
This Article  
 
Share  
Bibliographic References  
Add to:  
Digg Furl Spurl Blink Simpy Del.icio.us Y!MyWeb  
Search  
 
ASCII Text  x  
Mario Botsch, Olga Sorkine, "On Linear Variational Surface Deformation Methods," IEEE Transactions on Visualization and Computer Graphics, vol. 14, no. 1, pp. 213230, January/February, 2008.  
BibTex  x  
@article{ 10.1109/TVCG.2007.1054, author = {Mario Botsch and Olga Sorkine}, title = {On Linear Variational Surface Deformation Methods}, journal ={IEEE Transactions on Visualization and Computer Graphics}, volume = {14}, number = {1}, issn = {10772626}, year = {2008}, pages = {213230}, doi = {http://doi.ieeecomputersociety.org/10.1109/TVCG.2007.1054}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE Transactions on Visualization and Computer Graphics TI  On Linear Variational Surface Deformation Methods IS  1 SN  10772626 SP213 EP230 EPD  213230 A1  Mario Botsch, A1  Olga Sorkine, PY  2008 KW  mesh editing KW  linear optimization KW  discrete differential operators VL  14 JA  IEEE Transactions on Visualization and Computer Graphics ER   
[1] B. Aksoylu, A. Khodakovsky, and P. Schröder, “Multilevel Solvers for Unstructured Surface Meshes,” SIAM J. Scientific Computing, vol. 26, no. 4, pp. 11461165, 2005.
[2] M. Alexa, “Local Control for Mesh Morphing,” Proc. Int'l Conf. Shape Modeling and Applications (SMI '01), pp. 209215, 2001.
[3] M. Alexa, “Differential Coordinates for Local Mesh Morphing and Deformation,” The Visual Computer, vol. 19, no. 2, pp. 105114, 2003.
[4] O.K.C. Au, C.L. Tai, L. Liu, and H. Fu, “Dual Laplacian Editing for Meshes,” IEEE Trans. Visualization and Computer Graphics, vol. 12, no. 3, pp. 386395, MayJune 2006.
[5] K.J. Bathe, Finite Element Procedures. Prentice Hall, 1995.
[6] D. Bechmann, “Space Deformation Models Survey,” Computers and Graphics, vol. 18, no. 4, pp. 571586, 1994.
[7] M. Botsch, D. Bommes, and L. Kobbelt, “Efficient Linear System Solvers for Mesh Processing,” IMA Math. of Surfaces XI, pp. 6283, 2005.
[8] M. Botsch and L. Kobbelt, “A Robust Procedure to Eliminate Degenerate Faces from Triangle Meshes,” Proc. Sixth Int'l Fall Workshop Vision, Modeling, and Visualization (VMV '01), pp. 402410, 2001.
[9] M. Botsch and L. Kobbelt, “Multiresolution Surface Representation Based on Displacement Volumes,” Computer Graphics Forum (Proc. Eurographics), vol. 22, no. 3, pp. 483491, 2003.
[10] M. Botsch and L. Kobbelt, “An Intuitive Framework for RealTime Freeform Modeling,” ACM Trans. Graphics (Proc. ACM SIGGRAPH), vol. 23, no. 3, pp. 630634, 2004.
[11] M. Botsch and L. Kobbelt, “A Remeshing Approach to Multiresolution Modeling,” Proc. Eurographics/ACM SIGGRAPH Symp. Geometry Processing, pp. 189196, 2004.
[12] M. Botsch, M. Pauly, M. Gross, and L. Kobbelt, “PriMo: Coupled Prisms for Intuitive Surface Modeling,” Proc. Eurographics/ACM SIGGRAPH Symp. Geometry Processing, pp. 1120, 2006.
[13] M. Botsch, M. Pauly, C. Rössl, S. Bischoff, and L. Kobbelt, “Geometric Modeling Based on Triangle Meshes,” Eurographics Course Notes, 2006.
[14] M. Botsch, R. Sumner, M. Pauly, and M. Gross, “Deformation Transfer for DetailPreserving Surface Editing,” Proc. 11th Int'l Fall Workshop Vision, Modeling, and Visualization (VMV '06), pp. 357364, 2006.
[15] G. Celniker and D. Gossard, “Deformable Curve and Surface FiniteElements for FreeForm Shape Design,” Proc. ACM SIGGRAPH '91, pp. 257266, 1991.
