Abstracts Physics

Physically Based Simulation

by David Bell

In this thesis, we provide an overview of the physical simulation of several types of systems. We elaborate on different approaches and describe their benefits and drawbacks. In chapter 1, we provide a brief history of computer animation and physical simulation in particular. This underscores the importance of the work done in the remaining chapters. In chapter 2, we describe the structure of a differential equation solver which is integral to simulation of models described in chapters 3 and 4. We explore various implementations of the different components of the solver and how these effect the overall runtime. In chapter 3, we explore our first models for physical simulation: the particle and the generalized rigid body. As these comprise the majority of physical simulation, an in-depth description of the physics that determine their behavior is provided. We also describe how to convert behavioral constraints into force laws that can be used in our system. In chapter 4, we move on to physical simulation involving hierarchical skeletons. We describe how they are evaluated and provide two models for simulating the change in the skeleton given a goal position for an end-effector. Finally, in chapter 5 we discuss the issue of collision detection and resolution. We describe how to calculate the nearest points between two polyhedra and then we use this describe efficient schemes for collision detection. We then describe a simplified algorithm for particle-plane collisions and a general algorithm for polytopic collisions.