Real-time Simulation of Physically Realistic Global Deformation

Real-time simulation and animation of global deformation of 3D objects, using finite element method ( FEM), is difficult due to the following 3 fundamental problems: (1) The linear elastic model is inappropriate for simulating large motion and large deformations (unacceptable distortion will occur); (2) The time step for dynamic integration has to be drastically reduced to simulate collisions; (3) The size of the problem (the number of elements in the FEM mesh) is one order of magnitude larger than a 2D problem. In this paper, we present a novel approach to counter these 3 difficulties: (1) using quadratic strain instead of the popular linear strain to simulate arbitrarily large motion and global deformation of a 3D object; (2) applying an implicit simplified impulse to a decoupled system, which makes an integration step for collision as cheap as a regular dynamic integration step; (3) using a graded mesh instead of a uniform mesh, which reduces the asymptotic complexity of a 3D problem to that of a 2D problem.

[1]  J. Z. Zhu,et al.  The finite element method , 1977 .

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

[3]  Keith Waters,et al.  A muscle model for animation three-dimensional facial expression , 1987, SIGGRAPH.

[4]  Demetri Terzopoulos,et al.  Modeling inelastic deformation: viscolelasticity, plasticity, fracture , 1988, SIGGRAPH.

[5]  Demetri Terzopoulos,et al.  Physically-based facial modelling, analysis, and animation , 1990, Comput. Animat. Virtual Worlds.

[6]  George Celniker,et al.  Deformable curve and surface finite-elements for free-form shape design , 1991, SIGGRAPH.

[7]  Andrew P. Witkin,et al.  Dynamic simulation of non-penetrating flexible bodies , 1992, SIGGRAPH.

[8]  Steven D. Pieper,et al.  Interactive graphics for plastic surgery: a task-level analysis and implementation , 1992, I3D '92.

[9]  David Zeltzer,et al.  Pump it up: computer animation of a biomechanically based model of muscle using the finite element method , 1992, SIGGRAPH.

[10]  Edward J. Nicolson.  Tactile Sensing and Control of a Planar Manipulator , 1994 .

[11]  Xavier Provot,et al.  Deformation Constraints in a Mass-Spring Model to Describe Rigid Cloth Behavior , 1995 .

[12]  Pierre Baconnier,et al.  Physically‐Based Deformations Constrained in Displacements and Volume , 1996, Comput. Graph. Forum.

[13]  Bernd Girod,et al.  Anatomy-based facial tissue modeling using the finite element method , 1996, Proceedings of Seventh Annual IEEE Visualization '96.

[14]  Andrew Witkin.  An Introduction to Physically Based Modeling: Differential Equation Basics , 1997 .

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

[16]  Herve Delingette,et al.  Real-Time Elastic Deformations of Soft Tissues for Surgery Simulation , 1999, IEEE Trans. Vis. Comput. Graph..