[16] F. Cirak, M. Ortiz, and P. Schröder, “Subdivision Surfaces: A New Paradigm for ThinShell FiniteElement Analysis,” Int'l J. Numerical Methods in Eng., vol. 47, no. 12, pp. 20392072, 2000.
[17] F. Cirak, M. Scott, P. Schröder, M. Ortiz, and E. Antonsson, “Integrated Modeling, FiniteElement Analysis, and Design for ThinShell Structures Using Subdivision,” ComputerAided Design, vol. 34, no. 2, pp. 137148, 2002.
[18] M. Desbrun, M. Meyer, P. Schröder, and A.H. Barr, “Implicit Fairing of Irregular Meshes Using Diffusion and Curvature Flow,” Proc. ACM SIGGRAPH '99, pp. 317324, 1999.
[19] M.P. do Carmo, Differential Geometry of Curves and Surfaces. Prentice Hall, 1976.
[20] M. Eck, T. DeRose, T. Duchamp, H. Hoppe, M. Lounsbery, and W. Stuetzle, “Multiresolution Analysis of Arbitrary Meshes,” Proc. ACM SIGGRAPH '95, pp. 173182, 1995.
[21] R. Fattal, D. Lischinski, and M. Werman, “Gradient Domain High Dynamic Range Compression,” ACM Trans. Graphics (Proc. ACM SIGGRAPH), vol. 21, no. 3, pp. 249256, 2002.
[22] D. Forsey and R. Bartels, “Hierarchical Bspline refinement,” Proc. ACM SIGGRAPH, pp. 205212, 1988.
[23] H. Fu, O.K.C. Au, and C.L. Tai, “Effective Derivation of Similarity Transformations for Implicit Laplacian Mesh Editing,” Computer Graphics Forum, vol. 26, no. 1, pp. 3445, 2007.
[24] M. Garland, “Multiresolution Modeling: Survey & Future Opportunities,” Eurographics State of the Art Report, 1999.
[25] G.H. Golub and C.F. Van Loan, Matrix Computations, third ed. Johns Hopkins Univ. Press, 1996.
[26] G. Greiner and J. Loos, “Data Dependent Thin Plate Energy and Its Use in Interactive Surface Modeling,” Computer Graphics Forum (Proc. Eurographics), vol. 15, no. 3, pp. 175185, 1996.
[27] E. Grinspun, Y. Gingold, J. Reisman, and D. Zorin, “Computing Discrete Shape Operators on General Meshes,” Computer Graphics Forum (Proc. Eurographics), vol. 25, no. 3, pp. 547556, 2006.
[28] H.W. Guggenheimer, Differential Geometry. McGrawHill, 1963.
[29] I. Guskov, W. Sweldens, and P. Schröder, “Multiresolution Signal Processing for Meshes,” Proc. ACM SIGGRAPH, pp. 325334, 1999.
[30] I. Guskov, K. Vidimče, W. Sweldens, and P. Schröder, “Normal Meshes,” Proc. ACM SIGGRAPH, pp. 95102, 2000.
[31] J. Huang, X. Shi, X. Liu, K. Zhou, L.Y. Wei, S. Teng, H. Bao, B. Guo, and H.Y. Shum, “Subspace Gradient Domain Mesh Deformation,” ACM Trans. Graphics (Proc. ACM SIGGRAPH), vol. 25, no. 3, pp. 11261134, 2006.
[32] T.J.R. Hughes, The Finite Element Method: Linear Static and Dynamic Finite Element Analysis. Prentice Hall, 1987.
[33] T. Igarashi, T. Moscovich, and J.F. Hughes, “AsRigidAsPossible Shape Manipulation,” ACM Trans. Graphics (Proc. ACM SIGGRAPH), vol. 24, no. 3, pp.11341141, 2005.
[34] L. Kobbelt, S. Campagna, J. Vorsatz, and H.P. Seidel, “Interactive MultiResolution Modeling on Arbitrary Meshes,” Proc. ACM SIGGRAPH, pp. 105114, 1998.
[35] L. Kobbelt, J. Vorsatz, and H.P. Seidel, “Multiresolution Hierarchies on Unstructured Triangle Meshes,” Computational Geometry: Theory and Applications, vol. 14, pp. 524, 1999.
