On the Collision Detection Problem of Two Moving Objects Described by Algebraic Sets

In this paper, the collision problem of two moving objects is investigated. The objects are described by two algebraic sets (ellipses or circles in the paper). The collision problem discussed involves both static and dynamic case. The static case is that each object moves with known velocity. We use nonlinear programming to decide whether the objects collide. The dynamic case is that each object is controlled by a constraint external force which can be regulated online. For the dynamic case, the collision problem can be modelled as a Minmax problem which can be solved by using differential games. If collision occurs, the time and place of the first collision are given. The moving trajectories are provided in the paper. Partially supported by a National Key Basic Research Project of China (2004CB318000).