判断两个凸多面体是否相交的一个快速算法

在机器人路径规划中,碰撞检测算法占有十分重要的地位.在智能机器人仿真系统中,碰撞检测耗用的时间在整个路径规划过程所用时间中占有相当大的比例.于是，如何进一步提高碰撞检测的速度在智能机器人路径规划系统中就起到了非常关键的作用.而碰撞检测问题最终转化为判断三维空间中两个凸多面体是否相交的问题.就这一问题,给出了一种新的算法,其思想是取一个从一个凸多面体指向另一个多面体的向量,根据两个多面体中的面与这一向量的相对位置关系来寻找相交的平面.即有两个多面体的交点位于这一平面，若能找到一个相交平面则可以断定两个多面体

A Fast Algorithm to Determine Whether the Intersection of Two Convex Regions Is Empty

Collision detection algorithms play a very important role in the field of robot path planning. In a simulation system of intelligent robot, collision detection takes up a large portion of the time for the robot to plan a complete path from the initial position to the final position. So how to reduce the time the robot uses to detect collision becomes a key problem. But collision detection finally will transform to a problem to determine whether the intersection of two convex regions formed by linear inequalities is empty or not. The authors present a new algorithm in this paper. Firstly, a vector pointing from one polyhedron to the other is picked. Then the authors start to find an intersection plane of one polyhedron based on the scalar product of the norm vector of the plane and the picked vector. If such a plane is found, the intersection of the two convex polyhedra is not empty.