Collision detection of a moving polygon in the presence of polygonal obstacles in the plane

This paper presents a new approach for the following collision detection problem in the plane: Let a simple polygon P rotate at a center &ogr; with constant angular velocity ω and translate towards a set of polygonal obstacles S with constant velocity ν. Given P and S as well as their initial positions, and given also the velocities of P, determine whether or not P will collide with any element of S and report the collided elements of S if collisions occurred. An O(mn) worst-case optimal algorithm is proposed to solve this problem, where n is the number of vertices of P and m is the number of vertices of the obstacles in S