Eigen deformation of 3D models

Recent advances in mesh deformations have been dominated by two techniques: one uses an intermediate structure like a cage which transfers the user intended moves to the mesh, the other lets the user to impart the moves to the mesh directly. The former one lets the user deform the model in real-time and also preserve the shape with sophisticated techniques like Green Coordinates. The direct techniques on the other hand free the user from the burden of creating an appropriate cage though they take more computing time to solve larger non-linear optimizations. It would be ideal to develop a cage-free technique that provides real-time deformation while respecting the local geometry. Using a simple eigen-framework, we devise such a technique. Our framework creates an implicit skeleton automatically. The user only specifies the motion in a simple and intuitive manner, and our algorithm computes a deformation whose quality is similar to that of the cage-based scheme with Green Coordinates.

[1]  Christian Rössl,et al.  Laplacian surface editing , 2004, SGP '04.

[2]  Olga Sorkine-Hornung,et al.  On Linear Variational Surface Deformation Methods , 2008, IEEE Transactions on Visualization and Computer Graphics.

[3]  Olga Sorkine-Hornung,et al.  Context‐Aware Skeletal Shape Deformation , 2007, Comput. Graph. Forum.

[4]  Katsutoshi Ootsubo,et al.  t-FFD: free-form deformation by using triangular mesh , 2003, SM '03.

[5]  Mark Meyer,et al.  Harmonic coordinates for character articulation , 2007, ACM Trans. Graph..

[6]  Markus H. Gross,et al.  PriMo: coupled prisms for intuitive surface modeling , 2006, SGP '06.

[7]  Thomas W. Sederberg,et al.  Free-form deformation of solid geometric models , 1986, SIGGRAPH.

[8]  Martin Reimers,et al.  Mean value coordinates in 3D , 2005, Comput. Aided Geom. Des..

[9]  Olga Sorkine-Hornung,et al.  Bounded biharmonic weights for real-time deformation , 2011, Commun. ACM.

[10]  Hans-Peter Seidel,et al.  Spherical barycentric coordinates , 2006, SGP '06.

[11]  Michael S. Floater,et al.  Mean value coordinates , 2003, Comput. Aided Geom. Des..

[12]  Hans-Peter Seidel,et al.  Free-form skeleton-driven mesh deformations , 2003, SM '03.

[13]  Daniel Cohen-Or,et al.  Green Coordinates , 2008, ACM Trans. Graph..

[14]  Leif Kobbelt,et al.  Real‐Time Shape Editing using Radial Basis Functions , 2005, Comput. Graph. Forum.

[15]  Mathieu Desbrun,et al.  A geometric construction of coordinates for convex polyhedra using polar duals , 2005, SGP '05.

[16]  Xiaohu Guo,et al.  Spectral mesh deformation , 2008, The Visual Computer.

[17]  Konrad Polthier,et al.  On approximation of the Laplace–Beltrami operator and the Willmore energy of surfaces , 2011, Comput. Graph. Forum.

[18]  Ulrich Pinkall,et al.  Computing Discrete Minimal Surfaces and Their Conjugates , 1993, Exp. Math..

[19]  Olga Sorkine-Hornung,et al.  Differential Representations for Mesh Processing , 2006, Comput. Graph. Forum.

[20]  Kenneth I. Joy,et al.  Free-form deformations with lattices of arbitrary topology , 1996, SIGGRAPH.

[21]  Hong Qin,et al.  Medial axis extraction and shape manipulation of solid objects using parabolic PDEs , 2004, SM '04.

[22]  Craig Gotsman,et al.  Spectral compression of mesh geometry , 2000, EuroCG.

[23]  Kun Zhou,et al.  Large mesh deformation using the volumetric graph Laplacian , 2005, ACM Trans. Graph..

[24]  Niklas Peinecke,et al.  Laplace-Beltrami spectra as 'Shape-DNA' of surfaces and solids , 2006, Comput. Aided Des..

[25]  Mark Meyer,et al.  Implicit fairing of irregular meshes using diffusion and curvature flow , 1999, SIGGRAPH.

[26]  Tamal K. Dey,et al.  Convergence, stability, and discrete approximation of Laplace spectra , 2010, SODA '10.

[27]  Jovan Popovic,et al.  Automatic rigging and animation of 3D characters , 2007, ACM Trans. Graph..

[28]  Bruno Lévy,et al.  Laplace-Beltrami Eigenfunctions Towards an Algorithm That "Understands" Geometry , 2006, IEEE International Conference on Shape Modeling and Applications 2006 (SMI'06).

[29]  Craig Gotsman,et al.  Variational harmonic maps for space deformation , 2009, ACM Trans. Graph..

[30]  Joe D. Warren,et al.  Barycentric coordinates for convex polytopes , 1996, Adv. Comput. Math..

[31]  Yan Cao,et al.  Spectral Surface Deformation with Dual Mesh , 2008 .

[32]  Christoph von Tycowicz,et al.  Interactive surface modeling using modal analysis , 2011, TOGS.

[33]  Mikhail Belkin,et al.  Discrete laplace operator on meshed surfaces , 2008, SCG '08.

[34]  Marc Alexa,et al.  As-rigid-as-possible surface modeling , 2007, Symposium on Geometry Processing.

[35]  Bruno Lévy,et al.  Spectral Mesh Processing , 2009, SIGGRAPH '10.