Collision response analysis and fracture simulation of deformable objects for computer graphics
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Computer Animation is a sub-field of computer graphics with an emphasis on the time-dependent description of interested events. It has been used in many disciplines such as entertainment, scientific visualization, industrial design, multimedia, etc. Modeling of deformable objects in a dynamic interaction and/or fracture process has been an active research topic in the past decade. The main objective of this thesis is to provide a new effective approach to address the dynamic interaction and fracture simulation. With respect to the dynamic interaction between deformable objects, this thesis proposes a new semi-explicit local collision response analysis (CRA) algorithm which is better than most of previous approaches in three aspects: computational efficiency, accuracy mid generality. The computational cost of the semi-explicit local CRA algorithm is guaranteed to be O('n') for each time step, which is especially desirable for the collision response analysis of complex systems. With the use of the Lagrange multiplier method, the send-explicit local CPA algorithm avoids shortcomings associated with the penalty method and provides an accurate description of detailed local deformation during a collision process. The generic geometric constraint and the Gauss-Seidel iteration for enforcing the loading constraint such as Coulomb friction law make the semi-explicit local CRA algorithm to be general enough to handle arbitrary oblique collisions. The experimental results indicate that the semi-explicit local CRA approach is capable of capturing all the key features during collision of deformable objects and matches closely with the theoretical solution of a classic collision problem in solid mechanics. In the fracture simulation, a new element-split method is proposed, which has a sounder mechanical basis than previous approaches in computer graphics and is more flexible to accommodate different material fracture criteria such that different failure patterns are obtained accordingly. Quantitative simulation results show that the element-split approach is consistent with the theoretical Mohr's circle analysis and the slip-line theory in plasticity, while qualitative results indicate its visual effectiveness.