In the recent years medical diagnosis and surgery planning often require the precise evaluation of joint movements. This has led to exploit reconstructed three-dimensional models of the joint tissues obtained from CT or MR Images (for bones, cartilages, etc.). In such context, efficiently and precisely detecting collisions among the virtual tissues is critical for guaranteeing the quality of any further analysis. The common methods of collision detection are usually designed for general purpose applications in computer graphics or CAD–CAM. Hence they face worst case scenarios when handling the quasi-perfect concavity–convexity matching of the articular surfaces. In this paper, we present two fast collision detection methods that take advantage of the relative proximity and the nature of the movement to discard unnecessary calculations. The proposed approaches also accurately provide the penetration depths along two functional directions, without any approximation. They are compared with other collision detection methods and tested in different biomedical scenarios related to the human hip joint.