This paper introduces a fast continuous collision detection technique for polyhedral rigid bodies. As opposed to most collision detection techniques, the computation of the first contact time between two objects is inherently part of the algorithm. The method can thus robustly prevent objects interpenetrations or collisions misses, even when objects are thin or have large velocities. The method is valid for general objects (polygon soups), handles multiple moving objects and acyclic articulated bodies, and is efficient in low and high coherency situations. Moreover, the method can be used to speed up existent continuous collision detection methods for parametric or implicit rigid surfaces. The collision detection algorithms have been successfully coupled to a real-time dynamics simulator. Various experiments are conducted that show the method's ability to produce high-quality interaction (precise objects positioning for example) between models up to tens of thousands of triangles, which couldn't have been performed with previous continuous methods.Discrete methods Most previous collision detection methods are discrete: they sample the objects motions and detect objects interpenetrations (see for example 1,2,6,10,11,12,13,17,25,29 ). As a result, these methods may miss collisions (tunneling effect). While an adaptative time-step and predictive methods can be used to correct this problem in offline applications, this may not be suitable in interactive applications when a relatively high and constant frame-rate is required. Moreover, discrete collision detection requires backtracking methods to compute the first contact time, which is necessary in constraintbased analytical dynamics simulations. Depending on the Figure 1. Precise car door positioning. The continuous collision detection technique described in this paper allows to precisely (without any objects interpenetration) and interactively position the door. The car skeleton is about 29000 triangles. The door is about 16000 triangles (3d models ©Renault).