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The collision detection problem is easily stated: \Given two objects and desired motions, decide whether the objects will come into collision over a given time span". The solution of this problem is useful, both in robotics and other problem domains. We describe a method for solving collision detection that involves transforming the problem into an intersection detection problem over space-time. We give the theoretical basis for the solution, and describe an e cient implementation based on describing the objects and motions constructively. We also consider the related problems of describing the collision region, and of detecting collisions when there are a more than two moving objects.