Rigid body simulation

Rigid Body Simulation deals with trying to model real world physical situations computationally by applying Newton’s laws of motion to perfectly rigid bodies. Work done in this area is used in the animation industry, haptic displays in robotics, and 3D games, so there is a real need for algorithms that work in realtime. The two main areas of research in rigid body simulation are collision detection and collision response. Collision detection involves using computational geometry to come up with algorithms with low complexities, as intersection detection can become computationally expensive when simulating a large number of bodies. In this thesis we will largely be looking at collision response. In the real world when objects collide they deform and it is this deformation that causes the forces between the objects. However simulating how objects deform takes a prohibitively long amount of time so instead the area of collision response looks at other empirical laws to calculate the forces, while keeping the objects rigid. A lot of the physics involved is no harder than what is taught in a high school mechanics course, but there are notable exceptions, and we find that when we deal with objects moving in 3D we have to include terms which allow for more interesting and un-intuitive movement such as gyroscopic stability. In this thesis we will look at the various schemes proposed to deal with collision response and the problems that arise from trying to implement such algorithms robustly.