[36] V. Kraevoy and A. Sheffer, “MeanValue Geometry Encoding,” Int'l J. Shape Modeling, vol. 12, no. 1, pp. 2946, 2006.
[37] A. Lee, H. Moreton, and H. Hoppe, “Displaced Subdivision Surfaces,” Proc. ACM SIGGRAPH, pp. 8594, 2000.
[38] S. Lee, “Interactive Multiresolution Editing of Arbitrary Meshes,” Computer Graphics Forum, vol. 18, no. 3, pp. 7382, 1999.
[39] Y. Lipman, D. CohenOr, R. Gal, and D. Levin, “Volume and Shape Preservation via Moving Frame Manipulation,” ACM Trans. Graphics, vol. 26, no. 1, 2007.
[40] Y. Lipman, O. Sorkine, M. Alexa, D. CohenOr, D. Levin, C. Rössl, and H.P. Seidel, “Laplacian Framework for Interactive Mesh Editing,” Int'l J. Shape Modeling, vol. 11, no. 1, pp. 4362, 2005.
[41] Y. Lipman, O. Sorkine, D. CohenOr, D. Levin, C. Rössl, and H.P. Seidel, “Differential Coordinates for Interactive Mesh Editing,” Proc. Int'l Conf. Shape Modeling (SMI '04), pp. 181190, 2004.
[42] Y. Lipman, O. Sorkine, D. Levin, and D. CohenOr, “Linear RotationInvariant Coordinates for Meshes,” ACM Trans. Graphics (Proc. ACM SIGGRAPH), vol. 24, no. 3, pp. 479487, 2005.
[43] M. Marinov, M. Botsch, and L. Kobbelt, “GPUBased Multiresolution Deformation Using Approximate Normal Field Reconstruction,” J. Graphics Tools, vol. 12, no. 1, pp. 2746, 2007.
[44] M. Marinov and L. Kobbelt, “Automatic Generation of Structure Preserving Multiresolution Models,” Computer Graphics Forum (Proc. Eurographics), vol. 24, no. 3, pp. 479486, 2005.
[45] M. Meyer, M. Desbrun, P. Schröder, and A.H. Barr, “Discrete DifferentialGeometry Operators for Triangulated 2Manifolds,” Visualization and Math. III, H.C. Hege and K. Polthier, eds., pp. 3557, 2003.
[46] T. Milliron, R.J. Jensen, R. Barzel, and A. Finkelstein, “A Framework for Geometric Warps and Deformations,” ACM Trans. Graphics, vol. 21, no. 1, pp. 2051, 2002.
[47] H.P. Moreton and C.H. Séquin, “Functional Optimization for Fair Surface Design,” Proc. SIGGRAPH, pp. 167176, 1992.
[48] 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.
[49] A. Nealen, O. Sorkine, M. Alexa, and D. CohenOr, “A SketchBased Interface for DetailPreserving Mesh Editing,” ACM Trans. Graphics (Proc. ACM SIGGRAPH), vol. 24, no. 3, pp. 11421147, 2005.
[50] P. Pérez, M. Gangnet, and A. Blake, “Poisson Image Editing,” ACM Trans. Graphics (Proc. ACM SIGGRAPH), vol. 22, no. 3, pp.313318, 2003.
[51] U. Pinkall and K. Polthier, “Computing Discrete Minimal Surfaces and Their Conjugates,” Experimental Math., vol. 2, no. 1, pp. 1536, 1993.
[52] T. Popa, D. Julius, and A. Sheffer, “MaterialAware Mesh Deformations,” Proc. IEEE Int'l Conf. Shape Modeling and Applications (SMI '06). pp. 141152, 2006.
[53] A. Sheffer and V. Kraevoy, “Pyramid Coordinates for Morphing and Deformation,” Proc. Second Int'l Symp. 3D Data Processing, Visualization, and Transmission (3DPVT '04), pp. 6875, 2004.
[54] L. Shi, Y. Yu, N. Bell, and W.W. Feng, “A Fast Multigrid Algorithm for Mesh Deformation,” ACM Trans. Graphics (Proc. ACM SIGGRAPH), vol. 25, no. 3, pp. 11081117, 2006.
