptive virtual node algorithm with robust mesh cutting, Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation, pp.77-85, 2014.

M. Wicke, M. Botsch, and M. Gross, A Finite Element Method on Convex Polyhedra, Computer Graphics Forum, pp.355-364, 2007.
DOI : 10.1007/BF02127699

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=

P. Wriggers, Nonlinear finite element methods, 2008.

J. Wu, C. Dick, and R. Westermann, Interactive highresolution boundary surfaces for deformable bodies with changing topology, Proceedings of 8th Workshop on Virtual Reality Interaction and Physical Simulation (VRIPHYS) 2011, pp.29-38, 2011.

J. Wu, C. Dick, and R. Westermann, Efficient collision detection for composite finite element simulation of cuts in deformable bodies, The Visual Computer, vol.1, issue.2, pp.739-749, 2013.
DOI : 10.1109/TOH.2008.1

J. Wu, R. Westermann, and C. Dick, A Survey of Physically Based Simulation of Cuts in Deformable Bodies, Eurographics Stateof-the-Art Report, 2014.
DOI : 10.1117/12.594379

J. Wu, R. Westermann, and C. Dick, Real-time haptic cutting of high resolution soft tissues, Studies in Health Technology and Informatics (Proc. Medicine Meets Virtual Reality), pp.469-475, 2014.

Z. Yaniv and K. Cleary, Image-guided procedures: A review, Computer Aided Interventions and Medical Robotics, vol.3, pp.1-63, 2006.

Y. Zhang, C. Bajaj, and B. Sohn, 3d finite element meshing from imaging data Computer methods in applied mechanics and engineering, pp.5083-5106, 2005.

J. Zhu, R. Michael, and . Lyu, Progressive Finite Newton Approach To Real-time Nonrigid Surface Detection, 2007 IEEE Conference on Computer Vision and Pattern Recognition, pp.1-8, 2007.
DOI : 10.1109/CVPR.2007.383200

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=