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.