Computer Graphics came into the medical world especially after the arrival of 3D medical imaging. Computer Graphics techniques are already integrated in the diagnosis procedure by means of the visual tridimensional analysis of computer tomography, magnetic resonance and even ultrasound data. The representations they provide, nevertheless, are static pictures of the patients' body, lacking in functional information. We believe that the next step in computer assisted diagnosis and surgery planning depends on the development of functional 3D models of human body. It is in this context that we propose a model of articulations based on biomechanics. Such model is able to simulate the joint functionality in order to allow for a number of medical applications. It was developed focusing on the following requirements: it must be at the same time simple enough to be implemented on computer, and realistic enough to allow for medical applications; it must be visual in order for applications to be able to explore the joint in a 3D simulation environment. Then, we propose to combine kinematical motion for the parts that can be considered as rigid, such as bones, and physical simulation of the soft tissues. We also deal with the interaction between the different elements of the joint, and for that we propose a specific contact management model. Our kinematical skeleton is based on anatomy. Special considerations have been taken to include anatomical features like axis displacements, range of motion control, and joints coupling. Once a 3D model of the skeleton is built, it can be simulated by data coming from motion capture or can be specified by a specialist, a clinician for instance. Our deformation model is an extension of the classical mass-spring systems. A spherical volume is considered around mass points, and mechanical properties of real materials can be used to parameterize the model. Viscoelasticity, anisotropy and non-linearity of the tissues are simulated. We particularly proposed a method to configure the mass-spring matrix such that the objects behave according to a predefined Young's modulus. A contact management model is also proposed to deal with the geometric interactions between the elements inside the joint. After having tested several approaches, we proposed a new method for collision detection which measures in constant time the signed distance to the closest point for each point of two meshes subject to collide. We also proposed a method for collision response which acts directly on the surfaces geometry, in a way that the physical behavior relies on the propagation of reaction forces produced inside the tissue. Finally, we proposed a 3D model of a joint combining the three elements: anatomical skeleton motion, biomechanical soft tissues deformation, and contact management. On the top of that we built a virtual hip joint and implemented a set of medical applications prototypes. Such applications allow for assessment of stress distribution on the articular surfaces, range of motion estimation based on ligament constraint, ligament elasticity estimation from clinically measured range of motion, and pre- and post-operative evaluation of stress distribution. Although our model provides physicians with a number of useful variables for diagnosis and surgery planning, it should be improved for effective clinical use. Validation has been done partially. However, a global clinical validation is necessary. Patient specific data are still difficult to obtain, especially individualized mechanical properties of tissues. The characterization of material properties in our soft tissues model can also be improved by including control over the shear modulus
