Real‐Time Subspace Integration for Example‐Based Elastic Material

Example‐based material allows simulating complex material behaviors in an art‐directed way. This paper presents a method for fast subspace integration for example‐based elastic material, which is suitable for real‐time simulation in computer graphics. At the core of the method is the formulation of a new potential using example‐based Green strain tensors. By using this potential, the deformation can be attracted towards the example‐based deformation feature space, the example weights can be explicitly obtained and the internal force can be decomposed into the conventional one and an additional one induced by the examples. The real‐time subspace integration is then developed with subspace integration costs independent of geometric complexity, and both the reduced conventional internal force and additional one being cubic polynomials in reduced coordinates. Experiments demonstrate that our method can achieve real‐time simulation while providing comparable quality with the prior art.

[1]  Greg Turk,et al.  Keyframe control of complex particle systems using the adjoint method , 2006, SCA '06.

[2]  Christoph von Tycowicz,et al.  Interactive spacetime control of deformable objects , 2012, ACM Trans. Graph..

[3]  Takeo Igarashi,et al.  Real-time example-based elastic deformation , 2012, SCA '12.

[4]  John C. Platt,et al.  Elastically deformable models , 1987, SIGGRAPH.

[5]  Nancy Argüelles,et al.  Author ' s , 2008 .

[6]  Andrew P. Witkin,et al.  Spacetime constraints , 1988, SIGGRAPH.

[7]  Wilmot Li,et al.  Dynamic Sprites , 2013, MIG.

[8]  Hyeong-Seok Ko,et al.  Modal warping: real-time simulation of large rotational deformation and manipulation , 2004, IEEE Transactions on Visualization and Computer Graphics.

[9]  R. D. Wood,et al.  Nonlinear Continuum Mechanics for Finite Element Analysis , 1997 .

[10]  Mario Botsch,et al.  Example‐Driven Deformations Based on Discrete Shells , 2011, Comput. Graph. Forum.

[11]  Eitan Grinspun,et al.  Example-based elastic materials , 2011, ACM Trans. Graph..

[12]  Alex Pentland,et al.  Good vibrations: modal dynamics for graphics and animation , 1989, SIGGRAPH.

[13]  M. Otaduy,et al.  Capture and modeling of non-linear heterogeneous soft tissue , 2009, ACM Trans. Graph..

[14]  Markus H. Gross,et al.  Efficient simulation of example-based materials , 2012, SCA '12.

[15]  Markus H. Gross,et al.  Deformable objects alive! , 2012, ACM Trans. Graph..

[16]  Theodore Kim,et al.  Optimizing cubature for efficient integration of subspace deformations , 2008, SIGGRAPH Asia '08.

[17]  Morten Bro-Nielsen,et al.  Real‐time Volumetric Deformable Models for Surgery Simulation using Finite Elements and Condensation , 1996, Comput. Graph. Forum.

[18]  Jernej Barbic,et al.  Real-Time subspace integration for St. Venant-Kirchhoff deformable models , 2005, ACM Trans. Graph..

[19]  Denis Zorin,et al.  Subspace integration with local deformations , 2013, ACM Trans. Graph..

[20]  Jernej Barbic,et al.  Real-time large-deformation substructuring , 2011, ACM Trans. Graph..

[21]  Matthias Zwicker,et al.  Mesh-based inverse kinematics , 2005, ACM Trans. Graph..

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

[23]  Chen Shen,et al.  Interactive Deformation Using Modal Analysis with Constraints , 2003, Graphics Interface.

[24]  Doug L. James,et al.  Optimizing cubature for efficient integration of subspace deformations , 2008, SIGGRAPH 2008.

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

[26]  Jernej Barbic,et al.  Deformable object animation using reduced optimal control , 2009, ACM Trans. Graph..

[27]  Wojciech Matusik,et al.  Capture and modeling of non-linear heterogeneous soft tissue , 2009, ACM Trans. Graph..

[28]  Ken-ichi Anjyo,et al.  Directable animation of elastic objects , 2005, SCA '05.

[29]  Andrew Nealen,et al.  Physically Based Deformable Models in Computer Graphics , 2006, Comput. Graph. Forum.

[30]  Ronald Fedkiw,et al.  Arbitrary cutting of deformable tetrahedralized objects , 2007, SCA '07.

[31]  Xun Wang,et al.  Fast corotational simulation for example-driven deformation , 2014, Comput. Graph..

[32]  Markus H. Gross,et al.  Interactive Virtual Materials , 2004, Graphics Interface.

[33]  Doug L. James,et al.  Real-Time subspace integration for St. Venant-Kirchhoff deformable models , 2005, SIGGRAPH 2005.

[34]  Jernej Barbic,et al.  Vega: Non‐Linear FEM Deformable Object Simulator , 2013, Comput. Graph. Forum.

[35]  Andrew P. Witkin,et al.  Large steps in cloth simulation , 1998, SIGGRAPH.

[36]  Eitan Grinspun,et al.  CHARMS: a simple framework for adaptive simulation , 2002, ACM Trans. Graph..

[37]  Guoping Wang,et al.  Example‐Based Materials in Laplace–Beltrami Shape Space , 2015, Comput. Graph. Forum.

[38]  Mark Pauly,et al.  Projective dynamics , 2014, ACM Trans. Graph..