Distance constraints are widely used in many applications ranging from robotics to chemistry and CAD. Classical tehniques for solving such continuous constraints are based on a branch and prune algorithm which combines domain filtering techniques (local consistencies) and domain splitting.The main drawback of these methods comes from the fact that constraints are handled independently and in a blind way i.e., local consistencies do not take advantage of the specific semantic properties of the constraints.We introduce in this thesis two approaches for the design of a global constraint for distance relations. The first technique is based on the introduction of redundant constraints direcly infered from geometrical properties of the system. The second approach is a dedicated global filtering algorithm.This work led to the design of a domain decomposition technique which exploits the particular structure of the distance relations.Lastly, we generalize this splitting strategy to a larger class of numerical constraints.
