N -dimensional rigid body dynamics

Abstract

I present a formulation for Rigid Body Dynamics that is independent of the dimension of the space. I describe the state and equations of motion of rigid bodies using geometric algebra. Using collision detection algorithms extended to n D I resolve collisions and contact between bodies. My implementation is 4D, but the techniques described here apply to any number of dimensions. I display these four-dimensional rigid bodies by taking a three-dimensional slice through them. I allow the user to manipulate these bodies in real-time.