In three dimensional animatio, we mainly distinguish two important approaches, based either on descriptive or dynamic models. In the first one, the control of interpolating trajectories is essential. I describe a method giving the user the same interactive possibilities for orientation trajectories as for positions. Real-time control of orientations of quaternions and due to the notion of sperical tangent. A high level 3D interface manages user interactions. Motion dynamics is defined by an automatic parametrisation taking elementary mechanical laws into account. Finally, thes techniques are applied to the interactive modeling of sweep objects. Key-frame animation systems are not well suited to the realistic animation of complex objects. With this objective, animation systems based on dynamic laws have been introduced. I propose a method offering the control possibilities of key-frame animation systems and the realism of dynamic models. The principe is to minimize energy along the path. The motion equations for rigid articulated bodies are built in a symbolic form. The minimization step is performed with an optimal control algorithm, treating the motion equations in their continuous form.
