Collision detection among virtual objects is one of the main concerns in virtual reality and computer graphics. Usually the methods developed for collision detection are for either very general cases or very specific applications. The first main goal of this thesis is to propose accurate methods for collision detection in computer graphics for rotating or sliding objects. The methods take advantage of the limitation imposed on the rotating/sliding objects in order to ignore unnecessary calculations of the general methods and speed up the processing. In addition to finding the collision, the methods can also return penetration depths in either radial or cylindrical direction, which can be useful for further applications. The second main goal is to apply the proposed collision detection methods in biomedical research related to human hip joints. In fact, during the past few years, femoroacetabular impingement (FAI) was recognized as the leading pathomechanism contributing to a significant number of so-called "primary" hip osteoarthritis. Thus, having medical simulation of hip joint can help both physicians and surgeons for better diagnosis and surgical planning. For diagnosing some of the human joint diseases, it is important to obtain the joint's range of motion. By modifying the pre-processing stage of one of the collision detection methods, a new fast method for finding maximum range of motion in human joint was proposed and tested. The method is working without doing any collision detection tests and its accuracy does not depend on the rotational steps. We also suggested a novel fast strategy for diagnosing hip diseases based on hip contact penetration depths. In this strategy, the contact penetration depths during hip movement are calculated for diagnosing hip impingements, by using the proposed collision detection methods. The strategy has been tested on pathological hip models during a daily activity. The results were found correlated with the contact stresses estimated by finite element method (FEM). By evaluating the results, the strategy proved to be capable for distinguishing among different hip pathologies (e.g. cam and pincer impingements). In orthopedic simulations, the behavior of the bones and the related tissues are usually investigated during their movements about an estimated center of rotation. We also evaluated the importance of the hip joint center of rotation in medical simulations. For this reason, different centers of rotation calculated by five different methods were applied for hip movements about different medical axes of rotation. By calculating the hip contact penetration depths of ten patients during hip movements (using the proposed collision detection methods), the sensitivity of hip simulations to hip center of rotation has been evaluated. Hip contact pressure has been a notable parameter to evaluate the physical conditions inside the hip joint. Many computational approaches estimate the pressure and contact pressures via finite element methods (FEM) by using 3D meshes of the tissues. Although this type of simulation can provide a good evaluation of hip problems, the process may be very time consuming. Also, these mechanical methods strongly depend on the movement details. We proposed and tested a fast statistical model for estimating hip contact pressures during its movement, without performing mechanical simulations and without any need for movement details. The estimation is done by evaluating geometric features extracted from 3D meshes of hip tissues, in order to link an unknown target hip model to some already mechanically evaluated training hip models.