Real-time simulation of physically realistic global deformations

Abstract

In this thesis, we model and simulate large global deformations of linear viscous materials. Furthermore, we simulate the dynamic behaviors of such deformations using finite element methods (FEM). Real-time simulation and animation of global deformation of 3D objects, using the finite element method, is difficult due to the following 3 fundamental problems: (1) The linear elastic model is inappropriate for simulating large motions and large deformations (unacceptable distortion will occur); (2) The time step for dynamic integration has to be drastically reduced to simulate collisions, if the traditional penalty methods are applied; (3) The size of the problem (the number of elements in the FEM mesh) is in n magnitude larger than that of a 2D problem. In this thesis, we counter these 3 difficulties as following: (1) using quadratic strain instead of the popular linear strain to simulate arbitrarily large motions and global deformations of a 3D object; (2) applying an efficient collision constraint 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. In order to preserve some of the subtle material properties such as viscous elasticity, we also present an alternative real-time solution without compromising the mass matrix in the FEM system. Instead of decoupling the system by diagonalizing the mass and damping matrix, we preprocess the system using modified nested dissection, which improves the sparsity of the system. In this thesis, we also present how we can apply the same FEM model to simulate haptic feedback to a human operation in the virtual environment.