[55] K. Shoemake and T. Duff, “Matrix Animation and Polar Decomposition,” Proc. Conf. Graphics Interface, pp. 258264, 1992.
[56] O. Sorkine, “Differential Representations for Mesh Processing,” Computer Graphics Forum, vol. 25, no. 4, pp. 789807, 2006.
[57] O. Sorkine, “Laplacian Mesh Processing,” PhD dissertation, School of Computer Science, Tel Aviv Univ., 2006.
[58] O. Sorkine and D. CohenOr, “LeastSquares Meshes,” Proc. IEEE Int'l Conf. Shape Modeling and Applications (SMI '04), pp. 191199, 2004.
[59] O. Sorkine, D. CohenOr, and S. Toledo, “HighPass Quantization for Mesh Encoding,” Proc. Eurographics/ACM SIGGRAPH Symp. Geometry Processing, pp. 4251, 2003.
[60] O. Sorkine, Y. Lipman, D. CohenOr, M. Alexa, C. Rössl, and H.P. Seidel, “Laplacian Surface Editing,” Proc. Eurographics/ACM SIGGRAPH Symp. Geometry Processing, pp. 179188, 2004.
[61] R.W. Sumner and J. Popović, “Deformation Transfer for Triangle Meshes,” ACM Trans. Graphics (Proc. ACM SIGGRAPH), vol. 23, no. 3, pp. 399405, 2004.
[62] R.W. Sumner, M. Zwicker, and C. Gotsman, “MeshBased Inverse Kinematics,” ACM Trans. Graphics (Proc. ACM SIGGRAPH), vol. 24, no. 3, pp. 488495, 2005.
[63] G. Taubin, “A Signal Processing Approach to Fair Surface Design,” Proc. ACM SIGGRAPH '95, pp. 351358, 1995.
[64] D. Terzopoulos, J. Platt, A. Barr, and K. Fleischer, “Elastically Deformable Models,” Proc. ACM SIGGRAPH '87, pp. 205214, 1987.
[65] B. Thomaszewski, M. Wacker, and W. Strasser, “A Consistent Bending Model for Cloth Simulation with Corotational Subdivision Finite Elements,” Proc. ACM SIGGRAPH/Eurographics Symp. Computer Animation, pp. 107116, 2006.
[66] W. von Funck, H. Theisel, and H.P. Seidel, “Vector Field Based Shape Deformations,” ACM Trans. Graphics (Proc. ACM SIGGRAPH), vol. 25, no. 3, pp.11181125, 2006.
[67] M. Wardetzky, M. Bergou, D. Harmon, D. Zorin, and E. Grinspun, “Discrete Quadratic Curvature Energies,” Computer Aided Geometric Design, to appear, 2007.
[68] W. Welch and A. Witkin, “Variational Surface Modeling,” Proc. ACM SIGGRAPH '92, pp. 157166, 1992.
[69] D. Xu, H. Zhang, Q. Wang, and H. Bao, “Poisson Shape Interpolation,” Proc. Ninth ACM Symp. Solid and Physical Modeling (SPM '05), pp. 267274, 2005.
[70] G. Xu, “Discrete LaplaceBeltrami Operators and Their Convergence,” ComputerAided Geometric Design, vol. 21, no. 8, pp. 767784, 2004.
[71] Y. Yu, K. Zhou, D. Xu, X. Shi, H. Bao, B. Guo, and H.Y. Shum, “Mesh Editing with PoissonBased Gradient Field Manipulation,” ACM Trans. Graphics (Proc. ACM SIGGRAPH), vol. 23, no. 3, pp. 644651, 2004.
[72] R. Zayer, C. Rössl, Z. Karni, and H.P. Seidel, “Harmonic Guidance for Surface Deformation,” Computer Graphics Forum (Proc. Eurographics), pp. 601609, 2005.
[73] K. Zhou, J. Huang, J. Snyder, X. Liu, H. Bao, B. Guo, and H.Y. Shum, “Large Mesh Deformation Using the Volumetric Graph Laplacian,” ACM Trans. Graphics (Proc. ACM SIGGRAPH), vol. 24, no. 3, pp. 496503, 2005.
[74] D. Zorin, P. Schröder, and W. Sweldens, “Interactive Multiresolution Mesh Editing,” Proc. ACM SIGGRAPH '97, pp. 259268, 1997.