Efficient collision detection among moving spheres with unknown trajectories

Abstract

Collision detection is critical for applications that handle spatial interactions among objects. In many applications, such as computer games, crowd simulations, and particle systems, it is often the case that either a user is allowed to move an object at his/her will, or an object moves under rules that are hard to describe by exact mathematical formulae. Thus, the trajectory of the object is not easily known in advance. In this dissertation, we present a new algorithm that efficiently detects the collisions among spheres moving with unknown trajectories. Given the maximum magnitude of acceleration of a sphere, we represent its bounding volume, called a time-varying bound, as a moving sphere of variable radius. We check the collision between two spheres when their time-varying bounds collide with each other. Because of the compact representation of these bounds, we can generalize the event-driven approach [20] for collision detection among moving spheres to this more demanding case. This event-driven approach [20], however, is inefficient in handling the spheres in contact. For a pair of spheres in contact, it repeatedly checks the collision between the spheres. We enhance the efficiency of the proposed event-driven approach by handling the spheres in contact. We excessively reduce the number of collision checks among time-varying bounds by avoiding any collision checks between time-varying bounds while their original spheres touch each other and move in the same velocity. The proposed algorithm shows interactive performance in detecting the collisions among thousands of moving spheres with unknown trajectories, without any help from hardware. Based on the proposed event-driven approach, we simulate group behaviors. The complex behaviors of a group evolve from the interactions among the members of the group. We approximate every member as its bounding sphere and calculate the time-varying bound. When two time-varying bounds for a pair of members collide, the m...