Statistical and Directable Methods for Large-Scale Rigid Body Simulation

This dissertation describes several techniques to improve performance and controllability of large-scale rigid body simulations. We first describe a statistical simulation method that replaces certain stages of rigid body simulation with a statistically- based approximation. We begin by collecting statistical data regarding changes in linear and angular momentum for collisions of a given object. From the data, we extract a statistical ?signature? for the object, giving a compact representation of the object?s response to collision events. During object simulation, both the collision detection and the collision response calculations are replaced by simpler calculations based on the statistical signature. In addition, based on our statistical simulator, we develop a mixed rigid body simulator that combines an impulse-based with a statistically-based collision response method. This allows us to maintain high accuracy in important parts of the scene while achieving greater efficiency by simplifying less important parts of the simulation. The resulting system gives speedups of more than an order of magnitude on several large rigid body simulations while maintaining high accuracy in key places and capturing overall statistical behavior in other places.

Also, we introduce two methods for directing pile behavior to form the desired shapes. To fill up the space inside the desired shapes and maintain the stability of the desired pile shapes, our methods analyze the configurations and status of all objects and properly select some candidates to have their degrees of freedom (DOFs) reduced. Our first method utilizes the idea of angles of repose to perform the analysis. According to the desired angle of repose, we create an additional spatial structure to track the piling status and select suitable objects to reduce their DOFs. In our second method, we adapt equilibrium analysis in a local scheme to find ?stable? objects of the stacking structure. Then, we restrict their DOFs by adding constraints on them for stabilizing the structure. Overall, our directing methods generate a wider variety of piled structures than possible with strict physically-based simulation.