Femoro-Acetabular Impingement (FAI) is a hip joint disease which affects and impairs the range of hip motion during performing activities of daily living, jogging, walking, or climbing stairs due to the bony abnormalities of the joint. Ballet dancers and athletes (e.g. gymnasts and hockey players) put their hips at the risk of FAI by extremely moving the hip mainly by excessively rotating the joint.In this research, we introduce a visualization system which helps surgeons to analyze the range of hip motions as well as to have a better communication with patients. These goals are achieved by presenting three dimensional (3D) visualizations of motion envelope by examining the maximum possible rotation of the digital hip bones. Our computer simulation system estimates, analyzes and visualizes the maximum hip range of motion (ROM) for the constructed 3D bone models that are extracted from Magnetic Resonance Images (MRI) after segmenting the bones. These tasks are accomplished by first calculating Hip Joint Center (HJC) which is center of rotation of femoral head on the 3D segmented MRI models followed by simulating hip motions with examining impingement between the femur and the acetabulum using our collision detection system. In our collision detection system, surfaces of femoral head and acetabulum bones are sampled in the spherical coordinates based on rasterization and interpolation. Then, the distance between the femoral head and acetabulum are computed to prevent impingement between them. The maximum motion degree of femur bone within depression of acetabulum in every direction iii during the digital simulation shows the ROMs of the inputted MRI of the hip joint. Six primary plane motions (flexion/extension, abduction/adduction and internal/external rotation) as well as various combinations of these motions (maximum rotation of the hip between every two rotational movements) and successive movements (maximum rotational movement of the hip per another rotational movement) are simulated and analyzed along with 3D visualization of estimated range of these motions.Generally, the ROM differs by some factors such as age, gender, ethnicity, and geographic location. For instance, newborns up to age two have considerably greater motion in hip flexion and hip abduction than adults. Our system by 3D visualization of motion envelope will provide a platform to understand quicker and better the effect of bony morphology of the hip joint on the possible ROM.We also examine the long-standing question about moving center of rotation related to ROM.We found out the ROM becomes bigger especially when the center moves outward to the direction of acetabulum axis.This thesis does not consider the effect of muscle and other surrounding connective tissue on the hip ROM since they can be altered significantly by physical training to show the potential of maximum ROM. For example a ballerina has a bigger ROM leading a bigger motion envelope compared with non-dancers. Hence we visualize the range of joint motions and their envel...